Applied Calphad in Materials
Engineering
Habilitation Colloquium
Materials Science
Erwin Povoden-Karadeniz
Vienna, 05.11.2020
Agenda
 I. The aim of applied Calphad
Calphad-based materials development
 II. The Calphad fundament
 III. Applied Calphad
Integration of Calphad thermodynamics into kinetic,
microstructural modeling, mechanical modeling frame
 IV. Applied Calphad for understanding of mechanisms that
contribute to the microstructural evolution and function of
different materials
i. Spinodal decomposition versus nucleation and growth
ii. The nature of an alloy transformation - martensite reversion
iii. Cooperative strengthening nano-precipitates
iv. The role of point defects
 V. Summary and outlook
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I.
The Aim of
Applied Calphad
From Calphad modeling to understanding of
mechanisms of phase transformations and
predictive simulation of microstructural evolution
 Physics-based materials development
 Optimization of product stability / usability, control of
degradation during service.
 Process optimization
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Calphad-based materials
development
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Calphad-based materials development
 V-Ti-Ni alloy design
experimental
Zhang, Cann, Maisel, Qu, Plancher, Springer, Povoden-Karadeniz,
Gao, Ren, Grabowski, Tasan, Acta Mater. 196 (2020) 710.
Application Hydrogen storage
membranes - Prevent brittle Ti2Ni and
sigma!
Previous experiments (blue dot) 
Ti2Ni at lower temperatures during
heat treatment!
Hypothesis: Coherent superelastic
nanoparticles support reversible
(stress – stress removal) martensitic
transformation
 Investigate stable TiNi+b-field for
this kind of alloy design
Ternary isothermal equilibrium phase diagram represents Gibbs energy minimum
single-phase, two-phase, three-phase equilibria.
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experimental
Zhang, Cann, Maisel, Qu, Plancher, Springer,
Povoden-Karadeniz, Gao, Ren, Grabowski,
Tasan, Acta Mater. 196 (2020) 710.
Calphad-assessed phase diagram with refined phase boundaries 
optimised alloy composition in two-phase field calculable along T.
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V,Ti
Va
V,Ti
Hypothesis: Coherent superelastic
B2-ordered TiNi nanoparticles
possible to form in bcc (V,Ti) when the
molar volume between matrix and
precipitates is very small.
Calphad-assessed molar volume of
bcc-TiV
8.22e-6
Vm(B2)=8.21e-6m3 (0K)
Δ=0.12%
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Exp. prove: Coherent superelastic
TiNi nanoparticles
after casting and 2h aging at 900°C
Zhang, Cann, Maisel, Qu, Plancher, Springer, Povoden-Karadeniz,
Gao, Ren, Grabowski, Tasan, Acta Mater. 196 (2020) 710.
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Each triangle axis in ternary phase diagram
represents thermodynamics of one underlying
binary system
E. Povoden-Karadeniz, D. Cirstea,
P. Lang, T. Wojcik, E. Kozeschnik,
CALPHAD, 2013, 41, 128-39.
?
T0 :
Gm(B2)=Gm(B19´)
The max. theoretic temperature for martensitic transformation, T0
can be calculated by Calphad thermodynamics
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Metallic membrane for
hydrogen purification
Effect of transformation
toughening 
less fatigue cracking
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II.
