  The compounds Sr$_{3}$Cr$_{2}$O$_{8}$ and Ba$_{3}$Cr$_{2}$O$_{8}$ are
insulating dimerized antiferromagnets with Cr$^{5+}$ magnetic ions. These
spin-$\frac{1}{2}$ ions form hexagonal bilayers with a strong intradimer
antiferromagnetic interaction, that leads to a singlet ground state and gapped
triplet states. We report on the effect on the magnetic properties of
Sr$_{3}$Cr$_{2}$O$_{8}$ by introducing chemical disorder upon replacing Sr by
Ba. Two single crystals of Ba$_{3-x}$Sr$_{x}$Cr$_{2}$O$_{8}$ with $x=2.9$
(3.33\% of $mixing$) and $x=2.8$ (6.66\%) were grown in a four-mirror type
optical floating-zone furnace. The magnetic properties on these compounds were
studied by magnetization measurements. Inelastic neutron scattering
measurements on Ba$_{0.1}$Sr$_{2.9}$Cr$_{2}$O$_{8}$ were performed in order to
determine the interaction constants and the spin gap for $x=2.9$. The
intradimer interaction constant is found to be $J_0$=5.332(2) meV, about 4\%
smaller than that of pure Sr$_{3}$Cr$_{2}$O$_{8}$, while the interdimer
exchange interaction $J_e$ is smaller by 6.9\%. These results indicate a
noticeable change in the magnetic properties by a random substitution effect.
