Molecular Dynamics Simulation of Linear Harmonic Lattices at Finite Temperature

LIU Bai-yi-li; TANG Shao-qiang

doi:10.3879/j.issn.1000-0887.2015.01.005

Volume 36 Issue 1

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(1): 61-69

LIU Bai-yi-li, TANG Shao-qiang. Molecular Dynamics Simulation of Linear Harmonic Lattices at Finite Temperature[J]. Applied Mathematics and Mechanics, 2015, 36(1): 61-69. doi: 10.3879/j.issn.1000-0887.2015.01.005

Citation:

PDF( 2192 KB)

Molecular Dynamics Simulation of Linear Harmonic Lattices at Finite Temperature

doi: 10.3879/j.issn.1000-0887.2015.01.005

CAPT of Peking University; College of Engineering, Peking University, Beijing 100871, P.R.China

Funds: The National Natural Science Foundation of China(11272009)

Received Date: 2014-09-24
Rev Recd Date: 2014-11-02
Publish Date: 2015-01-15

Abstract

Abstract

A heat jet approach for atomic simulation at finite temperature in both local space and time was proposed based on the 2-way boundary condition and phonon heat bath, without any dissipation factor and empirical parameter introduced. A subsystem was extracted from a space lattice for analysis of the exact molecular dynamics lest the entire lattice was to be solved numerically. For an extracted linear harmonic chain, the 2-way boundary condition allowed effective incoming waves fully enter the subsystem, and meanwhile, non-thermal motion and thermal fluctuation propagate freely out of the subsystem, to realize dynamic equilibrium of the system energy. During numerical calculation, the 2-way boundary condition worked like a wave diode which let in the positive-going waves while keeping out the negative-going ones. The normal mode of phonon heat bath well described the atomic heat vibration, then it was decoupled into positive-going and negative-going input waves of which the former was used to build the heat source term. For the molecular dynamics simulation of linear harmonic chains, the numerical tests demonstrate effectiveness of the proposed heat jet approach, which makes the chain rapidly reach the expectant temperature, keeps it in a steady state thereafter, and reasonably depicted the additional non-thermal atomic motion at finite temperature.
- heat jet,
- finite temperature,
- atomic simulation,
- harmonic lattice

FullText(HTML)

References(15)

References

[1]	Liu W K, Karpov E G, Park H S.Nano Mechanics and Materials: Theory, Multi-Scale Methods and Applications[M]. John Wiley & Sons, Ltd, 2006.
[2]	Dupuy L M, Tadmor E B, Miller R E, Phillips R. Finite-temperature quasicontinuum: molecular dynamics without all the atoms[J].Phys Rev Lett,2005,95(6): 060202.
[3]	Mathew N, Picu R C, Bloomfield M. Concurrent coupling of atomistic and continuum models at finite temperature[J].Computer Methods in Applied Mechanics and Engineering,2011,200(5/8): 765-773.
[4]	XIANG Mei-zhen, CUI Jun-zhi, LI Bo-wen, TIAN Xia. Atom-continuum coupled model for thermo-mechanical behavior of materials in micro-nano scales[J].Science China: Physics, Mechanics & Astronomy,2012,55(6): 1125-1137.
[5]	Jiang H, Huang Y, Hwang K C. A finite-temperature continuum theory based on interatomic potentials[J].Journal of Engineering Materials and Technology,2005,127(4): 408-416.
[6]	Lepri S, Livi R, Politi A. Thermal conduction in classical low-dimensional lattices[J].Physics Reports,2003,377(1): 1-80.
[7]	Berendsen H J C, Postma J P M, Van Gunsteren W F, DiNola A, Haak J R. Molecular dynamics with coupling to an external bath[J].The Journal of Chemical Physics,1984,81(8): 3684-3690.
[8]	Bussi G, Parrinello M. Accurate sampling using Langevin dynamics[J].Physical Review E,2007,75: 056707.
[9]	Andersen H C. Molecular dynamics simulations at constant pressure and/or temperature[J].The Journal of Chemical Physics,1980,72(4): 2384-2393.
[10]	Nosé S. A unified formulation of the constant temperature molecular dynamics methods[J].The Journal of Chemical Physics,1984,81(1): 511-519.
[11]	Hoover W G. Canonical dynamics: equilibrium phase-space distributions[J].Physical Review A,1985,31: 1695.
[12]	Karpov E G, Park H S, Liu W K. A phonon heat bath approach for the atomistic and multiscale simulation of solids[J].International Journal for Numerical Methods in Engineering,2007,70(3): 351-378.
[13]	Wang X, Tang S. Matching boundary conditions for lattice dynamics[J].International Journal for Numerical Methods in Engineering,2013,93(12): 1255-1285.
[14]	TANG Shao-qiang. A two-way interfacial condition for lattice simulations[J].Adv Appl Math Mech,2010,2(1): 45-55.
[15]	Born M, Huang K.Dynamical Theory of Crystal Lattices [M]. Oxford: Clarendon, 1954.