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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.

We calculate the stability of the MAX-phase materials ${\mathrm{Zr}}_{n+1}{\mathrm{AlC}}_{n}$ and ${\mathrm{Ti}}_{n+1}{\mathrm{AlC}}_{n}$ in the context of the M-A-X ternary phase diagrams and competing binary and ternary compounds, as a function of temperature, by applying density functional theory (DFT) within the quasiharmonic approximation. By examining the convex hull of free energy we find that the Zr-based MAX phases are thermodynamically unstable at room temperature and below with respect to decomposition to carbide and intermetallics, although with increasing temperature the ${\mathrm{Zr}}_{3}{\mathrm{AlC}}_{2}$ phase becomes stable. On the other hand, the pure ${\mathrm{Ti}}_{2}\mathrm{AlC}$ phase is thermodynamically stable at room temperature, consistent with the success in its synthesis.

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.

The technique of plasmonic ELISA is utilised here to detect the HIV-1 protein gp120 with the ultralow limit of detection of 8 × 10(-20) M (10(-17) g mL(-1)) in an independent laboratory. It was corroborated that changes in the concentration of hydrogen peroxide as small as 0.05 μM could lead to nanoparticle solutions of completely different tonality.

We review and discuss methods for including the role of point defects in calculations of the free energy, composition and phase stability of elements and compounds. Our principle aim is to explain and to reconcile, with examples, the perspectives on this problem that are often strikingly different between exponents of CALPHAD, and others working in the overlapping fields of physics, chemistry and materials science. Current methodologies described here include the compound energy formalism of CALPHAD, besides the rather different but related canonical and grand-canonical formalisms. We show how the calculation of appropriate defect formation energies should be formulated, how they are included in the different formalisms and in turn how these yield equilibrium defect concentrations and their contribution to free energies and chemical potentials. Furthermore, we briefly review the current state-of-the-art and challenges in determining point defect properties from first-principles calculations as well as from experimental measurements.

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.

This article discusses some of the many-body potentials used for simulations of processes and energies in materials at the atomic scale, emphasizing their motivation and underlying physical concepts, particularly where these are not entirely empirical. The perspective is somewhat historical and describes the importance of developments of the theory of electrons in solids for the derivation of many-body (or many-atom) potential models. The models include density-dependent pairwise potentials, effective medium and embedded-atom models, and polarizable ion models. As a recent radical departure from approaches derived from the physics of electrons, the development of models based on information theory is also described.

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.

We report results of first-principles calculations on the thermodynamic stability of different Sr adatom structures that have been proposed to explain some of the observed reconstructions of the (001) surface of strontium titanate (Kubo and Nozoye 2003 Surf. Sci. 542 177). From surface free energy calculations, a phase diagram is constructed indicating the range of conditions over which each structure is most stable. These results are compared with Kubo and Nozoye's experimental observations. It is concluded that low Sr adatom coverage structures can only be explained if the surface is far from equilibrium. Intermediate coverage structures are stable only if the surface is in or very nearly in equilibrium with the strontium oxide.

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.

I attempt an overview of the nature of interatomic forces in materials based on the ideas of density functional theory and the variational principle, without details of the mathematics involved. In ionic materials and simple metals, arguments based on electrostatics and linear response have a firm foundation in quantum mechanics, and are key elements for making simplified models. In other materials it is possible to simplify the many-body theory to such an extent that useful analytic models emerge.

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’.

We have studied the (110) surface of NiAl, an ordered alloy of B2 structure, using a plane-wave pseudopotential method. The clean surface and several oxidized surfaces were investigated, with oxygen coverages up to 1.5 ML (1 ML = 1 O-atom per surface metal atom). In order to compare the energies of the oxidized structures, which comprise different numbers of metal and oxygen atoms, one has to take account of the chemical potentials of the Ni, Al and O. To this end, for each system, we have applied simple analytic models to study their surface energy as a function of temperature, alloy stoichiometry (assumed to be near 50–50) and oxygen partial pressure. The calculations predict how, at oxygen pressures just above the threshold for decomposing NiAl, the clean surface should be coated by an alumina layer, with the consequent depletion of Ni near the surface. Varying stoichiometry has the relatively minor effect of shifting the crossovers in oxygen pressure at which different oxidized surfaces become stable.

For the first time, very precise experimental data on the atomistic structure of a metal/oxide interface were obtained by quantitative high-resolution transmission electron microscopy (HRTEM). They are compared with the results of ab initio density-functional theory (DFT) calculations for the same real interface structure, performed without the need for introducing artificial coherency strains. The model system of this study is the coherent (001)-oriented interface between Al and MgAl2O4 in parallel orientation. By means of quantitative HRTEM we determined the relative translation of the two crystals with picometre precision, and also within this error limit our ab initio calculations correctly predict the experimental structure. The electron density distribution obtained by the calculations indicates a directional bonding between the metal and the oxide beyond the concept of the image charge model. Furthermore, we have carried out ab initio DFT calculations for the (001) interface between Ag and...

In an earlier report we explored structural correlations at a liquid-solid interface 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 fcc crystalline positions while liquid atoms were free to move. A direct correlation between the amount of ordering in the liquid phase and the underlying substrate orientation was found. In the present paper we extend this study to the case of a fixed bcc substrate in contact with liquid aluminium. We find surprisingly similar results for the density profiles of both (100) and (110) substrates. However, there is a far greater in-plane ordering in the (100) than for the (110) system. For the (100) substrates we observe adsorption of liquid atoms into the terminating plane of the bcc (100) substrate, effectively transforming the bcc (100) plane into an fcc (100) plane.

We present a force field for bulk alumina (Al2O3), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with density functional theory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.

