Effect of absorption on dynamical Bragg diffraction of x-rays on a crystal modulated by strong ultrasound

Abstract

A theory of x-ray diffraction in crystals with electron density modulated due to acoustic wave propagation is developed for Bragg geometry of scattering. Expressions, describing modifications of diffraction spectrum as well as an integrated diffraction intensity are derived and analysed in certain extreme cases. Special attention is paid to the behaviour of diffraction intensity under a strong acoustic field applied to a crystal. The crucial role of x-ray absorption in acoustically induced diffraction effects is established. It was shown that acoustic modulation results in significant increase of diffraction intensity up to a limiting value, which is inversely proportional to the x-ray absorption coefficient.

X-ray Bragg Diffraction in a Strong Acoustic Field

“…Detailed theoretical analysis (Polikarpov, 1996;Polikarpov & Zolotoyabko, 1997) allowed the derivation of expressions describing the diffraction spectrum and integrated diffraction intensity in the form of a series over parameter p. Generally, these expressions may be used for computer simulations and selected examples of such calculations are given in Fig. 7.…”

“…Under ultrasonic excitation, a set of satellites related to the inelastic scattering processes with wavevector transfer, H + px (p = +1, -t-2 .... ), appears in the diffraction spectrum, each satellite having a width, Gp, proportional to the Bessel function of the pth order, Jp (HW), and the height, Ip < 1, reduced due to the X-ray absorption on the characteristic length, Lp (Polikarpov, 1996): L, (10) Lp _ [~(HW) + $2] 1/2" Excitation of satellites leads to considerable modifications in spectrum width and integrated intensity. Detailed theoretical analysis (Polikarpov, 1996;Polikarpov & Zolotoyabko, 1997) allowed the derivation of expressions describing the diffraction spectrum and integrated diffraction intensity in the form of a series over parameter p. Generally, these expressions may be used for computer simulations and selected examples of such calculations are given in Fig. 7.…”

Investigation of surface acoustic wave fields in silicon crystals by x-ray diffraction: A dynamical theory approach

“…Most of them deal, however, only with bulk acoustic waves, 8,9 or with SAWs but without any comparison with experimental data. 10,11 Recently some of us have published a paper showing that rocking curves of a SAW excited LiNbO 3 crystal can be well simulated by using a dynamical theory model. 12 The aim of this paper is to present the results of an additional investigation for a crystal of a nonpiezoelectric material such as Si and to assess the degree of accuracy of the simulation in the quantitative analysis of acoustic wave fields in such crystals.…”

Acoustically adjustable LiNbO3 double-crystal monochromator for synchrotron radiation

“…In the Bragg case the maximum gain of the integrated diffraction intensity is estimated 16 to be Ϸ(L a /L e ), so that x-ray absorption is seen to be of crucial importance. In other words, under ultrasonic excitation, dynamic x-ray diffraction is gradually transformed into the kinematic type, increasing the integrated diffraction intensity which, at high ultrasonic amplitudes, asymptotically tends to the kinematic limit.…”