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) such as those found in uniaixally loaded dynamic compression experiments. In this paper we derive a general form for the (\theta_B, \phi) dependence of the diffraction for an arbitrarily deformed sample in arbitrary geometry. 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 small strain solutions previously reported

Measurement of competing pathways in a shock-induced phase transition in zirconium by femtosecond diffraction

The traditional picture of solid-solid phase transformations assumes an ordered parent phase transforms into an ordered daughter phase via a single unique pathway. Zirconium and its prototypical phase transition from hexagonal close-packed (hcp) to simple hexagonal (hex-3) structure has generated considerable controversy over several decades regarding which mechanism mediates the transformation. However, a lack of in situ measurements over the relevant atomistic timescales has hindered our ability to identify the true pathway. In this study, we exploit femtosecond X-ray diffraction coupled with nanosecond laser compression to give unprecedented insights into the complexities of how materials transform at the lattice level. We observe single-crystal zirconium changing from hcp to a hex-3 structure via not one but three competing pathways simultaneously. Concurrently, we also observe a broad diffuse background underlying the sharp Bragg diffraction during the transition. We corroborate our observation of the diffuse signal with multimillion-atom molecular dynamics simulations using a machine-learned interatomic potential. Our study demonstrates that the traditional mechanistic view of transitions may fail for even an elemental metal and that the mechanisms by which materials transform are far more intricate than generally thought

Simulations of in situ X-ray diffraction from uniaxially compressed highly textured polycrystalline targets

A growing number of shock compression experiments, especially those involving laser compression, are taking advantage of in situ x-ray diffraction as a tool to interrogate structure and microstructure evolution. Although these experiments are becoming increasingly sophisticated, there has been little work on exploiting the textured nature of polycrystalline targets to gain information on sample response. Here, we describe how to generate simulated x-ray diffraction patterns from materials with an arbitrary texture function subject to a general deformation gradient. We will present simulations of Debye-Scherrer x-ray diffraction from highly textured polycrystalline targets that have been subjected to uniaxial compression, as may occur under planar shock conditions. In particular, we study samples with a fibre texture, and find that the azimuthal dependence of the diffraction patterns contains information that, in principle, affords discrimination between a number of similar shock-deformation mechanisms. For certain cases we compare our method with results obtained by taking the Fourier Transform of the atomic positions calculated by classical molecular dynamics simulations. Illustrative results are presented for the shock-induced $\alpha$-$\epsilon$ phase transition in iron, the $\alpha$-$\omega$ transition in titanium and deformation due to twinning in tantalum that is initially preferentially textured along [001] and [011]. The simulations are relevant to experiments that can now be performed using 4th generation light sources, where single-shot x-ray diffraction patterns from crystals compressed via laser-ablation can be obtained on timescales shorter than a phonon period

Femtosecond X-Ray Diffraction Studies of the Reversal of the Microstructural Effects of Plastic Deformation during Shock Release of Tantalum

We have used femtosecond x-ray diffraction (XRD) to study laser-shocked fiber-textured polycrystalline tantalum targets as the 37-253 GPa shock waves break out from the free surface. We extract the time and depth-dependent strain profiles within the Ta target as the rarefaction wave travels back into the bulk of the sample. In agreement with molecular dynamics (MD) simulations the lattice rotation and the twins that are formed under shock-compression are observed to be almost fully eliminated by the rarefaction process

Coordination changes in liquid tin under shock compression determined using in situ femtosecond x-ray diffraction

Little is known regarding the liquid structure of materials compressed to extreme conditions, and even less is known about liquid structures undergoing rapid compression on nanosecond timescales. Here, we report on liquid structure factor and radial distribution function measurements of tin shock compressed to 84(19) GPa. High-quality, femtosecond x-ray diffraction measurements at the Linac Coherent Light Source were used to extract the liquid diffuse scattering signal. From the radial distribution function, we find that the structural evolution of the liquid with increasing pressure mimics the evolution of the solid phase. With increasing pressure, we find that the liquid structure evolves from a complex structure, with a low coordination number, to a simple liquid structure with a coordination number of 12. We provide a pathway for future experiments to study liquids at elevated pressures using high-energy lasers to shock compress materials beyond the reach of static diamond anvil cell techniques

