A statistical mechanical theory for the origin of rigidity in crystalline solids

It is known that if local atomic rearrangements leading to exchange of neighbours are allowed, no crystalline solid can be rigid in the thermodynamic limit. We show that crystals loose rigidity as a consequence of a symmetry breaking, first order, phase transition at zero deformation [1]. The usual rigid, elastic, response to shape changes, a defining character of a crystalline solid, occurs because the time needed for such rearrangements diverge as the magnitude of deformation approaches zero. This picture gives us a fundamentally new viewpoint on the phenomenon of yielding, i.e. the loss of rigidity of a crystal when deformed beyond a limit, viz. the yield point. The phenomenon of yielding is now simply the nucleation of bubbles of the thermodynamically stable phase within the metastable, rigid crystal. An outcome of this theory is that the yield point is always a weak function of the rate of deformation and vanishes in the quasistatic and thermodynamic limits. The analytic form derived by us for the yield point as a function of the rate of deformation is able to explain experimental data over 15 orders of magnitudes in time [2]. Finite size effects, that are substantial, are also shown to be responsible for creating the illusion of a non-zero quasistatic yield point in small crystals. Finally these results can be understood within a Ginzburg Landau theory where lattice dislocations arise naturally at interfaces between rigid and stress free states.

1] P. Nath et al., Proc. Natl. Acad. Sci. USA 115, E4322 (2018).
[2] V. S. Reddy et al. Phys. Rev. Lett. 124, 025503 (2020).