07 Data Modeling for Thermodynamics

Thermo-Calc Software

www.thermocalc.com

MAI Data Management Workshop:

Data Modeling for Thermodynamics and Other Properties

June 8-10, 2011 - Dayton, OH

P K Mason(1), A. Engstrm(2), J. Bratberg(2), Q. Chen(2)1. Thermo-Calc Software Inc2. Thermo-Calc Software AB

Thermo-Calc SoftwareSoftware: Thermo-CalcSoftware for thermodynamic calculations that can be applied to a range of applications including: Calculating stable and meta-stable phase equilibrium Transformation temperatures Amount and composition of phases Thermochemical data such as;

enthalpies heat capacity, activities, etc.

Predicting driving forces and transformation temperatures And much more.

Thermodynamic Database

R- and -phase

Alloy 1

( ) im xPTG ,,( )

0

,,

=

=

i

im

xG

xPTGNG

Thermo-Calc SoftwareSoftware: DICTRA

2.60 m

Ball screw for the AirbusA380 aircraft: a martensitic as carburized stainless steel

0,0

0,4

0,8

1,2

1,6

2,0

2,4

2,8

3,2

3,6

4,0

4,4

4,8

0 100 200 300 400 500 600 700 800 900m

%C

profil carbone calcul en fin d'enrichissement

profil carbone calcul aprs 3h de diffusion

Fe-12Cr-2Ni-2Mo-0.12C at 955C:Calculated carbon profile at the end of the enrichment step

Calculated carbon profile after 3h of diffusion

Example: Simulation of carbon evolution in high alloyed steels by Aubert & Duval, France.

Turpin et al., Met. Trans. A 36(2005), pp. 2751-60

Distance from surface (m)

Carb

on co

ntent

(%)

Carburizing and decarburization Microsegregation during solidification Precipitate growth and dissolution Precipitate coarsening Interdiffusion in coating/substrate TLP bonding of alloys and much more

Thermo-Calc SoftwareWhere does CALPHAD fit?

Thermodynamics: Gibbs energy

Diffusion: Mobility

Phase Field Method

Langer-Schwartz

First Principles Calculation

From atoms to microstructure: The aim is to predict microstructure evolution and materials properties.

CALPHAD f()

Interfacial energy & Volume & Elastic constants

The development of consistent databases where each phase is described separately using models based on physical principles and parameters assessed from experimental data is a key feature of this technique.

Thermo-Calc Software

Thermodynamic data

Thermo-Calc SoftwareComputational thermodynamics and CALPHAD (1)

Thermochemical measurements:

Enthalpy

Entropy

Heat capacity

Activity

Phase equilibria:

Liquidus

Solidus

Phase boundary

Gibbs Energy of Individual Phases

Applications

),,( PTxfGm =

Thermo-Calc SoftwareComputational thermodynamics and CALPHAD (2)

N. Saunders and A.P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, Pergamon Materials Series, 1998

Thermo-Calc Software

A thermodynamic database in our understanding means a collection of polynomials describing the Gibbs energy for the individual phases of a system, as a function of temperature, (pressure) and composition.

Thermodynamic database (1)

( ) im xPTfG ,,=

Advantages of the tdb format- open framework ASCII text file- essentially a mark up language- extendable with a variety of key words- not limited to one software code or application- can have more than one description (tdb) for the same systemLimitations of the tdb format- Not a linked, SQL type relational database, or HTML, XML- therefore changes made in one tdb do not translate to other tdbs automatically. need for an improved system of management?

Thermo-Calc SoftwareThermodynamic database (2)PARAMETER G(HCP_A3,CO:VA;0) 298.15 +GHSERCO;,,N ! PARAMETER G(HCP_A3,NI:VA;0) 298.15 +GHCPNI;,,N !FUNCTION GHSERCO 298.15 +310.241+133.36601*T-25.0861*T*LN(T)-.002654739*T**2-1.7348E-07*T**3+72527*T**(-1) 1768.0 Y -17197.666+253.28374*T-40.5*T*LN(T)+9.3488E+30*T**(-9);,, N !FUNCTION GHSERNI 298.15 -5179.159+117.854*T-22.096*T*LN(T)-.0048407*T**2;1728.0 Y -27840.655+279.135*T-43.1*T*LN(T)+1.12754E+31*T**(-9);,, N !PARAMETER L(HCP_A3,CO,NI:VA;0) 298.15 -1620-.385*T;,,N !PARAMETER TC(HCP_A3,CO:VA;0) 298.15 +1396;,,N !PARAMETER BMAGN(HCP_A3,CO:VA;0) 298.15 1.35;,,N !PARAMETER TC(HCP_A3,NI:VA;0) 298.15 633;,,N !PARAMETER BMAGN(HCP_A3,NI:VA;0) 298.15 .52;,,N !PARAMETER TC(HCP_A3,CO,NI:VA;0) 298.15 411;,,N !PARAMETER TC(HCP_A3,CO,NI:VA;1) 298.15 -99;,,N!PARAMETER BMAGN(HCP_A3,CO,NI:VA;0) 298.15 1.046;,,N !PARAMETER BMAGN(HCP_A3,CO,NI:VA;1) 298.15 .165;,,N !

