1. Outline: THERMOCALC program – various versions (other programes: MTDATA, FACTSAGE, PANDAT..) Database – pure metals, metalic solutions, intermetalics Macros for calculation of binary phase diagrams Prediction of phase equilibria in complex systems Calculation of phase equilibria by Thermocalc software Prof. Jan Vřešťál, Masaryk University in Brno, Czech Republic

2. Thermocalc as the software for calculation of phase diagrams by the Calphad method can be used for calculation of phase diagrams using Compound Energy Formalism (CEF) for the Gibbs energy models listed in the lecture. The examples can be divided into 2 parts: 1. Examples using existing databases (solder, steel) 1. 1. Calculation of single equilibrium (TC does not discriminate upper case and lower case in the name of commands) Solder.tdb: AgPd.tcm, Steel.tdb: FeNi.tcm 1.2. Calculation of phase diagrams Solder.tdb: AgPd.tcm – continue, BiSn.tcm – continue, BiCu.tcm (zoom), BiIn.tcm, CuSn.tcm Steel.tdb: FeNi.tcm – continue CrNi.tcm Examples of using Thermocalc

3. 1.3. Include magnetism and/or miscibility gap Solder.tdb: AgPd.tcm – exclude misc-gap (delete starting point at 400 K) Steel.tdb: FeNi.tcm – without „A_P_D Mag_ord BCC_A2“ no phase diagram 1.4. Calculate thermodynamic functions at chosen temperature Solder.tdb: AgPd.tcm,(G liquid :old,new), BiSn.tcm - continue 1.5. Phase diagram with metastable phases Steel.tdb: Fe-C – phases all: equilibrium with graphite Reject phase graphite: equilibrium with diamond Reject phase graphite, diamond: equilibrium with cementite 1.6. Calculate consecutive equilibrium compositions – step command: Solder.tdb: BiInstep.tcm, Steel.tdb: CrNistep.tcm, CuNistep.tcm 1.7. Calculate Scheil solidification scheme: Solder.tdb: Scheil-BiIn.tcm, Steel.tdb: Scheil-CrNi.tcm, Scheil-CuNi.tcm 1.8. Calculate ternary phase diagram Solder.tdb: Isothermal section: BiCuSn1000.tcm Isoplethal section: BiCuSn10Cu.tcm Steel.tdb: FeCrNi1273.tcm

4. 2. Examples to create own database for verification of published parameters (special separate database) 2.1. Ta-V system: C.A. Danon, C. Servant: A thermodynamic evaluation of Ta-V system. J. of Alloy and Comp. 366 (2004) 191-200 2. 2. Cr-Zr system: J. Pavlů, J.Vřešťál, M. Šob: Stability of Laves Phases in the Cr-Zr system. Calphad 33 (2009) 382-387 2.3. Ru-Ge system: J.Zálešák: Final Report of Computational Thermodynamics. 2010. Improve founded errors by the proper change of parameters, when necessary. --------------------------------------------------------------------------------------------------------- 3. Examples to create experimental datafile (.POP-file) for the PARROT progam (PANDAT Program) (special statements necessary to be used – see User Guide )

5. Structure of database - ThermoCalc Definition of reference states of elements Definition of phases and their constituents - models Records: Values of thermodynamic functions (pure components, compounds, solutions, ordered phases) Advantage: Communication with other programes: diffusion, solidification…. and with other databases

6. Definition of reference state of elements - example ELEMENT /- ELECTRON_GAS 0.0000E+00 0.0000E+00 0.0000E+00 ! ELEMENT VA VACUUM 0.0000E+00 0.0000E+00 0.0000E+00 ! ELEMENT IN TETRAGONAL_A6 114.82 0.0000E+00 0.0000E+00 ! ELEMENT SN BCT_A5 118.69 0.0000E+00 0.0000E+00 ! ELEMENT ZN HCP_A3 65.39 0.0000E+00 0.0000E+00 ! ELEMENT BI RHOMBO_A7 208.98 0.0000E+00 0.0000E+00 ! ELEMENT AG FCC_A1 107.87 0.0000E+00 0.0000E+00 !

