Diffraction analysis of incommensurate phases in crystals of quasi-binary system Sn2P2(S1−xSex)6

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Abstract
X-ray analysis of Sn2P2(S1 − xSex)6 single crystals with 0 < x < 1 is performed in the temperature interval 70 to 400 K in which there exist the incommensurate modulated structures. Crystallographic characteristics of the modulation wave are obtained: the direction of a wave vector q at an angle 9° with respect to the [100] direction in the (010) plane; the polarization plane (010); the transversal wave of tin atoms displacement. A description of (3 + l)-dimensional space group for incommensurate phase is given. Temperature and concentrational dependencies for crystallographic characteristics are obtained. It is shown that the Lifshitz point on the concentrational phase diagram corresponds to a composition with X = 0.28 at T = 280 K. We have analyzed the evolution of thermal expansion tensor in the range of phase transition. The temperature boundaries for incommensurate phase range are shown to be fixed by the knees of thermal expansion and inside the temperature range the “C” parameter remains unchanged (invar effect). Tin atoms displacement direction in the modulation wave is shown to be normal to the “invar” plane (010).