Prediction of Debye-Scherrer diffraction patterns in arbitrarily strained samples

The prediction of Debye-Scherrer diffraction patterns from strained samples is typically conducted in the small strain limit. Although valid for small deviations from the hydrostat (such as the conditions of finite strength typically observed in diamond anvil cells) this assertion is likely to fail for the large strain anisotropies (often of order 10% in normal strain) found in uniaxially loaded dynamic compression experiments. In this paper, we derive a general form for the (θB,ϕ) dependence of the diffraction for an arbitrarily deformed polycrystalline sample in any geometry, and of any crystal symmetry. We show that this formula is consistent with ray traced diffraction for highly strained computationally generated polycrystals, and that the formula shows deviations from the widely used small strain solutions previously reported