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In this study we investigate, using all-atom molecular-dynamics computer simulations, the in-plane diffusion of a doxorubicin drug molecule in a thin film of water confined between two silica surfaces. We find that the molecule diffuses along the channel in the manner of a Gaussian diffusion process, but with parameters that vary according to its varying transversal position. Our analysis identifies that four Gaussians, each describing particle motion in a given transversal region, are needed to adequately describe the data. Each of these processes by itself evolves with time at a rate slower than that associated with classical Brownian motion due to a predominance of anticorrelated displacements. Long adsorption events lead to ageing, a property observed when the diffusion is intermittently hindered for periods of time with an average duration which is theoretically infinite. This study presents a simple system in which many interesting features of anomalous diffusion can be explored. It exposes the complexity of diffusion in nanoconfinement and highlights the need to develop new understanding.

Interface diffusion along a metal/ceramic interface present in numerous energy and electronic devices can critically affect their performance and stability. Hole formation in a polycrystalline Ni film on an α-Al2O3 substrate coupled with a continuum diffusion analysis demonstrates that Ni diffusion along the Ni/α-Al2O3 interface is surprisingly fast. Ab initio calculations demonstrate that both Ni vacancy formation and migration energies at the coherent Ni/α-Al2O3 interface are much smaller than in bulk Ni, suggesting that the activation energy for diffusion along coherent Ni/α-Al2O3 interfaces is comparable to that along (incoherent/high angle) grain boundaries. Based on these results, we develop a simple model for diffusion along metal/ceramic interfaces, apply it to a wide range of metal/ceramic systems and validate it with several ab initio calculations. These results suggest that fast metal diffusion along metal/ceramic interfaces should be common, but is not universal., Little is known about diffusion along metal/ceramic interfaces even though it controls the physical behavior and lifetimes of many devices (including batteries, microelectronics, and jet engines). Here, the authors show that diffusion along a nickel/sapphire interface is abnormally fast due to nickel vacancies and generalise their findings to a wide-range of metal/ceramic systems.

Vacancies in iron are hydrogen traps, important in the understanding of hydrogen embrittlement of steel. We present a grand canonical approach to computing the trap occupancy as a function of both temperature and hydrogen concentration from practically zero to super-saturation. Our method couples a purpose-made machine-learned H-Fe potential, which enables rapid sampling with near density functional theory accuracy, with a statistical mechanical calculation of the trap occu- pancy using the technique of nested sampling. In contrast to the conventional assumption (based on Oriani theory) that at industrially relevant hydrogen concentrations and ambient conditions vacancy traps are are fully occupied, we find that vacancy traps are less than fully occupied under these conditions, necessitating a reevaluation of how we think about “mobile hydrogen” in iron and steel.

Enhanced ionic conductivity observed in a heteroepitaxial multilayer of yttria-stabilised zirconia and (YSZ) and strontium titanate (STO) has variously been attributed to lattice dilation or a disordered oxygen sublattice, leading to high interfacial mobility of anions, as compared to those of the constituent bulk oxides. We seek to understand the mechanism of ionic motion in such heterostructures by first simulating the atomic structure assuming coherent interfaces. After investigating possible low-energy interface structures using a genetic algorithm, we perform molecular dynamics simulations on these structures to examine the anionic diffusivity in the system. We find that the extreme biaxial tensile strain in the YSZ layer, as imposed between layers of STO, induces phases that differ from fluorite. The lowest energy structure is an unknown phase, which we refer to as quasi-cubic and whose cation sublattice resembles an extension of the perovskite; this structure does not lead to enhanced ionic conductivity, in contradiction to some reports in the literature.

We present an approach that enables an efficient and accurate study of dynamically unstable crystals over the full temperature range. The approach is based on an interatomic potential fitted to ab initio molecular dynamics energies for both the high- and low-temperature stable phases. We verify by comparison to explicit ab initio simulations that such a bespoke potential, for which we use here the functional form of the embedded atom method, provides accurate transformation temperatures and atomistic features of the transformation. The accuracy of the potential makes it an ideal tool to study the important impact of finite size and finite time effects. We apply our approach to the dynamically unstable $\ensuremath{\beta}$ (bcc) titanium phase and study in detail the transformation to the low-temperature stable hexagonal $\ensuremath{\omega}$ phase. We find a large set of previously unreported linear-chain disordered (LCD) structures made up of three types of ${[111]}_{\ensuremath{\beta}}$ linear-chain defects that exhibit randomly disordered arrangements in the ${(111)}_{\ensuremath{\beta}}$ plane.

We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature-dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a $\ifmmode\times\else\texttimes\fi{}10$ speedup on comparable free energy approaches at the level of density functional theory, with average errors less than 1 meV/atom. As a demonstration we make predictions on the thermodynamics of substoichiometric ${\mathrm{ZrC}}_{x}$, including vacancy concentration and heat capacity.

