arXiv subjects

S. L. Dudarev

Publications and source records attributed to S. L. Dudarev.

At least 19 recordsLinked to original sources

arXiv2024

Mechanical Model for a Full Fusion Tokamak Enabled by Supercomputing

Determining stress and strain in a component of a fusion power plant involves defining boundary conditions for the mechanical equilibrium equations, implying the availability of a full reactor model for defining those conditions. To address this fundamental challenge of reactor design, a finite element method (FEM) model for the Mega-Ampere Spherical Tokamak Upgrade (MAST-U) fusion tokamak, operating at the Culham Campus of UKAEA, has been developed and applied to assess mechanical deformations, strain, and stress in the full tokamak structure, taken as a proxy for a fusion power plant. The model, handling 127 million finite elements using about 800 processors in parallel, illustrates the level of fidelity of structural simulations of a complex nuclear device made possible by the modern supercomputing systems. The model predicts gravitational and atmospheric pressure-induced deformations in broad agreement with observations, and enables computing the spectrum of acoustic vibrations of a tokamak, arising from mechanical disturbances like an earthquake or a plasma disruption. We introduce the notion of the density of stress to characterise the distribution of stress in the entire solid body of the tokamak, and to predict the magnitude and locations of stress concentrations. The model enables defining computational requirements for simulating a whole operating fusion power plant, and provides a digital foundation for the assessment of reactor performance as well as for specifying the relevant materials testing programme.

physics.app-ph↗

arXiv2024

Simulated TEM imaging of a heavily irradiated metal

We recast the Howie-Whelan equations for generating simulated transmission electron microscope (TEM) images, replacing the dependence on local atomic displacements with atomic positions only. This allows very rapid computation of simulated TEM images for arbitrarily complex atomistic configurations of lattice defects and dislocations in the dynamical two beam approximation. Large scale massively-overlapping cascade simulations performed with molecular dynamics, are used to generate representative high-dose nanoscale irradiation damage in tungsten at room temperature, and we compare the simulated TEM images to experimental TEM images with similar irradiation and imaging conditions. The simulated TEM shows 'white-dot' damage in weak-beam dark-field imaging conditions, in line with our experimental observations and as expected from previous studies, and in bright-field conditions a dislocation network is observed. In this work we can also compare the images to the nanoscale lattice defects in the original atomic structures, and find that at high dose the white spots are not only created by small dislocation loops, but rather arise from nanoscale fluctuations in strains around curved sections of dislocation lines.

cond-mat.mtrl-sci↗

arXiv2023

The Einstein-de Haas Effect in an $\textrm{Fe}_{15}$ Cluster

Classical models of spin-lattice coupling are at present unable to accurately reproduce results for numerous properties of ferromagnetic materials, such as heat transport coefficients or the sudden collapse of the magnetic moment in hcp-Fe under pressure. This inability has been attributed to the absence of a proper treatment of effects that are inherently quantum mechanical in nature, notably spin-orbit coupling. This paper introduces a time-dependent, non-collinear tight binding model, complete with spin-orbit coupling and vector Stoner exchange terms, that is capable of simulating the Einstein-de Haas effect in a ferromagnetic $\textrm{Fe}_{15}$ cluster. The tight binding model is used to investigate the adiabaticity timescales that determine the response of the orbital and spin angular momenta to a rotating, externally applied $B$ field, and we show that the qualitative behaviours of our simulations can be extrapolated to realistic timescales by use of the adiabatic theorem. An analysis of the trends in the torque contributions with respect to the field strength demonstrates that SOC is necessary to observe a transfer of angular momentum from the electrons to the nuclei at experimentally realistic $B$ fields. The simulations presented in this paper demonstrate the Einstein-de Haas effect from first principles using a Fe cluster.

cond-mat.mtrl-sci↗

arXiv2020

Statistical mechanics of kinks on a gliding screw dislocation

The ability of a body-centered cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility exhibiting complex dependence on temperature, stress, and dislocation segment length. We derive an analytical expression for the velocity of dislocation glide, based on a statistical mechanics argument, and identify an apparent phase transition marked by a critical temperature above which the activation energy for glide effectively halves, changing from the formation energy of a double kink to that of a single kink. The analysis is in quantitative agreement with direct kinetic Monte Carlo simulations.

