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Statistical Physics Group

Lattice dynamics and bosonic excitations in glasses and disordered crystals

We recently settled a long-standing debate about the structural origin of the low-frequency excess of vibrational excitations in the phonon density of states of disordered solids widely known as the boson peak. Using numerical diagonalization of model systems of glasses and defective crystals, we showed that the atomic-level structural origin of this effect is not due to bond-orientational disorder (which is a measure of the spread in the angular orientations of bonds in solids) as was believed so far, but is due instead to a more subtle form of disorder, which is the lack of local inversion-symmetry on a given atom of an amorphous solid. This breaking of point-group symmetry is intimately related to the concept of nonaffine motions (see the section below on mechanical response) and a new order parameter based on local inversion symmetry can be shown to correlate strongly with the boson peak as a function of the atomic connectivity (mean number of nearest-neighbours) Z. In defective crystals with point defects or randomly-cut bonds, bond-orientational disorder is absent, whereas local inversion symmetry is broken around the point defects. The density of states (shown below, normalized by the Debye law) is however exactly the same for random networks (RN) with strong bond-orientational disorder and for defective crystals (FCC) with perfect bond-orientational order at all values of atomic connectivity Z, while both systems are affected by breaking of local inversion symmetry.


Our results also show that the van Hove singularities which appear at the pseudo-Brillouin zone boundaries cannot contribute significantly to the boson peak because they contribute distinct peaks at much higher frequencies than the boson peak.

More information can be found in R. Milkus and A. Zaccone, Phys. Rev. B 93, 094204 (2016).

Amorphous solids: multi-scale mechanical response and the glass transition

The mechanical response of disordered solids is governed by nonaffine displacements which are controlled by the microscopic atomic-level structure of the solid.


While the atoms in a liquid move fast and can explore all the available space, atoms in the glass (amorphous solid) are confined to a "cage" made by their nearest neighbours, and one needs to spend a lot more energy to displace them from their "cages". However, the random arrangement has a subtle implication for the rigidity of glass with respect to crystal, and for the way a glass deforms, or moves, when you apply a force on it. Upon applying a force on the crystal, every atom receives the same forces from its neighbours, but these forces cancel to zero because every atom has a mirror-image of itself across the center which is exerting the same force in the opposite direction. These forces then cancel themselves out completely in a crystal, but they cannot in a glass because there is no mirror-image atoms to cancel the force exerted by the neighbours. More details in A. Zaccone & E. Scossa-Romano, Phys. Rev. B 83, 184205 (2011). In this paper we provide the microscopic derivation of the scaling G~(z-2d) found in jammed packings, from the first principles analysis of nonaffine deformations.

Based on the nonaffine mechanical response, a mathematical theory of the glass transition in terms of macroscopic behavior can be formulated. The theory predicts the elastic constant using structural data as input (e.g. the structure factor from scattering experiments).


More details in A. Zaccone & E.M. Terentjev, Phys. Rev. Lett. 110, 178002 (2013).

Biomolecular self-assembly across multiple length-scales

We are interested in developing a theoretical framework to link the level of single protein conformation with the level of aggregate morphology and growth.


Several proteins may aggregate in superstructures as they undergo conformational changes (unfolding or partial unfolding). These superstructures are linked with diseases such as Alzheimer's, and they typically occur in fibrillar (right), spherulitic (center), or amorphous (left) form. Our goal is to mathematically predict these different morphologies depending on molecular level (single protein) processes in solution, through a multi-fractal approach first proposed in V. Fodera', A. Zaccone, M. Lattuada, A. Donald, Phys. Rev. Lett. 111, 108105 (2013).


List of publications