Thermodynamics of the incommensurate state in Rb_2WO_4: on the Lifshitz point in A`A``BX_4 compounds

TL;DR

This study investigates the thermodynamics of phase transitions in Rb2WO4 and related compounds, revealing an unusual Lifshitz point where three first-order transition lines converge, influenced by crystal elasticity and tetrahedral orientation.

Contribution

It identifies and characterizes the Lifshitz point in A'A''BX4 compounds, linking phase transition behavior to lattice parameters and elastic coupling, which was not previously established.

Findings

First-order phase transitions with entropy jumps in Rb2WO4 and related compounds.

Existence of a Lifshitz point at c/a ~ 1.26 where three transition lines meet.

Coupling of elasticity and tetrahedral orientation influences transition discontinuity.

Abstract

We consider the evolution of the phase transition from the parent hexagonal phase $P6_{3}/mmc$ to the orthorhombic phase $Pmcn$ that occurs in several compounds of $A'A''BX_{4}$ family as a function of the hcp lattice parameter $c/a$. For compounds of $K_{2}SO_{4}$ type with $c/a$ larger than the threshold value 1.26 the direct first-order transition $Pmcn-P6_{3}/mmc$ is characterized by the large entropy jump $Rln2$. For compounds $Rb_{2}WO_{4}$, $K_{2}MoO_{4}$, $K_{2}WO_{4}$ with $c/a<1.26$ this transition occurs via an intermediate incommensurate $(Inc)$ phase. DSC measurements were performed in $Rb_{2}WO_{4}$ to characterize the thermodynamics of the $Pmcn-Inc-P6_{3}/mmc$ transitions. It was found that both transitions are again of the first order with entropy jumps $0.2Rln2 and $0.3Rln2$. Therefore, at $c/a ~ 1.26$ the $A'A''BX_{4}$ compounds reveal an unusual Lifshitz point where three first order transition lines meet. We propose the coupling of crystal elasticity with $BX_{4}$ tetrahedra orientation as a possible source of the transitions discontinuity.