1. Phase diagrams by thermodynamic calculations
Basics of thermodynamics : lections 1 and 2
Experimental methods to measure thermodynamic properties: lection 3
Phase diagrams of unary, binary and ternary systems: lections 4, 5 and 6
Potential diagrams : lection 7
Experimental methods to investigate phase diagrams: static methods (lection 8)
Experimental methods to investigate phase diagrams: dynamic methods (lection 9)
Thermodynamic modeling of solid, gas and liquid phases (lections 10 and 11)
Gphase=f(T,P,xi)
Solid phases (stoichiometric, solid solutions)
Models for solid solutions: substitutional, sub-lattice model
Liquid models: substitutional , associate, partially ionic, quasi-chemical, cell
Gas: ideal gas containing various species
CALPHAD method: lection 12
Practicum presents how to calculate phase diagrams for binary system (T-x diagrams, property diagram, phase fraction diagram, Scheil simulation, metastable phase diagram). It also includes calculations of phase diagrams for ternary systems (isothermal sections, vertical sections, liquidus surface), potential diagrams and their relations with other diagrams)

2. Phase diagram is a chart showing conditions (pressure, temperature, composition , volume etc.) at which thermodynamically distinct phases occur and coexist in equilibrium.
Unary system
Gibbs energy G
Temperature
The Gibbs energy of phase with constant composition at temperature T is expressed by
GT = HT - ST ∙T,
where HT and ST are enthalpy and entropy at temperature T.
The enthalpy and entropy at temperature T are expressed by equations:
where DH0f,el298 is enthalpy of formation from elements, S0298 standard entropy and CP is heat capacity, which also depends on temperature: CP= A+B∙T+C/T2 (Maier – Kelly equation)

3. Binary phase diagrams
The Gibbs energy of solution phase depends on pressure, temperature and composition x:
G(T,p,x)
Temperature
G, Gibbs energy
Mole fraction xB
Mole fraction
Activity
Ideal behavior

4. Ternary phase diagrams
Liquidus surface
Isothermal sections

5. Ternary Four-Phase Equilibrium Eutectic
Vertical sections (Isopleths)
Ternary Four-Phase Equilibrium
Eutectic

6. Potential diagrams Types of diagrams:
1. Potential diagrams – two potentials
2. Mixed diagrams – one potential and one ratio of extensive properties
3. Extensive properties diagrams – two ratios of extensive properties

7. THERMO-CALC software for thermodynamic calculations
SYS: go to module
DATABASE, Scheil, BIN, TERN
To make Scheil simulation, or to calculate phase diagram in BIN or TER module
go da - go to database module
TDB Database selection (user, commercial databases TCFE6, SSUB4)
sw-da switch database
def-e define elements - elements selection
l-sys list system (elements, phases, constituents)
Constituents - list of phases with models used
get
go TAB (calculate thermodynamic properties of phases or reactions)
go gi (Gibbs energy system ) l-p-d (see phase description )
l-d list data to make new database or TCM file for PARROT
go POLY3
Calculate single equilibrium
set-cond (set conditions T, P ,xi-xn-1, N=1)
c-e compute equilibrium
l-e list equilibrium
2. Calculations of phase diagrams by step or map
s-a-v 1 x(el) (ranges of axis variable and increment )
one axis – step command (e.g. to calculate mixing enthalpy vs. composition)
two axis – map (e.g. x-T diagram, isothermal section)
three axis – map (liquidus surface)
PARROT
Optimisation of
parameters
Post (to see the diagram)