The Calphad fundament
Computer Coupling of Phase Diagrams and
Thermochemistry
Thermodynamic base
State functions and equilibrium
Thermdynamic equilibrium: Global Gmin
 State variables T, P, N, V
 State functions U, H, G, S
G=U-TS+pV
konst. p
G=H-TS
G=A+BT+CTln(T)...
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Originally – Calculation of Phase Diagrams
 Thermodynamic databases with stored molar Gibbs
energies of all phases for determination of the
thermodynamic phase stabilities of alloys, compounds,
functional oxides, …
Povoden-Karadeniz, Kozeschnik, Proceedings of Thermec 2016, 1513-1518.
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The Compound Energy Formalism
Phase (A,B)a(C,D)b
„Pure“ Compounds of the phase:
A:C, A:D, B:C, B:D
ex
2
G  0 LAB  X A X B  1LAB  X A X B ( X A  X B ) 
LAB  X A X B ( X A  X B ) 2  ... n LAB  X A X B ( X A  X B ) n
The expression of the excess Gibbs energy of mixing thanks to the Redlich-Kister
polynomials allows to describe many different real cases with a large flexibility.
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Element partitioning
 Calphad modeling of composition-dependent Gibbs energy Chemical
potential
 Ni-base superalloy - equilibrium
 Fe-Co-Mo – continuous heating kinetics
Ritter, Sowa, Schauer, Gruber, Göhler, Rettig,
Povoden-Karadeniz, Körner,. Singer, Metal.
Mater. Trans. A 49A, 2018, 3206-3216.
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Calphad power – Calphad limitations
Power and limitations odf Calphad application beyond
thermodynamic computations
 Power: Relatively simple bottom-up extension to high-order
systems – main G-determination by unaries, binaries,
ternaries, above (quaternary, …) typically ideal extensions
 Limitation: Empiric nature of G-polynomials - recent
developments: physical Cp). Question of unaries – lattice
stabilities – how to obtain correct lattice stabilites? Recent
developments: first principles Hm, first principles Gm.
 Limitation: Extensions beyond experimentally assessed
composition range: Redlich-Kister mixing polynomials –
recent developments: appropriate modeling of local mixing,
difficult.
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III.
Applied Calphad
Integration of Calphad thermodynamics into
kinetic, microstructural modeling, mechanical
modeling frame
Calphad modeling of diffusivities
Tracer diffusion - spontaneous
mixing of molecules taking place
in the absence of concentration
(or chemical potential) gradient.
B
Ni-Mo fcc, mc_ni.ddb
MQ(FCC_A1&MO,MO:*) 254975+R*T*LN(5.5301e-5);
MQ(FCC_A1&MO,NI:*) -267585-79.5*T;
O
C
N
S
Ni
Wc
Ru
Re
Al
Si
Si
Chemical diffusion - in the presence of
concentration (or chemical potential) gradient 
transport of mass.
Non-equilibrium process
Wang, Zhu, Wang, Metal.Mater.Trans. A 48A(2017)943.
In a nonequilibrium frame such as precipitation kinetics, the quality of employed
diffusion evolution (T, N) depends on the quality of Calphad thermodynamics
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Scheme: Calphad integration into a kinetic framework
CALPHAD solution
enthalpies, chemical
potentials, Gibbs
energies
Diffusion
SFFK
A
B
GBB   N  zL,eff  Esol
•B
Mechanical
and
microstructural
models
n
4 k3 
 m
G   N 0i 0i  
 k   cki  ki    4 k2 k
3 
i 1
k 1
i 1
 k 1
n
m
nS  zS ,eff
16
3
G  
2
3 
aE 2 
 G0 

