Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

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.

DFT study of the electronic properties and the cubic to tetragonal phase transition in RbCaF3

“…As commonly obtained with LDA, the equilibrium lattice constant is too short (by 0.1 Å) compared to experiment, while PBE shows the opposite trend (a 0 too large by 0.07 Å). As expected [29,30], both, PBEsol and WC, improve the agreement with experiment, since their values for a 0 are 4.444 and 4.449 Å, respectively, which basically coincide with the experimental value 4.448 Å [16]. The same conclusion is reached for the bulk modulus B, since PBEsol (52.5 GPa) and WC (50.8 GPa) also lead to excellent agreement with experiment (50 GPa), while LDA and PBE lead to overestimation and underestimation, respectively.…”

“…VII. The continuous (i.e., second-order) nature of the pressure-driven phase transition we detect at zero temperature as opposed to the first-order character of the experimentally observed high-pressure phase transition at ambient temperature can be understood within the framework of the recently developed finite strain Landau theory [29,30], as is argued in Sec. VIII.…”

Equation of State of Polycrystalline Stishovite Across the Tetragonal‐Orthorhombic Phase Transition

“…Linking equations (4)-(12) to the EOS (1) of stishovite (Table 2), the spontaneous strains can be calculated as a function of finite strain, that is, volume. Our approach is similar to previous formulations based on the Lagrangian definition of strain (Tröster et al, 2002(Tröster et al, , 2014. The Landau and coupling coefficients can be obtained by a least squares fit of calculated to experimentally observed spontaneous strains.…”

Symmetry-Adapted Finite Strain Landau Theory Applied to KMnF3

“…Following Ref. [9], we content ourselves to just include OP-strain couplings of type Q 2 ij and obtain…”

“…FSLT constitutes a careful extension of Landau theory beyond coupling to infinitesimal strain, fully taking into account the nonlinear elastic effects at finite strain. Its capabilities have been demonstrated in a number of applications to HPPTs [5][6][7][8][9][10]. However, as it stands, the numerical scheme underlying FSLT is still quite involved, and many practical workers in the field of HPPTs may be hesitant to go through the mathematical hardships it seems to pose.…”