Atomistic simulation of sodium–gadolinium molybdate of stoichiometric (Na$_{1/2}$Gd$_{1/2}$MoO$_{4}$) and cation-deficient (Na$_{2/7}$Gd$_{4/7}$MoO$_{4}$) compositions

Crystals of sodium–gadolinium molybdates of two compositions: stoichiometric (Na$_{1/2}$Gd$_{1/2}$MoO$_{4}$) and cation-deficient (Na$_{2/7}$Gd$_{4/7}$MoO$_{4}$) composition in which 1/7 of the corresponding cation positions are not occupied are simulated by the method of interatomic potentials. For cation-deficient crystals, two kinds of cation position distribution are considered: the statistical distribution of sodium, gadolinium, and unoccupied cation positions in the $I$4$_{1}/a$ structure and their partial ordering in the $I$ space group. As a result of the simulation, structural characteristics of sodium–gadolinium molybdates agreeing well with the known experimental data are obtained. In addition, a number of important elastic and thermodynamic properties of these compounds are predicted. The results obtained in the partial-occupancy approximation and by constructing a 7 $\times$ 2 $\times$ 2 supercell are compared. The local structure of sodium–gadolinium molybdates are analyzed in detail. The influence of the deviation from the stoichiometry as well as cation ordering on the properties of these crystals is discussed.