(1  ) 


CNT
 G*    
J  N 0 Zb exp exp 
 kT   t 
*
Povoden-Karadeniz, Kozeschnik, Proceedings of Thermec 2016, 1513-1518.
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Multi-scale embedding of Calphad
 T-t evolution of detrimental intermetallics Re-containing intermetallics
in Ni-base superalloys
sss-effect of alloying elements in Ni
Matuszewski, Doctoral Thesis, Erlangen, 2016.
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Zhang, Deng, Xiao, Li, Hu,
Comp.Mater.Sci. 68(2013)132.
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IV.
Applied Calphad for understanding of
mechanisms that contribute to the
microstructural evolution of materials 
understanding mechanisms  applied
Calphad for physics-based development of
new materials
i. Spinodal decomposition versus
nucleation and growth
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Miscibility gap – spinodal – nucleation and growth
Source:
http://pruffle.mit.edu/3.00/L
ecture_32_web/node3.html
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Calphad-evaluated spinodal
LIMI, edged.
Rouzbahani2001, doctoral thesis.
Fe-25Co-15Mo (wt.%)
a  
-phase dissolved
-phase approx. 10%
Povoden-Karadeniz,
Eidenberger, Lang, Stechauner,
Leitner, Kozeschnik, J. Alloys
Cmpd., 2014, 587, 158-70.
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Spinodal decomposition versus nucleation & growth
Spinodal decomposition
scale approximation (Langer-Baron-Miller):
Blue: Low Mo
Red: High Mo
2D-Mo concentration profiles.
Eidenberger2010, doctoral thesis.
Povoden-Karadeniz, Eidenberger, Lang,
Stechauner, Leitner, Kozeschnik, J. Alloys
Cmpd., 2014, 587, 158-70.
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ii. The nature of an alloy
transformation –
martensite reversion
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Alloy phase transformations
 Fe-9Mn (wt.%), martensitic metastable hcp
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Evaluating the nature of alloy transformation
Reversion of hcp-martensite to austenite
Exp.: Dilatometry
3D-APT
Moszner, Povoden-Karadeniz, Pogatscher, Uggowitzer, Estrin,
Gerstl, Kozeschnik, Löffler, Acta Mater., 2014, 72, 99-109.
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 Partitioning and transformation thermodynamics
Moszner, Povoden-Karadeniz, Pogatscher, Uggowitzer, Estrin,
Gerstl, Kozeschnik, Löffler, Acta Mater., 2014, 72, 99-109.
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iii. Cooperative strengthening nanoprecipitates
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Cooperative nano-precipitates
metastable/stable couples
 Ni-base superalloy IN718 –
patent early 1960ies, GE
Aeroengine CFM56
(A320, small parts, e.g. bearings)
´
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´
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d
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 Ni-base superalloy IN718
17Cr2.8Mo4.75Nb0.2Al
21Cr3.3Mo5.5Nb0.8Al
´
´´
´
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´
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d
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ΔV(´)=0.7%
ΔV(´´)=1.5%
´
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´
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´´
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Calphad for prec. kinetics  strengthening simulation
Drexler, Oberwinkler, Primig, Turk,
Povoden-Karadeniz, Heinemann, Ecker, Stockinger,
Mater. Sci. Eng. A, A723, 2018, 314-323.
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iv. The role of point defects
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The role of point defects
Stabilisation of metastable precipitates
Al
Povoden-Karadeniz, Lang,
Warczok, Falahati, Jun,
Kozeschnik, CALPHAD,
2013, 43, 94-104.
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Redrawn from Matsuda et
al., Metal. Mater. Trans. A
29A, 1998(1161).
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Vacancy thermodynamics  kinetic vacancy effects
 Enthalpy of vacancy formation
 equilibrium defect concentrations govern potentially
S„available“ quenched-in vacancies
y  exp( E f / RT )
eq
0
PARAMETER HMVA(BCC_A2,FE)
+163000; pov10
 x(Va)773K=9.7x10-12
PARAMETER HMVA(FCC_A1,AL)
+64200; pov10
 x(Va)773K=4.6x10-5
PARAMETER HMVA(FCC_A1,CU)
+125000; pov10
PARAMETER HMVA(FCC_A1,Ni)
+134000; pov15
Source: ttps://www.matcalc-engineering.com/index.php/matcalcsoftware/distributors/2-uncategorised/130-vacancy-evolution-in-al-alloys.
Povoden-Karadeniz,
thermodynamic mc_al database
https://www.matcalc.at/images/stories/
Download/Database/mc_al_v2.029.tdb
Vacancy/solute, vacancy/precipitate interactions, vacancy sinks (dislocations, interfaces)
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Cluster and GP-zones modeling
 Co-cluster – simple solution model
fcc Si
(Mg,Si)
( Mg , Si )


