Crystal theory of metals: calculation of the elastic constants

The approximate equations of motion for the electrons in a cyclic lattice of a metal are set up with the help of the self-consistent field. The displacements of the ions are then considered as perturbations of the motion of the electrons. The change of the boundary is compensated by a co-ordinate transformation. The change of the potential energy of the lattice due to a homogeneous deformation is calculated by the perturbation method. The calculated values of the elastic constants are found to be in satisfactory agreement with the observed values.