  Quasiperiodic tilings are often considered as structure models of
quasicrystals. In this context, it is important to study the nature of the
diffraction measures for tilings. In this article, we investigate the
diffraction measures for S-adic tilings in R^d, which are constructed from a
family of geometric substitution rules. In particular, we firstly give a
sufficient condition for the absolutely continuous component of the diffraction
measure for an S-adic tiling to be zero. Next, we prove this sufficient
condition for "almost all" binary block-substitution cases and thus prove the
absence of the absolutely continuous diffraction spectrum for most of the
S-adic tilings from a family of binary block substitutions.
