Quasiharmonic approximation for a double Morse-type local potential model: Application to aKH2PO4-type phase diagram

Abstract

In order to describe a structural phase transition at low temperature, a quantum particle within a local potential is considered. According to the general formalism presented by Salje et al. ͓Z. Phys. B 82, 399 ͑1991͔͒, a quasiharmonic approximation is applied to the local potential and the interaction is replaced by the mean field one. The rigorous effective potential is reduced from a double Morse-type potential. The order parameter, the variance, and the effective soft frequency are given by analytic equations with potential parameters. As an application, a molecular motion of H 2 PO 4 in KDP is considered and the disappearance of the ordered phase at low temperature under high pressure is discussed. The difference between KDP and DKDP crystals are described successfully by the presented model.

Order–Disorder and Displacive Transitions in a Quantum Ising Model

“…Another tractable method is to replace V (x) by an effective harmonic potential; this is called here as quasi-harmonic model (QHM), where the effective frequency is determined by a self-consistent relation. 17,18 Both QIM and QHM give the Barrett's relation for the susceptibility. Therefore the quantum behaviors at low temperature are able to take into account in the simple QIM.…”

Single-Crystal Neutron Structural Analyses of Potassium Dihydrogen Phosphate and Potassium Dideuterium Phosphate

“…Under hydrostatic pressure, a small R O−O turns the double-minimum potential for protons/deuterons into a single-minimum type; finally, the transition temperatures disappear. 33) If hydrogen localizes by O1 below T c , then the tetragonal PO 4 3− (site symmetry of S 4 ) changes into H 2 PO 4 − (site symmetry of C 2 ), in which P shifts toward the O2 side and induces a dipole moment along the c-axis. Simultaneously, the K + ion − , except for the small difference in bond length between O1-D and O1-H.…”

Hydrogen Atom of KH2AsO4 Determined by Neutron Diffraction Study

“…17) In order to explain the T c -pressure phase diagram, the mass of the quantum particle is estimated not as the proton mass but as the effective one, which is about half the mass of the H 2 PO 4 molecule. 15,18) This will be appropriate also for KDA. The heavy H 2 AsO 4 may have low molecular-vibration frequencies, which may work to increase the transition temperature, but the large size of the tetragonal molecule may weaken the interaction to decrease the transition temperature.…”