Interatomic potentials for modelling radiation defects and dislocations in tungsten

Origin of Deformation Twinning in bcc Tungsten and Molybdenum

Twinning is profuse in bcc transition metals (TMs) except bulk W and Mo. However, W and Mo nanocrystals surprisingly exhibit twinning during room temperature compression, which is completely unexpected as established nucleation mechanisms are not viable in them. Here, we reveal the physical origin of deformation twinning in W and Mo. We employ density functional theory (DFT) and a reduced-constraint slip method to compute the stress-dependent generalized stacking fault enthalpy (GSFH), the thermodynamic quantity to be minimized under constant loading. The simple slipped structures and GSFH lines show that compressive stresses stabilize a two-layer twin embryo, which can grow rapidly via twinning disconnections with negligible energy barriers. Direct atomistic simulations unveil the explicit twinning path in agreement with the DFT GSFH lines. Twinning is thus the preferred deformation mechanism in W and Mo when shear stresses are coupled with high compressive stresses. Furthermore, twinnability can be related to the elastic constants of a stacking fault phase (SFP). The hcp phase may serve as a candidate SFP for the {112}⟨1[over ¯]1[over ¯]1⟩ twinning system in bcc TMs and alloys, which is coincident with the {111}⟨112[over ¯]⟩ twinning in fcc structures.

The Evolution of Structural Defects under Irradiation in W by Molecular Dynamics Simulation

Tungsten (W) can be used in plasma-facing components in a fusion reactor because of its excellent radiation resistance. Some studies have found that nanocrystalline metals with a high density of grain boundary show a higher ability to resist radiation damage compared to conventional coarse-grained materials. However, the interaction mechanism between grain boundary and defect is still unclear. In the present study, molecular dynamics simulations were carried out to explore the difference of defect evolution in single-crystal and bicrystal W, while the effects of temperature and the energy of the primary knocked atom (PKA) were taken into account. The irradiation process was simulated at the temperature range of 300 to 1500 K, and the PKA energy varied from 1 to 15 keV. The results show that the generation of defects is more sensitive to the energy of PKA than temperature; the number of defects increases at the thermal spike stage with the increase of the PKA energy, but the correlation with temperature is not strong. The presence of the grain boundary prevented the recombination of interstitial atoms and vacancies during the collision cascades, and the vacancies were more likely to form large clusters than interstitial atoms in the bicrystal models. This can be ascribed to the strong segregation tendency of the interstitial atoms to grain boundaries. The simulations provide useful information for understanding the role of grain boundaries in the evolution of irradiated structural defects.

Phenomenological potentials for the refractory metals Cr, Mo and W

Cohesion in the refractory metals Cr, Mo, and W is phenomenologically described in this work via an-body energy functional with a set of physically motivated parameters that were optimized to reproduce selected experimental properties characteristic of perfect and defective crystals. The functional contains four terms accounting for the hard-core repulsion, the Thomas-Fermi kinetic energy repulsion and for contributions to the binding energy ofsanddvalence electrons. Lattice dynamics, molecular statics, and molecular dynamics calculations show that this model describes satisfactorily thermodynamic properties of the studied metals whereas, unlike other empirical approaches from the literature, predictions of phonon dispersion relations and of surface and point defect energetics reveal in fair good agreement with experiments. These results suggest that the present model is well adapted to large-scale simulations and whenever total energy calculations of thermodynamic properties are unfeasible.

Atomic Simulations of the Interaction between a Dislocation Loop and Vacancy-Type Defects in Tungsten

