Investigation of ultrasonic fields by time-resolved x-ray diffraction

Time resolved detection in both detector and synchrotron resolution mode are presented. Using this technique the response of the Bragg profile in perfect Silicon to a MHz ultrasonic wave field has been studied on the high resolution triple crystal diffractometer at the ESRF high energy beamline ID15A. High photon energies up to 500 keV have been used for the analysis of a longitudinal acoustic wave in the 10 mm bulk. First, conventional time averaged rocking curves show intensity gains by up to a factor of 50, and a reciprocal space mapping reveals full information on the acoustic wave vector. Secondly, time and space resolved reflection curves have been taken. They give detailed insights into the properties of the acoustic wave field in space and time. In particular, they allow us to identify uniquely true standing waves without parasitic strain components or higher harmonic excitation. Time averaged and snapshots of the time resolved rocking curves represent different aspects of the density of states for the lattice parameter distribution. They are understood analytically by the elliptic integral K and the inverse circle function, respectively.

[1]  B. Warren,et al.  X-Ray Diffraction , 2014 .

[2]  Roberto Colella,et al.  X-Ray-Diffraction Studies of Acoustoelectrically Amplified Phonon Beams , 1975 .

[3]  A. Magerl,et al.  Neutron backscattering on vibrating silicon crystals-experimental results on the neutron backscattering spectrometer IN10 , 1993 .

[4]  A. Remhof,et al.  Ultrasound-Induced Gradient Crystals Observed by High-Energy X-rays , 1997 .

[5]  B. Sander,et al.  X-ray diffraction profiles in strained crystals undergoing ultrasonic excitation. The laue case , 1995 .

[6]  E. Zolotoyabko,et al.  Determination of crystal imperfection by X‐ray diffraction in a strong acoustic field , 1992 .

[7]  Seishi Kikuta,et al.  High Frequency Time Modulation of the X-Ray Beam Diffracted from a LiNbO3 Crystal by Surface Acoustic Waves , 1984 .

[8]  Neutron Storage in a Longitudinally Vibrating Silicon Crystal , 1998 .

[9]  B. S. Berry,et al.  Anelastic Relaxation in Crystalline Solids , 1972 .

[10]  M. Brunel,et al.  Diffraction of a focused X-ray beam by surface acoustic waves , 1995 .

[11]  P. H. Carr,et al.  The Effect of Piezoelectric Oscillation on the Intensity of X-ray Reflections from Quartz , 1931 .

[12]  B. S. Berry,et al.  Anelasticity and Internal Friction Due to Point Defects in Crystals , 1966 .

[13]  On high-resolution reciprocal-space mapping with a triple-crystal diffractometer for high-energy X-rays. , 1998, Journal of synchrotron radiation.

[14]  I. M. Pyshik,et al.  Table of integrals, series, and products , 1965 .