GCL

G
x

GMg xMg
_ MGSI
Si Si
 RT ( xSi ln xSi  xMg ln xMg )  xSi xMg LMgSi
 Ordered GP-zones: CEF split model
(Al%,Mg,Si)0.25(Al%,Mg,Si)0.25(Al,Mg%,Si)0.25(Al,Mg,Si%)0.25
Gm  G ( xi )  G ( y )
Gmord ( yis )  Gm4ssl ( yis )  G ( yis  xi )
dis
m
°H
ord
m
4 ssl
m
s
i
fcc Mg
Mg
(J/mol) referred to Al fcc, Mg hcp and Si diamond
Compound
DFT (0 K), GGA
CALPHAD 298.15 K
Al3Mg L12
-780
-669
AlMg L10
-146
-487
AlMg3 L12
+605
+633
Al3Si L12
+10652
+9727
AlSi L10
+21030
+17434
AlSi3 L12
+35578
+36092
m
Al2MgSi L10
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39
+3350
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Metastable preciptate thermodynamics ...
Al-alloy +Mg, Si - AA6016
Povoden-Karadeniz, Lang, Warczok, Falahati,
Jun, Kozeschnik, CALPHAD, 2013, 43, 94-104.
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
nS  zS ,eff
N  zL ,eff
...and related kinetics
Al-alloy +Mg, Si - AA6016
 Esol
Solution enthalpy, J/mol
60000
40000
20000
0
GP_MAT Al_B_DP Mg5Si6
Mg2Si
Interfacial Energy, J/m2
0.4
0.3
0.2
0.1
0
GP_MAT Al_B_DP Mg5Si6
Mg2Si
Povoden-Karadeniz, Lang, Öksüz, Jun, Rafiezadeh, Falahati, Kozeschnik, Mater. Sci. Forum, 2013, 765, 476-80.
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Extended cluster modeling
 Natural aging of 6xxx Al + Mg,Si alloy
•
Poznak, Marceau, Sanders,
Mater.Si.Eng.A 721 (2018) 47.
Cluster and GP-zones sizes
Cluster chemistry
Al3Mg
Phase fractions
GP
Al3Mg
Mg
GP
MgSi-Cl
MgSi-Cl
Si
Si-Cl
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Poznak, Marceau, Sanders,
Mater.Si.Eng.A 721 (2018) 47.
Cluster and GP-zones sizes
Cluster chemistry
Si
Phase fractions
GP
GP
Si-Cl
Mg
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Si-Cl
Num. fluct.
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The role of point defects – functional materials
Oxygen vacancies controlling oxygen reduction reaction
Bork, Povoden-Karadeniz, Carrillo, Rupp, Acta Mater., 2019.
 Perovskite reduction
 Hydrogen yield
A: (La+3,Sr+2)
B: (Mn+2,+3,+4,Cr+2,+3,+4)
O (fully oxidized)
Lu, Zhu, Agrafiotis, Vieten, Roebm Sattler,
Progr.Energ.Comb.Sci. 75(2019)100785.
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Thermodynamic base: Perovskite database
Subsystem La-Cr-Mn-O-(Va)
1273K
Source: PovodenKaradeniz, Doctoral
Thesis, ETH Zurich, 2008.
(La+3,Sr+2)(Cr+2,Cr+3,Cr+4,Mn+2,Mn+3,Mn+4)(O-2,Va)
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Thermodynamic base: Perovskite database
Extension to La-Sr-Cr-Mn-O-(Va)
Applications: SOFC, Solar to fuel
(La+3,Sr+2)(Cr+2,Cr+3,Cr+4,Mn+2,Mn+3,Mn+4)(O-2,Va)
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Thermodynamics for solar to fuel efficiency evaluation
Essential water splitting reaction I (high T)
Essential water splitting reaction II (low T)
Partial state functions
determine driving force for H2O conversion
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V.
Summary –
we are on the way to...
Physics-based understanding of mechanisms
of phase transformations –> predict materials
response during complex processes for
complex alloy systems
Physics-based understanding of phase
stabilities in complex oxide systems including
defect chemistry, reduction and oxidation.
The future:
Applied Calphad for virtual materials design
of complex materials combinations and
predictive performance assessment under
varying conditions: high T and T-cycling,
creep stress, corrosive atmospheres, redoxgradients
SOFC – a complex multi-materials system
Stainless steels, Ni-base
Source: Povoden-Karadeniz, Doctoral Thesis, ETH Zurich, 2008.
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Discussed papers of habilitation manuscript
E. Povoden-Karadeniz, P. Lang, P. Warczok, A. Falahati, W. Jun, E. Kozeschnik, CALPHAD
modeling of metastable phases in the Al-Mg-Si system, CALPHAD, 2013, 43, 94-104.
E. Povoden-Karadeniz, D. Cirstea, P. Lang, T. Wojcik, E. Kozeschnik, Thermodynamics of TiNi SMA alloys, CALPHAD, 2013, 41, 128-39.
A.H. Bork, E. Povoden-Karadeniz, A.J. Carrillo, J.L.M. Rupp, Thermodynamic Assessment of
the Solar-to-Fuel Performance of La 0.6Sr 0.4Mn 1-YCr yO3-σ Perovskite Solid Solution
Series, Acta Mater., 2019.
N.C. Ritter, R. Sowa, J.C. Schauer, D. Gruber, T. Göhler, R. Rettig, E. Povoden-Karadeniz,
C. Körner, R.F. Singer, Effects of solid solution strengthening elements Mo, Re, Ru, and W
