Liss et. al.: Time Resolved Study...

High resolution X-ray diffraction at the high energy beamline ID15A of the European Synchrotron Radiation Facility has been applied for the investigation of perfect silicon crystals subjected to compressional ultrasound in the 10 MHz range. Photon energies between 50 keV and 300 keV were used to penetrate thick samples in Laue geometry. Time resolutions of 20 ns with the germanium detector alone and down to 200 ps taking advantage of the time structure in 16 bunch mode of the machine allow to follow the evolution of the Bragg profiles in detail. Pure modes of oscillations can be distinguished clearly from higher harmonic contamination and distorted wave fields. A typical scan in the rocking angle - time domain is given in figure (1). The measured distributions of the lattice parameter is interpreted at the different phases in time, for the zero transition and the moment with maximum amplitude of the standing wave as well as time averaged, see figure (2). Mathematically they lead to the Dirac delta function, the inverse circle function and the complete elliptic integral K, respectively.

The spatial dependence of the standing wave has been scanned by slits limiting the scattering volume. The wave field very close to the transducer compared to a position further away is observed to be more disturbed in both, space and time. Further 20 µm slits define the beam section behind the Borrmann triangle in a white beam setup and an analyzer crystal optionally probes for rays diffracted from compressed or expanded regions. Qualitatively, three regions of diffraction theory can be studied depending on ultrasonic excitation, developing from the unexcited section pattern through a slightly excited where the beam rays follow adiabatically the gradients in lattice parameter towards the strongly exited case where the standing wave pattern is simply projected into the exit beam. Transfer matrix simulations are started for the theoretical investigation of the three dimensional diffraction pattern highly resolved in space, momentum and time.

K.-D. Liss, A. Magerl, A. Remhof, R. Hock, "Ultrasound induced gradient crystals observed by high energy X-rays" Acta Crystallographica, (1997). A(53): p. 181-186.

K.-D. Liss, A. Magerl, R. Hock, A. Remhof, B. Waibel, "Towards a new (Q, t) regime by time-resolved X-ray diffraction:&127 ultra-sound excited crystals as an example" Europhysics Letters, (1997). 40(4): p. 369-374.

Figure 1: Intensity distribution in the rocking-angle time coordinate plane, a). Nodes and anti-nodes of the standing waves are distinguished clearly. b) shows a section through the center of the rocking curve having maximal intensity when the rocking curve is narrowest while the integrated intensity, c), remains constant as a function of time,. The latter does not depend on the momentary strain state and indicates that the diffraction is kinematic. The excitation frequency is 15.5991 MHz.

Figure 2: Snap shots for an excited crystal at moments where the lattice is mostly relaxed and at maximum strain given by the large dots in a) and b), respectively. Plot c) gives time averaged data obtained without any timing setup. All three curves follow well the behavior predicted by the theory, a Dirac delta function in a), an inverse circle function in b) and an complete elliptic integral of the first kind in c). The theoretical distributions are given by the dotted lines whereas the continuos lines in b) and c) are folded with the same Lorentzian resolution function.

HIGHLY TIME RESOLVED STUDY ON THE INFLUENCE OF ULTRASONIC EXCITATION IN A BRAGG DIFFRACTING CRYSTAL