, (X = Bi/Sb, Y = Te/Se)*

Topological systems with various Bi/Sb and Te/Se concentrations have been studied with a view towards tuning topological phase transitions, and we try to clarify this by varying the lattice parameters in this family of materials and driving electronic topological-to-trivial phase transitions. We first investigate disorder on each site and perform first-principles calculations on (Bi_1-xSb_x)₂Y₃ and X₂(Te_ySe_1-y)₃ (X=Bi/Sb, Y=Te/Se) in which we systematically vary the c/a ratio of lattice constants to study the topological phase transition, before studying alloying on all sites. To model substitutional disorder, we have constructed supercells, alloying on one sublattice, where the atomic pair correlations are zero up to the third nearest neighbor shell, and we vary the impurity concentration across the phase diagram with the goal of identifying the influence of each atomic species on the transition. We determine the bulk electronic structure and pay special attention to the band inversion near the topological transition.