1. Calculations of phase diagrams using Thermo-Calc software package Equilibrium calculation using the Gibbs energy minimisation 1. The Gibbs energy for a system 2. The Gibbs energy for a phase Unary system: Sn (calculation of melting temperature, plotting thermodynamic functions) Phase diagram for the Sn-Bi system (Temperature - Composition) Calculation of invariant reaction (T, phase compositions, enthalpy) Calculation of thermodynamic properties of liquid phase Calculation of phase fraction diagram for Bi concentration 5, 25 and 43 mol.% Scheil solidification simulation for Sn-Bi alloys Calculation of phase diagram for Fe-C system 1.Stable diagram 2. Metastable diagram Content

2. The Gibbs for a system and for a phase 1+3+5: G 135 =n 1 G 1 +n 3 G 3 +n 5 G 5 1+2+4: G 124 =n 1 G 1 +n 2 G 2 +n 4 G 4 1+3+4: G 134 =n 1 G 1 +n 3 G 3 +n 4 G 4 2+4+5: G 245 =n 2 G 2 +n 4 G 4 +n 5 G 5 2+4+6: G 246 =n 2 G 2 +n 4 G 4 +n 6 G 6 2+3+5: G 235 =n 2 G 2 +n 3 G 3 +n 5 G 5 3+4+6: G 346 =n 3 G 3 +n 4 G 4 +n 6 G 6 3+5+6: G 356 =n 3 G 3 +n 5 G 5 +n 6 G 6

3. The Gibbs for a system and for a phase

5. Property diagrams for unary system (Sn) T m =505 K (232°C) L=Sn-Bct  H tr =-7.029 kJ/mol

6. Phase diagram of the Sn-Bi phase diagram

7. Calculation of enthalpy (  H) of reaction 1Liq=a(Sn)+b(Bi) X (Sn) X Liq X (Bi) c=(X (Bi) -X (Sn) ) a=(X(Bi)-XLiq)/c b=(X Liq -X (Sn) )/c  H(T inv )=a  H (Sn) +b  H (Bi) -  H Liq  H(412K)=-7.717 kJ/mol-at. c b a Stoichiometric coefficients a and b of invariant reaction are calculated by lever rule

8. Calculation of thermodynamic properties of liquid phase Thermodynamic functions of mixing (enthalpy, entropy, Gibbs energy) in Liquid phase at 300°C Activity of Bi and Sn in Liqiud phase at 300°C

9. Phase fraction diagrams IIIIIII II III

10. Scheil solidification simulation ξ(liq) n – fraction of liquid calculated by lever rule at T n Nonequilibrium solidification of Cu-Ni alloy D.R. Askeland, P.P. Phule „The science and engineering of materials“ p. 370

11. Scheil solidification simulation for Sn-5Bi alloy

12. Scheil solidification simulation for Sn-25Bi alloy

13. Scheil solidification simulation for Sn-43Bi alloy

14. Phase relations in the Fe-C system Fig.1. Stable diagramFig. 2. Metastable diagram