Fast-ion conduction and local environments in BIMEVOX.

The energy landscape of the fast-ion conductor Bi4V2O11 is studied using density functional theory. There are a large number of energy minima, dominated by low-lying thermally accessible configurations in which there are equal numbers of oxygen vacancies in each vanadium-oxygen layer, a range of vanadium coordinations and a large variation in Bi-O and V-O distances. By dividing local minima in the energy landscape into sets of configurations, we then examine diffusion in each different layer using ab initio molecular dynamics. These simulations show that the diffusion mechanism mainly takes place in the 〈110〉 directions in the vanadium layers, involving the cooperative motion of the oxide ions between the O(2) and O(3) sites in these layers, but not O(1) in the Bi-O layers, in agreement with experiment. O(1) vacancies in the Bi-O layers are readily filled by the migration of oxygens from the V-O layers. The calculated ionic conductivity is in reasonable agreement with the experiment. We compare ion conduction in δ-Bi4V2O11 with that in δ-Bi2O3. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Cooperative excitations in superionic PbF2.

Links between dynamical Frenkel defects and collective diffusion of fluorides in ß-PbF2 are explored using Born-Oppenheimer molecular dynamics. The calculated self-diffusion coefficient and ionic conductivity are 3.2 × 10-5 cm2 s-1 and 2.4 Ω-1 cm-1 at 1000 K in excellent agreement with pulsed field gradient and conductivity measurements. The calculated ratio of the tracer-diffusion coefficient and the conductivity-diffusion coefficient (the Haven ratio) is slightly less than unity (about 0.85), which in previous work has been interpreted as providing evidence against collective 'multi-ion' diffusion. By contrast, our molecular dynamics simulations show that fluoride diffusion is highly collective. Analysis of different mechanisms shows a preference for direct collinear 'kick-out' chains where a fluoride enters an occupied tetrahedral hole/cavity and pushes the resident fluoride out of its cavity. Jumps into an occupied cavity leave behind a vacancy, thereby forming dynamic Frenkel defects which trigger a chain of migrating fluorides assisted by local relaxations of the lead ions to accommodate these chains. The calculated lifetime of the Frenkel defects and the collective chains is approximately 1 ps in good agreement with that found from neutron diffraction. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

First principles calculations on order and disorder in La2Ce2O7 and Nd2Ce2O7.

In this paper, we highlight the connection between the local structure and collective dynamics of the defective fluorites La2Ce2O7 and Nd2Ce2O7. The local and average structure is explored by investigating a large number of different structural models and snapshots from Born-Oppenheimer Molecular dynamics calculations. Both compounds show a strong preference for local oxygen vacancy order similar to that found in the C-type structure. This suggests that previous studies, where Nd2Ce2O7 and La2Ce2O7 are viewed as disordered defective fluorites, or as a pyrochlore for the latter, did not capture the nature of local order in the disordered phase. We observe more collective chains of migrating oxygen in Nd2Ce2O7- a manifestation of a stronger preference for a dynamic local oxygen vacancy order - than in La2Ce2O7. The stronger preference for 〈210〉 vacancy-vacancy alignments can explain why long range ordering is identified by distinct C-type like superlattice peaks in neutron diffraction patterns for Nd2Ce2O7 whereas they appear to be almost invisible in La2Ce2O7.

C-type related order in the defective fluorites La2Ce2O7 and Nd2Ce2O7 studied by neutron scattering and ab initio MD simulations.

