Temperature dependence of the elastic constants ofLiKSO4through a first-order structural phase transition

Abstract

Resonant ultrasound spectroscopy has been used to measure the complete set of elastic constants of LiKSO 4 over the temperature range of 200 to 300 K including both the hexagonal room temperature phase and the lower temperature trigonal phase. Large step changes are observed in all the elastic constants, except C 13 , at 213 K on cooling and at 243 K on warming. These step changes are associated with the hexagonal/trigonal crystallographic phase transition. The bulk modulus is approximately 15% higher in the trigonal phase than in the hexagonal phase. The hexagonal-phase elastic constants exhibit very little temperature dependence while the trigonal-phase elastic constants show a stronger dependence on temperature. The transitions are noted to be quite sluggish, taking a few hours to equilibrate. The results are described in terms of a Landau-type free energy expansion using two Ising-like order parameters with strong coupling between the two parameters. Biquadratic coupling between the order parameters and strains is shown to account for the step changes in the elastic constants as well as the temperature dependence in the trigonal phase. Coupling linear in the strains is shown to be insufficient to explain the results.

Elastic constants of natural quartz

“…Our approach requires multiple solutions of this eigenvalue problem for a continuously changing elastic-stiffness tensor, and this separation is a critical step. Willis and colleagues 13 used RUS to study the hexagonal-trigonal phase transformation in LiKSO 4 . Their study provides a good example of applying Landau theory to a second-order or near-second-order phase transition.…”

Temperature dependence of the elastic moduli of polycrystalline LaAlxNi5−x and LaSnxNi5−x

“…The overall result, for typical materials, is that the elastic moduli approach 0 K with zero slope and decrease monotonically with increasing temperature. This simple picture is not applicable to materials undergoing phase transitions [22,23] or to materials with more complicated electronic structures [24][25][26]. Figs.…”

Phase field crystal based prediction of temperature and density dependence of elastic constants through a structural phase transition

“…While the variation of the elastic constants with temperature is only to be expected, the behaviour of the elastic constants in certain temperature ranges may come as a surprise to some. For example, results reported in [4] for LiKSO 4 (reproduced here in Figure 1) show that the elastic constants C 11 , C 12 and C 44 are multi-valued in certain temperature ranges. Although we do not attempt to model LiKSO 4 here, the analytical formulae we obtain for the elastic constants predicted by the PFC model considered in [1] are also found to be multi-valued in certain temperature ranges corresponding to regions where two or more phases coexist.…”

“…Consider a system originally in an unstrained state with volume Ω 0 and average density ρ 0 . The system is then subjected to a strain ε resulting in the system having density ρ ε and volume Ω ε given by (2) and 3, and order parameterφ ε given by (4). Traditionally, the elastic constants have been computed using the expression…”