GAMMA PRIME PRECIPITATION MECHANISMS AND/67531/metadc700080/...Nickel-base superalloys have been emerged as materials for gas turbines used for jet propulsion and electricity generation

APPROVED: Rajarshi Banerjee, Major Professor Peter Collins, Committee Member Srinivasan Srivilliputhur, Committee Member James Williams, Committee Member Alan Needleman, Committee Member Nigel Shepherd, Chair of the Department of

Materials Science and Engineering Costas Tsatsoulis, Dean of the College of

Engineering Mark Wardell, Dean of the Toulouse Graduate

School

GAMMA PRIME PRECIPITATION MECHANISMS AND

SOLUTE PARTITIONING IN Ni-BASE ALLOYS

Tanaporn Rojhirunsakool, B. Eng, M.S

Dissertation Prepared for the Degree of

DOCTOR OF PHILOSOPHY

UNIVERSITY OF NORTH TEXAS

August 2014

Rojhirunsakool, Tanaporn. Gamma Prime Precipitation Mechanisms and

Solute Partitioning in Ni-base Alloys. Doctor of Philosophy (Materials Science and

Engineering), August 2014, 153 pp., 11 tables, 44 figures, c hapter references.

Nickel-base superalloys have been emerged as materials for gas turbines used for jet

propulsion and electricity generation. The strength of the superalloys depends mainly from an

ordered precipitates of L12 structure, so called gamma prime (γ’) dispersed within the disorder γ

matrix. The Ni-base alloys investigated in this dissertation comprise both model alloy systems

based on Ni-Al-Cr and Ni-Al-Co as well as the commercial alloy Rene N5.

Classical nucleation and growth mechanism dominates the γ’ precipitation process in

slowed-cooled Ni-Al-Cr alloys. The effect of Al and Cr additions on γ’ precipitate size

distribution as well as morphological and compositional development of γ’ precipitates were

characterized by coupling transmission electron microscopy (TEM) and 3D atom probe (3DAP)

techniques. Rapid quenching Ni-Al-Cr alloy experiences a non-classical precipitation

mechanism. Structural evolution of the γ’ precipitates formed and subsequent isothermal

annealing at 600 °C were investigated by coupling TEM and synchrotron-based high-energy x-

ray diffraction (XRD). Compositional evolution of the non-classically formed γ’ precipitates was

determined by 3DAP and Langer, Bar-on and Miller (LBM) method. Besides homogeneous

nucleation, the mechanism of heterogeneous γ’ precipitation involving a discontinuous

precipitation mechanism, as a function of temperature, was the primary focus of study in case of

the Ni-Al-Co alloy. This investigation coupled SEM, SEM-EBSD, TEM and 3DAP techniques.

Lastly, solute partitioning and enrichment of minor refractory elements across/at the γ/ γ’

interfaces in the commercially used single crystal Rene N5 superalloy was investigated by using

an advantage of nano-scale composition investigation of 3DAP technique.

ii

Copyright 2014

by

Tanaporn Rojhirunsakool

iii

ACKNOWLEDGEMENTS

I would like to express my deepest appreciation to my advisor, Dr. Rajarshi Banerjee who

has been a tremendous mentor for me. I am very glad that he did not say “No” when Dr.

Shepherd asked you to take this girl to be one of your group members. I was very lucky that day.

Since that day, his continuous support and guidance throughout my research allow me to grow as

a research scientist. I am very grateful for his scientific advice and insightful discussion. Without

his guidance and persistent help this dissertation would not be possible.

I also thank the members of my Ph.D committees, Dr. Peter Collins, Dr. Srinivasan

Srivilliputhur, Dr. Jim Williams, Dr. Alan Needleman for their scientific advice and suggestions.

Dr. Jay Tiley from AFRL and Dr. Doug Konitzer form GE Aviation for being great collaborators

and mentors. Dr. Junyeon Hwang and Dr. Soumya Nag have always motivated and support

thoughout my graduate life at UNT. They are friends, mentors, teachers, and my babysitters. For

last 5 years at UNT, I would not be able to survive in graduate school without them.

A good support team is very important for my graduate life. I am thankful to all past and

present group members and friends; Antariksh, Sundeep, Ankit, Peeyush, Tushar, Subhashish,

Deep, Talukdar, Bharat and Mantri for providing help and support. I am glad to work with you

all. I also would like to thank all my Thai friends who make my life at UNT more memorable.

I especially thank my mom, dad, sister and brother. My family always stands by my side,

support me on my hard time, and provide unconditional love and care. Special thanks to my

boyfriend, Oil, he has been with me in every good and bad moments. He has supported me

though my entire graduate life. These past five year have not been easy both academically and

personally without him. Last but not least, thanks to you all who make me who I am today.

iv

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ............................................................................................................ ii LIST OF TABLES ........................................................................................................................ vii LIST OF FIGURES ..................................................................................................................... viii CHAPTER 1 INTRODUCTION .................................................................................................... 1

1.1 References ............................................................................................................... 6 CHAPTER 2 LITERATURE REVIEWS ....................................................................................... 7

2.1 Physical Metallurgy of Nickel-Base Alloy and Superalloys .................................. 7

2.2 Evolution of γ’ Precipitates during Isothermal Annealing .................................... 10

2.3 Influence of Cooling Rate on γ’ Size Distribution ................................................ 12

2.4 Decomposition Pathway Involving Order-Disorder Transformation and Phase Separation ............................................................................................................. 15

2.5 Discontinuous Precipitation .................................................................................. 22

2.6 Influence of Rhenium on Microstructure and Mechanical Properties of Ni-Base Superalloys ............................................................................................................ 24

2.7 References ............................................................................................................. 28 CHAPTER 3 PROCESSING AND CHARACTERIZATION TOOLS ....................................... 34

3.1 Introduction ........................................................................................................... 34

3.2 Alloy Preparation .................................................................................................. 34

3.3 Processing Tools ................................................................................................... 35

3.3.1 Mechanical Cutting ................................................................................... 35

3.3.2 Heat Treatment .......................................................................................... 35

3.3.3 Sample Preparation ................................................................................... 36

3.4 Characterization Tools .......................................................................................... 37

3.4.1 Scanning Electron Microscopy ................................................................. 37

3.4.2 Dual-Beam Focused Ion Beam (FIB) ....................................................... 38

3.4.3 Transmission Electron Microscopy .......................................................... 39

v

3.4.4 Atom Probe Tomography ......................................................................... 41

3.4.5 Synchrotron-Base High-Energy X-Ray Diffraction ................................. 43

3.5 References ............................................................................................................. 45 CHAPTER 4 INFLUENCE OF COMPOSITION ON MONOMODAL VERSUS MULTIMODAL γ′ PRECIPITATION IN Ni-Al-Cr ALLOYS ................................................... 47

4.1 Introduction ........................................................................................................... 47

4.2 Experimental Procedures ...................................................................................... 48

4.3 Results and Discussion ......................................................................................... 49

4.3.1 Microstructures of Ni-8Al-8Cr and Ni-10Al-10Cr Alloys during Continuous Cooling .................................................................................. 49

4.3.2 Compositional Profile of γ and γ’ Phases of Ni-8Al-8Cr and Ni-10Al-10Cr Alloys ........................................................................................................ 52

4.3.3 Growth and Coarsening Regimes of Ni-8Al-8Cr Alloy ........................... 56

4.4 Summary ............................................................................................................... 58

4.5 Conclusion ............................................................................................................ 61 CHAPTER 5 NON-CLASSICAL MECHANISM OF GAMMA PRIME PRECIPITATION IN Ni-Al-Cr ALLOYS ....................................................................................................................... 63

5.1 Introduction ........................................................................................................... 63

5.2 Experimental Methods .......................................................................................... 65

5.3 Results and Discussion ......................................................................................... 67

5.3.1 Investigation of Early Stages Decomposition of γ’ Precipitates: Disorder-Order Transformation of Ordered γ’ Precipitates. .................................... 67

5.3.2 Early Stages of Decomposition of γ’ Precipitation at 600 °C ................... 69

5.3.3 Structural Evolution of Ordered γ’ Precipitates during Isothermal Annealing at 600 ºC Post Rapid Quenching .............................................................. 78

5.3.4 Compositional Evolution of Ordered γ’ Precipitates during Isothermal Annealing at 600 ºC Post Rapid Quenching ............................................ 79

5.3.5 Statistical Analysis of Frequency Distribution Plots during Isothermal Annealing at 600 ºC Post Rapid Quenching ............................................ 83

5.3.6 Synchrotron-Base X-Ray Diffraction Studies on Evolution of γ’ Volume Fraction and γ and γ’ Lattice Parameters .................................................. 87

5.4 Summary .............................................................................................................. 92

5.5 Conclusion .................................................................................................................. 94

5.6 References ............................................................................................................. 96

vi

CHAPTER 6 COMPETING MECHANISMS OF HOMOGENEOUS AND DISCONTINUOUS γ’ PRECIPITATION IN Ni-Al-Co ALLOYS ............................................................................ 100

6.1 Introduction ......................................................................................................... 100

6.2 Experimental Methods ........................................................................................ 100

6.3 Results and Discussion ....................................................................................... 101

6.3.1 Liquid Nitrogen Quenching after Solution Treatment above γ’ Solvus Temperature ............................................................................................ 101

6.3.2 High Temperature Annealing at 800ºC (near γ’ Solvus Temperature) ... 105

6.3.3 Low Temperature Annealing at 600 ºC .................................................. 109

6.4 Summary and Conclusion ................................................................................... 123

6.5 References ........................................................................................................... 125 CHAPTER 7 EFFECT OF HEAT TREATMENT ON SOLUTE PARTITIONING IN NI-BASE SINGLE CRYSTAL RENE N5 SUPERALLOYS..................................................................... 127

7.1 Introduction ......................................................................................................... 127

7.2 Experimental Procedure ...................................................................................... 128

7.3 Results and Discussion ............................................................................................. 129

7.3.1 Microstructural Evolution of the γ+ γ’ Phases ........................................ 129

7.3.2 Compositional Partitioning across, and Interfacial Segregation at, γ / γ’ Interfaces ................................................................................................. 131

7.3.3 Effect of Kinetics on Elemental Enrichment near The γ/ γ’ Interfaces .. 140

7.4 Summary and Conclusion ................................................................................... 142

7.5 References ........................................................................................................... 144 CHAPTER 8 FUTURE AND CONCLUSION .......................................................................... 145 APPENDIX: BINOMIAL DISTRIBUTION AND LANGER-BAR-ON-MILLER METHOD ..................................................................................................................................................... 150

vii

LIST OF TABLES

Page

Table 4.1 The far-field γ matrix, adjacent γ matrix and γ’ compositions of Al and Cr content and interface width of continuous cooled Ni-8Al-8Cr and Ni-10Al-10Cr samples. ........................... 54

Table 5.1 Composition of γ and γ’ phases and Al composition gradient as a function of annealing time ............................................................................................................................................... 76

Table 5.2 Al composition obtained from LBM fitting of as-quenched and annealed Ni-8Al-8Cr samples .......................................................................................................................................... 85

Table 5.3 FWHM of (100) peak of γ’ phase, intensity ratio of (100)γ’/(111)γ+γ’, intensity ratio of (100)γ’/(200)γ+γ’, and γ’particle size calculation based on FWHM of (100) peak of γ’ phase ... 89

Table 5.4 Lattice parameter of γ and γ’ phases and lattice misfit of as-quenched and 600 °C annealed samples .......................................................................................................................... 92

Table 6.1. The misorientation (angle-axis pairs), Σ boundaries (if present), their deviation from ideality, and the orientation (plane) of each grain boundary of the grain boundaries containing the coarser lamellar product. ....................................................................................................... 123

Table 7.1 Bulk chemical compositions of Ni base Rene N5 superalloys (all value in wt%) ..... 128

Table 7.2. Partitioning ratio, 𝐾𝐾𝐾𝐾𝐾𝐾′/𝐾𝐾γ, from APT analyses for all heat treatment conditions ..... 134

Table 7.3. Gibbsian interfacial excess of W and Re in as-cast, heat-treated, and thermally cycle samples ........................................................................................................................................ 138

Table 7.4 Composition and volume fraction of the γ’ precipitates in as-cast, heat-treated, and thermally cycled samples ............................................................................................................ 139

Table 7.5 Composition of the γ matrix in as-cast, heat-treated, and thermally cycled samples . 139

viii

LIST OF FIGURES

Page

Figure 1.1 Summary diagram of the dissertation structure. ............................................................ 5

Figure 2.1 Arrangement of Ni and Al in a) the ordered γ’ phase with L12 crystal structure and b) the disorder γ phase [2] ................................................................................................................... 9

Figure 2.2 Schematic diagram illustration the evolution of γ’ precipitates during isothermal annealing [3] ................................................................................................................................. 11

Figure 2.3 Schematic diagrams of phase diagram and free energy-composition curve of order-disorder transformation by nucleation and growth process[31] ................................................... 16

Figure 2.4 Phase diagram and free energy-composition curve of ordered and disordered phases at T2. At temperature T2 the decomposition occurs via continuous ordering of homogeneously ordered, single phase at point B’ and is followed by nucleation of the disordered phase at point C’.[31] .......................................................................................................................................... 17

Figure 2.5 Schematic diagram of free energy-composition-order parameter η plot for temperature T2[31] ....................................................................................................................... 18

Figure 2.6 a) Phase diagram and b) schematic plot of disordered and ordered phase at temperature T3 [31] ...................................................................................................................... 19

Figure 3.1 Schematic diagram of the atom probe tomography[12]. ............................................. 40

Figure 3.2 The experimental hall in 11-I-DC sector at APS [8]. .................................................. 43

Figure 4.1 A partial ternary phase diagram of Ni-Al-Cr system at 600 °C generated by PANDATTM software.................................................................................................................... 47

Figure 4.2 a) DFTEM image of continuously cooled Ni-8Al-8Cr at% sample, recorded using one of the superlattice reflections in a <001>zone axis pattern shown in b). c) A low magnification SEM micrograph of continuously cooled Ni-10Al-10Cr at% sample d) EFTEM image of continuously cooled Ni-10Al-10Cr at% sample, obtained using the Cr-M edge. ........................ 50

Figure 4.3 Primary and secondary precipitate size distributions of Ni-10Al-10Cr alloy. ............ 50

Figure 4.4 Normalized particle size distribution of primary and secondary γ’ precipitates. ........ 51

Figure 4.5 a) 3D-APT reconstruction of continuous cooled Ni-8Al-8Cr at% sample using 10%Al isosurface. b) The proxigram plotted corresponding to isosurface in a) across γ/γ’ interface as a function of distance C) 3-D reconstruction of 12 at% Al isosurface of primary γ’ and secondary γ’ of continuous cooled Ni-10Al-10Cr alloy. d) and e)The proxigram corresponding to isosurface in c) delineated 12 at% Al isosurface of primary γ’ and secondary γ’, respectively ........................ 54

ix

Figure 4.6 a) DF image of Ni-8Al-8Cr at% sample after isothermal aging at 600 ˚C for 256 hours, post continuous cooling b) SADP corresponding to the dark-field image. c) 3-D reconstruction of 10 at% Al isoconcentration surface delineating d) proximity histogram for Al and Cr corresponding to 10 at% Al isosurface shown in c). ................................................................... 56

Figure 4.7 Schematic representations of the variation in nucleation rate in logarithm scale versus temperature for both Ni-8Al-8Cr and Ni-10Al-10Cr alloys. ........................................................ 59

Figure 4.8 Schematic diagram of primary and secondary γ’ nucleation during continuous cooling ....................................................................................................................................................... 59

Figure 5.1 a) SAD pattern of as-quenched Ni-8Al-8Cr sample b) LBM plot with Al concentration of as-quenched Ni-8Al-8Cr sample c) Intensity vs 2 theta plot obtained from high-energy XRD .................................................................................................................................. 67

Figure 5.2 SAD pattern of 5 min annealed at 600 °C after quenched of Ni-8Al-8Cr sample showing superlattice reflections at <100> and <110>. ................................................................. 69

Figure 5.3 a) HAADF-STEM and b) its corresponding FFT of disordered region in 5 min annealed Ni-8Al-8Cr sample. c) HAADF-STEM and d) its corresponding FFT of ordered region in 5 min annealed Ni-8Al-8Cr sample…………………………………………………………...70

Figure 5.4 a) a filtered image of figure 5.3(b) processed by selected both superlattice and fundamental reflections. Square and circle boxes correspond to the disordered and ordered regions.. ......................................................................................................................................... 71

Figure 5.5 a) A HAADF-STEM and b) the corresponding intensity profile of disordered region. c) A HAADF-STEM and b) the corresponding intensity profile ordered region. Both a) and c) were parts of Fig. 5.4(a). ............................................................................................................... 73

Figure 5.6 a) 3D reconstruction of 5 min annealed sample obtained from 3DAP and b) the corresponding proxigram delineated by using 10 at% across the Al-lean and Al-enriched regions........................................................................................................................................................ 73

Figure 5.7 DFTEM micrographs of annealed at 600 °C Ni-8Al-8Cr samples for a) 30 min b) 2hr c) 16hr and d) 256 hr. .................................................................................................................... 78

Figure 5.8 Compositional profile of Al and Cr across the γ/ γ’ interfaces as a function of annealing time at 600 °C. .............................................................................................................. 81

Figure 5.9 LBM plots of annealed Ni-8Al-8Cr samples at 600 °C for a) 5 min, b) 15 min, c) 30 min, d) 2hr, e) 2hr, f) 16 hr, and e) 256 hr. ................................................................................... 85

Figure 5.10 a) Intensity of (100) peak of the γ’ phase of the as-quenched and 600 °C annealed Ni-8Al-8Cr samples. b) FWHM of (100) peak of the γ’ phase and volume fraction determined by a ratio of (100)γ’/(111) γ + γ’ as a function of annealing time. .................................................... 87

x

Figure 6.1 a) A SEM micrograph of an as-quenched Ni-12.5Al-37.5Co sample b) A DFTEM micrograph and <001> SAD pattern as an inset c) An APT reconstruction of a 40x40x60 nm3 volume, delineated by 12 at% Al isosurfaces. d) The compositional profile across γ/γ’ interfaces for Al and Co corresponding to the isosurfaces shown in c). ..................................................... 103

Figure 6.2 a) Low and b) high magnification of SEM micrographs of the Ni-12.5Al-37.5Co alloy after high temperature annealing at 800 °C for 70 hr, post rapid quenching. c) A DFTEM and SAD pattern of the same sample showing cuboidal γ’ precipitates ............................................ 106

Figure 6.3 a) A 25x25x25 nm3 3DAP reconstruction of the 800°C/70hr annealed sample and b) the corresponding proxigram. ..................................................................................................... 106

Figure 6.4 a) SEM micrograph of 600 ºC/256 hr annealed Ni-Al-Co sample. b) A corresponding inverse pole figure (IPF) of the same area and the stereo-triangle. ............................................ 107

Figure 6.5 DFTEM micrograph of Ni-37.5Co-12.5Al alloy after 600 °C annealing for 10 min showing a) homogeneous γ’ precipitation b) discontinuous γ’ precipitation near the grain boundary and c) discontinuous γ’ precipitation in the grain interior, inset in Fig. 6.5(c)). ........ 110

Figure 6.6 a) A low magnification of SEM micrograph of 600 °C/1 hr annealed Ni-Al-Co sample. b) A DFTEM micrograph of the same sample showing discontinuous γ+ γ’ lamellar product in the grain interior. ......................................................................................................................... 111

Figure 6.7 a) Low and b) high magnification of SEM micrographs of discontinuous γ+ γ’ product near the grain boundary. c) and d) Energy-filtered micrographs showing lameallation achieving by lamellar branching. ................................................................................................................ 113

Figure 6.8 a) SEM micrograph showing reaction fronts and original grain boundary. b) The reaction fronts and the original grain boundary of the long term annealing at 600 °C (600 °C/256hr). ........................................................................................................................... 116

Figure 6.9 a) 3DAP reconstruction of long term annealing at low temperature (600 °C/256 hr) showing Ni and Co ions and Al isosurface superimposed with Ni ions. b) The corresponding proxigram delineated by using Al=12 at%. ................................................................................ 117

Figure 6.10 a) A SEM image of a scanned area b) A IPF map of the same area as a). c) The CSL boundaries superimposed on top of an Image Quality (IQ) map of the scanned area. d) A plot of a fraction of total number of grain boundaries containing the coarse discontinuous precipitation versus misorientation angle superimposed on a random distribution of grain boundary ........... 119

Figure 7.1 Low magnification SEM micrographs of a) as-cast b) heat-treated and c) thermally cycled sample of single-crystal Rene N5 samples. ..................................................................... 129

Figure 7.2 High magnification SEM micrographs of a) as-cast b) heat-treated and c) thermally cycled sample of single-crystal Rene N5 samples. ..................................................................... 129

xi

Figure 7.3 a) A HAADF-STEM micrograph of the thermally cycled sample capturing γ channel and rafted γ’ precipitate. b) A high magnification of the interface between the rafted γ +γ’ structure and γ channel showing cuboidal γ’ precipitates inside the γ channel. ......................... 131

Figure 7.4 a) 3D-APT reconstruction of as-cast sample. b) The proxigram plotted corresponding to isosurface in a) across γ/γ’ interface as a function of distance C) 3-D APT reconstruction of heat-treated sample d) The proxigram of heat-treated sample. ................................................... 135

Figure 7.5 3D-APT reconstruction of a) rafted γ + γ’ structure and c) small cuboidal γ’ precipitates located in the γ channel. b) and d) The proxigram plotted corresponding to isosurface in a) and c) across γ/γ’ interface. ................................................................................................ 136

Figure 7.6 2D contour plots of a) Re and b) W in the thermally cycled sample showing the enrichment near/at the γ/ γ’interface. .......................................................................................... 137

Figure 7.7 a) SEM micrograph of γ and γ’ structure in long-term heat treatment at 1650 ˚F for 100 hr after industrial heat treatment b) APT reconstruction capturing two γ’ precipitates and the γ channel between them c) Composition profile across the γ / γ’ interfaces showing both γ and γ’ phases reach equilibrium stage. .................................................................................................. 142

1

CHAPTER 1

INTRODUCTION

High temperature materials have been developed to maintain excellent mechanical

properties at elevated temperatures. Nickel-base superalloys have been emerged as materials for

high temperature applications. They have been used as integral parts of gas turbines used for jet

propulsion and electricity generation gas turbines. For these applications, the performance

characteristics are limited by operating temperature that the materials can be tolerated. Desired

characteristics of these materials include an ability to withstand loading at an operating

temperature close to their melting point, high resistance to mechanical degradation over a period

of time, and high resistance of severe operating environments. The high temperature properties

of the superalloys depend strongly on the combination of alloying elements since these promote

precipitation hardening. In general, the precipitation hardening often mainly by an ordered

precipitates of L12 structure, so called gamma prime (γ’) and gamma double prime (γ’’), in case

of Fe-base superalloy dispersed within the disorder γ matrix. Precipitation hardening arises from

a a/2 <110>{111} dislocation travels in g matrix cannot enter the γ’ precipitates without forming

an anti-phase boundary (APB) and therefore that the dislocation must travel in pairs to remove

the APB introduced by the first dislocation. The anti-phase boundary energy, γAPB represents a

barrier which dislocations must be overcome to cut the precipitates. The higher γAPB is the

substantial order strengthening expected. The order strengthening outweighs other contributions

due to stacking fault energy, Orawan strengthening, difference in modulus [1]. The mechanical

properties of Ni-base superalloys depend critically on the microstructure of γ and γ’ phases,

where morphology, size distribution, and composition of the γ’ precipitates are governed by

mechanism of γ’ precipitation. The prevalent use of Ni-base superalloys necessitates extensive

2

studies on binary and ternary γ + γ’ systems such as Ni-Al, Ni-Al-Cr, Ni-Al-Co, Ni-Al-Mo alloys.

The Ni-base alloys investigated in this dissertation comprise both model alloy systems

based on Ni-Al-Cr and Ni-Al-Co as well as the commercial alloy Rene N5, used for turbine

blade applications in jet engines. Both Ni-Al-Cr and Ni-Al-Co are basic ternary alloys,

comprising elements contained in most Ni-base superalloys. These two alloys were employed to

study fundamental aspects of γ’ precipitation mechanisms.

Gamma prime precipitation mechanisms in Ni-base alloys can be broadly classified into

categories of homogeneous or heterogeneous nucleation. Homogeneous nucleation occurs

spontaneously and randomly whereas heterogeneous nucleation takes place at preferential

nucleation sites such as grain boundaries [2]. The heterogeneous process is associated with a

discontinuous or abrupt change in orientation and composition between the precipitates and the

matrix [3-5]. These two processes are very competitive, depending on decomposition

temperature. In general, homogeneous nucleation requires large undercooling or driving force to

overcome a critical nucleus size or a nucleation barrier. This phenomenon is known as a classical

nucleation and growth process [2]. Classical nucleation process is categorized by large

composition fluctuations over a small space. The precipitation of this mode forms with a near-

equilibrium composition since the critical nucleus forms. However, there are certain

homogeneous solid-solid transformations where there is no barrier for nucleation, such as phase

separation via spinodal decomposition [6-11]. When subjected to rapid quenching from the

single γ phase-field, the highly supersaturated and undercooled γ solid solution is unstable or

metastable with respect to ordering or phase separation. Small composition fluctuations over a

large space produce solute-rich and solute-lean regions. Thus it decreases the total free energy of

the system. It should be noted that precipitation mediated by spinodal decomposition takes places

3

with non-equilibrium compositions of the precipitate and matrix phases in the initial stages of the

transformation. “Up-hill” diffusion proceeds until the equilibrium composition of both parent

and precipitate phases can be achieved.

Conversely, classical nucleation and growth mechanism dominates the γ’ precipitation

process in slowed-cooled Ni-Al-Cr alloys. The morphological and compositional development of

γ’ precipitates in Ni-8Al-8Cr and Ni-10Al-10Cr alloys were characterized in detail by coupling

transmission electron microscopy (TEM) and 3D atom probe (3DAP). Also, the effect of Al and

Cr additions on γ’ precipitate size distribution were also investigated for the two alloys.

While slow cooling rate of Ni-8Al-8Cr and Ni-10Al-10Cr alloys results in classical

nucleation and growth of γ’ precipitates, rapid quenching from a single γ phase field can alter the

precipitation mechanism. In order to verify this, the mechanism of γ’ precipitation in a liquid

nitrogen-quenched Ni-8Al-8Cr sample was investigated. Structural evolution of the γ

precipitates formed via a non-classical mechanism in as-quenched condition as well as

subsequent isothermal annealing at 600 °C was investigated by coupling TEM and synchrotron-

based high-energy x-ray diffraction. In addition, in-situ high-energy x-ray diffraction was

employed to determine the lattice parameter of both γ and γ’ phases, and consequently the lattice

misfit between the two phases. Evolution of γ’ precipitate size as a function of annealing time

was calculated by applying the Scherrer equation using a full width at half max (FWHM) of the

(100) superlattice peak of the γ’ phase. Compositional evolution of the non-classically formed γ’

precipitates was determined by 3DAP. Analysis of the compositional fluctuations in the

supersaturated matrix was carried out by means of compositional profiles (proximity histogram

analysis) across the γ/ γ’ interfaces as well as the statistical Langer, Bar-on and Miller (LBM)

method.

4

Besides homogeneous nucleation, the mechanism of heterogeneous γ’ precipitation

involving a discontinuous precipitation mechanism, as a function of temperature, was the

primary focus of study in case of the Ni-Al-Co alloy. Depending on the decomposition

temperature, or undercooling, the γ’ phase in Ni-Al-Co alloys can either precipitate

homogeneously, or via a discontinuous precipitation mechanism, or a combination of both

mechanisms, within the γ matrix. This investigation coupled SEM, TEM and 3DAP techniques.

Orientation microscopy (OM) studies using SEM-based electron backscatter diffraction (EBSD)

technique were carried out to determine the influence of misorientation across γ grain boundaries

on the nucleation, growth and coarsening of the discontinuous product. Microstructural evolution

as a function of annealing time was studied by coupling TEM and 3DAP. The 3DAP results

provided compositions and solute partitioning for both γ and γ’ phases. The experimental results

clearly demonstrated that the decomposition temperature plays a key role on the mechanism of

solid-state precipitation in this alloy.

Lastly, the dissertation extends the study of the γ’ precipitation mechanism and solute

partitioning to a real life Ni-base superalloy. The commercially used single crystal Rene N5

superalloy was developed as a second generation superalloy, with better creep resistance than the

first generation for single crystal turbine blade alloys. However, the alloy development process

was largely achieved in an empirical manner without a detailed physical understanding of the

role played by the key alloying elements on the microstructure and mechanical properties.

