The trigonal-field splitting of ${}_{}{}^2{}_{}{}^{}E$ into $\overline{E}$ and $2\overline{A}$ states is found to be $\overline{E}-2\mathrm{}\overline{A}=-120\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ by identifying $2\overline{A}$. The no-phonon lines of deuterated samples are isotope shifted 6 ${\mathrm{cm}}^{-1\mathrm{}}$ to the red. The following generalizations suffice to relate the spectra of the Cr-alums: (i) They are due to ${}_{}{}^4{}_{}{}^{}A_2^{}{}_{}{}^{}\to \overline{E}$, $2\overline{A}\left({}_{}{}^2{}_{}{}^{}E\right)$ transitions. The splitting of ${}_{}{}^2{}_{}{}^{}E$ is large for the $\beta$-alums, small for the $\alpha$-alums. (ii) Sulfate-group disorder, found in all $\alpha$-alums, complicates their spectra by adding inequivalent ${\mathrm{Cr}}^{3+}$ sites.

• Received 20 December 1971

DOI:https://doi.org/10.1103/PhysRevB.6.797