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2015--Zhou-X-W-Ward-D-K-Foster-M-E--C-Cu

Citation: X.W. Zhou, D.K. Ward, and M.E. Foster (2015), "An analytical bond-order potential for carbon", Journal of Computational Chemistry, 36(23), 1719-1735. DOI: 10.1002/jcc.23949.
Abstract: Carbon is the most widely studied material today because it exhibits special properties not seen in any other materials when in nano dimensions such as nanotube and graphene. Reduction of material defects created during synthesis has become critical to realize the full potential of carbon structures. Molecular dynamics (MD) simulations, in principle, allow defect formation mechanisms to be studied with high fidelity, and can, therefore, help guide experiments for defect reduction. Such MD simulations must satisfy a set of stringent requirements. First, they must employ an interatomic potential formalism that is transferable to a variety of carbon structures. Second, the potential needs to be appropriately parameterized to capture the property trends of important carbon structures, in particular, diamond, graphite, graphene, and nanotubes. Most importantly, the potential must predict the crystalline growth of the correct phases during direct MD simulations of synthesis to achieve a predictive simulation of defect formation. Because an unlimited number of structures not included in the potential parameterization are encountered, the literature carbon potentials are often not sufficient for growth simulations. We have developed an analytical bond order potential for carbon, and have made it available through the public MD simulation package LAMMPS. We demonstrate that our potential reasonably captures the property trends of important carbon phases. Stringent MD simulations convincingly show that our potential accounts not only for the crystalline growth of graphene, graphite, and carbon nanotubes but also for the transformation of graphite to diamond at high pressure.

Notes: Notes from Dr. Zhou about the C-Cu interactions: "The C-Cu potential was constructed from the carbon potential (2015--Zhou-X-W-Ward-D-K-Foster-M-E--C) and Cu of the Al-Cu and Cu-H potentials (2016--Zhou-X-W-Ward-D-K-Foster-M-E--Al-Cu, 2015--Zhou-X-W-Ward-D-K-Foster-M-Zimmerman-J-A--Cu-H), except that a Morse potential is added to the Cu so that the cohesive energy of Cu is deliberately significantly increased but the lattice constant of Cu is unchanged. This allows simulations of growth of C on Cu to be performed at temperatures higher than the Cu melting temperature (to accelerate the simulations) without other negative consequencies."

Related Models:
LAMMPS pair_style bop (2015--Zhou-X-W--C-Cu--LAMMPS--ipr1)
See Computed Properties
Notes: This file was taken from the August 22, 2018 LAMMPS distribution and listed as having been created by X.W. Zhou (Sandia)
File(s):

Implementation Information

This page displays computed properties for the 2015--Zhou-X-W--C-Cu--LAMMPS--ipr1 implementation of the 2015--Zhou-X-W-Ward-D-K-Foster-M-E--C-Cu potential. Computed values for other implementations can be seen by clicking on the links below:

Diatom Energy vs. Interatomic Spacing

Plots of the potential energy vs interatomic spacing, r, are shown below for all diatom sets associated with the interatomic potential. This calculation provides insights into the functional form of the potential's two-body interactions. A system consisting of only two atoms is created, and the potential energy is evaluated for the atoms separated by 0.02 Å <= r <= 6.0> Å in intervals of 0.02 Å. Two plots are shown: one for the "standard" interaction distance range, and one for small values of r. The small r plot is useful for determining whether the potential is suitable for radiation studies.

The calculation method used is available as the iprPy diatom_scan calculation method.

Clicking on the image of a plot will open an interactive version of it in a new tab. The underlying data for the plots can be downloaded by clicking on the links above each plot.

Notes and Disclaimers:

  • These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
  • As this calculation only involves two atoms, it neglects any multi-body interactions that may be important in molecules, liquids and crystals.
  • NIST disclaimer

Version Information:

  • 2019-11-14. Maximum value range on the shortrange plots are now limited to "expected" levels as details are otherwise lost.
  • 2019-08-07. Plots added.

