  A wide variety of morphologies arise due to the tetragonal anisotropy in
interfacial free energy. In this paper, we report on a family of Extended
Cahn-Hilliard (ECH) models for incorporating tetragonal anisotropy in
interfacial free energy. We list the non-zero and independent parameters that
are introduced in our model and list the constraints on them. For appropriate
choice of these parameters, our model can produce a many of the morphologies
seen in tetragonal systems such as di-pyramids, rods, plates and their
truncated variants. We analyse these morphologies and show that they indeed are
equilibrium morphologies consistent with the Wulff construction.
