  Morphologies in phase separating systems can significantly influence the
final properties of materials. We present extensive Monte Carlo (MC) simulation
results on the segregation kinetics of the critical binary (AB) mixture with a
fraction of bond disorder (BD) introduced in a regular manner. We focus on
studying the effect of various quench temperatures on the growth kinetics and
scaling properties of evolving morphologies. The two-dimensional (2d) kinetic
Ising system with conserved spin exchange kinetics is used to model the system.
We observe that domain morphologies change from their usual interconnected
bicontinuous isotropic patterns at zero BD to short strips and lamellar
patterns (anisotropy) with increasing BD at shallow quench. The domain
evolution remains extremely slow at deep quench and for lower fractions of BD,
and thus, morphologies appear very similar; however, we observed lamellar
patterns at high BD. The scaling behavior represented by the correlation
function and the structure factor changes significantly with quench depths for
a higher fraction of BD. In contrast, a tiny deviation from the scaling is
observed at a lower fraction of disorder for shallow quenches. The growth law
is consistent with the Lifshitz-Slyozov (LS) growth law (\phi->1/3) for shallow
quench and at low fractions of BD studied here. At a high fraction of BD, the
length scale crossovers gradually from an early time LS growth to the diffusion
dynamics (\phi->1/2) during intermediate times for both deep and shallow
quenches. The domain growth freezes (\phi->0) to a finite size when the system
evolves to an equilibrium (stable) lamellar morphology in the asymptotic time
limit on the time scale of our simulation. However, no significant changes are
observed in the scaling behavior at lower fractions of BD for the deep quench.
