  First principles computations of Raman intensities were performed for
perovskite-family compound CaAl$_{1/2}$Nb$_{1/2}$O$_3$ (CAN). This compound
features 1:1 (NaCl-type) ordering of Al and Nb superimposed onto the $b^-b^-c+$
octahedral tilting. Raman tensor for CAN was computed using the package for
first-principles computations ABINIT (URL \underline {http://www.abinit.org}).
Computations performed for both untilted cubic ($Fm\bar{3}m$) and tilted
monoclinic ($P2_1/n$) CAN structures showed that the strongest Raman lines are
associated with the ordering of Al and Nb. The computed spectrum agreed
qualitatively with the experimental data measured on powder (CAN is available
in polycrystalline form only). The effect of cation disorder on the Raman
intensities was considered using phenomenological theory of light scattering in
the vicinity of a phase transition. We suggest that, for certain modes, the
corresponding Raman intensities depend primarily on the average long range
order while, for other modes, the intensities are determined by fluctuations of
the order parameter.
