Книга
93 17858

Chukov, Vitalii N.
Topological laws of the Rayleigh wave scattering and violation of the Rayleigh and generalized Laue-Bragg-Wulff laws / V. N. Chukov; Russian acad. of sciences, N. M. Emanuel inst. of biochemical physics, Center of acoustic microscopy. – Moscow : Preprint : IBCP RAS, 2018. – 59 p. : fig.
Бібліогр.: с. 52 - 57 (93 назви).

The problem of the surface acoustic Rayleigh wave scattering on a deterministic cylindrically symmetrical roughness occupying finite size region of an isotropic solid free surface is solved in the Born (the Rayleigh-Born) approximation of the perturbation theory in a roughness amplitude. Formula for the displacement field in the scattered Rayleigh wave at a big distance from the roughness, as compared to rough region radius d, and asymptotic formulas for it in the Rayleigh, i.e. long-wave length λ>>d, and in the Bragg, i.e. short-wavelength λ>>d, limits are derived. The Rayleigh limit of scattering is investigated. The generalized Laue-Bragg-Wulff law of scattering in the Bragg limit is obtained for a continuous roughness having single discontinuity at the end of a rough region. It is the analog of the Bragg (the Laue-Bragg-Wulff) conditions of the resonances of scattering for the Rayleigh rays interference in crystals. It describes the short-wavelength and angular oscillations of the indicatrix of scattering. The new laws of scattering are obtained for the Rayleigh and Bragg limits. They define the frequency and angular dependences of the indicatrix of scattering and are caused by a strong modulation of scattering by a roughness form in the both limits. They establish the topological symmetry of a long- and short-wavelength scatterings and, thereby, enable its violation by means of a strong scattering modulation by a superposition of a roughness forms corresponding to these new different definite laws of scattering. Transitions to the more long- or short-wave length limits of scattering restore this topological symmetry in the concrete limit. This topological symmetry itself includes violation of the Rayleigh and the generalized Laue-Bragg-Wulff laws of scattering as well as violation of the fundamental physical conception that the incident wave does not sense structure of a roughness in the Rayleigh limit, since all points of a roughness oscillate in a scattering with the same phase. The new laws exceed the analogical conception in the Bragg limit, that wave scattering takes place on the roughness discontinuities and has a big sensibility of the scattered waves phase to discontinuities arrangement, by the results about a strong modulation of scattering by the structure of a roughness in the near vicinity of these discontinuities and by the analytical dependence of the scattering intensity on the amplitude of each scatterer in arbitrary lattice of discontinuities, missing in literature so far. It is obtained that a strong modulation of scattering by a roughness form, giving the new laws in the Rayleigh limit and violating the Rayleigh law, violates as well the law of the Bragg limit about maximum scattering in the vicinity of the forward direction. So the scatterings of the Rayleigh and Bragg limits, as well as resonance scattering λ ~ d, topologically intersect in the space of wave-vectors transmitted in a scattering from incident to scattered wave.



Предметні рубрики = МАТЕМАТИКА. ПРИРОДНИЧІ НАУКИ : Хімія. Кристалографія. Мінералогія : фізична хімія : хімічна структура речовини : атомні та молекулярні спектри : оптичні спектри, спектрохімічні серії : релеївські та бріллюенівські спектри розсіяння
Предметні рубрики = МАТЕМАТИКА. ПРИРОДНИЧІ НАУКИ : Хімія. Кристалографія. Мінералогія : мінералогічні науки, кристалографія, мінералогія : кристалографія : тонка структура кристалів, теорія дисконтинууму кристалів : аналіз кристалів із застосуванням рентгенівських променів, рентгенографічний аналіз, рентгенографічне дослідження структури кристалів

1670775 ОФ