Compact A15 Frank-Kasper nano-phases at the origin of dislocation loops in face-centred cubic metals.

It is generally considered that the elementary building blocks of defects in face-centred cubic (fcc) metals, e.g., interstitial dumbbells, coalesce directly into ever larger 2D dislocation loops, implying a continuous coarsening process. Here, we reveal that, prior to the formation of dislocation loops, interstitial atoms in fcc metals cluster into compact 3D inclusions of A15 Frank-Kasper phase. After reaching the critical size, A15 nano-phase inclusions act as a source of prismatic or faulted dislocation loops, dependent on the energy landscape of the host material. Using cutting-edge atomistic simulations we demonstrate this scenario in Al, Cu, and Ni. Our results explain the enigmatic 3D cluster structures observed in experiments combining diffuse X-ray scattering and resistivity recovery. Formation of compact nano-phase inclusions in fcc structure, along with previous observations in bcc structure, suggests that the fundamental mechanisms of interstitial defect formation are more complex than historically assumed and require a general revision. Interstitial-mediated formation of compact 3D precipitates can be a generic phenomenon, which should be further explored in systems with different crystallographic lattices.

On Sampling Minimum Energy Path.

Sampling the minimum energy path (MEP) between two minima of a system is often hindered by the presence of an energy barrier separating the two metastable states. As a consequence, direct sampling based on molecular dynamics or Markov Chain Monte Carlo methods becomes inefficient, the crossing of the energy barrier being associated to a rare event. Augmented sampling methods based on the definition of collective variables or reaction coordinates allow us to circumvent this limitation at the price of an arbitrary choice of the dimensionality reduction algorithm. We couple the statistical sampling techniques, namely, metadynamics and invertible neural networks, with autoencoders so as to gradually learn the MEP and the collective variable at the same time. Learning is achieved through a succession of two steps: statistical sampling of the most probable path between the two minima and redefinition of the collective variable from the updated data points. The prototypical Mueller potential with nearly orthogonal minima is employed to demonstrate the ability of such coupling to unravel a complex MEP.

Capabilities and limits of autoencoders for extracting collective variables in atomistic materials science.

Free energy calculations in materials science are routinely hindered by the need to provide reaction coordinates that can meaningfully partition atomic configuration space, a prerequisite for most enhanced sampling approaches. Recent studies on molecular systems have highlighted the possibility of constructing appropriate collective variables directly from atomic motions through deep learning techniques. Here we extend this class of approaches to condensed matter problems, for which we encode the finite temperature collective variable by an iterative procedure starting from 0 K features of the energy landscape i.e. activation events or migration mechanisms given by a minimum - saddle point - minimum sequence. We employ the autoencoder neural networks in order to build a scalar collective variable for use with the adaptive biasing force method. Particular attention is given to design choices required for application to crystalline systems with defects, including the filtering of thermal motions which otherwise dominate the autoencoder input. The machine-learning workflow is tested on body-centered cubic iron and its common defects, such as small vacancy or self-interstitial clusters and screw dislocations. For localized defects, excellent collective variables as well as derivatives, necessary for free energy sampling, are systematically obtained. However, the approach has a limited accuracy when dealing with reaction coordinates that include atomic displacements of a magnitude comparable to thermal motions, e.g. the ones produced by the long-range elastic field of dislocations. We then combine the extraction of collective variables by autoencoders with an adaptive biasing force free energy method based on Bayesian inference. Using a vacancy migration as an example, we demonstrate the performance of coupling these two approaches for simultaneous discovery of reaction coordinates and free energy sampling in systems with localized defects.

Reinforcing materials modelling by encoding the structures of defects in crystalline solids into distortion scores.

This work revises the concept of defects in crystalline solids and proposes a universal strategy for their characterization at the atomic scale using outlier detection based on statistical distances. The proposed strategy provides a generic measure that describes the distortion score of local atomic environments. This score facilitates automatic defect localization and enables a stratified description of defects, which allows to distinguish the zones with different levels of distortion within the structure. This work proposes applications for advanced materials modelling ranging from the surrogate concept for the energy per atom to the relevant information selection for evaluation of energy barriers from the mean force. Moreover, this concept can serve for design of robust interatomic machine learning potentials and high-throughput analysis of their databases. The proposed definition of defects opens up many perspectives for materials design and characterization, promoting thereby the development of novel techniques in materials science.

Quantum de-trapping and transport of heavy defects in tungsten.

The diffusion of defects in crystalline materials1 controls macroscopic behaviour of a wide range of processes, including alloying, precipitation, phase transformation and creep2. In real materials, intrinsic defects are unavoidably bound to static trapping centres such as impurity atoms, meaning that their diffusion is dominated by de-trapping processes. It is generally believed that de-trapping occurs only by thermal activation. Here, we report the direct observation of the quantum de-trapping of defects below around one-third of the Debye temperature. We successfully monitored the de-trapping and migration of self-interstitial atom clusters, strongly trapped by impurity atoms in tungsten, by triggering de-trapping out of equilibrium at cryogenic temperatures, using high-energy electron irradiation and in situ transmission electron microscopy. The quantum-assisted de-trapping leads to low-temperature diffusion rates orders of magnitude higher than a naive classical estimate suggests. Our analysis shows that this phenomenon is generic to any crystalline material.

