I will review our recent attempts to understand the equilibrium and non-equilibrium behaviour of non-affine fluctuations in solids. We measure local non-affinity $\chi$ by a systematic coarse graining of microscopic atomic displacements. This generates a local elastic deformation tensor $D$ and the non-affinity as the extent to which the displacements are not representable as affine deformations of a reference crystal. We calculate the statistics of $\chi$ and $D$ and their spatio-temporal correlations for solids at low temperatures, within a harmonic approximation. The calculation allows us to identify the dominant non-affine fluctuation modes, which have an interpretation as precursors for the nucleation of lattice defects.

In a second part I describe a phase transition that results when total non-affinity is biased by an appropriate conjugate field, in a two-dimensional network solid. Monte Carlo simulations reveal that the network supports, apart from the homogeneous phase, a "pleated" phase that has stress localised in rows of pleats and eliminated from the rest of the lattice. The kinetics of the phase transition is extremely slow in molecular dynamics simulation near coexistence, due to very large free energy barriers. When the external field is increased beyond coexistence to lower these barriers, the network exhibits rich dynamic behaviour: it transforms into a metastable phase with the stress now localised in a disordered arrangement of pleats. The pattern of pleats shows ageing dynamics and slow relaxation to equilibrium. Our predictions should be amenable to experimental testing using tethered colloidal solids in dynamic laser traps.

References: Phys Rev E 87:042801, 2013; Soft Matter 11:4517, 2015; JSTAT P06025, 2015; arXiv:1612.00574