The electronic (band) structure of polycrystalline Al2O3, in particular the density of near-band edge grain-boundary localized states, plays a significant role in a host of high-temperature phenomena, including sintering, high-temperature creep, oxygen permeability in dense “dry” Al2O3 ceramics, and Al2O3 scale formation on Al2O3 scale-forming alloys. All these phenomena involve creation or annihilation of charged point defects (vacancies and/or interstitials) at grain boundaries and interfaces, and must of necessity involve electrons and holes. Thus, the density of states associated with grain boundaries in Al2O3 assume great importance, and has been calculated using DFT for both nominally undoped and Y-doped Σ7 bi-crystal boundaries. These quantum mechanical calculations must be taken into account when considering why Y2O3 segregation to Al2O3 grain boundaries is so effective in enhancing high-temperature creep resistance of polycrystalline Al2O3, and in understanding the reactive element effect in Al2O3 scale-forming alloys. Finally, a case will be made that grain-boundary diffusion is mediated by the migration of a class of grain-boundary ledge defects called disconnections, which are characterized by a step height h and a Burgers vector b.

We report molecular dynamics simulations and their analysis for a mixed tilt and twist grain boundary vicinal to the $\mathrm{\ensuremath{\Sigma}}7$ symmetric tilt boundary of the type ${1\phantom{\rule{0.16em}{0ex}}2\phantom{\rule{0.16em}{0ex}}3}$ in aluminum. When minimized in energy at $0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, a grain boundary of this type exhibits nanofacets that contain kinks. We observe that at higher temperatures of migration simulations, given extended annealing times, it is energetically favorable for these nanofacets to coalesce into a large terrace-facet structure. Therefore, we initiate the simulations from such a structure and study as a function of applied driving force and temperature how the boundary migrates. We find the migration of a faceted boundary can be described in terms of the flow of steps. The migration is dominated at lower driving force by the collective motion of the steps incorporated in the facet, and at higher driving forces by the step detachment from the terrace-facet junction and propagation of steps across the terraces. The velocity of steps on terraces is faster than their velocity when incorporated in the facet, and very much faster than the velocity of the facet profile itself, which is almost stationary. A simple kinetic Monte Carlo model matches the broad kinematic features revealed by the molecular dynamics. Since the mechanisms seem likely to be very general on kinked grain-boundary planes, the step-flow description is a promising approach to more quantitative modeling of general grain boundaries.

Under the sponsorship of the U.S. National Science Foundation, a workshop on emerging research opportunities in ceramic and glass science was held in September 2016. Reported here are proceedings of the workshop. The report details eight challenges identified through workshop discussions: Ceramic processing: Programmable design and assembly; The defect genome: Understanding, characterizing, and predicting defects across time and length scales; Functionalizing defects for unprecedented properties; Ceramic flatlands: Defining structure-property relations in free-standing, supported, and confined two-dimensional ceramics; Ceramics in the extreme: Discovery and design strategies; Ceramics in the extreme: Behavior of multimaterial systems; Understanding and exploiting glasses and melts under extreme conditions; and Rational design of functional glasses guided by predictive modeling. It is anticipated that these challenges, once met, will promote basic understanding and ultimately enable advancements within multiple sectors, including energy, environment, manufacturing, security, and health care., National Science Foundation (U.S.) (Award DMR-1619666)

A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells – a honeycomb pattern. Reactions with the environment constitute the boundary conditions and drive the transport between the surfaces. Time-dependent simulations solving the Poisson equation self-consistently with the Nernst-Planck flux equations for the mobile species are performed. In the resulting Poisson-Nernst-Planck system of equations, the electrostatic potential is obtained from the Poisson equation in its integral form by summation. The model is used to interpret alumina membrane oxygen permeation experiments, in which different oxygen gas pressures are applied at opposite membrane surfaces and the resulting flux of oxygen molecules through the membrane is measured. Simulation results involving four mobile species, charged aluminum and oxygen vacancies, electrons, and holes, provide a complete description of the measurements and insight into the microscopic processes underpinning the oxygen permeation of the membrane. Most notably, the hypothesized transition between p-type and n-type ionic conductivity of the alumina grain boundaries as a function of the applied oxygen gas pressure is observed in the simulations. The range of validity of a simple analytic model for the oxygen permeation rate, similar to the Wagner theory of metal oxidation, is quantified by comparison to the numeric simulations. The three-dimensional model we develop here is readily adaptable to problems such as transport in a solid state electrode, or corrosion scale growth.

La 1 − x Sr x Co 0.25 Fe 0.75 O 3 − δ is known as one of the best cathode materials for permeation membranes and solid oxide fuel cells. Optimization of its chemical composition is a challenging problem. One of the key properties is concentration of oxygen vacancies, which is controlled by their formation energies. Ab initio calculations were employed in order to study the formation of oxygen vacancies in La 1 − x Sr x Co 0.25 Fe 0.75 O 3 − δ perovskites by varying the Sr content from x = 12.5% to 50%. The formation energies were obtained for different stoichiometries as functions of temperature and oxygen partial pressure. For this purpose we calculated the phonon frequencies in the solid phase and the chemical potential of oxygen. We have shown that the phonon contribution to the free energy of formation becomes increasingly important in La 1 − x Sr x Co 0.25 Fe 0.75 O 3 − δ not only with rising temperature but also with rising Sr content. We find that the formation energies decrease significantly with increasing Sr content due to the phonon contribution. A simple explanation is proposed for the increasing role of phonons in the oxygen vacancy formation energies on the basis of phonon mode changes in comparison to defect-free materials. A careful analysis of the experimental results from the literature is also presented.

