Stability of amorphous structures with voids

We consider the stability of an amorphous solid state allowing the presence of holes in the structure. We use the density functional method for computing the free energy of the inhomogeneous metastable liquid. For a one component Lennard-Jones liquid we consider here the nature of the amorphous structure which are thermodynamically more favourable compared to the homogeneous liquid state. We explore here the nature of the heterogeneous state described by overlapping density profiles as compared to the strongly localized crystalline structure.