Assignment in Physical Metallurgy

Theme : Metallic Glasses

Department of Mechanical Engineering

University of Thessaly

January 2016

Professor : Gregory Haidemenopoulos

Student : Kleanthis-Konstantinos Karagiannis

1

ABSTRACT

The recent research in the field of materials science aims in discovery of new “hyper-

materials”. This kind of materials would combine various desirable properties like

toughness, high yield stress, corrosion and wear resistance and others. One

quintessential material is the metallic glass, which can be stronger and harder than

conventional metals and this is the reason why so much research is transacted

nowadays throughout the modern built world. So the purpose of this study is to

show the unique properties of metallic glasses and by the same time to clarify how

diffusion and other significant metallurgical characteristics are responsible for these.

Specifically, the aspects explored are the processes for producing metallic glasses,

their microstructure and thermodynamics and kinetics behind one major

transformation, crystal to glass. In contrast with the various advantages mentioned

two factors limitate the “glory” of metallic glasses, the great precised-techniques

needed for their production and brittleness which makes them vulnerable towards

cyclic fatigue.

keywords

Bulk metallic glass I diffusion І amorphous І glass transition temperature Tg

2

CONTENTS

Introduction

Literature review

Discussion

Conclusions

References

3

INTRODUCTION

Since 1960, when metallic glasses were first established by Caltech University, many scientists have tried to explain their unique mechanical properties. So far research was mainly focused on crystalline metals, but now this material displays an amorphous microstructure. This characteristic adds two additional factors that have to be seriously concerned, absence of long-range order and grain boundaries. Such specifics were only encountered in liquids and gasses, so scientists first looked for similarities with metallic glasses. For example diffusion in metallic glasses has to do with thermally activated, highly collective atomic processes and this has to be taken into concern before producing or using such materials. As far as the production many processes have been tried such as quenching from the liquid state, e.g., by melt spinning or splat quenching, or being produced by vapor condensation and sputter deposition. Other techniques for production of amorphous solids are solid-state reaction, ion implantation, neutron irradiation, ball milling and high-pressure application. The success of these preparation methods depends on the thermodynamic and kinetic aspects of the crystal to glass transformation, and the investigation of these aspects is the main concern of this study.

4

LITERATURE REVIEW

Duwez and co-workers (Clement et al., 1960) were the first to produce a metallic

glass. They reported glass formation by rapid cooling of an Au-Si alloy melt. Duwez’s

group proved that the process of nucleation and growth of crystalline phases could

be kinetically bypassed in certain alloy melts, so a frozen liquid was produced. The

history of bulk metallic glasses probably started with the work of Chen (1974), at Bell

Laboratories, who succeeded in forming millimeter-diameter rods of ternary Pd-Cu-

Si alloys by suction casting methods at cooling rates of about 103 K/s. In the early

1980s, Turnbull and co-workers (Drehmann et al., 1982; Kui et al., 1984) carried out

experiments on Pd-Ni-P alloy melts and were able to demonstrate that these alloys

form bulk-metallic-glass ingots of centimeter size at cooling rates of only 10 K/s.

Around 1990 the field of bulk metallic glasses developed rapidly when Inoue and co-

workers in Sendai succeeded in producing amorphous aluminum alloys. They found

exceptional glass-forming ability in rare-earth-rich alloys such as La-Al-Ni and La-Al-

Cu (Inoue et al., 1990). Glassy rods and bars with casting thicknesses of several

millimeters were obtained. Studying similar quaternary and quinary alloys, the Inoue

group developed alloys (e.g., La-Al-Cu-Ni) that form glasses at cooling rates lower

than 100 K/s and critical casting thicknesses up to 1 cm (Inoue et al., 1992). A similar

family of Mgbased alloys (e.g., Mg-Y-Cu, Mg-Y-Ni; Inoue, 1995) and a family of Zr

based alloys (e.g., Zr-Cu-Ni-Al; Inoue et al., 1990b) were also developed.

Before procceding to the main part of the study it is crucial to define two

characteristic temperatures. The first is the fictive temperature, which is the

temperature where the extrapolations of the supercooled melt and glass lines

intersect in a diagram of volume or enthalpy-versus-temperature for a glass forming

alloy. The second is the glass transition temperature, in which a supercooled melt

transforms to glass.

