Alper Kinaci, Justin B. Haskins, Tahir \cCa\ug\in
In systems evolving under classical dynamics, using Einstein relation is one
method to calculate lattice thermal conductivity. This method, in theory, is
equivalent to Green-Kubo approach and it does not require a derivation of an
analytical form for the heat current. However, in application of Einstein
relation to molecular dynamics (MD), a discrepancy exists regarding the
calculation of the energy moment (inte- grated heat current) R. The classical
definition for the energy moment for a single particle is the total energy of
the particle multiplied by its unwrapped coordinate in simulation domain. The
total energy moment of the system is then calculated by summation over all
particles. With this formulation of R, Einstein relation gives incorrect
thermal conductivity (i.e. zero) for non-diffusive solid systems in MD under
periodic boundary conditions. In this paper, we propose a new formulation for R
that produces correct thermal conductivity and overcomes some of the
difficulties en- countered when calculating J. We apply it to solid argon and
silicon defined by two- and n-body interactions. For the silicon, we also
investigated the effect of porosity in the lattice. In accordance with the
experimental studies, we determined substantial reduction in thermal
conductivity as a consequence of porosity, internal surface area and the
existence of surface surface rattlers.
View original:
http://arxiv.org/abs/1201.6684
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