Download data

Click on plot to load interactive version

2015--Zhou-X-W--C-Cu--LAMMPS--ipr1/diatom

Click on plot to load interactive version

2015--Zhou-X-W--C-Cu--LAMMPS--ipr1/diatom_short

Cohesive Energy vs. Interatomic Spacing

Plots of potential energy vs interatomic spacing, r, are shown below for a number of crystal structures. The structures are generated based on the ideal atomic positions and b/a and c/a lattice parameter ratios for a given crystal prototype. The size of the system is then uniformly scaled, and the energy calculated without relaxing the system. To obtain these plots, values of r are evaluated every 0.02 Å up to 6 Å.

The calculation method used is available as the iprPy E_vs_r_scan calculation method.

Clicking on the image of a plot will open an interactive version of it in a new tab. The underlying data for the plots can be downloaded by clicking on the links above each plot.

Notes and Disclaimers:

  • These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
  • The minima identified by this calculation do not guarantee that the associated crystal structures will be stable since no relaxation is performed.
  • NIST disclaimer

Version Information:

  • 2020-12-18. Descriptions, tables and plots updated to reflect that the energy values are the measuredper atom potential energy rather than cohesive energy as some potentials have non-zero isolated atom energies.
  • 2019-02-04. Values regenerated with even r spacings of 0.02 Å, and now include values less than 2 Å when possible. Updated calculation method and parameters enhance compatibility with more potential styles.
  • 2019-04-26. Results for hcp, double hcp, α-As and L10 prototypes regenerated from different unit cell representations. Only α-As results show noticable (>1e-5 eV) difference due to using a different coordinate for Wykoff site c position.
  • 2018-06-13. Values for MEAM potentials corrected. Dynamic versions of the plots moved to separate pages to improve page loading. Cosmetic changes to how data is shown and updates to the documentation.
  • 2017-01-11. Replaced png pictures with interactive Bokeh plots. Data regenerated with 200 values of r instead of 300.
  • 2016-09-28. Plots for binary structures added. Data and plots for elemental structures regenerated. Data values match the values of the previous version. Data table formatting slightly changed to increase precision and ensure spaces between large values. Composition added to plot title and structure names made longer.
  • 2016-04-07. Plots for elemental structures added.

Select a composition:

Download data

Click on plot to load interactive version

2015--Zhou-X-W--C-Cu--LAMMPS--ipr1/EvsR.C

Crystal Structure Predictions

Computed lattice constants and cohesive/potential energies are displayed for a variety of crystal structures. The values displayed here are obtained using the following process.

  1. Initial crystal structure guesses are taken from:
    1. The iprPy E_vs_r_scan calculation results (shown above) by identifying all energy minima along the measured curves for a given crystal prototype + composition.
    2. Structures in the Materials Project and OQMD DFT databases.
  2. All initial guesses are relaxed using three independent methods using a 10x10x10 supercell:
    1. "box": The system's lattice constants are adjusted to zero pressure without internal relaxations using the iprPy relax_box calculation with a strainrange of 1e-6.
    2. "static": The system's lattice and atomic positions are statically relaxed using the iprPy relax_static calculation with a minimization force tolerance of 1e-10 eV/Angstrom.
    3. "dynamic": The system's lattice and atomic positions are dynamically relaxed for 10000 timesteps of 0.01 ps using the iprPy relax_dynamic calculation with an nph integration plus Langevin thermostat. The final configuration is then used as input in running an iprPy relax_static calculation with a minimization force tolerance of 1e-10 eV/Angstrom.
  3. The relaxed structures obtained from #2 are then evaluated using the spglib package to identify an ideal crystal unit cell based on the results.
  4. The space group information of the ideal unit cells is compared to the space group information of the corresponding reference structures to identify which structures transformed upon relaxation. The structures that did not transform to a different structure are listed in the table(s) below. The "method" field indicates the most rigorous relaxation method where the structure did not transform. The space group information is also used to match the DFT reference structures to the used prototype, where possible.
  5. The cohesive energy, Ecoh, is calculated from the measured potential energy per atom, Epot$, by subtracting the isolated energy averaged across all atoms in the unit cell. The isolated atom energies of each species model is obtained either by evaluating a single atom atomic configuration, or by identifying the first energy plateau from the diatom scan calculations for r > 2 Å.

