The discovery of new nonlinear optical borates is continuously ongoing, driven by the great diversity of their crystal structures and the ability of boron to adopt linear, trigonal, and tetrahedral coordination. Boron mineralogy is also extremely diverse, primarily represented by minerals formed in hydrothermal, skarn, and sedimentary environments. Well-known minerals include pinnoite (MgB₂O₄·3H₂O) (Genkina and Malinovskii 1983), inderite (Mg₂B₆O₁₁·15H₂O) (Corazza 1976), kurnakovite (Mg₂B₆O₁₁·15H₂O) (Corazza 1974), hydroboracite, CaMg[B₃O₄(OH)₃]2·3H₂O (Ashirov et al. 1962), inyoite, Ca[B₃O₃(OH)₃]·4H₂O (Clark 1959), meyerhofferite (Ca₂B₆O₆(OH)₁₀·2H₂O) (Clark and Christ 1960), colemanite (Ca[B₃O₄(OH)₃]·H₂O) (Christ et al. 1958), and priceite (Ca₂B₅O₇(OH)₅ · H₂O) (Wallwork et al. 2002). Significantly fewer strontium borates are known, among which are such minerals as veatchite (Sr₂B₁₁O₁₆(OH)₅·H₂O) (Grice and Pring 2012), tunellite (SrB₆O₁₀·4H₂O)(Clark 1964), and strontioborite (Sr[B₈O₁₁(OH)₄]) (Brovkin et al. 1975; Pekov et al. 2024). There are many examples of natural objects inspiring researchers to discover new functional materials.

Strontioborite, Sr[B₈O₁₁(OH)₄], is a rare mineral which status has recently been revalidated after being discredited for decades (Pekov et al. 2024). Recently, a good nonlinear optical response was discovered in the AEB₈O₁₁(OH)₄ family, where AE = Ca, Sr (Gong et al. 2020). Good nonlinear optical properties of Sr[B₈O₁₁(OH)₄]:Eu²⁺ were investigated in (Liang et al. 2021). Synthetic analogues, including Ca[B₈O₁₁(OH)₄] (Yamnova et al. 2005; Wiggin and Weller 2005), Ba(B₈O₁₁(OH)₄) (Sun et al. 2010), Pb[B₈O₁₁(OH)₄] (Belokoneva et al. 1999; Wang et al. 2006), Eu(B₈O₁₁(OH)₄) (Polinski et al. 2013) and Sn(B₈O₁₁(OH)₄) (Schönegger et al. 2018), together with strontioborite, form a family of hydrous alkaline earth borate compounds M[B₈O₁₁(OH)₄] (M = Ca, Sr, Ba, Pb, Eu, Sn) whose crystalline structure consists of [B₈O₁₁(OH)₄]²⁻ layers (8B:5Δ3T:[φ]<Δ2T>|<Δ2T>|<Δ2T>|2Δ). Strontioborite and its synthetic calcium analogue are isostructural. They crystallize in the monoclinic space group P2₁ with similar unit cell parameters and their structures consist of layers of [B₈O₁₁(OH)₄]²⁻ polyanions interconnected by 9-coordinate Sr²⁺/Ca²⁺ cations. Pb[B₈O₁₁(OH)₄], Ba(B₈O₁₁(OH)₄) and Sn([B₈O₁₁(OH)₄) are homeotypic members of this family. While they contain the identical FBB, they crystallize in the centrosymmetric space group P2₁/n. The larger Pb²⁺ cation adopts a different, 6-coordinate environment, and the overall configuration of the layers and their stacking sequence differs from the Ca/Sr pair, leading to a distinct supramolecular 3D network linked by both Pb–O bonds and hydrogen bonding.

Thermogravimetric analysis of Pb(B₈O₁₁(OH)₄) revealed that its structure remains stable up to approximately 400°C after which it undergoes a sharp weight loss attributed to the dehydration of hydroxyl groups (Wang et al. 2006). Similarly, Ca[B₈O₁₁(OH)₄], has been structurally characterized at low temperatures, confirming the presence of these hydroxyls, which are the functional groups most susceptible to thermal decomposition (Wiggin and Weller 2005). Despite a significant number of studies on strontioborite, the crystal structure of its synthetic analogue has not yet been determined. Therefore, this article aims to elucidate the thermal behavior of synthetic analogue of strontioborite by examining its decomposition mechanism, stability limits, and transformations it undergoes upon heating.

Synthesis.

