Temperature dependence of the elastic constants of LiKSO4 through a first-order structural phase transition

Density functional theory calculations of merohedric twinning in KLiSO4

Density functional theory (DFT) calculations have been performed on five models of periodic, polysynthetic twin interfaces in the ambient-temperature phase of KLiSO4, which has space group P63. The models represent the three merohedric twin laws (m||z, 2⊥z and 1̅) with boundary plane (1 0 1̅ 0), also with boundary plane (0 0 0 1) in case of m, and with boundary plane (1 2̅ 1 0) in case of 1̅. The models satisfy stoichiometry at the boundary plane and maintain the fourfold coordination of the Li and S atoms and the twofold coordination of the oxygen atoms. Relaxed lattice parameters and atomic positions were determined by DFT, using the DMol3 code with functional PBEsol. The energy difference between polysynthetic twin and single crystal per primitive cell of the twin is 0.0009 eV for m(0 0 0 1), 0.09 eV for 1̅(1 0 1̅ 0), 0.58 eV for m(1 0 1̅ 0) and 0.55 eV for 2(1 0 1̅ 0). In KLiSO4 crystals grown from aqueous solutions the first twin was frequently observed, similarly also the second twin in Cr-doped crystals, whereas the third twin appeared only rarely and the fourth was not observed. Not only for KLiSO4 but also for quartz, the energy of twins and the frequency of their occurrence are closely connected for crystals grown from aqueous solutions, whereas for the formation of transformation twins the availability of twin nuclei plays a major role.

Elastic constants of natural quartz

The elastic constants of a natural-quartz sphere using resonance-ultrasound spectroscopy (RUS) are measured. The measurements of the near-traction-free vibrational frequencies of the sphere are matched with the predicted frequencies from the dynamic theory of elasticity, with optimized estimates for the elastic constants driving the differences between these sets of frequencies to a minimal value. The present computational model, although based on earlier approaches, is the first application of RUS to trigonal-symmetry spheres. Quartz shows six independent elastic constants, and our estimates of these constants are close to those computed by other means. Except for C14, after a 1% mass-density correction, natural quartz and cultured quartz show the same elastic constants. Natural quartz shows higher internal frictions.