The calculation methods used are implemented into iprPy as the following calculation styles

Notes and Disclaimers:

  • These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
  • The presence of any structures in this list does not guarantee that those structures are stable. Also, the lowest energy structure may not be included in this list.
  • Multiple values for the same crystal structure but different lattice constants are possible. This is because multiple energy minima are possible for a given structure and interatomic potential. Having multiple energy minima for a structure does not necessarily make the potential "bad" as unwanted configurations may be unstable or correspond to conditions that may not be relevant to the problem of interest (eg. very high strains).
  • NIST disclaimer

Version Information:

  • 2022-05-27. The "box" method results have all been redone with an updated methodology more suited for non-orthogonal systems.
  • 2020-12-18. Cohesive energies have been corrected by making them relative to the energies of the isolated atoms. The previous cohesive energy values are now listed as the potential energies.
  • 2019-06-07. Structures with positive or near zero cohesive energies removed from the display tables. All values still present in the raw data files.
  • 2019-04-26. Calculations now computed for each implementation. Results for hcp, double hcp, α-As and L10 prototypes regenerated from different unit cell representations.
  • 2018-06-14. Methodology completely changed affecting how the information is displayed. Calculations involving MEAM potentials corrected.
  • 2016-09-28. Values for simple compounds added. All identified energy minima for each structure are listed. The existing elemental data was regenerated. Most values are consistent with before, but some differences have been noted. Specifically, variations are seen with some values for potentials where the elastic constants don't vary smoothly near the equilibrium state. Additionally, the inclusion of some high-energy structures has changed based on new criteria for identifying when structures have relaxed to another structure.
  • 2016-04-07. Values for elemental crystal structures added. Only values for the global energy minimum of each unique structure given.

Select a composition:

Download raw data (including filtered results)

Reference structure matches:
A1--Cu--fcc = oqmd-1214512
A15--beta-W = oqmd-1214957
A2--W--bcc = oqmd-1215135
A3'--alpha-La--double-hcp = oqmd-1215403
A3--Mg--hcp = oqmd-1215313
A4--C--dc = mp-66, oqmd-675640
A5--beta-Sn = oqmd-1215581
A6--In--bct = mp-1181996, oqmd-1215670
A7--alpha-As = mp-169, oqmd-594528
Ah--alpha-Po--sc = mp-998866, oqmd-636457, oqmd-1214601