In order to elucidate the role of this element in superalloy metallurgy, the binding energy of Re-Re pairs and the stability of small Re clusters in the nickel face-centred cubic (fcc) lattice is investigated using ab initio density functional theory. It is shown that the formation of Re-Re nearest neighbour pairs is energetically unfavourable, and that this repulsive energy is dramatically reduced as soon as the solute atoms move further apart from one another. Furthermore, small nearest neighbour and second neighbour Re clusters are found to be unstable. The calculations are repeated for W and Ta, which lie beside Re in the periodic table; the results are essentially the same, except that some Ta-Ta higher order pairs have a positive binding energy, consistent with the Ni-Ta binary phase diagram exhibiting several ordered intermetallics. The predictions show that Re clusters are unstable in fcc Ni and it is unlikely that clustering has a role in improving creep and fatigue properties (the rhenium-effect) in Ni-based superalloys. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Multilayered oxide heteroepitaxial systems, including that of a 1-nm-thick Y2O3-stabilised ZrO2 (YSZ) sandwiched between layers of SrTiO3 (STO) [1], have been a subject of much interest lately due to their significantly enhanced ionic conductivities as compared to the bulk materials. We aim to provide the foundation for understanding this increase in conductivity by considering the atomic configurations at the interfaces of such systems, specifically a ZrO2/STO multilayer system. Possible stable lattice structures of pure ZrO2 in the system are explored using a genetic algorithm in which the interatomic interactions are modelled by simple pair potentials. The energies of several of the more stable of these structures are then evaluated more accurately within density functional theory (DFT). We find that the fluorite ZrO2 phase is unstable as a coherently strained epitaxial layer in the multilayer system. Instead, anatase-, columbite-, rutile-, and pyrite-like ZrO2 epitaxies are found to be more stable, with the anatase-like epitaxy being the most stable structure over a wide range of chemical potential of the components. We also find a high energy metastable structure resembling the tetragonal fluorite structure which is predicted by DFT to be stabilised by SrO-terminated STO but not by TiO2-terminated STO.

The close spacing of electron energy levels at the Fermi surface of a metal allows for a ready exchange of energy between ionic and electronic subsystems. In molecular dynamics (MD) simulations of fast moving ions, the heat transfer to electrons is sometimes modelled as a frictional force that slows the ions. Quantum mechanical simulations lay bare these processes and reveal how best to characterise electronic friction and heating for direct incorporation into MD. In this paper, we discuss the limitations of the description of electronic damping as a viscous force, the validity of the two-temperature model, and how the non-adiabatic movement of electrons between bonds leads to directional stopping.

We review a combination of theoretical and experimental techniques that have been applied to the study of grain boundaries in SrTiO3, with particular attention to Σ3 and ( 100 )-oriented grain boundaries. Electron microscopy, which includes high-resolution transmission and high-angle annular dark-field methods, is discussed, with successful applications to mapping atomic columns and testing theoretical models. Then, we compare and contrast different techniques of electron holography that may be used to map electrostatic potentials. Problems with the current methods of interpretation in holography and impedance spectroscopy are highlighted in an attempt to reconcile their respective estimates of electrostatic potentials at grain boundaries. Then, standard theoretical tools for the atomistic simulation of boundary structures are critically reviewed, which include classical potentials and density functional theory. A promising genetic algorithm for discovering low-energy grain boundary structures is described and tested. Finally, the synergy of experiment, theory, and simulation that is required to understand boundaries is demonstrated, and we identify major challenges to understanding multicomponent systems.

Recent years have seen great advances in our ability to predict crystal structures from first principles. However, previous algorithms have focused on the prediction of bulk crystal structures, where the global minimum is the target. Here, we present a general atomistic approach to simulate in multicomponent systems the structures and free energies of grain boundaries and heterophase interfaces with fixed stoichiometric and non-stoichiometric compositions. The approach combines a new genetic algorithm using empirical interatomic potentials to explore the configurational phase space of boundaries, and thereafter refining structures and free energies with first-principles electronic structure methods. We introduce a structural order parameter to bias the genetic algorithm search away from the global minimum (which would be bulk crystal), while not favouring any particular structure types, unless they lower the energy. We demonstrate the power and efficiency of the algorithm by considering non-stoichiometric grain boundaries in a ternary oxide, SrTiO(3).

The defect formation energies of all possible charge states of point defects in TiO2, including titanium interstitials, titanium vacancies and oxygen vacancies, are calculated in the phase space of temperature, oxygen partial pressure and Fermi level by combining density functional theory (DFT) and thermodynamic calculations. The point defect phase diagram illustrates that fully charged defects dominate in most regimes. The calculations not only give reasonable defect formation energies compared with prior experimental measurements, but also predict n-type TiO2 at high T and low P O 2 , and p-type TiO2 at low T and high P O 2 , which agrees well with experimental data. In addition, we evaluate methods for correcting the effects of artificial electrostatic interactions caused by periodic boundary conditions in the DFT calculations, including the electrostatic potential alignment correction (ΔV correction) and the Makov–Payne correction.

