The Tersoff-mini potential

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Potential form

  • Restrictions: This potential has only been developed for single-element systems so far.
  • The site potential can be written as

\begin{equation} U_i = \frac{1}{2} \sum_{j \neq i} f_{\rm C}(r_{ij}) \left[ f_{\rm R}(r_{ij}) - b_{ij} f_{\rm A}(r_{ij}) \right]. \end{equation}

  • The function [math]f_{\rm C}[/math] is a cutoff function, which is 1 when [math]r_{ij}\lt R_{IJ}[/math] and 0 when [math]r_{ij}\gt S_{IJ}[/math] and takes the following form in the intermediate region:

\begin{equation} f_{\rm C}(r_{ij}) = \frac{1}{2} \left[ 1 + \cos \left( \pi \frac{r_{ij} - R}{S - R} \right) \right]. \end{equation}

  • The repulsive function [math]f_{\rm R}[/math] and the attractive function [math]f_{\rm A}[/math] take the following forms:

\begin{equation} f_{\rm R}(r_{ij}) = \frac{D_0}{S-1} \exp\left(\alpha r_0\sqrt{2S} \right) e^{-\alpha\sqrt{2S} r_{ij}}; \end{equation} \begin{equation} f_{\rm A}(r_{ij}) = \frac{D_0S}{S-1} \exp\left(\alpha r_0\sqrt{2/S} \right) e^{-\alpha\sqrt{2/S} r_{ij}}. \end{equation}


  • The bond-order function is

\begin{equation} b_{ij} = \left(1 + \zeta^{n}_{ij}\right)^{-\frac{1}{2n}}, \end{equation} where \begin{equation} \zeta_{ij} = \sum_{k\neq i, j} f_C(r_{ik}) g_{ijk}; \end{equation} \begin{equation} g_{ijk} = \beta \left(h-\cos\theta_{ijk}\right)^2. \end{equation}

Parameters

Parameter Units
[math]D_0[/math] eV
[math]\alpha[/math] A[math]^{-1}[/math]
[math]r_0[/math] A
[math]S[/math] dimensionless
[math]n[/math] dimensionless
[math]\beta[/math] dimensionless
[math]h[/math] dimensionless
[math]R[/math] A
[math]S[/math] A

Potential file format

Single-element systems

  • The potential file reads
   tersoff_mini 1
   D alpha r0 S beta n h R S

Double-element systems

  • We are still thinking about how the parameters should depend on the atom types. This is an important question and we want to figure it out by doing many tests.

References

  • [1] Zheyong Fan, Yanzhou Wang, Xiaokun Gu, Ping Qian, Yanjing Su, and Tapio Ala-Nissila, A minimal Tersoff potential for diamond silicon with improved descriptions of elastic and phonon transport properties, arXiv:1909.11474 [cond-mat.mtrl-sci]. Accepted to JPCM: https://iopscience.iop.org/article/10.1088/1361-648X/ab5c5f