Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels

Abstract

Abstract.Although the intellectual merits of computational modelling across various length and time scales are generally well accepted, good illustrative examples are often lacking. One way to begin appreciating the benefits of the multiscale approach is to first gain experience in probing complex physical phenomena at one scale at a time. Here we discuss materials modelling at two characteristic scales separately, the atomistic level where interactions are specified through classical potentials and the electronic level where interactions are treated quantum mechanically. The former is generally sufficient for dealing with mechanical deformation at large strain, whereas the latter is necessary for treating chemical reactions or electronic transport. We will discuss simulations of defect nucleation using molecular dynamics, the study of water-silica reactions using a tight-binding approach, the design of a semiconductor-oxide interface using density functional theory, and the analysis of conjugated polymer in molecular actuation using Hartree-Fock calculations. The diversity of the problems discussed notwithstanding, our intent is to lay the groundwork for future problems in materials research, a few will be mentioned, where modelling at the electronic and atomistic scales are needed in an integrated fashion. It is in these problems that the full potential of multiscale modelling can be realized.Mathematics Subject Classification. 74A25, 74A45, 74F25, 74M05, 81V55.

Revisiting quantum notions of stress

“…Multi-scale modelling techniques aim to identify the multiple natural length and time scales in a phenomenon and to transfer information across them in a seamless fashion (see the following representative articles: Li et al 1998;Miller & Tadmor 2002, 2007Curtin & Miller 2003;Park & Liu 2004;Liu et al 2006;Gavini et al 2007;Silva et al 2007;Kulkarni et al 2008;and references therein). This often requires reconciling the atomistic notions that represent the true mechanistic underpinnings behind a process, with coarse-grained (including continuum) ideas that serve to capture the essential physics in a phenomenological manner.…”

An energy-based method in phenomenological description of mechanical properties of nonlinear materials under plane stress

“…The knowledge about mechanisms of deformation under the influence of external loads and the relations between them can be very important in the design process. There is a lot of publications devoted to the modelling of mechanical properties based both on the ground of microstructure relations in the material (multi-scale modelling methods), see for example Silva et al (2007), Terada et al (2008), Speirs et al (2008), or on a phenomenological concept, see for example Wegner (2000Wegner ( , 2005. Because we consider mechanical properties on the base of a real experiment in which the object (material sample) and measured properties are usually in macro-scale, so using the phenomenological method as the way of modelling of the process, which is directly connected with the experiment, is recommended.…”

Material Characterization of Single Crystalline Cu Subjected to High Strain Rates and High Temperatures for Multiscale Simulation

“…Furthermore, nanoscale studies are considered as a useful way of approaching multiscale simulation to identify material properties across various ranges of length and time scales [4,[10][11][12]. Silva et al [12] discussed diverse problems to [13] used a hybrid simulation method using quantummechanical derivations with molecular dynamics simulations, in which they used hand-shaking algorithms between the finite-element and MD regions, and between MD and the quantum tight-binding regions.…”