In this paper we briefly discuss the problem of simulating non-adiabatic processes in systems that are usefully modelled using molecular dynamics. In particular we address the problems associated with metals, and describe two methods that can be applied: the Ehrenfest approximation and correlated electron-ion dynamics (CEID). The Ehrenfest approximation is used to successfully describe the friction force experienced by an energetic particle passing through a crystal, but is unable to describe the heating of a wire by an electric current. CEID restores the proper heating. (C) 2008 Elsevier B.V. All rights reserved.

A computational approach that integrates ab initio electronic structure and thermodynamic calculations is used to determine point defect stability in rutile TiO 2 over a range of temperatures, oxygen partial pressures and stoichiometries. Both donors (titanium interstitials and oxygen vacancies) and acceptors (titanium vacancies) are predicted to have shallow defect transition levels in the electronic-structure calculations. The resulting defect formation energies for all possible charge states are then used in thermodynamic calculations to predict the influence of temperature and oxygen partial pressure on the relative stabilities of the point defects. Their ordering is found to be the same as temperature increases and oxygen partial pressure decreases: titanium vacancy → oxygen vacancy → titanium interstitial. The charges on these defects, however, are quite sensitive to the Fermi level. Finally, the combined formation energies of point defect complexes, including Schottky, Frenkel and anti-Frenkel defects, are predicted to limit the further formation of point defects.

Computer simulation of the core structure and glide of ordinary screw dislocations in single-phase L10 TiAl and in two lamellae forming a twin γ/γ-interface has been performed using recently constructed Bond-Order Potentials (BOPs). BOPs represent a semi-empirical, numerically efficient scheme that works within the orthogonal tight-binding approximation and is able to capture the directionality of bonding. We have studied dislocation glide in perfect L10 TiAl and along a twin interface, transmission of an ordinary screw dislocation between lamellae, and the core structure, mobility and detachment of an interfacial screw dislocation from a twin boundary under applied shear stresses in directions parallel and perpendicular to a (111) plane. Our results show that the glide of ordinary straight screw dislocations under applied stresses in L10 TiAl is characterized by zigzag movement on two conjugated {111} planes. The non-planar core of the screw dislocation is distorted asymmetrically when the elastic centre...

Applying simulated annealing with a classical potential followed by screening of low-energy structures with density functional theory, we examined the atomic and electronic structures of the Σ 7 4 5 ¯ 1 0 [ 0 0 0 1 ] and Σ 7 2 3 ¯ 1 0 [ 0 0 0 1 ] symmetric tilt grain boundaries in α -Al2O3. The lowest energy Σ 7 4 5 ¯ 1 0 [ 0 0 0 1 ] boundary exhibits a pronounced pattern of alternating columns of exclusively four- or fivefold coordinated Al atoms, with a grain boundary energy of 1.84 Jm−2. For the Σ 7 2 3 ¯ 1 0 [ 0 0 0 1 ] boundary, numerous structures were found with energy just below 2.11 Jm−2. Furthermore, by analysing the full set of candidate structures generated by simulated annealing for the two grain boundaries, we find that the number of fivefold coordinated Al atoms tends to increase with grain boundary energy, which we can also correlate with the behaviour of the electronic density of states. On the other hand, we find no systematic trend with energy that might be expected for other quantities, notably the excess volume of the interface. We compare simulated high-resolution transmission electron microscope (HRTEM) images of the lowest energy calculated structures with experimental images. The disparate structural and electronic features of these two boundaries suggest reasons for their very different oxygen diffusion coefficients that have been observed experimentally.

Thermodynamic properties of ZrC are calculated up to the melting point (${T}^{\mathrm{melt}}\ensuremath{\approx}3700\phantom{\rule{0.28em}{0ex}}\text{K}$), using density functional theory (DFT) to obtain the fully anharmonic vibrational contribution, and including electronic excitations. A significant improvement is found in comparison to results calculated within the quasiharmonic approximation. The calculated thermal expansion is in better agreement with experiment and the heat capacity reproduces rather closely a CALPHAD estimate. The calculations are presented as an application of a development of the upsampled thermodynamic integration using Langevin dynamics (UP-TILD) approach. This development, referred to here as two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD), is the inclusion of tailored interatomic potentials to characterize an intermediate reference state of anharmonic vibrations on a two-stage path of thermodynamic integration between the original DFT quasiharmonic free energy and the fully anharmonic DFT free energy. This approach greatly accelerates the convergence of the calculation, giving a factor of improvement in efficiency of $\ensuremath{\sim}50$ in the present case compared to the original UP-TILD approach, and it can be applied to a wide range of materials.

Combining concepts of semiconductor physics and corrosion science, we develop a novel approach that allows us to perform ab initio calculations under controlled potentiostat conditions for electrochemical systems. The proposed approach can be straightforwardly applied in standard density functional theory codes. To demonstrate the performance and the opportunities opened by this approach, we study the chemical reactions that take place during initial corrosion at the water-Mg interface under anodic polarization. Based on this insight, we derive an atomistic model that explains the origin of the anodic hydrogen evolution.