Crystals of Sr[B₈O₁₁(OH)₄] were first obtained by us by mixing 0.100 g (0.432 mmol) of Ag₂O (Sigma Aldrich, 99.8%), 0.054 g (0.432 mmol) of SrF₂ (Sigma Aldrich, 99.0%), 0.534 g (4.315 mmol) of H₃BO₃ (Sigma Aldrich, 99.0%), and 0.814 g (7.767 mmol) of NH₄BF₄ (Sigma Aldrich, 99.8%). The reagents were placed in an evacuated quartz ampule, which was flame-sealed under 10^− 3 Pa. It was then heated to 280°C over two days, held at this temperature for 5 days, and cooled to room temperature over 5 days. The contents of the ampule were washed with a large amount of distilled water, after which transparent plate-like crystals were extracted. These crystals were subsequently identified as Sr[B₈O₁₁(OH)₄]. The resulting sample was a homogeneous specimen of this compound.

To obtain a homogeneous sample of this borate, we performed two syntheses. In the first case, freshly prepared SrO (0.876 g, 8.367 mmol) and H₃BO₃ (4.141 g, 66.973 mmol) (NevaReaktiv, Russia, 99.8%) were used, mixed in a molar ratio of 1:8. To obtain SrO, strontium carbonate (NevaReaktiv, Russia, 99.8%) was annealed at 1100°C for 5 hours. The mixture was thoroughly ground in an agate mortar and placed in a teflon autoclave. The autoclave was maintained at 200°C for a week, after which the furnace was turned off. The resulting sample was a mixture of Sr[B₈O₁₁(OH)₄] and boric acid (Fig. 1). The sample obtained in this way was studied by high-temperature X-ray powder diffraction.

We also attempted to synthesize this borate via the stoichiometric reaction: SrF₂ + 2H₃BO₃ + 3B₂O₃ = Sr[B₈O₁₁(OH)₄] + 2HF. For this purpose, 0.500 g (3.980 mmol) of SrF₂, 0.492 g (7.960 mmol) of H₃BO₃, and 0.831 g (11.941 mmol) of B₂O₃ were mixed. The mixture was homogenized in an agate mortar, placed in a quartz ampoule, which was flame-sealed under 10^− 3 Pa. The ampule was heated to 280°C over 2 days, held at this temperature for 5 days, and cooled to room temperature over 2 days. After this, the sample was thoroughly washed with a large amount of distilled water. The resulting sample consisted of 83 wt% Sr[B₈O₁₁(OH)₄], 10 wt% SrB₅O₇F₃, 5 wt% H₃BO₃, and 2 wt% SrF₂. The sample obtained in this way was studied by IR spectroscopy and thermal analysis.

Powder X-ray diffraction studies in a temperature range from 30 up to 900 °С were performed using an Ultima IV (Rigaku, Japan) powder diffractometer (CuKα, 40 kV/30 mA, DtexUltra PSD. The PDF-2 (2025) database and the PDXL software package (Rigaku, Japan) were used for phase analysis. The TOPAS 5.0 program (Bruker AXS) was applied for the refinement of unit cell parameters by Rietveld method. Thermal expansion coefficients (TECs) at various temperatures and graphic representations of their tensor figures were obtained using the ThetaToTensor software package (Bubnova et al. 2013).

Symmetry codes: (i) x, y, z–1; (ii) –x + 1, y–1/2, –z + 1.

IR spectroscopy and thermal analysis.

Entropy calculations.

Vibrational entropy calculations were performed using a combined approach with Quantum ESPRESSO and Phonopy. First-principles density functional theory (DFT) calculations were carried out using the Quantum ESPRESSO suite. The crystal structure was fully relaxed (both lattice parameters and atomic positions) until the total energy and forces converged to below 10^− 8 eV and 10^− 7 eV/Å, respectively. Force constants were calculated within the framework of density functional perturbation theory (DFPT) as implemented in Quantum ESPRESSO's ph.x module. A q-point mesh of 3 × 3 × 2 was used for the dynamical matrix calculation to ensure accurate phonon dispersion. The force constant matrix obtained from DFPT was then processed using Phonopy to construct the dynamical matrix over a dense mesh and to compute phonon density of states (DOS).

Topological calculations.

