Finite-strain Landau theory applied to the high-pressure phase transition of lead titanate

Abstract

Standard Landau theory coupled to infinitesimal strain allows a concise description of the temperature-driven ferroelectric tetragonal-to-cubic phase transition in PbTiO 3 at ambient pressure. Unfortunately, it fails to cover its high-pressure counterpart at ambient temperature. For example, the experimental transition pressure is vastly underestimated, and neither the change from first to second order with increasing pressure nor the unusual pressure dependence of the tetragonal unit cell parameters observed in experiment are reproduced. Here we demonstrate that a combination of density functional theory and a recently constructed finite-strain extension of Landau theory provides a natural mechanism for resolving these discrepancies between theory and experiment. Our approach also allows us to determine the full tetragonal-cubic phase boundary in the (P ,T) plane including an estimate of the tricritical point. We show that a careful analysis of the thermal elastic baseline is an essential ingredient to the success of this theory.

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.…”

“…5, where we can see that the magnitude of all elastic constants increase rather linearly with increasing pressure. This provides a necessary input for the finite strain Landau theory [29,30] as discussed in more detail in Sec. VIII.…”

Symmetry-Adapted Finite Strain Landau Theory Applied to KMnF3

“…In principle, the ability to do so depends mainly on the successful construction of a pressure-and temperature-dependent baseline, i.e., the cubic EOS V cubic = V cubic (P, T). In a previous paper [10], this task has been successfully carried out for the perovskite PbTiO 3 by combining zero temperature DFT calculations (see Appendix A for details) with the Debye approximation as implemented in the GIBBS2 package [22,23] to incorporate effects of thermal expansion (recently, we learned [24] that a similar approach also seems to work for MgSiO 3 ). Unfortunately, our corresponding efforts to derive V cubic (P, T) for KMF along the same lines have failed so far, however.…”

“…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.…”