▪ Abstract We review here the theory of the early stages of oxidation of the (110) surface of Ni1−x Alx, based on ab initio calculations using a plane-wave pseudopotential method. The clean surface and several oxidized surfaces have been investigated, with oxygen coverages up to 2ML of oxygen (1ML = 3 O atoms per 2 surface Al atoms). The theory to date is a description in terms of equilibrium thermodynamics, with a comparison of the free energies of several surfaces of different composition, implemented at the atomic scale. Three environmental parameters are singled out as control variables in this treatment, namely the alloy composition x (assumed to be near 0.5), the temperature T and the partial pressure of oxygen pO2. With certain reasonable approximations an analytic formula for the surface energy σ is derived in terms of these variables and some constants that are calculated ab initio together with others that are derived from experimental thermodynamic tables. At oxygen pressures just above the threshold for bulk oxidation of NiAl, the calculations explain the observed formation of a thin film of alumina in place of NiAl surface layers, with the consequent dissolution of Ni into the bulk. Ab initio calculations illustrate how the energetics of supplying Al to the surface depends on bulk stoichiometry, which alters the relative stability of different surface oxidation states so as to favour oxidation more if the alloy is Al-rich than if it is Ni-rich.

Embrittlement by the segregation of impurity elements to grain boundaries is one of a small number of phenomena that can lead to metallurgical failure by fast fracture. Here we settle a question that has been debated for over a hundred years: how can minute traces of bismuth in copper cause this ductile metal to fail in a brittle manner? Three hypotheses for Bi embrittlement of Cu exist: two assign an electronic effect to either a strengthening or weakening of bonds, the third postulates a simple atomic size effect. Here we report first principles quantum mechanical calculations that allow us to reject the electronic hypotheses, while supporting a size effect. We show that upon segregation to the grain boundary, the large Bi atoms weaken the interatomic bonding by pushing apart the Cu atoms at the interface. The resolution of the mechanism underlying grain boundary weakening should be relevant for all cases of embrittlement by oversize impurities.

Structural correlations at a liquid–solid interface were explored with molecular dynamics simulations of a model aluminium system using the Ercolessi–Adams potential and up to 4320 atoms. Substrate atoms were pinned to their equilibrium crystalline positions while liquid atoms were free to move. The density profile at the interface was investigated for different substrate crystallographic orientations and temperatures. An exponential decay of the density profile was observed, ρ ( z )∼e − κz , leading to the definition of κ as a quantitative measure of the ordering at the liquid solid interface. A direct correlation between the amount of ordering in the liquid phase and the underlying substrate orientation was found.

The Royal Society Scientific Discussion Meeting ‘The challenges of hydrogen and metals’ was held in Carlton House Terrace, London, UK, on 16–18 January 2017. This is the introductory article to the discussion meeting issue which includes contributed papers and seven discussion papers. Here, we introduce the motivation to hold the Meeting and give a brief overview of the contents. We conclude with acknowledgements. This article is part of the themed issue ‘The challenges of hydrogen and metals’.

Gallium impurities affect the atomic processes and material properties of aluminum metal to a high degree. Various ab initio calculations have been performed on a Sigma = 11 (113) symmetric tilt boundary in aluminum with and without some gallium substitutions. A simple interpretation of the results emerges, which can be applied to grain boundaries in general. The calculations relate to the energetics of gallium substitution on various sites, local relaxation effects, vibrational frequencies and a barrier to grain boundary migration. (C) 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.

We derive a formula, useful for first-principles calculations, which relates the free energy of an oxide/metal interface to the free energies of surfaces and the work of separation of the interface. We distinguish the latter mechanical quantity from the thermodynamic work of adhesion, and we describe explicitly how both may be calculated. Our formulas for interfacial and surface energies are cast in terms of quantities which can be calculated or looked up in tables, and include as additional parameters the ambient temperature and partial pressure of oxygen ${P}_{{\mathrm{O}}_{2}}.$ From total-energy calculations for the $\mathrm{Nb}(111)/\ensuremath{\alpha}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ (0001) interface, free Nb and ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ surfaces, we obtain firstly numerical estimates of the works of separation, which are independent of ${P}_{{\mathrm{O}}_{2}}.$ We then obtain surface energies, interfacial energies, and the equilibrium work of adhesion as a function of ${P}_{{\mathrm{O}}_{2}}.$

