Classification of perovskite structural types with dynamical octahedral tilting.

Perovskites ABX3 with delocalized positions of the X atoms represent a distinct class of dynamically distorted structures with peculiar structural relations and physical properties. The delocalization originates from atoms crossing shallow barriers of the potential energy surface. Quantum mechanically, they can be treated similar to light atoms in diffusive states. Many of these perovskite structures are widely used functional materials thanks to their particular physical properties, such as superconductivity, ferroelectricity and photo-activity. A number of these properties are related to static or dynamic motion of octahedral units. Yet, a full understanding of the relationships between perovskite crystal structure, chemical bonding and physical properties is currently missing. Several studies indicate the existence of dynamic disorder generated by anharmonic motion of octahedral units, e.g. in halide perovskite structures. To simplify structural analysis of such systems we derive a set of space groups for simple perovskites ABX3 with dynamical octahedral tilting. The derived space groups extend the well established space group tables for static tiltings by Glazer [Acta Cryst. B (1972). 28, 3384-3392], Aleksandrov [Ferroelectrics (1976). 24, 801-805] and Howard & Stokes [Acta Cryst. B (1998). 54, 782-789]. Ubiquity of dynamical tilting is demonstrated by an analysis of the structural data for perovskites reported in recent scientific publications and the signature of dynamic tilting in the corresponding structures is discussed, which can be summarized as follows: (a) volume increase upon a lowering of temperature, (b) apparent distortion of octahedra (where Jahn-Teller distortions can be ruled out), (c) mismatch between observed instantaneous symmetry and average symmetry, (d) deviation of the experimental space group from the theoretically predicted structures for static tilting, (e) inconsistency of lattice parameters with those suggested by the theory of static tilts, and (f) large displacement parameters for atoms at the X and B sites. Finally, the possible influence of dynamic disorder on the physical properties of halide perovskites is discussed.

Anharmonic effects on the dynamics of solid aluminium fromab initiosimulations.

Two approaches to simulations of phonon properties of solids beyond the harmonic approximation, the self-consistentab initiolattice dynamics (SCAILD) and decoupled anharmonic mode approximation (DAMA) are critically benchmarked against each other and molecular dynamics simulations using a density-functional-theory description of electronic states, and compared to experimental data for fcc aluminium. The temperature-dependence of phonon dispersion and the phonon density-of-states, heat capacity, and the mean atomic displacement for fcc aluminium are examined with these approaches at ambient pressure. A comparison of results obtained with the harmonic approximation to the ones predicted by SCAILD and DAMA reveal a negligible anharmonic contribution to phonon frequencies, a small, but significant influence on heat capacity, and a strong effect on atomic mean-square displacement. The phase space accessed with SCAILD and DAMA is reduced relative to molecular and harmonic lattice dynamics simulations. In particular the DAMA results are in good agreement with displacement amplitudes determined by the Debye-Waller factor in x-ray diffraction experiments.

Insight into structural phase transitions from the decoupled anharmonic mode approximation.

We develop a formalism (decoupled anharmonic mode approximation, DAMA) that allows calculation of the vibrational free energy using density functional theory even for materials which exhibit negative curvature of the potential energy surface with respect to atomic displacements. We investigate vibrational modes beyond the harmonic approximation and approximate the potential energy surface with the superposition of the accurate potential along each normal mode. We show that the free energy can stabilize crystal structures at finite temperatures which appear dynamically unstable at T = 0. The DAMA formalism is computationally fast because it avoids statistical sampling through molecular dynamics calculations, and is in principle completely ab initio. It is free of statistical uncertainties and independent of model parameters, but can give insight into the mechanism of a structural phase transition. We apply the formalism to the perovskite cryolite, and investigate the temperature-driven phase transition from the P21/n to the Immm space group. We calculate a phase transition temperature between 710 and 950 K, in fair agreement with the experimental value of 885 K. This can be related to the underestimation of the interaction of the vibrational states. We also calculate the main axes of the thermal ellipsoid and can explain the experimentally observed increase of its volume for the fluorine by 200-300% throughout the phase transition. Our calculations suggest the appearance of tunneling states in the high temperature phase. The convergence of the vibrational DOS and of the critical temperature with respect of reciprocal space sampling is investigated using the polarizable-ion model.