X-Ray Images of Ultrasonic Waves in a Crystal

Abstract

Topographic x-ray diffraction images of ultrasonic waves in a thick silicon crystal are presented. The stationary nodal pattern of an acoustic field in the crystal is displayed, including that due to a set of plane standing waves. The images were achieved by making use of the anomalous transmission of x rays, and are of preliminary nature.

Silicon-crystal rocking curves under X-ray acoustic resonance conditions

“…For small absorption local intensity changes of the diffraction spot and the reflection integral intensity increase were found in the first region (Haruta, 1967) and in the second region satellites whose positions were in agreement with the kinematic diffraction theory were observed on the rocking curves (K6hler, M6hling & Peibst, 1974;LeRoux, Colella & Bray, 1975). In thick crystals ultrasonic vibrations suppress X-ray anomalous transmission (Saccocio, Lopez & Lazara, 1967;Hauer & Burns, 1975;LeRoux, Colella & Bray, 1976). The dependence of these diffraction effects on K s was not of resonance nature.…”

Coherent and diffuse X-ray scattering in crystals modulated by a surface acoustic wave

“…Since the pioneering papers of Fox & Carr (1931), Langer (1931) and Barrett & Howe (1932), diffraction of X-rays and neutrons in a crystal volume modulated by ultrasonic waves has attracted a large number of experimental and theoretical studies (White, 1950;Saccocio et al, 1967;Haruta, 1967;Carlson et al, 1971;Kö hler et al, 1974;LeRoux et al, 1975LeRoux et al, , 1976Entin & Assur, 1981;Chapman et al, 1983;Punegov & Pavlov, 1994). The observed experimental rocking curves were explained using the dynamical scattering theory (Kö hler et al, 1974;Authier, 2001), including the phenomenon of X-ray acoustic resonance (Entin & Assur, 1981;Punegov & Pavlov, 1994).…”

Bulk strains in Si induced by thickness mode ultrasonic waves and analysed with x-ray Bragg diffraction

“…To carry out stroboscopic measurements with standing ultrasonic waves, the phase of the ultrasonic wave has to be synchronized with the x-ray or neutron detection, so that different diffraction intensities are detected at different phases of the standing ultrasonic wave. Three main techniques are reported in the literature: shock waves (SWs) [2,4,5,10,16], SAWs [1,2,6,[17][18][19] and continuous ultrasonic waves (CWs) [13,14,[20][21][22][23][24]. In the case of SWs, the crystal (piezoelectric or not) is subjected to bursts of longitudinal ultrasonic waves being analysed in Laue or Bragg diffraction geometry.…”

“…For SAWs, the crystal (piezoelectric or not) is subjected to surface transversal acoustic waves and is analysed only in Bragg geometry. In the case of CWs, different measurements have been made with piezoelectric [20][21][22][23] or non-piezoelectric [13,14,24] materials and also with magneto-acoustic materials [25,26] in Bragg or in Laue diffraction geometry. However, monitoring deformations in non-piezoelectric materials, with x-ray diffraction in Bragg geometry and longitudinal ultrasonic waves, using an external transducer, has been reported only recently [24].…”