Theoretical derivation of the crystallographic parameters of polytypes of long-period stacking ordered structures with the period of 13 and 14 in hexagonal close-packed system

Based on crystallographic theory, there are 63 kinds of polytypes of 13H long-period stacking order(LPSO) structure,126 kinds of polytypes of 14H LPSO structure, 120 kinds of polytypes of 39R LPSO structure, and 223 kinds of polytypes of 42R LPSO structure in a hexagonal close-packed(HCP) system, and their stacking sequences and space groups have been derived in detail. The result provides a theoretical explanation for the various polytypes of the LPSO structure.