Specifically, Re has been found to remarkably improve the creep strength of these alloys at very

high temperatures (1000-1150 °C) [11]. There are substantial controversies regarding to how Re

can improve the creep properties. Therefore, the primary focus of this study is to understand

solute partitioning and enrichment of minor refractory elements, such as Re and W, across/at the

5

γ/ γ’ interfaces. The partitioning ratio between γ and γ’ phases and solute enrichment at these

interfaces as a function of heat treatments were investigated. These microstructural factors can

play an important role on mechanical properties.

The focus areas of this dissertation, stated in the preceding discussion, are summarized in Fig. 1.1.

Fig 1.1 Summary diagram of the dissertation structure

6

1.1 References

[1] Porter DA, Easterling KE (1992) Phase transformations in metals and alloys, CRC press

[2] Braszczyńska-Malik KN (2009) Discontinuous and continuous precipitation in magnesium–aluminium type alloys. J Alloys Compounds 477.

[3] Vaughan D (1968) Grain boundary precipitation in an Al-Cu alloy. Acta Metallurgica 16

[4] Duly D, Simon J, Brechet Y (1995) On the competition between continuous and discontinuous precipitations in binary Mg Al alloys. Acta metallurgica et materialia 43

[5] Soffa W, Laughlin D (1982) Recent experimental studies of continuous transformations in alloys: an overview.

[6] Soffa WA, Laughlin DE (1989) Decomposition and ordering processes involving thermodynamically first-order order → disorder transformations. Acta Metallurgica 37. DOI:10.1016/0001-6160(89)90338-6

[7] Viswanathan GB, Banerjee R, Singh A et al (2011) Precipitation of ordered phases in metallic solid solutions: A synergistic clustering and ordering process. Scr Mater 65. DOI:10.1016/j.scriptamat.2011.06.002

[8] Zhao J, Notis M (1998) Spinodal decomposition, ordering transformation, and discontinuous precipitation in a Cu–15Ni–8Sn alloy. Acta materialia 46

[9] Laughlin DE, Soffa W (1985) Spinodal structures. ASM Handbook. 9

[10] Laughlin DE, Cahn JW (1975) Spinodal decomposition in age hardening copper-titanium alloys. Acta Metallurgica 23

[11] Rüsing J, Wanderka N, Czubayko U et al (2002) Rhenium distribution in the matrix and near the particle–matrix interface in a model Ni–Al–Ta–Re superalloy. Scr Mater 46

[12] Reed RC (2006) The superalloys: fundamentals and applications. Cambridge University Press

7

CHAPTER 2

LITERATURE REVIEWS

This chapter presents background and physical metallurgy of Ni-base alloy and Ni-base

superalloys. Extensive literature reviews on effect of cooling rate on γ’ particle size distribution,

classical versus non-classical nucleation mechanism of the γ’ precipitates, and homogeneous

versus discontinuous precipitation of the γ’ precipitates are discussed. Further, development of

superalloys with addition of Re element and effect of Re on microstructure and mechanical

properties on commercial Ni-base superalloys are discussed.

2.1 Physical Metallurgy of Nickel-Base Alloy and Superalloys

With nickel as a solvent and about ten other alloying elements, Ni-base superalloys have

been used as a high temperature application. Some of the alloying elements contain significant

quantities such as Cr, Co, Al, and Ti. Some are minor elements such as Re, Mo, Hf, W, B, and C.

Their microstructure and phases in this alloy determine their mechanical properties. The

microstructure of typical superalloys consists of:

1. The gamma phase, γ. This phase is disorder fcc structure. It typically forms a

continuous matrix phase. It contains significant amount of Ni, Cr and Co.

2. The gamma prime phase, γ’. This phase is an ordered, fcc-base structure. The ordered

phase has an L12 structure. It contains significant amount of Al and Ti.

3. Carbides and borides. Carbon usually combines with reactive elements such as Ti, Ni,

Cr, Hf to form MC carbides. These carbides prefer to locate on the grain boundaries.

Similar to carbides, borides combine with elements such as Cr and Mo to form

borides that prefer to reside on the gain boundaries.

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There are other phases that can be found in certain alloys such as topologically close

packed (TCP) phases, Laves, phase, sigma (σ) phase, and more. These phases are detrimental to

mechanical properties at elevated temperature during service. Thus, one needs to avoid these

phases by changing or adding alloying elements.

In general, refractory elements with large differences in electronic structure and atomic

radii compared to Ni are added. Mo, W, Nb, and Re are contributed as solid solution strengthener

of the γ matrix. Ti, Ta, Nb, and V are added as the formation and strengthening the γ’ phase by

substituting to Al in Ni3Al [1,2].

The remarkable mechanical properties of superalloys particularly come from the gamma

prime (γ’) phase. It displays a primitive cubic, L12 crystal structure. In the binary Ni-Al alloys,

L12 crystal structure has Al atoms at the cube corner and Ni atoms at the centers of the faces, as

shown in Fig. 2.1. Each Ni atom has 4 Al and 8 Ni atoms as nearest neighbor and each Al has 12

Ni atoms as nearest neighbor. The stoichiometry of this crystal structure is Ni3Al. The lattice

parameter, a, of the γ’ phase at room temperature is 0.3570 nm which equals to an Al-Al distance.

The γ’ lattice parameter is only ~1.5% larger than that of the disorder γ phase. The substitution of

other alloying elements changes its lattice parameter depending on the size of the substitutes.

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Since the lattice parameter of the two phases is similar, the γ/γ’ interface remain coherent

and interfacial energy between the two is relatively low. Lattice misfit (𝛿𝛿) between the two

phases is

𝛿𝛿 = 2(𝑎𝑎𝛾𝛾′ − 𝑎𝑎𝛾𝛾)/(𝑎𝑎𝛾𝛾′ + 𝑎𝑎𝛾𝛾)

where γ’ and γ are lattice parameters of γ’ and γ phases. It is well known that the lattice misfit

influence significantly on properties of the superalloys due to the coherency of the γ/ γ’

interface. Further, since the difference in lattice parameter of the γ and γ’ phase is trivial, selected

electron diffraction (SAD) pattern obtained form transmission electron microscopy (TEM) shows

maxima on {110}, {200}, {220} of fundamental reflections, and so on due to the combination of

the disorder γ phase and the ordered γ’ phase. {100} and {110} reflections, so called superlattice

reflections, correspond to the ordered γ’ phase. These reflections show minimum intensity

compared to the fundamental reflections. Further, the orientation relationship between these two

phase can be obtained from SAD pattern and described by

Fig. 2.1 Arrangement of Ni and Al in a) the ordered γ’ phase with L12 crystal structure and b) the disorder γ phase [2]

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{100}γ //{100} γ’

<010> γ // <010> γ’

The relationship is referred to as cube-cube relationship.

2.2 Evolution of γ’ Precipitates during Isothermal Annealing

Ricks et al. [3] studied on evolution of γ’ precipitates during isothermal annealing. The

results showed that with increasing an annealing times the morphological development of γ’

precipitates changes in sequences as spheres, cube, arrays of cubes, and finally dendrite (Fig.

2.2). Changes in morphology of the γ’ precipitates were found to be an effect of lattice misfit.

For alloys with low misfit, γ’ precipitates grow larger before changing the morphology from

spheres to cubes when the effect of misfit plays a role.

In case of Ni-Al-Cr alloy, addition of Cr to binary Ni-Al alloy reduces the lattice misfit

significantly. In certain alloy, such as Ni-8Al-8Cr alloy, it is nearly zero misfit [4]; thus; γ’

precipitates remains spherical to large spherical morphology after long term annealing at high

temperature [5].

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Fig. 2.2 Schematic diagram illustration the evolution of γ’ precipitates during isothermal annealing [3]

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2.3 Influence of Cooling Rate on γ’ Size Distribution

The γ - γ’ microstructure in Ni-base alloys can be controlled via a combination of

composition and cooling rate from the high temperature single γ phase field during processing.

The resulting morphology and size distribution of γ’ precipitates determine the mechanical

properties of these alloys [2,3,6-10]. Microstructural evolution in Ni-Al-Cr system is strongly

dependent on the solute concentration and cooling rate [10-16]. Increase in Al content increases

the γ’ solvus temperature whereas increase in Cr content typically decreases the γ’ solvus

temperature [17]. The influence of cooling rate on γ’ precipitation has been extensively

investigated. Faster cooling rates from γ’ supersolvus temperatures, typically lead to the

formation of a monomodal size distribution of refined γ’ precipitates [18-20]. In contrast,

relatively slower cooling rates lead to the formation of γ’ precipitates with a bimodal size

distribution or in some cases even a multi-modal size distribution [8,13,19,21,22]. Previous

studies have been revealed that bimodal distribution provides optimal mechanical properties for a

turbine disk [8]. The development of multiple size ranges of γ’ precipitates during continuous

cooling or slow cooling has often been attributed to multiple distinct nucleation bursts at

different undercoolings below the γ’ solvus [8,13,21]. These multiple nucleation bursts in turn

result from the complex interplay of continuous increasing thermodynamic driving force for

nucleation (chemical free energy difference) due to increasing undercooling, reduction in this

driving force due to previous nucleation events, and, the rapidly declining diffusivity of alloying

elements with decreasing temperature. At lower undercoolings (or higher temperatures, just

below the γ’ solvus temperature) lower driving force for nucleation coupled with higher

diffusivities leads to the first burst of γ’ nucleation forming the first generation of precipitates

with low nucleation density, which will be referred to as primary γ’ precipitates. It should be

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noted that industry often refers to this first generation of γ’ precipitates formed during continuous

cooling, as secondary γ’, since they refer to the γ’ retained from the casting process, that does not

dissolve during supersolvus solutionizing, as primary γ’. At higher undercoolings or low

temperature reduced diffusivity of atoms leads to supersaturation of γ’-forming elements away

from the diffusion fields of the growing primary γ’ precipitates, and coupled with a greater

thermodynamic driving force results in further bursts of nucleation consequently forming what

will be referred to as secondary (or tertiary in some cases) γ’ precipitates with a high nucleation

density [13,19,21]. Radis et al. [13] in a recent paper have employed classical nucleation theory

involving long range diffusion of atoms to understand nucleation kinetics of both monomodal as

well as multi-modal size distributions of γ’ precipitates in the commercial nickel base superalloy

UDIMET 720. Mao et al. [23] performed a continuous cooling at different cooling rates in

U720LI alloys. At very high cooling rate (111 °C/ min) monomodal size distribution was found

while bimodal distribution was found at 27 °C /min quench rate. The authors suggested that a

competition of undercooling and diffusion governs the formation of the secondary γ’

precipitates; lower temperature leads to smaller particle size and higher number of particle

density. Further, Mao et al. [10] observed that a morphology of the γ’ precipitates in Rene 88

alloy changes from spherical to cuboidal morphology with increasing cooling rate.

Atom probe tomography (APT) has been extensively used for three-dimensional (3D)

characterization of the morphology, size distribution, and, composition of fine nanometer-scale γ’

precipitates in Ni-base alloys and these studies have been extensively reviewed in recent articles

in the published literature [18,20,24-28]. The primary emphasis of these studies has been the

determination of the size, morphology, and, composition of the γ’ precipitates within the γ matrix

during the early stages of precipitation in these alloys during annealing after rapid quenching

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from the high temperature single γ phase field. Therefore, typically these studies have focused on

a monomodal size distribution of refined γ’ precipitates [18-20]. In addition, such APT studies

have also focused on the partitioning of the solute elements between these two phases and the

segregation of certain solute elements across the γ / γ’ interface as well as to grain boundaries.

Hwang et al. [27,28] studied the compositional partitioning across the γ / γ’ interfaces on

commercially used Rene 88 superalloy by using APT. They found that the equilibrium

composition of the primary and secondary γ’ precipitates are different. In addition, the interface

width of the primary γ’ precipitates is sharper compared to that of the secondary γ’ precipitates.

This was the first attempt to compare the interface width between different generations of the γ’

precipitates.

Phase field simulation has gained a great advantage over the experimental investigations.

Earlier the phase field model obtained accurate prediction only on isothermal annealing

conditions, which was accounted only for variation in Thermodynamics factor such as

compositions and long-range order parameters. Langer and Schwartz [29] developed a new

phase field model that could predict microstructural evolution involving nucleation and growth

process. It can predict a particle size distribution for non-isothermal annealing. Recently, Wen et

al. [21] have developed a phase field method to understand the formation of bimodal size

distribution of γ’ precipitates during continuous cooling at various cooling rates. A bimodal

microstructure is obtained by two successive events. The first nucleation forms at low

undercooling and shuts off by soft impingement at intermediate temperature. With decreasing

temperature, the supersaturated matrix is developed at high undercooling and thus the second

burst of nucleation is formed. Simmons et al. [30] employed the phase field simulation in three

different cooling rate schemes. For isothermal and slow cooling rate, the monomodal particle

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distribution is observed and a nucleation event is stopped by a soft impingement process.

Bimodal distribution is observed in case of an intermediate cooling rate. With even faster cooling

rate, the secondary γ’ precipitates never stop by the soft impingement. The critical inter-particle

spacing is not established. However, the nucleation eventually stops due to slow diffusion at low

temperature.

Extensive studies have been investigated in the effect of cooling rate on particle size

distribution and morphological development by employed many characterization techniques

including TEM and APT and simulation modeling such as phase field model.

2.4 Decomposition Pathway Involving Order-Disorder Transformation and Phase Separation

Gamma prime precipitation mechanisms in Ni-base alloys can be broadly classified into

categories of homogeneous or heterogeneous nucleation. Homogeneous nucleation occurs

spontaneously and randomly whereas heterogeneous nucleation takes place at preferential

nucleation sites such as grain boundaries [19]. These two processes are very competitive,

depending on decomposition temperature. Here, only homogeneous nucleation will be discussed.

When a disordered solid solution is rapidly quenched from the single γ phase field to

room temperature, it results in a two-phase mixture of γ and γ’s. Decomposition of the

supersaturated γ solid solution may take place via concurrent chemical clustering and ordering

processes. Typically these two processes are considered mutually exclusive. Chemical clustering

involves a preference towards formation of bonds between like atoms, leading to compositional

partitioning within the metallic solid solution, while ordering involves a preference towards the

formation of bonds between unlike atoms leading to an ordered structure. However, when alloy

subjected to rapid quenching, the highly supersaturated and undercooled single γ phase is often

unstable, more precisely metastable, with respect to the ensuing ordering or phase separation

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[31]. The homogeneous decomposition of the supersaturated γ solid solution may take place via

multiple transformation pathways. In the past, significant research efforts have been devoted to

investigate the precipitation mechanism of the γ’ phase. In most cases, the FCC to L12

transformation is a first order transition, involving classical nucleation and growth, wherein

precipitates of the ordered γ’ phase with a near-equilibrium composition will be randomly

nucleated throughout the matrix [8,14,18,32,33]. A second pathway is where the supersaturated γ

solid solution undergoes spinodal decomposition to form solute-rich and solute-depleted regions,

followed by ordering within those regions that are richer in solutes such as Al and Ti [26,31,34-

39]. Other alternative pathways include decomposition wherein the degree of ordering increases

[40] or decomposition that occurs via congruent ordering before phase separation [31,41-43].

Congruent ordering process [31,43] occurs where disordered single phase transforms to an

ordered, single phase without compositional change via nucleation and growth within the

metastable disordered solution.

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Fig. 2.3(a) shows a phase diagram configuration of nucleation and growth process. A

solid solution rapidly quenched from single-phase field of disordered α phase at temperature TQ

into T1 temperature at a composition of c0. The system first has a free energy at point A (Fig.

2.3(b)) and retains the disordered α state. The free energy of the disordered α phase is metastable

with respect to the ordered γ phase since the curvature of the free energy-composition curve for

the disordered α phase is positive. The system will reduce its free energy to point B in Fig. 2.3(b)

and decompose into two-phase mixture of α+γ. The ordered γ phase forms with an equilibrium

composition of 𝑐𝑐𝛾𝛾𝑒𝑒. The relative volume fraction of the two-phase mixtures can be determined by

a lever rule.

Fig. 2.3 Schematic diagrams of phase diagram and free energy-composition curve of order-disorder transformation by nucleation and growth process [31]

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If a solid solution is quenched to temperature T2 below the ordering stability 𝑇𝑇𝑖𝑖− as shown

in Fig. 2.4(a). The free energy- composition plot of the temperature T2 is presented in Fig. 2.4(b).

The hatched region of the disordered α phase becomes unstable with respect to the ordering.

Composition c0 on point A’ starts continuously order by decreasing the free energy to point B’ on

the ordered γ free energy curve. The homogeneous, single phase B’ is metastable with respect to

the stable two phase mixture and then the free energy of the system will further decreases to

point C’ by nucleation of the disordered phase.

Fig. 2.5 represents possibilities pathway of the decomposition of point A’ at temperature

T2. Different states of thermodynamic stability of disordered phase with respect to ordering are

illustrated. P(A’) is in the hatched region where disordered state is unstable with respect to

ordering. P(A’) ,is on the disordered state and has order parameter of η=0, continuous orders to

𝜂𝜂0∗ at point Q(B’) where homogeneously ordered, single phase occurs. It is worth noting that the

free energy at point P(A’) do not have a nucleation barrier; thus, the decomposition of

continuous ordering occur without a nucleation step. Second possibility of the as-quenched

Fig. 2.4 Phase diagram and free energy-composition curve of ordered and disordered phases at T2. At temperature T2 the decomposition occurs via continuous ordering of homogeneously ordered, single phase at point B’ and is followed by nucleation of the disordered phase at point C’[31]

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disordered α phase is shown at point P’. Point P’, located outside the hatched region, is

metastable with respect to ordering because there is a nucleation barrier between the disordered

and ordered phase. Point P’ will decrease the free energy of the system by a congruent ordering.

Congruent ordering take places via nucleation and growth process of homogeneously ordered,

single phase of γ from point P’ to at point Q’ without a compositional change. This process is

defined by Khachaturyan et al. [43].

If a supersaturation of α disordered phase is quenched to temperature T3 within a hatched

region shown in Fig. 2.6(a). Point R in a free energy plot at temperature T3 of α disordered phase

become unstable with respect to ordering (Fig. 2.6(b)) and will continuously ordered to the

homogeneously ordered, single phase of γ to point S. At point S, the free energy is unstable since

the curvature of the free energy is negative (𝜕𝜕𝜕𝜕𝜕𝜕𝑐𝑐 < 0). The supersaturation of the disordered α

phase decomposes into two-ordered phases with different compositions. As spinodal

decomposition process takes place, the composition of the two phases move along the free

energy curve. The solute-depleted regions will move from point S to point U where disorder α

Fig. 2.5 Schematic diagram of free energy-composition-order parameter η plot for temperature T2 [31]

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phase is achieved with an equilibrium composition of 𝑐𝑐𝛼𝛼𝑒𝑒 . Spontaneously, the solute-rich regions

will move from point S down to the ordered γ phase with an equilibrium composition of 𝑐𝑐𝛾𝛾𝑒𝑒.

Furthermore, Fig. 2.6 shows the different regions of the phase diagram. The crosshatched

region between T0 (the locus point where the order and disorder phases have the same free

energies at particular composition) and 𝑇𝑇𝑖𝑖−(ordering instability) can take place via congruent

ordering followed by spinodal decomposition. However, the spinodal decomposition takes place

and followed by ordering in the hatched region between 𝑇𝑇𝑖𝑖−(ordering instability) and Ts (the

spinodal curve)

Extensive studies have been investigated in non-classical nucleation mechanism. Yoshida

et al. [44] and Kostorz et al. [45] employed high resolution TEM and small angle neutron

scattering (SANS) in Ni-12at%Ti. It clearly indicated that the γ’ precipitates exhibit with the

amplification wave within the disordered solid solution. Both electron and x-ray diffraction

clearly show the L12 phase in the as-quenched condition. Broaden SANS peaks were captured in

the early stage of nucleation. Broaden SANS peaks occur due to composition fluctuation in the

Fig. 2.6 a) Phase diagram and b) schematic plot of disordered and ordered phase at temperature T3 [31]

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disordered matrix leading to observable difference of lattice parameter of solute-rich and solute-

depleted regions. γ’ precipitates grow leading to sharpen the peak with little change of lattice

parameter. Grune and Haasen [46] investigated Ni-12at%Ti alloy using field ion microscopy

(FIM). A concentration amplitude and wavelength of fluctuation increases with time found after

550 °C aging for 64 hr. It can be concluded that the Ni-Ti system decomposes continuous

transformation preceded by continuous ordering. Pareige et al. [39] reported ordering and phase

separation taking place in a model Ni-Cr-Al alloy using a combined Monte Carlo (MC)

simulation and experimental approach that included results from atom probe tomography (APT).

Their results indicated that the precipitation mechanism of the γ’ phase occurs via classical

nucleation and growth in a low supersaturated Ni-Cr-Al alloy, whereas decomposition of a high

supersaturated alloy takes place via congruent ordering followed by phase separation. A more

recent study, carried out by Viswanathan et al. [35], investigated the precipitation mechanism of

the γ’ phase in a rapidly quenched commercially used Ni-base superalloy, Rene 88 DT. The

experimental observations indicate that phase separation occurring in the γ matrix develops

nanometer scale domains that are depleted in Co, Cr, and Mo. The concentration of Al and Ti

showed a reverse trend in these domains. The Cr depleted domains, which are also depleted in

Co and Mo and enriched in Ti and Al, subsequently undergo chemical ordering to form γ’

precipitates exhibiting the L12 ordered structure. The presence of such ordering was observed via

high resolution scanning transmission electron microscopy (STEM), where the ordered regions

were only confined within the Cr-depleted pockets. Also APT results showed that the Cr-rich

and Cr-depleted domains were interconnected and exhibited compositions that were far-from-

equilibrium. Coupling the two observations presented above, Viswanathan et al. suggested the

possibility of phase separation within the γ matrix preceding the ordering process in fast

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quenched Rene 88 DT [4].

To date, the thermodynamically second order order-disorder transformation appears to be

associated with the miscibility gap. Several attempts have been done to identify the miscibility

gap in well–known spinodally decomposed Al-Li system. Experimental evidences were clearly

shown that the degree of order in early stage of L12 domain formed is much lower than that of

fully order structure. However, there is no clear evidence of miscibility gap in the phase diagram

of this system.

Although extensive research were studied on the ordering and phase separation process,

there are substantial controversies regarding to non-classical nucleation mechanism in Ni-base

alloys and sequence of nucleation processes.

2.5 Discontinuous Precipitation

As mentioned in 2.4, gamma prime precipitation mechanisms in Ni-base alloys can be

broadly classified into categories of homogeneous or heterogeneous nucleation. In a

supersaturated solid solution, precipitation can take place either continuously (homogeneously)

or discontinuously [32,33,47-49]. Discontinuous precipitation is a solid-state reaction where a

supersaturated solid solution decomposes to solute-depleted matrix and solute-rich precipitates

across a migrating boundary or reaction front resulting in a two-phase lamellar product. This

reaction is characterized by a discontinuous or abrupt change in orientation and composition

between the matrix and the precipitate phase. It has been observed in a number of alloy systems

such as Ni-In [50,51], Co-Mo [52,53], Co-W [54], Ni-Al [55], Ni-Co-Al [32,33], even in a high-

refractory Ni base superalloys [49].

Discontinuous precipitation in Ni-Al alloys is known to occur very slowly [55]. However

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addition of cobalt promotes the discontinuous precipitation [9]. Apart from that the two major

contributions of cobalt to alloy properties are the reduction of matrix stacking fault energy and

the increase in the γ’ solvus temperature [2,56,57]. In Ni-Co-Al alloy, the supersaturated disorder

matrix decomposes to γ’ precipitates of L12 ordered structure and solute-depleted γ matrix. In

most cases, continuous and discontinuous precipitations occur simultaneously. However, only

under certain condition of composition and temperature, discontinuous precipitation can be

observed. These processes are competitive and discontinuous precipitation is usually confined by

continuous precipitation to grain boundary regions. Only an alloy with cobalt concentration more

than 38 at% will transform to discontinuous γ’ precipitation completely [33]. Kainuma et al.,

[48] studied phase equilibria among γ (A1), γ’ (L12) and β (B2) phase of the Ni-Co-Al system.

A range microstructure (fine blocky, plate like, Widmanstatten and lamellar) has been observed

with varying cobalt concentration in Ni-20Co-25Al, Ni-30Co-25Al, Ni-40Co-25Al and Ni-

60Co-25Al alloys. Also there were differences in the discontinuous products. For example the

discontinuous precipitation that was observed in Ni-60Co-25Al alloy resulted in β+γ phases at

700 °C, rather than γ and γ’ phases observed in Ni-40Co-12.5Al alloy.

It is widely known that the discontinuous precipitation is influenced by grain inclination

[58], grain boundary misorientation [59] and orientation relationship between the grain

boundaries and precipitate habit planes [60] along with grain boundary mobility and diffusivity.

It has been observed that minimum of 1% precipitate-matrix lattice mismatch is initially required

as a criterion for discontinuous precipitation. Hagel and Beattie [9] concluded that in Co-Ni

alloys where the γ’/γ misfit strain > 1%, a lamellar microstructure is observed. However, in many

alloys like Ni-Al [55], Ni-Ti [61], and Ni-Co-Al [32,33], the misfit strain is < 1% and yet they

exhibit discontinuous precipitation.

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Within a particular alloy that shows discontinuous precipitation, high angle grain

boundaries are found to be the most potential areas for discontinuous reaction fronts to proceed,

mainly due to their higher mobility and diffusivities [62]. Matsuoka et al. [63] have reported that

only boundaries with a minimum misorientation of 22° can initiate discontinuous precipitation in

Cr-Ni based austenitic stainless steel. Also, recent study on Cu-Ti alloy observed that high angle

grain boundaries with a special coincident site lattice (CSL) relationship are not a preferred

initiation site for discontinuous precipitation [64,65]. It is suggested that a high energy, rather

than only high angle grain boundary is likely to be the initiation site. An absence of the

discontinuous precipitation has been reported on low energy boundaries like twin boundaries, as

well as for low angle boundaries that have poor mobility. Further, dynamic properties also

depend on the microstructure and vary from one-grain boundary to another in polycrystalline

materials. Hence, a non-uniform growth of the discontinuous precipitation from different

boundaries in the same microstructure can be observed in most of the experimental studies.

2.6 Influence of Rhenium on Microstructure and Mechanical Properties of Ni-Base

Superalloys

The first generation of superalloys was developed in the 1980s. Subsequent generations

have shown significant improvements in creep strength; second-generation superalloys provide

an increase of approximately 30°C in creep strength than the first-generation single crystal, and

recently developed third-generation superalloys exhibit a 60°C improvement from first-

generation superalloys [1]. The main difference in chemical composition of the first-, second-,

and the third-generation superalloys is rhenium content— rhenium-free, 3 wt % Re, and 6 wt %

Re, respectively [66,67].

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Furthermore, with increasing of Re concentration local hardness of γ matrix increases in

different generations of superalloys [68]. In addition, Re partitions mostly to γ matrix leading an

increase in a lattice spacing of Ni lattice in γ matrix. Thus, negative lattice misfit is achieved [69]

and significantly reduces the γ’ coarsening kinetics [70-73] and posses a better creep resistance

[74].

However, introduction of Re concentration in the superalloys leads to expense of density,

castability, cost and microstructural instability [1,75]. Excessive amount of Re addition results in

TCP formation that deteriorates the mechanical properties [75-77]. Also, Re is a costly rare earth

element; the reduction or elimination of Re is desirable as it will decrease cost. Understanding

the role of Re in improving creep properties can help researchers develop a low-cost monocrystal

turbine blade material that maintains all necessary mechanical properties and provides better

understanding of the acceptable window for low-angle grain boundaries on airfoil properties.

Because Re has been found to remarkably improve creep strength at very high

temperatures (1000-1150 °C) [78], addition of Re element in this alloy has been extensively

introduced to rhenium-containing single-crystal superalloys to service in high-temperature

application. The so-called rhenium-effect began in the late 1980s. This pioneering work started

when the alloys CMSX-2 and PWA 1480 were doped with approximately 1 at % Re content

[25,79]. Rhenium clustering has been raised as a cause of the rhenium-effect. A occurrence of

small inhomogeneity of Re distribution in the matrix has been suggested by the 1 D ladder

diagram. The authors concluded that Re clusters could act as efficient obstacles against the

dislocation motion at high temperatures. Rusing et al. [78] employed TEM and 3DAP studies on

Re31 superalloys and found that Re partitions mainly the γ matrix where it forms clusters of

approximately 1 nm. Further, Wanderka et al. [80] employed layer-by-layer analysis of (001)

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planes of the γ’-L12 structure by APFIM technique in Re-containing CMSX-4 alloy. Re clusters

was found in the γ matrix. Re clusters are likely to consist of 5 Re atoms, where 3 Re sit in

planes and one of each Re atom sits in lower and upper atomic plane.

