First-Principles investigation of Pressure-Induced structural transformations of barium borates in the BaO-B₂O₃-BaF₂ system in the range of 0–10 GPa

First-principles calculations within the density functional theory of the stability of barium borates of the BaO-B₂O₃-BaF₂ ternary system have been performed at the pressure of up to 10 GPa. A brief summary on the known structures of ambient and high-pressure phases in the BaO–B₂O₃ and BaF₂–Ba₃B₂O₆ subsystems has been provided. In the BaO–B₂O₃ subsystem the Ba₃B₂O₆, BaB₂O₄, and BaB₄O₇ phases tentatively are stable at up to 10 GPa, while the other known ambient-pressure borates Ba₅B₄O₁₁, Ba₂B₆O₁₁, and BaB₈O₁₃ decompose under the pressure of above 7.1, 0.6, and 2 GPa, respectively. Two new high-pressure polymorphic modifications of BaB₂O₄ compound, BaB₂O₄-Pna2₁ and BaB₂O₄-Pa3-, stable above 1.0 and 6.1 GPa, respectively, have been predicted. In the BaF₂–Ba₃B₂O₆ subsystem Ba₇(BO₃)_4-xF_2+3x solid solution is suggested to be stable in the considered pressure range, and Ba₅(BO₃)₃F is suggested to decompose into Ba₃B₂O₆ and Ba₇(BO₃)_4-xF_2+3x at pressures above 3–5 GPa. It has been shown that the enthalpy of Ba₇(BO₃)_4-xF_2+3x strongly depends on the distribution of the [(BO₃)F]⁴⁻ and [F₄]⁴⁻ groups in the structure. We consider the results obtained as a necessary basis for an experimental study aimed at obtaining barium borates under pressures of up to 10 GPa and studying their structure and properties.