 
Summary: Finitetemperature quasicontinuum method for multiscale analysis of silicon nanostructures
Z. Tang, H. Zhao, G. Li, and N. R. Aluru
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology,
University of Illinois at UrbanaChampaign, Illinois 61801, USA
Received 22 December 2005; revised manuscript received 1 April 2006; published 23 August 2006
In this paper, we extend the quasicontinuum approach for a multiscale analysis of silicon nanostructures at
finite temperature. The quasicontinuum method uses the classical continuum mechanics framework, but the
constitutive response of the system is determined by employing an atomistic description. For finitetemperature
solid systems under isothermal conditions, the constitutive response is determined by using the Helmholtz free
energy density. The static part of the Helmholtz free energy density is obtained directly from the interatomic
potential while the vibrational part is calculated by using the theory of quantummechanical lattice dynamics.
Specifically, we investigate three quasiharmonic models, namely the real space quasiharmonic model, the local
quasiharmonic model, and the reciprocal space quasiharmonic model, to compute the vibrational free energy.
Using the finitetemperature quasicontinuum method, we compute the effect of the temperature and strain on
the phonon density of states, phonon Grüneisen parameters, and the elastic properties of the Tersoff silicon. We
also compute the mechanical response of silicon nanostructures for various external loads and the results are
compared to molecular dynamics simulations.
DOI: 10.1103/PhysRevB.74.064110 PACS number s : 46.15. x, 62.25. g, 02.70. c
I. INTRODUCTION
Rapid advances in nanotechnology have led to the fabri
