Mixed-layer compounds from the tetradymite group, in the range Bi2Te3-Bi8Te3, were studied by HRTEM. The formula S′(Bi2kX3)·L′[Bi2(k+1)X3] (X = chalcogen; S′, L′ = number of short and long modules, respectively) was introduced as a working model. Diffraction patterns show that all phases are N-fold (N = layers in the stacking sequence) superstructures of a rhombohedral subcell with c/3 = d1 ~ 0.2 nm. The patterns, with two brightest reflections about the middle of d1*, are described by monotonic decrease of two modulations with increase in Bi: (1) q = γcsub* (q ~ homoatomic interval; γ = 1.8–1.64 for analytical range; csub ~ 3d1), based on displacive modulation between chalcogen and Bi atoms; and (2) qF = γFcsub*;qF= (i/N)d1* = idN*, i = S′ + L′, relating changes in module size and number to displacements in a basic substructure.

The qF model, besides underpinning the stacking sequences, was adapted to incorporate the homology for S′, L′ modules related by k. The displacements are quantifiable by fractional shifts between reflections in the derived and basic structures. The condition for “the brightest two reflections about the middle of d1* to be separated by idN*” is fulfilled only if the shift at this position is minimal (equal to 1/Nb; Nb = layers in the basic structure). This model and accompanying program compiled to find suitable Nb and simulate intensity pattern(s) can be used to (1) constrain stacking sequences estimated from observation; (2) predict polysomes as larger building blocks; and (3) discriminate single-phases from random polysomes.

The formula nBi2·mBi2X3 describing the configuration for Bi2kX3 modules by n/m = k − 1 is proven by lattice fringes, but is not underpinned by qF and does not constrain assumed homology.

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