cond-mat.mtrl-sci↗

arXiv2019

Parametrization of LSDA+$U$ for noncollinear magnetic configurations: Multipolar magnetism in UO$_2$

To explore the formation of noncollinear magnetic configurations in materials with strongly correlated electrons, we derive a noncollinear LSDA+$U$ model involving only one parameter $U$, as opposed to the difference between the Hubbard and Stoner parameters $U-J$. Computing $U$ in the constrained random phase approximation, we investigate noncollinear magnetism of uranium dioxide UO$_2$ and find that the spin-orbit coupling (SOC) stabilizes the 3$\textbf{k}$ ordered magnetic ground state. The estimated SOC strength in UO$_2$ is as large as 0.73 eV per uranium atom, making spin and orbital degrees of freedom virtually inseparable. Using a multipolar pseudospin Hamiltonian, we show how octupolar and dipole-dipole exchange coupling help establish the 3$\textbf{k}$ magnetic ground state with canted ordering of uranium $f$-orbitals. The cooperative Jahn-Teller effect does not appear to play a significant part in stabilizing the noncollinear 3$\textbf{k}$ state, which has the lowest energy even in an undistorted lattice. The choice of parameter $U$ in the LSDA+$U$ model has a notable quantitative effect on the predicted properties of UO$_2$, in particular on the magnetic exchange interaction and, perhaps trivially, on the band gap: The value of $U=3.46$ eV computed fully $ab$ $initio$ delivers the band gap of 2.11~eV in good agreement with experiment, and a balanced account of other pertinent energy scales.

cond-mat.str-el↗

arXiv2019

The microscopic Einstein-de Haas effect

The Einstein-de Haas (EdH) effect, where the spin angular momentum of electrons is transferred to the mechanical angular momentum of atoms, was established experimentally in 1915. While a semi-classical explanation of the effect exists, modern electronic structure methods have not yet been applied to modelling the phenomenon. In this paper we investigate its microscopic origins by means of a non-collinear tight-binding model of an $\textrm{O}_2$ dimer, which includes the effects of spin-orbit coupling, coupling to an external magnetic field, and vector Stoner exchange. By varying an external magnetic field in the presence of spin-orbit coupling, a torque can be generated on the dimer, validating the presence of the EdH effect. Avoided energy level crossings and the rate of change of magnetic field determine the evolution of the spin. We find also that the torque exerted on the nuclei by the electrons in a time-varying $B$ field is not only due to the EdH effect. Other contributions arise from field-induced changes in the electronic orbital angular momentum and from the direct action of the Faraday electric field associated with the time-varying magnetic field.

cond-mat.mes-hall↗

arXiv2019

The Dynamics of Magnetism in Fe-Cr Alloys with Cr Clustering

The dynamics of magnetic moments in iron-chromium alloys with different levels of Cr clustering show unusual features resulting from the fact that even in a perfect body-centred cubic structure, magnetic moments experience geometric magnetic frustration resembling that of a spin glass. Due to the long range exchange coupling and configuration randomness, magnetic moments of Cr solutes remain non-collinear at all temperatures. To characterise magnetic properties of Fe-Cr alloys, we explore the temperature dependence of magnetisation, susceptibility, Curie temperature and spin-spin correlations with spatial resolution. The static and dynamic magnetic properties are correlated with the microstructure of Fe-Cr, where magnetisation and susceptibility are determined by the size of Cr precipitates at nominal Cr concentrations. The Curie temperature is always maximised when the solute concentration of Cr in the $α$ phase is close to 5 to 6 at.\%, and the susceptibility of Fe atoms is always enhanced at the boundary between a precipitate and solid solution. Interaction between Cr and Fe stimulates magnetic disorder, lowering the effective Curie temperature. Dynamic simulation of evolution of magnetic correlations shows that the spin-spin relaxation time in Fe-Cr alloys is in the 20 to 40 ps range.

