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-xF2+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-xF2+3x at pressures above 3–5 GPa. It has been shown that the enthalpy of Ba7(BO3)4-xF2+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.
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