Scaling up the lattice dynamics of amorphous materials by orders of magnitude

Abstract

We generalise the non-affine theory of viscoelasticity for use with large, well-sampled systems of arbitrary chemical complexity. Having in mind predictions of mechanical and vibrational properties of amorphous systems with atomistic resolution, we propose an extension of the Kernel Polynomial Method (KPM) for the computation of the vibrational density of states (VDOS) and the eigenmodes, including the $\Gamma$-correlator of the affine force-field, which is a key ingredient of lattice-dynamic calculations of viscoelasticity. We show that the results converge well to the solution obtained by direct diagonalization (DD) of the Hessian (dynamical) matrix. As is well known, the DD approach has prohibitively high computational requirements for systems with $N=10^4$ atoms or larger. Instead, the KPM approach developed here allows one to scale up lattice dynamic calculations of real materials up to $10^6$ atoms, with a hugely more favorable (linear) scaling of computation time and memory consumption with $N$.

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Cited by in corpus (8)

• Plasticity in amorphous solids is mediated by topological defects in the displacement field
• General theory of the viscosity of liquids and solids from nonaffine particle motions
• Linear Viscoelastic Response of the Vertex Model with Internal and External Dissipation: Normal Modes Analysis
• Predicting plasticity of amorphous solids from instantaneous normal modes
• Timescale bridging in atomistic simulations of epoxy polymer mechanics using non-affine deformation theory
• Ioffe-Regel criterion and viscoelastic properties of amorphous solids
• Hedgehog topological defects in 3D amorphous solids
• Geometric indicators of local plasticity in glasses measured by scanning small-beam diffraction