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.

Вырожденная структура двойников превращения и оценка плотности дислокаций мартенситных кристаллов

In the dynamic theory of martensitic transformations, the wave mechanism of controlling martensite crystal growth is determined by the superposition of wave beams of quasi-longitudinal (or longitudinal) waves carrying the “tensile–compression” deformation in the orthogonal directions. The wave beam formation is considered to be a result of the formation of excited (vibrational) states. The existence of transformation twins is interpreted as a result of a matched propagation with respect to long-wave ( l waves) and short-wave ( s waves) shifts. The matching condition is analyzed for the γ–α martensitic transformation in iron-base alloys. It is shown for the first time that the transition to a degenerate twin structure with the allowance for the medium discreteness enables one to estimate the dislocation density in crystals with habit {557}, which agrees with that observed experimentally.