Classical density functional theory and the phase-field crystal method using a rational function to describe the two-body direct correlation function

N. Pisutha-Arnond, V. W. L. Chan, M. Iyer, V. Gavini, and K. Thornton

Phys. Rev. E 87, 013313 – Published 30 January 2013

Abstract

We introduce a new approach to represent a two-body direct correlation function (DCF) in order to alleviate the computational demand of classical density functional theory (CDFT) and enhance the predictive capability of the phase-field crystal (PFC) method. The approach utilizes a rational function fit (RFF) to approximate the two-body DCF in Fourier space. We use the RFF to show that short-wavelength contributions of the two-body DCF play an important role in determining the thermodynamic properties of materials. We further show that using the RFF to empirically parametrize the two-body DCF allows us to obtain the thermodynamic properties of solids and liquids that agree with the results of CDFT simulations with the full two-body DCF without incurring significant computational costs. In addition, the RFF can also be used to improve the representation of the two-body DCF in the PFC method. Last, the RFF allows for a real-space reformulation of the CDFT and PFC method, which enables descriptions of nonperiodic systems and the use of nonuniform and adaptive grids.

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Received 6 July 2012

DOI:https://doi.org/10.1103/PhysRevE.87.013313

Authors & Affiliations

N. Pisutha-Arnond^1,*, V. W. L. Chan^1,†, M. Iyer^2,‡, V. Gavini^2,§, and K. Thornton^1,∥

¹Materials Science and Engineering Department, University of Michigan, Ann Arbor, Michigan, 48109, USA
²Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA

^*nirand@umich.edu
^†vicchan@umich.edu
^‡mrinal@umich.edu
^§vikramg@umich.edu
^∥kthorn@umich.edu

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Vol. 87, Iss. 1 — January 2013

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Physical Review E

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