Mottura et al. have been investigated on Re clustering by various techniques. First, an

extended x-ray absorption fine structure (EXAFS) technique was used to study a local atomic

structure around the solute atoms in a binary Ni-Re alloy. EXAF result did not displayed double

peaks in the x-ray abruption spectra which indicates the Re clustering. Later, they employed a

purpose-built algorithm applied to an atom probe dataset to characterize the distribution of Re in

the binary Ni-Re alloy and the commercial CMSX-4 superalloy. Re atoms were found to be

consistent with the random distribution of this solute in both alloys [81]. Further, the DFT

calculation was performed to measure a binding energy of Re-Re pair and a stability of small Re

clusters. The prediction showed that Re-Re nearest neighbor pair is energetically prohibited.

Thus, it is unlikely that Re clusters can form in Ni matrix [82]. Thus, none of the EXAF, APT

and DFT techniques was found that existing Re clusters in the Ni matrix indicating that Re

clusters are not a justification of better creep resistance.

Extensive investigations have been made into the enrichment of rhenium close to γ / γ’

interfaces. Rusing et al. [78] also focused on the distribution of Re across the γ / γ’ interfaces.

The authors found that no local enrichment of Re occurred on the γ side near γ/γ’ interface in

heat-treated Ni-Al-Ta-Re alloy. However, Warren et al. [83] have found clear evidence that Re

atoms pile-up ahead of the growing γ’ particles in the γ matrix in high-temperature creep and low

cycle fatigue samples of single-crystal RR 3000 superalloy. This enrichment of Re occurs during

the cooling process when γ’ is growing and rejects Re atoms into γ phase. The Re enrichment

ahead of the γ / γ’ interfaces was claimed to reduce creep rate [71]. Consequently, broader bow

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waves ahead of the growing particles due to the inhomogeneity of Re distribution inhibit the

growth and coarsening of the γ’ precipitates. Mottura et al. [81] employed the phase-field

simulation and confirmed that the enrichment of Re ahead of γ / γ’ interfaces is due to the

rejection of Re during cooling from high temperatures.

Yoon et al. [72] studied the effect of Re addition on a model Ni-Cr-Al superalloy. They

found that in contrast to the commercial single-crystal superalloy Rene N6, for all aging times,

the concentration profiles across γ / γ’ interfaces exhibit no indication of Re enrichment on the

model Ni-Cr-Al superalloy [84,85]. The authors concluded that the difference between the two

alloys arises from the interaction of multiple alloying elements in the commercial superalloy, the

thermal history of the alloys, or the effect of lattice parameter misfit between γ and γ’ phase. The

calculated lattice misfit in the quaternary Ni-Cr-Al-Re alloy was -0.6%, compared to +0.05% for

Rene N6.

Kindrachuk et al. [73] studied the effect of Re on the microstructure of Ni-Fe-base

Inconel 706 alloy. They found that the kinetics of microhardness degradation was similar in Re-

modified Re706 compared to base-In706 alloy. The effect of Re addition to this alloy was

ineffective due to a smaller volume fraction of Re partitioning to γ / γ’ matrix compared with

other Re-containing alloys[78,80,83,84] where Re partitioning in modified Re 706 and other Re-

containing alloys have ~30 vol% 75 vol%, respectively.

Ge et al. studied distribution of Re in a second generation DD6 superalloy by means of

scanning transmission electron microscopy (STEM) and energy dispersive x-ray spectroscopy

(EDS). The uncrept DD6 alloy showed no evidence of Re enrichment at γ / γ’ interfaces.

However, the Re enrichment was found after creep testing in the same alloy. This result was

contradicted with [81,85]. Further investigation showed that the enrichment of Re near the

28

dislocation core was found where dislocations are close to the γ / γ’ interfaces, possibly due to a

higher concentration of Re near the interface compared to other regions. In addition, the

enrichment was not evenly distributed but was found in form of clusters.

Given the above, the physical understanding of how Re improves the high-temperature

creep strength of Ni-base superalloys has remained unclear.

2.7 References

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[3] Ricks R, Porter A, Ecob R (1983) The growth of γ′ precipitates in nickel-base superalloys. Acta Metallurgica 31

[4] Taylor A, Floyd R (1952) The constitution of nickel-rich alloys of the nickel-titanium-aluminium System. J.Inst.Metals 81

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[8] Sarosi P, Wang B, Simmons J et al (2007) Formation of multimodal size distributions of γ′ in a nickel-base superalloy during interrupted continuous cooling. Scr Mater 57

[9] Hagel W, Beattie Jr H (1959) High-temperature aging structures in $ gamma $'-hardened austenitic alloys. Trans.Met.Soc.AIME 215

[10] Mao J, Chang K, Yang W et al (2002) Cooling precipitation and strengthening study in powder metallurgy superalloy Rene88DT. Materials Science and Engineering: A 332. DOI:http://dx.doi.org/10.1016/S0921-5093(01)01758-0

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[11] Babu S, Miller M, Vitek J et al (2001) Characterization of the microstructure evolution in a nickel base superalloy during continuous cooling conditions. Acta materialia 49

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[13] Radis R, Schaffer M, Albu M et al (2009) Multimodal size distributions of γ′ precipitates during continuous cooling of UDIMET 720 Li. Acta Materialia 57

[14] Rojhirunsakool T, Meher S, Hwang J et al (2013) Influence of composition on monomodal versus multimodal γ′ precipitation in Ni–Al–Cr alloys. J Mater Sci 48

[15] Singh A, Nag S, Chattopadhyay S et al (2013) Mechanisms related to different generations of γ′ precipitation during continuous cooling of a nickel base superalloy. Acta Materialia 61

[16] Singh A, Nag S, Hwang J et al (2011) Influence of cooling rate on the development of multiple generations of γ′ precipitates in a commercial nickel base superalloy. Mater Charact 62

[17] Caron P (2000) High γ′ solvus new generation nickel-based superalloys for single crystal turbine blade applications. Superalloys


[19] Porter DA, Easterling KE (1992) Phase Transformations in Metals and Alloys, (Revised Reprint). CRC press

[20] Booth-Morrison C, Weninger J, Sudbrack CK et al (2008) Effects of solute concentrations on kinetic pathways in Ni–Al–Cr alloys. Acta Materialia 56

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[22] Payton E, Phillips P, Mills M (2010) Semi-automated characterization of the phase in Ni-based superalloys via high-resolution backscatter imaging. Materials Science and Engineering: A 527

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[24] Miller M (2001) Contributions of atom probe tomography to the understanding of nickel-based superalloys. Micron 32

[25] Blavette D, Caron P, Khan T (1988) An atom-probe study of some fine-scale microstructural features in Ni-based single crystal superalloys. Superalloys 1988

30

[26] Ardell A, Nicholson RB (1966) On the modulated structure of aged Ni-Al alloys: with an Appendix On the elastic interaction between inclusions by JD Eshelby Cavendish Laboratory, University of Cambridge, England. Acta metallurgica 14

[27] Hwang J, Nag S, Singh A et al (2009) Compositional Variations between Different Generations of γ′ Precipitates Forming during Continuous Cooling of a Commercial Nickel-Base Superalloy. Metallurgical and Materials Transactions A 40

[28] Hwang J, Nag S, Singh A et al (2009) Evolution of the γ/γ′ interface width in a commercial nickel base superalloy studied by three-dimensional atom probe tomography. Scr Mater 61

[29] Langer J, Schwartz A (1980) Kinetics of nucleation in near-critical fluids. Physical Review A 21

[30] Simmons J, Wen Y, Shen C et al (2004) Microstructural development involving nucleation and growth phenomena simulated with the phase field method. Materials Science and Engineering: A 365


[32] Davies C, Nash P, Stevens R (1980) Precipitation in Ni-Co-Al alloys. J Mater Sci 15

[33] Davies C, Nash P, Stevens R et al (1985) Precipitation in Ni-Co-Al alloys. J Mater Sci 20



[36] Laughlin D, Soffa W (1988) In: Anonymous Physical Properties and Thermodynamic Behaviour of Minerals. Springer



[39] Pareige C, Soisson F, Martin G et al (1999) Ordering and phase separation in Ni–Cr–Al: Monte Carlo simulations vs three-dimensional atom probe. Acta materialia 47

[40] Tanner L, Leamy H (1974) In: Anonymous Order-Disorder Transformations in Alloys.

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Springer

[41] Sato T, Kamio A (1990) Ordered Structures in the Early Stage of Decomposition in an Al-7. 9 mol% Li Alloy. Mat.Trans.JIM 31

[42] Schmitz G, Hono K, Haasen P (1994) High resolution electron microscopy of the early decomposition stage of Al Li alloys. Acta metallurgica et materialia 42

[43] Khachaturyan A, Lindsey T, Morris J (1988) Theoretical investigation of the precipitation of δ'in Al-Li. Metallurgical Transactions A 19

[44] Yoshida H, Arita M, Cerri A et al (1986) High resolution electron microscopic studies of Ni-9.3 and 14.7 at.% Ti alloys. Acta Metallurgica 34

[45] Kostorz G, Komura S, Furukawa H (1988) Dynamics of Ordering Processes in Condensed Matter.

[46] Grüne R, Haasen P (1986) Spinodal decomposition of Ni-Ti. Le Journal de Physique Colloques 47

[47] Duly D, Simon J, Brechet Y (1995) On the competition between continuous and discontinuous precipitations in binary Mg Al alloys. Acta metallurgica et materialia 43

[48] Kainuma R, Ise M, Jia C et al (1996) Phase equilibria and microstructural control in the Ni-Co-Al system. Intermetallics 4

[49] Nystrom J, Pollock T, Murphy W et al (1997) Discontinuous cellular precipitation in a high-refractory nickel-base superalloy. Metallurgical and Materials Transactions A 28

[50] Chuang T, Fournelle R, Gust W et al (1988) Discontinuous coarsening of discontinuous precipitate in a Ni-7.5 at.% In alloy. Acta Metallurgica 36

[51] Geber G (1995) An APFIM/TEM investigation of the discontinuous precipitation in a Ni In alloy. Appl Surf Sci 87

[52] Gust W, Predel B, Mehra SN (1975) Die kinetik der feinlamellaren diskontinuierlichen ausscheidung in Co-Mo-Mischkristallen. Materials Science and Engineering 21. DOI:http://dx.doi.org/10.1016/0025-5416(75)90207-4

[53] Lee S, Lee K, Chuang T (1998) Discontinuous coarsening of discontinuous precipitates in a Co–6 at.% Mo alloy. Materials Science and Engineering: A 251. DOI:http://dx.doi.org/10.1016/S0921-5093(98)00624-8

[54] Ziȩba P, Cliff G, Lorimer GW (1997) Discontinuous precipitation in cobalt-tungsten alloys.

32

Acta materialia 45

[55] Williams R (1959) Aging of Nickel-Base Aluminium Alloys. Trans.TMS-AIME 215

[56] Betteridge W, Heslop J The Nimonic alloys and other nicklbase high-temperature alloys (1974). Edward Arnold (Publishers) Ltd., London

[57] Mourer DP, Huron ES, Backman DG et al (2002) Ni based superalloy and its use as gas turbine disks, shafts, and impellers

[58] Vaughan D (1968) Grain boundary precipitation in an Al- Cu alloy. Acta Metallurgica 16

[59] Unwin P, Nicholson R (1969) The nucleation and initial stages of growth of grain boundary precipitates in Al-Zn-Mg and Al-Mg alloys. Acta Metallurgica 17

[60] Butler EP, Swann PR (1976) In situ observations of the nucleation and initial growth of grain boundary precipitates in an Al-Zn-Mg alloy. Acta Metallurgica 24. DOI:http://dx.doi.org/10.1016/0001-6160(76)90009-2

[61] Mihalisin J, Decker R (1960) Phase transformations in nickel-rich nickel-titanium-aluminum Alloys. Trans.AIME 218

[62] Gust W (1979) Phase transformations. Institution of Metallurgists, London

[63] Matsuoka S, Mangan M, Shiflet G et al (1994) Solid–solid phase transformations Proceedings.

[64] Boonyachut N, Laughlin D (2009) Influence of boundary structure on cellular nucleation in Cu-3 w/oTi age-hardening alloys. J Mater Sci 44

[65] Unwin P, Nicholson R (1969) The nucleation and initial stages of growth of grain boundary precipitates in Al-Zn-Mg and Al-Mg alloys. Acta Metallurgica 17

[66] Walston W, Schaeffer J, Murphy W (1996) A new type of microstructural instability in superalloys-SRZ. Superalloys 1996

[67] Erickson GL (1995) A new, third-generation, single-crystal, casting superalloy. JOM 47

[68] Durst K, Göken M (2004) Micromechanical characterisation of the influence of rhenium on the mechanical properties in nickel-base superalloys. Materials Science and Engineering: A 387

[69] Epishin A, Brückner U, Portella P et al (2003) Influence of small rhenium additions on the lattice spacing of nickel solid solution. Scr Mater 48

[70] Giamei A, Anton D (1985) Rhenium additions to a Ni-base superalloy: effects on microstructure. Metallurgical transactions A 16

33

[71] Ge B, Luo Y, Li J et al (2012) Study of γ/γ′ interfacial width in a nickel-based superalloy by scanning transmission electron microscopy. Philosophical Magazine Letters 92

[72] Yoon KE, Noebe RD, Seidman DN (2007) Effects of rhenium addition on the temporal evolution of the nanostructure and chemistry of a model Ni–Cr–Al superalloy. II: Analysis of the coarsening behavior. Acta materialia 55

[73] Kindrachuk V, Wanderka N, Banhart J et al (2008) Effect of rhenium addition on the microstructure of the superalloy Inconel 706. Acta Materialia 56

[74] Tian S, Su Y, Qian B et al (2012) Creep behavior of a single crystal nickel-based superalloy containing 4.2% Re. Mater Des 37

[75] Rae C, Reed R (2001) The precipitation of topologically close-packed phases in rhenium-containing superalloys. Acta Materialia 49

[76] Harris K, Erickson G, Sikkenga S et al (1992) Development of the rhenium containing superalloys CMSX-4 & CM 186 LC for single crystal blade and directionally solidified vane applications in advanced turbine engines. Superalloys 1992 297

[77] Pessah M, Caron P, Khan T (1992) Effect of mu phase on the mechanical properties of a nickel-base single crystal superalloy. ONERA, TP


[79] Blavette D, Caron P, Khan T (1986) An atom probe investigation of the role of rhenium additions in improving creep resistance of Ni-base superalloys. Scripta metallurgica 20

[80] Wanderka N, Glatzel U (1995) Chemical composition measurements of a nickel-base superalloy by atom probe field ion microscopy. Materials Science and Engineering: A 203

[81] Mottura A, Warnken N, Miller MK et al (2010) Atom probe tomography analysis of the distribution of rhenium in nickel alloys. Acta Materialia 58

[82] Mottura A, Finnis M, Reed R (2012) On the possibility of rhenium clustering in nickel-based superalloys. Acta Materialia 60

[83] Warren P, Cerezo A, Smith G (1998) An atom probe study of the distribution of rhenium in a nickel-based superalloy. Materials Science and Engineering: A 250

[84] Yoon KE, Noebe RD, Hellman OC et al (2004) Dependence of interfacial excess on the threshold value of the isoconcentration surface. Surf Interface Anal 36

[85] Yoon KE, Isheim D, Noebe RD et al (2001) Nanoscale studies of the chemistry of a René N6 superalloy. Interface Science 9

34

CHAPTER 3

PROCESSING AND CHARACTERIZATION TOOLS

3.1 Introduction

This chapter presents processing steps from alloy preparation, sample preparation, to

characterization tools. Processing tools, heat treatment, and sample preparation are discussed.

Various techniques have been employed for microstructural characterization such as scanning

electron microscopy (SEM), grain orientation study by electron backscatter diffraction (EBSD),

transmission electron microscopy (TEM), 3D atom probe tomography (3DAP), as well as

synchrotron-base high-energy x-ray diffraction (XRD).

3.2 Alloy Preparation

Materials used in the study including Ni-8Al-8Cr at%, Ni-10Al-10Cr at% and Ni-37.5Al-

12.5Co at% alloys were melted and fabricated at Wright-Patterson Air Force Research

Laboratory, Ohio under the AFRL ISES Contract (Contract number FA8650-08-C-5226).

Commercially used single crystal Ni-base superalloys, Rene N5 were obtained from

General Electric (GE), Aviation. This work has been supported by an NSF Industry/University

Cooperative Research Center (I/UCRC) under Center for Advanced Non-Ferrous Structural

Alloys (CANFSA). It was established by Colorado School of Mines (CSM) and University of

North Texas (UNT) with industry including GE Aviation. As cast, full heat-treated and thermally

cycled sample of single-crystal Rene N5 alloys were fabricated at GE Aviation and brought to

UNT for characterization.

35

3.3 Processing Tools

3.3.1 Mechanical Cutting

A Mitsubishi FX10 Wire Electric Discharge Machine (EDM) and an Allied High Tech

Products Inc. Techcut4TM, a rotary low speed saw, were used to cut the bulk alloys into small

sections of desired dimensions prior to and after subjecting them to heat treatments. The wire

EDM cuts the sample by passing a high voltage through a thin brass wire that machines the

sample with very low dimensional tolerances. The whole assembly is submerged in a deionized

water tank during operation. The sample is then cut by running programs that are written in

general and machine (G and M) codes for CNC machines. The codes can be modified according

to the final geometry that is desired. The codes are then simulated on a cathode ray tube (CRT)

screen, which shows how the machine will run. EDM is a robust tool as it allows for cutting

samples in any desired shapes and can be used for preparing 3 mm conventional discs for

transmission electron microscopy (TEM). On the other hand, when sample size tolerances and

sample geometry were not a limiting factor, small coupons were cut using a low speed diamond

saw.

3.3.2 Heat Treatment

Samples were prepared by mechanical cutting into pieces suitable for heat treatment

purposes. For rapid quenching studies, samples were encapsulated in a quartz tube filling with

argon and was subsequently solutionized at a single γ phase field at 1150 °C for 30 minutes

followed by rapidly quenched in liquid nitrogen bath to room temperature. For continuous

cooling studies, samples were solutionized above the γ’ solvus temperature at 1150 °C for 30

36

min and continuous cooled in furnace with average cooling rate of 14 °C/min in Ar atmosphere.

Subsequent annealing of highly sensitive oxidized samples were also encapsulated in a quartz

tube filling with argon and followed by water quenching to room temperature.

3.3.3 Sample Preparation

After being subjected to heat treatment, the annealed samples were prepared for

characterization by conventional metallographic technique. Samples were first polished with

coarse silicon carbide (SiC) polishing paper upto 1200 grits, and followed by cloth polished with

colloidal silica from coarse 1um to 0.05 um particle size until mirror finish was achieved.

The polishing method mentioned above is satisfied for surface and phase analysis in SEM

study. For orientation microscopy (OM) studies using electron backscatter diffraction (EBSD)

technique, surface roughness of the sample is critical. Further polishing with 0.05 um particle

size of colloidal silica suspension in Buehler VibrometTM, a vibratory polisher, for 12 hr. Then,

sample will be cleaned with dilute soap in water and then methanol in an ultrasonic cleaner.

Samples for transmission electron microscopy (TEM) were prepared via conventional

routes, consisting of mechanical grinding, dimple grinding and, finally ion-beam milling until

electron transparency was achieved. Samples were thinned by hand polishing to a thickness of

100 nm or less. Dimple grinding is used to further thinned using a Fischione instruments Model

200 dimpling grinder to a thickness of about 30-50 m. Once th

achieved, the sample was then ion milled in low energy Argon using Fischione Instruments

Model 1010 TEM Ion Mill till small hole forms. Basic TEM imaging including dark-field TEM

images and selected area diffraction (SAD) patterns were conducted on a FEI Tecnai F20 field

emission gun transmission electron microscope, operated at 200 KV. Site specific TEM sample

37

for high resolution TEM imaging was done using electron backscatter diffraction technique, for

<001> grain location, equipped in a FEI dual-beam focused ion beam (FIB) instrument. Atomic

resolution- atomic mass contrast (Z- contrast) imaging was done on the site specific <001> grain

sample and was carried out in high angle annular dark field (HAADF)-STEM mode on FEI Titan

300 kV microscope, equipped with a CEOS probe aberration corrector. HAADF-STEM images

were done by Dr. Babu Viswanathan at Ohio State University.

Sample for APT studies were cut from bulk material, prepared by conventional

metallographic technique. Samples then were prepared using the FIB technique using a FEI

Nova Nanolab 200 system. Low-voltage milling was used in the final stage of milling to reduce

Ga implantation in the tips. The final tip diameter of the atom probe specimens was 50-70 nm.

All APT experiments were carried out in the voltage evaporation mode at a temperature of 60 K

with target evaporation of 0.5%. Data analyses were carried out using CAMECA IVAS 3.6

software.

3.4 Characterization Tools

3.4.1 Scanning Electron Microscopy

High-resolution field emission scanning electron microscope FEI Nova NanoSEM 230TM

was used for basic microstructure imaging. The SEM is equipped with an Everhardt Thornley

Secondary Electron detector (ETD), a charged couple detector (CCD) and a detachable solid-

state backscatter electron detector (BSED). Energy dispersive x-ray detector (EDS) and an

EDAX DigiViewTM IV electron backscatter detector (EBSD) are outfitted for composition

analysis and crystallographic orientation studies, respectively. EDAX Genesis software package

was used for composition analysis and TSL OIM Data collection software was used for EBSD

38

data acquisition. TSL OIM Data Analysis 5.3 was used for analysis of the orientation microscopy

data. The basic principles of EBSD are discussed in brief in the following section. The details of

SEM imaging SEM techniques are discussed elsewhere.

In order to study the crystallography orientation, the EBSD analysis was carried out. The

highly polished sample is placed in the SEM and tilted at an angle of ≈70° with respect to the

horizontal axis toward the EBSD detector. The phosphor screen of the EBSD detector is at an

angle of ~90° to the pole piece. The EBSD detector needs to be inserted with care in order to not

hit the sample stage. A region of interest must be selected and its image is recorded. In this

configuration, some of the electrons leaving from the sample might meet a Bragg condition.

These electrons will collide and excite the phosphor screen causing the florescence. Thus, an

electron backscatter diffraction (EBSD) pattern is formed when many different planes diffract

different electrons to form Kikuchi bands, which correspond to each of the lattice diffracting

planes. These Kikuchi bands are used to determine the crystallographic orientation of grains in

the sample. TSL OM analysis software is used for data analysis. The grain orientation map can

be used to determine the grain misorientation, nature of the grain boundary, grain size, and grain

texture [1].

3.4.2 Dual-Beam Focused Ion Beam (FIB)

The FEI Nova 200 NanolabTM focused ion beam is an extension of the SEM where the

instrument is equipped with an accelerated Ga ion beam, platinum (Pt) source, nanomanipulator

as well as the electron beam column. Ga ion beam and Pt source are used for etching and

deposition. The omniprobe AutoprobeTM 250 nano-manipulator is allowed to extraction of a

milled-region or used for micro-mechanical testing. Nanoscale chemical analysis and orientation

39

studies may be performed with an EDS and EBSD detectors that equipped with the system. The

secondary electron image resolution at the dual beam coincidence point is 1.5 nm at 15 kV. The

FIB optics has better than 7 nm image resolutions at 30 kV.

FIB mostly is used as a sample preparation instrument for transmission electron

microscopy and atom probe tomography studies. Ga ion column is used to make a trench for site-

specific TEM samples and APT tips. For APT tips preparation, sample is tilted to 22° with

respect to the horizontal axis. Wedge shape lift-out with the width of 2 um is milled with Ga ion.

Length of the lift out is dependent on number of APT tips need to be made. The single wedge is

used to make multiple APT tips. To do this, the lift-out is placed on the Si post and deposited

with Pt. This process is repeated until the lift-out is used up. The tips are made with an angular

milling. The final tip is in a form of needle with diameter of ~ 50-70 nm. For TEM sample

preparation, the sample is tilted to 52° with respect to the horizontal axis. Rectangular trench is

milled with Ga ion. The trench is transferred to a copper grid by using the omniprobe

nanomanipulator. Milling process is first done at 30 kV milling. The sample thickness in this

state is now~ 600-700 nm. Low voltage milling at 5 kV is carried out at the last step in order to

remove a Ga penetration and amorphous material. The final polishing with low voltage milling is

done until the electron transparency is achieved.

3.4.3 Transmission Electron Microscopy

Transmission electron microscopy (TEM) investigation was carried out in two different

TEM. An FEI Tecnai G2 F20 super-twin STEMTM microscope operating at 200 kV, located at

University of North Texas, was used to carry out basic diffraction and imaging studies. The

microscope has a super twin objective lens (1.2 nm chromatic (Cc) and spherical aberration (Cs)).

40

The super twin objective lens allows for 80° α+β tilt combination and give an information limit

with 0.14 nm. The energy spread of the electron gun is 0.7 eV. Tecnai TEM has a magnification

range form 25x to 1,030 kx. It is equipped with high angle annular dark field (HAADF) for

scanning TEM (STEM) imaging, energy dispersive detector (EDS) for elemental composition

analysis. Energy-filtered TEM (EFTEM) and electron energy loss spectroscopy (EELS) are

capable with this TEM.

An FEI Titan8-300 microscope, operating at 300 keV, was used for high-resolution

(HAADF) scanning TEM imaging. Titan microscope is located in The Ohio State University.

HAADF-STEM images were done by Dr.Babu Viswanathan. Titan is equipped with a Cs

corrector and a monochromator. The Cs corrector is a dual hexapole and is used to compensate a

positive Cs of lens system. The chromatic aberration is equipped to reduce a Wein filter

monochromator resulting to reducing a energy beam spread to less than 0.1 eV. The microscope

has a 0.2 nm point resolution and information limit of 0.07 nm. The HRSTEM resolution is 0.13

nm and HRSTEM images were done using the axis Fischione HAADF-STEM detector. More

details of TEM instrumentation can be found in Transmission electron microscopy book by

Williams and Carter [2].

41

3.4.4 Atom Probe Tomography

An Imago Scientific Local Electrode Atom Probe (LEAP 3000X HRTM) instrument

provides a three dimensional analytical mapping of material with atomic-scale resolution and

offers an insight of chemical composition as well as an atomic structure [3]. The instrument

consists of micro-counter-electrodes in the scanning atom probe and advent of large field-of-

view allows the volume of the reconstruction extend to several hundred nanometer in size. Atom

probe tomography employs the principle of field evaporation to remove the atoms at the apex of

the needle-shaped sample. Field evaporation involves the ionization of the surface atoms

subjected to an electric field source. The atoms at the apex or surface atoms are accelerated by

the electric field toward a detector. The evaporation event is succeeded right after the ionization

of these atoms. The ionization is induced by either high voltage or laser pulses that transmitted to

the surface atoms. The specimen is located at an extremely low temperature (5-80 K) to achieve

the highest spatial resolution providing a direct imaging of the atoms.

Fig. 3.1 Schematic diagram of the atom probe tomography [12].

42

As mentioned earlier, the APT experiment requires a very sharp needle-shaped tip when

subjected to a high positive voltage, V. An estimation of the electric field needed to apply at the

APT tip’s surface [4] is

𝐹𝐹 = 𝑉𝑉𝑘𝑘𝑓𝑓𝑅𝑅

where, F is an electric field induced at the surface of the tip which has radius of curvature

R. kf is referred to a field reduction factor and is a constant that accounts for tip shape and the

electrostatic environment[5]. In case of metallic materials, the electric field evaporation

penetrates less than 10-10 m. Thus, only atoms at the surface are affected by the field evaporation

process. This results in an evaporation of atom-by-atom and atomic-layer after atomic-layer

yielding a high depth resolution of the atom probe. However, the evaporation field penetrates

much deeper into the tip for non-metallic materials. This results in the evaporation of the group

of several atoms. Thus, non-metallic materials yield less depth resolution of the atom probe than

the metallic materials.

When using high voltage pulsing to achieve the field evaporation, fast high voltage of a

few nanoseconds is used. According to the evaporation rate formula, the atoms likely to

evaporate at a frequency related to their vibration. The vibration of atoms has a range of 10-13 to

10-11 seconds [6]. When subjected to the high voltage pulsing, not all atoms are evaporating at

the same instant. This uncertainty causes an inaccurate determination of the mass-to-charge ratio

and hence elemental identification. Delayed atoms can evaporate with part of the energy pulse.

