Egil Bakken

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.

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.

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.

DFT-study of the energetics of perovskite-type oxides LaMO3 (M = Sc–Cu)

The generalized gradient approximation to density functional theory is benchmarked for the calculation of formation enthalpies of lanthanide perovskite-type oxides LaMO3 (M = Sc–Cu). Three different reaction pathways (from elements, mono and sesquioxides) have been investigated and the systematic errors associated with electron correlation due to overbinding of the oxygen molecule, electron self-interaction within localized 3d states, and geometrical relaxations are analyzed by critical comparison with a large number of experimental data. Calculated formation enthalpies from elements and sesquioxides are in good agreement with experiment when the overbinding of O2 is corrected for using the Wang ad hoc factor of 131 kJ mol−1 O2. By contrast, the calculated formation enthalpies from monoxides are systematically too low which are attributable to strong self-interactions due to localized 3d states in MO. The effects of relaxation and choice of magnetic structure on the enthalpies of formation are analyzed.

Heat capacity of SrFeO3−δ; δ = 0.50, 0.25 and 0.15 – configurational entropy of structural entities in grossly non-stoichiometric oxides

The heat capacity of SrFeO3−δ; δ = 0.50, 0.25 and 0.15 has been determined for 10 < T/K < ≈ 800 K by adiabatic calorimetry. The total heat capacity has been analysed and the entropy of the magnetic and structural order–disorder transitions derived. The excess heat capacity of SrFeO2.50 relative to the mixture of the binary constituent oxides is large even far below TN = 685 K due both to vibrational and magnetic effects. Lattice energy simulations show that the maximum in the excess heat capacity observed at around 60 K is due to a change in the vibrational density of state with origin in changes in the shortest Sr–O bond length on formation of the ternary oxide from the binary ones. While the entropy of the magnetic order–disorder transitions appear to be close to the ideal spin-only values, the entropy of the structural order–disorder transitions are much smaller than expected assuming random distribution of the relevant species on the different sub-lattices. A statistical analysis of the effect of enthalpically preferred structural entities (square pyramids or tetrahedra) on the configurational entropy is presented. A significantly reduced configurational entropy in qualitative agreement with the experiments is obtained.