Real-time microstructure of shock-compressed single crystals from X-ray diffraction line profiles

Methods to obtain and analyze high-resolution real-time X-ray diffraction (XRD) measurements from shock-compressed single crystals are presented. Procedures for extracting microstructural information - the focus of this work - from XRD line profiles are described. To obtain quantitative results, careful consideration of the experimental geometry is needed, including the single-crystal nature of the sample and the removal of instrumental broadening. These issues are discussed in detail. Williamson-Hall (WH) and profile synthesis (PS) analysis procedures are presented. More accurate than WH, the PS procedure relies on a forward calculation in which a line profile is synthesized by convoluting the instrumental line profile with a line profile determined from a diffraction simulation. The diffraction simulation uses the actual experimental geometry and a model microstructure for the shocked crystal. The shocked-crystal microstructural parameters were determined by optimizing the match between the synthesized and measured line profiles. XRD measurements on an Al crystal, shocked along [100] to 7.1 GPa using plate-impact loading, are used to demonstrate the WH and PS analysis methods. In the present analysis, the microstructural line broadening arises because of a distribution of longitudinal elastic microstrains. The WH analysis resulted in FWHM longitudinal microstrain distributions of 0.22 and 0.38% for Lorentzian and Gaussian line shape assumptions, respectively. The optimal FWHM longitudinal microstrain for the PS method was 0.35% with a pseudo-Voigt distribution (40% Lorentzian-60% Gaussian). The line profile measurements and PS analysis presented in this work provide new insight into the heterogeneous distribution of elastic strains in crystals undergoing elastic-plastic deformation during shock compression. Such microstrain distribution measurements are complementary to continuum measurements, which represent averages of the heterogeneous strains or stresses. The PS analysis is a general method capable of incorporating microstructural models more complex than the microstrain distribution model used in this work. As a next step, the PS method will be applied to line profiles of multiple diffraction peaks to separate strain-and size-broadening effects in shocked crystals.