7. Definition of phases and their constituents - example (see models) PHASE LIQUID:L Z 1 1 ! CONSTITUENT LIQUID:L :AG,BI,IN,SN,ZN : ! $ PHASE BCT_A5 Z 1 1 ! CONSTITUENT BCT_A5 :AG,BI,IN,SN,ZN : ! $ PHASE TETRAGONAL_A6 Z 2 1 1 ! CONSTITUENT TETRAGONAL_A6 :AG,BI,IN,SN,ZN:VA : ! $ PHASE FCC_A1 Z 2 1 1 ! CONSTITUENT FCC_A1 :AG,BI,IN,SN,ZN:VA : ! $ PHASE FCT Z 1 1 ! CONSTITUENT FCT :AG,BI,IN,SN,ZN : !

8. Structure of records – G o - example G(PHASE,ELEMENT1;0) G(PHASE,ELEMENT2;0) TM BM T(lower) Polynomial for G(T,p) T(upper) N/Y Literature ! PARA G(BCC,Cr;0) 298.15 GHSERCR 6000 N SGTE ! FUN GHSERCR 298.15 -8856.94+157.48*T- 26.908*T*LN(T)+.00189435*T**2-1.47721 E-06*T**3+139250*T**(-1); 6000 N SGTE !

9. Structure of records - G E - example L(PHASE,ELEM.1,ELEM.2;ORDER OF INTERACTION) TM BM T(lower) L- Redlich - Kister polynomial T(upper) Literature ! G E = x 1 x 2  i L i (x 1 – x 2 ) i - R-K polynomial PARAM L(FCC_A1,CR,FE:VA;0) 298. 10833.-7.477*T; 6000. HQ91 !

10. Calculation of phase diagram - example Macro (AgSn.log) : GO DATA sw avr define-element Sn Ag Reject phase /all Restore phase bct_a5 fcc liq hcp epsilon get $-------------------------- GO GES list-phase-data fcc @?continue $-------------------------- GO POLY set-condition t=973 x(Ag)=0.95 p=1E5 n=1 Calculate-equilibria set-axis-variable 1 x(Ag) 0 1.025 s-a-v 2 t 300 1200 10 map $-------------------------- POST set-diagram-axis x m-f Sn s-d-a y t-C make-experimental-datafile SnAg.dat set-title Sn-Ag Phase diagram plot SCREEN set-interactive

11. Basic types of phase diagrams Systems with complete miscibility of components in solid phase Systems with incomplete miscibility of components in solid phase – primary solid solutions - eutectics - peritectics Systems of components with no solubility in solid phase (eutectics, peritectics) Systems with intermedial phases - compounds (Hume-Rothery– „electrons“: Cu 7 Zn 3 ) - intermetallic phases (Zintl – „ions“: K 4 Sn 9 ) - intermetallic phases (covalent: GaAs) - ordered phases (CuAu), - Frank-Kasper phases ( , , Laves - topologically ordered) Secondary solid solutions (components soluble in intermedial phases)

12. Models for solid solutions and liquid (example) FCC: 2\ 1 1 BCC:2 \ 1 3 HCP:2 \ 1 0.5 Liquid:1 \ 1

13. Models for intermetallics (example) Laves_C14:2 \ 2 1or3 \ 4 6 2 Laves_C15:2 \ 2 1 Laves_C36:2 \ 2 1or3 \ 8 12 4 Assignment of lattice sites in models Sublattice 1 2 3 Laves_C14 4f 6h 2a (Cr) Laves_C15 8a 16d (two sublattice model) Laves_C36 4e, 4f 6g, 6h 4f (Cr)

14. Creating database Problems: Condition of database consistency - models used - names used - numerical data used