Study of the anisotropy of α-33S single crystal thermal expansion

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Abstract

A technique for arbitrary symmetry crystals unit cell parameters refining on modern single-crystal diffractometers is described. The technique is based on the 2D detector position calibration. The elementary orthorhombic unit cell parameters of the α-33S single crystal have been refined. The anisotropy of parameters changes in the range of 90–350 K has been studied. It is shown that the relative increase in parameter c is 6.4%. The obtained dependences are approximated by second–third degree polynomials. The absolute increase in cell volume is 138.4 A3, and the relative increase is 4.3%. The temperature dependencies of the thermal expansion tensor elements has been refined. The coefficients of α-33S thermal expansion tensor at the room temperature are: α11 = 15.35 × 10–5, α22 = 8.56 × 10–5, α33 = 9.12 × 10–5 К–1.

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About the authors

P. S. Serebrennikova

Novosibirsk State University; Nikolaev Institute of Inorganic Chemistry Siberian Branch of Russian Academy of Sciences

Author for correspondence.
Email: serebrennikova@niic.nsc.ru
Russian Federation, Novosibirsk; Novosibirsk

A. V. Panchenko

Novosibirsk State University

Email: serebrennikova@niic.nsc.ru
Russian Federation, Novosibirsk

N. В. Egorov

Tomsk Polytechnic University

Email: serebrennikova@niic.nsc.ru
Russian Federation, Tomsk

S. А. Gromilov

Novosibirsk State University; Nikolaev Institute of Inorganic Chemistry Siberian Branch of Russian Academy of Sciences

Email: serebrennikova@niic.nsc.ru
Russian Federation, Novosibirsk; Novosibirsk

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Supplementary files

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2. Fig. 1. Diffraction patterns (Bruker D8 Venture, MoKα radiation, ω scanning in the 3° range) of a single crystal of α-S in different orientations. The approximate value of the interplanar distance is shown next to the arcs. The indices of the reflections, by which the cell parameters were refined, are shown. The insets show the profiles of the doublets.

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3. Fig. 2. The process of refining the parameters of the unit cell of the 3 α-S single crystal at room temperature using the “Equator” method. Bold lines show flat sections of two-dimensional profiles and the X-coordinates of the maxima of two reflections of the external standard. The ratio ∆2θ/∆X determines the angular size of the pixel γ and allows calculating the angular position of the Kα1-component of the 16 0 0 reflection.

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4. Fig. 3. Result of calibration of the detector position D = 109 mm, 2θD = –70° of the Bruker D8 Venture diffractometer based on the results of surveying the external standard Si. The SearchXY-2θ program was used. Only the Kα1 components of the reflections involved in the final refinement of the detector position are shown.

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5. Fig. 4. Experimental temperature dependences of the parameters and volume of the unit cell of the 3 α-S single crystal, constructed using the “Equator” method, and the result of their approximation by polynomials.

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6. Fig. 5. Dependences of the unit cell parameter α-S on temperature according to data from different sources.

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7. Fig. 6. The type of thermal expansion tensor α-S (a) and the dependence of its elements α11 (1), α22 (2), α33 (3) on temperature (b).

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