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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The strontium titanate $\ensuremath{\Sigma}3\phantom{\rule{0.3em}{0ex}}(112)\phantom{\rule{0.3em}{0ex}}[\overline{1}10]$ grain boundary has been investigated using aberration-corrected high-resolution transmission electron microscopy and exit wave-function reconstruction. By quantitatively comparing the experimental exit wave phase with that expected from relaxed model structures obtained by density-functional theory, it has been possible to differentiate between two proposed structures not significantly different in their calculated energies, and to deduce information about three-dimensional atomic arrangements near the boundary using the reconstructed exit wave-function phase.

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 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.

A method for calculating free-energy differences based on a free-energy perturbation (FEP) formalism in an alloy system described by two different Hamiltonians is reported. The intended application is the calculation of solid-liquid phase equilibria in alloys with the accuracy of first-principles electronic density-functional theory (DFT). For this purpose free energies are derived with a classical interatomic potential, and FEP calculations are used to compute corrections to these reference values. For practical applications of this approach, due to the relatively high computational cost of DFT calculations, it is critical that the FEP calculations converge rapidly in terms of the number of samples used to estimate relevant ensemble averages. This issue is investigated in the current study employing two classical interatomic-potential models for Ni-Cu. These models yield differences in predicted phase-boundary temperatures of approximately 100 K, comparable to those that might be expected between a DFT Hamiltonian and a well-fit classical potential. We show that for pure elements the FEP calculations converge rapidly with the number of samples, yielding free-energy differences converged to within a fraction of a meV/atom in a few dozen energy calculations. For a concentrated equiatomic alloy similar precision requires roughly a hundred samples. The results suggest that the proposed methodology could provide a computationally tractable framework for calculating solid-liquid phase equilibria in concentrated alloys with DFT accuracy.

The technological importance of polycrystalline strontium titanate $({\text{SrTiO}}_{3})$ is directly linked to its interfacial and grain boundary properties, which are at present poorly understood. A complete understanding (including links with experiment) requires information from many length scales, including electronic and atomistic, up to microstructural and macroscopic. In addition, the size and complexity of many general grain boundaries makes first-principles simulations prohibitively expensive. We have tested the ability of a number of interatomic potentials from the literature to accurately describe at least the structures of some simple grain boundaries in ${\text{SrTiO}}_{3}$. The potentials we have tested are of three types: rigid ion model with either fixed formal or partial charges and shell model. We have also performed a detailed density functional theory (DFT) study of the same boundaries and used this data (interface structures and energies) to validate the interatomic potentials. Our conclusion is that none of the potentials can reproduce the energy ordering of the boundaries predicted by the DFT calculations. The boundary structures produced by some of the potentials do however agree reasonably well with the DFT structures. We discuss the implications of our findings for ionic oxide grain boundary research and critically examine the rigid ion and shell model approximations.

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

Density functional theory calculations have been used to study relaxed interstitial configurations in FeCr alloys. The ionic and electronic ground states of 69 interstitial structures have been determined. Interstitials were placed in alloys with up to 14 at. % Cr. Cr atoms were either monatomically dispersed or clustered together within a periodically repeated supercell consisting of 4x4x4 cubes of bcc unit cells. The distance between the interstitials and Cr atoms was varied within the supercells. It is shown that Cr atoms beyond third-nearest-neighbor distance from the interstitial can still have an interaction with it of up to 0.9 eV. The multibody nature of the Cr-Cr interactions causes the Cr-interstitial interaction to be strongly concentration dependent. The Cr-Cr interaction in defect-free alloys is also dependent on the overall Cr concentration. The effective Cr-Cr repulsion is weaker in alloys than in an environment of pure Fe. Apart from the Cr concentration, the Cr-interstitial interaction also depends on the dispersion level of Cr atoms beyond third-nearest-neighbor distance from the interstitial. The formation energy differences between dumbbell interstitials with different orientations are independent of the Cr concentration. We show that the long-range influence of Cr atoms on the interstitial is not due to the interstitial strain field protruding into Cr-rich parts of the supercells. The Fermi-level and band energies were found not to be the sole governing parameter in determining the formation energies. Implications for the construction of empirical potentials are discussed.

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 have been used to study the mixing behavior of Fe-Cr alloys. The heats of formation $\ensuremath{\Delta}{E}_{f}$ of 65 Fe-Cr structures in their magnetic ground states have been determined. A positive $\ensuremath{\Delta}{E}_{f}$ is found over most of the concentration range. From 0--12 % Cr a small negative $\ensuremath{\Delta}{E}_{f}$ down to $\ensuremath{-}8\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$/atom is found. The origin of the negative $\ensuremath{\Delta}{E}_{f}$ in Fe-rich structures is traced to the solution energy of single Cr atoms. At low concentration, Cr atoms in Fe repel each other, causing ordering. The Cr-Cr interactions are well reproduced even without the self-consistent relaxation of the electron density and the positions of atoms. Multi-ion (or concentration-dependent) interactions are indispensable in order to describe the whole phase diagram. The interesting magnetic situation that arises when ferromagnetic and antiferromagnetic metals are mixed in different ratios is discussed with reference to nearest- and next-nearest-neighbor clusters of Cr in Fe. Magnetic frustration leads to a strong dependence of the Cr moment on the number of Cr neighbors. The ``normal'' chemical-mixing energy and the influence of magnetism are distinguished by comparing magnetic and nonmagnetic calculations for similar systems.

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