Updates to documentation: equation.

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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
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)
@ -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,
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
in a parameter file which is specified by the
"pair_coeff"_pair_coeff.html command. Parameter files for different