Updates to documentation: equation.

This commit is contained in:
DallasTrinkle
2017-04-28 15:08:59 -05:00
parent 8cc8441367
commit a0b61d17b5
2 changed files with 24 additions and 1 deletions

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@ -0,0 +1,13 @@
\documentclass[12pt]{article}
\begin{document}
$$
E=\sum_{i<j}\phi_{ij}(r_{ij})+\sum_{i}U_i(n_{i}),
$$
$$
n_{i}=\sum_{j\ne i}\rho_j(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}fi_{j}(r_{ij})f_{k}(r_{ik})g_{jk}[\cos(\theta_{jik})]
$$
\end{document}

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@ -23,7 +23,8 @@ pair_coeff * * Ti.meam.spline Ti Ti Ti :pre
The {meam/spline} style computes pairwise interactions for metals The {meam/spline} style computes pairwise interactions for metals
using a variant of modified embedded-atom method (MEAM) potentials using a variant of modified embedded-atom method (MEAM) potentials
"(Lenosky)"_#Lenosky1. The total energy E is given by "(Lenosky)"_#Lenosky1. For a single species ("old-style") MEAM,
the total energy E is given by
:c,image(Eqs/pair_meam_spline.jpg) :c,image(Eqs/pair_meam_spline.jpg)
@ -31,6 +32,15 @@ where rho_i is the density at atom I, theta_jik is the angle between
atoms J, I, and K centered on atom I. The five functions Phi, U, rho, atoms J, I, and K centered on atom I. The five functions Phi, U, rho,
f, and g are represented by cubic splines. f, and g are represented by cubic splines.
The {meam/spline} style also supports a new style multicomponent
modified embedded-atom method (MEAM) potential, where the total energy
E is given by
:c,image(Eqs/pair_meam_spline_multicomponent.jpg)
where the five functions Phi, U, rho, f, and g depend on the chemistry
of the atoms in the interaction.
The cutoffs and the coefficients for these spline functions are listed The cutoffs and the coefficients for these spline functions are listed
in a parameter file which is specified by the in a parameter file which is specified by the
"pair_coeff"_pair_coeff.html command. Parameter files for different "pair_coeff"_pair_coeff.html command. Parameter files for different