Three-body bond-order (Tersoff-style) potential by Purja Pun and Mishin (2017) v000

Moon-ki Choi; Daniel S. Karls; Ganga P. Purja Pun; Yuri Mishin

doi:10.25950/23639742

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ThreeBodyBondOrder_PPM__MD_184422512875_000

Title A single sentence description.	Three-body bond-order (Tersoff-style) potential by Purja Pun and Mishin (2017) v000
Description	This is a model driver for an optimized interatomic potential based on a modified Tersoff form originally constructed for bulk silicon and 2D silicon (silicene). The silicon potential reproduces a wide range of properties of Si and improves over existing potentials with respect to point defect structures and energies, surface energies and reconstructions, thermal expansion, melting temperature and other properties.
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Moon-ki Choi
Maintainer	Moon-ki Choi
Implementer	Moon-ki Choi Daniel S. Karls
Developer	Ganga P. Purja Pun Yuri Mishin
Published on KIM	2019
How to Cite	This Model Driver originally published in [1] is archived in OpenKIM [2-4]. [1] Pun GPP, Mishin Y. Optimized interatomic potential for silicon and its application to thermal stability of silicene. Phys Rev B. 2017;95(22):224103. doi:10.1103/PhysRevB.95.224103 [2] Choi M-ki, Karls DS, Pun GPP, Mishin Y. Three-body bond-order (Tersoff-style) potential by Purja Pun and Mishin (2017) v000. OpenKIM; 2019. doi:10.25950/23639742 [3] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [4] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a
Funding	Not available

Short KIM ID The unique KIM identifier code.	MD_184422512875_000
Extended KIM ID The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.	ThreeBodyBondOrder_PPM__MD_184422512875_000
DOI	10.25950/23639742 https://doi.org/10.25950/23639742 https://commons.datacite.org/doi.org/10.25950/23639742
KIM Item Type	Model Driver
KIM API Version	2.0
Programming Language(s) The programming languages used in the code and the percentage of the code written in each one.	100.00% C

Models using this Model Driver

ThreeBodyBondOrder_PPM_PurjaPunMishin_2017_Si__MO_566683736730_000

Ganga Purja Pun and Yuri Mishin developed this bond order potential form of silicon. Previous potentials such as the modified embedded-atom method (MEAM) potential [1], Stillinger-Weber (SW) potential [2], and modified Tersoff potential (MOD) [3] have some limitations in computing mechanical and thermal properties for bulk of Silicon (specially at high temperature). The new potential is an extension of the MOD Tersoff-type potential. The developers tested four potentials (MEAM, SW, MOD, and the new potential) with respect to the mechanical and energetic properties of bulk and low-dimensional structures including Si clusters and single and bilayer silicene (a 2D allotrope of Si). The new potential performed better than earlier potential overcoming limitations such as an overestimated thermal expansion (at high temperature) and the volume effect of melting.

### Potential ###

The total energy is given by

$$E = \frac{1}{2} \sum_{i \ne j}\phi_{ij}(r_{ij})$$,

where $$r_{ij}$$ is the distance between atom i and j and the bond energy $$\phi_{ij}$$ is taken as

$$\phi_{ij}=f_{c}(r_{ij})[A\space exp(-\lambda_{1}r_{ij})-b_{ij}\space B\space exp(-\lambda_{2}r_{ij})+c_0]$$.

The bond order $$b_{ij}$$ is given by

$$b_{ij} = (1+\xi_{ij}^\eta)^{-\delta}$$,

where

$$\eta_{ij} = \sum_{k\ne i,j}f_{c}(r_{ij})g(\theta_{ijk})exp[\alpha(r_{ij}-r_{ik})^\beta]$$,

where $$f_{c} (r_{ij})$$ has the form

$$
\begin{align*}
&f_{c}(r) = \left\{\begin{aligned}
&1,\space r \leq  R_1 \\
&\frac{1}{2} + \frac{9}{16}\space cos(\pi\frac{r-R_1}{R_2 - R_1}) - \frac{1}{16} cos(3\pi \frac{r-R_1}{R_2 - R_1}),\space R_1 \lt\space r \lt\space R_2  \\
&0,\space r \geq R_2 \\
\end{aligned}
\right.
\end{align*}
$$.

Here, $$R_1$$ and $$R_2$$ are cutoff radii. The outer cutoff  $$R_2$$  is chosen between the first and second coordination shells of the diamond cubic structure. The angular function $$g(\theta_{ijk})$$ is

$$
g(\theta) = c_1 + \frac{c_2 (h - cos\theta)^2}{c_3 + (h - cos\theta)^2} \times \{ 1 + c_4 exp[-c_5 (h-cos\theta)^2] \} 
$$,

where $$\theta_{ijk}$$ is the angle between bonds i-j and i-k.

### Reference: ###

[1] S. Ryu, C. R. Weinberger, M. I. Baskes, and W. Cai, Improved modified embedded-atom method potentials for gold and silicon, Modell. Simul. Mater. Sci. Eng. 17, 075008 (2009).
[2] F. H. Stillinger and T. A. Weber, Computer simulation of local order in condensed phases of silicon, Phys. Rev. B 31, 5262 (1985).
[3] T. Kumagai, S. Izumi, S. Hara, and S. Sakai, Development of bond-order potentials that can reproduce the elastic constants and melting point of silicon for classical molecular dynamics simulation, Comput. Mater. Sci. 39, 457 (2007).

Wiki Contributors

2019-05-13T20:29:50.625747	tadmor
2019-05-08T11:56:28.431089	MKChoi
2019-05-07T13:21:01.679655	MKChoi
2019-05-07T13:14:10.438902	MKChoi
2019-05-07T13:13:30.885880	MKChoi
2019-05-06T20:23:14.706278	MKChoi
2019-05-06T17:13:13.301250	MKChoi
2019-05-06T17:11:42.491497	MKChoi

ThreeBodyBondOrder_PPM__MD_184422512875_000

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