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To clarify the synthesis mechanism of cubic boron nitride (cBN) with catalysts at high temperature and high pressure, we calculate the surface energy of the main phases in the Li-N-B synthesis system using the first-principle method. Based on the density functional theory, the surface energy of low-index surfaces of cBN, hexagonal boron nitride (hBN), and lithium boron nitride (Li3BN2) at the cBN synthetic temperature of 1700 K and synthetic pressure of 5.0 GPa is calculated. The surface energy of the main low-index surfaces of cBN is σ (111) > σ (001) > σ (110), that of hBN is σ101¯0 > σ112¯0 > σ (0001), and that of Li3BN2 is σ (100) > σ (110) > σ (001). The energy orders of the main low-index surfaces were well contrary to the corresponding orders of the valence electron density of the low-index surfaces of cBN, hBN, and Li3BN2, which were calculated by the empirical electron theory (EET) of solids and molecules. The result shows that the calculation results in this paper are well consistent with the previous results of the EET theory and support for the results of the “direct transformation of hBN to cBN under the catalysis of Li3BN2” obtained by the EET theory.

The Analysis of the Transformation Mechanism of cBN Crystals with the First-Principle Calculation