© 2010 The Japan Institute of Metals

We calculated the electronic and lattice properties of 30H-BN which are *sp*^{3}-bonded compounds. The 30H polytype has various over 6000000 structures. Their possible symmetries and hexagonalities (H[%]) are P6_{3}mc and P3m1, and 6.7%∼93.3%, respectively. Hexagonality is a ratio of the number of hexagonal (h) character and the total number of cubic (c) and h characters in a unit cell. Two structures in the 30H polytype are considered in this study. Their stacking sequences (ABC notation) are ABCABCABCABCABCACBACBACBACBACB (P6_{3}mc, H = 6.7%) and ABCBCBCBCBCBCBCBCBCBCBCBCBCBCB (P3m1, H =93.3%). Their lattice properties were optimized automatically by the total energy pseudopotential method. Calculated total energies of 30H-BN are in the order of ABCABCABCABCABCACBACBACBACBACB (6.7%) < ABCBCBCBCBCBCBCBCBCBCBCBCBCBCB (93.3%). Values in parentheses are hexagonalities (%). This means the former is energetically more favorable than the latter. The total energy of the BN polytype increases with increasing hexagonality. We calculated their electronic band structures, the band gap values, the valence band maximum (VBM), and conduction band minimum (CBM). Their electronic band structures are non-metallic and band gaps are indirect.

(Received 2010/4/23; Accepted 2010/5/24; Published 2010/8/25)

**Keywords:** 30H-BN, polytype, electronic band structure, first principles

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