Basal-plane incommensurate phases in hexagonal-close-packed structures

Abstract

An Ising model with competing interactions is used to study the appearance of incommensurate phases in the basal plane of a hexagonal-close-packed structure. The calculated mean-field phase diagram reveals various 1q-incommensurate and lock-in phases. The results are applied to explain the basal-plane incommensurate phase in some compounds of the AЈAЉBX 4 family, like K 2 MoO 4 , K 2 WO 4 , Rb 2 WO 4 , and to describe the sequence of high-temperature phase transitions in other compounds of this family. ͓S0163-1829͑98͒03909-5͔

Thermodynamics of the incommensurate state inRb2WO4:The Lifshitz point inLuk’yanchuk1, Jório2, Saint‐Grégoire3 2000Phys. Rev. BSelf Cite11030View full textAdd to dashboardCite

“…The high-temperature order-disorder transitions in A ′ A ′′ BX 4 compounds are described by the in-site averages of the vertical orientation of BX 4 tetrahedra, σ i =< S i > where the pseudo-spin S i is equal to ±1 for the up/down tetrahedra orientations [3]. The variables σ i are equal to zero in the disordered high-temperature phase P 6 3 /mmc.…”

“…[4][5][6][7][8][9][10] in Table I as function of the geometrical factor c/a of their hcp structure. As was shown in our previous study [3] this is the unique parameter that drives the actual phase sequence: for c/a > 1.26 the transition is direct, whereas for c/a < 1.26 the sequence (2) takes place.…”

“…Introducing in Sec. III the corresponding coupling to the mean-field treatment of the hcp Ising model [3] and comparing the results with the measured jumps of the lattice constant and molar entropy we demonstrate that this coupling can be responsible for the transitions discontinuity.…”

“…The transition Inc − P 6 3 /mmc should also be of the second order as a transition to the incommensurate phase of the type II. The recently proposed hcp Ising model [3] correctly describes the high-temperature phase diagram of A ′ A ′′ BX 4 compounds. In this model the P mcn − P 6 3 /mmc and Inc − P 6 3 /mmc transitions are of the second order.…”

Phonons and hybrid modes in the high and low temperature far infrared dynamics of hexagonal TmMnO3

“…It is however worth mentioning that as in some high temperature compounds with basal plane of hexagonal structure there might be up/down vertical sublattice orientational distortion contributing to band broadening. [26,27] This would then add an intrinsic extra factor associated with possible bitetrahedra misalignments in passing from highest temperature centrosymmetric P63/mnm to the P6 3 cm space group.…”