Elasticity in crystals with a high density of local defects: Insights from ultra-soft colloids

Abstract

In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a microscopic basis to include and account for the motion of point defects in an otherwise ordered crystalline structure. We study the elastic properties of a point-defect rich crystal within a first principles theoretical framework derived from the microscopic equations of motion. This framework allows us to make specific predictions pertaining to the mechanical properties that we can validate through deformation experiments performed in molecular dynamics simulations.

Continuum mechanics for the elastic properties of crystals: Microscopic approach based on projection-operator formalism

“…τ α (q) at q → 0, on the other hand, has symmetries similar to the generalised elastic constant µ α (q) which is associated [11] with the coupling between the coarse-grained density δn and displacement fields δu α in a defect rich crystal; the symmetery holds τ αβ = τ βα , as can be shown with the rotational LMBW equation [11,27,28]. As we show in the Appendix C 1, the elastic coefficients λ αβ , µ α and ν are the same as the ones in [10,11,14] and in the hydrodynamic limit, they become…”

“…Moreover, the components J gg ′ can be obtained from the direct correlation function c(r 1 , r 2 ). Previous works [11,14] by the authors, explored this connection in great detail and here we present these relations for the sake of completeness.…”

“…Appendix C summarises their microscopic definitions for the sake of completeness. References [10,11,14] present these important mechanical properties and by detailing their relation to the inverse density correlation matrix (Eq. (2.23)), show ways of determining them in crystalline solids with local defects.…”

“…Cluster crystals are defect-rich crystals, where an inhomogeneously distributed number of soft particles occupies lattice sites [12,13]. An extensive examination of the elastic properties of the same cluster crystals, taken up by Ganguly et al [14], infers how local disorder quantitatively impacts mechanical response. The perspective for the elasticity of hard-sphere crystals, presented by Lin et al [15] highlights the influence of microscopic interactions and direct correlations on the thermo-mechanics.…”

“…Finally, an alternative and equivalent approach has been presented by Mabillard and Gaspard [19,20]. Their approach, unlike [4,5,10,11,[14][15][16][17], avoids the explicit use of projection operators.…”