This instant referred as energy deficit [7]. This process results in a spread of the energy of the

atoms. Therefore, mass spectrum peaks generally display a sharp peak with a long tail

corresponding to the energy deficit.

Reconstructions obtained from atom probe tomography offers an ability to map the

43

positions of individual atoms inside a material. The development of the proximity histogram or

proxigram algorithms allows the measurement of compositional profiles in three dimensions.

One needs to apply an isoconcentration surface which specifically identify features in the

reconstruction such as precipitates, interface, and grain boundaries. Atom positions are correlated

with respect to their distance to the local perpendicular to the isosurface. The algorithm then

generates a histogram, which measure a population of the atoms in radial distance away form the

isosurface. Finally, a concentration profile is generated. Another statistical analysis of the

composition obtained form APT is frequency distribution. This technique employs a constant

number of atoms per voxel block of each solute atom. The calculated frequency distribution then

compares with a theoretical distribution expected if the atom occurred randomly.

3.4.5 Synchrotron-Base High-Energy X-Ray Diffraction

The Advance Photon Source (APS) at Argonne National Laboratory funded by U.S.

Department of Energy. The APS offers the brightest ring generated x-ray beam in the Western

Hemisphere. APS facility consists of 5 main components: the linear accelerator, the booster

synchrotron, electron storage ring, insertion device, and the experimental halls. In the linear

accelerator, electrons emitted from a heated cathode head and get accelerated by high voltage

alternating electric fields at 450 MeV. With this, electrons travel at more than 99.999% of the

speed of light. Then, electrons are injected to the booster synchrotron and further get accelerated

to 7 GeV. Now electrons are travelling with more than 99.999999% of the speed of light. The

7GeV electrons are injected into the 1,104-meter-circumference storage ring. Insertion devices

are inserted and let electrons to pass to the experimental halls.

Synchrotron high-energy x-rays at APS have energy of 115 keV with a penetration length

44

in iron upto 4mm. High-energy x-ray diffraction measurement was carried out in transmitted

geometry. The photons are scattered mostly in forward direction with small angle diffraction.

Thus, x-ray pattern can cover a large range of the lattice spacing. Further, with long penetration

depth, it is more reliable and less background subtraction. Thus, structural information obtained

is a property of bulk materials [8].

High-energy x-ray studies in this dissertation were carried out in high-energy beam line

11-ID-C [8]. A bent Bragg Si(311) crystal monochromator equipped with the 115keV x-ray

beam give a flux of 1011 photons per second with beam size of 1x1mm2. 2D Perkin Elmer Si flat

panel was used as a detector for x-ray diffraction patterns. Linkam TS1500 furnace was equipped

with x-ray beam line to employ an in-situ x-ray diffraction study. Sample thickness for the in-situ

study is ~ 1mm. The temperature of the furnace was recorded in a time-temperature text file. 2D

circular diffraction patterns were recorded every 18 seconds interval. Powder diffraction

analyses were carried out with FIT2D software [9]. This software specializes in the integration of

Debye-Scherrer rings from 2-D detectors, to 1-D “2-theta'” scans, and to other scans. Standard

cerium oxide with lattice parameter of 5.4111Å was used for calibration of sample-to-detector

distance. The sample-to-detector distance was ~1793 nm in all studies. The wavelength of the x-

Fig. 3.2 The experimental hall in 11-I-DC sector at APS [8].

45

ray beam was given as 0.11165 A°. The intensity versus 2theta plot was export to the .chi file in

order to further analyze by using GSAS and its interface EXPGUI. GSAS software [10] was used

to fit crystallographic and magnetic structural models to x-ray and neutron single-crystal and

powder diffraction data. It is also used for lattice parameter determination, simulation of powder

diffraction, and for texture analysis. EXPGUI program [11] is a graphical user interface for

GSAS.

3.5 References

[1] Schwartz AJ, Kumar M, Adams BL et al (2009) Electron backscatter diffraction in materials science. Springer [2] Williams DB, Carter CB (1996) The transmission electron microscope. Springer [3] Kelly TF, Miller MK (2007) Atom probe tomography. Rev Sci Instrum 78 [4] Gault B, Moody MP, Cairney JM et al (2012) Atom probe microscopy. Springer [5] Gomer R (1961) Field emission and field ionization. Harvard University Press Cambridge, MA [6] Kellogg G (1984) Measurement of activation energies for field evaporation of tungsten ions as a function of electric field. Physical Review B 29 [7] Müller EW, Krishnaswamy S (2003) Energy deficits in pulsed field evaporation and deficit compensated atom‐probe designs. Rev Sci Instrum 45 [8] Ren Y (2012) High-energy synchrotron x-ray diffraction and its application to in situ structural phase-transition studies in complex sample environments. JOM 64 [9] Hammersley A (1997) FIT2D: an introduction and overview. European Synchrotron Radiation Facility Internal Report ESRF97HA02T [10] Larson AC, Von Dreele RB (1994) Gsas. General structure analysis system. LANSCE, MS-H805, Los Alamos, New Mexico [11] Toby BH (2001) EXPGUI, a graphical user interface for GSAS. Journal of Applied Crystallography 34

46

[12] Miller MK, Forbes R (2009) Atom probe tomography. Mater Charac 60

47

CHAPTER 4

INFLUENCE OF COMPOSITION ON MONOMODAL VERSUS MULTIMODAL γ′

PRECIPITATION IN Ni-Al-Cr ALLOYS1

4.1 Introduction

Ni-Al-Cr forms the basis of many technologically important and commercially used Ni-

base superalloys. The microstructure primarily consists of finely dispersed precipitates of the

ordered γ’ phase, with the L12 structure, within a disordered face-centered cubic γ matrix [1].

The present study investigates the influence of Al and Cr content on γ’ precipitation

during continuous cooling of two alloys, Ni-8Al-8Cr at% and Ni-10Al-10Cr at%. Previous

reports indicate that increasing the alloying additions, Al and Cr, by 2 at% from Ni-8Al-8Cr to

Ni-10Al-10Cr not only increases the volume fraction of γ’, but also increases the γ’ solvus

temperature [2,3], in the latter alloy. A partial ternary phase diagram of Ni-8Al-8Cr and Ni-

10Al-10Cr at 600 °C (shown in Fig. 4.1), generated based on solution thermodynamic models

using the PANDAT™ software, predicts the equilibrium volume fraction of γ’ precipitates to be

15.1% and 51.5% with corresponding solvus temperatures of 725.9 °C and 938.3 °C,

respectively for the Ni-8Al-8Cr and Ni-10Al-10Cr compositions.

1 Parts of this chapter have been previously published, either in part or in full, from T. Rojhirunsakool, S. Meher, J. Hwang, S. Nag, J. Tiley, and R. Banerjee, Journal of Materials Science, 2013, 48, 2, pp. 825-831

48

4.2 Experimental Procedures

Arc-melted ingots of nominal composition Ni-8Al-8Cr at% and Ni-10Al-10Cr at% were

used for these experiments. As-cast materials were electro-discharge machined into thin sections

and were subsequently γ solution heat treated at 1150 °C for 30 minutes and then continuous

cooled in furnace at an average rate of 14 °C/min in an argon atmosphere. Samples for

transmission electron microscopy (TEM) were prepared via mechanical grinding, followed by

dimple grinding and, finally ion-beam milling until electron transparency. Ion-beam milling was

done by low energy Ar on a Fischione model 1010 system. TEM samples were conducted on a

FEI Tecnai F20TM field emission gun transmission electron microscope, operated at 200 KV.

Energy filtered transmission electron microscopy (EFTEM) images were obtained using Cr-M

edge (at 42 eV). Samples for APT were prepared using the dual-beam focused ion beam

technique using a FEI Nova Nanolab 200 system. APT experiments were conducted using a

CAMECA local electrode atom probe 3000X HRTM instrument. All APT experiments were

Fig. 4.1 A partial ternary phase diagram of Ni-Al-Cr system at 600 °C generated by PANDATTM software showing two nominal compositions of Ni-8Al-8Cr (at%) and Ni-10Al-10Cr (at%). Two different tie lines are determined from equilibrium composition of those alloys.

49

carried out in the laser evaporation mode at a temperature of 50 K with pulse rate of 160 KHz

and target evaporation of 0.5%. Data analyses were carried out using CAMECA IVASTM 3.6

software.

4.3 Results and Discussion

4.3.1 Microstructures of Ni-8Al-8Cr and Ni-10Al-10Cr Alloys during Continuous Cooling

A comparison of the microstructures of the Ni-8Al-8Cr and Ni-10Al-10Cr alloys,

continuously-cooled at the same nominal rate after solution-treatment, is shown in Fig. 4.2. Thus,

Fig. 4.2(a) shows a dark-field TEM image, recorded using one of the superlattice reflections in a

<001> zone axis pattern, shown in Fig. 4.2(b) from the continuously-cooled (average cooling

rate ~ 14°C/min) Ni-8Al-8Cr sample. The γ’ precipitates, clearly visible in this dark-field image

(Fig. 4.2(a)), exhibit a monomodal size distribution with an average size ~10 nm. Fig. 4.2(c)

shows a low magnification SEM image recorded from the continuous cooled Ni-10Al-10Cr

sample, where the primary γ’ size are clearly visible. An EFTEM image, recorded from the

continuous cooled Ni-10Al-10Cr sample, shown in Fig. 4.2(d), obtained using the Cr-M edge,

clearly shows multiple populations of γ’ precipitates. A relatively low density of nucleation sites

and larger size scale of primary γ’ precipitates in Ni-10Al-10Cr sample suggest that they formed

at a higher temperature as compared to Ni-8Al-8Cr, while experiencing the same cooling rate. In

addition, EFTEM image, such as Fig. 4.2(d), exhibits the evidence of secondary γ’ precipitates in

Ni-10Al-10Cr alloy, resulting in two distinct populations of precipitates, as shown in the

precipitate size distribution (PSD) plotted in Fig. 4.3. The size distribution of primary γ’

precipitates, has been measured based on multiple SEM images, such as the one showing in Fig.

4.2(c). Based on these measurements, primary γ’ precipitates range in size from 40 to 140 nm

50

with an average ~ 95 nm. Smaller size secondary γ’, measured from different EFTEM images

recorded at different TEM sample locations, such as the one showing in Fig. 4.2(d), have sizes

ranging from 3 to 17 nm with an average diameter ~10nm. 500 primary precipitates and 100

secondary precipitates, were measured, and this data was used for plotting the size distribution

graph. Both the primary and secondary precipitate sizes (Fig. 4.3) appear to follow Gaussian

distributions. Normalized precipitate size distribution (PSD) of primary and secondary γ’

precipitatates were carried out in order to justify the broadening of precipitate size distribution.

Normalized PSD was calculated by taking a ratio of particular radius to average radius of the

particle, then plot into a frequency distribution. Primary γ’ size distribution is relatively

broadened in size with a full width of normalized PSD value of 1.4, as shown in Fig. 4.4(a),

compared to the secondary γ’ size distribution, with the full width of normalized PSD value of

1.05 (Fig. 4.4(b)) in case of Ni-10Al-10Cr alloy. In contrast, only a single population of γ’

precipitates is observed in case of continuously cooled Ni-8Al-8Cr alloy.

51

a b

c d

50 nm 1 um

20 nm

Fig. 4.2 a) Dark field TEM image of continuously cooled Ni-8Al-8Cr at% sample, recorded using one of the superlattice reflections in a <001>zone axis pattern shown in b). c) A low magnification SEM micrograph of continuously cooled Ni-10Al-10Cr at% sample d) EFTEM image of continuously cooled Ni-10Al-10Cr at% sample, obtained using the Cr-M edge.

Fig. 4.3 Primary and secondary precipitate size distributions of Ni-10Al-10Cr alloy.

Primary γ’ precipitates Secondary γ’ precipitates Gaussian fit

52

4.3.2 Compositional Profile of γ and γ’ Phases of Ni-8Al-8Cr and Ni-10Al-10Cr Alloys

A three-dimensional atom probe (3DAP) reconstruction of size 40x40x130 nm3,

corresponding to the Ni-8Al-8Cr alloy, is shown in Fig. 4.5(a). The γ’ precipitate interfaces have

been delineated using a 10 at% Al isoconcentration surface (or isosurface in short), together with

Ni atoms shown in red. Fig. 4.5(c) shows a 3DAP reconstruction of the Ni-10Al-10Cr alloy, with

γ’ interfaces delineated using a 12 at% Al isosurface, showing fractions of two large primary γ’

precipitates, separated by a thin γ channel. Within the γ channel a large number density of highly

refined γ’ precipitates are clearly visible. It is worth noting that changing the isosurface value

does not affect phase composition or interface width. Composition profiles for Al and Cr across

the γ / γ’ interface in case of the Ni-8Al-8Cr alloy, have been shown as proximity histograms

[17] in Fig. 4.5(b). The elemental partitioning of Al to the γ’, and Cr to the γ phase is clearly

evident. Fig. 4.5(d) and Fig. 4.5(e) show the Al and Cr proxigrams of primary and secondary γ’

in case of Ni-10Al-10Cr. The sizes scale of the γ’ precipitates, delineated by the Al isosurfaces,

in the 3D reconstructions, shown in Figs. 4.5(a) and 4.5(c), correspond to the size scale of the

precipitates visible in the dark-field and EFTEM images (Figs. 4.2(a) and (d)). For both alloy

Fig 3.4 Normalized particle size distribution of primary and secondary γ’ precipitates

b

53

compositions, γ’ precipitates exhibit a near-equilibrium composition ~ Ni-16.4Al-6Cr [6,18-19],

suggesting γ’ precipitation via a classical nucleation and growth mechanism. Comparing the Al

and Cr proxigrams (Figs. 4.5(b), (d), (e)), it is evident that while local equilibrium has been

established near the γ/γ’ interfaces, there is a far-field departure from equilibrium in the γ matrix,

involving an excess of Al and a depletion content of Cr. This effect appears to be more

pronounced in case of the primary and secondary γ’ precipitates in the Ni-10Al-10Cr alloy. The

interface width has been determined based on the difference of the local γ and γ’ compositions.

The γ/γ’ interface width is greater than 4 nm for Al and ~3 nm for Cr, in case of the Ni-8Al-8Cr

alloy. While the γ/γ’ compositional width is ~4 nm for Al, the value appears to be substantially

larger for Cr (~5 nm) in case of Ni-10Al-10Cr. The rather diffuse nature of the Cr profile in case

of this alloy needs further investigation. The γ’ and local as well as far-field γ compositions

together with the corresponding interface widths are summarized in Table 4.1.

54

Table 4.1 The far-field γ matrix, adjacent γ matrix and γ’ compositions of Al and Cr content and interface width of continuous cooled Ni-8Al-8Cr and Ni-10Al-10Cr samples.

Condition Proximity histogram compositions (at%) Interface

width (nm)

Far-field

γ matrix

Adjacent

γ matrix

γ’ Al Cr

Al Cr Al Cr Al Cr

Ni-8Al-8Cr Continuous cooling 8.2 7 7.4 8 16.4 6 > 4 3.0

Continuous cooling

+ 600 °C, 256 h

5.7 6.6 5.8 6.6 16 5.1 3.2 2.5

Ni-10Al-10Cr Continuous cooling:

Primary γ’

5.5 14 4 15.1 16.3 7 3.9 4.9

Continuous cooling:

Secondary γ’

6.2 13.3 4.5 15.1 17.8

7 3.85 4.8

55

Fig. 4.5 a) 3D-APT reconstruction of continuous cooled Ni-8Al-8Cr at% sample using 10%Al isosurface. b) The proxigram plotted corresponding to isosurface in a) across γ/γ’ interface as a function of distance C) 3-D reconstruction of 12 at% Al isosurface of primary γ’ and secondary γ’ of continuous cooled Ni-10Al-10Cr alloy. d) and e)The proxigram corresponding to isosurface in c) delineated 12 at% Al isosurface of primary γ’ and secondary γ’, respectively

56

4.3.3 Growth and Coarsening Regimes of Ni-8Al-8Cr Alloy

Fig. 4.6 shows the microstructure of the Ni-8Al-8Cr alloy after isothermal annealing at

600°C for 256 hours, post continuous cooling. The growth and coarsening of the monomodal γ’

distribution is clearly visible in the dark-field TEM image shown in Fig. 4.6(a). The

corresponding <011> zone axis diffraction pattern is shown in Fig. 4.6(b). The larger γ’

precipitate size is also confirmed by the 3DAP reconstruction (Fig. 4.6(c)). The Al and Cr

proxigram composition profiles, shown in Fig. 4.6(d), clearly exhibit that γ’ composition remains

the same as in case of the continuously cooled sample. In contrast, the average γ matrix

composition after isothermal annealing increases in Cr content while decreasing in Al content, as

compared to the continuously cooled condition due to the growth of the large number of γ’

precipitates. Furthermore, the differences between the γ compositions near and far from the γ/γ’

interface has also substantially reduced after isothermal annealing. Interestingly, the

compositional width of the interface (for both Al and Cr profiles) decreases after isothermal

annealing.

57

Fig 4.6 a) Dark field image of Ni-8Al-8Cr at% sample after isothermal aging at 600 ˚C for 256 hours, post continuous cooling b) SADP corresponding to the dark-field image. c) 3-D reconstruction of 10 at% Al isoconcentration surface delineating d) proximity histogram for Al and Cr corresponding to 10 at% Al isosurface shown in c).

58

4.4 Summary

Based on these experimental observations, the nucleation and growth of γ’ precipitates

during the continuous cooling of both Ni-10Al-10Cr and Ni-8Al-8Cr alloys can be compared and

contrasted. This comparison can be rationalized based on a simple schematic plot of the

nucleation rate in logarithm scale versus temperature during continuous cooling, as shown in Fig.

4.7. Thus, in case of Ni-10Al-10Cr (referred to as alloy 1 in Fig. 4.7), the primary γ’ results from

the first nucleation burst at higher temperatures near the solvus temperature, at a critical

undercooling ∆T(1) shown in Fig. 4.7. Consequently, a low nucleation rate resulting in a low

number density of precipitates is observed. These primary γ’ precipitates grow rather rapidly due

to the fast diffusion rates at these high temperatures and thereby reduce the supersaturation of the

γ matrix. However, it should be noted that only local near-field equilibrium is established

between the γ and γ’ phases across the interface (schematic diagram illustatrated in Fig. 4.8). The

far-field γ composition still retains a super-saturation of Al and an under-saturation of Cr.

Nucleation of precipitates can continue as long as there is no overlap of the long-range diffusion

fields from adjacent primary γ’ precipitates, also referred to as soft impingement. However, as

soon as soft impingement takes place, nucleation of primary precipitates is shut down as shown

in Fig. 4.7 as well as discussed by Radis et al. [4] and Wen et al. [5]. The growth of the primary γ’

precipitates is also slowed down due to a soft impingement. Further continuous cooling,

eventually leads to increased supersaturation within the retained γ matrix, resulting in sufficient

driving force for a second nucleation burst at lower temperatures [5-8]. This second burst leads

to the formation of secondary γ’ precipitates as shown in Fig. 4.6. While the secondary

nucleation burst occurs at lower temperature, it should be noted that the γ matrix composition has

changed due to the precipitation of primary γ’. Hence, the critical undercooling corresponding to

59

this secondary burst is still similar to that for the primary burst. However, due to the lower

temperatures, the diffusion is severely restricted leading to a longer time period before soft

impingement of can take place. Consequently, the secondary γ’ nucleation burst persists over a

wider temperature range, as shown in Fig. 4.7. This larger temperature range results in a broader

size distribution of fine scale precipitates, as shown in Fig 4.2(b), and an effectively larger

nucleation rate, as reflected in Fig. 4.7. In case of the Ni-8Al-8Cr alloy, referred to as alloy 2 in

Fig. 4.7, the substantially lower γ’ solvus temperature as compared with Ni-10Al-10Cr, leads to a

much lower temperature at which the primary γ’ nucleation burst takes place. Assuming that the

critical undercooling required for γ’ nucleation in alloy 2 is nominally the same (∆T(2)≈∆T(1)), the

lower nucleation temperature results in substantially reduced diffusivities leading to longer time

periods to soft impingement, consequently allowing nucleation to continue for a longer time

period (or wider temperature window) as shown in Fig. 4.6. Therefore, in principle the primary γ’

nucleation burst in case of Ni-8Al-8Cr mimics the features reflected by the secondary γ’

nucleation burst in case of Ni-10Al-10Cr. The higher number density of γ’ precipitates in this

case eventually leads to shorter inter-precipitate separation allowing for the intervening γ matrix

to achieve a composition closer to equilibrium. This prevents the development of any substantial

supersaturation within the γ matrix thus preventing a second nucleation burst. Additionally, the

lower temperatures and diffusivities also kinetically hinder any second nucleation burst. This

also explains the monomodal γ’ size distribution in case of the Ni-8Al-8Cr alloy.

60

Fig. 4.7 Schematic representations of the variation in nucleation rate in logarithm scale versus temperature for both Ni-8Al-8Cr and Ni-10Al-10Cr alloys.

Fig. 4.8 Schematic diagram of primary and secondary γ’ nucleation during continuous cooling

61

4.5 Conclusion

The present study investigates the influence of composition on precipitation of γ’ during

continuous cooling of two Ni-Al-Cr alloys, Ni-8Al-8Cr and Ni-10Al-10Cr (compositions in at%),

at the same nominal cooling rate. The results of this investigation can be summarized as follows:

• While Ni-8Al-8Cr exhibits a monomodal size distribution of γ’ precipitates, a multimodal

size distribution is observed in Ni-10Al-10Cr sample when both alloys are subjected to

the same nominal cooling rate.

• In case of Ni-10Al-10Cr, the primary γ’ occurs as a result of the first nucleation burst at

higher temperatures near the γ’ solvus temperature, i.e. at low undercooling. While these

primary γ’ precipitates grow rather rapidly due to the fast diffusion rates, thereby reduce

the average supersatuation of the γ matrix, only local equilibrium is established between

the γ and γ’ compositions across the interface. The far-field γ composition still retains a

super-saturation of Al and an under-saturation of Cr, leading to sufficient driving force

for a second nucleation burst at lower temperatures.

• In case of Ni-8Al-8Cr, the substantially lower γ’ solvus temperature results in the primary

γ’ nucleation burst taking place at a much lower temperature as compared to the Ni-10Al-

10Cr alloy. Nucleation takes place over a wider temperature window, leading to a larger

number density of highly refined γ’ precipitates. The shorter inter-precipitates distances

and slower kinetics prevent any second nucleation burst in this alloy.

• The higher equilibrium volume fraction of γ’, coupled with the higher γ’ solvus

temperature for the Ni-10Al-10Cr alloy, as compared with the Ni-8Al-8Cr alloy, has a

strong influence on the number of γ’ nucleation bursts observed during continuous

cooling, as well as the temperatures at which these occur.

62

4.6 References


[2] Hong YM, Mishima Y, Suzuki T (1988) Accurate determination of γ′ solvus in Ni-Al-X Ternary Systems. 133

[3] Caron P (2000) High γ' solvus new generation nickel-based superalloys for single crystal turbine blade applications. Superalloys

[4] Radis R, Schaffer M, Albu M et al (2009) Multimodal size distributions of γ′ precipitates during continuous cooling of UDIMET 720 Li. Acta Materialia 57

[5] Wen Y, Simmons J, Shen C et al (2003) Phase-field modeling of bimodal particle size distributions during continuous cooling. Acta materialia 51

[6] Wen Y, Wang B, Simmons J et al (2006) A phase-field model for heat treatment applications in Ni-based alloys. Acta materialia 54

[7] Payton E, Phillips P, Mills M (2010) Semi-automated characterization of the phase in Ni-based superalloys via high-resolution backscatter imaging. Materials Science and Engineering: A 527

[8] Babu S, Miller M, Vitek J et al (2001) Characterization of the microstructure evolution in a nickel base superalloy during continuous cooling conditions. Acta materialia 49

63

CHAPTER 5

NON-CLASSICAL MECHANISM OF GAMMA PRIME PRECIPITATION

IN Ni-Al-Cr ALLOYS

5.1 Introduction

Multicomponent nickel-base superalloys are typically used in manufacturing critical

aircraft components e.g. turbine engines, land-based gears etc., where these parts are regularly

subjected to elevated temperatures [1]. To ensure reliable performance at demanding service

conditions, it is crucial to understand the mechanisms resulting in the microstructure of Ni-base

superalloys, because such structure will ultimately determine their high-temperature mechanical

properties such as creep strength [2-5]. Microstructure of commercially available Ni-base

superalloys, such as Rene 88, Rene N5, CMSX-4, typically consist of ordered γ’ precipitate

phase embedded inside disordered γ matrix [1]. It is well known that γ’ formation occurs via

order-disorder transformation [6-9].

As discussed in the last chapter, classical nucleation and growth mechanism dominates

the γ’ precipitation process in slowed-cooled Ni-Al-Cr alloys. Rapid quenching from a single γ

phase field can alter the precipitation mechanism. However, very little is known regarding the

early stages of γ’ formation when subjected to rapid quenching. To address this issue,

microstructural evolution of a rapidly quenched Ni-Al-Cr alloy was examined in details by

combining several structural and compositional characterization techniques.

Rapid quenching of a Ni-Al-Cr alloy, from the single γ phase field to room temperature,

results in a two-phase mixture of γ and γ’ [7, 10, 11]. The supersaturated solid solution of

γ matrix decomposes via two concurrent but mutually exclusive processes [9, 12-14]: chemical

clustering and ordering. Chemical clustering involves preferential bond formation between like

64

atoms, leading to compositional partitioning within the metallic solid solution, while ordering

involves bonding between unlike atoms leading to an ordered structure.

When the alloy is subjected to rapid quenching, the highly supersaturated and

undercooled single γ phase is often unstable, more precisely metastable, with respect to the

ensuing ordering or phase separation [9], and the supersaturated γ solid solution can decompose

through multiple transformation pathways.

In the past, significant research efforts have been devoted to investigate the precipitation

mechanism of the γ’ phase. In most cases, the FCC to L12 transformation is a first order

transition, involving classical nucleation and growth, wherein precipitates of the ordered γ’ phase

with a near-equilibrium composition will be randomly nucleated throughout the matrix [15-19].

The second type of reported pathway, involves spinodal decomposition of the supersaturated γ

solid solution into solute-rich and solute-depleted regions, followed by ordering within the

solute-rich regions containing elements like Al and Ti [6, 9, 12, 14, 20-23]. Other alternative

pathways include decomposition with continuous increase in the degree of ordering [24] or

decomposition via congruent ordering followed by phase separation [7, 25-27].

Thus, there has been substantial controversy in the literature regarding the sequence of

decomposition, whether or not spinodal decomposition precedes the ordering process in γ+ γ’

system in Ni-base alloy. In many cases, ordering precedes the spinodal process since the ordering

process require short atomic diffusion in small space while the spinodal involves the

compositional fluctuation in large space [9, 12, 14, 22, 28], although few exceptions were also

observed [7, 27, 29, 30]. Few studies on non-classical mechanism were investigated on the Ni-

Al-Cr alloy. Pareige et al. [6] have reported the precipitation mechanism of the γ’ phase occurs

via classical nucleation and growth in a low supersaturated alloy, whereas decomposition of a

65

highly supersaturated alloy takes place via congruent ordering followed by phase separation.

Given above, the precipitation mechanism of the γ' phase has remained unclear.

This chapter focuses on the formation and temporal evolution of ordered γ’ precipitates

with far-from-equilibrium compositions resulting from rapid quenching from supersolvus

temperatures. Rapidly quenched samples were, subsequently, isothermally annealed at 600ºC to

256 hr. Structural characterization of the evolving γ’ phase was performed with synchrotron-base

high-energy x-ray diffraction and transmission electron microscopy (TEM), while compositional

characterization was carried out with three –dimensional atom probe tomography (3DAP).

5.2 Experimental Methods

Arc-melted ingots of nominal composition Ni-8Al-8Cr at% were used for these

experiments. The as-cast alloys was electro-discharge machined into thin sections and such

sections were subsequently, to prevent oxidation during heat treatments, encapsulated in a quartz

tube containing argon. The alloys specimens (inside the quartz-tubes) were solutionized in a

single γ phase field at 1150 °C for 30 minutes followed by rapid quenching into liquid nitrogen.

After quenching, samples were subjected to isothermal annealing at 600 °C for 5 min, 15 min, 30

min, 2 hr, 16 hr, and 256 hr.

