Applicability of exponentially attractive and repulsive interactomic potential functions in the description of cubic crystals

The well-known Morse function φ (r) = D exp −2α (r−r0) −2 exp −α (r−r0) can be considered to be a particular case of the general family of potential functions with exponential attraction and exponential repulsion, viz. , φm (r) = D/ (m−1) exp−mα (r−r0) −m × exp−α (r−r0). This study examines the suitability of applying the functions φm (r) to the description of mechanical properties of cubic crystals. For bcc lattices, the ratio C11/C12 for the theoretical model of the crystal made up of atoms with φm (r) interatomic interactions is shown to be too small to provide a realistic description of bcc metals; also, the bcc crystals are found to be inherently unstable for larger values of αa0, where a0 is the lattice parameter of the crystal. For fcc lattices, however, the theoretical model of the crystal is found to be mechanically stable for arbitrary (i. e. , m1) exponentially attractive and repulsive interactions and the elastic moduli C11 and C12 of the theoretical fcc crystals are found to be capable of conforming to the respective experimental values of fcc metals. The results are in agreement with Born's analyses of lattice stability. Numerical values of D, α, and r0 are calculated for several different values of the parameter m for fcc Ni using experimental values of C11, C12, and lattice parameter. The element Ni is selected because, among the fcc metals, Ni most closely obeys the Cauchy condition C12 = C44. The functions φm are then used to calculate theoretical pressure versus volume (P-V) behavior (at pressures large enough to produce considerable anharmonicity) and the results are compared with experiment; good agreement is found between the calculated and experimental P-V relations.