Tungsten (W) is considered to be the most promising plasma-facing material in fusion reactors. During their service, severe irradiation conditions create plenty of point defects in W, which can significantly degrade their performance. In this work, we first employ the molecular static simulations to investigate the interaction between a 1/2[111] dislocation loop and a vacancy-type defect including a vacancy, di-vacancy, and vacancy cluster in W. The distributions of the binding energies of a 1/2[111] interstitial and vacancy dislocation loop to a vacancy along different directions at 0 K are obtained, which are validated by using the elasticity theory. The calculated distributions of the binding energies of a 1/2[111] interstitial dislocation loop to a di-vacancy and a vacancy cluster, showing a similar behavior to the case of a vacancy. Furthermore, we use the molecular dynamics simulation to study the effect of a vacancy cluster on the mobility of the 1/2[111] interstitial dislocation loop. The interaction is closely related to the temperature and their relative positions. A vacancy cluster can attract the 1/2[111] interstitial dislocation loop and pin it at low temperatures. At high temperatures, the 1/2[111] interstitial dislocation loop can move randomly. These results will help us to understand the essence of the interaction behaviors between the dislocation loop and a vacancy-type defect and provide necessary parameters for mesoscopic scale simulations.

Using first-principles calculations to predict the mechanical properties of transmuting tungsten under first wall fusion power-plant conditions

Tungsten and tungsten alloys are being considered as leading candidates for structural and functional materials in future fusion energy devices. The most attractive properties of tungsten for the design of magnetic and inertial fusion energy reactors are its high melting point, high thermal conductivity, low sputtering yield and low long-term disposal radioactive footprint. Yet, despite these relevant features, tungsten also presents a very low fracture toughness, mostly associated with inter-granular failure and bulk plasticity, that limits its applications. Significant neutron-induced transmutation happens in these tungsten components during nuclear fusion reactions, creating transmutant elements including Re, Os and Ta. Density functional theory (DFT) calculations that allow the calculation of defect and solute energetics are critical to better understand the behavior and evolution of tungsten-based materials in a fusion energy environment. In this study, we present a novel computational approach to perform DFT calculations on transmuting materials. In particular, we predict elastic and plastic mechanical properties (such as bulk modulus, shear modulus, ductility parameter, etc) on a variety of W-X compositions that result when pure tungsten is exposed to the EU-DEMO fusion first wall conditions for ten years.

Machine-learning interatomic potential for W-Mo alloys

In this work, we develop a machine-learning interatomic potential for W_xMo_1-xrandom alloys. The potential is trained using the Gaussian approximation potential framework and density functional theory data produced by the Viennaab initiosimulation package. The potential focuses on properties such as elastic properties, melting, and point defects for the whole range of W_xMo_1-xcompositions. Moreover, we use all-electron density functional theory data to fit an adjusted Ziegler-Biersack-Littmarck potential for the short-range repulsive interaction. We use the potential to investigate the effect of alloying on the threshold displacement energies and find a significant dependence on the local chemical environment and element of the primary recoiling atom.

Absence of a Crystal Direction Regime in which Sputtering Corresponds to Amorphous Material

Erosion of material by energetic ions, i.e., sputtering, is widely used in industry and research. Using experiments and simulations that, independently of each other, obtain the sputter yield of thousands of individual grains, we demonstrate here that the sputter yield for heavy keV ions on metals changes as a continuous function of the crystal direction. Moreover, we show that polycrystalline metals with randomly oriented grains do not sputter with the same yield as the amorphous material. The key reason for this is attributed to linear collision sequences rather than channeling.

In operando active learning of interatomic interaction during large-scale simulations

A well-known drawback of state-of-the-art machine-learning interatomic potentials is their poor ability to extrapolate beyond the training domain. For small-scale problems with tens to hundreds of atoms this can be solved by using active learning which is able to select atomic configurations on which a potential attempts extrapolation and add them to the ab initio-computed training set. In this sense an active learning algorithm can be viewed as an on-the-fly interpolation of an ab initio model. For large-scale problems, possibly involving tens of thousands of atoms, this is not feasible because one cannot afford even a single density functional theory (DFT) computation with such a large number of atoms.

This work marks a new milestone toward fully automatic ab initio-accurate large-scale atomistic simulations. We develop an active learning algorithm that identifies local subregions of the simulation region where the potential extrapolates. Then the algorithm constructs periodic configurations out of these local, non-periodic subregions, sufficiently small to be computable with plane-wave DFT codes, in order to obtain accurate ab initio energies. We benchmark our algorithm on the problem of screw dislocation motion in bcc tungsten and show that our algorithm reaches ab initio accuracy, down to typical magnitudes of numerical noise in DFT codes. We show that our algorithm reproduces material properties such as core structure, Peierls barrier, and Peierls stress. This unleashes new capabilities for computational materials science toward applications which have currently been out of scope if approached solely by ab initio methods.

