Heat capacity of layer lattice

(a) Consider a dielectric crystal made up of layers of atoms, with rigid coupling between layers so that the motion of the atoms is restricted to the plane of the layer, Show that the phonon heat capacity in the Debye approximation in the low temperature limit is proportional to T².

(b) Suppose instead, as in many layer structures, that adjacent layers arc very weakly bound to each other. What form would you expect the phonon heat capacity to approach at extremely low temperatures?