Statistical analysis of Zhdanov sequences in polytypes of SiC, CdI₂ and ZnS

Abstract

A statistical analysis of different numbers in the Zhdanov sequence of polytypes of SiC, CdI₂ and ZnS is made. A simple binomial model is used for SiC and CdI₂. It is shown that in SiC the various polytypes could conform to the hypothesis that they are built up of random combination of blocks of 3's and 2's with finite probabilities which have been estimated from experimental observations. Relative probabilities of various polytypes are worked out. A similar analysis is made for CdI₂ with 2's and 1's in the Zhdanov symbol. The observed distribution of different numbers for ZnS shows a systematic larger occurrence of odd numbers over even.