The effect of ultrasound on the diffraction in a deformed crystal under the conditions of X-ray acoustic resonance

Abstract

Theoretical, experimental and numerical analysis of the effect of acoustic vibrations on the X-ray diffraction in a slightly deformed single crystal is presented. We have found for the first time that the sensitivity of the diffraction with respect to small static deformation is highest for the case of X-ray acoustic resonance.

Neutron Bragg Diffraction on a Bent Silicon Single Crystal Excited by Ultrasound

“…A correct consideration of simultaneous influence of both the types of crystalline lattice deformation -static (bending) and dynamic (displacement of atoms in US wave) ones -on the diffraction of neutrons in Laue's geometry was given in works [3,11], where numerically (by the method of successive approximations) and, for separate cases, analytically a modified Takagi-Taupin equation was solved; in [5], for this purpose Green's functions were employed. In the case of Bragg's geometry, the mathematical problem becomes much more complicated owing to specific boundary conditions, and, to our knowledge, has so far no analytical solution.…”

“…The authors of [4,[7][8][9] report the results of theoretical and experimental data for the behaviour of neutrons and Xrays [11,12] at Laue's diffraction in deformed silicon single crystals under highfrequency (λ s << τ) excitations. Their analysis has shown that in smoothly deformed Si crystals the US effect is expressed in violation of the adiabatic conditions for the movement of tie points on the dispersion surfaces.…”

Neutron Laue Diffraction in Perfect and Deformed Silicon Single Crystals Under Ultrasound Excitation

“…This dependence can be used for determination of the B pr value. As was shown earlier [14], to observe the interference effects associated with the neutron scattering from the ultrasound lattice oscillations a good uniformity of the acoustic field inside the crystal is needed: ΔW/W not worse than 10%. Figure 3 shows the US influence on the relative intensity of the neutron diffraction in a perfect and a deformed crystal.…”

Neutron Diffraction on Acoustic Waves in a Perfect and Deformed Single Crystals

“…In deformed crystals, which are of great practical interest, the effect of US on diffraction has been investigated much less. In [14,45,46] the results of theoretical and experimental investigations of neutrons and X-rays for the case of Laue diffraction in deformed silicon single crystals under high-frequency (νs >> νres) and in conditions of the neutron (X-ray) -acoustic resonance (νs≈νres) are reported. The analysis has shown that in a deformed Si crystal ultrasound results in violation of the adiabatic conditions for the movement of tie points on the dispersion surfaces.…”

“…Curve 11 demonstrates the shift of the Ids minimum over Vs with an increase in h. The simultaneous effect of both deformation types of a crystal lattice, static bending and dynamic atomic displacement in an US wave, on the neutron diffraction in the Laue geometry was taken into account in [14,46] where numerically (by the method of successive approximation) and, for separate cases, analytically by a modified Takagi-Taupin equation was solved. In [49], for this purpose Green's functions were used for Laue case.…”