Chris E. Mohn

Oxygen-deficient perovskites: linking structure, energetics and ion transport

The present review focuses on links between structure, energetics and ion transport in oxygen-deficient perovskite oxides, ABO(3-delta). The perfect long-range order, convenient for interpretations of the structure and properties of ordered materials, is evidently not present in disordered materials and highly defective perovskite oxides are spatially inhomogeneous on an intermediate length scale. Although this makes a fundamental description of these and other disordered materials very difficult, it is becoming increasingly clear that this complexity is often essential for the functional properties. In the present review we advocate a potential energy barrier description of the disordered state in which the possible local (or inherent) structures are seen to correspond to separate local minima on the potential energy surface. We interpret the average structure observed experimentally at any temperature as a time and spatial average of the different local structures which are energetically accessible. The local structure is largely affected by preferences for certain polyhedron coordinations and the oxidation state stability of the transition metals, and the strong long-range electrostatic interactions present in non-stoichiometric oxides imply that only a small fraction of the local energy minima on the potential energy surface are accessible at most temperatures. We will show that models neglecting the spatial inhomogeneity and thus the local structure serve as useful empirical tools for particular purposes, e.g. for understanding the main features of the complex redox properties that are so crucial for many applications of these oxides. The short-range order is on the other hand central for understanding ionic transport. Oxide ion transport involves the transformation of one energetically accessible local structure into another. Thus, strongly correlated transport mechanisms are expected; in addition to the movement of the oxygen ions giving rise to the transport, other ions are involved and even the A and B atoms move appreciably in a cooperative fashion along the transition path. Such strongly correlated or collective ionic migration mechanisms should be considered for fast oxide ion conductors in general and in particular for systems forming superstructures at low temperatures. Structural criteria for fast ion conduction are discussed. A high density of low-lying local energy minima is certainly a prerequisite and for perovskite-related A(2)B(2)O(5) oxides, those containing B atoms that have energetic preference for tetrahedral coordination geometry are especially promising.

Neutron total scattering study of the delta and beta phases of Bi2O3

The highly disordered structure of the delta phase of Bi2O3, which possesses the highest known oxide-ion conductivity, has been studied using neutron powder diffraction. A detailed analysis of data collected at 1033(3) K using Rietveld refinement indicates that the time-averaged structure of delta-Bi2O3 can be described using the accepted model of a disordered, anion-deficient fluorite structure in space group Fm3m. However, reverse Monte Carlo modelling of the total (Bragg plus diffuse) scattering demonstrates that the local anion environment around the Bi3+ resembles the distorted square pyramidal arrangement found within the stable alpha and metastable beta phases at ambient temperature, which is characteristic of the cations 6s2 lone-pair configuration. Similarities between the structures of the highly disordered delta phase and the ambient temperature metastable beta phase are used to support this assignment and assess the validity of previous structural models based on short-range ordering of vacancies within the cubic lattice of delta-Bi2O3.

Simulation of mineral solid solutions at zero and high pressure using lattice statics, lattice dynamics and Monte Carlo methods

We discuss how two techniques, based on (1) lattice statics/lattice dynamics simulations and (2) Monte Carlo methods may be used to calculate the thermodynamic properties of oxide mixtures at zero and high pressure. The lattice statics/lattice dynamics calculations involve a full free energy structural optimization of each of a number of configurations, followed by thermodynamic averaging. Strategies for generating a suitable set of configurations are discussed. We compare results obtained by random generation with those obtained using radial distribution functions or explicit symmetry arguments to obtain approximate or exact weightings respectively for individual configurations. The Monte Carlo simulations include the explicit interchange of cations and use the semigrand canonical ensemble for chemical potential differences. Both methods are readily applied to high pressures and elevated temperatures without the need for any new parametrization. Agreement between the two techniques is better at high pressures where anharmonic terms are smaller. We compare in detail the use of each technique for properties such as enthalpies, entropies, volume and free energies of mixing at zero and high pressure and thus calculation of the phase diagram. We assess the vibrational contributions to these quantities and compare results with those in the dilute limit. The techniques are illustrated throughout using MnO?MgO and should be readily applicable to more complicated systems.

Analytical model for island growth in atomic layer deposition using geometrical principles

Island growth has been shown to also occur for atomic layer deposition (ALD) processes. This article presents a relatively simple analytical model using geometrical principles with few independent variables on evolution of thickness and roughness in island-dominated ALD processes. The model is well suited for the fitting of experimental data to extract parameters such as density of islands and growth rate. It allows islands of various shapes, but most of the attention here is devoted to cone and hemispherical shaped islands in a hexagonal grid on a flat substrate. For a selection of cases, exact analytical expressions are derived. The model shows that it is possible to reproduce the growth characteristics of substrate-inhibited growth of both types 1 and 2 with a suitable choice of functional form of the islands. Finally it is compared with previously advanced models describing substrate-inhibited growth.

