Ultrafast temperature diagnosis of dynamically compressed matter using millielectronvolt inelastic x-ray scattering beyond the first Brillouin zone

We present calculations of the millielectronvolt-scale x-ray scattering spectra of multilayered dynamic-compression targets comprising an unstructured ablator layer and a crystalline, textured sample layer. Our model builds on the classic formulation of x-ray thermal diffuse scattering by Warren [B. E. Warren, Acta Crystallogr. 6, 803 (1953)] and includes both elastic and first-order (single-phonon) inelastic scattering contributions to the dynamic structure factor $S(\mathbf{q},\omega)$. We focus on the umklapp scattering regime (i.e., at momentum transfers outside the first Brillouin zone) where the ablator scattering that threatens to overwhelm the inelastic scattering from the crystalline layer of interest is suppressed. We show that, despite the considerably more complex structure of the inelastic scattering spectra in this intermediate-$q$ regime, it is still possible to reliably deduce the temperature of the crystal using Dornheim's Laplace-transform--based formalism [Dornheim et al., Phys. Plasmas 30, 042707 (2023)], regardless of the details of the sample's texture.