Foils for transmission electron microscopy were prepared via conventional routes,

consisting of mechanical grinding, dimple grinding and ion-beam milling until electron

transparency was achieved. Ion-beam milling was done by low energy Argon on a Fischione

model 1010 system. The TEM foils were examined using a FEI Tecnai F20TM field emission

gun transmission electron microscope (TEM) operated at 200 KV. Site-specific TEM foils,

oriented along <001> were prepared with a FEI (FEI Nova Nanolab 200TM) dual-beam FIB

66

(focused ion beam) equipped with an electron-backscattered detector (EBSD). Atomic

resolution- atomic number contrast (Z- contrast) imaging was done on the site specific <001>

grain sample and was carried out in high-angle annular dark field scanning TEM (HAADF-

STEM) mode with a FEI Titan 300 kV microscope, equipped with a CEOS probe aberration

corrector.

Atom probe tips were milled from bulk material using the FIB technique in a FEI Nova

Nanolab 200 system. Low-voltage milling was used in the final stage of milling to reduce Ga

implantation in the tips. The final tip diameter of the atom probe specimens was 50-70 nm.

3DAP experiments were conducted using an IMAGO local electrode atom probe 3000X HR

instrument. All 3DAP experiments were carried out in the voltage evaporation mode at a

temperature of 60 K with target evaporation of 0.5%. Data analyses were carried out using

CAMECA IVAS 3.6 software.

High-energy x-ray diffraction (XRD) experiments were performed at synchrotron

beamline 11-ID-C, operating at 115 keV, at the Advanced Photon Source (APS) at Argonne

National Laboratory. For room temperature experiments, the samples were placed on a stage,

which was aligned with the x-ray beam. For in-situ experiments, a sample cut to 1 mm thickness

was placed in Linkam TS1500 furnace. The samples were heated with a constant rate of 120 °C

/min from rom temperature to 600 °C and held up to 5 hr. Diffraction patterns, generated by the

interaction of the incoming x-ray beam (0.2 x 0.2 um2 size) were collected using a 2D Si flat-

panel PerkinElmer detector. During data collection the furnace was rocked from -5 to 5 degree.

Diffraction patterns were collected every 18 seconds interval. The sample-to-detector distance

was calibrated using a cerium oxide reference material (CeO powder) for both types of

experiment and was ~ 1793 mm. For data analyses, integration over all azimuth angles at

67

constant scattering angle was performed using the FIT2D software package [31] to obtain the

corresponding one-dimensional diffraction patterns (intensity versus scattering angle). A

Rietveld refinement of the resulting one-dimensional X-ray diffraction patterns was performed

using the General Structure and Analysis System (GSAS) [32] and its graphical user interface

(EXPGUI) [33] to determine the lattice parameters of the γ and γ’ phases as a function of time.


5.3.1 Investigation of Early Stages Decomposition of γ’ Precipitates: Disorder-Order

Transformation of Ordered γ’ Precipitates.

Fig. 5.1(a) shows selected area diffraction (SAD) pattern of rapidly quenched of (as-

quenched) Ni-8Al-8Cr sample recorded along the <001> zone axis. In this diffraction pattern

only shows the fundamental reflections of the primary γ matrix. The SAD pattern did not

indicated the presence superlattice reflections, corresponding to L12-type ordered γ’ precipitation,

at <100> and <110> locations in the [001] SAD in Fig. 5.1(a). In addition, satellite reflections

around the primary matrix reflections, which are typically the signature of phase separation via

spinodal decomposition, were not discernable.

68

Fig. 5.1(b) shows the frequency distribution from 3DAP reconstruction dataset obtained

from sampling the as-quenched sample. The frequency distribution was generated as follows: the

whole reconstruction was divided to numbers of bins. Each bin contains 100 atoms. The

composition of these bins for one specific constituent (Al in this case) was plotted with respect to

the number of bins corresponding to a particular composition [34]. In a random solid solution,

such a frequency distribution plot would exactly match a binomial distribution [35]. The above-

mentioned technique is more commonly known as the Langer, Bar-on and Miller (LBM) method

[36, 37]. In Fig. 5.1(b), the Gaussian fitting (labeled as a red line) was superimposed on the

Fig. 5.1 a) SAD pattern of as-quenched Ni-8Al-8Cr sample showing no evidence of superlattice reflections. b) LBM plot with Al concentration of as-quenched Ni-8Al-8Cr sample obtained from 3DAP showing observed data perfectly match with the random binomial distribution. c) Intensity vs 2theta plot obtained from high-energy XRD of as-quenched Ni-8Al-8Cr sample showing a presence of (100) peak of γ’ phase.

69

observed data (squared datum on black line). There appears to be no discernable difference

between the Gaussian fit and observed data. Implication of this result will be discussed in

conjunction with the high-energy XRD results presented in the following paragraph.

Since limited analyzed volume of the ordered γ’ phase is sampled using TEM and 3DAP

techniques. High-energy XRD at a synchrotron source was utilized to examine a larger analyzed

volume of the as-quenched sample. The high-energy XRD result is shown as intensity versus 2

theta plots in Fig. 5.1(c). The plot revealed a discernably diffuse peak corresponding to (100)

superlattice peak (d=3.6 A°) of the γ’ phase at 2θ = 1.8°, in addition to main peaks of the γ

matrix such as (111), (200), and (220). The small (100) superlattice peak of the γ’ phase is

further highlighted as an inset in Fig. 5.1(c). (210) and (211) peaks of γ’ phase were not

observed presumably due to a large grain size and non-random grain orientation of the as-

quenched sample. However, the SAD result obtained from TEM did not reveal any superlattice

spots, possibly due to the weak ordering at the early stages in the as-quenched sample. The

combined high-energy XRD, TEM and 3DAP results indicate that the ordering process took

place without a compositional change during rapid quenching from a single phase field of γ to

room temperature.

5.3.2 Early Stages of Decomposition of γ’ Precipitation at 600 °C

Fig. 5.2 shows a SAD pattern of <100>zone axis of Ni-8Al-8Cr sample that was rapidly

quenched and subsequently annealed at 600 ºC for 5 min. In this diffraction pattern, the presence

of <100> and <110> superlattice spots, along with the fundamental γ reflections, indicate an L12-

type ordered γ’ precipitation forming during the very early stages of annealing at 600 ºC.

However, the SAD pattern does not show any evidence of satellite reflections around the primary

70

γ matrix reflections. Note that such satellite reflections are typically associated with phase

separation via spinodal decomposition [14, 21, 23, 30, 38, 39].

To understand the early stages of γ’ formation, high angle annular dark field scanning

TEM (HAADF-STEM) technique has been employed to investigate an atomic scale of γ’

precipitates. High-resolution atomic mass (Z)- contrast images of HAADF-STEM mode were

carried out using an aberration-corrected FEI Titan 300 KV TEM at The Ohio State University.

Figs. 5.3(a) and (c) show HAADF-STEM image from the Ni-8Al-8Cr annealed for 5 min at

600 °C recorded along <001>zone axis, while Figs. 5.3(b) and 5.3(d) are their corresponding fast

Fourier transforms (FFT), respectively. FFT is a mathematic algorithm that represents in the

high-resolution phase contrast image in the reciprocal space. In other words, the FFT

representation is similar to a diffraction pattern [40]. FFT in Fig. 5.3(b) shows fundamental

reflections that obtained from the disordered γ matrix, similar to the SAD of the as-quenched Ni-

8Al-8Cr sample (Fig. 5.1(a)).

Fig. 5.2 SAD pattern of 5 min annealed at 600 °C after quenched of Ni-8Al-8Cr sample showing superlattice reflections at <100> and <110>.

71

a b

c d

(100)

(010)

Fig. 5.3 a) HAADF-STEM and b) its corresponding FFT of disordered region in 5 min annealed Ni-8Al-8Cr sample. c) HAADF-STEM and d) its corresponding FFT of ordered region in 5 min annealed Ni-8Al-8Cr sample.

72

However, the other region of the same sample (Fig. 5.3(d)) shows superlattice reflections

corresponding to the γ’ phase along with the fundamental γ reflections. Note that the FFT

presented in Fig. 5.3(d) is comparable to the [001] SAD shown in Fig. 5.2. HAADF-STEM of

the disordered region (Fig. 5.3(a)) exhibits the same intensity of atomic column throughout the

image. However, the HAAD-STEM of the ordered region (Fig. 5.3(c)) does not show significant

difference of periodic atomic column intensity corresponding alternating atomic planes

characteristic of L12 structure. This is possibly due to a presence of image background noise.

In order to minimize the background signals of the HADDF-STEM image, a Fourier

mask-filtering technique was applied. In the Fourier reciprocal space of image or FFT, in order

to perform mask filtering, one needs to select certain spatial frequencies in a reciprocal space. In

this case, both superlattice and fundamental reflections were chosen. Then, a filtered image

obtained from those reflections could be constructed by inverse FFT (IFFT) process.

Filtered image

Fig. 5.4 a) a filtered image of figure 5.3(b) processed by selected both superlattice and fundamental reflections. Square and circle boxes correspond to the disordered and ordered regions. b) a filtered image of figure 5.3(b) processed by selected only superlattice reflections from 5 min annealed Ni-8Al-8Cr sample

a b

73

A filtered image obtained from both fundamental and superlattice reflections is shown in

Fig. 5.4(a). The intensity contrast is directly correlated with atomic mass contrast (Z-contrast),

where brighter regions contains higher concentration of heavier alloying elements such as Cr,

whereas darker regions contains higher concentration of lighter alloying elements such as Al. In

Fig. 5.4 (a) the disordered regions are indicated by squares, while the ordered regions are marked

as circles. Note that the ordered regions contain alternating atomic columns of high (bright) and

low (dark) intensities corresponding to Cr and Al atomic columns. This pattern of the alternating

planes of bright (Cr sublattice) and dark (Al sublattice) atomic columns is consistent with an L12

ordered structure of γ’ precipitates viewed along the <100>zone axis. Subsequently, a filtered

image was constructed to obtain a clearer morphology of the ordered regions by selecting only

superlattice reflections and blocking the central transmitted beam in the FFT. Interesting, these

regions of brighter and darker contrasts of ordered regions in Fig. 5.4(b) appear to be

interconnected. This feature is known as a characteristic of a spinodally-decomposed

microstructure [6, 13, 21].

The intensity from the HAADF-STEM images in the ordered and disordered regions

were further analyzed to qualitatively evaluate the variation in intensity profiles between the two

phases. Figs. 5.5(a) and 5.5(c) show the selected regions of disordered and ordered phases from

the Fig. 5.4(a), respectively. The corresponding intensity profile of disordered region (Fig.

5.5(b)) shows the same contrast for all columns indicating a random solid solution, while Fig.

5.5(a) reveal that the ordered domain shows a periodic contrast due to the presence of Cr and Al

atomic columns. At the disordered/ordered transition a periodic intensity shows a variation of the

intensity when going towards the ordered domains. Inside the ordered domain, a periodic

intensity variation is clearly exhibited. The observed ordered domain is ~ 2 nm based on the

74

intensity profile.

0 1 2 3

Inte

nsity

(Arb

itary

unit)

Distance (nm)0 1 2 3

Inte

nsity

(A

rbita

yun

it)

Distance (nm)

c

d

a

b

Fig 5.5 a) A high magnification HAADF-STEM and b) the corresponding intensity profile of disordered region c) A high magnification HAADF-STEM and b) the corresponding intensity profile ordered region. Both a) and c) were parts of Fig. 5.4(a).

4

6

8

10

12

-4 -3 -2 -1 0 1 2 3

Al-rich Al-lean

5 mins

Com

p (a

t%) a b

Fig. 5.6 a) 3D reconstruction of 5 min annealed sample obtained from 3DAP and b) the corresponding proxigram delineated by using 10 at% across the Al-lean and Al-enriched regions.

75

The 3D reconstruction of the 3DAP results obtained from 5 min annealed sample is

shown in Fig. 5.6(a). Utilizing 10 at% Al isoconcentration surfaces [41, 42], 3DAP results

indicated interconnected Al-enriched pockets. Furthermore, the regions with more than 10% Al,

enclosed by concave interfaces in the 3DAP reconstruction, shown in Fig. 5.6(a), are very similar

in size-scale to the ordered domains observed in the aberration-corrected HAADF-STEM image

in Fig. 5.5(c). Thus, it can be deduced that these Al-enriched regions correspond to the γ’

precipitates while the regions having less than 10 %Al correspond to the γ matrix. Similar to

HAADF-STEM in Fig. 5.4(b), the interconnected nature of these compositionally phase

separated regions is a possible indication of a spinodally-decomposed matrix. In addition,

corresponding compositional profile across γ / γ’ interfaces

in Fig. 5.6(b)) indicated that there are a slightly increase of Al concentration and decrease of Cr

concentration within the regions enclosed by the isoconcentration surfaces. The other side of the

γ / γ’ interfaces shows the opposite trend. Al-enriched region where Al is slightly higher than

the nominal composition (Al= 8 at%) is postulated as γ’ precipitates. Thus, the proxigram

presented in Fig. 5.6(b), indicated that (i) composition of the Al-enriched region is far from

equilibrium and (ii) exhibits a large composition gradient across the γ/γ’ interface compared to a

long term annealing at 600 °C for 256 hr (Fig. 5.8(i)). The composition of the γ matrix and γ’

precipitates in 5 min annealed Ni-8Al-8Cr sample are listed in Table 5.1

76

Table 5.1 Composition of γ and γ’ phases and Al composition gradient as a function of annealing time

γ matrix γ ’ phase Al Compositional

gradient Al Cr Al Cr

600°C/ 5 min 6.5 7.6 10 9 1.8

600°C/ 15 min 8.0 8.5 15 7.4 1.5

600°C/ 30 min 7.4 8 16 8 1.6

600°C/ 2 hr 7.7 7.8 16 6.7 1.1

600°C/ 16 hr 6.1 8.5 18 6.1 1.6

600°C/ 256 hr 6.5 8.1 18 6 1.4

77

The interconnected nature of these compositionally phase separated regions is a possible

indication of a spinodally-decomposed matrix exhibiting a continuous variation and far-from

equilibrium in composition, rather than discrete pockets that reach an equilibrium composition

via a classical nucleation and growth process. This is in accordance with the prediction of Cahn

and Hilliard [5] who mentioned that at lower supersaturations (lower undercooling) the nucleus

exhibits more classical-like behavior with a near-equilibrium composition and the region around

this classical nucleus also approaches an equilibrium composition. However as the

supersaturation increases, corresponding to larger undercoolings (or lower precipitation

temperatures) experienced during rapid cooling, the nucleus starts loosing its resemblance to a

classical nucleus. Thus at higher undercooling, both Helmholtz free energy as well as gradient

energy factors contribute to the diffuseness of the interface. Also no part of this non-classical

nucleus is approximately homogeneous and the composition at its center is substantially lower

than that of a classical nucleus – consistent with our 3DAP results from 5 min/ 600ºC (Fig. 5.6).

Another similar non-classical decomposition pathway that has been discussed in the

literature and also applicable to γ’ precipitation within the disordered γ matrix, is phase

separation (or composition clustering) via spinodal decomposition followed by ordering within

the appropriate phase separated pockets [1,9]. Such decomposition is expected to take place in

systems that have been undercooled to a large extent below the equilibrium transformation

temperature. When a disordered solid solution is rapidly cooled (or quenched) from a single-

phase field to a temperature corresponding to a two-phase field, the resulting highly undercooled

and supersaturated disordered solid solution is often unstable (or metastable) with respect to both

clustering and ordering processes [9]. Experimental evidence of such a decomposition pathway

in nickel base alloys has been previously reported in the literature in case of binary Ni-Al [43]

78

and Ni-Ti alloys [38], as well as in the recent study on very fast quenched Rene 88 DT [22].

5.3.3 Structural Evolution of Ordered γ’ Precipitates during Isothermal Annealing at 600 ºC Post

Rapid Quenching

Fig. 5.7(a) shows dark field TEM image recorded using one of the {100} superlattice

reflections in <001> zone axis for Ni-8Al-8Cr samples that were rapidly quenched and

subsequently annealed at 600 ºC for 30 min. Similarly, Figs. 5.7(b)-(d) show dark field TEM

images obtained using {111} superlattice reflection in <011> zone axis for samples that were

annealed at 600ºC for 2 hr, 16 hr, and 256 hr, respectively. The corresponding SAD patterns are

shown as insets in Fig. 5.7. The γ’ precipitates first appear as discrete particles after annealing

for 30 min, respectively, as shown in Fig. 5.7(b) and substantially grow and coarsen after

annealing for 2, 16 and 256 hr (Figs. 5.7(c)-(e)). It is worth noting that the dark field TEM

images in Fig. 5.7 have been obtained using only one superlattice reflection, thus capturing the

volume fraction corresponding to just one variant of γ’ precipitates. Thus, the actual number

density of γ’ precipitates captured in 3DAP reconstruction are much higher than what they

appear in Fig. 5.7. Also, all annealed samples at 600ºC show γ’ precipitates with near-spherical

morphologies.

79

5.3.4 Compositional Evolution of Ordered γ’ Precipitates during Isothermal Annealing at 600 ºC

Post Rapid Quenching

The compositional analyses of the rapidly quenched and subsequently annealed at 600 ºC

series of samples across γ/γ’ interfaces have been carried out using 3DAP. The γ/γ’ interfaces

have been delineated by selecting an appropriate Al iso-concentration value [44]. Al was chosen

as the preferred element because it strongly partitions between the γ and γ’ phases in this alloy.

The 3D reconstruction is generated using Al=10 at% isosurface, and Figs. 5.8(a)-(e) show 3DAP

Fig. 5.7 Dark field micrographs of annealed at 600 °C Ni-8Al-8Cr samples for a)30 min b) 2hr c) 16hr and d) 256 hr.

30 min

20 nm

2 hr

256 hr

50 nm

20 nm

a b

d c

20 nm

16 hr

80

reconstructions using a 10 at% Al isosurface (blue) of the samples which were isothermally

annealed at 600°C for 15min, 30 min, 2 hr, 16 hr, and 256 hr, respectively. The isosurfaces

delineate multiple fine-scale γ’ precipitates for all annealing times. The 3DAP reconstructions

corresponding to the 15 and 30 min annealed samples clearly show an increase in the size of γ’

precipitates without any indications of interconnectivity as observed in case of the 5 min

annealed sample (Fig. 5.6(a)). For all the annealing times, the corresponding proximity

histograms or proxigrams are plotted in Figs. 5.8(f)-(j) for 15min, 30 min, 2 hr, 16 hr, and 256 hr,

respectively. As observed from Figs. 5.8(f) and (g), during the early stages of annealing (15 min

and 30min), the compositional gradient (between Al-rich and Al-lean regions) across the γ/γ’

interface is very diffuse- as observed from 5 min annealed sample (Fig. 5.6(b)). However for

longer annealing times, this compositional gradient becomes sharper. Since Al exhibits the

largest partitioning across the γ/γ’ interfaces, the corresponding width of the Al compositional

gradient for all annealing times are listed in Table 5.1. These gradients were determined using a

method that uses 90% of the steady state of the γ composition and 10% of steady state of γ’

compositions [42, 45, 46]. The width of the Al gradient changes from 1.8 nm (after 5 min of

annealing) to 1.4 nm after 256 hr at 600ºC. Since the spreading across the interface due to

trajectory aberrations or preferential retention [47, 48] will be the same for all samples, while the

actual compositional profile at the interface is likely to be sharper than that measured using the

proxigram analysis, it is possible to relatively compare the interface widths between the samples

using this analysis technique.

In all proxigrams, Al partitions to the γ’ precipitates, while Cr slightly partitions to the γ

phase. The proxigrams in Fig. 5.8 shows a progressive change in the γ’ precipitate composition

during isothermal annealing post rapid quenching. Thus when compared with 5 min annealed

81

sample, 256 hr annealing at 600 ºC significant increases the Al concentration in γ’ precipitates

from 10% to 18 at%. Conversely, the concentration of Cr slightly decreases from 9 to 6 at%.

These results demonstrate that the γ’ precipitates start with a far-from equilibrium composition

and on subsequent isothermal annealing gets enriched in Al and depleted in Cr to reach a near-

equilibrium composition. The γ matrix follows an opposite trend where the concentration of Al

reaches an expected equilibrium value (6.5 at%) and that of Cr slightly increases (7.6 at% to 8.1

at%, respectively) on annealing for 256 hr annealing. The Al and Cr concentrations of the γ

matrix and γ’ precipitates for all annealing times have been listed in Table 5.1.

Furthermore, in the long term annealing case (Fig. 5.8(j)), the compositions of γ and γ’

phases are nearest to equilibrium, because the end point composition of γ’ and γ phases obtained

from the 256 hr annealed sample is consistent with the thermodynamics models (using

PANDAT™ software) for Ni-18Al-6Cr and Ni-6Al-10Cr, respectively.

82

γ

γ’

6

8

10

12

14

16

-3 -2 -1 0 1

68

1012141618

-4 -3 -2 -1 0 1

Com

p (a

t%)

γ γ’

γ’ γ

68

101214161820

-4 -3 -2 -1 0 1

15 min

30 min

2 hr

γ γ’

Com

p (a

t%)

Com

p (a

t%)

a

b

c

f

g

h

468

101214161820

-5 -3 -1 1

γ γ’

2468

101214161820

-10 -8 -6 -4 -2 0 2 4 6

γ’ γ

16 hr

256 hr

Com

p (a

t%)

Com

p (a

t%)

d

e

i

j

Fig. 5.8 Compositional profile of Al and Cr across the γ/ γ’ interfaces as a function of annealing time at 600 °C.

83

5.3.5 Statistical Analysis of Frequency Distribution Plots during Isothermal Annealing at 600 ºC

Post Rapid Quenching

The tendency for phase separation within the annealed samples was further investigated

in detailed by performing statistical analysis on the 3DAP data. Similar to the frequency

distribution of the as-quenched sample (Fig. 5.1 (b)), for each 3DAP reconstruction dataset

several 100 atoms bins were chosen and the composition of these bins for one specific

constituent (Al was chosen in this case) was plotted with respect to the number of bins for that

particular composition. In a random solid solution, such a frequency distribution plot would

exactly match with the binomial distribution for a particular dataset. This technique is more

commonly known as the Langer, Bar-on and Miller (LBM) method [36, 37]. The presence of a

phase separation or compositional clustering within the dataset leads to a deviation from the

perfect binomial distribution, that is usually manifested as a peak broadening eventually leading

to one or more splits developing in the peak.

Using the LBM method, the frequency distribution plot for a dataset corresponding to a

phase separated system, exhibiting a split peak, can be fitted into two Gaussian distribution

functions of equal width, centered at concentrations, μ1 and μ2. The composition amplitude, ΔC,

is given by μ2 - μ1. Note, that this method gives only an approximate estimation of the phase

compositions. In this study, c0 is estimated as the average composition (bulk composition) of Al

in the alloy, while μ1 and μ2 are the compositions of the γ’ and γ phases, respectively. More

detailed of binomial distribution and LBM method are listed in Appendix A.

Fig. 5.9 shows frequency distribution plots corresponding to the 5 min annealed, 15 min

annealed, 30 min annealed, 2 hr annealed, 16 hr annealed, and 256 hr annealed samples. As

mentioned above (Fig. 5.1(b)), the as-quenched sample does not exhibit any indication of phase

84

separation as the plots perfectly fit with the perfect binomial distribution. After 5 min annealing

at 600 °C, a frequency distribution plot is no longer fit the perfect binomial plot. In fact, there is

a marginal deviation from the perfect one; thus, the Gaussian fitting can be de-convoluted into

two peaks. Thus, the fitted peaks of the two Gaussians correspond to the Al concentration

present in the γ and γ’ phases. Upon annealing, the frequency distribution initially decreases in

amplitude with a broadened peak away from the random binomial plot. After 16 hr of annealing

the frequency distribution plot clearly exhibits the onset of peak tail. The long tail in this

distribution represent smaller number of bins containing high concentration of Al as a result of

Al partitioning due to γ’ formation. After long term annealing at 600 °C for 256 hr, the frequency

distribution plot clearly shows a peak tail. To calculate a volume fraction of the γ’ phase, an area

under each of the curve nominally was computed. In addition, the equilibrium volume fraction of

the γ’ phase was achieved in the longest annealing time (256 hr) as 15%. Based on solution

thermodynamic models implemented in PandatTM software, the equilibrium volume fraction of

the γ’ phase at 600 ºC for the Ni-8Al-8Cr alloy was calculated as 15%.

The frequency distribution plots, furthermore, clearly reveal that with increased annealing

time the Al content in the γ’ precipitates progressively increases, thus confirming that the

precipitate composition tend towards equilibrium composition. Thus, the μ2 values in Table 5.2,

an indication of the Al concentration in the γ’ precipitates, changes from 10.2 at% in the 5 min

annealed to 16 at% in the 256 hr annealed condition. The Al composition of γ’ phase in LBM

(Al=16 at%) is slightly less compared to ones obtained from proxigram (Fig. 5.8(j)) and

PANDAT™ software which are Al=18 at%. Although both proxigram and LBM plot were

generated from 3DAP data, lower Al concentration obtained form LBM plots possibly results

from averaging of the Al concentration within the atom bin. Furthermore, comparing the Al

85

composition of the γ matrix shown in Table 5.2, it changes minimally from approximately

Al=7.4 at% after 5 min to Al=7.8 at%, after 15 min, and then reduces back to Al=7.3 at% after

256 hr annealing. In contrast to the γ’ phase, the composition of Al and Cr in the γ phase change

insignificantly. These results substantiate the observation of a non-equilibrium, rapidly quenched

γ’ precipitation in Ni-8Al-8Cr alloy.

Table 5.2 Al composition obtained from LBM fitting of as-quenched and annealed Ni-8Al-8Cr samples

Samples Mean %Al

(c0)

Al Composition from Gaussian fitting

γ Matrix (μ1) γ’ precipitates

(μ2)

As-quench 9.2 - -

600°C/ 5 min 7.9 7.4 10.2

600°C/ 15 min 8.3 7.8 10.5

600°C/ 30 min 8.2 7.8 10.9

600°C/ 2 hr 7.6 6.6 8.9

600°C/ 16 hr 8.1 7.8 11.7

600°C/ 256 hr 8.5 7.3 16

86

a b

c d

f e

16 hrs

Fig. 5.9 LBM plots of annealed Ni-8Al-8Cr samples at 600 °C for a) 5 min, b) 15 min, c) 30 min, d) 2hr, e) 2hr, f) 16 hr, and e) 256 hr.

87

5.3.6 Synchrotron-Base X-Ray Diffraction Studies on Evolution of γ’ Volume Fraction and γ

and γ’ Lattice Parameters

As-quenched Ni-8Al-8Cr sample was also examined via synchrotron-base high-energy x-

ray diffraction (XRD) at room temperature. Further, the as-quenched Ni-8Al-8Cr sample has

been investigated via in-situ XRD at 600 °C up to 5 hr using a high temperature furnace

equipped on the synchrotron source beam line 11-ID-C at Advanced Photon Source (APS) a the

Argonne National Laboratory. The diffraction was captured every 18 seconds interval.

In the as-quenched Ni-8Al-8Cr sample, synchrotron-base high-energy x-ray diffraction

result revealed the presence of a very diffuse (001) superlattice peak, attributable to the γ’ phase

(Fig. 5.10(a)). In-situ high-energy x-ray diffraction studies were carried out at 600 °C. Sample

was placed in Ar atmosphere. A progressive change in the intensity of the (100) superlattice

peaks from the γ’ phase as a function of annealing time is shown in Fig. 5.10(a). The intensity of

(100) superlattice peak of the γ’ phase gradually increases in peak height as well as an integrated

intensity (area under the curve). The increase in intensity of the (100) superlattice peak

corresponds to an increase in volume fraction of the γ’ phase within the disorder γ matrix [49].

To determine a change in volume fraction of the γ’ phase, integrated intensity of each annealing

time needs to be calculated. Since a relatively large γ grain size compared with a small beam size

induced an artificial texture effect, this texture effect can be reduced by analyzing relative

intensities of the same family of the diffraction peaks such as I100,γ’/I200,γ+γ’ and

I110, ,γ’/I220, , γ+γ’ [50]. These relative intensities are given in Table 5.3. Using the integrated

intensities data given in Table 5.3, the intensity ratio of γ’/ γ + γ’ was plotted in Fig. 5.10(b). As

the annealing time increases, the intensity ratio of γ’/ γ + γ’ corresponding volume fraction of γ’

88

phase increases dramatically as seen in Fig. 5.10(a).

a

b

Fig. 5.10 a) Intensity of (100) peak of the γ’ phase of the as-quenched and 600 °C annealed Ni-8Al-8Cr samples. b) FWHM of (100) peak of the γ’ phase and volume fraction determined by a ratio of (100)γ’/(111) γ + γ’ as a function of annealing time.