cond-mat.mtrl-sci↗

arXiv2018

Hybrid mean field and real space model for vacancy diffusion-mediated annealing of radiation defects

In a fusion or advanced fission reactor, high energy neutrons induce the formation of extended defect clusters in structural component materials, degrading their properties over time. Such damage can be partially recovered via a thermal annealing treatment. Therefore, for the design and operation of fusion and advanced fission nuclear energy systems it is critical to estimate and predict the annealing timescales for arbitrary configurations of defect clusters. In our earlier paper [I. Rovelli, S. L. Dudarev, and A. P. Sutton, J. Mech. Phys. Solids 103, 121 (2017)] we extended the Green function formulation by Gu, Xiang et al. [Y. Gu, Y. Xiang, S. S. Quek, and D. J. Srolovitz, J. Mech. Phys. Solids 83, 319 (2015)] for the climb of curved dislocations, to include the evaporation and growth of cavities and vacancy clusters, and take into account the effect of free surfaces. In this work, we further develop this model to include the effect of radiation defects that are below the experimental detection limit, via a mean field approach coupled with an explicit treatment of the evolution of discrete defect clusters distributed in real space. We show that randomly distributed small defects screen diffusive interactions between larger discrete clusters. The evolution of the coupled system is modelled self-consistently. We also simulate the evolution of defects in an infinite laterally extended thin film, using the Ewald summation of screened Yukawa-type diffusive propagators.

cond-mat.mtrl-sci↗

arXiv2017

Dynamic Simulation of Structural Phase Transitions in Magnetic Iron

The occurrence of bcc-fcc ($α$-$γ$) and fcc-bcc ($γ$-$δ$) phase transitions in magnetic iron stems from the interplay between magnetic excitations and lattice vibrations. However, this fact has never been proven by a direct dynamic simulation, treating non-collinear magnetic fluctuations and dynamics of atoms, and their coupling at a finite temperature. Starting from a large set of data generated by ab initio simulations, we derive non-collinear magnetic many-body potentials for bcc and fcc iron describing fluctuations in the vicinity of near perfect lattice positions. We then use spin-lattice dynamics simulations to evaluate the difference between free energies of bcc and fcc phases, assessing their relative stability within a unified dynamic picture. We find two intersections between the bcc and fcc free energy curves, which correspond to $α$-$γ$ bcc-fcc and $γ$-$δ$ fcc-bcc phase transitions. The maximum fcc-bcc free energy difference over the temperature interval between the two phase transition points is 2 meV, in agreement with other experimental and theoretical estimates.

cond-mat.mtrl-sci↗

arXiv2017

Chromium-vacancy clusters in dilute bcc Fe-Cr alloys: an ab initio study

Using an ab initio approach, we explore the stability of small vacancy and vacancy-chromium clusters in dilute body-centred cubic Fe-Cr alloys. To explain experimental observations described in C.D. Hardie et al., J. Nucl. Mater. 439, 33 (2013) and showing the occurrence of Cr segregation in low-Cr alloys, we investigate if chromium can form stable bound configurations with vacancies in alloys with chromium concentration below the low-temperature chromium solubility limit of 10-11 at. %. We find that a single vacancy can attract up to four Cr atoms in the most energetically favourable cluster configuration. The binding energy of a cluster containing a single vacancy and from one to eight Cr atoms can be well described by a linear function of the number of chromium atoms in the second, third and fifth nearest neighbour coordination. The magnetic origin of the binding energy trend is confirmed by a correlation between the average value of the magnetic moment of a Cr atom and the binding energy. Similar trends are also found for di-vacancy-Cr clusters, confirming that they likely also characterise larger systems not yet accessible to ab initio calculations. The ratio of the binding energy to the number of Cr atoms increased more than twice in the di-vacancy case in comparison with a single vacancy case.