prototypemethodEcoh (eV/atom)Epot (eV/atom)a0 (Å)b0 (Å)c0 (Å)α (degrees)β (degrees)γ (degrees)
oqmd-589492dynamic-7.4028-7.40282.45622.456253.49590.090.0120.0
mp-569416dynamic-7.4028-7.40282.45622.456257.264190.090.0120.0
oqmd-589493static-7.4028-7.40282.45622.456228.951890.090.0120.0
oqmd-683819dynamic-7.4028-7.40282.45624.25426.666190.090.090.0
oqmd-589493dynamic-7.4028-7.40282.45622.456228.95690.090.0120.0
mp-606949dynamic-7.4028-7.40282.45622.456231.98390.090.0120.0
A7--alpha-Asdynamic-7.4028-7.40282.45622.456210.213190.090.0120.0
oqmd-589492static-7.4028-7.40282.45622.456253.480490.090.0120.0
mp-632329dynamic-7.4028-7.40284.25422.45623.160190.093.690.0
oqmd-590101static-7.4028-7.40282.45622.45626.795790.090.0120.0
mp-568286dynamic-7.4028-7.40284.25422.45628.028390.090.090.0
mp-632329static-7.4028-7.40284.25422.45623.159590.093.790.0
mp-937760dynamic-7.4028-7.40282.45624.25427.9890.090.090.0
mp-568806static-7.4028-7.40282.45622.45623.8390.090.0120.0
oqmd-590101dynamic-7.4028-7.40282.45622.45626.796590.090.0120.0
mp-568363dynamic-7.4028-7.40284.25422.45628.149990.090.090.0
mp-990448dynamic-7.4028-7.40282.45622.45629.999190.090.0120.0
mp-1040425dynamic-7.4028-7.40282.45622.456219.998390.090.0120.0
oqmd-1214690static-7.4028-7.40282.45624.25426.676790.090.090.0
mp-569567dynamic-7.3759-7.37592.43942.439441.826290.090.0120.0
mp-616440dynamic-7.3759-7.37592.43942.439415.933890.090.0120.0
A4--C--dcdynamic-7.3759-7.37593.44983.44983.449890.090.090.0
oqmd-599491dynamic-7.3759-7.37592.43942.439411.950390.090.0120.0
mp-569517dynamic-7.3759-7.37592.43942.439429.875990.090.0120.0
oqmd-599489dynamic-7.3759-7.37592.43942.43943.983490.090.0120.0
oqmd-599489box-7.3758-7.37582.4392.4393.984690.090.0120.0
mp-47box-7.3758-7.37582.4392.4393.984790.090.0120.0
mp-616440box-7.3752-7.37522.43942.439415.933990.090.0120.0
oqmd-599492box-7.3751-7.37512.43922.439215.93690.090.0120.0
mp-611448box-7.3749-7.37492.43932.439311.951190.090.0120.0
oqmd-599491box-7.3749-7.37492.43932.439311.951890.090.0120.0
mp-569567box-7.3748-7.37482.43962.439641.821590.090.0120.0
oqmd-599493box-7.3747-7.37472.43932.439329.878690.090.0120.0
mp-569517box-7.3747-7.37472.43942.439429.877390.090.0120.0
mp-611426box-7.3746-7.37462.43922.43927.968190.090.0120.0
oqmd-599490box-7.3744-7.37442.43932.43937.967990.090.0120.0
mp-1008374box-7.1626-7.16262.48797.72832.467290.090.090.0
oqmd-637130dynamic-6.8589-6.85898.8752.44554.074590.090.090.0
oqmd-637352dynamic-6.8551-6.85518.95732.44584.066890.096.490.0
mp-1190171box-6.832-6.8328.97812.43324.088890.090.090.0
oqmd-637130box-6.8315-6.83158.98522.43354.087290.090.090.0
oqmd-637352box-6.8311-6.83119.0472.43724.076190.096.290.0
mp-1080826box-6.8311-6.83119.04432.4374.077590.096.290.0
mp-1078845box-6.7995-6.79954.18518.77162.412290.090.090.0
mp-568028dynamic-6.7136-6.71367.892713.7969.326290.090.090.0
mp-683919box-6.7036-6.703610.242817.529417.994990.090.090.0
oqmd-689315box-6.6945-6.694510.136217.576418.032290.090.090.0
oqmd-610557box-6.687-6.6874.73925.61094.271990.090.090.0
oqmd-610556box-6.6835-6.68354.73825.6144.272290.090.090.0
mp-568410box-6.6737-6.67374.73575.62334.272590.090.090.0
oqmd-677227dynamic-6.6573-6.657314.05114.05114.05190.090.090.0
mp-1196583dynamic-6.6573-6.657314.305114.305114.305190.090.090.0