Understanding the growth of Al2O3 scales requires knowledge of the details of the chemical reactions at the scale–gas and scale–metal interfaces, which in turn requires specifying how the creation/annihilation of O and Al vacancies occurs at these interfaces. The availability of the necessary electrons and holes to allow for such creation/annihilation is a crucial aspect of the scaling reaction. The electronic band structure of polycrystalline Al2O3 thus plays a decisive role in scale formation and is considered in detail, including the implications of a density functional theory (DFT) calculation of the band structure of a Σ7 { 4 5 ¯ 1 0 } bicrystal boundary, for which the atomic structure of the boundary was known from an independent DFT energy-minimization calculation and comparisons with an atomic-resolution transmission electron micrograph of the same boundary. DFT calculations of the formation energy of O and Al vacancies in bulk Al2O3 in various charge states as a function of the Fermi energy suggested that electronic conduction in Al2O3 scales most likely involves excitation of both electrons and holes, which are localized on singly charged O vacancies, V O and doubly charged Al vacancies, V Al ″ , respectively. We also consider the variation of the Fermi level across the scale and bending (“tilting”) of the conduction band minimum and valence band maximum due to the electric field developed during the scaling reaction. The band structure calculations suggest a new mechanism for the “reactive element” effect—a consequence of segregation of Y, Hf, etc., to grain boundaries in Al2O3 scales, which results in improved oxidation resistance—namely, that the effect is due to the modification of the near-band edge grain-boundary defect states rather than any blocking of diffusion pathways, as previously postulated. Secondly, Al2O3 scale formation is dominated by grain boundary as opposed to lattice diffusion, and there is unambiguous evidence for both O and Al countercurrent transport in Al2O3 scale-forming alloys. We postulate that such transport is mediated by migration of grain boundary disconnections containing charged jogs, rather than by jumping of isolated point defects in random high-angle grain boundaries.

Hybrid-exchange density functional theory has been used to model the electronic structure of LaCoO${}_{3}$. Based on a rhombohedral unit cell of $R\overline{3}c$ symmetry containing two Co atoms we find a mixed spin phase, comprising alternating low and high spin Co${}^{+3}$ ions, with a total energy at 0 K just 57 meV per formula unit above that of a nonmagnetic semiconducting ground state. In the mixed spin phase the high-spin Co${}^{+3}$ ions have spin moments of $3.1\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ and the state is insulating with a band gap of 2.2 eV. Our calculations suggest that the effective on-site Coulomb repulsion energy ${U}_{\mathrm{eff}}$ on Co${}^{+3}$ ions is spin dependent. The ${U}_{\mathrm{eff}}$ on Co${}^{+3}$ ions is 7.1 eV and 8.5 eV for the nonmagnetic ground state and for the magnetic high spin state, respectively. For the mixed spin state, two different ${U}_{\mathrm{eff}}$ are estimated for two Co${}^{+3}$ ions in the unit cell having different spin states, 8.0 eV for the high-spin Co${}^{+3}$ ion and 7.0 eV for the low-spin Co${}^{+3}$ ion. An estimate of the harmonic phonon free energy suggests that this mixed spin phase would become the more stable phase as the temperature increases, which is consistent with experimental evidence. An alternative intermediate spin state is higher in energy at all temperatures.

International audience

Atomistic simulations are a primary means of understanding the damage done to metallic materials by high energy particulate radiation. In many situations the electrons in a target material are known to exert a strong influence on the rate and type of damage. The dynamic exchange of energy between electrons and ions can act to damp the ionic motion, to inhibit the production of defects or to quench in damage, depending on the situation. Finding ways to incorporate these electronic effects into atomistic simulations of radiation damage is a topic of current major interest, driven by materials science challenges in diverse areas such as energy production and device manufacture. In this review, we discuss the range of approaches that have been used to tackle these challenges. We compare augmented classical models of various kinds and consider recent work applying semi-classical techniques to allow the explicit incorporation of quantum mechanical electrons within atomistic simulations of radiation damage. We also outline the body of theoretical work on stopping power and electron-phonon coupling used to inform efforts to incorporate electronic effects in atomistic simulations and to evaluate their performance.

Atom probe tomography (APT) is used to characterise the distributions of rhenium in a binary Ni-Re alloy and the nickel-based single-crystal CMSX-4 superalloy. A purpose-built algorithm is developed to quantify the size distribution of solute clusters, and applied to the APT datasets to critique the hypothesis that rhenium is prone to the formation of clusters in these systems. No evidence is found to indicate that rhenium forms solute clusters above the level expected from random fluctuations. In CMSX-4, enrichment of Re is detected in the matrix phase close to the matrix/precipitate (γ/γ′) phase boundaries. Phase field modelling indicates that this is due to the migration of the γ/γ′ interface during cooling from the temperature of operation. Thus, neither clustering of rhenium nor interface enrichments can be the cause of the enhancement in high temperature mechanical properties conferred by rhenium alloying. © 2009 Acta Materialia Inc.