This work presents a structural investigation of La2-xNdxCe2O7 (x = 0.0, 0.5, 1.0, 1.5, 2.0) using X-ray powder diffraction and total scattering neutron powder diffraction, analysed using Rietveld and the reverse Monte Carlo method (RMC). Ab initio molecular dynamics (MD) modelling is also performed for further investigations of the local order. The main intensities in the neutron diffraction data for the La2-xNdxCe2O7 series correspond to the fluorite structure. However, additional C-type superlattice peaks are visible for x > 0 and increase in intensity with increasing x. The Nd-containing compositions (x > 0) are best fitted with Rietveld analysis by using a combination of oxygen deficient fluorite and oxygen excess C-type structures. No indications of cation order are found in the RMC or Rietveld analysis, and the absence of cation order is supported by the MD modelling. We argue that the superlattice peaks originate from oxygen vacancy ordering and associated shift in the cation position away from the ideal fluorite site similar to that in the C-type structure, which is seen from the Rietveld refinements and the observed ordering in the MD modelling. The vacancies favour alignments in the 〈110〉, 〈111〉 and especially the 〈210〉 direction. Moreover, we find that such ordering might also be found to a small extent in La2Ce2O7, explaining the discernible modulated background between the fluorite peaks. The observed overlap of the main Bragg peaks between the fluorite and C-type phase supports the co-existence of vacancy ordered and more disordered domains. This is further supported by the observed similarity of the radial distribution functions as modelled with MD. The increase in long range oxygen vacancy order with increasing Nd-content in La2-xNdxCe2O7 corresponds well with the lower oxide ion conductivity in Nd2Ce2O7 compared to La2Ce2O7 reported earlier.

Topography of the potential energy hypersurface and criteria for fast-ion conduction in perovskite-related A2B2O5 oxides.

We discuss the importance of the topography of the potential energy hypersurface for the ionic conductivity of perovskite-related A(2)B(2)O(5) oxides. A correlation between the energetic preference of the cations for different coordination geometries and the ionic conductivity is proposed based on a first principles periodic density functional theory study of selected possible structures for Ba(2)In(2)O(5), Sr(2)Fe(2)O(5), Sr(2)Mn(2)O(5), and La(2)Ni(2)O(5). There are a large number of low-energy local minima on the potential energy hypersurfaces of the two first compounds due to an energetic preference for BO(4) tetrahedra. Tetrahedral environments are energetically unfavorable for Mn(III) in Sr(2)Mn(2)O(5) and for Ni(II) in La(2)Ni(2)O(5), and the number of low-energy configurations is relatively low in these two cases. Consistent with our findings, in contrast to Sr(2)Fe(2)O(5) and Ba(2)In(2)O(5), Sr(2)Mn(2)O(5) and La(2)Ni(2)O(5) do not exhibit transitions to disordered phases on heating, and there appear to be no reports of enhanced ionic conductivity for these compounds. Thus we suggest that the possibility of many different oxygen orderings associated with a variety of low-energy connectivity schemes within tetrahedral layers such as in the brownmillerite-based structures of Sr(2)Fe(2)O(5) and Ba(2)In(2)O(5) is a prerequisite for high ionic conductivity in perovskite-related A(2)B(2)O(5) oxides.

Predicting complex mineral structures using genetic algorithms.

We show that symmetry-adapted genetic algorithms are capable of finding the ground state of a range of complex crystalline phases including layered- and incommensurate super-structures. This opens the way for the atomistic prediction of complex crystal structures of functional materials and mineral phases.

Diffusion within α-CuI studied using ab initio molecular dynamics simulations.

The structure and dynamics of superionic α-CuI are studied in detail by means of ab initio Born-Oppenheimer molecular dynamics simulations. The extreme cation disorder and a soft immobile face centred cubic sublattice are evident from the highly diffuse atomic density profiles. The Cu-Cu pair distribution function and distribution of Cu-I-Cu bond angles possess distinct peaks at 2.6 Å and 60° respectively, which are markedly lower than the values expected from the average cationic density, pointing to the presence of pronounced short-range copper-copper correlations. Comparison with lattice static calculations shows that these correlations and the marked shift in the cationic density profile in the ⟨111⟩ directions are associated with a locally distorted cation sublattice, and that the movements within the tetrahedral cavities involve rapid jumps into and out of shallow basins on the system potential energy surface. On average, the iodines are surrounded by three coppers within their first coordination shell, with the fourth copper being located in a transition zone between two neighbouring iodine cavities. However, time-resolved analysis reveals that the local structure actually involves a mixture of threefold-, fourfold- and fivefold-coordinated iodines. Examination of the ionic trajectories shows that the copper ions jump rapidly to nearest neighbouring tetrahedral cavities (aligned in the ⟨100⟩ directions) following a markedly curved trajectory and often involving short-lived (∼1 ps) interstitial positions. The nature of the correlated diffusion underlying the unusually high fraction of coppers with short residence time can be attributed to the presence of a large number of 'unsuccessful' jumps and the likelihood of cooperative motion of pairs of coppers. The calculated diffusion coefficient at 750 K, D(Cu) = 2.8 × 10(-5) cm(2) s(-1), is in excellent agreement with that found experimentally.

