X-Ray Topographic and Polarisation-Optical Study of the Low-Temperature Phase Transitions and Domain Structures of KLiSO₄

Abstract

The transformations between the three polar “low-temperature” phases of KLiSO ₄ III (space group P6 ₃ ), IV (P31c) and V (C1c1 or P112 ₁ ), were investigated by low-temperature X-ray topography and polarisation optics. The disappearance of the phase-III growth twinning (twin law “m‖[001]”) and the appearance of the phase-IV transformation twins (twin law “2‖ [001]”) during the very sluggish III → IV transition (ca. 225 K, thermal hysteresis ≈ 50 K) was directly observed. In both phases the domain boundaries are parallel (0001), normal to the polar axis [001] (pronounced memory effect). The III → IV transition is strongly promoted by dislocations. The IV-V transition (190 K) shows the formation of three pseudo-hexagonal domains and the local metastable coexistence of phases III, IV and V. The ambiguities of the phase-V symmetry are discussed.

Keywords:

• KLiSO₄
• phase transitions
• domain structures
• X-ray topography
• polarisation optics

Acknowledgment

The authors are indebted to the Deutsche Forschungsgemeinschaft for financial support through the research grant Ha 401/27 and the Graduiertenkolleg 162 “Schmelze, Erstarrung, Grenzflächen”, to P. Willms for providing the X-ray diffraction data of phases IV and V, and to J. Thar and R.A. Becker for the preparation of the figures.

Dedicated to Jan Fousek and Vaclav Janovec in Prague

Notes

*Average value for very sluggish transition; hysteresis width up to 50 K.

^§Due to frequent coexistence of phase V with “remnants” of phases III and IV it is difficult to ascertain the reflection conditions unambiguously.

^#This twin law can alternatively be described by one of the three twin mirror planes {110}, bisecting the angle between the (structural) mirror planes {100} of point group 31m, or by one of the three twin rotations 6¹ (60°), 6³ (180°) and 6⁵ (300°), i.e. by the elements of the coset [37, section 3.3.4.1] of point group 31m with respect to the composite symmetry 6mm.

*The reflections 31 and 12 are not symmetrically equivalent but form Friedel pairs with equal structure factor moduli due to negligible anomalous scattering. The second reflection has been used because of easier adjustment of (110) plates for X-ray topography.

*The birefringence path differences generating these interference colours in Fig. 6 are estimated as follows: The birefringence Δ n _ac = n _a – n _c of KLiSO₄ is very low, 5.5 × 10⁻⁴ at room temperature [41] (about 20 times smaller than for quartz) and decreases to roughly 4.5 × 10⁻⁴ around 190 K for phase III. With a plate thickness of about 0.8 mm, the path difference is 360 nm, corresponding to 1. order yellow interference colour. For phase IV, Δ n _ac is by about 3 × 10⁻⁴ larger at 190 K than for phase III [39], i.e. Δ n _ac ≈ 7.5 × 10⁻⁴, leading to a path difference of about 600 nm and 2. order blue interference colour.