The electron energy-loss near-edge structure ~ELNES! at the oxygen K-edge has been investigated in a range of yttria-stabilized zirconia ~YSZ! materials. The electronic structure of the three polymorphs of pure ZrO2 and of the doped YSZ structure close to the 33 mol %Y2O3 composition have been calculated using a full-potential linear muffin-tin orbital method ~NFP-LMTO! as well as a pseudopotential based technique. Calculations of the ELNES dipole transition matrix elements in the framework of the NFP-LMTO scheme and inclusion of core hole screening within Slater’s transition state theory enable the ELNES to be computed. Good agreement between the experimental and calculated ELNES is obtained for pure monoclinic ZrO2. The agreement is less good with the ideal tetragonal and cubic structures. This is because the inclusion of defects is essential in the calculation of the YSZ ELNES. If the model used contains ordered defects such as vacancies and metal Y planes, agreement between the calculated and experimental O K-edges is significantly improved. The calculations show how the five different O environments of Zr 2Y2O7 are connected with the features observed in the experimental spectra and demonstrate clearly the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

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 ${P}_{{\mathrm{O}}_{2}}.$

We predict the existence of an isostructural first-order phase transition in high-pressure Al-rich NiAl alloys, between vacancy-rich and antisite-rich phases. A critical point terminates the region of phase coexistence. The driving force for this phase transition is the positive defect mixing enthalpy originating from elastic interaction between vacancies and antisites on the Ni sublattice. We highlight the similarity between the critical behavior of Al-rich alloys and that of binary liquid mixtures. Analogous isostructural phase transitions are expected in other compounds with constitutional defects.

We calculate using a density functional pseudopotential method the atomic and electronic structure of the (0001) surface of α-alumina (Al2O3). The material is studied in the form of a slab with periodic boundary conditions, containing up to eight layers of the stoichiometric Al2O3 units. Five different terminations of the surface are calculated, representing different surface excesses of oxygen, and their free energies are estimated as a function of oxygen partial pressure. Internal relaxations of the atomic positions are obtained. The aluminium terminated surface, which is stoichiometric, has the lowest surface energy for a wide range of oxygen pressures.

We describe two measures of the local atomic density in a monatomic crystal. A new measure has the form of a function of the sum of inverse powers of the neighbour distance, and it is accurate to 2% for six simple crystalline reference structures ranging from diamond to face-centred cubic. For any periodic structure, reproduces the global average density exactly for any uniform dilation or compression in the limit of an infinite cut-off, and to high accuracy with a smooth cut-off. We compare it with a Gaussian measure of local density for large constant-volume strains of the six reference structures. The changes in are an order of magnitude less than the shear strains for bond-length changes of < 10%. However, is even less sensitive to constant-volume strains. is also transferable between structures, provided that a constant self-term (an on-site term) is included in the density. The measure of local density is primarily intended for atomistic simulations of inhomogeneous systems in which the atom-atom interactions or other terms describing the energy depend on the local volume.

Ab-initio density functional calculations were performed on the geometric and the electronic structures of coherent cube-on-cube interfaces between spinel (MgAl 2 O 4 ) and the two metals Al and Ag. The calculations were carried out in the local density approximation (LDA) employing norm-conserving pseudopotentials and a mixed basis set of plane waves and local orbitals. The cohesive properties of the bulk materials are determined in good agreement with experiment. Four different high-symmetry translation states between the metal atoms and an Al-O or a Mg termination layer of the spinel are investigated at the unrelaxed interface distance. For Al a marked preference for the on-top O position on the Al-O layer is found, whereas for Ag the hollow-site positions are slightly preferred over the on-top O position on the Al-O layer. An optimization of the interface distance yields a distinct energy minimum at 1.90 A for Al/MgAl 2 O 4 on the on-top O site, in very good agreement with experiment. For Ag the total-energy curves of the different adhesion sites intersect and enable a low-energy dissociation path.

We discuss the thermodynamics of point defects in an ordered A m B n alloy for small deviations from the stoichiometric composition. The concentrations of the two kinds of antisite and vacancy are function of three basic energies of formation and of the stoichiometry. We derive general formulae for them which can be solved numerically. Analytic formulae for the chemical potentials are derived in terms of the point-defect concentrations. Simple analytic formulae are derived for the concentrations which are valid when the constitutional defects (which dominate at low temperatures) continue to dominate the thermally excited defects of the same type at higher temperatures. The energies entering these formulae are defined in a general way, suitable for ab initio or semiempirical methods of calculation. We illustrate the results with calculations for NiAl using three different central N-body potentials. A significant effect is due to the temperature dependence of the formation energies.

Gallium as an impurity in aluminium is an extreme example of a grain boundary embrittler. The energetics of substituting Ga in various sites, individually and together, has been calculated by ab initio techniques in a Sigma = 11 (1 1 3) symmetric tilt boundary. This boundary has one relatively short nearest-neighbour distance across the boundary, which is relaxed on substitution by Ga. A picture is developed of the attraction of Ga towards the tight sites in the Al grain boundaries, and of its role as a substitutional embrittling impurity.

A methodology for calculating the contribution of charged defects to the configurational free energy of an ionic crystal is introduced. The temperature-independent Wang-Landau Monte Carlo technique is applied to a simple model of a solid electrolyte, consisting of charged positive and negative defects on a lattice. The electrostatic energy is computed on lattices with periodic boundary conditions, and used to calculate the density of states and statistical-thermodynamic potentials of this system. The free energy as a function of defect concentration and temperature is accurately described by a regular solution model up to concentrations of 10% of defects, well beyond the range described by the ideal solution theory. The approach, supplemented by short-ranged terms in the energy, is proposed as an alternative to free energy methods that require a number of simulations to be carried out over a range of temperatures.

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.