Recovery of Metastable Dense Bi Synthesized by Shock Compression

X-ray free electron laser (XFEL) sources have revolutionized our capability to study ultrafast material behavior. Using an XFEL, we revisit the structural dynamics of shock compressed bismuth, resolving the transition sequence on shock release in unprecedented details. Unlike previous studies that found the phase-transition sequence on shock release to largely adhere to the equilibrium phase diagram (i.e., Bi-V → Bi-III → Bi-II → Bi-I), our results clearly reveal previously unseen, non-equilibrium behavior at these conditions. On pressure release from the Bi-V phase at 5 GPa, the Bi-III phase is not formed but rather a new metastable form of Bi. This new phase transforms into the Bi-II phase which in turn transforms into a phase of Bi which is not observed on compression. We determine this phase to be isostructural with β-Sn and recover it to ambient pressure where it exists for 20 ns before transforming back to the Bi-I phase. The structural relationship between the tetragonal β-Sn phase and the Bi-II phase (from which it forms) is discussed. Our results show the effect that rapid compression rates can have on the phase selection in a transforming material and show great promise for recovering high-pressure polymorphs with novel material properties in the future

Femtosecond quantification of void evolution during rapid material failure

Understanding high-velocity impact, and the subsequent high strain rate material deformation and potential catastrophic failure, is of critical importance across a range of scientific and engineering disciplines that include astrophysics, materials science, and aerospace engineering. The deformation and failure mechanisms are not thoroughly understood, given the challenges of experimentally quantifying material evolution at extremely short time scales. Here, copper foils are rapidly strained via picosecond laser ablation and probed in situ with femtosecond x-ray free electron (XFEL) pulses. Small-angle x-ray scattering (SAXS) monitors the void distribution evolution, while wide-angle scattering (WAXS) simultaneously determines the strain evolution. The ability to quantifiably characterize the nanoscale during high strain rate failure with ultrafast SAXS, complementing WAXS, represents a broadening in the range of science that can be performed with XFEL. It is shown that ultimate failure occurs via void nucleation, growth, and coalescence, and the data agree well with molecular dynamics simulations

Femtosecond diffraction studies of solid and liquid phase changes in shock-compressed bismuth

Bismuth has long been a prototypical system for investigating phase transformations and melting at high pressure. Despite decades of experimental study, however, the lattice-level response of Bi to rapid (shock) compression and the relationship between structures occurring dynamically and those observed during slow (static) compression, are still not clearly understood. We have determined the structural response of shock-compressed Bi to 68 GPa using femtosecond X-ray diffraction, thereby revealing the phase transition sequence and equation-of-state in unprecedented detail for the first time. We show that shocked-Bi exhibits a marked departure from equilibrium behavior - the incommensurate Bi-III phase is not observed, but rather a new metastable phase, and the Bi-V phase is formed at significantly lower pressures compared to static compression studies. We also directly measure structural changes in a shocked liquid for the first time. These observations reveal new behaviour in the solid and liquid phases of a shocked material and give important insights into the validity of comparing static and dynamic datasets

X-ray diffraction studies of laser-shocked crystals

When materials are shock compressed, they undergo changes in microstructure that act to relieve the large shear stresses associated with the compression. The plasticity mechanisms that mediate this transition such as slip and twinning remain poorly understood, especially in the case of polycrystals, which make up the majority of real world materials. This work presents a theoretical outline for analysing Debye-Scherrer diffraction experiments under large strains. A method is demonstrated to measure both the components of strain in the normal and transverse directions, as well as crystal orientation using highly textured samples. These theoretical predictions are compared with simulated diffraction patterns from molecular dynamics simulations. This technique is applied to two different experiments on tantalum. The first provides a measurement of the timescale for plastic deformation, which we find similar to comparable experiments in copper, while the second provides the first in situ of observation of twinning in shock compressed metal