Table 1. Physical Properties of Superhard B–N–O Compounds with Cohesive Energy >6.75 eV Discovered in This Study^a.

crystal	ρ	K	G	E	ν	AU	KIC	H	EgPBE/Eg	Ecoh	Eform
B5N3O2	0.151	286	257	593	0.155	0.294	4.38	42	4.3/5.5	6.761
B5N3O3	0.150	279	255	586	0.150	0.088	4.09	43	6.3/7.6	6.935	83
B6N4O2	0.156	322	284	658	0.160	0.121	5.26	44	3.0/4.4	6.810
B6N4O3	0.155	292	268	616	0.149	0.311	4.33	45	4.5/5.7	6.900	120
B7N5O2	0.146	272	241	559	0.157	0.336	4.09	40	3.6/4.6	6.776
B7N5O3	0.158	306	283	649	0.147	0.276	4.54	47	4.1/5.3	6.904	117
B9N7O2	0.161	330	296	683	0.154	0.139	5.31	46	3.2/4.5	6.802
B9N7O3	0.160	318	301	688	0.140	0.245	4.42	50	3.9/5.1	6.926	97
c-BN	0.168	373	383	856	0.118	0.172	4.73	64	4.5/5.3	7.028	0
B2O3	0.101	35	33	75	0.127	2.347	0.14	12	6.3/8.9	7.008	0

^aDensity ρ (atom/ų), bulk modulus K (GPa), shear modulus G (GPa), Young’s modulus E (GPa), Poisson’s ratio ν, universal elastic anisotropy A^U, fracture toughness K_IC (MPa·m^1/2), hardness H (GPa), bandgap E_g (eV), cohesive energy E_coh (eV/atom), and formation energy E_form (meV/atom). The fracture toughness is based on the empirical model by Mazhnik and Oganov.⁵⁸ The bandgaps are computed respectively with the standard Perdew–Burke–Ernzerhof (PBE)⁴⁹ functional and the Tran-Blaha modified Becke-Johnson (TB-mBJ)^63,64 exchange potential for improved bandgap estimation. For benchmark, the experimental hardness H^exp = 50–70 GPa for c-BN,¹⁴ and H^exp = 1.5 GPa for B₂O₃.⁶⁵ The experimental bandgap E_g^exp=6.36 eV for c-BN,⁶⁶ and E_g > 10 eV for B₂O₃.⁶⁷