Non-affine droplets and deformation of crystalline solids
Prof. Surajit Sengupta (S. N. Bose Centre, Kolkata)

Deformation, plasticity and failure of crystalline solids can be explained in terms of topological excitations viz. dislocations and disclinations. On the other hand, recently, there has been a lot of progress in our understanding deformation behavior of amorphous, glassy or soft solids in terms of droplet fluctuations, i.e. regions which are particularly amenable to local, "non-affine", deformations under the influence of external load. Such droplets have been variously christened as "Eshelby regions", "Cooperatively rearranging regions" or "Shear Transformation Zones". May the deformation behaviour in crystalline materials be similarly analyzed in terms of such droplet fluctuations? Such an alternate description, if it exists, will be useful because it may lead to a more general theory of deformation of solids applicable to both amorphous and crystalline substances as well as any intermediate structure.

In this talk we shall try to discover whether such a droplet description exist for a crystalline, single component, Lennard Jones solid in two dimensions. We analyze strain fluctuations within configurations in the solid phase and examine in detail ``extreme' particle displacements where the local topology undergoes change. Such ``non-affine' fluctuations are fairly common even at densities and temperatures where stable dislocation pairs may not exist. These non-affine deformations are seen to cluster into droplets, with the fraction of particles in the droplets increasing with lower mean solid density approaching 20% of the total number in the vicinity of the liquid-solid phase boundary. We monitor the geometry, local equation of state, density correlations, and Van Hove functions of these droplets. We provide evidence that these non-affine heterogeneities should be interpreted as being droplet fluctuations from nearby metastable minima. The local excess pressure of the droplets plotted against the local number density shows a van der Waals loop with distinct branches corresponding to liquid-like compact and string-like glassy droplets. The distinction between liquid-like and glassy droplets disappears above a well-defined temperature. When an external stress is imposed, the liquid-like droplets percolate for a value of stress lower than the yield point. The percolating droplets of large non-affine regions appear to be precursors of shear bands along which the solid begins to flow when stress finally exceeds the yield threshold. We identify the percolation of non-affine droplets with the onset of an-elasticity in the solid.

Reference 1) Tamoghna Das, Surajit Sengupta and Madan Rao, Phys. Rev. E, 82, 041115 (2010).