Thermo-Calc SoftwareCALPHAD Methodology

StartLiterature Survey

Reassessment ofrelated systems treated

with the previous models.

Choice of models forGibbs energy of the

various phases.

Selection ofexperimentalinformation.Estimation oflacking data.

Parameterevaluation:

Optimizationand

Estimations.

Comparisons between experimental data and

model calculations.

Analysis of theextrapolations to

higher order systems

Assessed description.

Reconsideration of themodels accepted.

New experimentalstudy.

Reconsideration of selecteddata. Identification of

inconsistent information..

Reconsideration of weights or parameters to be

optimized.

Consideration of higher-orderinformation.

Reevaluationof lower-order

parameters.

Thermo-Calc SoftwareThermodynamic Modeling

Gibbs energy per mole for a solution phase is normally divided in:

phm

xsm

idealmmm GGGGG +++=

0

Ideal solution model Regular solution model Real solution

reference surface

configurational contribution physical contributionexcess term

Thermo-Calc SoftwareBinary - Real solutions

oBB

oAAm GxGxG +=

0

( )BBAAidealm xxxxRTG lnln +=

xsm

idealmmm GGGG ++=

0

=

=0

, )(k

kBABA

kBA

xsm xxLxxG

( )....)()( 2,2,1,0 BABABABABABA xxLxxLLxx ++=

Redlich-Kister Expansion

Thermo-Calc SoftwareTernary solutions

oCC

oBB

oAAm GxGxGxG ++=

0

( )CCBBAAidealm xxxxxxRTG lnlnln ++=

....++= > >> i ij jk

ijkkjii ij

ijjixsm IxxxIxxG

From Binary

From Ternary

xsm

idealmmm GGGG ++=

0

Thermo-Calc SoftwareThe POP file

Experiments are described like an equilibrium calculation.

CHANGE-STATUS PHASE FCC LIQ=FIX 1SET-COND T=1000 P=1E5LABEL AFLEXPERIMENT X(LIQ,CR)=0.22 : 0.02COMMENT give the journal or other source

CHANGE-STATUS LIQ=FIX 1SET-REFERENCE-STATE CR LIQ * 1E5SET-REFERENCE-STATE FE LIQ * 1E5SET-COND T=2000 P=1E5 X(CR)=.15EXPERIMENT HMR=-4500:500

Thermo-Calc Software

Normally collected from the literature Reliable data is selected and critically assessed Both phase diagram data or thermodynamic data (H,Cp...) can be used

Hm

(Liq

uid)

Binary and ternary systems

Thermo-Calc SoftwareTCNI5: A database for Ni superalloysAl B C Co Cr Fe Hf Mo N Nb Ni Pd Pt Re Si Ta Ti V W

B xC x xCo x x xCr x x x xFe x x x x xHf x x x x x xMo x x x x x x xN x x x x x xNb x x x x x x x x xNi x x x x x x x x x xPd x x x x x x x x x xPt x x x x x x x x x xRe x x x x x x x x x x x xSi x x x x x x x x x x x x x xTa x x x x x x x x x x x x x x xTi x x x x x x x x x x x x x x x xV x x x x x x x x x x x x x x x x xW x x x x x x x x x x x x x x x x x xZr x x x x x x x x x x x x x x x x x x x

20 + 3 elements. Nearly all binary subsystems assessed for full range composition All Ni containing ternaries plus other ternary systems also

assessed to full range of composition 292 intermetallic and solution phases

Thermo-Calc Software

From: Saunders & Miedownik: Calphad -a comprehensive review

iationAveragedevd %4