# Tersoff potential¶

The Tersoff potential [Ter88b] in atomicrex follows the implementation in Lammps. This version supports multi-component systems with all parameters being dependent on the types of the atoms involved, i.e. the two-body terms dependent on the types of atoms $$i$$ and $$j$$, whereas the three-body terms depend on the types of atoms $$i$$, $$j$$, and $$k$$. Note that in the analytic bond-order potential (ABOP) form [Bre90] the three-body terms are usually dependent on the types of atoms $$i$$ and $$k$$, only (see e.g., [AlbNorAve02], [AlbNorNor02], [ErhAlb05], [JusErhTra05]). If you want to obtain this behavior please resort to the ABOP form.

The Tersoff potential form can be written

$E = \frac{1}{2} \sum_i \sum_{j\neq i} V_{ij}$

with

$V_{ij} = f_c(r_{ij}) \left[f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right].$

Here, $$V_R(r) = A\exp(-\lambda_1 r)$$ and $$V_A(r) = -B\exp(-\lambda_2 r)$$ are repulsive and attractive pair potential branches, respectively, and $$f_c(r_{ij})$$ is a cut-off function that is unity and decays sinusodially in the interval $$(R-D,R+D)$$, beyond which it vanishes. The three-body contributions arise due to the bond-order parameter

$b_{ij} = \left( 1+\beta^n\zeta_{ij}^n \right)^{-\frac{1}{2n}}$

where

$\zeta_{ij} = \sum_{k\neq i,j} f_c(r_{ij})g(\theta_{ijk})\exp \left[ \lambda_3^m(r_{ij}-r_{ik})^m \right].$

The angular dependence is due to the factor

$g(\theta) = \gamma_{ijk} \left( 1+\frac{c^2}{d^2} - \frac{c^2}{d^2 + (h - \cos \theta)^2}\right).$

Parameter files are written in Lammps/Tersoff format.

The following code snippet, to be inserted in the <potentials> block, illustrates the definition of this potential type in the input file.

<tersoff id="Co" species-a="*" species-b="*">
<param-file>Co.tersoff</param-file>
<fit-dof>
<A tag="CoCoCo" enabled="true" />
<B tag="CoCoCo" enabled="true" />
<lambda1 tag="CoCoCo" enabled="true" />
<lambda2 tag="CoCoCo" enabled="true" />
<gamma tag="CoCoCo" enabled="true"/>
<lambda3 tag="CoCoCo" enabled="true" />
<c tag="CoCoCo" enabled="false" />
<d tag="CoCoCo" enabled="false" />
<theta0 tag="CoCoCo" enabled="false" />
</fit-dof>
</tersoff>


Warning

Note that the species-a and species-b attributes should always be set to *. The assignment of atom types is handled using the information in the tag attribute.

Elements and attributes

• <param-file>: Name of file with input parameters in Lammps/Tersoff format
• <export-potential> (optional): Name of file, to which potential parameters are being written in Lammps/Tersoff format [Default: no file is written].

Further information

An extensive list of references is provided here.