Prediction of Mechanical Twinning in Magnesium Silicate Post-Perovskite.

The plastic properties of MgSiO3 post-perovskite are considered to be one of the key issues necessary for understanding the seismic anisotropy at the bottom of the mantle in the so-called D" layer. Although plastic slip in MgSiO3 post-perovskite has attracted considerable attention, the twinning mechanism has not been addressed, despite some experimental evidence from low-pressure analogues. On the basis of a numerical mechanical model, we present a twin nucleation model for post-perovskite involving the emission of 1/6 <110> partial dislocations. Relying on first-principles calculations with no adjustable parameters, we show that {110} twin wall formation resulting from the interaction of multiple twin dislocations occurs at a twinning stress comparable in magnitude to the most readily occurring slip system in post-perovskite. Because dislocation activities and twinning are competitive strain-producing mechanisms, twinning should be considered in future models of crystallographic preferred orientations in post-perovskite to better interpret seismic anisotropy in the lowermost lower mantle.

Modeling defects and plasticity in MgSiO3 post-perovskite: Part 3-Screw and edge [001] dislocations.

In this study, we investigate the complex structure of [001] screw and edge dislocation cores in MgSiO3 post-perovskite at the atomic scale. Both [001] screw and edge dislocations exhibit spontaneous dissociation in (010) into two symmetric partials characterized by the presence of <100> component. In case of edge dislocations, dissociation occurs into ½<101> partials, while for the screw dislocations the <100> component reaches only 15%. Under applied stress, both [001](010) screw and edge dislocations behave similarly. Above the Peierls stress, the two partials glide together while keeping their stacking-fault widths (~11 and ~42 Å for the screw and edge dislocations, respectively) constant. The Peierls stress opposed to the glide of [001](010) screw dislocations is 3 GPa, while that of edge dislocations is 33% lower. Relying on the observed characteristics of the dislocation cores, we estimate the efficiency of [001](010) dislocation glide under the P-T conditions relevant to the lowermost mantle and demonstrate that dislocation creep for this slip system would occur in the so-called athermal regime where lattice friction for the considered slip system vanishes when the temperature rises above the critical T a value of ~2,000 K.

Low viscosity and high attenuation in MgSiO3 post-perovskite inferred from atomic-scale calculations.

This work represents a numerical study of the thermal activation for dislocation glide of the [100](010) slip system in MgSiO3 post-perovskite (Mg-ppv) at 120 GPa. We propose an approach based on a one-dimensional line tension model in conjunction with atomic-scale calculations. In this model, the key parameters, namely, the line tension and the Peierls barrier, are obtained from density functional theory calculations. We find a Peierls stress σp = 2.1 GPa and a line tension Γ = 9.2 eV/Å, which lead to a kink-pair enthalpy (under zero stress) of 2.69 eV. These values confirm that this slip system bears a very low lattice friction because it vanishes for temperatures above approximately 500 K under mantle conditions. In the Earth's mantle, high-pressure Mg-ppv silicate is thus expected to become as ductile as ferropericlase. These results confirm the hypothesis of a weak layer in the D″ layer where Mg-ppv is present. Easy glide along [100](010) suggests strong preferred orientations with (010) planes aligned. Highly mobile [100] dislocations are also likely to respond to stresses related to seismic waves, leading to energy dissipation and strong attenuation.

Modeling defects and plasticity in MgSiO3 post-perovskite: Part 1-generalized stacking faults.

In this work, we examine the transferability of a pairwise potential model (derived for MgSiO3 perovskite) to accurately compute the excess energies of the generalized stacking faults (GSF, also called γ-surfaces) in MgSiO3 post-perovskite. All calculations have been performed at 120 GPa, a pressure relevant to the D″ layer. Taking into account an important aspect of crystal chemistry for complex materials, we consider in detail all possible locations of slip planes in the post-perovskite structure. The γ-surface calculations emphasize the easiness of glide of slip systems with the smallest shear vector [100] and of the [001](010) slip system. Our results are in agreement with previous ab initio calculations. This validates the use the chosen potential model for further full atomistic modeling of dislocations in MgSiO3 post-perovskite.

Modeling defects and plasticity in MgSiO3 post-perovskite: Part 2-screw and edge [100] dislocations.

In this study, we propose a full atomistic study of [100] dislocations in MgSiO3 post-perovskite based on the pairwise potential parameterized by Oganov et al. (Phys Earth Planet Inter 122:277-288, 2000) for MgSiO3 perovskite. We model screw dislocations to identify planes where they glide easier. We show that despite a small tendency to core spreading in {011}, [100] screw dislocations glide very easily (Peierls stress of 1 GPa) in (010) where only Mg-O bonds are to be sheared. Crossing the Si-layers results in a higher lattice friction as shown by the Peierls stress of [100](001): 17.5 GPa. Glide of [100] screw dislocations in {011} appears also to be highly unfavorable. Whatever the planes, (010), (001) or {011}, edge dislocations are characterized by a wider core (of the order of 2b). Contrary to screw character, they bear negligible lattice friction (0.1 GPa) for each slip system. The layered structure of post-perovskite results in a drastic reduction in lattice friction opposed to the easiest slip systems compared to perovskite.