89

Further, it is worth noting that a full width at half maximum (FWHM) of (100)

superlattice peak of the γ’ phase is very broaden (0.207°) in the as-quenched sample compared

to a FWHM of the fundamental peak (111)γ+ γ’ and (200)γ+ γ’ which are 0.02 and 0.025 degree,

respectively. The FWHM of (100) peak of the γ’ phase is ~10 times broader of (111)γ+ γ’ and

(200)γ+ γ’. Fig. 5.10(b) also shows the progressive change in the FWHM of (100) superlattice

peak of the γ’ phase as a function of annealing time. With increasing the annealing time, the

FWHM of (100) peak of the γ’ phase gets sharper from 0.207°, 0.214°, 0.164°, 0.158°, 0.150°,

0.126°, to 0.117° in the as-quenched, 5 min annealed, 15 min annealed, 30 min annealed, 1 hr

annealed, 2 hr annealed and 5 hr annealed samples, respectively. The FWHM value of (100)

peak of the γ’ phase as a function of annealing time are summarized in Table 5.3.

Table 5.3 FWHM of (100) peak of γ’ phase, intensity ratio of (100)γ’/(111)γ+γ’, intensity ratio of (100)γ’/(200)γ+γ’, and γ’particle size calculation based on FWHM of (100) peak of γ’ phase

Time FWHM (100)γ’

(degree) FWHM (100)γ’ (radian)

I(100)γ’ /I(111) γ+γ’

x100 pct I(100)γ’/I(200) γ+γ’ x 100 pct

Particle size base on FWHM

(100)γ’ (A°) As-quenched 0.207 0.00361 3.5 2.6 29.1 600 C/0 min 0.214 0.00374 6.7 5.2 28.1 600 C/5 min 0.164 0.00286 7.3 5.2 36.7 600 C/15 min 0.158 0.00276 6.9 5.3 38.1 600 C/ 30 min 0.150 0.00262 8.3 6.5 40.1

600 C/1 hr 0.150 0.00262 9.8 7.7 40.1 600 C/2 hr 0.126 0.00220 12.3 7.7 47.7 600 C/5 hr 0.117 0.00204 13.6 9.6 51.4

Peak broadening of (100) superlattice peak of the γ’ phase could be caused from many

factors such as chemical heterogeneities, stress gradients, microstresses, and crystalline

90

smallness [51]. Chemical heterogeneities, stress gradients, and microstresses would have

influenced on FWHM of both superlattice peaks as wells as the fundamental peaks. As

mentioned above, the FWHM of the fundamental peaks are approximately 0.02° whereas the

FWHM of the superlattice peaks are about 0.2°. However, the size difference in γ grain and γ’

precipitates located inside the γ grain possibly results in large difference of FWHM of

superlattice and fundamental peaks. Scherrer equation [52, 53] has been employed to determine

an average size of nano-crystallites. According to Scherrer formula, the average crystallite size

(crystallite diameter), L, is:

𝐿𝐿 =𝐾𝐾𝐾𝐾

𝛽𝛽𝑐𝑐𝛽𝛽𝛽𝛽𝛽𝛽

where λ is the x-ray wavelength in A°, β is the FWHM of the diffraction peak profile in radian, θ

is a Bragg angle, and K is a constant of proportionality depending on a shape and the size

distribution of the crystal.

The XRD studies have been conducted with λ= 0.11165 A°. The (100) superlattice peak

of the γ’ phase is located at 2θ= 1.786°. K is 0.94 for spherical crystals with cubic symmetry [54].

In the as-quenched condition, a calculated average crystallite size of γ’ precipitates is 29.06 A° (3

nm). The average size of γ’ precipitates increases with annealing time at 600 °C as 36, 38, 40, 40,

47, 51 A° after 5 min annealed, 15 min annealed, 30 min annealed, 1 hr annealed, 2 hr annealed

and 5 hr annealed samples, respectively. Since the x-ray diffraction detects only regions where a

periodic arrangement (referred to crystallites) within the ordered γ’ phase, the crystallite size

may not include regions such as interface where a periodic arrangement of the ordered structure

are partially lost. Thus, the calculated crystallite size based on the FWHM of the (100)

superlattice peak of the γ’ phase might be smaller than ones observed in DFTEM (Fig. 5.7).

91

These results are summarized in Table 5.3.

For nickel-base alloy with low γ’ volume fraction and low lattice misfits between γ and γ’

phases, fundamental and superlattice peaks are overlap and make it difficult to de-convolute

individual phase contributions and measure lattice parameters. Although the superlattice peaks of

the ordered phase provided locations for determining lattice parameters, the intensity is usually

low for (100) and (110) peaks. With an advantage of high-energy synchrotron source in this

study, lattice parameters of both γ and γ’ phases were determined. Rietveld refinement was

employed to fit the experimental data and computational model by using GSAS and EXPGUI.

Table 5.4 summarizes the lattice parameters of both γ and γ’ phases and their lattice misfits as a

function of time. It shows that the lattice parameter of the γ phase in the as-quenched sample is

3.5419 A°. When the same sample was subjected to isothermal annealing at 600 °C the lattice

parameter of the γ phase increased to 3.5686 A° as a result of thermal expansion. Similarly, the

lattice parameter of the γ’ phase increased from 3.5406 A° in the as-quenched condition to

3.5646 A° after 600 °C annealing. During 600 °C annealing, there are no significant change of

lattice parameter of both γ and γ’ phases from 0 min to 5hr annealing. Lattice misfit between

both γ and γ’ lattices was calculated from 𝛿𝛿 = 2(𝑎𝑎𝛾𝛾′ − 𝑎𝑎𝛾𝛾)/(𝑎𝑎𝛾𝛾′ + 𝑎𝑎𝛾𝛾). From Table 5.4, lattice

parameters of the γ’ phase are less than those of the γ phase. Thus, it leads to a negative lattice

misfit in both as-quenched sample and annealed samples. These results agree with previous

studies [50, 55, 56].

92

Table 5.4 Lattice parameter of γ and γ’ phases and lattice misfit of as-quenched and 600 °C annealed samples

Peaks Lattice parameter of the γ phase

Lattice parameter of the γ' phase

Lattice misfit (%)

As-quenched 3.5419 3.5406 -0.02 600 °C/0 min 3.5700 3.5639 -0.11 600 °C/5 min 3.5702 3.5632 -0.13 600 °C/15 min 3.5687 3.5642 -0.08 600 °C/30 min 3.5700 3.5669 -0.06

600 °C/1 hr 3.5698 3.5660 -0.07 600 °C/2 hr 3.5689 3.5686 -0.01 600 °C/5 hr 3.5686 3.5646 -0.07

5.4 Summary

This chapter examined the formation and temporal evolution of ordered γ’ precipitates

with far-from-equilibrium compositions resulting from rapid quenching from supersolvus

temperatures. The study couples high-energy x-ray diffraction, transmission electron microscopy

(TEM) as well as atom probe tomography (3DAP) techniques to study the structural and

compositional changes associated with isothermal annealing of rapidly quenched Ni-8Al-8Cr

alloy.

• In the as-quenched sample, synchrotron-base high-energy x-ray diffraction result

revealed the diffuse intensity of (100) superlattice peak which corresponds to the

γ’ phase. SAD. LBM plot obtained from 3DAP data showed no evidence of

compositional variation arising from the γ’ phase. Thus, the decomposition of the

93

γ’ phase occur via congruent ordering without a composition change.

• After isothermal annealing at 600 °C for 5min, the order γ’ precipitates were

developed. SAD pattern showed the diffuse superlattice spots of the γ’ phase due

to a week ordering. HAADF-STEM captured the interconnected feature of

structural ordered phase indicating a spinodal-like structure. Also, the ordered

domains’ size is 3nm based on intensity profile. Proxigram and LBM methods

showed a variation of Al and Cr in this sample. The Al-enriched region which

corresponds to the γ’ precipitates exhibited with a far-from equilibrium.

• Temporal evolution of γ’ morphology has been investigated. Dark-field TEM

micrographs shows a progressive change of the γ’ particle size. Proxigrams across

the γ/γ’ interfaces show an increase of Al and decrease of Cr concentration in the

γ’ precipitates with annealing time. The γ’ precipitates achieved the equilibrium

composition after 600 °C annealing for 2 hr. LBM method was used for more

statistical analysis of Al composition in both γ and γ’ phases.

• In situ high-energy XRD studies were conducted to investigate the evolution of γ’

phase. With increasing annealing time, FWHM of the (100) peak of the γ’ phase

got shaper and the integrated intensity got higher. Lattice parameter of γ and γ’

phases had not change with annealing time but got expanded when heating from

room temperature. Further, the γ’ particle sizes were calculated based on

Scherrer’s equation and the results agreed with particle size observed in DFTEM.

94

5.5 Conclusion

When a disordered solid solution is rapidly quenched from the single γ phase field to

room temperature, the decomposition pathway resulting in the two-phase mixture of γ and γ’ can

be altered from the typically observed nucleation and growth mechanism. This is largely because

the γ to γ+γ’ decomposition takes place at a much lower temperature as compared with the

equilibrium transformation temperature. Consequently the decomposition pathway involves a

highly supersaturated and undercooled single γ phase which is often unstable, more precisely

metastable, with respect to the ensuing ordering or phase separation process [9], resulting in a

non-classical decomposition pathway for γ’ precipitation.

There has been substantial controversy in the literature regarding the sequence of

decomposition, whether or not spinodal decomposition precedes the ordering process. Our

finding reported that synchrotron-base high-energy x-ray diffraction results revealed the presence

of a very diffuse (001) superlattice peak, attributable to the γ’ phase, in the as-quenched sample.

However, electron diffraction results obtained from TEM did not reveal any superlattice spots,

possibly due to the weak ordering at the early stages in the quenched sample. However, results

from the 3DAP analysis of the same sample, carried out using the proxigram and LBM tools, did

not exhibit any significant compositional deviation from a random solid solution. Based on these

results it can be concluded that a congruent ordering process, without a composition change, took

place within the disordered γ phase during the quenching.

During the early stages of annealing, after 5 min at 600 °C, both high-energy XRD and

TEM results indicated the presence of γ’ phase. Very small γ’ domains, with diffuse interfaces,

were observed in HAADF-STEM images from this annealed condition. The regions of dark

contrast in the HAADF-STEM micrograph, exhibited an interconnected nature, which is

95

characteristic of a spinodally-decomposed structure. Furthermore, frequency distribution analysis

of the atom probe dataset revealed marginal deviations from a binomial distribution, indicating

the early stages of phase separation or compositional clustering. Additionally, proxigram from

the same condition, 5 min annealing at 600 ºC, showed minimal compositional partitioning

across the γ / γ’ interfaces. The experimentally observed Al content in the γ’ domains, at the early

stages of annealing at 600°C, is substantially below the equilibrium composition of

Ni3(Alx,Cr1-x) in the long term annealed samples at the same temperature. With increasing

annealing time, the size and the volume fraction of the γ’ precipitates increased along with an

increase in their Al content, and at later stages of annealing (256 hr) γ’ composition approached

equilibrium composition.

Furthermore, the synchrotron-base x-ray diffraction results indicated that there is no

discernable difference in the lattice parameters of the γ’ precipitates and the γ matrix, suggesting

that addition of Cr significantly reduces the precipitate-matrix lattice misfit, in agreement with

previous report [57]. Thus, satellite reflections arising from the composition fluctuation of Al-

rich and Al-depleted regions in the early stages of annealing (5min annealing at 600ºC) could not

be observed due to the similar lattice parameters of both phases.

It can be concluded that in the Ni-8Al-8Cr alloy investigated in the present study, the

decomposition of the supersaturated solid solution takes place via ordering followed by phase

separation since the ordering process involves localized atomic arrangement whereas the phase

separation requires a long-range diffusion in large space. Such a decomposition pathway is in

agreement with previous reports in the literature [7, 9, 22, 25-27].

96

5.6 References


[2] Caron P, Khan T (1983) Improvement of creep strength in a nickel-base single-crystal superalloy by heat treatment. Materials Science and Engineering 61

[3] Murakumo T, Kobayashi T, Koizumi Y et al (2004) Creep behaviour of Ni-base single-crystal superalloys with various γ< sup>′ volume fraction. Acta Materialia 52

[4] Tian S, Su Y, Qian B et al (2012) Creep behavior of a single crystal nickel-based superalloy containing 4.2% Re. Mater Des 37

[5] Pollock T, Argon A (1992) Creep resistance of CMSX-3 nickel base superalloy single crystals. Acta Metallurgica et Materialia 40

[6] Pareige C, Soisson F, Martin G et al (1999) Ordering and phase separation in Ni–Cr–Al: Monte Carlo simulations vs three-dimensional atom probe. Acta materialia 47

[7] Corey CL, Rosenblum BZ, Greene GM (1973) The ordering transition in Ni< sub> 3 Al alloys. Acta metallurgica 21

[8] Blavette D, Bostel A (1984) Phase composition and long range order in γ′ phase of a nickel base single crystal superalloy CMSX2: An atom probe study. Acta Metallurgica 32. DOI:http://dx.doi.org/10.1016/0001-6160(84)90154-8


[10] Booth-Morrison C, Weninger J, Sudbrack CK et al (2008) Effects of solute concentrations on kinetic pathways in Ni–Al–Cr alloys. Acta Materialia 56

[11] Sudbrack CK, Yoon KE, Noebe RD et al (2006) Temporal evolution of the nanostructure and phase compositions in a model Ni–Al–Cr alloy. Acta materialia 54


[13] Laughlin DE, Soffa W (1985) Spinodal structures. ASM Handbook. 9

[14] Laughlin D, Soffa W (1988) In: Anonymous physical properties and thermodynamic behaviour of minerals. Springer

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[17] Rojhirunsakool T, Meher S, Hwang J et al (2013) Influence of composition on monomodal versus multimodal γ′ precipitation in Ni–Al–Cr alloys. J Mater Sci 48

[18] Sarosi P, Wang B, Simmons J et al (2007) Formation of multimodal size distributions of γ′ in a nickel-base superalloy during interrupted continuous cooling. Scr Mater 57


[20] Ardell A, Nicholson RB (1966) On the modulated structure of aged Ni-Al alloys: with an Appendix On the elastic interaction between inclusions by JD Eshelby‡‡ Cavendish Laboratory, University of Cambridge, England. Acta metallurgica 14




[24] Tanner L, Leamy H (1974) In: Anonymous order-disorder transformations in alloys. Springer

[25] Gentry W, Fine M (1972) Precipitation in Ni-11.1 at.% Al and Ni-13.8 at.% Al alloys. Acta Metallurgica 20

[26] Sato T, Kamio A (1990) Ordered structures in the early stage of decomposition in an Al-7.9 mol% Li Alloy. Mat.Trans. JIM 31

[27] Schmitz G, Hono K, Haasen P (1994) High resolution electron microscopy of the early decomposition stage of Al-Li alloys. Acta metallurgica et materialia 42


[29] Hono K, Babu S, Hiraga K et al (1992) Atom probe study of early stage phase decomposition in an Al-7.8 at.% Li alloy. Acta metallurgica et materialia 40

[30] Saito K, Watanabe R (1969) Precipitation in Ni-12 at.% Ti alloy. Japanese Journal of

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Applied Physics 8

[31] Hammersley A (1997) FIT2D: an introduction and overview. European Synchrotron Radiation Facility Internal Report ESRF97HA02T

[32] Larson AC, Von Dreele RB (1994) Gsas. General Structure Analysis System. LANSCE, MS-H805, Los Alamos, New Mexico

[33] Toby BH (2001) EXPGUI, a graphical user interface for GSAS. Journal of Applied Crystallography 34

[34] Gault B, Moody MP, Cairney JM et al (2012) Atom probe microscopy. Springer

[35] Miller MK, Cerezo A, Hetherington M et al (1996) Atom probe field ion microscopy. Clarendon Press Oxford

[36] Langer JS, Bar-on M, Miller HD (1975) Phys. Rev. A 11:1417–1429

[37] Hetherington M, Hyde J, Miller M et al (1991) Measurement of the amplitude of a spinodal. Surf Sci 246

[38] Laughlin D (1976) Spinodal decomposition in nickel based nickel-titanium allols. Acta Metallurgica 24

[39] Radmilovic V, Fox A, Thomas G (1989) Spinodal decomposition of Al-rich Al-Li alloys. Acta Metallurgica 37

[40] Williams DB, Carter CB (1996) The transmission electron microscope. Springer

[41] Hwang J, Nag S, Singh A et al (2009) Compositional Variations between Different Generations of γ′ Precipitates Forming during Continuous Cooling of a Commercial Nickel-Base Superalloy. Metallurgical and Materials Transactions A 40


[43] Hill S, Ralph B (1982) Continuous phase separation in a nickel-aluminium alloy. Acta Metallurgica 30

[44] Miller MK, Miller MK (2000) Atom probe tomography: analysis at the atomic level. Kluwer Academic/Plenum Publishers New York

[45] Camus PP, Larson DJ (1994) Median-style filters for noise reduction in composition analyses. Appl Surf Sci 76

[46] Larson D, Foord D, Petford-Long A et al (1999) Field-ion specimen preparation using

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focused ion-beam milling. Ultramicroscopy 79

[47] Blavette D, Duval P, Letellier L et al (1996) Atomic-scale APFIM and TEM investigation of grain boundary microchemistry in Astroloy nickel base superalloys. Acta materialia 44

[48] Felfer P, Ringer S, Cairney J (2010) Atomic resolution grain boundary analysis using atom probe tomography. Microscopy and Microanalysis 16

[49] Tiley J, Viswanathan G, Hwang J et al (2010) Evaluation of gamma prime volume fractions and lattice misfits in a nickel base superalloy using the external standard X-ray diffraction method. Materials Science and Engineering: A 528

[50] Tiley JS, Senkov O, Viswanathan G et al (2013) A methodology for determination of γ′ site occupancies in nickel superalloys using atom probe tomography and x-ray diffraction. Metallurgical and Materials Transactions A 44

[51] Ungar T (2004) Microstructural parameters from x-ray diffraction peak broadening. Scr Mater 51

[52] Patterson A (1939) The Scherrer formula for x-ray particle size determination. Physical review 56

[53] Polat S, Dvorack M, Chen H (1985) An in situ X-ray diffraction study of precipitation from a supersaturated solid solution: The γ'precipitate in a Ni-12.5% Si alloy. Acta Metallurgica 33

[54] Langford Jt, Wilson A (1978) Scherrer after sixty years: a survey and some new results in the determination of crystallite size. Journal of Applied Crystallography 11

[55] Ai C, Li S, Zhang H et al (2014) Effect of withdrawal rate on microstructure and lattice misfit of a Ni3Al based single crystal superalloy. J Alloys Compounds 592. DOI:http://dx.doi.org/10.1016/j.jallcom.2013.12.262

[56] Wu Q, Li S (2012) Alloying element additions to Ni3Al: Site preferences and effects on elastic properties from first-principles calculations. Computational Materials Science 53. DOI:http://dx.doi.org/10.1016/j.commatsci.2011.09.016

[57] Taylor A, Floyd R (1952) The constitution of nickel-rich alloys of the nickel-titanium-aluminium system. J.Inst.Metals 81

100

CHAPTER 6

COMPETING MECHANISMS OF HOMOGENEOUS AND DISCONTINUOUS γ’

PRECIPITATION IN Ni-Al-Co ALLOYS

6.1 Introduction

In a supersaturated solid solution, precipitation can take place either continuously or

discontinuously [1-5]. Discontinuous precipitation is a solid-state reaction where a

supersaturated solid solution decomposes to solute-depleted matrix and solute-rich precipitates

across a migrating boundary or reaction front resulting in a two-phase lamellar product. This

reaction is characterized by a discontinuous or abrupt change in orientation and composition

between the matrix and the precipitate phase. It has been observed in a number of alloy systems

such as Ni-In [6, 7], Co-Mo [8, 9], Co-W [10], Ni-Al [11], Ni-Co-Al [1, 2], even in a high-

refractory Ni base superalloy [5].

In the present work, the primary focus is on investigating the competing discontinuous

and continuous precipitation mechanisms governing γ’ precipitation as a function of temperature

by coupling scanning electron microscopy including orientation mapping studies, transmission

electron microscopy, and three dimensional atom probe microscopy.

6.2 Experimental Methods

Arc-melted ingots of nominal composition Ni-12.5Al-37.5Co at% (Ni-6%Al-40%Co

wt%) were used for these experiments. As-cast materials were electro-discharge machined into

thin sections and were encapsulated in a quartz tube filling with argon and was subsequently γ

solution heat treated at 1150 °C for 30 minutes, followed by rapidly quenched in liquid nitrogen

bath to room temperature. After quenching, samples were subjected to isothermal annealing at

101

600 °C for 10 min, 1 hr and 256 hr, and 800 °C for 70 hr. Standard metallographic techniques

were used for scanning electron microscopy (SEM) studies using an FEI Nova 230 NanoSEM TM

microscope, equipped with a back-scatter detector and an electron backscatter diffraction

(EBSD) detector. The orientation mapping (OM) studies were conducted to determine

misorientations between different sets of γ grains. Following the SEM studies, samples for

transmission electron microscopy (TEM) were prepared via conventional routes, consisting of

mechanical grinding, followed by dimple grinding and, finally ion-beam milling to electron

transparency. Ion-beam milling was done using low energy Argon gas on a Fischione model

1010TM system. TEM samples were conducted on a FEI Tecnai F20 field emission gun

transmission electron microscope, operated at 200 KV. Samples for three-dimensional atom

probe (3D APT) microscopy were prepared using the FEI Nova200 TM dual-beam focused ion

beam (FIB) system. After the annular milling process the final tip diameter of the atom probe

specimens was 50-70 nm. APT experiments were conducted using a CAMECA LEAP 3000X TM

HR instrument. All APT experiments were carried out in the voltage evaporation mode at a

temperature of 60 K with pulse rate of 160 KHz and target evaporation of 0.5%. Data analyses

were carried out using CAMECA IVAS 3.6 TM software.


6.3.1 Liquid Nitrogen Quenching after Solution Treatment above γ’ Solvus Temperature

Fig. 6.1(a) shows a backscatter SEM micrograph from the solution-treated

(1150°C/30min) followed by liquid nitrogen quenched Ni-12.5Al-37.5Co alloy, where a grain

boundary triple junction is clearly visible. Even when imaged at higher magnifications in the

SEM, there was no indication of γ’ precipitation at this scale of observation. However TEM

102

observations of the same sample clearly revealed fine scale γ’ precipitation as evidenced by the

selected area diffraction (SAD) pattern, recorded along <001> zone axis (inset in Fig. 6.1(b))

clearly showing <100> and <110> superlattice reflections, along with the fundamental

reflections from the disordered γ matrix. This indicates that ordered L12, γ’ precipitates have

formed in the as-quenched condition. The corresponding centered-dark field TEM image,

recorded using one of the <100> superlattice reflections is shown in Fig. 6.1(b). The γ’

precipitates exhibit a near-spherical, monomodal size distribution with an average size of less

than 5 nm. An APT reconstruction of the as-quenched sample, of size 40x40x60 nm3 is shown in

Fig. 6.1(c), where the Al-rich γ’ precipitates have been clearly delineated using a 12at% Al iso-

concentration surface (also referred to as isosurface). It should be noted that this particular Al

concentration value for constructing the isosurface was chosen based on an estimation of γ’

precipitates’ sizes (≈ 5 nm), obtained by averaging over multiple TEM dark-field images (such

as the one shown in Fig. 6.1(b)). The variation of Al and Co across the γ/ γ’ interface has been

shown using a proximity histogram or proxigram in Fig. 6.1(d), generated using the commercial

IVAS™ software [12, 13]. The proxigram clearly reveals the partitioning of Al and Co between

the γ and γ’ phases, even though this sample experienced a rapid cooling rate (Al partitions to the

γ’ phase while Co partitions to the γ phase). The compositional gradient across the γ/γ’ interface

appears to be very diffuse (~3nm). These gradients were determined using a method that uses

90% of the steady state and 10% of steady state γ’ compositions [12, 14, 15]. The composition

of these nano-scale quenched γ’ precipitates, Ni-25Al-17Co, is almost identical to those of larger

well-developed precipitates after long term annealing at 600°C for 256 hr (to be discussed later

in this chapter). Therefore, it appears that the as-quenched precipitates exhibit a near-equilibrium

composition right from the early stages of their formation. This composition is also comparable

103

to the predictions afforded by solution thermodynamic models, such as the commercially

available PANDAT™ software, which predicts the γ’ composition for a nominal alloy

composition of Ni-12.5Al-37.5Co at 800°C to be Ni-22Al-14Co. Since γ’ precipitates with the

L12 ordered structure have a stoichiometry of 3:1 for the ratio of Ni sublattice sites to Al

sublattice sites, assuming a stoichiometric γ’ phase in the Ni-Co-Al alloy under study leads to

stoichiometry of (Ni+Co)3Al, indicating that the Co atoms occupy the Ni sublattice in the γ’

phase.

104

50 nm 10 um

0

5

10

15

20

25

30

35

40

-4 -3 -2 -1 0 1

Com

posi

tion

(at%

)

Distance ( nm)

Al %

γ’

γ

60 n

m

40 nm

a b

c d

Fig. 6.1 a) A low magnification of SEM micrograph of an as-quenched Ni-12.5Al-37.5Co sample showing no γ’ precipitation at this scale. b) A dark-field TEM micrograph with corresponding <100> and <110> superlattice reflections on <001> SAD pattern as an inset showing a near-spherical morphology of γ’phase. c) An APT reconstruction of a 40x40x60 nm3 volume, delineated by 12 at% Al isosurfaces, showing γ’ precipitates. d) The compositional profile across γ/γ’ interfaces for Al and Co corresponding to the isosurfaces shown in c).

105

6.3.2 High Temperature Annealing at 800ºC (near γ’ Solvus Temperature)

Figs. 6.2(a) and (b) show low and high magnification of backscatter SEM micrographs of

the Ni-12.5Al-37.5Co alloy after high temperature annealing at 800 °C for 70 hr, post rapid

quenching. The microstructure clearly shows a discontinuous lamellar γ+γ’ product near the

grain boundaries. Additionally, homogeneously refined γ’ precipitates are also observed within

the γ grains. The SAD pattern, shown as an inset in Fig 6.2(c), shows the strong <100>

superlattice spots corresponding to the ordered γ’ precipitates, along with the fundamental γ

matrix reflections. A dark-field TEM micrograph of a region inside a γ grain, recorded using one

of the {100} superlattice reflections, shows the presence of cuboidal γ’ precipitates ~100 nm in

size. The γ’ morphology observed in this 800°C annealed sample is typical of that most

commonly observed in commercially used Ni base superalloys. It should be noted that compared

with the as quenched condition, where the γ’ precipitates were found to be more spherical in

shape, long term annealing at 800 °C yielded a cuboidal morphology of these γ’ precipitates.

This morphological change is a consequence of increasing contribution from elastic strain energy

with increase in precipitates size (~5nm for as quenched condition to ~100nm for the 800°C long

term annealed sample), thus aligning the precipitates along elastically soft <001> directions of

the γ matrix. This result agrees with most alloys where homogenous γ’ precipitation, via classical

nucleation and growth, is usually observed at a temperature close to the γ’ solvus temperature (γ’

solvus temperature of Ni-12.5Al-37.5Co alloy = 850 °C) [2, 3, 16].

A 25x25x25 nm3 3DAP reconstruction of the 800°C/70hr annealed sample is shown in

Fig. 6.3(a). This reconstruction captures only a part of a γ’ precipitate delineated using a

12at%Al isosurface. Additionally, Fig. 6.3(b) also shows the Ni atoms in green to clearly reveal

106

the γ matrix within the reconstruction volume. Similar to the as-quenched condition (Fig. 6.1(d)),

the corresponding proximity histogram (Fig. 6.3(b)) shows that Al partitions to the γ’ phase

whereas Co partitions to the γ matrix. From the proxigram the composition of the γ’ phase and

the γ/γ’ interface width were determined to be Ni-22Al-16Co and ~2nm respectively. The

solution thermodynamic predictions (based on PANDATTM) of the equilibrium γ’ composition at

800°C, Ni-23Al-16Co, are in good agreement with the experimentally measured composition

from 3DAP, indicating that the precipitates have achieved their equilibrium composition.

Assuming perfect stoichiometry of 25% of Al sites in the L12 structure, one of two possibilities

exists; either 3 at% of Co occupies Al-sites and the rest occupies Ni-sites in the γ’ phase resulting

in the stoichiometry (Ni+Co)3(Al+Co) or 3 at% Ni occupies the Al sites and all the Co atoms

occupy the Ni sites resulting in a stoichiometry of (Ni+Co)3(Al+Ni) This result clearly indicates

that at 800°C, there are likely to be at least 3 at% of anti-site defects in the γ’ precipitates in this

alloy.