5

DISCUSSION

A first glance of some thermodynamic and kinetic aspects of crystal to glass

transformation would be very useful. Whenever the glass-forming conditions come

into consideration two diagrams can provide a clear view of the phenomenon,

enthalpy and volume-versus-temperature. In this study an enthalpy-versus-

temperature is used as showed in Fig. 1. At first we point out the melting

temperature Tm above of which the whole material is melt. By decrease of

temperature the crystal line begins and that means the onset of nucleation of the

crystalline phase.

Fig. 1. Enthalpy-versus-temperature diagram of a glass-forming material.

Exactly below the Tm one envisage a sudden decrease of enthalpy to a typical value

for crystals and by further cooling enthalpy takes an even smaller value. By

increasing the cooling rate the nucleus formation is avoided and the melted

structure remains. Further increase does not affect the value of enthalpy, while the

material is in metastable configurational equilibrium, until the deviation of the

current condition and onset of a line of gradually decreasing slope. By the same time

a massive increase of viscosity of about 15 orders of magnitude occurs until a critical

point is reached where viscosity no longer depends on temperature. At this point the

previous melted material transforms to a rigid glass. According to Fig. 1 the

temperature region which matches between the enthalpies of the equilibrated liquid

and the glass is called glass transformation region.

6

Both metallic glasses and their supercooled melts are metastable and this is proved

by two factors, they can attain crystal structure and then one or more crystal phases

are formed and additionally their properties have a strong influence from their

thermal history. The second fact has to do with structural relaxation, a type of

physical aging, which for example may change the properties of a glass when it is

reheated in glass transformation range. In order to explain structural relaxation it

would be very useful to introduce another diagram, Fig. 2.

Fig.2. Volume-versus-temperature diagram of a glass forming material.

One could envisage an alteration in volume by causing a specific treatment to a

metallic glass. For example, if a fast-cooled glass is reheated to a temperature

between the glass transformation range, but below the fictive temperature, then its

new structure would be analogous to this new temperature. At this example a

reduction in volume is achieved and the difference of volume is usually called excess

volume. Also a slight change in density could be observed. Although, this can play an

important role in the mechanical properties of a metallic glass. So it is crucial to

know the so-called thermal history of the glass before using it, which is the way it

was produced.

Subsequently, a deepening in metallic glass formation will be achieved by

investigating nucleation and growth of crystal state in a crystalline diffusion couple.

7

A physical mixture of these two metals has a free energy given by the dotted line in

Fig.3.

Fig. 3. Free energy diagram for the

Au-La system at 300 K.

It is obvious that free energy decreases by the formation of glass from the

crystalline metals over a range of composition. The dashed lines represent the

common tangent of the final solutions with the amorphous phase and separate

Au-amorphous from La-amorphous fields for metastable equilibrium of

amorphous alloy with the metals. Circled crosses give give free energy of

intermetallic compounds. Open circles indicate compositions where a single

phase product yields. And left filled (right filled) circles represent multilayers in

which Au (La) metal remained in metastable equilibrium with the amorphous

product. By the same time a different experiment was conducted and similar

phenomena in Ni-Zr binary alloy. In contrast with previous alloy, now

formation of a planar layer of the intermetallic compound ZrNi occurred after

reaction of the couple for 12 hours. The nucleation and growth of this

compound separates the amorphous layer from the remaining Zr metal layer.

Also the contact between the amorphous layer and Ni is reduced by voids, that

are connected to Kirkendall effect. More specifically, growth of the amorphous

layer is accompanied by gradual formation of the above mentioned Kirkendall

voids, at the interface between Ni and the amorphous interlayer. Further

differences of these two alloy systems are envisaged through comparison

between their free energy diagrams. Fig. 4 depicts the excess free energy of

mixing of the Ni-Zr system at a temperature of 550 K, where metallic glasses

form and grow in thin film diffusion couples.

8

Fig. 4. Free energy diagram for the binary Ni-Zr system at 550 K.

