Title:	Nonaffine displacements in crystalline solids in the harmonic limit
Authors:	Ganguly, Saswati Sengupta, Surajit Sollich, Peter Rao, Madan
Keywords:	Elasticity Glasses amorphous solids General theory
Issue Date:	Apr-2013
Publisher:	American Physical Society
Citation:	Physical Review E, 2013, Vol.87, p042801
Abstract:	A systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor D as well as a positive definite scalar χ measuring nonaffinity, i.e., the extent to which the displacements are not representable as affine deformations of a reference crystal. We perform an exact calculation of the statistics of χ and D and their spatial correlations for solids at low temperatures, within a harmonic approximation and in one and two dimensions. We obtain the joint distribution P(χ,D) and the two-point spatial correlation functions for χ and D. We show that nonaffine and affine deformations are coupled even in a harmonic solid, with a strength that depends on the size of the coarse-graining volume Ω and dimensionality. As a corollary to our work, we identify the field hχ conjugate to χ and show that this field may be tuned to produce a transition to a state where the ensemble average <χ> and the correlation length of χ diverge. Our work should be useful as a template for understanding nonaffine displacements in realistic systems with or without disorder and as a means for developing computational tools for studying the effects of nonaffine displacements in melting, plastic flow, and the glass transition.
Description:	Open Access.
URI:	http://hdl.handle.net/2289/5556
ISSN:	1539-3755 1550-2376 (Online)
Alternative Location:	http://dx.doi.org/10.1103/PhysRevE.87.042801 http://adsabs.harvard.edu/abs/2013PhRvE..87d2801G http://arxiv.org/abs/1212.6377
Copyright:	2013 American Physical Society
Appears in Collections:	Research Papers (TP)

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