90 lines
3.0 KiB
ReStructuredText
90 lines
3.0 KiB
ReStructuredText
.. index:: pair_style kolmogorov/crespi/z
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pair_style kolmogorov/crespi/z command
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======================================
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Syntax
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""""""
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.. code-block:: LAMMPS
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pair_style [hybrid/overlay ...] kolmogorov/crespi/z cutoff
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Examples
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""""""""
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.. code-block:: LAMMPS
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pair_style hybrid/overlay kolmogorov/crespi/z 20.0
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pair_coeff * * none
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pair_coeff 1 2 kolmogorov/crespi/z CC.KC C C
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pair_style hybrid/overlay rebo kolmogorov/crespi/z 14.0
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pair_coeff * * rebo CH.rebo C C
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pair_coeff 1 2 kolmogorov/crespi/z CC.KC C C
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Description
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"""""""""""
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The *kolmogorov/crespi/z* style computes the Kolmogorov-Crespi interaction
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potential as described in :ref:`(Kolmogorov) <KC05>`. An important simplification is made,
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which is to take all normals along the z-axis.
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.. math::
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E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\
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V_{ij} = & e^{-\lambda(r_{ij} -z_0}) \left[ C + f(\rho_{ij}) + f(\rho_{ji}) \right] - A \left( \frac{r_{ij}}{z_0}\right)^{-6} + A \left( \frac{\textrm{cutoff}}{z_0}\right)^{-6} \\
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\rho_{ij}^2 = & \rho_{ji}^2 = x_{ij}^2 + y_{ij}^2 \qquad \qquad (\mathbf{n}_i \equiv \mathbf{\hat{z}}) \\
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f(\rho) = & e^{-(\rho/\delta)^2} \sum_{n=0}^2 C_{2n} \left( \rho/\delta \right)^{2n}
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It is important to have a sufficiently large cutoff to ensure smooth forces.
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Energies are shifted so that they go continuously to zero at the cutoff assuming
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that the exponential part of :math:`V_{ij}` (first term) decays sufficiently fast.
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This shift is achieved by the last term in the equation for :math:`V_{ij}` above.
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This potential is intended for interactions between two layers of graphene.
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Therefore, to avoid interaction between layers in multi-layered materials,
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each layer should have a separate atom type and interactions should only
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be computed between atom types of neighboring layers.
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The parameter file (e.g. CC.KC), is intended for use with metal
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:doc:`units <units>`, with energies in meV. An additional parameter, *S*\ ,
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is available to facilitate scaling of energies in accordance with
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:ref:`(vanWijk) <vanWijk>`.
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This potential must be used in combination with hybrid/overlay.
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Other interactions can be set to zero using pair_style *none*\ .
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Restrictions
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""""""""""""
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This fix is part of the USER-MISC package. It is only enabled if
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LAMMPS was built with that package. See the :doc:`Build package <Build_package>` doc page for more info.
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Related commands
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""""""""""""""""
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:doc:`pair_coeff <pair_coeff>`,
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:doc:`pair_none <pair_none>`,
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:doc:`pair_style hybrid/overlay <pair_hybrid>`,
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:doc:`pair_style drip <pair_drip>`,
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:doc:`pair_style ilp/graphene/hbn <pair_ilp_graphene_hbn>`.
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:doc:`pair_style kolmogorov/crespi/full <pair_kolmogorov_crespi_full>`,
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:doc:`pair_style lebedeva/z <pair_lebedeva_z>`
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Default
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"""""""
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none
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----------
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.. _KC05:
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**(Kolmogorov)** A. N. Kolmogorov, V. H. Crespi, Phys. Rev. B 71, 235415 (2005)
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.. _vanWijk:
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**(vanWijk)** M. M. van Wijk, A. Schuring, M. I. Katsnelson, and A. Fasolino,
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Physical Review Letters, 113, 135504 (2014)
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