Mechanical and vibrational properties of network structures

We discuss how concepts from rigidity percolation can be used to understand the low frequency excitations and elastic properties of network glasses like Ge_xAs_ySe_1-x-t-y. When the mean coordination 〈r〉 = 2 + 2x + y is low, these materials are soft and their properties are strongly influenced by low frequency phonons. We use a bond depleted diamond lattice to mimic the coordination properties of the glass. We show that a model with only covalent forces is unstable for 〈rm〉 < 2.4, but can be stabilized by small additional forces. We calculate the elastic constants and the density of states as a function of 〈r〉. Despite the simplicity of the model, the rounded phase transition at 〈r> = 2.4 is consistent with recent experimental results involving ultrasonics and inelastic neutron scattering on Ge_xse_1-x glasses. The floppy modes, observed in inelastic neutron scattering, disappear as 〈r〉 increases from 2 up to around 2.4.