Figure compares the energy differences ∆𝐴 between the Pnma and R3 ̅ m phases of Bi2S3, Bi2Se3 and Bi2Te3. In all three, we find that the Pnma phase is lowered in energy relative to the competing R3 ̅ m phase with increasing temperature, indicating that the former is stabilized by differences in the vibrational free energy. For Bi2S3, this means that the energy difference between the ground-state Pnma and the R3 ̅ m phase increases sharply with temperature. For Bi2Se3 and Bi2Te3, on the other hand, the free-energy differences between the Pnma and R3 ̅ m phases fall with temperature. For Bi2Se3, the ∆𝐴 falls from ~1.8 kJ mol -1 atom -1 at 0 K to 0.75 kJ mol -1 atom -1 at 1000 K, whereas for Bi2Te3 the differences range from ~5.5 kJ mol -1 atom -1 at 0 K to ~3.9 kJ mol - phase transitions and predict the same qualitative stability ordering as the lattice energies (c.f.