developing calphad databases for thermophysical properties · for thermophysical properties of...
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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