The atomic adjacency matrix was constructed by the domain method based on atomic Voronoi-Dirichlet Polyhedra (VDP) (Blatov et al. 1995). A pair of i-th and j-th atoms was considered bound (either covalently or nonvalently) once they had a common face of VDP intersecting the line linking them. Faces characterized by solid angles Ω_ij < 3σ(Ω) ≈ 1.5% of 4π steradians were neglected. To simplify anionic substructures, the cluster topological representation was used in the same fashion as previously for Na₁₇B₂₄O₄₂I₅ and related borates (Volkov et al. 2024). A cluster representation is obtained by classifying all bonds of a crystal structure as intercluster using the following topological criterion (Blatov et al. 2014): an intracluster bond must belong to at least one small cycle, while an intercluster bond must belong only to large cycles. Chemically, this means that intracluster bonds form rather dense groups, while intercluster bonds connect these groups together. If all the bonds are ordered by the size N_i of the minimal cycle to which they belong and there is such ζ that N_ζ+1 – N_ζ > 2 holds, then all bonds with i ≤ ζ are assumed intracluster, while those with i > ζ are assumed intercluster. Upon this, 2-coordinated (2-c) vertices (oxygen atoms) in between a pair of clusters were contracted from the net to further simplify it (Shevchenko and Blatov 2021), and finally a standard topological representation for the revealed clusters was performed by pulling clusters to their mass centers. Calculations were carried out in ToposPro package v. 5.5.4.1(Blatov et al. 2014), and the obtained nets were classified in accordance with RCSR classification (O’Keeffe et al. 2008). Effective coordination numbers (ECoNs) (Hoppe 1979) were calculated with the aid of Python-script crystchemlib (Rashchenko 2025).

The infrared spectrum of the synthesized Sr[B₈O₁₁(OH)₄] was recorded and analyzed in comparison with established literature data (Fig. 5, Table S1) (Sun et al. 2010; Ortner et al. 2015; Wang and Liang 2019; Pekov et al. 2024). The majority of the peaks are attributed to Sr[B₈O₁₁(OH)₄]; peaks of impurities, H₃BO₃, SrB₅O₇F₃ are also observed. The spectrum is divided into two primary regions: the high-frequency region (3000–3500 cm^− 1) and the fingerprint region (400–1600 cm^− 1).

In the high-frequency region, several bands corresponding to O–H stretching vibrations (ν O–H) are observed. These include a strong band at 3354 cm^− 1, medium-intensity bands at 3164 cm^− 1 and weaker features at 3398 cm^− 1 and 3015 cm^− 1. A shoulder peak at 1628 cm⁻¹ is assigned to the H–O–H bending mode (δ H–O–H), likely indicating the presence of adsorbed water.

The fingerprint region contains the complex set of vibrations arising from the borate anion network. The antisymmetric stretching vibrations of trigonally coordinated boron (νₐₛ B(3)–O) are identified as a shoulder at 1410 cm^− 1 and medium bands at 1369 cm^− 1 and 1327 cm^− 1. The symmetric stretching modes of B(3)–O (νₛ B(3)–O) appear as medium-intensity bands at 969 cm⁻¹ and 939 cm⁻¹. Vibrations involving tetrahedrally coordinated boron (B(4)) are also prominent. The antisymmetric stretches (νₐₛ B(4)–O) produce strong bands at 1112 cm^− 1 and 1042 cm^− 1, a weaker band at 1011 cm^− 1, and contribute to weaker features at 1217 cm^− 1 and 1195 cm^− 1. The latter bands also involve in-plane B–O–H bending modes. Strong bands at 889 cm^− 1 and 820 cm^− 1 are attributed to symmetric B(4)–O stretches (νₛ B(4)–O) coupled with O–B–O bending deformations.

The low-frequency region (below 800 cm^− 1) is rich in deformation modes. Multiple strong and medium bands between 744 cm^− 1 and 594 cm^− 1 are assigned to out-of-plane bending of B(3)–O units (δ B(3)–O), deformations of tetrahedrally coordinated boron, and various terminal and bridging O–B–O bending modes (δ [O–B–O]). A notable strong band at 536 cm^− 1 is associated with bending of both B(3)–O and B(4)–O bonds. Weaker bands observed at 492 cm^− 1 and below 454 cm^− 1 are attributed to specific B(4)–O deformations and mixed lattice vibrational modes, respectively.

Based on single-crystal X-ray diffraction data, the crystal structure of Sr[B₈O₁₁(OH)₄], a synthetic analogue of strontioborite, was determined in this work. Its thermal behavior was studied by high-temperature powder X-ray diffraction and thermal analysis methods. It was shown that the compound is stable up to ~ 390°C, after which it undergoes dehydration, forming an X-ray amorphous phase; above 720°C, Sr₃B₁₄O₂₄ crystallizes. The thermal expansion of the compound is anisotropic: it is minimal within the plane of the layers and maximal in the direction nearly perpendicular to them, which is explained by the orientation of rigid hexaborate groups.