107

Fig. 6.2 a) Low and b) high magnification of backscatter SEM micrographs of the Ni-12.5Al-37.5Co alloy after high temperature annealing at 800 °C for 70 hr, post rapid quenching. c) A DFTEM and SAD pattern of the same sample showing cuboidal γ’ precipitates

10 um

a

3 um

b

c

100 nm

Fig. 6.3 a) A 25x25x25 nm3 3DAP reconstruction of the 800°C/70hr annealed sample and b) the corresponding proxigram.

b

γ

γ’

a

25 nm

25 n

m

108

As mentioned earlier, a discontinuous lamellar γ+γ’ product near the grain boundaries and

refined γ’ precipitates within the γ grains were observed in the case of long term annealing at

high temperature (800°C/70 hr). Interestingly, the discontinuous lamellar product was not

observed in all grain boundaries. Thus, further investigation of effect of grain boundary

misorientation on discontinuous precipitation was carried out. SEM-EBSD technique was

employed to determine the grain boundary nature. Figs. 6.4(a) and (b) show a high magnification

SEM image of a scanned area of this sample where coarse discontinuous lamellar regions can be

observed adjacent to the grain boundaries. A triple junction of the grain boundaries was captured.

Two of the three grains exhibit the discontinuous lamellar γ+γ’ product near the grain boundaries.

The other grain does not show the discontinuous product but exhibit fine cuboidal γ’ precipitates

in the grain interior toward the grain boundary. The orientation distribution of the γ grains in the

scanned area is represented by the inversed pole figure (IPF) map shown in Fig. 6.4(b)

(corresponding to exactly the same region as shown in Fig. 6.4(a)), where the colors correspond

5.1 °

51.7°

47.6 °

5 um 4 um

Fig. 6.4 a) SEM micrograph of 600 ºC/256 hr annealed Ni-Al-Co sample showing discontinuous precipitaiton near the grain boundaries and homogeneous precipitation in the grain interior. b) A corresponding inverse pole figure (IPF) of the same area and the stereo-triangle.

b a

109

to particular crystallographic orientations, as indicated by the stereo-triangle in Fig. 6.4(b). The

IPF map clearly revealed grain orientations that are labeled by different colors. Line

measurement between two grains was employed to determine a grain misorientation between

those two. Between grain 1 and grain 2, grain misorientation is 51.2°. Between grain 1 and grain

3, grain misorientation is 47.6°. Between grain 2 and grain 3, grain misorientation is 5.1°. These

results show that discontinuous lamellar product exhibits only on high grain misorientation

whereas continuous precipitation dominates on low grain misorientation. High grain

misorientation results in high diffusivities at the grain boundary. At high temperature, volume

diffusion in a grain interior is relative higher compared to grain boundary diffusion. Then,

homogeneous, cuboidal precipitates grow faster and reduce supersaturation in the γ matrix. Thus,

homogeneous precipitation is always observed both in the grain interior and near the grain

boundary. However, discontinuous precipitation can be competed with homogeneous

precipitation when the grain boundary diffusion is assisted with the high grain misorientation

energy. Although with the assistance of the misorientation energy volume diffusion at 800 °C

homogeneous precipitation confines discontinuous precipitation only near the grain boundaries.

6.3.3 Low Temperature Annealing at 600 ºC

6.3.3.1 Early Stages of Annealing (for 10 min)

Fig. 6.5(a) shows a dark-field TEM micrograph of Ni-37.5Co-12.5Al alloy after 600 °C

annealing for 10 min, recorded using one of the {100} superlattice reflections (an inset in Fig.

6.5(a)), shows the presence of near-spherical γ’ precipitates, which is similar to the as-quenched

sample. The precipitates’ dimension increase from less than 5 nm in as-quenched sample to 5-10

nm after annealing for 10 min at 600 °C. However, in other regions of this sample, fine scale

110

lamellae of γ and γ’ phases were observed near the grain boundaries (Fig. 6.3(b)). The average

lamellae spacing was 10-15 nm. It is suggested that discontinuous precipitation possibly

nucleates from the grain boundaries and reaction fronts of γ and γ’ phase lamellae consume

continuous precipitation formed from quenching (Fig. 6.1(b)). Thus, the early stage annealing for

10 min captured a transformation of homogeneous precipitation to discontinuous precipitation of

the γ and γ’ phases.

111

20 nm

a

20 nm

c

100 nm

b

Fig. 6.5 DFTEM micrograph of Ni-37.5Co-12.5Al alloy after 600 °C annealing for 10 min showing a) homogeneous γ’ precipitation recorded using one of the {100} superlattice reflections (an inset in Fig. 6.5(a)), b) discontinuous γ’ precipitation near the grain boundary, recorded using one of the {110} superlattice reflections (an inset in Fig. 6.5(b)) and c) discontinuous γ’ precipitation in the grain interior, recorded using one of the {110} superlattice reflections (an inset in Fig. 6.5(c)).

112

6.3.3.2 Short Term Annealing (for 1 hr)

SEM micrograph of a short term annealing of low temperature annealing at 600 °C (Fig.

6(a)) does not reveal any γ’ precipitates either at grain boundaries or in the grain interior,

presumably due to their highly refined nature. However, TEM investigation of the same sample

clearly revealed the presence of a discontinuous γ+γ’ product. Thus the observed microstructure

exhibited fine scale lamellae of γ and γ’, that presented uniformly throughout the γ grains (Fig.

6(b)). The inter-lamellar spacing was observed to be ~10-15 nm. There was no evidence of the

homogeneously precipitated spherical γ’ phase that was observed in the as-quenched alloy.

However, similar to the discrete cuboidal γ’ precipitates observed in the 800°C annealed sample,

a cube on cube orientation relationship was maintained within the lamellar structure between the

γ and γ’ phases, with [001]γ || [001]γ’ and (001)γ || (001)γ’, determined based on the SAD pattern

shown as an inset in Fig. 6(b). Both the SEM (Fig 6(a)) and dark field TEM (Fig. 6(b)) images

showed no evidence of coarsening of the discontinuous product at the grain boundaries.

10 um 50 nm

a b

Fig. 6.6 a) A low magnification of SEM micrograph of 600 °C/1 hr annealed Ni-Al-Co sample. b) A DFTEM micrograph of the same sample showing discontinuous γ+ γ’ lamellar product in the grain interior.

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6.3.3.3 Long Term Annealing (for 256 hr)

Discontinuous coarsening succeeded the reaction fronts during extended isothermal

treatment at 600 °C to develop a coarser distribution of the primary products. Coarser γ + γ’

lamellae products replaced the fine discontinuous products that exhibited after 1 hr annealing at

600 °C. Backscatter SEM images from the 600°C/256hr annealed sample, shown in Figs. 6.7(a)

and (b) show a coarser lamellar γ + γ’ product, adjacent to certain specific grain boundaries,

often growing preferentially on only one side of the boundary. This observation is consistent

with other finding where the growth in only one direction dominates in the temperature range

above 50% of a γ’ solvus temperature [17] (γ’ solvus temperature = 850 °C). Further, these

coarser lamellae appear to be nearly perpendicular to the original boundary plane. However, the

advancing reaction front is rarely completely planar. In fact, the reaction front is usually curved,

thus the isothermal lamellae growth continues by maintaining the necessary chemical potential

gradient across the migrating boundary [18]. In some cases, such as Fig. 6.7(b), finer scale

lamellar structure within the grain where the diffusivity is limited. It should be noted that often

the coarsened γ+γ’ lamellar product extends substantially into the grain interior adjacent to the

boundary. After 600°C/256 hr annealing, the inter-lamellar spacing increased to ~20-30 nm.

Additionally, the longer annealing time also led to a higher volume fraction of the discontinuous

product towards attaining the equilibrium volume fraction of γ’ in the alloy at 600°C. The

increase in the volume fraction of the lamellar product can be achieved either by lamellar

branching or by repeated nucleation at the grain boundary (Figs. 6.7(c) and 7(d)), as discussed

previously in the literature [2]. Further, Fig. 6.7(c) shows an Energy Filtered TEM (EFTEM)

image (using the Co M2,3 edge at 60eV) of one such region containing discontinuous lamellar γ+γ’

product on both sides of a prior γ grain boundary. The image clearly shows two distinctly

114

different sets of lamellae on both sides of the grain boundary. While the top lamellae appear to

have emanated from the grain boundary and are roughly perpendicular to it, the bottom set of

lamellae appear to intersect the same grain boundary at an angle. On a global scale even though

discontinuous γ’ products were observed everywhere, a wide range of inter-lamellar spacing

were observed. This typically suggested that growth and coarsening rates of the lamellar γ+γ’

product varied from grain to grain, coupled with the issues of two-dimensional sectioning of the

three-dimensional lamellar product, in the viewing direction of the TEM images.

a

10 um

b

5 um

200 nm 100 nm

c d

Fig. 6.7 a) Low and b) high magnification of SEM micrographs of discontinuous γ+ γ’ product near the grain boundary. c) and d) Energy-filtered micrographs showing lameallation achieving by lamellar branching.

115

Closer investigation on the coarser discontinuous γ+ γ’ product was carried out via a site-

specific TEM micrographs. SEM micrograph in Fig. 6.8(a) shows a grain boundary where

coarser discontinuous product exhibited. Adjacent grains do not show discontinuous product due

to their highly refined nature. HAADF-STEM micrograph (Fig. 6.8(b)) presents the same gain

boundary as the SEM image in Fig. 6.8(a). The reaction front was marked by curved-dotted lines

in red, and the original grain boundary was marked by straight-dotted lines in blue. The reaction

fronts of coarser discontinuous product invaded from the right grain into the left grain. A high

magnification of the same reaction fronts (Fig. 6.8(b)) shows that while the reaction fronts are

growing they are drawing solute atoms from the existing finer lamellar from the left grain.

Interestingly, these coarser lamellae did not exhibit the same lamellar orientation compared with

the right grain where it was originally. In fact, these coarser lamellae exhibit nearly

perpendicular to the original boundary plan disregarding to the original lamellar orientation.

From Fig. 6.8(b), lamellae product dimension at the reaction front was 77 nm and larger than that

at the original grain boundary (39nm). Lamellar product on the left grain and right grain were ~

13 nm and ~8nm, respectively.

Fig. 6.9(a) shows a 3DAP reconstruction of volume 60x60x50 nm3, clearly capturing the

lamellar structure of alternating γ and γ’ phases. Ni atoms (green) and Co atoms are shown here

where Al ions were omitted for clarification. Alternating view of the 3DAP reconstruction shows

Al iso-concentration surfaces generated using 12at%Al (red) superimposed with Ni ions, to

clearly show the lamellar structure. The interlamellar spacing observed in this APT

reconstruction was 20 nm, in agreement with the range obtained from the TEM observations

from the same region. The corresponding proxigram obtained using the 12at%Al iso-

concentration surface, shown in Fig. 6.9(b), reveals that the γ’ phase has an Al content of 25at%.

116

This is consistent with the previous results for the as-quenched condition, confirming that the

(Ni+Co)3Al stoichiometry is maintained after 600°C/256hrs annealing. The Al isosurface also

showed a sharp γ/γ’ interface width (< 2nm), even though the Co isosurface revealed a

marginally more diffuse interface.

117

Fig. 6.8 a) Backscatter SEM micrograph showing reaction fronts and original grain boundary. b) The reaction fronts (marked with curved-dotted line in red) and the original grain boundary (marked with straight-dotted line in blue) of the long term annealing at 600 °C (600 °C/256hr).

50 nm

13 nm

77 nm

39 nm

8 nm

5 um

a

b

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6.3.3.3.1 Grain Misorientation and Interfacial Energy

Among all the samples that were investigated, the specimen that was aged for 256 hr at

600ºC exhibited widespread regions of discontinuous precipitation. However as observed from

Fig. 6.7 the coarseness of the γ+γ’ lamellar product (based on the inter-lamellar spacing) varied

significantly depending on the particular grain boundary as well as the grain into which it is

growing. Since this sample was compositionally homogenous, it is highly likely that the nature

of the grain boundary (grain boundary plane normal and misorientation across the boundary)

plays a role in determining the growth and coarsening rates of the lamellar product. Further

investigation of this possibility was carried out by SEM-EBSD studies of the 600ºC/256 hr

annealed sample. Fig. 6.10(a) shows a low magnification SEM image of a scanned area of this

sample where coarse discontinuous lamellar regions can be observed adjacent to certain grain

boundaries (shown by arrows). The overall orientation distribution of the γ grains in this region

0

10

20

30

40

50

60

70

-8 -6 -4 -2 0 2 4 6

Com

posi

tion

(at%

)

Distance (nm)

Al %

Co %

a b Ni+Co

Al iso with Ni ions

Fig. 6.9 a) 3DAP reconstruction of long term annealing at low temperature (600 °C/256 hr) showing Ni and Co ions and Al isosurface superimposed with Ni ions. b) The corresponding proxigram delineated by using Al=12 at%.

119

is represented by the Inversed pole figure (IPF) map shown in Fig. 6.10(b) (corresponding to

exactly the same region as shown in Fig. 6.10(a)), where the colors correspond to particular

crystallographic orientations, as indicated by the stereo-triangle in Fig 6.10(b). This IPF map

revealed relatively random grain orientations within the region under study. Fig. 6.10(c) shows

the same region in Figs. 6.10(a) and 10(b), however in this image the various coincident site

lattice (CSL) boundaries have been superimposed on top of an Image Quality (IQ) map. As we

know, a CSL boundary is defined based on the coincident sites between the two lattice

orientations across the boundary. The degree of fit (Σ) of the two grains is described by the

reciprocal of the ratio of coincidence sites to the total number of sites. A boundary that contains a

high density of coincident lattice points typically has a lower sigma value and is also expected to

have low energy because of the better atomic fit. Larger sigma values imply larger unit cells in

the boundary and fewer coincident lattice points and consequently higher energies. Thus after

analyzing the data in Fig 6.10(c) it was found that ∑3, ∑45a, ∑9, and ∑11 boundaries are the

most prevalent special boundaries present in this region. 42.3% of the total grain boundaries are

∑3 type (60 ° rotation of {111} plane) that is likely to be annealing twins. It should be noted that

an extensive amount of annealing twins are formed in the Ni-Co-Al alloys as it has a

considerable low stacking fault energy due to the addition of Co [19, 20]. Based on this analogy

in Fig. 5c the special boundaries like ∑3, ∑45a, ∑9, and ∑11 are color coded as red, blue, green

and yellow, respectively. All other grain boundaries are not CSL boundaries and therefore have

not been marked. Comparing the SEM image in Fig. 10(a) with this color-coded grain boundary

map in Fig. 10(c), it is clear that in most cases coarser discontinuous products are only formed

(shown by white arrows in Fig. 6.10(a)) adjacent to high energy boundaries while the special low

energy CSL boundaries do not exhibit the coarser lamellar product. However, it should also be

120

noted that all random high angle boundaries (non-CSL) do not exhibit coarsened lamellar

products.

50 um 50 um

0 10 20 30 40 50 600.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

GB with Discontinous PPT Random distribuion of GB

Frac

tion

(No.

of G

B w

ith D

P/ to

tal N

o. o

f GB

with

DP

Misorientation angle(degree)

a b

c d

Fig. 6.10 a) A low magnification SEM image of a scanned area of this sample where coarse discontinuous lamellar regions can be observed adjacent to certain grain boundaries (shown by arrows). b) A IPF map of the same area as a). c) The coincident site lattice (CSL) boundaries superimposed on top of an Image Quality (IQ) map of the scanned area. d) A plot of a fraction of total number of grain boundaries containing the coarse discontinuous precipitation versus misorientation angle in black squares superimposed on a random distribution of grain boundary (red circles).

121

Subsequent analyses of the EBSD data were carried out on only grain boundaries

containing the coarser lamellar product. The orientation (plane) of each grain boundary

exhibiting the coarser lamellar product adjacent to it, as well the misorientation in terms of

angle-axis pairs, Σ boundaries (if present) and their deviation from ideality has been listed in

Table 6.1. As expected, most of the coarser discontinuous products are observed on high angle

grain boundaries that do not correspond to special CSL boundaries. However, some exceptions

should be noted, where certain grain boundaries containing the coarser discontinuous product lie

near a CSL orientation, such as a boundary with a deviation of 3° from a ∑11 boundary, one with

a deviation of 2.1° from a ∑31b boundary, and one with a deviation of 2.2° from a ∑45a

boundary.

A plot of a fraction of total number of grain boundaries containing the coarse

discontinuous precipitation versus misorientation angle is shown in Fig. 6.10(d) (shown as black

squares). This is basically a graphical representation of the data that is listed in Table 6.1. As

seen from the plot, no coarse discontinuous product is present between the misorientation angles

of 0° and 15°. A maximum fraction (~0.35) of grain boundaries containing coarse discontinuous

products has a misorientation angle ~35°. Between the misorientation angles of 40° and 55°, the

coarse discontinuous product is observed on an average of 15% (equivalent to a fraction of 0.15)

of the grain boundaries. However, no coarser lamellar product is observed at a misorientation of

60°. Mackenzie [21] calculated a distribution of the grain boundary misorientations in a

completely randomly oriented polycrystalline sample of a cubic material and the data from that

study has been plotted in Fig. 6.10(d) (shown by red circles) together with the experimental data

from the present study. Comparing the two plots, it is clear that the experimental data that

pertains to coarsening of the discontinuous γ+γ’ product adjacent to certain grain boundaries does

122

not follow the grain boundary distribution plot for a random polycrystalline sample. In fact the

random grain distribution (red circles in Fig. 6.10(d)) has a sharp peak at 45° whereas the

experimental results show a peak at 35°. Thus, it indicates that the coarsening of the lamellar

discontinuous γ+γ’ product does not occur randomly on all grain boundaries.

At low angle boundaries, with a misorientation angle of less than 15°, no coarse

discontinuous γ+γ’ product is observed presumably due to their low energy. However, coarse

discontinuous γ+γ’ product is observed at high angle boundaries (those with misorientation

angles greater than 15°). High angle boundaries typically exhibit a high degree of structural

disorder, leading to higher energy values for such boundaries. These high angle boundaries are

favorable pathways for short-circuit diffusion of solute elements. It is worth noting that not all

high angle boundaries exhibit a higher degree of structural disorder. Thus CSL boundaries with

high misorientation angles still have relatively low energies since they are well matched and do

not exhibit a substantial degree of structural disorder. These boundaries are not good short-circuit

diffusion paths for solute atoms and therefore do not exhibit significant coarsening of the

discontinuous lamellar γ+γ’ product. For example twin boundaries (60° misorientation around

<111>, ∑3) do not exhibit the coarser discontinuous γ+γ’ product, as clearly observed from

Table 6.1 as well as the plot in Fig. 6.10(d). Furthermore, it should be noted that even though

high energy- high angle grain boundaries are generally prevalent, not all of those boundaries are

equally effective as short-circuit diffusion paths. While comparing the potency of discontinuous

coarsening other factors like grain boundary structure and actual grain boundary energy does

come into play as well.

123

Table 6.1. The misorientation (angle-axis pairs), Σ boundaries (if present), their deviation from ideality, and the orientation (plane) of each grain boundary of the grain boundaries containing the coarser lamellar product.

Misorientation Sigma Boundary Deviation Plane (p1) Plane (p2) Rotation

angle Rotation axis

29.6 -9 24 -10 45a 2.2 1 1 -19 -2 23 -10 30.3 -7 18 -7 - - 21 -17 -11 -22 15 11 30.9 14 11 19 - - -18 -1 -1 -10 21 -2 36 -22 -16 11 - - -3 23 -10 -14 19 2

47.1 11 -13 -16 - - 3 -22 11 -11 19 0 34.7 9 15 11 - - -12 -6 13 -12 14 3 51.7 -6 -13 6 31b 2.1 7 2 -21 -14 25 -1 45.5 -15 -22 15 - - 11 0 -25 -16 25 1 38.5 20 17 13 - - -20 -7 21 -20 19 7 30.6 -18 -23 7 - - 17 -20 -4 -16 17 9 30.7 -13 -17 5 - - 10 -21 2 10 18 13 30.6 11 9 15 - - -22 -15 -8 -12 10 5 30.6 14 11 19 - - -18 -5 -3 -15 21 2 52.8 2 -12 -17 - - -20 17 13 -8 27 -7 43.9 -15 -16 -9 - - 5 -11 12 -5 16 -4 40.7 7 -10 10 - - 6 -8 -1 -9 -1 18 54 -8 10 -1 - - 12 -26 3 -23 -8 14

19.6 27 8 -2 - - -14 -2 19 -9 14 -21 20 26 8 -1 - - -17 -3 22 -6 9 -13

42.8 14 -5 -3 - - -21 18 5 -9 -12 -16 47.7 19 20 0 11 3 4 3 16 -22 -18 -9 34.3 -21 7 5 - - 27 -2 6 1 -30 4

6.4 Summary and Conclusion

The present study investigates the competing mechanisms of continuous and

discontinuous precipitation of γ’ phase in Ni-37.5Co-12.5Al alloy in as-quenched, 800 °C

annealing and 600 °C annealing. The results of this investigation can be summarized as

followed:

• In very rapid quenching post solutionizing, γ’ precipitates initially exhibit a near-spherical,

monomodal size distribution with an average size of less than 5 nm The proxigram obtained

124

from APT clearly shows the partitioning of Al and Co at a nanometer scale. Al partitions to

the γ’ phase while Co partitions to the γ phase. The compositional gradient across the γ/γ’

interface appears to be very diffuse (~3nm). The γ’ precipitates exhibit a near-equilibrium

composition with Ni-25Al-17Co

• Long term annealing at 800 °C sample shows both continuous and discontinuous

precipitations. A cuboidal shape of the γ’ precipitates was observed inside the grain and

discontinuous precipitation was confined near grain boundary by these continuous

precipitation. The composition of γ’ phase and the γ/γ’ interface width were determined to be

Ni-22Al-16Co and ~2nm respectively. To maintain perfect stoichiometry of 25% of Ni3Al in

L12 structure, possibly 3 at% of Co occupies Al-sites and the rest occupies Ni-sites in the γ’

phase as (Ni+Co)3(22Al+3Co)

• In case of low temperature annealing at 600 °C, an earliest stage annealing of 10 mins shows

discontinuous precipitation near the grain boundaries as well as the near spherical

morphology inside the grains. After 1 hr annealing, discontinuous precipitation completely

transform and no spherical morphology of γ’ was observed. Coarsening of g and g’ lamellae

can be observed after long term annealing (256 hrs). Proxigram shows consistent result with

the the as-quenched condition where as (Ni+Co)3Al stoichiometry was obtained. Even

though discontinuous γ’ products were observed everywhere, a wide range of interlamellae

spacing was observed. This suggested that growth and coarsening rates of lamellar regions

significantly depended on the grain in which they are growing.

• The discontinuous precipitation does not nucleate randomly on grain boundaries. The

nucleation of the discontinuous precipitation prefer on high-energy boundary, rather than

125

high angle boundary. CSL and twin boundaries are not favorable pathway for nucleation site

of the discontinuous product.

6.5 References



[3] Duly D, Simon J, Brechet Y (1995) On the competition between continuous and discontinuous precipitations in binary Mg-Al alloys. Acta metallurgica et materialia 43

[4] Kainuma R, Ise M, Jia C et al (1996) Phase equilibria and microstructural control in the Ni-Co-Al system. Intermetallics 4

[5] Nystrom J, Pollock T, Murphy W et al (1997) Discontinuous cellular precipitation in a high-refractory nickel-base superalloy. Metallurgical and Materials Transactions A 28

[6] Chuang T, Fournelle R, Gust W et al (1988) Discontinuous coarsening of discontinuous precipitate in a Ni-7.5 at.% In alloy. Acta Metallurgica 36

[7] Geber G (1995) An APFIM/TEM investigation of the discontinuous precipitation in a Ni In alloy. Appl Surf Sci 87

[8] Gust W, Predel B, Mehra SN (1975) Die kinetik der feinlamellaren diskontinuierlichen ausscheidung in CoMo-Mischkristallen. Materials Science and Engineering 21. DOI:http://dx.doi.org/10.1016/0025-5416(75)90207-4

[9] Lee S, Lee K, Chuang T (1998) Discontinuous coarsening of discontinuous precipitates in a Co–6 at.% Mo alloy. Materials Science and Engineering: A 251. DOI:http://dx.doi.org/10.1016/S0921-5093(98)00624-8

[10] Ziȩba P, Cliff G, Lorimer GW (1997) Discontinuous precipitation in cobalt-tungsten alloys. Acta materialia 45

[11] Williams R (1959) Aging of nickel-base aluminium alloys. Trans.TMS-AIME 215


[13] Hwang J, Nag S, Singh A et al (2009) Compositional variations between different

126

generations of γ′ precipitates forming during continuous cooling of a commercial nickel-base superalloy. Metallurgical and Materials Transactions A 40

[14] Camus PP, Larson DJ (1994) Median-style filters for noise reduction in composition analyses. Appl Surf Sci 76

[15] Larson D, Foord D, Petford-Long A et al (1999) Field-ion specimen preparation using focused ion-beam milling. Ultramicroscopy 79

[16] Braszczyńska-Malik KN (2009) Discontinuous and continuous precipitation in magnesium–aluminium type alloys. J Alloys Compounds 477. DOI:10.1016/j.jallcom.2008.11.008

[17] Baumann S, Michael J, Williams D (1981) Initiation and growth of the grain boundary discontinuous precipitation reaction. Acta Metallurgica 29

[18] Fournelle R, Clark J (1972) The genesis of the cellular precipitation reaction. Metallurgical Transactions 3

[19] Gui C, Sato A, Gu Y et al (2005) Microstructure and yield strength of UDIMET 720LI alloyed with Co-16.9 Wt Pct Ti. Metallurgical and Materials Transactions A 36

[20] Jarrett RN, Tien JK (1982) Effects of cobalt on structure, microchemistry and properties of a wrought nickel-base superalloy. Metallurgical Transactions A 13

[21] Mackenzie J (1958) Second paper on statistics associated with the random disorientation of cubes. Biometrika 45

127

CHAPTER 7

EFFECT OF HEAT TREATMENT ON SOLUTE PARTITIONING IN NI-BASE SINGLE

CRYSTAL RENE N5 SUPERALLOYS

7.1 Introduction

Previous chapters discussed on precipitation mechanism of the γ’ phase of model alloys.

This chapter extends the study of the γ’ precipitation mechanism and solute partitioning to a real

life Ni-base superalloy.

Nickel-base superalloys have been designed for use in high-temperature applications such

as the gas turbine engines needed for jet propulsion and electricity generation. Their remarkable

mechanical properties at high temperatures are known due to finely dispersed γ’ precipitates,

with an L12 structure, within a disordered face-centered cubic γ matrix. To improve the high-

temperature mechanical properties of superalloys, ten or more elements, including Al, Cr, Mo,

Hf, Re, Ru, Ti, W, B, and C, have been added in considerable quantities to provide solid solution

hardening of the γ matrix phase. However, the alloy development process was largely achieved

in an empirical manner without a detailed physical understanding of the role played by the key

alloying elements on the microstructure and mechanical properties of Ni-base superalloys.

Specifically, Re has been found to remarkably improve the creep strength of these alloys at very

high temperatures (1000-1150 °C) [1]. Addition of Re element in this alloy has been extensively

introduced to rhenium-containing single-crystal superalloys for use in commercial high-

temperature application materials. As Table 7.1 shows, Rene N5, a commercial second-

generation superalloy, contains Re up to about 3 wt %, 5 wt % W, 6.5 wt % Ta, and 0.15 wt %

Hf [2].

128

Table 7.1 Bulk chemical compositions of Ni base Rene N5 superalloys (all value in wt%)

Ni Co Cr Al Ta W Mo Re Hf C B

Bal 7.5 7 6.2 6.5 5 1.5 3 0.15 0.05 0.004

The primary focuses of this study project are to increase understanding of the influence of

heat treatment on the partitioning of the minor elements across the γ/ γ’ interfaces and Re

enrichment in the γ matrix near the γ/ γ’ interfaces.

7.2 Experimental Procedure

As-cast, heat-treated, and thermally cycled single-crystal blade alloy Rene N5 samples

were provided by GE Aviation and investigated at UNT. Microstructural analyses were

performed using a combination of scanning electron microscopy (SEM), transmission electron

microscopy (TEM), and atom probe tomography (APT). Standard metallographic techniques,

including wet polishing and cloth polishing with colloidal silica suspension, were used for SEM

sample preparation. The TEM samples were prepared via mechanical grinding, followed by

dimple grinding, and finally ion-beam milling until electron transparency was achieved. TEM

analysis was conducted on a FEI Tecnai F20 field emission gun TEM, operated at 200 kV. The

APT samples were prepared using a dual-beam focused ion-beam technique with a final tip

diameter of ~70 nm. APT experiments were carried out using a laser evaporation mode at

temperature of 40 K with pulse rate of 160 kHz. Data analyses were carried out using CAMECA

IVASTM 3.6 software.

