Thermal scattering of X-rays by crystals II. The thermal scattering of the face-centred cubic and the close-packed hexagonal lattices

Abstract

The results of the preceding paper (Part I) are here applied to two special lattices, the face-centred cubic and the close-packed hexagonal lattices. In both cases the assumption is made that only next-neighbour atoms act on one another. In the case of the cubic lattice the number of atomic constants turns out to be equal to that of the elastic constants, so that the dynamical matrix can be expressed in terms of the latter. Numerical calculations are performed taking for the elastic constants those of potassium chloride; the results are compared with those obtained by Iona who used the correct ionic forces. Then the scattering matrix is calculated and a diagram of equi-diffusion lines is drawn which covers a part of the reciprocal space containing nine lattice points. In the case of the hexagonal lattice the number of atomic constants is greater than that of the elastic constants. The dynamical matrix is given in terms of the former; but equi-diffusion lines are constructed only for the vicinity of the selective reflexions (Jahn case) where the scattering can be expressed in terms of the elastic constants.