Effect of ordered defects on the crystal structure of In-rich ternary compounds of the Cu–In–Se system

A comparative study of the unit cell parameters and volume of the chalcopyrite-related ordered defect compounds and other In-rich phases of the Cu-In-Se ternary system is made. These compounds fall on the tie-line of (Cud2Se)(sub 1-x)(In2Se3)(sub x). It is found that the unit cell parameters and volume of the compounds that can be derived from the formula Cu(n-3)In)n+1)Se2n, where in = 4, 5, 6, 7, 8, and 9, decrease with an increase in the fraction of cation vacancies to the total number of cation positions, m, or interacting donor-acceptor defect pairs (In(2+)Cu, 2V(-1)(sub Cu)) per unit l in the chemical formula. The reduction in the unit cell dimensions is explained as due to the decrease in the effective cation radius caused by the increase in m or l. This behavior is consistent with Vegard's law. However, the unit cell parameters of other In-rich phases such as CuIn4Se6 and CuIn4Se7 reported in the literature do not follow this trend. It must be noted that with indium having a 3+ oxidation state, the formation of these materials can only be explained if the valence of Cu atoms is 0 and 2+, respectively, different from the 1+ expected for the members of the Cu2Se-In2Se3 system.