Theoretical strength of a perfect crystal with exponentially attractive and repulsive interatomic interactions

Abstract

Numerical calculations are made of the theoretical strength of fcc crystals with two‐body exponentially attractive and exponentially repulsive interatomic interactions; the crystals are subjected to unconstrained (100) uniaxial tension and compression. The calculations are made from the point of view of mechanical lattice stability; the general theory has been presented in an earlier paper. The numerical values of the parameters characterizing the interatomic interactions were calculated from the elastic moduli C₁₁ and C₁₂ and the stress‐free equilibrium value of lattice parameter for Ni; the element Ni was selected for this purpose because (i) the Cauchy condition is not severely violated for Ni, (ii) the correct (i.e., experimental) linear elastic stress‐strain behavior is exhibited by the theoretical model of the crystal, and (iii) reasonably good agreement is obtained between theoretically calculated and experimentally observed anharmonic pressure‐vs‐volume behavior. Calculations are carried out using relatively short‐range steep and long‐range shallow atomic potential functions; remarkably good agreement is found among results of calculations made wth the different atomic potentials. The theoretical strength and corresponding strain in tension is about 1.6 × 10¹¹ dyn/cm² and 10.5%, respectively. The modes of lattice failure are examined. Under sufficient compression, the lattice slips into a stress‐free bcc structure which appears at a local energy maximum; the bcc structure is mechanically unstable.