To the question of the interference function main peak area

Abstract

One way to study a structure of regularly located elements is the interpretation of scattering pattern on such structure of corresponding radiation. The most striking examples are the scattering of light by a diffraction grating and the scattering of x-ray radiation by a crystalline sample. Among many factors in the intensity of obtained scattering pattern, the interference function of Laue occupies a special place. The properties of this function have long been expounded in classical monographs. However, as shown in this paper, some authors make mathematical error when making the limit as the number of scattering objects (the number of diffraction grating lines or the number of atoms in the crystal) tends to infinity. The situation is aggravated by the fact that along with an analytical calculation of such limit, simple method of qualitative estimation, which gives the same false result, is offered. Leaving a detailed analysis of the error, the author sets the goal of to express an exact value for this limiting transition. The correctness of the obtained analytical result is confirmed by numerical calculation. The article shows that the ratio of limiting value of the area under the interference function main peak to value of the area under the interference function in one period is 2/p·Si(2p). An alternative method is also proposed for the known geometric construction, which allows one to estimate the limiting value of the area of the main peak.