Relationship between the thermodynamic excess properties of mixing and the elastic moduli in the monazite-type ceramics

Using ab initio quantum chemistry we computed the excess thermodynamic properties and the elastic moduli for a series of monazite-type single substitution solid solutions (Ln1−xLnxPO4). We found that the Margules interaction parameters of all the solid solutions can be described by a simple function of the endmembers volume mismatch ΔV  , i.e. W(kJ/mol)=0.616(ΔV(cm3/mol))2W(kJ/mol)=0.616(ΔV(cm3/mol))2. We show that the obtained relationship could be also derived by considering the strain energy resulting from the substitution of cations of different sizes, knowing the Young's modulus and the volumes of endmembers. This indicates that the strain resulting from the structural incorporation of cations is a major factor responsible for arising of the excess properties in monazite-type ceramics. Our results show thus a way to estimate the excess thermodynamic properties of solid solutions from the structural and elastic parameters, namely the endmembers volumes and the Young's modulus, which could be easily measured or computed.