The stability of crystal lattices. III

Abstract

The energy density of a cubic lattice, homogeneously deformed by a force acting in the direction of one axis, is calculated, and the equilibrium conditions and the stability conditions for any arbitrary small additional deformations are derived. A special assumption is made as to the law of force between the atoms, and the numerical calculations are performed for the face-centred lattice. In this way the strain as a function of the deformation is calculated and, from the stability conditions, the tensile strength is determined. The results are not in agreement with the experimental facts, and the possible reasons for this disagreement are discussed.