Exploring the link between crystal defects and non-affine displacement fluctuations

Abstract

We generalize, and then use, a recently introduced formalism to study thermal fluctuations of atomic displacements in several two and three dimensional crystals. We study both close packed as well as open crystals with multi atom bases. Atomic displacement fluctuations in a solid, once coarse-grained over some neighborhood may be decomposed into two mutually orthogonal components. In any dimension $d$ there are always $d^2$ {\em affine} displacements representing local strains and rotations of the ideal reference configuration. In addition, there exists a number of {\em non-affine} localized displacement modes that cannot be represented as strains or rotations. The number of these modes depends on $d$ and the size of the coarse graining region. All thermodynamic averages and correlation functions concerning the affine and non-affine displacements may be computed within a harmonic theory. We show that for compact crystals, such as the square and triangular in $d=2$ and the simple, body-centered and face-centered cubic crystals in $d=3$, a single set of $d-$fold degenerate modes always dominate the non-affine sub-space and are separated from the rest by a large gap. These modes may be identified with specific precursor configurations that lead to lattice defects. Deformation mechanisms such as lattice slips and stacking faults in close packed crystals can also be understood within this framework. The qualitative features of these conclusions are expected to be independent of the details of the atomic interactions.

References in corpus (19)

• Graphene: Status and Prospects
• Dynamics of Viscoplastic Deformation in Amorphous Solids
• Deformation and Failure of Amorphous Solidlike Materials
• Long-range strain correlations in sheared colloidal glasses
• Local inversion-symmetry breaking controls the boson peak in glasses and crystals
• Deformation of crystals: Connections with statistical physics
• Elastic properties of 2D colloidal crystals from video microscopy
• Local thermal energy as a structural indicator in glasses
• Direct observation of percolation in the yielding transition of colloidal glasses
• Microscopic origin of nonlinear non-affine deformation and stress overshoot in bulk metallic glasses
• Non-affine displacements in crystalline solids in the harmonic limit
• Do thermodynamically stable rigid solids exist?
• Strong long-range relaxations of structural defects in graphene simulated using a new semi-empirical potential
• Equilibrium and dynamic pleating of a crystalline bonded network
• A microscopic continuum model for defect dynamics in metallic glasses
• Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise
• Plastic deformation of a permanently bonded network: stress relaxation by pleats
• Translationally invariant colloidal crystal templates
• Dynamical solid-liquid transition through oscillatory shear

Cited by in corpus (4)

• A nucleation theory for yielding of nearly defect-free crystals: understanding rate dependent yield points
• Continuum mechanics for the elastic properties of crystals: Microscopic approach based on projection-operator formalism
• Pattern stabilisation in swarms of programmable active matter: a probe for turbulence at large length scales
• Elasticity in crystals with high density of local defects : insights from ultra-soft colloids