Thermo-Calc Software

Thermo-Calc Software

Computational Tool for Precipitation Simulation in Multicomponent Alloys

www.thermocalc.com

Multicomponent Alloys

TC-PRISMA 2.0


TC-PRISMA A general computational tool for simulating kinetics of

diffusion controlled multi-particle precipitation process in multi-

component and multi-phase alloy systems. TC-PRISMA is based on

Langer-Schwartz theory [1], and it adopts Kampmann-Wagner

numerical (KWN) method [2] to compute the concurrent nucleation,

growth, and coarsening of dispersed phase(s).

[1] Langer J, Schwartz A. Phys. Rev. A 1980;21:948-958.

[2] Wagner R, Kampmann R. Homogeneous Second Phase Precipitation. In: Haasen

P, editor. Materials Science and Technology: A Comprehensive Treatment. Weinheim:

Wiley-VCH, 1991. p. 213.



New functionalities introduced for TC-Prisma 2.0:

Handling of non-isothermal conditions.

Post-processing of multimodal distribution

Estimation of interfacial energies.


primary γγγγ’(1.2-1.5µµµµm)

tertiary γ’ (10-20nm)

secondary γ’ (110-200nm)

γ/γγ/γγ/γγ/γ’ Microstructure in Heat Treated IN100

(1.2-1.5µµµµm)

• Non-Isothermal 3-Step Heat Treatment

H.-J. Jou, P. Voorhees, G.B. Olson, Superalloy 2004, pp.877-886.


γ/γγ/γγ/γγ/γ’ Microstructure in U720 Li

• Continuous cooling at 0.0167 K/s

R. Radis et al., Acta Materialia, 57(2009)5739-5747

Thermo-Calc SoftwareNi-12 at%Al


Cooling rate: 6.5E-6 K/s

primary

secondary

overall

Size Distribution Mean Radius

tertiary



Composition Pathway Thermodynamic driving force



Nucleation rateThermodynamic driving force


Cooling rates: 6.5E-4, 6.5E-2, 6.5 K/s

Composition Pathway Thermodynamic driving force


Cooling rates: 6.5E-4, 6.5E-2, 6.5 K/s



Size Distribution

Thermo-Calc SoftwareNi-8Al-8Cr and Ni-10Al-10Cr


Exp


Vertical Section Ni-xAl-xCr Thermodynamic driving force



Thermo-Calc SoftwareU720Li

Precipitation Kinetics during Continuous Cooling

wt.% 1* 2**

Al 2.53 2.46

B 0.014

C 0.014 0.025

Co 14.43 14.75

Cr 15.92 16.35

γ′γ′γ′γ′ γγγγ

Databases: TTNI8+MOBNI1

* Radis et al., Superalloys 2008 ** Mao et al., Metall. Mater. Trans. A, 32A(10) 2441(2001)

Cr 15.92 16.35

Fe 0.09 0.06

Mo 2.96 3.02

Ti 4.96 4.99

W 1.26 1.3

Zr 0.035

Ni Bal Bal

Thermo-Calc SoftwareU720Li : Cooling Rate Effect

Size Distribution

Siz

e D

istr

ibut

ion

(1/m

4 )

1e+27

1e+28

1e+29

1e+30

1e+31

1e+32

1e+33

1e+34

Par

ticle

Siz

e (n

m)

1000

Mean Particle Size

Particle Radius (nm)

0.1 1 10 100

Siz

e D

istr

ibut

ion

(1/m

1e+18

1e+19

1e+20

1e+21

1e+22

1e+23

1e+24

1e+25

1e+26

1e+27

78 oC/s1.625 oC/s0.217 oC/s

Cooling Rate ( oC/s)

0.1 1 10 100 1000

Par

ticle

Siz

e (n

m)

10

100

Mao et al. Radis et al.

Regression line for calculated resultsCalculated using Radis et al.'s compositionCalculated using Mao et al.'s composition


Secondary/Tertiary γ′γ′γ′γ′ during Cooling + Agingwt.%*

Al 2.51

B 0.014

C 0.011

Co 14.66

Cr 16.14

Mo 2.98

γ′γ′γ′γ′ γγγγ

No primary γ′ is considered, but γ matrix concentration is adjusted due to primary γ′ formation at 1105oC (based on equilibrium calculation)

* M.P.Jackson and R.C.Reed, Mater. Sci. Eng. A259(1999)85-97

Mo 2.98

Si 0.05

Ti 5.08

W 1.23

Ni Bal

Heat Treatment: cooling from 1105oC to 400 oC, followed by aging at 700oC for 24hrs

Time


Secondary γ′γ′γ′γ′ Size After Cooling + Aging

Ave

rage

Siz

e of

Sec

onda

ry

γγ γγ' (n

m)

200

300

400

500

Jackson and ReedCalculated

Cooling Rate ( oC/min)

0 50 100 150 200 250 300

Ave

rage

Siz

e of

Sec

onda

ry

0

100

Simulations are good for large to intermediate cooling rate ( > 1oC/s)

Future model improvements include multiple nucleation sites, mean field deviation, loss of coherency, interfacial energy variation, interface mobility, morphology change ….


Classic or non-classic

thermodynamics

Atomistic modeling -

molecular dynamics

Estimation of interfacial energy

Distribution of Al-Li α/δ’ interfacial energy value found in literature

molecular dynamics

and Monte Carlo

method

First principles

1999Noble, Mater Sci Engr, A266, 80-85

Thermo-Calc SoftwareOur first approximation

σ = ∆s sc sol

A l

N ZE

N Z( )2∆ = Ω −sol P ME X X

For a binary matrix and precipitate of the same structure that

can be described by a regular solution model*

Misciblity gap of non-regular solution phase

Matrix and precipitate of different structure

Multicomponent system

∆ solE

* Based on Becker R. Ann Phys 1938;424:128

Thermo-Calc SoftwareSome example results

System Phases Estimation (J/m2) Literature (J/m2)

Al-Li α/δ’ 0.011 0.004 to 0.115

Cu-Ti Cu/Cu4Ti 0.035 0.067, 0.031

Ni-Al-Cr γ/γ’ 0.022 0.023

Co-W-C Co/WC 0.68 0.44 to 1.09

Thermo-Calc SoftwareFuture Investigations

Entropy effect

Diffusiveness of interface

Incoherency

Size effectSize effect

Grain boundary energy

Thermo-Calc SoftwareSummary

A non-isothermal model has been developed in TC-PRISMA 2.0 and has been successfully applied to simulate multi-modal particle size distribution of γ′ precipitates in Ni-base superalloys

More GUI outputs have been provided to facilitate separate analyses of particle size distribution, mean size, volume fraction, and number density

A model has been developed to estimate the interfacial energy between matrix and precipitate phases

Documents

Thermo-Calc Software