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Developing CALPHAD databases

for thermophysical properties

of metals and alloys

Hai-Lin Chen, Masoomeh Ghasemi, Qing Chen*

Thermo-Calc Software AB

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Phase diagram for a M42 high speed

steel, Fe-4Cr-5Mo-8W-2V-0.3Mn-0.3Si-

C(wt%).

Property diagram for a M42 high speed

steel, Fe-4Cr- 5Mo-8W-2V-0.3Mn-0.3Si-

0.9C.

Phase diagrams are the beginning of wisdom

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We need an Einstein in metallurgy to be able to

see into 5 or 6 dimensional space – and some

genius – and he would have to be a very great one,

to predict what phase constitution in such

systems would be, if the fearful amount of the

currently necessary experimental work is to be

avoided.

- Robert F. Mehl, 1959

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From Dr. C. Campbell, NIST, USA

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fcc

NiG

fcc

FeG

bcc

FeG

bcc

NiG

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m

Eideal

mi

o

i

im GTSGxG

lkji

lkjilkji

kji

kjikji

ji

jijim

E

Lxxxx

Lxxx

LxxG

,,,

,,

,

n

n

i

ix2

Maximum Equiatomic Contribution

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10

2

1

M

M

M

M

9991

191211

DD

DDD

D

Atomic mobility

Database

Self-diffusivity

Impurity diffusivity

Intrinsic diffusivity

Tracer diffusivity

Chemical Diffusivity

J.O. Andersson and J. Ågren, J. Appl. Phys., 72 (1992) 1350.

0

1exp( )i

i

QM D

RT RT

0

ln

ln

i i

i

RT RTM

Q RT D

1exp( )i

iMRT RT

j E

i j i i

j

x

0

E jk jkl

i j k i j k l i

j k j l k

x x x x x

Redlich-Kister Expansion (RKE)

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lattice parameter

molar volume density thermal

expansion coefficient

relative length change

lattice mismatch

The effect of Si content on the densities of Al-Si alloys

liquid solid Casting shrinkage

0

0

0

exp( 3 )

exp

T

mT

A

V T V dT

V V

0 0 0

i E

i

i

V xV V

i E

A i A A

i

V xV V Al-Fe-C phase diagram and iso-density contour lines at 1100 °C, calculated with TCFE9. (g/cm3)

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https://new.siemens.com/global/en/company/stories/research-technologies/additivemanufacturing/additive-manufacturing-

simulation-of-molten-metal.html

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Thermal conductivity / resistivity

Electric conductivity / resistivity

Viscosity

Their temperature dependence

Their composition dependence

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Wiedemann-Franz law

𝜅𝑒𝜎= 𝐿0𝑇

𝐿0 =𝜋2

3∙𝑘𝐵2

𝑒2= 2.4453 × 10−8𝑊 ∙ 𝛺 𝐾2

𝑻𝒉𝒆 𝑺𝒐𝒎𝒎𝒆𝒓𝒇𝒆𝒍𝒅 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑳𝒐𝒓𝒆𝒏𝒛 𝒏𝒖𝒎𝒃𝒆𝒓

𝒌 = 𝒌𝒆 + 𝒌𝒈

Thermal conductivity

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Major scatterings

Electron-phonon scattering

Electron-electron scattering

Impurity

scattering

Defect

scattering

Electrical resistivity & Electronic thermal conductivity

Lattice thermal conductivity

Phonon-electron scattering

low temperatures

Phonon-Phonon scattering

Umklapp processes high temperatures

Phonon-Phonon scattering

Normal processes

Impurity and defect scatterings

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Au-Cu, electrical resistivity

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Au-Cu, thermal conductivity

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HEA alloys

Jin et. al. Sci. Rep. 6(2016)20159

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Viscosity

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Case study: Fe-Cr-Ni • Binary systems:

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

0 0.2 0.4 0.6 0.8 1

Vis

cosi

ty (

mP

a.s)

x(Ni)

Fe-Ni, 1873 K

Kaptay

exp, 1873K

Kozlov

Gasior

Seetharaman

Shick

Calphad3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

Vis

cosi

ty (

mP

a.s)

x(Cr)

Cr-Fe 1873 K

Kaptay

Ershov1974

Kamaeva2012

Arkharov1977

Kobatake2013

Pavers1969

Kozlov

Gasior

Seetharaman

Shick

Calphad

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1

Vis

cosi

ty (

mP

a.s)

x(Ni)

Cr-Ni, 1873 K

Kaptay

exp, 1873K

Kozlov

Gasior

Seetharaman

Shick

Calphad

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Case study: Fe-Cr-Ni

• Ternary viscosities

1775 K 20% Cr

Kobatake 2013

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7.2

1800 K

TiAl-8Nb (at%)

Einstein-Roscoe eq:

𝜂 = 𝜂0(1 − 𝑐)−2.5

where c is the volume fraction of solid and solid particles of different sizes are assumed.

TiAl-8Nb (at%)

Exp data from: Wunderlich et al, Adv. Eng. Mater. (2018) 1800346

𝜂 = 2.18(1 − 0.4)−2.5= 𝟕. 𝟖 mPa. s

Case study: Ti-Al-Nb

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22.46

28.5

30.2

34.5

35.1

37.7

42.4

44.3

51.5

54.1

55.2

61

63.9

68.6

70.4

0 10 20 30 40 50 60 70 80

Present model

Zhang et al. 2013

Urbain 1987

Li et al. 2016

Suzuki and Jak 2013

Grundy et al. 2008

Shu 2015

Hu et al. 2012

Ray et al. 2004

Gan and Lai 2013

Shankar 2007

Riboud et al. 1981

Tang et al. 2010

Iida et al. 2000

Mill and Sridhar 1992

ERROR DEVIATIONS (PERCENT)

VIS

CO

ISTY

MO

DEL

S

Average deviations by each model predicting viscosities of CaO-MgO-Al2O3-SiO2 system *

* All the average deviations are calculated by Han et al. 2016 except the present one.

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Databases on

Thermal conductivity/resistivity

Electric conductivity/resistivity

Viscosity

Surfact tension

Congratulations!

Summary and Ongoing Work