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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 (SOC). This paper introduces a time-dependent, non-collinear tight binding model, complete with SOC and vector Stoner exchange terms, that is capable of simulating the Einstein-de Haas (EdH) effect in a ferromagnetic Fe15cluster. 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 appliedBfield, and we show that the qualitative behaviors 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 realisticBfields. The simulations presented in this paper demonstrate the EdH effect from first principles using a Fe cluster.
RESUMEN
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 semiclassical explanation of the effect exists, modern electronic structure methods have not yet been applied to model the phenomenon. In this paper, we investigate its microscopic origins by means of a noncollinear tight-binding model of an O2 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. The avoided energy level crossings and the rate of change of magnetic field determine the evolution of the spin. We also find that the torque exerted on the nuclei by the electrons in a time-varying B field is not only due to the EdH effect. The 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.
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The occurrence of segregation in dilute alloys under irradiation is a highly unusual phenomenon that has recently attracted attention, stimulated by the interest in the fundamental properties of alloys as well as by their applications. The fact that solute atoms segregate in alloys that, according to equilibrium thermodynamics, should exhibit full solubility, has significant practical implications, as the formation of precipitates strongly affects physical and mechanical properties of alloys. A lattice Hamiltonian, generalizing the so-called 'ABV' Ising model and including collective many-body inter-atomic interactions, has been developed to treat rhenium solute atoms and vacancies in tungsten as components of a ternary alloy. The phase stability of W-Re-vacancy alloys is assessed using a combination of density functional theory (DFT) calculations and cluster expansion (CE) simulations. The accuracy of CE parametrization is evaluated against the DFT data, and the cross-validation error is found to be less than 4.2 meV/atom. The free energy of W-Re-vacancy ternary alloys is computed as a function of temperature using quasi-canonical Monte Carlo simulations, using effective two, three and four-body interactions. In the low rhenium concentration range (<5 at.[Formula: see text]Re), solute segregation is found to occur in the form of voids decorated by Re atoms. These vacancy-rhenium clusters remain stable over a broad temperature range from 800 K to 1600 K. At lower temperatures, simulations predict the formation of Re-rich rhenium-vacancy clusters taking the form of sponge-like configurations that contain from 30 to 50 at.[Formula: see text]Re. The anomalous vacancy-mediated segregation of Re atoms in W can be rationalized by analyzing binding energy dependence as a function of Re to vacancy ratio as well as chemical Re-W and Re-vacancy interactions and short-range order parameters. DFT calculations show that rhenium-vacancy binding energies can be as high as 1.5 eV if the rhenium/vacancy ratio is in the range from 2.4 to 6.6. The predicted Re clustering agrees with experimental observations of precipitation in self-ion irradiated W-2[Formula: see text] Re alloys and neutron-irradiated alloys containing 1.4 at.[Formula: see text]Re.
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Knowledge of mechanical and physical property evolution due to irradiation damage is essential for the development of future fission and fusion reactors. Ion-irradiation provides an excellent proxy for studying irradiation damage, allowing high damage doses without sample activation. Limited ion-penetration-depth means that only few-micron-thick damaged layers are produced. Substantial effort has been devoted to probing the mechanical properties of these thin implanted layers. Yet, whilst key to reactor design, their thermal transport properties remain largely unexplored due to a lack of suitable measurement techniques. Here we demonstrate non-contact thermal diffusivity measurements in ion-implanted tungsten for nuclear fusion armour. Alloying with transmutation elements and the interaction of retained gas with implantation-induced defects both lead to dramatic reductions in thermal diffusivity. These changes are well captured by our modelling approaches. Our observations have important implications for the design of future fusion power plants.
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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.
RESUMEN
Using in situ transmission electron microscopy (TEM), we have observed nanometre scale dislocation loops formed when an ultra-high-purity tungsten foil is irradiated with a very low fluence of self-ions. Analysis of the TEM images has revealed the largest loops to be predominantly of prismatic 1/2ã111ã type and of vacancy character. The formation of such dislocation loops is surprising since isolated loops are expected to be highly mobile, and should escape from the foil. In this work we show that the observed size and number density of loops can be explained by the fact that the loops are not isolated-the loops formed in close proximity in the cascades interact with each other and with vacancy clusters, also formed in cascades, through long-range elastic fields, which prevent the escape of loops from the foil. We find that experimental observations are well reproduced by object Kinetic Monte Carlo simulations of evolution of cascades only if elastic interaction between the loops is taken into account. Our analysis highlights the profound effect of elastic interaction between defects on the microstructural evolution of irradiated materials.
