Interatomic force constants studies of AMF3perovskite-type crystals (A = K,Rb; M = Mg,Ni, Co,Zn, Mn)

A simple model involving only three force constants allows us to evaluate the short range interactions in perovskite fluorides from the experimental values of the elastic constants and the lattice parameters of these compounds. The results indicate that the A-F bonds are quite central in character whereas the M-F bonds are axially symmetric; thus the short range A-F interactions are assumed to have the Born-Mayer form:ZZZZZBy studying the variations of the force constants with respect to the lattice parameter r, it is determined that ρ = 0·232 , λ = 2·8 × 10^?8 ergs for K⁺-F^?; ρ = 0·232 , λ = 4·1 × 10^?8 ergs for Rb⁺-F^?; λ₂, ρ₂ and ρ₂ are respectively 6·9 × 10^?10 ergs, 0·34 , 0·98for Co²⁺-F^? and 2·9 × 10^?10 ergs, 0·46 , 1·40for Mn²⁺-F^?. Taking into account both the short range repulsive potential and the long range electrostatic potential we can study the variations of the lattice energy as a function of r near the equilibrium position and deduce a theoretical value of the lattice distance. In spite of the simplicity of the model, the discrepancy between the experimental and the theoretical values is less than 10 per cent for all the compounds.