Structure of acoustic Lauegram on the Ewald circle of reflection for the Rayleigh wave scattering

The acoustic Lauegram of the Rayleigh wave the Laue–Bragg–Wulff high-frequency scattering on a rectangle rough band of an isotropic solid, having periodic lattice of an arbitrary number of the roughness discontinuities, is theoretically investigated in details in dependence on the angle of scattering φ_s at a fixed ratio of the lattice unit cell size to the wavelength and parameters of the lattice. The Ewald conception of the circle of reflection is used. The problem of an arbitrary number, defined beforehand, of the resonances of scattering, i.e. nodes of the reciprocal lattice, for any φ_s, defined beforehand, lying on the Ewald circle of reflection, is first solved analytically in the present work in the classical case, i.e. without influence of the amplitude form-factor of the lattice. It is found, that increasing of the number of resonances for any φ_s is necessarily accompanied by the increasing of the Ewald circle of reflection radius, i.e. of the Rayleigh wave frequency, at fixed sizes of a discontinuities lattice. It is obtained first, that amplitude form-factor of the discontinuities lattice strongly influences the structure of the acoustic Lauegram: arbitrary number of the resonances of scattering for any φ_s can be placed on the Ewald circle of reflection without variation of its radius by using of the appropriate amplitude form-factor of a discontinuities lattice of a solid roughness.