On the Suppression of X‐Ray Anomalous Transmission by Acoustic Oscillations

Abstract

It is shown that the Debye-Waller factor describes correctly the Borrmann effect acoustic suppression only within the short-wave range (& < T , 1, ultrasonic wavelength, t extinction length).The suppression factor is expressed both, for long-wave (A, >t) and intermediate (As t) cases.An analysis of the published experimental data establishes that an incorrect description of the suppression effect by the Debye-Waller factor can cause an error of several orders when determining displacements by the measured attenuation of anomalous transmission. In some cases experimental results demonstrate the main contribution of X-ray acoustic resonance to the suppression effect. nOKa3aH0, ' I T 0 MHOWHTeJIb J(e6af1-Bannepa npaBHJIbH0 OIIllCbIBaeT aIFyCTElYeCKOe AJIIlHa BOJIHbI yJIbTpa3ByKa, t 3KCTMHKuEIOHHaFI JXJIEIHa). nOnyYeHb1 BbIpaXeHEIH HJIFI $aKTOpa IIOAaBJIeHkIfI B JXJIEIHHOBOJIHOBOM (As >T) EI npOMeXyTOYHOM (As NN t) CJXyYaFIX. noHasneHne a @ $ e~~a EopMaHa TomKO B KOPOTKOBOJIHOBOM npeaene (& < t, As I43 a~a~11i3a m%emuwxcfI B nwrepaType a~c n e p~~e~~a n b~b r x naHHbix cnenyeT, YTO Hesop-pemHoe onmame a $ + e~~a noaaBneHm c noMoubm #aKTopa J(e6am-Bannepa MOWeT JXaTb O L U E I~K~ B HeCKOJIbKO IIOpRnIFOB npEI OIIpeAeJIeHHEI CMeQeHEld no H3MepeH-HOMY ocna6ne~am aHOMaJIbHOr0 npOXOX~eHEIfI. B PfIJXe CJIyYaeB 3KCIlePEIMeHTaJIbHbIe B B#@eIFT IIOAaBJIeHEIfI. pe3ynb~a~bi yxa3b1sam~ Ha onpenemmu@ Bxnaa PeHTreHoaKycTHsecKoro p e 3 o~a~c a

X-ray diffraction in crystals in the presence of laser-induced dynamic gratings

“…Optically induced dynamical gratings were obtained and investigated much later, when high-power pulsed lasers became available [1]. Ultrasonically induced gratings under the conditions of XRD have already been investigated [5][6][7][8][9][10][11][12][13][14][15]. It is time to start investigations of optically induced dynamical gratings!…”

“…by the amplitude of coherent atomic oscillations. These resonances can be called x-ray-optic resonances by the analogy with x-rayacoustic resonance [6,7,[10][11].…”

“…This means that in the case of x-ray-polariton resonance, the effect of anomalous transmission of x-rays will be suppressed. (Suppression of x-ray anomalous transmission in the case of x-ray-acoustic resonance has been experimentally and theoretically investigated by Entin [7,31].) Changes in the intensity of diffraction can be very significant as a result of the differences in the absorption.…”

“…The influence of external variable fields (such as electromagnetic, ultrasonic, etc) on a crystal structure may result in changes of the refractive index of the crystal and, therefore, the conditions of propagation and diffraction of x-ray radiation. Thus, the resonance influence of ultrasonic waves on dynamical XRD may lead to a number of interference effects, which have been investigated both theoretically and experimentally [5][6][7][8][9][10][11][12][13][14][15].…”

Bragg and diffuse components of X-ray reflection measured using acoustic excitation of an Si crystal with oxide precipitates

“…Under X-ray acoustic resonance conditions (Entin, 1977(Entin, , 1978(Entin, , 1985(transverse ultrasound wave with wave vector lying in the reflecting plane perpendicular to the diffraction vector, with wavelength As equal to the extinction length A), the Borrmann effect is suppressed almost completely by extremely weak oscillations with an amplitude of the order of 10-12 m. The resonance is caused by the interferometric amplification of the interbranch scattering of Bloch waves when the quasimomentum conservation law, Ks = dKo (i.e. As = A), is fulfilled (Ks is the ultrasound wave vector, Ks = 2rr/As, AKo is the minimal value of the dispersion surface splitting, dKo = 2re~A).…”