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The compound Na 2 CaPO 4 F has at least three polymorphic modifications: monoclinic α (also known as the natural mineral nacaphite), orthorhombic β and rhombohedral γ. All three polymorphs have antiperovskite-type structures belonging to either 2 H (α and β) or 15 R (γ) polytypes. The β-phase was synthesized using CaF 2 , NaF and Na 3 PO 4 as initial reagents at 800 ​°C. Its crystal structure is orthorhombic (Pnma, a ​= ​5.3542(1), b ​= ​7.0878(2), c ​= ​12.2560(3) Å, V ​= ​465.11(3) Å3, Z ​= ​4) and based upon the chains of fluorine-centered face-sharing octahedra running along [100]. Upon heating, the β form is stable up to 640 ​°C, when it melts and, in the temperature range of 640–800 ​°C, the γ form crystallizes. Its crystal structure (rhombohedral, R 3 ¯ m , a ​= ​7.0272(3), c ​= ​40.609(2) Å, V ​= ​1736.66(18) Å3, Z ​= ​15) consists of framework based upon pentamers of face-sharing [F(Na,Ca) 6 ] octahedra connected to each other through common Na vertices. The strongest thermal expansion for both modifications is parallel to the modules of face-sharing anion-centered octahedra, whereas it is almost isotropic within the plane perpendicular to the modules. The information-theoretic structural complexity analysis points out to the possible metastable character of the β-polymorph. The proposed stability row of the Na 2 CaPO 4 F phases under ambient conditions corresponds to the following sequence: α ​> ​γ ​> ​β. This agrees well with the relations among their structural complexities, degrees of order, physical and information densities. The sequence of phase transitions α → β → γ proceeds via transitional metastable β-phase. The α → β transition is reversible and of the order-disorder type with the conservation of structural topology, whereas the β → γ transition is reconstructive and irreversible. The latter transition is associated with the transformation of the antiperovskite 2 H polytype into the 15 R polytype. The β-Na 2 CaPO 4 F transforms into γ-Na 2 CaPO 4 F in the temperature range 640–720 ​°C. The transition is not direct and involves melting of the initial phase and its re-crystallization. The crystal structure of γ-Na 2 CaPO 4 F is based on pentamers of face-sharing octahedra connected with each other through common Na1 vertices (instead of chains observed in other polymorphs). [Display omitted] • The possible metastable character of the β-polymorph is discussed on the base of the information-theoretic structural complexity analysis. • The α → β transition is reversible and has the order-disorder type, the β → γ transition is reconstructive and irreversible; • Thermal expansion of all three Na 2 CaPO 4 F polymorphs is anisotropic and has the same general features. [ABSTRACT FROM AUTHOR]

Thermal expansion of Ba silicates with tetrahedrally coordinated Si atoms in the temperature range of 25–1100 °C had been studied by high-temperature X-ray powder diffraction. The volume thermal expansion coefficients (TECs) are in the range 41–50×10 −6 °C −1 with an average value of 〈 α V 〉 = 45 × 10 − 6 ° C − 1 . In the structures with chain and layered silicate anions, thermal expansion is anisotropic: the direction of maximal TEC is parallel to the extension of the zweier chains of silicate tetrahedra, which are strained owing to the interactions with Ba 2+ . The strain is released during thermal expansion due to the increasing effective size of Ba 2+ induced by thermal vibrations. Information-theoretic analysis of the structural and topological complexities of Ba silicates indicates that their structural complexity is a function of the topological complexity of their silicate anions. The latter displays a non-linear behaviour with increasing SiO 2 content (=the increasing degree of polymerization and increasing dimensionality): it starts from simple topologies, reaches a maximum at topologies of intermediate complexity, and ends up at simple topologies again. The specificity of the interactions of Ba 2+ with the silicate anions results in higher complexity of high-temperature α -BaSi 2 O 5 compared to that of low-temperature β -BaSi 2 O 5 . This uncommon behaviour may be explained by the vibrational advantages provided by flatter and more complex silicate layers in the α -phase, which overcome negative differences in configurational entropies of the two modifications apparent in the differences of their structural Shannon information. [ABSTRACT FROM AUTHOR]

High-temperature phase transition of synthetic kogarkoite, Na 3 SO 4 F, has been studied by high-temperature X-ray powder and single-crystal diffraction. The temperature of the phase transition can be estimated as 112.5±12.5 °C. The low-temperature phase, α-Na 3 SO 4 F, at 293 K, is monoclinic, P 2 1 / m , a= 18.065(3), b= 6.958(1), c= 11.446(1) Å , β= 107.711(1)°, Z =12. The structure contains thirteen symmetrically independent Na sites with coordination numbers varying from 6 to 8, and six independent S sites. The high-temperature β-phase at 423 K is rhombohedral, R- 3 m , a= 6.94(1), c= 24.58(4) Å, Z =9. The crystal structure of both polymorphs of Na 3 SO 4 F can be described as a 9 R antiperovskite polytype based upon triplets of face-sharing [FNa 6 ] octahedra linked into a three-dimensional framework by sharing corners. In the α-modification, the SO 4 tetrahedra are completely ordered and located in the framework cavities. In the β-modification, there are only two symmetrically independent Na atoms in the structure. The main difference between the structures of the α- and β-phases is the degree of ordering of the SO 4 tetrahedra: in the α-modification, they are completely ordered, whereas, in the β-modification, the complete disorder is observed, which is manifested in a number of low-occupied O sites around fully occupied S sites. The phase transition is therefore has an order–disorder character and is associated with the decrease of structural complexity measured as an information content per unit cell [577.528 bits for the low- (α) and 154.830 bits for the high- (β) temperature modifications]. [ABSTRACT FROM AUTHOR]