# # CDDL HEADER START # # The contents of this file are subject to the terms of the Common Development # and Distribution License Version 1.0 (the "License"). # # You can obtain a copy of the license at # http://www.opensource.org/licenses/CDDL-1.0. See the License for the # specific language governing permissions and limitations under the License. # # When distributing Covered Code, include this CDDL HEADER in each file and # include the License file in a prominent location with the name LICENSE.CDDL. # If applicable, add the following below this CDDL HEADER, with the fields # enclosed by brackets "[]" replaced with your own identifying information: # # Portions Copyright (c) [yyyy] [name of copyright owner]. All rights reserved. # # CDDL HEADER END # # # Copyright (c) 2018, Regents of the University of Minnesota. # # Contributors: # Mingjian Wen # This directory contains Stillinger-Weber (SW) potential Model Driver for multiple species. 1. Use of a subset of all the supported species is valid. For example, if the model supports 3 species A, B, and C as listed in the parameter file, the use of a single species A (or B or C) or two species A and B (or A and C, or B and C) are valid. 2. The functional form has been rewritten from the standard SW functional form so as to separate the parameters to avoid inconvenience of using this Model Driver. The variable 'epsilon' in the standard SW potential is a dummy variable, so it is combined with 'A' and 'lambda'. The 'cutoff' of the standard SW potential is determined implicitly by 'cutoff' = 'a*sigma', where 'a' and 'sigma' are potential parameters. In this Model Driver, the 'cutoff' is defined explicitly. The benefit is that if 'sigma' is updated there is no need to update 'cutoff'. Above all, compared to the standard SW potential, the following redefinitions have been made: A := A*epsilon lambda := lambda*epsilon gamma := gamma*sigma cutoff := a*sigma Besides, the three-body parameter 'lambda' follows the below mixing rule: lambda_ijk = sqrt(lambda_ij*lambda_ik) Finally, it is assumed that the angle 'theta0' is the same for all three-body interactions. Consequently, the SW Driver for multiple species can be written as: E = sum_{i,j>i} phi_2(rij) + sum_{i, j!=i, k>j} phi_3(rij, rik, theta) phi_2(rij) = Aij*(Bij(rij/sigma_ij)^(-p) - (rij/sigma_ij)^(-q)) * exp(sigma_ij/(rij - cutoff_ij)) phi_3(rij,rik,theta) = sqrt(lambda_ij*lambda_ik)(cos[theta] - cos[theta0])^2 * exp(gamma_ij/(rij - cutoff_ij) + gamma_ik/(rik - cutoff_ik)) 3. One parameter file is needed, and it follows the format: first line: number of species Then each line lists two species and 9 parameters for the interaction between the two species: species1 species2 A B p q sigma lambda gamma costheta_0 cutoff where, species1 and species2 are valid KIM API particle species string; A and lambda in [eV]; sigma, gamma, and cutoff in [Angstrom]; others are unitless. References: 1. F. H. Stillinger and T. A. Weber, "Computer simulation of local order in condensed phases of silicon", Phys. Rev. B, vol. 31, 5262-5271, 1985. 2. Ellad B. Tadmor and Ronald E. Miller, Modeling Materials: Continuum, Atomistic and Multiscale Techniques, Cambridge University Press, 2011. 3. X. W. Zhou, D. K. Ward, and J. E. Martin, et al, "Stillinger-Weber potential for the II-VI elements Zn-Cd-Hg-S-Se-Te" Phys. Rev. B, 88, 085309, 2013.