Abstract

Random networks (e.g. actin networks) and disordered condensed matter (e.g. glasses) cannot be described by standard lattice dynamics concepts, due to the lack of periodicity of the lattice. We contributed to develop a formalism which extends lattice dynamics to aperiodic solids, including glasses (e.g. metallic glasses), by building on the key concept of nonaffine displacements. Atoms in a perfect centro-symmetric crystals are local centers of inversion symmetry. In disordered and defective lattices, this is no longer true. This simple symmetry consideration has huge implications for the dynamics: under an applied deformation field, forces received by a test atom from its neighbours cannot cancel by symmetry in the displaced position prescribed by the deformation tensor. Hence, the atomic displacement cannot be a simple affine transformation, but necessarily implies extra displacements necessary to keep mechanical equilibrium which are called non-affine displacements [1]. Implementing this basic fact in lattice dynamics leads to a number of predictions which can explain various anomalous features in: the elastic constants [2], the glass-liquid transition [3], the vibrational density of states and low-T specific heat of glasses [4], the non-linear deformation and yielding of glasses [5].

[1] A. Zaccone & E. Scossa-Romano, Phys. Rev. B 83 , 184205 (2011). [2] A. Zaccone & E.M. Terentjev, J. Appl. Phys. 115, 033510 (2014). [3] A. Zaccone & E. Terentjev, Phys. Rev. Lett. 110, 178002 (2013). [4] R. Milkus & A. Zaccone, Phys. Rev. B 93 , 094204 (2016). [5] A. Zaccone, P. Schall, E. M. Terentjev, Phys. Rev. B 90 , 140203® (2014).