THERMODYNAMIC MODEL
Wagner-Schottky model
Intermetallic compounds with B2 structure tend to be stable over a wide range of compositions. The wide homogeneity range is achieved by the incorporation of constitutional defects into the crystal structure. The W-S model has been frequently used for describing the relationship between enthalpy of formation and composition over the B2 phase region of some alloy systems. Calorimetric measurements were made in this study to obtain the parameters for the W-S model, which can be used for enthalpy prediction in Calphad modeling of the system.
The composition dependence of ΔHf of the B2 phase in Al-Ni-Fe using the W-S model is:
ΔHf = ΔH*(1+ x20) + ΔH12 x12 + ΔH13 x13 + ΔH20 x20 + ΔH21 x21 + ΔH23 x23
ΔH*= x ΔHfAlNi +
(1-x) ΔHfAlFe
The definitions of the parameters in the Wagner-Schottky model of the B2 phase.
| Parameter | Definition |
ΔHf |
Enthalpy of formation of B2 phase in Al-Ni-Fe |
ΔH* |
Enthalpy of formation of 1 mole of the ideally stoichiometric B2 phase |
ΔH12 |
Enthalpy of formation of 1 mole of Ni antistructure atoms in the β sublattice |
ΔH13 |
Enthalpy of formation of 1 mole of Fe antistructure atoms in the β sublattice |
ΔH20 |
Enhthalpy of formation of 1 mole of vacancies in the α sublattice |
ΔH21 |
Enthalpy of formation of 1 mole of Al antistructure atoms in the α sublattice |
ΔH23 |
Enthalpy of formation of 1 mole of Fe in the α sublattice |
x12 |
Concentration of Ni antistructure atoms in the β sublattice |
x13 |
Concentration of Fe antistructure atoms in the β sublattice |
x20 |
Concentration of vacancies in the α sublattice |
x21 |
Concentration of Al antistructure atoms in the α sublattice |
x23 |
Concentration of Fe antistructure atoms in the α sublattice |
ΔHfAlNi |
Enthalpy of formation of 1 mole of the ideally stoichiometric AlNi |
ΔHfAlFe |
Enthalpy of formation of 1 mole of the ideally stoichiometric AlFe |
Miedema's semi-empirical model
By using Miedema's semi-empirical model extended for ternary alloys, the standard enthalpy of formation, ΔHf 298K, can be calculated from:
ΔHf 298K = CA ƒBA ΔHinter (A in B) + CA ƒCA ΔHinter (A in C) + CB ƒBC ΔHinter (B in C)
CA and CB are the molar ratios
of A and B elements respectively in the corresponding compounds, ƒBA is the
degree of surface contact of an A atom with B neighbors
while the ƒCA is the degree of surface contact of an A atom with C neighbors.
ΔHinter is interfacial enthalpy.