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Thermal expansion of oxygen-containing compounds with triangular, tetrahedral, and mixed anionic groups

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1. Title Title of document Thermal expansion of oxygen-containing compounds with triangular, tetrahedral, and mixed anionic groups
2. Creator Author's name, affiliation, country R. S. Bubnova; National Research Centre “Kurchatov Institute” – Petersburg Nuclear Physics Institute (PNPI); Russian Federation
2. Creator Author's name, affiliation, country М. G. Krzhizhanovskaya; St. Petersburg State University; Russian Federation
2. Creator Author's name, affiliation, country S. K. Filatov; St. Petersburg State University; Russian Federation
3. Subject Discipline(s)
3. Subject Keyword(s)
4. Description Abstract

This study summarizes data on the thermal properties of 200 oxygen-based compounds composed of triangular (borates, carbonates, nitrates) and tetrahedral (silicates, sulfates) groups. Based on the systematization by S.K. Filatov, which relies on the residual charge Z per anionic polyhedron outside the polyhedron, the dependence of the volumetric thermal expansion coefficient αV and melting temperature of these compounds was analyzed. The residual charge Z of the anionic group characterizes the degree of "polymerization" of these groups. This approach was applied to mixed groups (tetrahedral groups with different central atom charges) and extended to heteropolyhedral anionic groups (oxygen triangles and tetrahedra in borates). It is shown that the volumetric thermal expansion increases, while the melting temperature decreases, with a reduction in the residual charge Z, due to the increasing dimensionality of the anion and the weakening of cation–oxygen bond strength. For anionic groups with the same residual charge Z, the variation in αV values allows for the determination of the influence of cation charge and size: thermal expansion increases with decreasing cation charge and increasing cation radius. Among the studied oxygen compounds, the lowest average volumetric expansion coefficients are observed for compounds with tetrahedral groups (borates <αV>3=22 × 10−6, borosilicates <αV>27=29×10−6, aluminosilicates <αV>27 = 28 × 10−6, silicates <αV>34 = 27 × 10−6 °С−1). Intermediate values are exhibited by compounds with triangular groups (borates <αV>32 = 41 × 10−6, carbonates <αV>10 = 40 × 10−6 °С−1) and borates with mixed anions (<αV>40 = 43 × 10−6 °С−1). The highest expansion is observed for sulfates with isolated tetrahedra (<αV>21 = 90 × 10−6 °С−1) and nitrates with isolated triangular groups (<αV>5 = 132 × 10−6 °С−1), which is attributed to the weakening of bonds outside the anionic complex.

5. Publisher Organizing agency, location The Russian Academy of Sciences
6. Contributor Sponsor(s) Government of the Russian Federation (125021702335-5)
Russian Science Foundation (22-13-00317)
Government of the Russian Federation (1023033000085-7-1.4.3)
7. Date (DD-MM-YYYY) 26.04.2025
8. Type Status & genre Peer-reviewed Article
8. Type Type Research Article
9. Format File format
10. Identifier Uniform Resource Identifier https://kazanmedjournal.ru/0023-4761/article/view/682966
10. Identifier Digital Object Identifier (DOI) 10.31857/S0023476125020063
10. Identifier eLIBRARY Document Number (EDN) BYSVQW
11. Source Title; vol., no. (year) Kristallografiâ; Vol 70, No 2 (2025)
12. Language English=en ru
13. Relation Supp. Files Fig. 1. Residual charge Z, calculated per one polyhedron, for different types of anions. (33KB)
Fig. 2. Coefficient of volume expansion αV (10–6 C–1) of compounds with isolated oxygen triangles depending on the residual charge Z. Borates are shown as circles, nitrates as diamonds, carbonates as crosses. (10KB)
Fig. 3. Comparison of anisotropy and thermal expansion tensor values ​​of MTO3 phases (T = B, C, N) of calcite (M = Lu, Ca, Na) (a) and aragonite (Nd, Ca, K) (b) structure [32]. (64KB)
Fig. 4. Dependence of the coefficient of volume expansion αV (10–6 °C–1) of borates built from triangles on the residual charge of the anion (Z) (a) and on the charge of the cation for different types of anions: b – isolated, residual charge (−3), c – double triangles, residual charge (−2), d – rings and chains of triangles, residual charge (−1). (32KB)
Fig. 5. Dependence of the coefficient of volume expansion αV (10–6 °C–1) of phases of the calcite and aragonite families on the cation charge (a) and the unit cell volume (b) for phases with the calcite structural type. Carbonates are shown as circles, LuBO3 as squares, NaNO3 as diamonds. (19KB)
Fig. 6. Dependence of the coefficient of volume expansion αV (10–6 °C–1) of compounds with tetrahedral anion groups (silicates, aluminosilicates, borosilicates) on the residual charge of the anion Z (a) and independently for each of these classes of compounds: b – silicates, c – aluminosilicates, d – borosilicates. Silicates are indicated by circles, aluminosilicates – by diamonds, borosilicates – by squares. (40KB)
Fig. 7. Dependence of the coefficient of volume expansion αV (10–6 °C–1) of 2D (a) and 3D (b) aluminosilicates on the residual charge Z. (15KB)
Fig. 8. Dependence of the coefficient of volumetric expansion αV (10−6 °C–1) of compounds of the structural types of leucite (a) and feldspars (b) on the volume of the unit cell. (33KB)
Fig. 9. Dependence of the coefficient of volume expansion αV (10–6 °C–1) on the cation charge for some sulfates, residual charge (−2) of the [S6+O4]2– anion. (8KB)
Fig. 10. Coefficient of volume expansion αV (10–6 °C–1) of borates depending on the residual charge: a – 0D, 1D, 2D and 3D borates, b – borates with mixed anions from triangles and tetrahedra, c – 1D borates, d – 2D borates, d – 3D borates. (43KB)
Fig. 11. Melting point of some groups of oxygen compounds depending on the residual charge: a – alkaline earth borates [20], b – barium silicates [120], c – rubidium borates [121, 122], d – cesium borates [123]. (35KB)
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15. Rights Copyright and permissions Copyright (c) 2025 Russian Academy of Sciences