Abstract
Landau theory (LT) is an indispensable cornerstone in the thermodynamic description of phase transitions. As with structural transitions, most applications require one to consistently take into account the role of strain. If temperature drives the transition, the relevant strains are, as a rule, small enough to be treated as infinitesimal, and therefore one can get away with linearized elasticity theory. However, for transitions driven by high pressure, strains may become so large that it is absolutely mandatory to treat them as finite and deal with the nonlinear nature of the accompanying elastic energy. In this paper, we explain how to set up and apply what is, in fact, the only possible consistent Landau theory of high-pressure phase transitions that systematically allows us to take these geometrical and physical nonlinearities into account. We also show how to incorporate available information on the pressure dependence of elastic constants taken from experiment or simulation. We apply our new theory to the example of the high-pressure cubic-tetragonal phase transition in strontium titanate, a model perovskite that has played a central role in the development of the theory of structural phase transitions. Armed with pressure-dependent elastic constants calculated by density-functional theory, we give an accurate description of recent high-precision experimental data and predict a number of elastic transition anomalies accessible to experiments.
- Received 29 August 2013
DOI:https://doi.org/10.1103/PhysRevX.4.031010
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Published by the American Physical Society
Popular Summary
High-pressure phase transitions in crystals and minerals occur in diverse fields such as astrophysics, seismology and geology, chemistry, and nanotechnology. Landau’s thermodynamic theory of structural phase transitions has been enormously successful at ambient pressures. However, a concise and fully consistent extension to high pressures—where finite strain has to be taken into account—has been missing up until now. We provide an extension of Landau’s theory using a careful combination of concepts from nonlinear elasticity theory and information supplied by experiments and electronic density-functional theory.
Precise knowledge of the elastic properties of earth-forming materials and their anomalies at pressure- and temperature-induced phase transitions is integral to understanding the physical properties of Earth (e.g., interpreting seismic signals from earthquakes). In theories based on the use of infinitesimal strain measures, neglecting the pressure dependence of the elastic constants and Landau coupling coefficients results in errors that can quickly reach 100%. The power of our new theory, in which we replace infinitesimal strain measures with the Lagrangian strain tensor, is illustrated by a practical application to recently published experimental data on the cubic-to-tetragonal high-pressure transition (10 GPa) at room temperature in the perovskite strontium titanate, one of the most studied archetypal model systems in the field of structural phase transitions.
We expect that our theory will be valuable for understanding phase-transition anomalies as a function of pressure and temperature and for predicting phase diagrams of earth- and planetary-forming materials.