Model Evaluations of Phase Diagrams of the Systems SrO - (Mn, Fe, Co, Ni)O
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Mat. Res. Soc. Symp. Proc. Vol. 398 0 1996 Materials Research Society
In this work we use interionic potentials obtained for dilute solid solutions from experimental data, and apply them for the binary systems considered and which were not investigated yet. This approach permits to avoid full energy and first principle calculations. MODEL A major approximation of the model used here is the assumption that the most significant 13 contribution to the excess free energy of mixing is the excess binding energy. It was shown that excess energy can be expressed as: Eex = n(' -
+ dis)
(1)
where C'is the free energy per molecule of the solute impurity in solution, Vis its free energy per molecule when it is in its own pure lattice, Edis is the lattice distortion contribution to the lattice energy per impurity molecule, and n is the number of impurity molecules. We assume that the binding energy consists of electrostatic and repulsive interactions, while the van der14 Waals interaction can be neglected. Repulsive interaction was applied in the Born-Mayer form WR
- a) + b++c++ exp( 2r- - aV-2) = b+_c+_ exp(r+ + r. P P
(2)
which takes into account interaction between second neighbours. Here r+ and r- are cation and anion radii respectively, r± is either the cation or the anion radius, a is an equilibrium distance between nearest neighbours, c.-, c±+ are Pauling constants, b+-, b++ and p are the potential parameters obtained from experimental data. The +- sign indicates nearest neighbours interaction, ±± refers to second nearest neighbours interaction (cation-cation or anion-anion). Potential parameters are determined from the lattice equilibrium condition and from the definition of the bulk modulus through the interatomic potential 15 . By this way p (hardness parameter) and some average b parameter can be calculated. This average value was used in eq.2 for the b+. parameter. Applying the values obtained for b+. and p, the parameters b++ (or b..) were calculated from the lattice equilibrium condition, when cation (or anion) is in the origin. This procedure leaves the calculated cohesive energy unchanged compared to the standard approach 15 , but permits at the same time to calculate independently the contribution of the cations and anions in the second nearest neighbour sites to the lattice distortion energy of a dilute solution. The interaction of the impurity and the host cations at second nearest neighbour sites was described by the same hardness parameter (p) and by a specific parameter, b,+, expressed as
bs+ = b'++ -D
(3)
Here, b'++ refers to the potential parameter in the pure solute crystal and D is an adjustable dimensionless parameter to be evaluated. Thus, all types of interionic interactions are defined and it is possible to calculate D from known excess energies 1 applying the Mott-Littleton method 8 to describe the lattice relaxation. Our calculations based on Brauer's 16 approach show that the contribution of the repulsive 650
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