cond-mat.mtrl-sci↗

arXiv2016

Spatial heterogeneity of W transmutation in a fusion device

Accurately quantifying the transmutation rate of tungsten (W) under neutron irradiation is a necessary requirement in the assessment of its performance as an armour material in a fusion power plant. The usual approach of calculating average responses, assuming large, homogenised material volumes, is insufficient to capture the full complexity of the transmutation picture in the context of a realistic fusion power plant design, particularly for rhenium (Re) production from W. Combined neutron transport and inventory simulations for representative {\it spatially heterogeneous} models of a fusion power plant show that the production rate of Re is strongly influenced by the local spatial environment. Localised variation in neutron moderation (slowing down) due to structural steel and coolant, particularly water, can dramatically increase Re production because of the huge cross sections of giant resolved resonances in the neutron-capture reaction of $^{186}$W at low neutron energies. Calculations using cross section data corrected for temperature (Doppler) effects suggest that temperature may have a relatively lesser influence on transmutation rates.

physics.ins-det↗

arXiv2015

Hubbard-like Hamiltonians for interacting electrons in s, p and d orbitals

Hubbard-like Hamiltonians are widely used to describe on-site Coulomb interactions in magnetic and strongly-correlated solids, but there is much confusion in the literature about the form these Hamiltonians should take for shells of p and d orbitals. This paper derives the most general s, p and d orbital Hubbard-like Hamiltonians consistent with the relevant symmetries, and presents them in ways convenient for practical calculations. We use the full configuration interaction method to study p and d orbital dimers and compare results obtained using the correct Hamiltonian and the collinear and vector Stoner Hamiltonians. The Stoner Hamiltonians can fail to describe properly the nature of the ground state, the time evolution of excited states, and the electronic heat capacity.

cond-mat.str-el↗

arXiv2015

The phonon drag force acting on a mobile crystal defect: full treatment of discreteness and non-linearity

Phonon scattering calculations predict the drag force acting on defects and dislocations rises linearly with temperature, in direct contradiction with molecular dynamics simulations that often finds the drag force to be independent of temperature. Using the Mori-Zwanzig projection technique, with no recourse to elasticity or scattering theories, we derive a general Langevin equation for a crystal defect, with full treatment of discreteness and non-linearity in the defect core. We obtain an analytical expression for the drag force that is evaluated in molecular statics and molecular dynamics, extracting the force on a defect directly from the inter-atomic forces. Our results show that a temperature independent drag force arises because vibrations in a discrete crystal are never independent of the defect motion, an implicit assumption in any phonon-based approach. This effect remains even when the Peierls barrier is effectively zero, invalidating qualitative explanations involving the radiation of phonons. We apply our methods to an interstitial defect in tungsten and solitons in the Frenkel-Kontorova model, finding very good agreement with trajectory-based estimations of the thermal drag force.

cond-mat.mtrl-sci↗

arXiv2015

Direct observation of size scaling and elastic interaction between nano-scale defects in collision cascades

Using in-situ transmission electron microscopy, we have directly observed nano-scale defects formed in ultra-high purity tungsten by low-dose high energy self-ion irradiation at 30K. At cryogenic temperature lattice defects have reduced mobility, so these microscope observations offer a window on the initial, primary damage caused by individual collision cascade events. Electron microscope images provide direct evidence for a power-law size distribution of nano-scale defects formed in high-energy cascades, with an upper size limit independent of the incident ion energy, as predicted by Sand et al. [Eur. Phys. Lett., 103:46003, (2013)]. Furthermore, the analysis of pair distribution functions of defects observed in the micrographs shows significant intra-cascade spatial correlations consistent with strong elastic interaction between the defects.

cond-mat.mtrl-sci↗

arXiv2015

Magnetic Cluster Expansion model for random and ordered magnetic face-centered cubic Fe-Ni-Cr alloys

