BaF ₂ –B ₂ O ₃ Fluorooxoborates: Insights into Electronic Structure, Mechanical Properties, and High-Pressure Stability

Barium fluorooxoborates have recently emerged as promising candidates for deep-ultraviolet optical materials, yet their electronic, vibrational, mechanical properties, and high-pressure behavior remain largely unexplored. In this work, we systematically investigate the thermodynamic stability, vibrational properties, electronic structure, and mechanical response of three intermediate compounds in the BaF 2 –B 2 O 3 system, BaB 2 O 3 F 2, BaB 4 O 6 F 2, and BaB 8 O 12 F 2, under hydrostatic pressures from 0 to 10 GPa using density functional theory. Convex hull analysis shows that BaB 2 O 3 F 2 is thermodynamically stable across the entire pressure range, whereas BaB 4 O 6 F 2 and BaB 8 O 12 F 2 become metastable above ∼1.5 GPa, decomposing into BaB 2 O 3 F 2 and B 2 O 3 . Phonon calculations confirm dynamic stability at ambient pressure, and the Raman spectra are calculated and described. Electronic structure calculations with the HSE06 hybrid functional yield for BaB 2 O 3 F 2, BaB 4 O 6 F 2, and BaB 8 O 12 F 2 large indirect band gaps of 8.55, 8.18, and 8.36 eV, respectively, which further increase under compression. Mechanical analysis indicates that all compounds satisfy the Born stability criteria. BaB 2 O 3 F 2 exhibits the highest stiffness and Vickers hardness, surpassing conventional nonlinear optical crystals such as β-BBO and KDP. BaB 8 O 12 F 2 offers balanced mechanical performance, while BaB 4 O 6 F 2 is significantly softer. Notably, BaB 8 O 12 F 2 remains dynamically and mechanically stable up to at least 10 GPa in a metastable state, whereas BaB 4 O 6 F 2 loses stability above ∼4 GPa. Collectively, these results establish the first pressure–composition phase diagram of the BaF 2 –B 2 O 3 system and demonstrate that barium fluorooxoborates combine deep-UV transparency with superior mechanical robustness, making them attractive for optical applications under extreme conditions.