Abstract

In this chapter, we present a finite temperature quasicontinuum method for 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 finite temperature 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 quantum-mechanical lattice dynamics. We describe three quasiharmonic models, namely the real space quasiharmonic model (QHM), the local quasiharmonic model (LQHM), and the reciprocal space quasiharmonic model (QHMK), to compute the vibrational free energy. We also describe a QHMG approach - where the quasiharmonic approximation is combined with the local phonon density of states (LPDOS). The LPDOS is efficiently calculated from the phonon Green's function (GF) by using a recursion method.

Original languageEnglish (US)
Title of host publicationMultiscale Methods
Subtitle of host publicationBridging the Scales in Science and Engineering
PublisherOxford University Press
Volume9780199233854
ISBN (Electronic)9780191715532
ISBN (Print)9780199233854
DOIs
StatePublished - Oct 1 2009

Fingerprint

Multiscale Methods
Finite Temperature
Silicon
Phonon
Free Energy
Hermann Von Helmholtz
Density of States
Energy Density
Lattice Dynamics
Interatomic Potential
Multiscale Analysis
Continuum Mechanics
Classical Mechanics
Nanostructures
Recursion
Model
Green's function
Approximation

Keywords

  • Finite temperature
  • LQHM
  • QHM
  • QHMK
  • QHMK
  • Quasicontinuum method
  • Silicon
  • Tersoff potential

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Tang, Z., & Aluru, N. R. (2009). Finite Temperature Multiscale Methods for Silicon NEMS. In Multiscale Methods: Bridging the Scales in Science and Engineering (Vol. 9780199233854). Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199233854.003.0013

Finite Temperature Multiscale Methods for Silicon NEMS. / Tang, Z.; Aluru, Narayana R.

Multiscale Methods: Bridging the Scales in Science and Engineering. Vol. 9780199233854 Oxford University Press, 2009.

Research output: Chapter in Book/Report/Conference proceedingChapter

Tang, Z & Aluru, NR 2009, Finite Temperature Multiscale Methods for Silicon NEMS. in Multiscale Methods: Bridging the Scales in Science and Engineering. vol. 9780199233854, Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199233854.003.0013
Tang Z, Aluru NR. Finite Temperature Multiscale Methods for Silicon NEMS. In Multiscale Methods: Bridging the Scales in Science and Engineering. Vol. 9780199233854. Oxford University Press. 2009 https://doi.org/10.1093/acprof:oso/9780199233854.003.0013
Tang, Z. ; Aluru, Narayana R. / Finite Temperature Multiscale Methods for Silicon NEMS. Multiscale Methods: Bridging the Scales in Science and Engineering. Vol. 9780199233854 Oxford University Press, 2009.
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