Anti-twinning in nanoscale tungsten

Nanomaterials often surprise us with unexpected phenomena. Here, we report a discovery of the anti-twinning deformation, previously thought impossible, in nanoscale body-centered cubic (BCC) tungsten crystals. By conducting in situ transmission electron microscopy nanomechanical testing, we observed the nucleation and growth of anti-twins in tungsten nanowires with diameters less than about 20 nm. During anti-twinning, a shear displacement of 1/3〈111〉 occurs on every successive {112} plane, in contrast to an opposite shear displacement of 1 / 6 〈 1 ¯ 1 ¯ 1 ¯ 〉 by ordinary twinning. This asymmetry in the atomic-scale shear pathway leads to a much higher resistance to anti-twinning than ordinary twinning. However, anti-twinning can become active in nanosized BCC crystals under ultrahigh stresses, due to the limited number of plastic shear carriers in small crystal volumes. Our finding of the anti-twinning phenomenon has implications for harnessing unconventional deformation mechanisms to achieve high mechanical preformation by nanomaterials.

Assessment of hardening due to non-coherent precipitates in tungsten-rhenium alloys at the atomic scale

In metallurgical applications, precipitation strengthening is of great technological importance to engineer materials with the required strength. While precipitation hardening is essential for many applications involving operation at elevated temperatures, its subsequent embrittlement can be a showstopper for the overall performance of a component. In the nuclear industry, irradiation-induced/enhanced precipitation and the resulting embrittlement often limit the lifetime of components. In fusion applications, tungsten (W) based alloys are known to harden and embrittle as a result of irradiation-assisted transmutation to rhenium (Re) and its subsequent precipitation into non-coherent precipitates. Hence, a fundamental understanding of the interaction of dislocations with non-coherent precipitates is of great interest. In the present work, the interaction of dislocations with non-coherent Re-rich σ, χ and hcp phase precipitates embedded in a bcc W matrix is assessed. Large-scale atomistic simulations are performed to clarify the interaction mechanisms and derive the obstacle strength of the precipitates in the quasi-static limit. Thereby the impact of precipitate shape, size, interspacing and composition is assessed. Based on those results, an analytical model to predict precipitation hardening of σ, χ and hcp phase particles in bcc W is proposed and compared to available experimental data from mechanical tests on irradiated materials.

Radiation damage in tungsten from cascade overlap with voids and vacancy clusters

We have performed a systematic molecular dynamics investigation of the effects of overlap of collision cascades in tungsten with pre-existing vacancy-type defects. In particular, we focus on the implications for fusion neutron irradiated tungsten in relation to comparisons with damage production under ion irradiation conditions. We find that overlap of a cascade with a vacancy-type defect decreases the number of new defects with roughly the same functional dependence as previously shown for interstitial clusters. We further find that different mechanisms govern the formation of dislocation loops, resulting in different Burgers vectors, depending on the degree of overlap between the cascade and the defect. Furthermore, we show that overlapping cascades consistently decrease the size of the pre-existing defect. We also observe void-induced cascade splitting at energies far below the subcascade splitting threshold in tungsten. The impact of these mechanisms on radiation damage accumulation and dose rate effects are discussed.

Collision cascades overlapping with self-interstitial defect clusters in Fe and W

Overlap of collision cascades with previously formed defect clusters become increasingly likely at radiation doses typical for materials in nuclear reactors. Using molecular dynamics, we systematically investigate the effects of different pre-existing self-interstitial clusters on the damage produced by an overlapping cascade in bcc iron and tungsten. We find that the number of new Frenkel pairs created in direct overlap with an interstitial cluster is reduced to essentially zero, when the size of the defect cluster is comparable to that of the disordered cascade volume. We develop an analytical model for this reduced defect production as a function of the spatial overlap between a cascade and a defect cluster of a given size. Furthermore, we discuss cascade-induced changes in the morphology of self-interstitial clusters, including transformations between [Formula: see text] and [Formula: see text] dislocation loops in iron and tungsten, and between C15 clusters and dislocation loops in iron. Our results provide crucial new cascade-overlap effects to be taken into account in multi-scale modelling of radiation damage in bcc metals.

