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 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 2 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 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 4 Calphad-based materials development DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 5 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 6 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 7 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% DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 8 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 9 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 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 10 Metallic membrane for hydrogen purification Effect of transformation toughening less fatigue cracking DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 11 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)... DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 13 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 14 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 15 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 16 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 17 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 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 19 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 20 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at Zhang, Deng, Xiao, Li, Hu, Comp.Mater.Sci. 68(2013)132. 21 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 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 23 Miscibility gap – spinodal – nucleation and growth Source: http://pruffle.mit.edu/3.00/L ecture_32_web/node3.html DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 24 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 25 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 26 ii. The nature of an alloy transformation – martensite reversion DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 27 Alloy phase transformations Fe-9Mn (wt.%), martensitic metastable hcp DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 28 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 29 Partitioning and transformation thermodynamics Moszner, Povoden-Karadeniz, Pogatscher, Uggowitzer, Estrin, Gerstl, Kozeschnik, Löffler, Acta Mater., 2014, 72, 99-109. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 30 iii. Cooperative strengthening nanoprecipitates DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 31 Cooperative nano-precipitates metastable/stable couples Ni-base superalloy IN718 – patent early 1960ies, GE Aeroengine CFM56 (A320, small parts, e.g. bearings) ´ DEFENSIO 05.11.2020 d ´ erwin.povoden-karadeniz@tuwien.ac.at d 32 Ni-base superalloy IN718 17Cr2.8Mo4.75Nb0.2Al 21Cr3.3Mo5.5Nb0.8Al ´ ´´ ´ DEFENSIO 05.11.2020 d ´ erwin.povoden-karadeniz@tuwien.ac.at d 33 ΔV(´)=0.7% ΔV(´´)=1.5% ´ DEFENSIO 05.11.2020 ´´ ´ erwin.povoden-karadeniz@tuwien.ac.at ´´ 34 Calphad for prec. kinetics strengthening simulation Drexler, Oberwinkler, Primig, Turk, Povoden-Karadeniz, Heinemann, Ecker, Stockinger, Mater. Sci. Eng. A, A723, 2018, 314-323. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 35 iv. The role of point defects DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 36 The role of point defects Stabilisation of metastable precipitates Al Povoden-Karadeniz, Lang, Warczok, Falahati, Jun, Kozeschnik, CALPHAD, 2013, 43, 94-104. DEFENSIO 05.11.2020 Redrawn from Matsuda et al., Metal. Mater. Trans. A 29A, 1998(1161). erwin.povoden-karadeniz@tuwien.ac.at 37 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) DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 38 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 DEFENSIO 05.11.2020 +7633 39 +3350 erwin.povoden-karadeniz@tuwien.ac.at 39 Metastable preciptate thermodynamics ... Al-alloy +Mg, Si - AA6016 Povoden-Karadeniz, Lang, Warczok, Falahati, Jun, Kozeschnik, CALPHAD, 2013, 43, 94-104. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 40 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. 41 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 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 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 42 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 DEFENSIO 05.11.2020 Si-Cl Num. fluct. erwin.povoden-karadeniz@tuwien.ac.at 43 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 44 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) DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 45 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) DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 46 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 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 47 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 50 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 51 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 52 Thank you for your kind attention! DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 53 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 54 DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 55 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. DEFENSIO 05.11.2020 erwin.povoden-karadeniz@tuwien.ac.at 56 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