modelling multicomponent precipitation kinetics with calphad … · thermo-calc software modelling...

Thermo-Calc Software

www.thermocalc.com

Modelling Multicomponent Precipitation Kinetics

with CALPHAD-Based Tools

Kaisheng Wu 1, Gustaf Sterner 2, Qing Chen2, Åke Jansson2,

Paul Mason1, Johan Bratberg 2 and Anders Engström 2

1Thermo-Calc Software Inc., 2Thermo-Calc Software AB

EUROMAT2013, September 8-13, 2013 Sevilla, Spain

Thermo-Calc Software Introduction: CALPHAD

CALPHAD method and CALPHAD-based tools play a

central role in materials design

Thermodynamics: Gibbs energy

Diffusion: Mobility

Phase Field Method

Langer-Schwartz

First Principles Calculation

CALPHAD f(r)

r

Interfacial energy & Volume & Elastic constants

CALPHAD-type databases where each phase is described

separately using models based on physical principles and

model parameters assessed from experimental and ab initio

data provide fundamental inputs for predicting microstructure

evolution and materials properties.

t

H or S


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.

Introduction: TC-PRISMA


Output

• Particle Size Distribution

• Number Density

• Average Particle Radius

• Volume Fraction

• Matrix composition

• Precipitate composition

• Nucleation rate

• Critical radius

• TTP

Input

• Thermodynamic data

• Kinetic data

• Alloy composition

• Temperature - Time

• Simulation time

• Property data (Interfacial

energy, volume, etc.)

• Nucleation sites and

related microstructure

information

TC-PRISMA

Introduction: In and Output

Thermo-Calc Software Introduction: Example of results

All above simulations made under isothermal conditions.


g/g’ Microstructure in U720 Li

Continuous cooling at 0.0167 K/s

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

Non-Isothermal Conditions

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


Exp

Continuous cooling from 1150 to 380 °C with a cooling rate of 14 °C/min.


Exp

s = 0.023 J/m2

Ni-8Al-8Cr have larger misfit between g and g compared to Ni-10Al-10Cr.

This will give an elastic energy contribution which has not been considered in the simulation.


Vertical Section Ni-xAl-xCr Thermodynamic driving force


Nucleation rate Thermodynamic driving force

Thermo-Calc Software U720Li

Databases: TTNI8+MOBNI1

Precipitation Kinetics during Continuous Cooling

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

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

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

g g

Thermo-Calc Software U720Li : Cooling Rate Effect

Size Distribution

Particle Radius (nm)

0.1 1 10 100

Siz

e D

istr

ibu

tio

n (

1/m

4)

1e+18

1e+19

1e+20

1e+21

1e+22

1e+23

1e+24

1e+25

1e+26

1e+27

1e+28

1e+29

1e+30

1e+31

1e+32

1e+33

1e+34

78 oC/s

1.625 oC/s

0.217 oC/s

Cooling Rate (oC/s)

0.1 1 10 100 1000

Part

icle

Siz

e (

nm

)

10

100

1000

Mao et al.

Radis et al.

Regression line for calculated results

Calculated using Radis et al.'s composition

Calculated using Mao et al.'s composition

Mean Particle Size

s = 0.025 J/m2

Alloy 1 Alloy 1 & 2


No primary g is considered, but g matrix concentration is adjusted due to primary g

formation at 1105oC (based on equilibrium calculation)

Secondary/Tertiary g during Cooling + Aging

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

wt.%*

Al 2.51

B 0.014

C 0.011

Co 14.66

Cr 16.14

Mo 2.98

Si 0.05

Ti 5.08

W 1.23

Ni Bal

g g

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

Time


Secondary g Size After Cooling + Aging

Cooling Rate (oC/min)

0 50 100 150 200 250 300

Avera

ge S

ize o

f S

ec

on

da

ry

' (n

m)

0

100

200

300

400

500

Jackson and Reed

Calculated

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 ….

s = 0.025 J/m2


Classic or non-classic

thermodynamics

Atomistic modeling -

molecular dynamics

and Monte Carlo

method

First principles

Estimation of interfacial energy

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

Distribution of Al-Li a/d’ interfacial

energy value found in literature

Thermo-Calc Software Our first approximation

s s sc solA l

N ZE

N Z )

2 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 Software Some example results

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

Al-Li a/d’ 0.011 0.004 to 0.115

Cu-Ti Cu/Cu4Ti 0.035 0.067, 0.031

Ni-Al-Cr g/g’ 0.022 0.023

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

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

Ni-Al-Cr g/g’ 0.022 0.023

Ni-Superalloys(Bulk) g/g’ 0.03~ 0.06 0.025

Ni-Superalloys(GB) g/g’ ~ 0.06 0.06

Used in Current Calculations

Interfacial energy shows composition and temperature independence

Estimated value seems better for grain boundary precipitation in multi-component alloys

Further developments include diffusiveness of interface, incoherency, size effect, grain

boundary energy…

Thermo-Calc Software Alloy 282

Cooling Rate ( oF/min )

0 400 800 1200 1600 2000 2400

Me

an

' S

ize

(n

m)

0

20

40

60

80

100

120

140

160

180

200

220

240

constant (0.025 J/m2)

model

experimental data

Cooling Rate ( oF/min)

0 400 800 1200 1600 2000 2400

Te

mp

era

ture

(oC

)

840

860

880

900

920

940

960

980

1000

constant (0.025 J/m2)

model

experimental data

Mean Particle Size (Bulk) CCT Starting Temperature

* Experimental data from B. Alexandrov et al., “Continuous heating and cooling transformation diagram in Ni-base superalloy

282”, TMS 2011

Databases: TCNI5+MOBNI2

Al Co Cr Fe Mo Ti Ni

wt.% 1.5 10.0 19.0 1.5 8.5 2.1 Bal.

Thermo-Calc Software Summary

A non-isothermal model has been developed in TC-PRISMA

and has been successfully applied to simulate multi-modal

particle size distribution of g 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 implemented to estimate the interfacial

energy between matrix and precipitate phases


www.thermocalc.com E-mail: info@thermocalc.

Thank You!

Thermo-Calc Software Theory: Conservation laws

T

XB B A

Liq

a

b

LS (Langer-Schwartz) and KWN (Kampmann and Wagner Numerical) Approach

) ),(),(),(

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Continuity equation

Mass balance

Thermo-Calc Software Models: Multicomponent Nucleation

kT

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tJtJ S

exp

2/1

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2

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n

n

n

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kTZ

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ii

DX

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baab

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23*

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G

VG

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Interfacial energy Volume

Classic Nucleation Theory Grain size, dislocation density, etc

Thermo-Calc Software Models: Multicomponent Growth Rate

) ) rMccc iiiiiii baababaab ///// r

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Q. C

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Advanced – Analytical Flux-balance Approximation

2 mm

VKG

r r

s

Simplified – Pseudo-steady state Approximation

Pseudo-binary dilute solution Approximation

r

D

XX

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baa

/

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e e

X VX

X X X RTr

a ba b

a b a

s

Cross diffusion

high supersaturation

modelling multicomponent precipitation kinetics with calphad … · thermo-calc software modelling...

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