A software is developed for determining the parameters of the thermal expansion tensor of the crystals of any system by a set of experimental diffraction data received using X-ray, synchrotron and other radiations at various temperatures. An algorithm is realized which allows carrying out all calculations from the experimental determination of the Bragg reflection angles to the calculation of the parameters of the thermal expansion tensor of the crystals, including the orientation of the tensor axes with respect to the crystallographic axes. The drawing of the 3D characteristic surface of the tensor and its 2D sections is also provided. The software is aimed at studying the anisotropy of the thermal expansion of the crystal materials and phase transitions, as well as revealing the mechanism and nature of the thermal behavior of substances.

The RietveldToTensorprogram is designed to study crystal lattice deformations using the Rietveld method from the X-ray powder diffraction data gathered under varying physical and chemical...

The paper presents a brief review of the present state of high-temperature borate crystal chemistry. This review summarizes the results of high- and low-temperature single crystal X-ray diffraction studies for more than 10 borate structures and high-temperature powder Xray diffraction data for about 65 borates. Thermal behavior of their crystal structures, thermal expansion, polymorphic transitions and their relationship to borate glasses are presented. These studies allow to formulate the basic principles of high-temperature borate crystal chemistry and to reveal the regularities of thermal behavior of borates. On heating, the BO

In the present study the thermal structure evolution is reviewed for known nonlinear optical borates such as β-BaB₂O₄, LiB₃O₅, CsLiB₆O₁₀, Li₂B₄O₇, K₂Al₂B₂O₇, and α-BiB₃O₆, based on single-crystal and powder X-ray diffraction data collected over wide temperature ranges. Temperature-dependent measurements of further borates are presented for the first time: α-BaB₂O₄ (295–673 K), β-BaB₂O₄ (98–693 K), LiB₃O₅ (98–650 K) and K₂Al₂B₂O₇ (98–348 K). In addition to the established criteria for nonlinear optical (NLO) properties of crystals, here the role of the anisotropy and anharmonicity of the thermal vibrations of atoms is analysed as well as changes in their coordination spheres and the anisotropy of the thermal expansion of the crystal structure. Non-centrosymmetric borates, especially those that have NLO properties, often show distinct anisotropies for each cation in comparison to centrosymmetric borates. All considered NLO borates contain BO₃ triangles, which are the principal cause of the strong anisotropy of the thermal expansion.