Elastic constants from microscopic strain fluctuations

Details Elastic constants from microscopic strain fluctuations Elastic constants from microscopic strain fluctuations

1999-06-04

arxiv.org/abs/cond-mat/9906063v2

Physics

Condensed Matter

24 pages REVTEX, 10 .ps figures, version accepted for publication in Physical Review E

Scientific paper

10.1103/PhysRevE.61.1072

Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $<\epsilon_{ij}\epsilon_{kl}>$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general enough to be able to handle a wide class of model systems including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of the ``soft'' and the hard disk triangular solids in two dimensions from molecular dynamics and Monte Carlo simulations. We compare our results with those from earlier simulations and density functional theory.

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