We investigate domain growth after a quench to the unstable region of the phase diagram on a lattice lacking translational invariance due to the presence of voids. The dynamical process is analyzed using a Ginzburg-Landau model with Langevin dynamics: studied numerically by means of a cell dynamical simulation in d = 2 for conserved order parameter at T-F = 0. We find that for short times ordering proceeds as on compact substrates (L(t) similar to t(1/3)); later on, when L(t) becomes comparable to the typical distance separating voids, coarsening occurs only via activated processes and for T-F = 0 the system Freezes out of equilibrium.