on transition temperatures in nickel-based superalloys with high gamma´-volume fraction:
comparison of experiment and Calphad calculations, Metal. Mater. Trans. A 49A, 2018,
3206-3216.
E. Povoden-Karadeniz, E. Eidenberger, P. Lang, G. Stechauner, H. Leitner, E. Kozeschnik,
Simulation of precipitate evolution in Fe-25Co-15Mo with Si addition based on
computational thermodynamics, J. Alloys Cmpd., 2014, 587, 158-70.
F. Moszner, E. Povoden-Karadeniz, S. Pogatscher, P.J. Uggowitzer, Y. Estrin, S.S.A. Gerstl,
E. Kozeschnik, J.F. Löffler, Reverse alpha´ ® gamma transformation mechanisms of
martensitic Fe-Mn and age-hardenable Fe-Mn-Pd alloys upon fast and slow continuous
heating, Acta Mater., 2014, 72, 99-109.
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Discussed papers of habilitation manuscript
P. Lang, E. Povoden-Karadeniz, W. Mayer, A. Falahati, E. Kozeschnik, The bustling nature of
vacancies in Al-alloys, Proceedings of the 8th Pacific Rim International Congress on
Advanced Materials and Processing, Wiley, 2013, 3181-88. ISBN: 978-0-470-94309-0.
A. Bork, E. Povoden-Karadeniz, J.L.M. Rupp, Modeling thermochemical solar-to-fuel
conversion: CALPHAD for thermodynamic assessment studies of perovskite, exemplified
for (La,Sr)MnO3, Adv. Energy Mater., 2016, 1601086.
E. Povoden-Karadeniz, E. Kozeschnik, Coupling of computational thermodynamics with
kinetic models for predictive simulations of materials properties, Proceedings of Thermec
2016, 1513-1518.
E. Povoden-Karadeniz, P. Lang, K.I. Öksüz, W. Jun, S. Rafiezadeh, A. Falahati, E.
Kozeschnik,Thermodynamics-Integrated Simulation of Precipitate Evolution in Al-Mg-SiAlloys, Mater. Sci. Forum, 2013, 765, 476-80.
A. Drexler, B. Oberwinkler, S. Primig, C. Turk, E. Povoden-Karadeniz, A. Heinemann, W.
Ecker, M. Stockinger, Experimental and numerical investigation of the gamma´´ and
gamma´ precipitation kinetics in Alloy 718, Mater. Sci. Eng. A, A723, 2018, 314-323.
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Thank you for your kind attention!
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Thermodynamische Grundlagen
Zustandsfunktionen und Gleichgewicht
Thermodynamisches Gleichgewicht: Globales Gmin
 Zustandsvariablen T, P, N, V
 Zustandsfunktionen U, H, G, S
H=U+pV
dU=dQ+dW
dW=-pdV
dH=qQ+dW+pdV+VdP
dH=dQ+VdP
(dH)P=dQ
Die Enthalpieänderung bei konstantem Druck ist gleich
der Wärme die dem System zugeführt wird.
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Thermodynamische Grundlagen
Zustandsfunktionen und Gleichgewicht
 Zustandsvariablen T, P, N, V
 Zustandsfunktionen U, H, G, S
Thermodynamische Definition von
Entropie (S): Maß für die
Energieabgabe
Bei Wärmezufuhr / T-Erhöhung,
direkt verknüpft mit dem Potential
atomarer Vibrationen um einen fixen
„Ruhezustand“ – Vibrationsentropie.
S steigt mit steigender T:
dQ=d(TS)
dQ=SdT+TdS
dS=dQ/T
DEFENSIO 05.11.2020
wenn T konst. 
Vibration
Rotation
Translation
Quelle: https://saylordotorg.github.io/text_generalchemistry-principles-patterns-and-applicationsv1.0/s22-04-entropy-changes-and-the-third.html#averill_1.0-ch18_s04_f01
erwin.povoden-karadeniz@tuwien.ac.at
57
8
CALPHAD approach
G(T) at p,X=constant
Stoichiometric phase
G  A  BT  CT ln T  DT 2  ET 3  FT 1
H
G
S
Cp
A to F are adjustable model parameters
G  H  TS
 G 
2
2
S  
   B  C (1  ln T )  2 DT  3ET  FT
 T 
H  G  TS  A  CT  DT 2  2 ET 3  2 FT 1
 H
Cp  
 T
Josiah Willard Gibbs
1839-1903

 S
T

 T
enthalpy
Gibbs energy
entropy
heat capacity
Thermodynamic properties are
derived from the Gibbs energy
polynomial!

2
2
  C  2 DT  6 ET  2 FT

...Solid solution phase, e.g. (Fe,Cr)3C: G(T,X) at p=constant
Excess energy terms of mixing of atoms (interactions)
The Gibbs energy function of a stoichiometric phase is achieved by optimising model
parameters with experimental thermodynamic and phase diagram data.
DEFENSIO 05.11.2020
erwin.povoden-karadeniz@tuwien.ac.at
58
Thermodynamische Grundlagen
Ungleichgewicht, Metastabilität
 Gleichgewichtsphasendiagramm – Gibbsenergie Minimum
Quelle:
mc-fe Thermodynamic Datenbank,
Povoden-Karadeniz, 2009 - 2020
liquid
liq+graph
fcc
_J/mol
1273K
1273K
fcc+graph
Ni
DEFENSIO 05.11.2020
Ni
erwin.povoden-karadeniz@tuwien.ac.at
59
DEFENSIO 05.11.2020
erwin.povoden-karadeniz@tuwien.ac.at
60