Group-theoretical treatment of the sphalerite-chalcopyrite order-disorder transition in CuInSe2

Landau's theory of second-order phase transitions is applied to the sphalerite-chalcopyrite order-disorder transition to show that this transition can take place continuously. Four different ordering symmetries are shown to arise from the irreducible representation corresponding to the ordered phase. At least two of these symmetries have been reported to occur in the ${\left({\mathrm{Cu}}_2\mathrm{Se}\right)}_x{\left({\mathrm{In}}_2{\mathrm{Se}}_3\right)}_{1-x}$ system. Implications for the phase diagram and properties of these important solar materials are discussed.