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# Copyright (c) 2012, Regents of the University of Minnesota.  All rights reserved.
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# Contributors:
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#    Valeriu Smirichinski
#    Amit Singh
#    Mingjian Wen


This directory contains the Balamane, Halicioglu and Tiller (1992) rescaling of the
Stillinger-Weber potential.

This Model implements the Stillinger-Weber (SW) potential for Si with a rescaled value
of epsilon parameter used in the SW potential. The original epsilon value was
2.1682 eV [Ref 1]. Balamane et al [Ref 2, 3] rescaled it to 2.315 eV so that
experimental cohesive energy E_coh = 4.63 eV can be obtained. The original SW
potential gives E_coh = 4.3364 eV.

The following files are in this directory:

Three_Body_Stillinger_Weber_Balamane_Si.params

  first line: 1 (number of species)

  Then the following 9 parameters:
  A(in ev) B p q sigma(in Angstrom) lambda(in eV) gamma(in Angstorm) costheta_0 cutoff

  Any additional lines will be silently ignored.


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

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. H. Balamane, T. Halicioglu and W. A. Tiller, "Comparative study of silicon empirical interatomic potentials", Phys. Rev. B, vol. 46, 2250-2279, 1992

3. Balamane et al., Phys. Rev. B, vol 40, 9999-10001, 1991

4. Ellad B. Tadmor and Ronald E. Miller, Modeling Materials: Continuum, Atomistic and Multiscale Techniques, Cambridge University Press, 2011


###############################################################################
The functional form of the SW potential is rewritten 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 - rcutij))

  phi_3(rij,rik,theta) = lambda_ijk(cos[theta] - cos[theta0])^2
                         *  exp(gamma_ij/(rij - rcutij) + gamma_ik/(rik - rcutik))

Compared to the standard SW potential, the following redefinitions have been made:
  A      := A*epsilon
  lambda := lambda*epsilon
  gamma  := gamma*sigma
  rcut   := a*sigma
