Multiple x-ray diffraction to determine transverse and longitudinal lattice deformation in shocked lithium fluoride

Experimental and analytic developments are described that utilize multiple x-ray diffraction to determine real-time, lattice deformation in directions parallel and perpendicular to shock-wave propagation in single crystals. Using a monochromatic x-ray source, two Bragg reflections were obtained simultaneously from LiF crystals shocked along the [111] and [100] directions. Symmetry permitted the transverse lattice deformation to be determined by measuring interplanar spacing longitudinally and in one other direction. We chose this to be a [110] direction in both cases because the intensity of the (220) reflection is high and because the transverse deformation component from this measurement is relatively large. Due to the complex geometry involved, an analytic model was required to calculate the (220) peak shift under the deformation conditions of interest. This model was used both to design experiments and to analyze the results. It was determined that shock compression below 4 GPa along the [111] orientation -- which results in macroscopic elastic deformation -- produced, as expected, no transverse lattice deformation. In contrast, shock compression along the [100] orientation -- which results in macroscopic elastic-plastic deformation -- produced equal interplanar spacing changes along the longitudinal and transverse directions. The analytic developments and the implications of our results are discussed