Oxide-ion disorder within the high temperature delta phase of Bi2O3.

The delta phase of Bi(2)O(3), which adopts an anion-deficient fluorite structure, has the highest known oxide-ion conductivity. Using a combination of neutron powder diffraction and Born-Oppenheimer molecular dynamics, the preferred local anion environment around the Bi(3+) within delta-Bi(2)O(3) is shown to be highly irregular, resembling the asymmetric "lone-pair" coordination found within many (fully ordered) oxides of Bi(3+) under ambient conditions. The asymmetric electron density around the Bi(3+) plays a central role in promoting the extreme anion disorder within delta-Bi(2)O(3), with the ion diffusion facilitated by extensive relaxations of both the surrounding anions and a "soft" cation sublattice. The validity of previously proposed structural models based on a cubic environment in which O(2-) vacancies are aligned in pairs in 100, 110, and 111 directions is discussed in light of these conclusions.

Ultrathin oxide films and heterojunctions: CaO layers on BaO and SrO.

We examine the form of the islands formed by CaO on BaO and SrO substrates using both periodic density functional theory and atomistic simulation techniques. (100) edges dominate the island morphology and we examine how the CaO adjusts to the substrate in small and medium sized islands and at much larger coverages. There is no direct overlay of CaO ion pairs over OBa or OSr pairs in the top substrate layer. Rather, island bond lengths are all much shorter than those even in bulk CaO, even in the interior of the islands, and more similar to those in CaO clusters and isolated thin films. Corner atoms are associated with particularly short Ca-O bond lengths and the low coordination numbers at such positions. The islands show a marked deviation from planarity which can be broadly rationalized in terms of different preferential bond lengths for Ca and O with substrate O and Ba (Sr), respectively. The marked preferences for particular bond lengths lead to the formation of loops or gaps in non-square islands, areas where islands interact and along the mid-edges of large islands. Exchange with the much larger cations in the substrate is surprisingly facile. Our results indicate the difficulties of preparing sharp, ordered thin oxide films even at low temperatures.

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 cation's 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.

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.

What can a "quantum black-box" do for the inorganic thermochemist?

Enthalpies of formation of ABO3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf) from the binary constituent oxides have been calculated by ab initio density functional theory. The resulting values compare well with the large number of experimental determinations reported in literature. The trends in the calculated enthalpies of formation correlate with the difference in acidity between the binary constituent oxides. Density functional theory is shown to be a valuable tool that should be used routinely in thermochemical studies of inorganic compounds.

Genetic mapping of the distribution of minima on the potential energy surface of disordered systems.

We show that genetic algorithms and energy minimizations in combination provide a highly efficient tool for mapping low-energy minima on the erratic and complex potential-energy surfaces of grossly disordered materials. The distribution of energy minima mimics with sufficient accuracy the low-energy portion of the parent distribution of minima and allows accurate calculation of configurational Boltzmann averaged structural and thermodynamic properties in cases where a small fraction of the minima is thermally accessible. The distribution of energy minima obtained using genetic algorithms is biased, and consequently the properties converge slowly at high temperatures. In contrast, an optimized set of a few randomly chosen configurations provides a statistical representable selection for the accurate calculation of configurational-averaged properties at high temperatures, but gives a poor description of the low-energy portion of minima. Thus the properties calculated using the random algorithm are hampered by the presence of systematic errors in cases where a small fraction of the minima is thermally accessible. The inherently slow convergence of both the genetic algorithm and the random selection at intermediate temperatures is tackled by combining the lower fraction of the distribution of minima obtained using genetic algorithms with the intermediate and upper fraction from the random (nonbiased) selection of configurations. For this purpose we introduce a cut-and-scale-type scheme. The resulting combined distribution allows accurate calculation of properties at all temperatures.

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.