Instabilities of High Speed Dislocations

Despite numerous theoretical models and simulation results, a clear physical picture of dislocations traveling at velocities comparable to the speed of sound in the medium remains elusive. Using two complementary atomistic methods to model uniformly moving screw dislocations, lattice dynamics and molecular dynamics, the existence of mechanical instabilities in the system is shown. These instabilities are found at material-dependent velocities far below the speed of sound. We show that these are the onset of an atomistic kinematic generation mechanism, which ultimately results in an avalanche of further dislocations. This homogeneous nucleation mechanism, observed but never fully explained before, is relevant in moderate and high strain rate phenomena including adiabatic shear banding, dynamic fracture, and shock loading. In principle, these mechanical instabilities do not prevent supersonic motion of dislocations.

Unsupervised Calculation of Free Energy Barriers in Large Crystalline Systems

The calculation of free energy differences for thermally activated mechanisms in the solid state are routinely hindered by the inability to define a set of collective variable functions that accurately describe the mechanism under study. Even when possible, the requirement of descriptors for each mechanism under study prevents implementation of free energy calculations in the growing range of automated material simulation schemes. We provide a solution, deriving a path-based, exact expression for free energy differences in the solid state which does not require a converged reaction pathway, collective variable functions, Gram matrix evaluations, or probability flux-based estimators. The generality and efficiency of our method is demonstrated on a complex transformation of C15 interstitial defects in iron and double kink nucleation on a screw dislocation in tungsten, the latter system consisting of more than 120 000 atoms. Both cases exhibit significant anharmonicity under experimentally relevant temperatures.

Fast, vacancy-free climb of prismatic dislocation loops in bcc metals

Vacancy-mediated climb models cannot account for the fast, direct coalescence of dislocation loops seen experimentally. An alternative mechanism, self climb, allows prismatic dislocation loops to move away from their glide surface via pipe diffusion around the loop perimeter, independent of any vacancy atmosphere. Despite the known importance of self climb, theoretical models require a typically unknown activation energy, hindering implementation in materials modeling. Here, extensive molecular statics calculations of pipe diffusion processes around irregular prismatic loops are used to map the energy landscape for self climb in iron and tungsten, finding a simple, material independent energy model after normalizing by the vacancy migration barrier. Kinetic Monte Carlo simulations yield a self climb activation energy of 2 (2.5) times the vacancy migration barrier for 1/2〈111〉 (〈100〉) dislocation loops. Dislocation dynamics simulations allowing self climb and glide show quantitative agreement with transmission electron microscopy observations of climbing prismatic loops in iron and tungsten, confirming that this novel form of vacancy-free climb is many orders of magnitude faster than what is predicted by traditional climb models. Self climb significantly influences the coarsening rate of defect networks, with important implications for post-irradiation annealing.

Effect of the variation of the electronic density of states of zirconium and tungsten on their respective thermal conductivity evolution with temperature

The thermal conductivity of zirconium and tungsten above 500 K is calculated with atomistic simulations using a combination of empirical potentials molecular dynamics and density functional theory calculations. The thermal conductivity is calculated in the framework of Kubo-Greenwood theory. The obtained values are in quantitative agreement with experiments. The fact that the conductivity of Zr increases with temperature while that of tungsten is essentially constant is reproduced by the calculations. The evolution with temperature of the electronic density of states of these two pseudo-gap metals proves to explain the observed variations of the conductivity.

Classical mobility of highly mobile crystal defects

Highly mobile crystal defects such as crowdions and prismatic dislocation loops exhibit an anomalous temperature independent mobility unexplained by phonon scattering analysis. Using a projection operator, without recourse to elasticity, we derive analytic expressions for the mobility of highly mobile defects and dislocations which may be efficiently evaluated in molecular dynamics simulation. The theory explains how a temperature-independent mobility arises because defect motion is not an eigenmode of the Hessian, an implicit assumption in all previous treatments.