A genetic algorithm for the atomistic design and global optimisation of substitutionally disordered materials

We present a genetic algorithm for the atomistic design and global optimisation of substitutionally disordered bulk materials and surfaces. Premature convergence which hamper conventional genetic algorithms due to problems with synchronisation is avoided using a symmetry adapted crossover. The algorithm outperforms previously reported Monte Carlo and genetic algorithm simulations for finding low energy minima of two simple alloy models without the need for any redesign.

Order–disorder in grossly non-stoichiometric SrFeO2.50— a simulation study

Configurational lattice energy techniques are used to investigate oxygen vacancy ordering and the order–disorder transition in SrFeO2.50. Vacancy disorder is shown to present many new challenges, largely due to the extensive relaxation in such grossly non-stoichiometric systems. With large supercells it is not feasible to optimise each individual configuration. Efficient methods for choosing a small number of representative configurations are discussed. Oxygen vacancy–vacancy interactions are considerable in SrFeO2.50 and lead to the formation of preferred local structural entities. While the low-temperature structure consists of an ordered arrangement of octahedra and tetrahedra, the disordered high-temperature structure may be described as a mixture of tetrahedra, square pyramids and octahedra. Fe atoms with coordination numbers lower than four are negligible. The assumption of an ideal solution of oxygen vacancies in such systems, commonly made in standard thermodynamic treatments, is questionable.

The Rotational g Tensor as a Benchmark for Density-Functional Theory Calculations of Molecular Magnetic Properties.

The rotational g factor for a large number of organic compounds has been investigated with density-functional theory. Rapid convergence toward the basis-set limit is ensured by the use of London atomic orbitals. A statistical analysis of the results has been carried out in comparison with accurate experimental data. It is shown that gradient-corrected and hybrid functionals reproduce experimental results most closely, with the Keal-Tozer KT2 functional being the most accurate.

Size mismatch effects in oxide solid solutions using Monte Carlo and configurational averaging

Local minima configurational averaging (CA) and Monte Carlo (MC) simulations are used to examine in detail the variation of thermodynamic and structural properties of binary oxide solid solutions with the volume mismatch between the end members. The maximum volume mismatch studied corresponds to that in the CaO MgO solid solution, a prototype example of a strongly non-ideal system with large miscibility gap. In addition, solid solutions of CaO-HypO using designed hypothetical atoms (Hyp) with atomic radii between those of Ca2+ and Mg2+ have been considered. Calculations on the hypothetical systems allow not only the systematic investigation of size mismatch, but also the detailed examination and comparison of the CA and MC methods. A particularly efficient implementation of the CA method is via the rapid calculation of the radial distribution function (RDF) for all possible arrangements obtained by distributing the different ions on their respective crystallographic sites followed by full structural optimisation of just one configuration from each group with the same RDF. Comparison of results from CA, using optimisations in the static limit, and MC indicates the importance of cell-size and vibrational effects, which can be particularly important for the largest size mismatches. The enthalpies, excess configurational entropies, vibrational entropies and volumes of mixing scale roughly quadratically for all but the largest volume mismatches. Equally sized atoms cluster together in the first coordination shell for all volume mismatches studied.

Collective ionic motion in oxide fast-ion-conductors

Structural correlations and dynamic disorder in the oxide fast-ion-conductor Ba2In2O5 are deduced from a systematic study of the energy-hypersurface using periodic density-functional theory examining 2 × 104 local energy minima. The structure observed experimentally is interpreted as a time and spatial average of those minima which are energetically-accessible. The nature of these has extensive implications for the ionic conductivity. Transition paths connecting minima, characterized using the nudge-elastic-band method, indicate that low-energy collective ion movements must play important roles in oxide fast-ion conductors such as Ba2In2O5. Saddle-points energies for collective transport are lower in energy than those for conventional single-jump mechanisms.

Predicting the Structure of Alloys Using Genetic Algorithms

We discuss a novel genetic algorithm that can be used to find global minima on the potential energy surface of disordered ceramics and alloys using a real-space symmetry adapted crossover. Due to a high number of symmetrically equivalent solutions of many alloys, conventional genetic algorithms using reasonable population sizes are unable to locate the global minima for even the smallest systems. We demonstrate the superior performance of the use of symmetry adapted crossover by the comparison of that of a conventional GA for finding global minima of two binary Ising-type alloys that either order or phase separate at low temperature. Comparison of different representations and crossover operations show that the use of real-space crossover outperforms crossover operators working on binary representations by several orders of magnitude.