A C-based implementation of the EDIP three-body bond-order potential of Bazant and Kaxiras.

Jump to: Files | Wiki

EDIP_BOP_C__MD_506186535567_000

There is a newer version of this item. See EDIP__MD_506186535567_002

Title A single sentence description.	A C-based implementation of the EDIP three-body bond-order potential of Bazant and Kaxiras.
Description	This model driver provides a C-based implementation of the three-body Environment Dependent Interatomic Potential (EDIP) developed by Martin Bazant and Efthemios Kaxiras and published in 1996. EDIP is a bond-order potential primarily used to simulate a wide variety of structures and defects associated with silicon and carbon. For more information on EDIP, please see http://web.mit.edu/bazant/www/EDIP/.
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Daniel S. Karls
Maintainer	Daniel S. Karls
Published on KIM	2014
How to Cite	Click here to download this citation in BibTeX format.
Funding	Not available

Short KIM ID The unique KIM identifier code.	MD_506186535567_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.	EDIP_BOP_C__MD_506186535567_000
Citable Link	https://openkim.org/cite/MD_506186535567_000
KIM Item Type	Model Driver
KIM API Version	1.5
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

Files

EDIP_BOP_C__MD_506186535567.c
EDIP_BOP_C__MD_506186535567_000.kim
LICENSE.CDDL
Makefile
README
kimprovenance.edn
kimspec.edn

Download

EDIP_BOP_C__MD_506186535567_000.txz	Tar+XZ	Linux and OS X archive
EDIP_BOP_C__MD_506186535567_000.zip	Zip	Windows archive

Wiki

## Description
This **Model Driver** implements the original Stillinger-Weber potential of Bazant and Kaxiras (used for silicon in its seminal publication).

## Parameters
Symbols:

$$ a, A, B, \rho, \sigma, \lambda, \gamma, b, c, \mu, Q_0, \eta, \beta, \alpha, u_1, u_2, u_3, u_4$$

Corresponding variables in code:
a, A, B, rh, sig, lam, gam, b, c, mu, Qo, eta, bet, alp, u1, u2, u3, u4

## Details

The total potential energy of a system of $$N$$ atoms is assumed to take the form $$ E = \sum_{i=1}^N E_i $$, where the contribution to the energy of atom $$ i $$ is given by

$$ E_i = \sum_{j \neq i} V_2(R_{ij},Z_i) + \sum_{j \neq i} \sum_{k \neq i, k > j} V_3 (\vec{R}_{ij},\vec{R}_{ik},Z_i) .$$

The "environmental dependence" of the energy (and, consequently, its derivatives) is introduced through the coordination $$Z$$, which takes the form

$$ Z_i = \sum_{m \neq i} f(R_{im}) $$

where

$$ f(r) = \begin{cases}
      1 &  \text{if  } r < c\\
      \exp{\left(\dfrac{\alpha}{1-x^{-3}}\right)} & \text{if  } c < r < a\\
      0 & \text{if  } r > a
    \end{cases} $$

and $$ x = \dfrac{( r-c )}{(a-c)} $$.
The two-body term $$V_2$$ of the energy includes an attractive part and a repulsive part:

$$ V_2(r,Z) = A \left[ \left(\dfrac{B}{r}\right)^{\rho} - p(Z) \right]\exp\left(\dfrac{\sigma}{r-a}\right)$$

with the bond-order function taking the form $$p(Z) = e^{-\beta Z^2}$$.

The three-body contribution $$V_3$$ to the energy consists of a product of radial and angular functions:

$$ V_3(\vec{R}_{ij}, \vec{R}_{ik}, Z_{i}) = g(R_{ij})g(R_{ik}) h(l_{ijk},Z_i) $$

where the bond angle of triplet $$ijk$$ is contained in $$l_{ijk} = \cos \theta_{ijk} = \vec{R}_{ij} \cdot \vec{R}_{ik} / R_{ij} R_{ik}$$.  The radial contribution is given by the function $$g(r) = \exp\left(\dfrac{\gamma}{r-a}\right)$$.  The angular contribution to $$V_3$$ is given by

$$ h(l,Z) = \lambda \left[ \left( 1 - e^{-Q(Z)(l+\tau(Z))^2)}\right)  + \eta Q(Z)\left(l+\tau(Z)\right)^2\right]$$

with the sensitivity of the three-body energy to coordination controlled by the function $$Q(Z) = Q_0 e^{-\mu Z}$$.  The function $$\tau(Z)$$, which controls the equilibrium angle of the three-body interaction, is chosen heuristically to have the form

$$ \tau(Z) = u_1 + u_2 \left( u_3 e^{-u_4 Z} - e^{-2 u_4 Z} \right).$$

Wiki Contributors

2014-06-22T11:16:52	karls
2014-06-22T06:13:03	tadmor
2014-06-22T06:11:28	tadmor
2014-06-22T05:44:01	tadmor
2014-06-21T19:43:12	karls
2014-06-21T19:42:41	karls