A Magnetic Cluster Expansion (MCE) model for ternary face-centered cubic Fe-Ni-Cr alloys has been developed using DFT data spanning binary and ternary alloy configurations. Using this MCE model Hamiltonian, we perform Monte Carlo simulations and explore magnetic structures of alloys over the entire range of alloy compositions, considering both random and ordered alloy structures. In random alloys, the removal of magnetic collinearity constraint reduces the total magnetic moment but does not affect the predicted range of compositions where the alloys adopt low temperature ferromagnetic configurations. During alloying of ordered fcc Fe-Ni compounds with Cr, chromium atoms tend to replace nickel rather than iron atoms. Replacement of Ni by Cr in alloys with high iron content increases the Curie temperature of the alloys. This can be explained by strong antiferromagnetic Fe-Cr coupling, similar to that found in bcc Fe-Cr solutions, where the Curie temperature increase, predicted by simulations as a function of Cr concentration, is confirmed by experimental observations.

cond-mat.mtrl-sci↗

arXiv2014

Developing Structural, High-heat flux and Plasma Facing Materials for a near-term DEMO Fusion Power Plant: the EU Assessment

The findings of the EU 'Materials Assessment Group' (MAG), within the 2012 EU Fusion Roadmap exercise, are discussed. MAG analysed the technological readiness of structural, plasma facing and high heat flux materials for a DEMO concept to be constructed in the early 2030s, proposing a coherent strategy for R&D up to a DEMO construction decision. Technical consequences for the materials required and the development, testing and modelling programmes, are analysed using: a systems engineering approach, considering reactor operational cycles, efficient maintenance and inspection requirements, and interaction with functional materials/coolants; and a project-based risk analysis, with R&D to mitigate risks from material shortcomings including development of specific risk mitigation materials.

physics.ins-det↗

arXiv2014

Trapping of He Clusters by Inert-Gas Impurities in Tungsten: First-Principles Predictions and Experimental Validation

Properties of point defects resulting from the incorporation of inert-gas atoms in bcc tungsten are investigated systematically using first-principles density functional theory (DFT) calculations. The most stable configuration for the interstitial neon, argon, krypton and xenon atoms is the tetrahedral site, similarly to what was found earlier for helium in W. The calculated formation energies for single inert-gas atoms at interstitial sites as well as at substitutional sites are much larger for Ne, Ar, Kr and Xe than for He. While the variation of the energy of insertion of inert-gas defects into interstitial configurations can be explained by a strong effect of their large atomic size, the trend exhibited by their substitutional energies is more likely related to the covalent interaction between the noble gas impurity atoms and the tungsten atoms. There is a remarkable variation exhibited by the energy of interaction between inert-gas impurities and vacancies, where a pronounced size effect is observed when going from He to Ne, Ar, Kr, Xe. The origin of this trend is explained by electronic structure calculations showing that p-orbitals play an important part in the formation of chemical bonds between a vacancy and an atom of any of the four inert-gas elements in comparison with helium, where the latter contains only 1s2 electrons in the outer shell. The binding energies of a helium atom trapped by five different defects (He-v, Ne-v, Ar-v, Kr-v, Xe-v, where v denotes a vacancy in bcc-W) are all in excellent agreement with experimental data derived from thermal desorption spectroscopy. Attachment of He clusters to inert gas impurity atom traps in tungsten is analysed as a function of the number of successive trapping helium atoms. Variation of the Young modulus due to inert-gas impurities is analysed on the basis of data derived from DFT calculations.

cond-mat.mtrl-sci↗

arXiv2014

Lattice swelling and modulus change in a helium-implanted tungsten alloy: X-ray micro-diffraction, surface acoustic wave measurements, and multiscale modelling

Using X-ray micro-diffraction and surface acoustic wave spectroscopy, we measure lattice swelling and elastic modulus changes in a W-1%Re alloy after implantation with 3110 appm of helium. A fraction of a percent observed lattice expansion gives rise to an order of magnitude larger reduction in the surface acoustic wave velocity. A multiscale elasticity, molecular dynamics, and density functional theory model is applied to the interpretation of observations. The measured lattice swelling is consistent with the relaxation volume of self-interstitial and helium-filled vacancy defects that dominate the helium-implanted material microstructure. Molecular dynamics simulations confirm the elasticity model for swelling. Elastic properties of the implanted surface layer also change due to defects. The reduction of surface acoustic wave velocity predicted by density functional theory calculations agrees remarkably well with experimental observations.

cond-mat.mtrl-sci↗