Structure family and polymorphous phase transition in the compounds with soft sublattice: Cu₂Se as an example

Quite a few interesting but controversial phenomena, such as simple chemical composition but complex structures, well-defined high-temperature cubic structure but intriguing phase transition, coexist in Cu₂Se, originating from the relatively rigid Se framework and "soft" Cu sublattice. However, the electrical transport properties are almost uninfluenced by such complex substructures, which make Cu₂Se a promising high-performance thermoelectric compound with extremely low thermal conductivity and good power factor. Our work reveals that the crystal structure of Cu₂Se at the temperature below the phase-transition point (∼400 K) should have a group of candidate structures that all contain a Se-dominated face-centered-cubic-like layered framework but nearly random site occupancy of atoms from the "soft" Cu sublattice. The energy differences among those structures are very low, implying the coexistence of various structures and thus an intrinsic structure complexity with a Se-based framework. Detailed analyses indicate that observed structures should be a random stacking of those representative structure units. The transition energy barriers between each two of those structures are estimated to be zero, leading to a polymorphous phase transition of Cu₂Se at increasing temperature. Those are all consistent with experimental observations.