129


7.3.1 Microstructural Evolution of the γ+ γ’ Phases

The comparison of low and high magnification of SEM micrograph shows

microstructures of as-cast, heat-treated, and thermally cycled Rene N5 samples shown in Fig. 7.1.

and 7.2. The morphological development of γ’ morphology when the as-cast sample is subjected

to full heat treatment and thermal cycling changes from arrays of cuboidal to more cuboidal in

shape and finally rafted structure.

Fig. 7.1 Low magnification SEM micrographs of a) as-cast b) heat-treated and c) thermally cycled sample of single-crystal Rene N5 samples.

2 µm 2 µm 2 µm

Fig. 7.2 High magnification SEM micrographs of a) as-cast b) heat-treated and c) thermally cycled sample of single-crystal Rene N5 samples.

a

a

b

b

c

c

130

Rafted γ+ γ’ structure observed in the thermally cycled sample occurs as a result of

directional coarsening of γ’ precipitates. Coarsening kinetics of the Ni-base superalloys typically

occurs above ~0.6 TM, where TM is the absolute melting temperature, facilitating dislocations

bypassing and thus lowering the long time creep strength. The driving forces for coarsening

process are i) the reduction in surface area at the γ/ γ’ interfaces, ii) a reduction in the γ/ γ’ lattice

mismatch strain, and iii) a reduction in the modulus misfit [3]. Directional coarsening or rafting

involves a simultaneous disappearance of some γ channels and widening of others. The size of

the rafted γ +γ’ precipitates in thermally cycled sample (Fig. 7.1(c)) are more than a micron and

much larger than cuboidal precipitates observed in both as-cast and heat-treated samples.

Closer analysis on the microstructure of the thermally cycled sample was carried out

using a high-angle annular dark field scanning TEM (HAADF-STEM) technique. HAADF-

STEM micrographs reveal smaller cuboidal γ’ precipitates inside the γ channel (Fig. 7.3(a)). A

high magnification of the interface between the rafted γ’ structure and γ channel is shown in Fig.

7.3(b). The size of the cuboidal γ’ precipitates ranges from 10 nm near the γ/γ’ interfaces and

increases to 50 nm when located inside the γ channel. These cuboidal γ’ precipitates possibly

form when the sample was cooling to room temperature after thermal cycling. The cuboidal γ’

precipitates exhibit similar morphology compared to ones in as-cast and full heat-treated samples.

However, the size of the cuboidal γ’ precipitates in the thermally cycled sample, which are ~50

nm (Fig. 7.3(b)) are four times smaller than the 200 nm size precipitates observed in the as-cast,

and fully heat-treated samples (Fig. 7.1(a)).

131

7.3.2 Compositional Partitioning across, and Interfacial Segregation at, γ / γ’ Interfaces

Atom probe tomography (APT) has been used to characterize compositional partitioning

of the minor elements across the γ/γ’ interfaces. Fig. 7.4(a) shows 3DAP reconstruction of as-

cast sample delineated by using 12%Al isoconcentration surface (or isosurface in short) filled in

blue corresponding to Al–rich region of the γ’ precipitates and Cr-rich region in red

corresponding to the γ matrix. In Fig. 7.4(c), the γ’ precipitate interfaces have been delineated

using 12%Al isosurface, together with Ni atoms shown in green. Only fractions of γ’ precipitates

are shown due to a small reconstruction size. The composition profiles of the minor elements

across γ / γ’ interfaces have been shown as proximity histograms in Figs. 7.4(b) and (d) for as-

cast and heat-treated samples and will discussed in conjunction with the thermally cycled sample

presented in the following paragraph.

As mention earlier in 7.3.1, the thermally cycled sample revealed two different size scale

Fig. 7.3 a) A low magnification of HAADF-STEM micrograph of the thermally cycled sample capturing γ channel and rafted γ’ precipitate. b) A high magnification of the interface between the rafted γ +γ’ structure and γ channel showing cuboidal γ’ precipitates inside the γ channel.

a

200 nm

b

50 nm

132

of the γ’ precipitates: the rafted γ+γ’ structure and the small cuboidal located inside the γ channel.

Fig. 7.5(a) shows 3DAP reconstructions of rafted γ+ γ’ structure in thermally cycled sample. The

reconstructions was delineated by using 12 %Al isosurface. It is worth noting that a part of the

rafted structure was captured due to its large size scale compared to the size of the reconstruction,

which is 60x60x 120 nm3. Further, Fig. 7.5(b) shows APT reconstruction of 40x40x60 nm3 of the

small cuboidal γ’ precipitates in the thermally cycled sample delineated by using 12%Al

isosurface. The region of higher composition of 12%Al is filled in blue to show the γ’

precipitates. Three γ’ precipitates were captured in this reconstruction. The γ’ precipitates

captured in the reconstruction are small cuboidal morphology particles, rather that the rafted

structure since the width of the rafted γ’ structure is significantly larger and less likely to capture

the rafted structure in the APT reconstruction of 40x40x60 nm3.

The compositional analyses of the as-cast, heat-treated, and thermally cycled samples

across the γ/γ’ interfaces have been carried out. In Figs. 7.4(b) and (d) and Figs. 7.5(b) and (d),

the proximity histograms of minor elements clearly show that Ta partitions to the γ’ precipitates

while Mo partitions to the γ matrix. W does not appear to preferentially segregate to either γ or γ’

phases but exhibits a clear pile-up at the γ / γ’ interface. Re preferentially partitions to the γ

matrix. However, the evidence of Re enrichment close to the γ / γ’ interfaces is present in heat-

treated and rafted γ+ γ’ structure in thermally cycled samples. In thermally cycled sample, the

evidence of Re enrichment close to the γ / γ’ interfaces is observed only in the rafted γ’

precipitates while, in case of small cuboidal morphology, the Re enrichment near the γ / γ’

interfaces is no longer observed. Small cuboidal γ’ precipitates in neither thermally cycled nor

as-cast samples exhibited an enrichment of Re near the γ / γ’ interfaces. Other elements follow

133

similar elemental partitioning trends for rafted and cuboidal γ’ precipitates. The effect of

different matrix composition in thermal cycling due to the partitioning associated with the rafted

γ’ precipitates is insignificant.

Hf is likely to partition to the γ matrix in the as-cast sample while it tends to partition to

the γ’ phase in the heat-treated sample. In the thermally cycled sample, Hf does not appear to

preferentially partition to either the γ or γ’ phase. In a recent study it was found that the reversal

of partitioning behavior from partition to γ’ phase to γ matrix phase is possibly determined by the

alloy composition[4]. However, in this current study, we are studying only one alloy composition

with three different conditions. Thus, there are other possibilities of reversed partitioning of Hf;

further experiments and analyses will be conducted to understand the effect of reversed

partitioning of Hf. The γ/γ’ partitioning ratio, 𝐾𝐾𝑖𝑖𝛾𝛾′/𝛾𝛾of minor elements in all conditions, including

Re, W, Ta, Mo, and Hf, were calculated by ratio of steady state composition of γ’ phase to γ

phase and are summarized in Table 7.2. 𝐾𝐾𝑖𝑖𝛾𝛾′/𝛾𝛾> 1 implies that a given element partitions to the γ’

phase and 𝐾𝐾𝑖𝑖𝛾𝛾′/𝛾𝛾< 1 implies that a given element partitions to the γ phase.

134

Table 7.2. Partitioning ratio, 𝐾𝐾𝑖𝑖𝛾𝛾′/𝛾𝛾γ, from APT analyses for all heat treatment conditions

Partitioning

ratio, Kiγ’/γ

As-cast Full

heat-treated

Thermally cycled HT +

Long term

annealing Rafted γ’ Cuboidal γ ’

KHfγ’/γ 0.25 2.64 1 1 1.3

KReγ’/γ 0.067 0.083 0.12 0.058 0.08

KWγ’/γ 0.88 1.16 0.86 0.96 1.2

KTaγ’/γ 25 25 11.5 30 9.1

KMoγ’/γ 0.41 0.46 0.42 0.37 0.57

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Fig. 7.4 a) 3D-APT reconstruction of as-cast sample delineated using 12%Al isosurface. b) The proxigram plotted corresponding to isosurface in a) across γ/γ’ interface as a function of distance C) 3-D APT reconstruction of heat-treated sample using 12 at% Al isosurface. d) The proxigram corresponding to isosurface in c) of heat-treated sample.

136

Fig. 7.5 3D-APT reconstruction of a) rafted γ + γ’ structure and c) small cuboidal γ’ precipitates located in the γ channel, delineated using 12%Al isosurface. b) and d) The proxigram plotted corresponding to isosurface in a) and c) across γ/γ’ interface, respectively.

137

A significant excess of Re and W at the γ/γ’ interfaces in the heat-treated and thermally

cycled samples were shown by proxigrams in Figs 7.4(d) and 7.5(b). 2D contour map was

employed to visualize the enrichment of minor elements. Figs. 7.6(a) and (b) shows enrichment

of Re and W near the γ/γ’ interfaces in the thermally cycled sample. The 2D contour map of W

Fig. 7.6 2D contour plots of a) Re and b) W in the thermally cycled sample showing the enrichment near/at the γ/ γ’interface.

138

(Fig. 7.6(b) in the thermally cycled sample does not clearly show the enrichment of W at the

interface due to the insignificant composition difference between the γ/γ’ interface and the base.

This can be confirmed with a Gibbsian interfacial calculation. The interfacial excess of solute is

expressed as a number of atoms per unit area of interface. Measurements have been calculated on

linear (1D) profiles of composition across the interface. Pronounced peaks in the concentration

profiles in both W and Re correspond to solute pile-ups near the interface. The calculated values

of interfacial excess of Re and W (ΓRe and Γw) are summarized in Table 7.3. The results show that

both W and Re pile-up strongest under the heat-treated condition; these elements pile-up at 1.03

and 1.88 atoms nm-2, respectively. The calculated value of interfacial excess of Re in heat-treated

condition is in good agreement with the previous calculation[5]. Previous study showed the

interfacial excess of Re is 2.41 atoms nm-2 in a heat-treated condition of Rene N6. Higher

interfacial excess value of Re in Yoon’s study was possibly due to a higher Re concentration,

which is 6 wt% versus 3 wt% in Rene N5. It is worth noting that W and Re pile-up at different

places on the interface. While the pile-up of Re is associated with the migration of the γ/γ’

interface during cooling to room temperature[6], the pile-up of W at the boundary might

originate from atomic misfit.

Table 7.3. Gibbsian interfacial excess of W and Re in as-cast, heat-treated, and thermally cycle samples

Interfacial excess of solute

(atoms nm-2

)

As-cast Heat-treated Thermally cycled

W 0.75 1.03 0.99 Re 1.22 1.88 1.33

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Table 7.4 Composition and volume fraction of the γ’ precipitates in as-cast, heat-treated, and thermally cycled samples

Table 7.5 Composition of the γ matrix in as-cast, heat-treated, and thermally cycled samples

γ’ Composition (at%)

Sample As-cast Heat-treated

Thermally cycled Heat-treated + long term annealing Rafted

structure Cuboidal γ’

Cr 2.5 2.4 2.4 2.6 2.8

Co 5 5 5 5.3 5.6

Al 17.5 17 17.5 17 17.7

γ’ volume fraction

69.19% 77.63% 50.5%

γ Composition (at%)

Sample As-cast Heat-treated

Thermally cycled Heat-

treated + long term annealing

Rafted structure Cuboidal γ’

Cr 25 22 20.5 21 20.3 Co 16 15.5 14.2 14.7 16.3 Al 3.5 3.2 4.3 4 4.2

140

A comparison of the major alloying elements in all cases shows that the concentrations

Al, Cr, and Co in the γ’ and γ phases are consistent in as-cast, heat-treated and thermally cycled

cases as shown in Table 7.4 and 7.5, respectively. The volume fraction measurement was done

on several SEM micrographs by using Image JTM. While, the volume fraction of the γ’ phase in

as-cast and heat-treated samples are comparable, the volume fraction of the γ’ phase decrease

significantly in the thermally cycled sample (Table 7.4). The decrease in the volume fraction in

thermally cycled sample indicates that some of the γ’ precipitates are dissolved back into the

matrix during thermal cycling. These γ’ precipitates later re-precipitate inside the γ channel

during the last cooling after thermal cycling to room temperature. SEM micrograph (Fig.7.2(c)

could not capture these small, cuboidal precipitates. Thus, the volume fraction measurement

obtained from only SEM micrographs is less in thermally cycled sample compared to the volume

fraction of other conditions.

7.3.3 Effect of Kinetics on Elemental Enrichment near The γ/ γ’ Interfaces

Long-term annealing was carried out in order to understand the elemental enrichment at

and near the γ / γ’ interfaces; the elements were subjected to long-term annealing at 1650 ˚F for

100 hours after industrial full heat treatment. As discussed in earlier in 7.3.1, W exhibits a clear

pile-up at the γ / γ’ interfaces in as-cast, heat-treated and thermally cycled samples. Re exhibits a

significant enrichment near the interfaces in the γ phase in the heat-treated and thermally cycled

samples. Fig. 7.7(a) shows similar size of cuboidal γ’ precipitates compared to that of the

industrial heat treatment (Fig. 7.2(b)). It can be concluded that coarsening of the γ’ precipitates in

the long- term annealed sample is very sluggish when compared with the heat-treated sample.

141

Again, APT has been used to determine a composition profile across the γ / γ’ interfaces.

Fig. 7.7(b) displays an APT reconstruction of 60x60x160 nm3, delineated by using 12%Al

isosurface, that shows γ’ precipitates in blue and γ matrix in pink; this reconstruction captures

two γ’ precipitates and the γ channel in between them. The composition profile across the γ / γ’

interfaces is demonstrated in Fig. 7.7(c). When compared with the composition profile of the

industrial heat-treated sample, the composition profile of the long-term annealed sample reveals

that there is no enrichment of either W or Re at and near the interfaces. It can be concluded that

kinetic factors play an important role for the solute enrichment. Measurement of the partitioning

ratio 𝐾𝐾𝐾𝐾𝐾𝐾′/𝐾𝐾 from the APT analysis of long-term annealed sample after industrial heat treatment is

summarized in Table 7.2.

142

7.4 Summary and Conclusion

The present study investigates the effect of heat treatment on solute partitioning across

the γ / γ’ interfaces. The result of this investigation can be summarized as follows:

The morphological development of γ’ begins with arrays of cuboidal shapes, becomes

more cuboidal in shape, and ends with a rafted structure after subjected to full heat treatment and

thermal cycling. The thermally cycled sample shows that smaller cuboidal γ’ precipitates form

Fig. 7.7 a) SEM micrograph of γ and γ’ structure in long-term heat treatment at 1650 ˚F for 100 hr after industrial heat treatment b) APT reconstruction delineated by using 12%Al isosurface capturing two γ’ precipitates and the γ channel between them c) Composition profile across the γ / γ’ interfaces showing both γ and γ’ phases reach equilibrium stage.

a b

c

143

inside the γ channel along with the coarse or rafted γ’ structure. These cuboidal γ’ precipitates

likely form when the sample cools to room temperature after thermal cycling.

Extensive studies have been investigated on the solute enrichment at the γ / γ’ interfaces

in Ni-base superalloys. However, the enrichment of Re and W at the γ / γ’ interfaces comparison

in different thermal history was shown for the first time. 3DAP reconstruction showed that Re

preferentially partitions to the γ matrix and the evidence of Re enrichment close to the γ / γ’

interfaces only appeared in the heat-treated and thermally cycled samples. Hf partitions to γ

matrix in the as-cast sample as expected, tends to partition to γ’ phase in the heat-treated sample

(unexpected), and does not appear to preferentially partition to either γ or γ’ phase in the

thermally cycled sample. The highest amount of excess of both W and Re enrichment was found

in the heat-treated samples.

In the thermally cycled samples, the evidence of Re enrichment close to the γ / γ’

interfaces is observed only in the rafted γ’ precipitates. However, the Re enrichment near the γ /

γ’ interfaces is no longer observed in case of small cuboidal morphology similar to that observed

in the as-cast sample.

Long term annealing was carried out and the result reveals that the industrial heat

treatment on Rene N5 sample could not achieve the equilibrium state. Thus, the result reveals

that kinetic factors play an important role for the W and Re enrichment at the γ / γ’ interfaces.

144

7.5 References


[2] O'Hara KS, Ross EW (1992) Cast columnar grain hollow nickel base alloy articles and alloy and heat treatment for making

[3] Acharya M, Fuchs G (2004) The effect of long-term thermal exposures on the microstructure and properties of CMSX-10 single crystal Ni-base superalloys. Materials Science and Engineering: A 381

[4] Mottura A, Warnken N, Miller MK et al (2010) Atom probe tomography analysis of the distribution of rhenium in nickel alloys. Acta Materialia 58

[5] Yoon KE, Noebe RD, Hellman OC et al (2004) Dependence of interfacial excess on the threshold value of the isoconcentration surface. Surf Interface Anal 36

[6] Yoon KE, Isheim D, Noebe RD et al (2001) Nanoscale studies of the chemistry of a René N6 superalloy. Interface Science 9

145

CHAPTER 8

FUTURE AND CONCLUSION

This dissertation focused on an insight of gamma prime precipitation mechanisms and

solute partitioning in Ni-base alloys. The studies covered various types of solid-state

transformation such as homogeneous and heterogeneous transformations, classical and non-

classical nucleation mechanisms. Solute partitioning across the γ/ γ’ interface were investigated

in model Ni-Al-Cr and Ni-Al-Co alloys as well as a commercially used single crystal Rene N5

superalloy.

The first contribution of the dissertation studied on influence of composition on γ’

particle size distribution. Precipitation of the slow-cooled Ni-8Al-8Cr and Ni-10-Al-10Cr alloys

was achieved by nucleation and growth process. Effect of Al and Cr additions on γ’ precipitate

size distribution during continuous cooling were investigated in this study. Addition of 2 at% of

Al and Cr from Ni-8Al-8Cr to Ni-10-10Cr alloys led to multimodal size distribution of the γ’

precipitates. In Ni-10Al-10Cr, the primary γ’ occurs at higher temperatures near the γ’ solvus

temperature These primary γ’ precipitates grow rapidly due to the fast diffusion rates, thereby

reduce the average supersaturation of the γ matrix, only local equilibrium is established between

the γ and γ’ compositions across the interface. The far-field γ composition still retains a super-

saturation of Al and an under-saturation of Cr, leading to sufficient driving force for a second

nucleation burst at lower temperatures. On the other hand, Ni-8Al-8Cr has substantially lower γ’

solvus temperature than that of Ni-10Al-10Cr alloy. The primary γ’ precipitates took place at a

much lower temperature. Nucleation took place over a wider temperature window, leading to a

larger number density of highly refined γ’ precipitates. The shorter inter-precipitates distances

and slower kinetics prevent any second nucleation burst in this alloy. The equilibrium volume

146

fraction of γ’, coupled with the γ’ solvus temperature has a strong influence on the number of γ’

nucleation bursts observed during continuous cooling, as well as the temperatures at which these

occur.

While classical nucleation and growth process dominated in the slow-cooled Ni-8Al-8Cr

alloy, rapid quenching of the same sample led to the non-classical nucleation where congruent

ordering process preceded the phase separation. Diffuse peaks corresponded to the ordered phase

of L12 structure was found in synchrotron-base high-energy x-ray diffraction. Compositional

analyses from proxigram and LBM methods did not exhibit any significant compositional

deviation from a random solid solution. While XRD revealed diffuse superlattice peak attributed

to the γ’ phase, selected area diffraction (SAD) pattern showed no superlattice spots which

correspond to the γ’ phase. This was possibly due to weak ordering of the ordered domains.

During the early stages of annealing at 600 °C, Both TEM and XRD revealed the γ’ phase.

HAADF-STEM micrograph, exhibited an interconnected nature, which is characteristic of a

spinodally-decomposed structure. Al content in the γ’ domains, at the early stages of annealing at

600°C, is substantially below the equilibrium composition in the long term annealed samples at

the same temperature. With increasing annealing time, the size and the volume fraction of the γ’

precipitates increased along with an increase in their Al content, and at later stages of annealing

(256 hr) γ’ composition approached equilibrium composition.

Besides homogeneous nucleation, the mechanism of heterogeneous γ’ precipitation

involving a discontinuous precipitation mechanism, as a function of temperature, was the

primary focus of study in case of the Ni-Al-Co alloy. Depending on the decomposition

temperature, or undercooling, the γ’ phase in Ni-Al-Co alloys can precipitate homogeneously,

via a discontinuous precipitation mechanism, or a combination of both, within the γ matrix. This

147

study coupled with scanning electron microscopy (including electron backscatter diffraction),

transmission electron microscopy, and three dimensional atom probe microscopy. At higher

annealing temperatures (~800°C), both homogeneous and discontinuous mechanisms appear to

be competitive with discontinuous precipitation confined to a narrow region adjacent to the grain

boundaries, while the grain interiors decompose via homogeneous precipitation. Contrastingly, at

lower annealing temperatures (~600°C), discontinuous precipitation is the predominant

precipitation mechanism, both along grain boundaries as well as in the grain interiors,

comprising straight coherent γ’ lamellae within the γ matrix. Furthermore, on long term

annealing at lower temperatures (~600°C), the discontinuous lamellar γ+γ’ product appears to

coarsen only at high angle grain boundaries. Such coarsening is not observed at special low

energy boundaries such as twin and other CSL boundaries.

In the last chapter, the dissertation extended the study of the γ’ precipitation mechanism

and solute partitioning to a real life Ni-base superalloy. Commercially used single crystal Rene

N5 superalloy was investigated as a function of heat treatment. The primary focus of this study

was to understand solute partitioning and enrichment of minor refractory elements, such as Re

and W, across/at the γ/ γ’ interfaces as a function of heat treatment. The morphological

development of γ’ begins with arrays of cuboidal shapes, becomes more cuboidal in shape, and

ends with a rafted structure after subjected to full heat treatment and thermal cycling. The

thermally cycled sample shows that smaller cuboidal γ’ precipitates form inside the γ channel

along with the coarse or rafted γ’ structure. These cuboidal γ’ precipitates likely form when the

sample cools to room temperature after thermal cycling. 3DAP technique was carried out to

characterize compositional partitioning and enrichment of the minor elements across the γ/γ’

interfaces. The enrichment of Re and W at the γ / γ’ interfaces comparison in different thermal

148

history was shown for the first time. 3DAP reconstruction showed that Re preferentially

partitions to the γ matrix and the evidence of Re enrichment close to the γ / γ’ interfaces only

appeared in the heat-treated and rafted structure in thermally cycled samples. Interestingly, Hf

partitions to γ matrix in the as-cast sample as expected, tends to partition to γ’ phase in the heat-

treated sample (unexpected), and does not appear to preferentially partition to either γ or γ’ phase

in the thermally cycled sample. The highest amount of excess of both W and Re enrichment was

found in the heat-treated samples. Long term annealing was carried out and the result reveals that

the industrial heat treatment on Rene N5 sample could not achieve the equilibrium state. It can

be concluded that kinetic factors play an important role for the W and Re enrichment at the γ/γ’

interfaces.

This dissertation mainly focused on the γ’ precipitation mechanisms and solute

partitioning in Ni-base alloys. Future works based on these studies can be extended further as

follow:

i) Investigation of nucleation burst temperatures of multimodal γ’ particle size

distribution by synchrotron-base high energy XRD technique.

ii) Further investigation on effect of composition on particle size distribution by

adding other alloy compositions in order to see the particle size trend.

iii) Site preference determination of Cr and Co in ternary Ni-Al-Cr and Ni-Al-Co

alloys, and combination of Cr and Co in quaternary Ni-Al-Cr-Co alloy. This

study can be achieved with the advantage of plane-by-plane analysis in 3DAP

technique and synchrotron-base high energy XRD.

149

iv) Site-specific APT on reaction fronts of discontinuous precipitation on low and

high temperature annealing to understand a compositional variation across these

interfaces.

v) Understanding effect of thermal cycling temperature on commercially used

single crystal Rene N5 superalloy on solute partitioning across the γ/ γ’

interface.

vi) Understanding the effect of Re addition on solute partitioning across the γ/ γ’

interfaces.

150

APPENDIX

BINOMIAL DISTRIBUTION AND LANGER-BAR-ON-MILLER METHOD

151

A.1 Binomial Distribution [1]

The binomial analysis is a grid-base frequency distribution technique. This technique is

employed by using a constant number of atoms in each bin. The frequency plot is constructed by

taking average composition of atoms of a particular element occur in each bin and compare with

a theoretical distribution which is expected for random distribution in the dataset. A theoretical

random distribution can be defined by the binomial probability distribution, Pb.

𝑓𝑓𝑏𝑏(𝑛𝑛) = 𝑁𝑁𝑃𝑃𝑏𝑏(𝑛𝑛) = 𝑁𝑁 𝑛𝑛𝑏𝑏!𝑛𝑛!(𝑛𝑛𝑏𝑏−𝑛𝑛)!

𝑋𝑋𝐴𝐴𝑛𝑛(1 − 𝑋𝑋𝐴𝐴)(𝑛𝑛𝑏𝑏−𝑛𝑛),

where a dataset which a fraction of A is XA. The reconstruction is divided into N bins in

total and 𝑓𝑓𝑏𝑏(𝑛𝑛) is an expected number of bins for a whole dataset where each bin contains n

atoms of element A. This technique assumes that all atoms of a given element in dataset are

taken from a single population.

For rapidly quenched and annealed of Ni-Al-Cr alloys, each 3DAP reconstruction dataset

was divided to several 100 atoms bins and the composition of these bins for one specific

constituent (Al was chosen in this case) was plotted with respect to the number of bins for that

particular composition.

A.2 Langer-Bar-on-Miller Models

A Langer-Bar-on-Miller technique was developed to fit the spinodal decomposition

mechanism. The computational method is based on the two-point distribution function, which

results to closure of the hierarchy of equations of motion for the high-order correlation functions.

This technique is proved to be accurate throughout the regions where the spinodal decomposition

takes place including the boundary regions where spinodal decomposition is difficult to

distinguish from the nucleation and growth process.

152

The spinodal decomposition theory was first developed by Hillert [2], Cahn [3,4] and

Hilliard [5] and cook [6] . The pioneer work by Hillert [1] was predicted a spinodal theory by

numerical investigation of a nonlinear, one–dimensional model. Later, Cahn [3,4] was developed

a more general linearized theory of the spinodal instability. Cook further added a role of thermal

fluctuation within a linear approximation. Further development of the spinodal theory was done

by Cahn by including nonlinear effects to determine the nature of the spinodal instability and

limit the growth. Langer, Bar-on, and Miller [7] developed a new technique by using a mean-

filed approximation. This technique is limited to very early stages of spinodal decomposition.

The authors proved that the technique would accurately predict to be used in an experiment.

A binomial distribution assumes that atoms of a given element are taken from a single

population. However, a Langer-Bar-on-Miller technique instead supposes that there are two-

phase mixtures in the dataset and the frequency distribution of a particular element can be

described as the sum of two displaced Gaussians:

𝑃𝑃(𝑐𝑐) = 𝑎𝑎1

𝜎𝜎1√2𝜋𝜋exp�−

(𝑐𝑐 − 𝜇𝜇1)2

2𝜎𝜎12� +

𝑎𝑎2𝜎𝜎2√2𝜋𝜋

exp�−(𝑐𝑐 − 𝜇𝜇2)2

2𝜎𝜎22�

The LBM equation is described by two Gaussian distribution functions of equal width,

centered at concentrations, μ1 and μ2, weighted by a1 and a2, respectively. The composition

amplitude, ΔC, is given by μ2 - μ1.

References:

[1] Gault B, Moody MP, Cairney JM, Ringer SP (2012) Atom Probe Microscopy, Springer

[2] Hillert M, (1961) A solid-solution model for inhomogeneous systems, Acta metallurgica. 9 525

153

[3] Cahn JW (1961) On spinodal decomposition, Acta metallurgica. 9 795-801.

[4] Cahn JW (1962) On spinodal decomposition in cubic crystals, Acta Metallurgica. 10 179-183.

[5] Hilliard J (1970) Phase transformations, American Society for Metals, Metals Park, Ohio 497.

[6] Cook H (1970) Brownian motion in spinodal decomposition, Acta Metallurgica. 18 297-306.

[7] Langer JS, Bar-on M, Miller HD (1975) New computational method in the theory of spinodal decomposition, Phys. Rev. A. 11 1417–1429.

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