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# Copyright (c) 2012, Regents of the University of Minnesota. All rights reserved.
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# Contributors:
# Ryan S. Elliott
# Ellad B. Tadmor
# Valeriu Smirichinski
# Amit Singh
This directory (Three_Body_Stillinger_Weber_Si__MO_405512056662_001) contains the Stillinger-Weber potential
Model based on the KIM Model Driver Three_Body_Stillinger_Weber. This Model
implements the Stillinger-Weber potential for Si.
The following files are in this directory:
LICENSE.CDDL
The Common Development and Distribution License (CDDL) Version 1.0 file
Makefile
makefile to compile and build the Model based on the specified KIM Model
Driver
README
This file
Three_Body_Stillinger_Weber_Si.params
Parameters file providing the Stillinger-Weber parameters for Si
This file must have the follwing format:
Line 1: A
Line 2: B
Line 3: p
Line 4: q
Line 5: a
Line 6: lambda
Line 7: gamma
Line 8: sigma in Angstrom
Line 9: epsilon in ev
Line 10: costheta_0
Any additional lines will be silently ignored.
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
Description:
/*******************************************************************************
* For three-body potential any potential energy function for N-particle system can be written in the
* following form of two-body and three-body terms:
F(1, 2, ...., N) = sum_{i; 1 <= i < j <= N} phi_two(r; r = r_ij)
+ sum_{i; 1 <= i \neq j < k <= N} phi_three(r_ij, r_ik, r_jk);
* For Stillinger-Weber, two-body term phi_two is
phi_two(r) = epsilon * f_2(r_cap; r_cap = r/sigma); where f_2 is
f_2(r_cap) = A * ( B*r_cap^(-p) - r_cap^-q ) * exp(1/(r_cap - a)); when r_cap < a
= 0 when r_cap >= a
* and three-body term phi_three is
phi_three(r_ij, r_ik, r_jk) = epsilon * f_3(r1_cap, r2_cap, r3_cap); where
r1_cap = r_ij/sigma, r2_cap = r_ik/sigma, r3_cap = r_jk/sigma, and
f_3(r1_cap, r2_cap, r3_cap) = lambda * (exp(gamma((1/(r1_cap - a)) + (1/(r2_cap - a))))) * (costheta_jik - costheta_0)^2; when r1_cap < a && r2_cap < a
= 0; otherwise
costheta_jik = (r_ij^2 + r_ik^2 - r_jk^2) / (2*r_ij*r_ik).
*******************************************************************************/