Chemical-structural modularity in the tetradymite group: A HRTEM study

Abstract

Mixed-layer compounds from the tetradymite group, in the range Bi₂Te₃-Bi₈Te₃, were studied by HRTEM. The formula S′(Bi_2kX₃)·L′[Bi_2(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 = γc_sub* (q ~ homoatomic interval; γ = 1.8-1.64 for analytical range; c_sub ~ 3d₁), based on displacive modulation between chalcogen and Bi atoms; and (2) q_F = γ_Fc_sub*; q_F = (i/N)d₁* = id_N*, i = S′ + L′, relating changes in module size and number to displacements in a basic substructure.

The q_F 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 id_N*” is fulfilled only if the shift at this position is minimal (equal to 1/N_b; N_b = layers in the basic structure). This model and accompanying program compiled to find suitable N_b 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 Bi_2kX₃ modules by n/m = k - 1 is proven by lattice fringes, but is not underpinned by q_F and does not constrain assumed homology.