As before the six intermetallic compounds, in respect with the equilibrium phase

diagram, are marked as crosses. In contrast to the Au-La diagram, all solid solution

phases have a negative free energy of mixing, which means that these phases can

form spontaneously. Due to this characteristic the ability of spontaneous alloying to

a solution with free energy above that of glass, while solution composition lays

outside the To lines that define the thermodynamic limits of homogenous metastable

crystalline phases, is possible. So a metastable crystalline solution is formed by

normal downhill thermal diffusion. But in the Au-La system the above described

situation can occur only inside the respective To(C) lines. As a result, a glassy

interlayer phase can be formed in two ways. At first, spontaneous dissolution of the

Ni in hcp-Zr or Zr in fcc-Ni is possible in very dilute concentrations which lie with the

respective To lines. The transform of the solutions to glass can be achieved either bi

heterogeneous nucleation of the glass at a preferred location in the diffusion couple

or by destabilization and catastrophic vitrification. On the other hand, in the Au-La

case the glass phase must form by nucleation at the original Au-La interface or at

some other preferred place. For further explanation the above phenomena will be

examined by kinetic aspects. It has been demonstrated that during the form of the

glass interlayer no presence of intermetallic compounds was observed, but no logical

explanation could be given by thermodynamic aspect. A good assumption would be

that forming of a critical nucleus is restricted due to the absence of mobility of one

of the atomic species. Another restriction would be the absence of a potentially low

energy or coherent interface between the intermetallic compound crystal and the

parent metals of the diffusion couple. This “kinetic barrier” is enhanced by the fact

that the successive atomic rearrangements needed for growth of an intermetallic

compound requires many correlated atomic jumps and as a result glass growth is

9

preferred. In order to model the kinetics behind the growth of a glassy interlayer a

set of phenomenological macroscopic equations can be used. For one-dimensional

amorphous interlayer growth the following set of coupled differential equations

would provide critical answers.

𝜕𝐶

𝜕𝑡= �̃�

𝜕2𝐶

𝜕𝑋2

𝐷 ̃𝜕𝐶

𝜕𝑋 = (1 − 𝐶1)

𝑑𝑋1

𝑑𝑡

−�̃� 𝜕𝐶

𝜕𝑋 = C2

𝑑𝑋2

𝑑𝑡

𝑑𝑋2

𝑑𝑡= 𝑓2(𝐶2 − 𝐶2

ₒ ≈ 𝜅2(𝐶2 − 𝐶2ₒ) + ⋯

𝑑𝑋1

𝑑𝑡= 𝑓1(𝐶1 − 𝐶1

ₒ ≈ 𝜅1(𝐶1 − 𝐶1ₒ) + ⋯

�̃� = the metal interdiffusion constant in the amorphous phase

C = C(X) = the concentration profile of metal no. 1 in the amorphous phase

𝐶1ₒ(𝐶2

ₒ) = the concentration of metal no. 1 (no. 2) in the amorphous phase which gives

equilibrium with “pure” metal no. 1 (no. 2)

X1(X2) = position of the interface separating the amorphous interlayer from metal no.

1 (no. 2)

C1(C2) = C(X1) (C(X2))

κ1(κ2) = kinetic response parameter for interface no. 1 (no. 2)

The metal interdiffusion constant �̃� was taken to be independent of composition of

the amorphous alloy. The parameters κ1 and κ2 are linear response parameters

which couple the interface motion to the degree of chemical non-equilibrium at the

interfaces. They have the dimensions of velocity. The first equation is the Fick

diffusion law in the amorphous interlayer, the two following equations are continuity

equations for fluxes at the interfaces and the two latest couple the concentration

profile to the moving interfaces. The above set of equations has been solved by

numerical methods and some interesting conclusions have been extracted. For long

times (𝑡 → ∞) the solution is

X2 = -�̃�/κ2 + √2𝑎�̃�𝑡 + …

where a is a constant in order of unity. So, this predicts a “shifted 𝑡1

2 “ law and this is

called interface-limited growth. At short times (t→0) the solution is

X1

X2

10

X2 = constant κ2t + …

At this instance growth of the amorphous interlayer is linear in time with rate

proportional to κ2 and this is referred to a diffusion-limited growth. At last the

relation of �̃� and temperature has to be taken into consideration. After studying the

growth of the amorphous interlayer in the binary Ni-Hf system the collected data

were fitted to the above solutions. So, estimates for �̃� can be made as shown in Fig.

5 below.

Fig.5. Arrhenius plot of intediffusion

constant vs. T-1 for interdiffusion of Ni

and Hf in a growing amorphous

interlayer.

