Loading doc/src/Eqs/pair_meam_spline.jpg +10.4 KiB (20.7 KiB) Loading image diff... doc/src/Eqs/pair_meam_spline.tex +3 −2 Original line number Diff line number Diff line \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} $$ E=\sum_{ij}\phi(r_{ij})+\sum_{i}U(\rho_{i}), E=\sum_{i<j}\phi(r_{ij})+\sum_{i}U(n_{i}), $$ $$ \rho_{i}=\sum_{j}\rho(r_{ij})+\sum_{jk}f(r_{ij})f(r_{ik})g[\cos(\theta_{jik})] n_{i}=\sum_{j}\rho(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}f(r_{ij})f(r_{ik})g[\cos(\theta_{jik})] $$ \end{document} doc/src/Eqs/pair_meam_spline_multicomponent.jpg 0 → 100644 +22.4 KiB Loading image diff... doc/src/Eqs/pair_meam_spline_multicomponent.tex 0 → 100644 +14 −0 Original line number Diff line number Diff line \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} $$ E=\sum_{i<j}\phi_{ij}(r_{ij})+\sum_{i}U_i(n_{i}), $$ $$ n_{i}=\sum_{j\ne i}\rho_j(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}f_{j}(r_{ij})f_{k}(r_{ik})g_{jk}[\cos(\theta_{jik})] $$ \end{document} doc/src/pair_meam_spline.txt +32 −8 Original line number Diff line number Diff line Loading @@ -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) Loading @@ -31,6 +32,20 @@ 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 "(Zhang)"_#Zhang1, 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. In particular, if there are N different chemistries, there are N different U, rho, and f functions, while there are N(N+1)/2 different Phi and g functions. The new style multicomponent MEAM potential files are indicated by the second line in the file starts with "meam/spline" followed by the number of elements and the name of each element. 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 Loading Loading @@ -59,7 +74,7 @@ N element names = mapping of spline-based MEAM elements to atom types :ul See the "pair_coeff"_pair_coeff.html doc page for alternate ways to specify the path for the potential file. As an example, imagine the Ti.meam.spline file has values for Ti. If As an example, imagine the Ti.meam.spline file has values for Ti (old style). If your LAMMPS simulation has 3 atoms types and they are all to be treated with this potentials, you would use the following pair_coeff command: Loading @@ -72,10 +87,19 @@ in the potential file. If a mapping value is specified as NULL, the mapping is not performed. This can be used when a {meam/spline} potential is used as part of the {hybrid} pair style. The NULL values are placeholders for atom types that will be used with other potentials. potentials. The old-style potential maps any non-NULL species named on the command line to that single type. An example with a two component spline (new style) is TiO.meam.spline, where the command NOTE: The {meam/spline} style currently supports only single-element MEAM potentials. It may be extended for alloy systems in the future. pair_coeff * * TiO.meam.spline Ti O :pre will map the 1st atom type to Ti and the second atom type to O. Note in this case that the species names need to match exactly with the names of the elements in the TiO.meam.spline file; otherwise an error will be raised. This behavior is different than the old style MEAM files. :line Loading Loading @@ -104,9 +128,6 @@ more instructions on how to use the accelerated styles effectively. [Mixing, shift, table, tail correction, restart, rRESPA info]: The current version of this pair style does not support multiple element types or mixing. It has been designed for pure elements only. This pair style does not support the "pair_modify"_pair_modify.html shift, table, and tail options. Loading Loading @@ -142,3 +163,6 @@ for more info. [(Lenosky)] Lenosky, Sadigh, Alonso, Bulatov, de la Rubia, Kim, Voter, Kress, Modelling Simulation Materials Science Engineering, 8, 825 (2000). :link(Zhang1) [(Zhang)] Zhang and Trinkle, Computational Materials Science, 124, 204-210 (2016). Loading
doc/src/Eqs/pair_meam_spline.tex +3 −2 Original line number Diff line number Diff line \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} $$ E=\sum_{ij}\phi(r_{ij})+\sum_{i}U(\rho_{i}), E=\sum_{i<j}\phi(r_{ij})+\sum_{i}U(n_{i}), $$ $$ \rho_{i}=\sum_{j}\rho(r_{ij})+\sum_{jk}f(r_{ij})f(r_{ik})g[\cos(\theta_{jik})] n_{i}=\sum_{j}\rho(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}f(r_{ij})f(r_{ik})g[\cos(\theta_{jik})] $$ \end{document}
doc/src/Eqs/pair_meam_spline_multicomponent.tex 0 → 100644 +14 −0 Original line number Diff line number Diff line \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} $$ E=\sum_{i<j}\phi_{ij}(r_{ij})+\sum_{i}U_i(n_{i}), $$ $$ n_{i}=\sum_{j\ne i}\rho_j(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}f_{j}(r_{ij})f_{k}(r_{ik})g_{jk}[\cos(\theta_{jik})] $$ \end{document}
doc/src/pair_meam_spline.txt +32 −8 Original line number Diff line number Diff line Loading @@ -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) Loading @@ -31,6 +32,20 @@ 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 "(Zhang)"_#Zhang1, 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. In particular, if there are N different chemistries, there are N different U, rho, and f functions, while there are N(N+1)/2 different Phi and g functions. The new style multicomponent MEAM potential files are indicated by the second line in the file starts with "meam/spline" followed by the number of elements and the name of each element. 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 Loading Loading @@ -59,7 +74,7 @@ N element names = mapping of spline-based MEAM elements to atom types :ul See the "pair_coeff"_pair_coeff.html doc page for alternate ways to specify the path for the potential file. As an example, imagine the Ti.meam.spline file has values for Ti. If As an example, imagine the Ti.meam.spline file has values for Ti (old style). If your LAMMPS simulation has 3 atoms types and they are all to be treated with this potentials, you would use the following pair_coeff command: Loading @@ -72,10 +87,19 @@ in the potential file. If a mapping value is specified as NULL, the mapping is not performed. This can be used when a {meam/spline} potential is used as part of the {hybrid} pair style. The NULL values are placeholders for atom types that will be used with other potentials. potentials. The old-style potential maps any non-NULL species named on the command line to that single type. An example with a two component spline (new style) is TiO.meam.spline, where the command NOTE: The {meam/spline} style currently supports only single-element MEAM potentials. It may be extended for alloy systems in the future. pair_coeff * * TiO.meam.spline Ti O :pre will map the 1st atom type to Ti and the second atom type to O. Note in this case that the species names need to match exactly with the names of the elements in the TiO.meam.spline file; otherwise an error will be raised. This behavior is different than the old style MEAM files. :line Loading Loading @@ -104,9 +128,6 @@ more instructions on how to use the accelerated styles effectively. [Mixing, shift, table, tail correction, restart, rRESPA info]: The current version of this pair style does not support multiple element types or mixing. It has been designed for pure elements only. This pair style does not support the "pair_modify"_pair_modify.html shift, table, and tail options. Loading Loading @@ -142,3 +163,6 @@ for more info. [(Lenosky)] Lenosky, Sadigh, Alonso, Bulatov, de la Rubia, Kim, Voter, Kress, Modelling Simulation Materials Science Engineering, 8, 825 (2000). :link(Zhang1) [(Zhang)] Zhang and Trinkle, Computational Materials Science, 124, 204-210 (2016).
