High Pressure Phase Transitions: DFT and Landau Theory

High-pressure phase transitions in crystals and minerals constitute a brisk area of modern science. In obtaining a correct physical picture of these transitions, it is necessary to combine quantum mechanics, thermodynamics and crystallography in an efficient way. In this respect, Landaus thermodynamic approach to structural phase transitions has been enormously successful at ambient pressures. However, only recently that the authors have succeeded in formulating a long-awaited extension to high pressures that consistently takes into account the accompanying nonlinear elastic energy [A. Tröster et. al., Phys. Rev. X, in print (2014)]. The main input required to apply this theory is information on the pressure-dependence of elastic constants, which is accessible by ab initio methods. The scientific goal of the present proposal is twofold: (i) We plan to develop and implement a new module into our well-established WIEN2k density functional code that allows to calculate the full stress tensor for any given unit cell geometry of a solid state system. This will make it possible to determine the pressure dependence of unit cell parameters, elastic constants and other important observables accessible to WIEN2k. Availability of a pressure tensor module will have a considerable impact on the large community of WIEN2k users, as it will allow to carry out all-electron calculations at high pressure for arbitrary crystal classes with benchmark precision. (ii)Armed with pressure-dependent elastic constants calculated from WIEN2k, we apply our novel finite strain extension of Landau theory to a variety of high pressure phase transitions, predominantly focusing in materials of perovskite structure and earth-forming materials. The outcome that can be expected from these calculations includes e.g. the interpretation of experimental scattering data, prediction of (P,T)-phase diagrams and the calculation of transition anomalies of elastic constants and seismic sound velocities. The results of this project will be of vital interest to a large community of scientists and will certainly have considerable impact on such diverse fields as astrophysics, seismology and geology, chemistry, material science or nanotechnology.

The present project "High-pressure phase transitions: DFT and Landau theory" had a twofold goal: (i) the implementation of the so-called "stress tensor" in the renowned and widely popular density functional program package "WIEN2k" and (ii) the further development of the combination of methods of phenomenological Landau theory and density functional theory (DFT) for the description of structural phase transitions in crystals under high pressure. The implementation of the stress tensor into a DFT code of the LAPW type represents a long standing problem of great theoretical and practical importance which several well-known international research groups have failed to solve despite significant efforts throughout the last 20 years. First, the existing theoretical approaches were subjected to a thorough mathematical analysis. Based on this, the hydrostatic part of the stress tensor in the local density approximation (LDA) was first numerically tested on a number of different cubic crystalline systems. We observed a strong undesirable dependence on the somewhat arbitrary choice of the so-called muffin-tin (MT) radii of the LAPW basis, which persisted even if one ignores the existence of a numerically large surface integral claimed by the previously published theoretical treatments. After a lengthy numerical analysis, this unwanted MT dependence could be traced back to the influence of so-called core leaks. After calculating and implementing the corresponding new correction terms and further extending our test implementation to so-called local orbitals, the problem could be considered as solved. The unavoidable waiting times between numerical tests were used to advance our previously constructed extension of the Landau Theory (LT) of structural phase transitions to high pressure. Studying the example of the ferroelectric phase transition in lead titanate, we demonstrated the important role of thermal expansion and the need for a correct definition of spontaneous strain. The elastic and electronic properties of the cubic and tetragonal phase of the perovskite PbCaF3 were subjected to an in-depth DFT analysis, and the observed anomalies were interpreted in the light of nonlinear LT. We also worked out a proposal for a synchrotron experiment to measure the high pressure behavior of the tetragonal elastic constant of strontium titanate, which was accepted and carried out by our collaborator Dr. B. Wehinger at the ESRF (Grenoble, F) in the summer of 2018. Unfortunately, the following evaluation was delayed due to career changes by Dr. Wehinger, so that so far no results have been extracted from the raw data that were accumulated in these measurements. The description of the high-pressure behavior of the perovskite KMnF3, whose thermal expansion is difficult to calculate due to the presence of antiferromagnetism, is currently nearing completion.