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A model lattice ab initio parameterized Heisenberg-Landau magnetic cluster expansion Hamiltonian spanning a broad range of alloy compositions and a large variety of chemical and magnetic configurations has been developed for face-centered cubic Fe-Ni alloys. The thermodynamic and magnetic properties of the alloys are explored using configuration and magnetic Monte Carlo simulations over a temperature range extending well over 1000 K. The predicted face-centered cubic-body-centered cubic coexistence curve, the phase stability of ordered Fe3Ni, FeNi, and FeNi3 intermetallic compounds, and the predicted temperatures of magnetic transitions simulated as functions of alloy composition agree well with experimental observations. Simulations show that magnetic interactions stabilize the face-centered cubic phase of Fe-Ni alloys. Both the model Hamiltonian simulations and ab initio data exhibit a particularly large number of magnetic configurations in a relatively narrow range of alloy compositions corresponding to the occurrence of the Invar effect.
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We have developed empirical interatomic potentials for studying radiation defects and dislocations in tungsten. The potentials use the embedded atom method formalism and are fitted to a mixed database, containing various experimentally measured properties of tungsten and ab initio formation energies of defects, as well as ab initio interatomic forces computed for random liquid configurations. The availability of data on atomic force fields proves critical for the development of the new potentials. Several point and extended defect configurations were used to test the transferability of the potentials. The trends predicted for the Peierls barrier of the [Formula: see text] screw dislocation are in qualitative agreement with ab initio calculations, enabling quantitative comparison of the predicted kink-pair formation energies with experimental data.
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We present a combined experimental and computational study of high temperature magnetic properties of Fe-Cr alloys with chromium content up to about 20 at.%. The magnetic cluster expansion method is applied to model the magnetic properties of random Fe-Cr alloys, and in particular the Curie transition temperature, as a function of alloy composition. We find that at low (3-6 at.%) Cr content the Curie temperature increases with the increase of Cr concentration. It is maximum at approximately 6 at.% Cr and then decreases for higher Cr content. The same feature is found in thermo-magnetic measurements performed on model Fe-Cr alloys, where a 5 at.% Cr alloy has a higher Curie temperature than pure Fe. The Curie temperatures of 10 and 15 at.% Cr alloys are found to be lower than the Curie temperature of pure Fe.
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A second generation of empirical potentials is produced for α-Fe within the framework of the magnetic potential formalism (Dudarev and Derlet 2005 J. Phys.: Condens. Matter 17 7097). A materials database that, in addition to ab initio-derived point defect formation energies, now includes third-order elastic constant and ab initio-derived string potential data controlling, respectively, the thermal expansion properties and the core structure of the 1/2(111) screw dislocation. Three parameterizations are presented in detail, all of which exhibit positive thermal expansion and produce a non-degenerate configuration for the relaxed 1/2(111) screw dislocation easy core structure. These potentials, along with two other published potentials, are investigated in terms of defect formation volume, early stage dislocation loop clustering energetics, (110) dumbbell interstitial diffusion, and the zero-stress 1/2(111) screw dislocation Peierls barrier and its corresponding kink formation energies.
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In molecular dynamics simulations, temperature is evaluated, via the equipartition principle, by computing the mean kinetic energy of atoms. There is no similar recipe yet for evaluating temperature of a dynamic system of interacting spins. By solving semiclassical Langevin spin-dynamics equations, and applying the fluctuation-dissipation theorem, we derive an equation for the temperature of a spin ensemble, expressed in terms of dynamic spin variables. The fact that definitions for the kinetic and spin temperatures are fully consistent is illustrated using large-scale spin dynamics and spin-lattice dynamics simulations.
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Body-centered-cubic iron develops an elastic instability, driven by spin fluctuations, near the alpha-gamma phase transition temperature T(c) = 912 degrees C that is associated with the dramatic reduction of the shear stiffness constant c' (c(11)-c(12))/2 near T(c). This reduction of c' has a profound effect on the temperature dependence of the anisotropic elastic self-energies of dislocations in iron. It also affects the relative stability of the a[100] and a/2[111] prismatic edge dislocation loops formed during irradiation. The difference between the anisotropic elastic free energies provides the fundamental explanation for the observed dominant occurrence of the a[100], as opposed to the a/2[111], Burgers vector configurations of prismatic dislocation loops in iron and iron-based alloys at high temperatures.
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The significance of the part played by the angular-dependent components of forces associated with d-d bonding between atoms in a transition metal has long remained a subject of debate. While almost all the large-scale molecular dynamics simulations of collision cascades and radiation damage in transition metals and alloys are currently performed using spherically symmetric many-body potentials, density functional calculations exhibit a highly anisotropic pattern of charge density deformation in and around the core of interstitial atom defects. This paper describes a fast second-order matrix recursion-based algorithm for including effects of angular anisotropy of d-d bonds in a large-scale molecular dynamics simulation.