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 σ > σ > 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.

中文翻译：

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cBN晶体转化机理的第一性原理计算分析

为了阐明高温高压催化剂合成立方氮化硼（cBN）的机理，我们使用第一性原理计算了Li-NB合成体系中主要相的表面能。基于密度泛函理论，计算了cBN、六方氮化硼(hBN)和氮化硼锂(Li3BN2)在cBN合成温度1700 K、合成压力5.0 GPa下低折射率表面的表面能。cBN主要低折射率表面的表面能为σ(111)>σ(001)>σ(110)，hBN为σ>σ>σ(0001)，Li3BN2为σ(100) > σ (110) > σ (001)。主要低折射率表面的能量级与 cBN、hBN 和 Li3BN2 低折射率表面的价电子密度的相应级相反，由固体和分子的经验电子理论 (EET) 计算得出。结果表明，本文计算结果与EET理论之前的结果非常吻合，支持了EET理论得到的“在Li3BN2的催化下hBN直接转化为cBN”的结果。