THE PROBLEM OF OBSERVING THE MAXIMUM OF A SUPERPOSITION WAVE FIELD

Abstract

The well-known Laue condition determining the intensity maximums of diffracted on an ideal crystal structure plane wave is discussed. Initially the consideration is performed for the near observation region and after that by means of applying the corresponding approximation the expression of superposition field is presented as a sum of plane waves. So, the description of the superposition field for the far observation region is made. It is proved that the Laue conditions, which are restrictions imposed on the values of the scattering wave vector, is more correctly to be considered as a pair of two conditions. The first condition relates to the wave vector of an incident wave and the second condition relates to the wave vector of an observation direction. In other words, to observe the maximums, it is not enough when only the difference (the scattering wave vector) of these two vectors satisfies the Laue condition. To observe the maximums, it is necessary that each of these vectors separately, i.e. the wave vector of the incident wave and the wave vector of the observation direction satisfy the Laue condition. It is shown that such a doubling of the maximum conditions leads to a decrease in the number of the observed maximums compared to the condition imposed only on the scattering wave vector. Within the framework of the previously developed method, a number of formerly known results related to the kinematic theory of diffraction of a plane wave by an ideal crystal structure were reproduced. It is assumed that the generation of secondary waves of each atom of the crystal is provoked by the presence in the volume of the crystal of a primary field, which in Fraunhofer formulation is considered in the form of a plane and time-harmonic wave. The intensity distribution, as well as the positions of the maxima of the diffraction pattern, was studied depending on the spatial parameters of the crystal lattice.