As far as the diffusion a differentiation must be made between conventional and

bulk metallic glasses.

Conventional metallic glasses

The below data take into consideration structural relaxation, because it can induce

changes in the final results.

Fig. 6. Diffusion profiles of Fe in as-quenched

Fe40Ni40B20 after various annealing times.

11

In the above diagram each sample is showed by a curvature with the information of

the annealing time. The straight line prove the thin-film solution (Gaussian solution)

for Fick’s second law

c(x,t) = 𝑆˳

√𝜋𝐷𝑡exp (−

𝑥2

4𝐷𝑡)

Probably, diffusion coefficients have a relation with time, because in different way

the profiles would be the same and Fig. 7 provides persuasive evidence.

Fig. 7. Time-averaged diffusivities as functions of the annealing time.

Obviously one could expect a decrease in diffusivity of a fast-quenched glass after

annealing at a temperature below the fictive temperature of the as-quenched glass,

because then volume is derated and so the structure is more dense. By adding the

concept of quasivacancies, which cause the excess volume and are mentioned as

localized defects that are stable over several jumps, a could explanation could be

given. It is known that in crystalline metals vacancies are necessary for self-diffusion,

but in as-quenched amorphous alloys the so-called quasivacancies anneal out when

they become mobile. So a decrease in the diffusivities is expected, until they reach

their relaxes-state values.

Bulk metallic glasses

Discovery of bulk metallic glasses opened the field of investigation for diffusion in

metallic glasses and their supercooled melts. Bulk metallic glasses offer the ability of

annealing for some time in the supercooled liquid state, beacause their

crystallization temperature Tx exists above Tg, while conventional glasses undergo

crystallization before the glass-transition temperature is reached. One widenly used

12

bulk metallic glass is the five-component alloy Zr46,75Ti8,25Cu7,5Ni10Be27,5 , known as

Vitreloy 4. The utility of this material lays in the fact that no sign of decomposition is

envisaged in the temperature range of glass transition, while other bulk metallic

glasses undergo spinodal decomposition into two amorphous phases. For example

Vitreloy 1 decomposes around 623 K within a few hours. In contrast, Vitreloy 4 lies

outside the miscibility gap. Additionally, many bulk metallic glasses exhibit a

“nonlinear” Arrhenius behavior. For example, the diffusivity in the glassy state is

higher than that predicted by a normal Arrhenius behavior, due to the fact that the

effective activation enthalpy and preexponential factor above the glass-

transformation temperature Tg are higher than below Tg. More research on Vitreloy

4 has proved that the diffusion times at low temperatures were too short in order to

catch the metastable state of the supercooled liquid at these temperatures, as

shown in Fig. 8.

Fig. 8. Time-

Temperature-

Transformation

diagram of

Vitreloy 4.

During every diffusional annealing depicted, crystallization was avoided and for further explanation open symbols correspond to annealing parameters that led to diffusivities below Tg, related to glassy state, while solid symbols and crosses are connected with conditions above the transition temperature, related to supercooled liquid state.

Preparation of metallic glasses

After having clarified the basic concept behind nucleation a growth in metallic glasses it would be understandable to analyze the preparation of them. Various methods have been developed for the preparation of conventional amorphous metals. They can be quenched from the liquid state, e.g., by melt spinning or splat quenching, and can be produced by vapor condensation and sputter deposition. Moreover, it is possible to transform crystalline solids into the amorphous state by

13

solid-state reaction, ion implantation, neutron irradiation, ball milling, high-pressure application, and other techniques. Melt spinning Melt spinning is one method of rapidly solidifying liquid metals to produce either

amorphous or microcrystalline microstructures, depending on such variables as melt

composition and cooling rate. A radio-frequency induction coil is used to heat the

metal in a crucible. When molten the alloy is ejected through either a single hole or a

row of holes onto a rotating brass wheel. The solid metal produced is spun in the

form of a ribbon.

Fig. 9. Melt spinning

Melt temperature : 350°-

400°C

Estimated cooling rate : 105-

106 Ks-1

Of course, before proceeding to the above procedure one must take the TTT diagram

for glass-forming alloys into consideration.

Fig. 10. Time-

temperature-

transformation

diagram for glass-

forming alloys.

