Description:

Abstract: While classical elasticity theory describes the mechanical deformation of solids without any reference whatsoever to the atomic constituents of matter, modern lattice dynamics provides quantitative ways to compute elastic constants in terms of atomic-scale configurations and interactions. Within this framework, the fundamental problem is reduced to evaluating forces and configurations in MD simulations. Nonetheless, for real solids (incl. crystals with defects and grain boundaries, non-centrosymmetric crystals, heated crystals, glasses), the elasticity is dominated by relaxational atomic motions that are not included in standard (Born-Huang) lattice dynamics [1-4]. These atomic motions are referred to, in the current literature, as “nonaffine motions”: they are associated with incompatible deformations, and are ubiquitous in real-life materials. In general, since they stem from the relaxation of local interatomic forces due to the lack of inversion symmetry, the nonaffine motions are linked to a significant decrease (softening) of the elastic constants, in particular the shear modulus. For example, nonaffine motions can quantitatively explain the mechanics of diverse systems such as the jamming transition and marginal elasticity of granular packings [2] as well as the experimentally observed elastic constants of α-quartz [3]. Nonaffine motions can also explain the frequency-dependent viscoelasticity of  disordered materials such as polymer glass [4]. This is because, on long time scales, the relaxational nonaffine motions dominate the mechanical response (the zero-frequency plateau modulus), whereas, at high external oscillation frequencies, they become gradually less significant compared to the affine or Born modulus. A recent atomistic implementation of this principle, called NALD (Nonaffine Lattice Dynamics), provides a new way to solve the time-scale bridging problem of materials mechanics [5,6], whereby traditional atomistic MD simulations are strongly limited by the simulation time-step, and its predictions are confined to deformation frequencies/time-scales that are too high to be accessible experimentally. Because NALD leverages the direct diagonalization of the Hessian matrix of the solid, it is perfectly feasible for the atomic-level description of the mechanical properties of nanostructured materials, in combination with the state of the art in interatomic forces and interactions. Finally, NALD also provides a way to quantitatively define topological defects in glassy materials akin to dislocations in crystals [7]. These well-defined topological defects have recently been observed experimentally for the first time in glasses [8] and are potentially the game changer for the hitherto elusive mechanism of plastic deformation and failure of glassy materials [9].

[1] J. C. Slonczewski and H. Thomas, Phys. Rev. B 1, 3599 (1970)

[2] A. Zaccone and E. Scossa-Romano, Phys. Rev. B 83, 184205 (2011)

[3] B. Cui, A. Zaccone, D. Rodney, J. Chem. Phys. 151, 224509 (2019)

[4] A. Zaccone “Theory of Disordered Solids”, Springer Monograph (2023)

[5] R. M. Elder, A. Zaccone, T. W. Sirk, ACS Macro Letters 8, 9, 1160–1165 (2019)

[6] V. Vaibhav, T. W. Sirk, A. Zaccone, Macromolecules 57, 23, 10885–10893 (2024)

[7] M. Baggioli, I. Kriuchevskyi, T. W. Sirk, A. Zaccone, Phys. Rev. Lett. 127, 015501 (2021)

[8] V. Vaibhav, A. Bera, A. C. Y. Liu, M. Baggioli, P. Keim & A. Zaccone, Nature Communications 16, 55 (2025)

[9] A. Bera, et al. PNAS Nexus, 3, 9, pgae315 (2024); A. Bera, A. Zaccone, M. Baggioli, https://arxiv.org/abs/2407.20631v1.

Alessio Zaccone received his Ph.D. from the Department of Chemistry of ETH Zurich in 2010. From 2010 till 2014 he was an Oppenheimer Research Fellow at the Cavendish Laboratory, University of Cambridge. After being on the faculty of Technical University Munich (2014–2015) and of University of Cambridge (2015–2018), he has been a full professor and chair of theoretical physics in the Department of Physics at the University of Milano. Awards include the ETH Silver Medal, the 2020 Gauss Professorship of the Göttingen Academy of Sciences, the Fellowship of Queens' College Cambridge, and an ERC Consolidator grant "Multimech". Research contributions include the exact solution to the jamming transition problem of granular matter (Zaccone & Scossa-Romano PRB 2011), the analytical solution to the random close packing problem in 2d and 3d (Zaccone PRL 2022), the theory of colloidal aggregation processes in shear flows (Zaccone et al PRE 2009), the theory of crystal nucleation under shear flow (Mura & Zaccone PRE 2016), the theoretical prediction of boson-like peaks in the vibrational spectra of crystals and glasses (Milkus & Zaccone PRB 2016; Baggioli & Zaccone PRL 2019), the molecular-level theory of the glass transition in polymers (Zaccone & Terentjev PRL 2013), the theoretical, computational and experimental discovery of topological defects in glasses (Baggioli, Kriuchevskyi, Sirk, Zaccone PRL 2021; Vaibhav et al. Nature Comm. 2025), and the theoretical predictions of superconductivity enhancement effects due to phonon anharmonicity (Setty, Baggioli, Zaccone PRB 2020) and thin-film confinement (Travaglino & Zaccone JAP 2023). Research interests range from the statistical physics of disordered systems (random packings, materials mechanics, granular packings, glasses and the glass transition, colloids, nonequilibrium thermodynamics) to solid-state physics and superconductivity.