The design of metals and alloys resistant to radiation damage involves the physics of electronic excitations and the creation of defects and microstructure. During irradiation damage of metals by high energy particles, energy is exchanged between ions and electrons. Such non-adiabatic processes violate the Born-Oppenheimer approximation, on which all conservative classical interatomic potentials rest. By treating the electrons of a metal explicitly and quantum mechanically we are able to explore the influence of electronic excitations on the ionic motion during irradiation damage. Simple theories suggest that moving ions should feel a damping force proportional to their velocity and directly opposed to it. In contrast, our simulations of a forced oscillating ion have revealed the full complexity of this force: in reality it is anisotropic and dependent on the ion velocity and local atomic environment. A large set of collision cascade simulations has allowed us to explore the form of the damping force further. We have a means of testing various schemes in the literature for incorporating such a force within molecular dynamics (MD) against our semi-classical evolution with explicitly modelled electrons. We find that a model in which the damping force is dependent upon the local electron density is superior to a simple fixed damping model. We also find that applying a lower kinetic energy cut-off for the damping force results in a worse model. A detailed examination of the nature of the forces reveals that there is much scope for further improving the electronic force models within MD. © 2010 Materials Research Society. Accepted version

Our understanding of the ``long range'' electrodynamic, electrostatic, and polar interactions that dominate the organization of small objects at separations beyond an interatomic bond length is reviewed. From this basic-forces perspective, a large number of systems are described from which one can learn about these organizing forces and how to modulate them. The many practical systems that harness these nanoscale forces are then surveyed. The survey reveals not only the promise of new devices and materials, but also the possibility of designing them more effectively.

The solid-liquid interface free energy \gamma sl is a key parameter controlling nucleation and growth during solidification and other phenomena. There are intrinsic difficulties in obtaining accurate experimental values, and the previous approaches to compute \gamma sl with atomistic simulations are computationally demanding. We propose a new approach, which is to obtain \gamma sl from a free energy map of the phase transition reconstructed by metadynamics. We apply this to the benchmark case of a Lennard-Jones potential and the results confirm the most reliable data obtained previously. We demonstrate several advantages of our new approach: it is simple to implement, robust and free of hysteresis problems, it allows a rigorous and unbiased estimate of the statistical uncertainty and it returns a good estimate of of the thermodynamic limit with system sizes of a just a few hundred atoms. It is therefore attractive for using with more realistic and specific models of interatomic forces., Comment: improved version with new figures and tuned metadynamics parameters

We address the calculation within density functional theory (DFT) of defect formation energies in alumina, a ceramic oxide often considered an archetype for a wide variety of other similar oxides. We examine the conditions under which calculated defect formation energies, especially those of charged defects, are independent of the principal approximations of the plane-wave DFT formalism, most significant of which is the finite-sized supercell in which the calculation must be performed. We introduce a variation on existing methods of extrapolation to infinite system size to reduce dependence of the result on finite-size errors in the electrostatic and elastic energies of a periodic supercell containing a defect. We also show how the results can be made relatively insensitive to the choice of exchange-correlation functional and pseudopotential by a suitable treatment of the chemical potentials of the atomic species. Our results for formation energies of charged defects are less sensitive than traditional approaches to supercell size and choices of exchange-correlation functional and pseudopotential, and differ notably from previous results.

The surface structure of magnetite ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(111)$ in contact with oxygen and water is investigated using spin-density functional theory plus on-site Coulomb interactions. The present results unravel apparent contradictions in the experimental data regarding the equilibrium stoichiometry of the bare surface termination. Both for 298 and $1200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the equilibrium structure is terminated by $\frac{1}{4}$ monolayer (ML) of iron (Fe) on top of a full oxygen layer, consistent with an earlier low-energy electron diffraction analysis. Nonetheless, the calculated negative slope of the surface energies vs oxygen partial pressure shows that a $\frac{1}{2}$ ML Fe termination would become stable under oxygen-poor conditions at high temperatures, in agreement to interpretation of scanning tunneling microscopy experiments. Initial water adsorption is dissociative and saturates when all Fe sites are occupied by OH groups, while the H atoms bind to surface oxygen. Further, water bridges the OH and H groups resulting in a unique type of H-bonded molecular water with its oxygen forming a hydronium-ion-like structure $\mathrm{O}{\mathrm{H}}_{3}^{+}\text{\ensuremath{-}}\mathrm{O}\mathrm{H}$. This water structure is different from the water dimeric structures found as yet on oxide and metal surfaces for partially dissociated $({\mathrm{H}}_{2}\mathrm{O}\text{\ensuremath{-}}\mathrm{O}\mathrm{H}\text{\ensuremath{-}}\mathrm{H})$ overlayers.

We describe a self consistent magnetic tight-binding theory based in an expansion of the Hohenberg-Kohn density functional to second order, about a non spin polarised reference density. We show how a first order expansion about a density having a trial input magnetic moment leads to the Stoner--Slater rigid band model. We employ a simple set of tight-binding parameters that accurately describes electronic structure and energetics, and show these to be transferable between first row transition metals and their alloys. We make a number of calculations of the electronic structure of dilute Cr impurities in Fe which we compare with results using the local spin density approximation. The rigid band model provides a powerful means for interpreting complex magnetic configurations in alloys; using this approach we are able to advance a simple and readily understood explanation for the observed anomaly in the enthalpy of mixing., Comment: Submitted to Phys Rev B

First principles calculations of the Sigma 5 (310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However numerical results show a striking equivalence between the alkali metal Na and the semi metal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unravelled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the nett reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect., Comment: 13 pages, 5 figures; Accepted in Phys. Rev. B