14

In fact, the big rate of cooling achieved by melt spinning allows the glass

transformation, as the crystallization “nose” is avoided. In case of bulk metallic

glasses, additional components play the role of stabilizers for the glassy phase,

because the existence shift the crystallization “nose” and glass formation can be

achieved by smaller cooling rates.

Ball milling

The process of ball milling is illustrated in Fig. 11. Powders are placed together with

hardened steel or WC balls in a sealed container which is shaken or violently

agitated. The powders are severely deformed, fractured and mutually cold welded

during collisions of the balls. The successive deformation and welding of grain leads

to a progressively refined lamellar type of domain structure when two elemental

metal powders are mechanically alloyed.

Fig. 11. Illustration of the process of

high energy ball-milling of a mixture

of two metal powders.

The process of amorphization by alloying of elemental powders leads to an ultrafine

composite in which a solid-state amorphizing reaction takes place. High dislocation

densities produced by sever deformation enhance atomic mobility in the interfacial

regions of the two metals. Together with the deformation itself and the expected

local temperature rises during collision events sufficient diffusion is permitted and

allows the amorphizing reaction to occur in the solid-state. The driving force in this

explanation is composition-induced destabilization of the crystalline solutions.

Rapid discharge forming

The heat of the material above the Tg temperature happens through ohmic heating,

while a short and intense pulse of electrical current is fired and delivers an energy

surpassing 1,000 joules in about 1 milisecond, about one megawatt of power. Now

the heated rod of the metallic glass can be injected into a mold and cooled with the

whole procedure lasting a few milliseconds. Despite being formed in open air the

molded rod is free of flow defects and oxidation. Thanks to this method metallic

15

glasses can be studied in their molten state and the crystallization process can be

examined on millisecond time scales.

Fig. 12. The metallic-glass rod

before heating and shaping (left),

the molded part (middle), the

final part trimmed of excess

material (right).

At last, little information can be given about the mechanical properties of metallic

glasses, but this is not the main purpose of this study. Superior strength and

hardness, and excellent corrosion and wear resistance, combined with their general

inability to undergo homogeneous plastic deformation are the main advantages that

are closely related to the above described phenomena. In contrast, the lack of

defects in the microstructure of metallic glasses makes them brittle and as result

they are weak against fatigue.

Fig. 13. Typical strengths and elastic limits for various materials.

16

CONCLUSIONS

Amorphous metallic alloys, also termed metallic glasses, are the paradigm of dense random packing. Conventional metallic glasses are very prone to crystallization and do not lend themselves for diffusion studies above the glass transition temperature. With the discovery of novel bulk-glass-forming alloys, diffusion in metallic systems can now be investigated from the glassy state up to the equilibrium melt. This is of considerable interest not only from the technological point of view but also in terms of fundamental science, particularly in connection with the glass transition. The construction of free energy diagrams that describe the variation of the enthalpy and Gibbs free energy of the crystalline phase in non-equilibrium states added essential thermodynamic evidence throughout the study. In all of the examples discussed, the concepts of a To and a Tm line play a key role in allowing one to determine when the crystalline phase becomes metastable in respect to a glass transformation. Also, a quick reference in the production methods of metallic glasses proved that progress in theoretical studies has great impact on practical issues. Besides, the main purpose of tis study, which has to do with thermodynamic and kinetic aspects, little information were given about mechanical properties of metallic glasses.

17

REFERENCES

G. N. Haidemenopoulos, (2000), Physical Metallurgy, Publications of University of

Thessaly

William L. Johnson, Thermodynamic and kinetic aspects of the crystal to glass

transformation in metallic materials, (1986)

Franz Faupel & Werner Frank et al., Diffusion in metallic glasses and supercooled

melts, REVIEWS OF MODERN PHYSICS, VOLUME 75, JANUARY 2003

A. Inoue, X.M. Wang and W. Zhang, Developments and applications of bulk metallic glasses, February 28, (2008) Michael Miller & Peter Liaw, (2008), Bulk metallic glasses, Springer publications K. L. Ngai, (2011), Relaxation and diffusion in complex systems, Springer publications Paul Heitjans & J�̈�rg K�̈�rger, (1998), Diffusion in condensed matter, Springer publications Helmut Mehrer, (2007), Diffusion in solids, Springer publications D. B. Miracle, A structural model for metallic glasses, Nat. Mater. 3(10), (2004) Phys.org , last access in 12/01/16