Exact solution of scattering problem on a chain of atoms vibrating in the triple-well potential

Abstract

The expression for the scattering intensity from a monatomic chain of atoms vibrating in an essentially anharmonic potential is obtained for the case of three minima. The calculations were performed in the framework of the Ising model approximating vibrations only by jumps from one well to another and using the Kramers-Wannier transfer-matrix. The behaviour of Bragg reflexions and diffuse scattering as functions of temperature, scattering vector and parameter r - the ratio of the central and lateral minima depths of the triple-well potential - are studied. The solution of the problem gives a clue to the understanding and detailed description of tilting and antitilting coexistence phenomena in perovskites such as NaNbO3, RbCaF3 and many others.