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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.