Group theory of phase transitions inA−15Oh3−Pm3n) structure

The results of a group-theory analysis of possible lower-symmetry phases arising from the $A-15$ structure are reported. The criteria which were employed are those of Landau and Lifschitz, and the chain subduction criterion. Potential order-parameter symmetries belonging to the ray representations at ${}_{}{}^{*}{}_{}{}^{}\overrightarrow{\mathrm{X}}$ and ${}_{}{}^{*}{}_{}{}^{}\overrightarrow{\mathrm{R}}$ were examined; cell doubling in one or two directions at ${}_{}{}^{*}{}_{}{}^{}\overrightarrow{\mathrm{X}}$ and in three directions at ${}_{}{}^{*}{}_{}{}^{}\overrightarrow{\mathrm{R}}$ were considered. The resulting space groups are tabulated, and comparisons with the few experimental results available are given.