Occupying the Chal sites with more polarizable anions may also facilitate stronger interlayer dispersion forces. In the Bi2(Se1-xSx)3 alloy, the preference would be to have S in the Chal sites and Se in the Chal sites, giving the favored 𝑥 = 1/3 stoichiometry. In Bi2(Se1-xTex)3, the preference would be for Se in the Chal sites and Te in the Chal sites, favoring the 𝑥 = 2/3 stoichiometry. That the favored compositions appear to have a stronger influence on the thermodynamics of the Bi2(Se1-xTex)3 alloy may be explained by the larger electronegativity difference between Se and Te and the fact that Te is the largest and most polarizable of the three chalcogens. We also note that this structural preference argument would explain why Bi2Te2S is stable in the R3 ̅ m phase. As expected following these arguments, the distribution of 𝑃 𝑛 for structures in the R3 ̅ m alloy models, particularly Bi2(Se1-xTex)3, are heavily skewed towards particular chalcogen arrangements in the alloy supercells (Figure ). For Bi2Se2S and Bi2SeTe2 at a formation temperature 𝑇 F = 800 K, the most probable chalcogen arrangements have 𝑃 𝑛 = 0.19 and 0.42, respectively, and the three structures (of 21) with the largest 𝑃 𝑛 collectively account for 41 and 76 % of the cumulative probability. Even for the 𝑥 = 1/2 solid solution of Bi2(Se1-xTex)3, where the number of configurations and hence the configurational entropy are a maximum, the most probable four structures with the largest 𝑃 𝑛 (4.8 % of the total) account for 68 % of the cumulative probability. This is in stark contrast to the Pnma Bi2(Se1-xSx)3 alloy, where for the 𝑥 = 1/3, 1/2 and 2/3 compositions the difference between the smallest and largest 𝑃 𝑛 are 6.3 × 10 -2 , 1.9 × 10 -2 and 5.1 × 10 -2 , respectively, indicating a much more homogenous distribution of configurations. It is interesting to note, however, that the calculations do predict a distribution over chalcogen arrangements in both Bi2Se2S and Bi2SeTe2, at least for high-temperature syntheses, which suggests these "line" compounds might contain significant concentrations of defects where chalcogen atoms swap from their ideal crystallographic sites (i.e. antisite defects). Despite the skewed distribution of the 𝑃 𝑛 , the predicted cell volume as a function of composition 𝑉(𝑥) at 𝑇 F = 800 K (Figure ) is close to linear in the Se content, as would be expected from Vegard's law. This implies that there is a small variation in the volumes 𝑉 𝑛 of individual structures.