  We present a model for a class of random binary lattices by introducing a
one-dimensional system where impurities are placed in one sublattice while host
atoms lie on the other sublattice. The source of disorder is the stochastic
fluctuation of the impurity energy from site to site. We study the optical
absorption spectra and the peculiarities of the motional narrowing effect at
the band edges for perturbative and nonperturbative degrees of disorder.
Analytical results agree well with numerical simulations.