Density-functional theory calculations, within the plane-wave-ultrasoft pseudopotential framework, were performed in the ⟨110⟩ projection for MgO and for the coherent {111} $\mathrm{Ag}\ensuremath{-}\mathrm{Mg}\mathrm{O}$ polar interface. First-principles calculations were incorporated in high-resolution transmission electron microscopy (HRTEM) simulations by converting the charge density into electron scattering factors to examine the influence of charge transfer, charge redistribution at the interface, and ionicity on the dynamical electron scattering and on calculated HRTEM images. It is concluded that the ionicity of oxides and the charge redistribution at interfaces play a significant role in HRTEM image simulations. In particular, the calculations show that at oxygen-terminated {111} $\mathrm{Ag}\mathrm{Mg}\mathrm{O}$ interfaces the first oxygen layer at the interface is much brighter than that in calculations with neutral atoms, in agreement with experimental observations.

s131d and s231d reconstructions of the (001) SrTiO3 surface were studied using the first-principles fullpotential linear muffin-tin orbital method. Surface energies were calculated as a function of TiO2 chemical potential, oxygen partial pressure and temperature. The s131d unreconstructed surfaces were found to be energetically stable for many of the conditions considered. Under conditions of very low oxygen partial pressure the s231d Ti2O3 reconstruction [Martin R. Castell, Surf. Sci. 505, 1 (2002)] is stable. The question as to why STM images of the s131d surfaces have not been obtained was addressed by calculating charge densities for each surface. These suggest that the s231d reconstructions would be easier to image than the s131d surfaces. The possibility that the presence of oxygen vacancies would destabilise the s131d surfaces was also investigated. If the s131d surfaces are unstable then there exists the further possibility that the s2 31d DL-TiO2 reconstruction [Natasha Erdman et al. Nature (London) 419, 55 (2002)] is stable in a TiO2-rich environment and for pO2 .10−18 atm.

The microscopic mechanism leading to stabilization of cubic and tetragonal forms of zirconia (ZrO$_2$) is analyzed by means of a self-consistent tight-binding model. Using this model, energies and structures of zirconia containing different vacancy concentrations are calculated, equivalent in concentration to the charge compensating vacancies associated with dissolved yttria (Y$_2$O$_3$) in the tetragonal and cubic phase fields (3.2 and 14.4% mol respectively). The model is shown to predict the large relaxations around an oxygen vacancy, and the clustering of vacancies along the $$ directions, in good agreement with experiments and first principles calculations. The vacancies alone are shown to explain the stabilization of cubic zirconia, and the mechanism is analyzed., 19 pages, 6 figures. To be published in J. Am. Ceram. Soc

The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding (SC-TB) model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free energy surfaces around the phase transition is then studied with a second set of calculations. These combine the thermodynamic integration technique with constrained MD simulations. The results seem to support the thesis of a second-order phase transition but with unusual, very anharmonic behaviour above the transition temperature.

One of the main factors which affects the bulk properties of multilayered perovskites is the atomic structure at the interface between different types of layers. We have applied Density Functional Perturbation Theory to investigate the polarisation properties of interfaces in two different phases of nonstoichiometric SrTiO3, the Ruddlesden-Poppper and Magneli phases. Our calculated Born effective charge tensors and high-frequency dielectric constants are compared for each type of interface and bulk SrTiO3. For both phases, we find that the presence of the interface introduces huge anisotropy into the Born effective charges of the participating ions. We attempt to interpret our results using a simplified tight binding model and analyse the limitations of such an approach.

We investigate the transfer of energy from a harmonically oscillating atom in a metal to the electronic subsystem, using a direct simulation method based on time-dependent tight-binding (TDTB). We present our results in terms of a viscous damping coefficient β to enable direct comparison with previous MD and Langevin dynamics simulations, over an ionic energy range relevant for radiation damage. Analysis of our results using time-dependent perturbation theory shows that the rate of energy transfer to the electrons is independent of the frequency of the driven atom at high electronic temperatures, but at low temperature may vary by an order of magnitude. Our simulations show β also to be dependent on the electronic temperature, the position of the atom within the unit cell and even the direction of oscillation. We conclude that a TDTB simulation can give the electronic damping for an infinite metal over a limited simulation time window dependent on system size, and show how to monitor errors in dynamic simulations due to finite-size effects.

With density functional theory we have performed molecular dynamics simulations of ZrC, which displayed spontaneous carbon Frenkel pair formation at a temperature of $3200\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, some 500\ifmmode^\circ\else\textdegree\fi{} below the melting point. To understand this behavior, rarely seen in equilibrium simulations, we quenched and examined a set of lattices containing a Frenkel pair. Five metastable structures were found, and their formation energies and electronic properties were studied. Their thermal generation was found to be facilitated by a reduction of between 0.7 and 1.5 eV in formation energy due to thermal expansion of the lattice. With input from a quasiharmonic description of the defect-free energy of formation, an ideal solution model was used to estimate lower bounds on their concentration as a function of temperature and stoichiometry. At 3000 K (0.81 of the melting temperature) their concentration was estimated to be 1.2% per mole in a stoichiometric crystal, and 0.3% per mole in a crystal with 10% per mole of constitutional vacancies. Their contribution to heat capacity, thermal expansion, and bulk modulus was estimated.