mp-667273dynamic-6.6573-6.657314.03314.03314.03390.090.090.0
oqmd-603085dynamic-6.6573-6.657313.843913.843913.843990.090.090.0
mp-1205283dynamic-6.6573-6.65739.653713.38869.395690.090.090.0
oqmd-684315dynamic-6.6573-6.65739.894814.86019.395290.090.090.0
mp-667273static-6.6573-6.657314.148914.148914.148990.090.090.0
oqmd-677227static-6.6573-6.657314.192614.192614.192690.090.090.0
mp-1196583static-6.6573-6.657314.415914.415914.415990.090.090.0
oqmd-603085static-6.6571-6.657113.997413.997413.997490.090.090.0
mp-1196583box-6.6562-6.656214.411114.411114.411190.090.090.0
oqmd-603085box-6.6562-6.656213.99513.99513.99590.090.090.0
mp-667273box-6.6557-6.655714.143914.143914.143990.090.090.0
oqmd-677227box-6.6495-6.649514.191814.191814.191890.090.090.0
mp-1147718box-6.6366-6.636610.249314.74119.254890.090.090.0
oqmd-595714box-6.6236-6.62369.12429.174914.563390.090.090.0
mp-630227box-6.6207-6.62079.18459.189115.273990.090.090.0
oqmd-684627box-6.6127-6.61279.16329.163215.201390.090.090.0
oqmd-614417box-6.5987-6.59879.18979.189724.265990.090.0120.0
mp-680372box-6.5965-6.59659.19899.198925.013290.090.0120.0
mp-568028box-6.5536-6.55368.521613.87559.58990.090.090.0
mp-1203645dynamic-6.5138-6.513810.2834.912216.577390.0111.190.0
mp-1018088dynamic-6.51-6.514.10824.10824.108290.090.090.0
mp-24static-6.5058-6.50584.30924.30924.309290.090.090.0
mp-24box-6.5058-6.50584.30944.30944.309490.090.090.0
oqmd-637443box-6.407-6.4075.20185.20185.201890.090.090.0
mp-1188817box-6.4066-6.40665.20185.20185.201890.090.090.0
oqmd-637353box-6.3873-6.38734.44354.44352.38490.090.090.0
mp-1008395box-6.3872-6.38724.44354.44352.38490.090.090.0
mp-1192619dynamic-6.2803-6.28037.88937.88937.889390.090.090.0
mp-624889box-6.2683-6.26834.69695.2415.819990.090.090.0
oqmd-610552box-6.2537-6.25374.65125.49936.498290.090.090.0
mp-1245190dynamic-6.2503-6.25039.934210.431810.469189.188.287.8
mp-579909box-6.2461-6.24614.6515.50586.894790.090.090.0
mp-1244964dynamic-6.2069-6.20699.449911.118311.3487.285.688.3
mp-1194362dynamic-6.131-6.1319.23566.31099.698990.0100.390.0
mp-1196857dynamic-6.0516-6.05169.114318.915.928890.090.090.0
mp-1244913dynamic-6.0057-6.005710.565210.691410.847892.491.792.6
mp-1205283box-5.7415-5.741510.422613.32629.112990.090.090.0
mp-1182684dynamic-5.66-5.6611.613111.855414.790590.090.290.0
oqmd-684315box-5.253-5.25310.483115.29289.244690.090.090.0
oqmd-585286box-4.9906-4.99065.00915.00915.009190.090.090.0
mp-570002box-4.9882-4.98825.00965.00965.009690.090.090.0
mp-1245190box-4.9261-4.926110.478211.089611.099391.290.991.5
mp-1244964box-4.5256-4.525610.515811.040511.923390.295.492.1
mp-1244913box-4.0884-4.088411.273111.466612.066181.588.886.5
mp-1182684box-4.0677-4.067714.446914.017118.437490.090.190.0
mp-1182692box-3.6402-3.64029.044310.38226.951481.482.166.4
mp-1205417box-3.4329-3.432913.792213.79227.91890.090.090.0
mp-1192619box-2.7546-2.754610.354710.354710.354790.090.090.0
oqmd-1214779box-2.6767-2.67679.9439.9439.94390.090.090.0
A6--In--bctstatic-2.6079-2.60791.71871.71876.243290.090.090.0
A3'--alpha-La--double-hcpbox-2.3096-2.30962.56052.56054.272290.090.0120.0
mp-1095534box-2.3082-2.308214.112214.11221.709690.090.090.0
Ah--alpha-Po--scstatic-2.2195-2.21951.82091.82091.820990.090.090.0
oqmd-1214868box-1.9228-1.92287.68017.68017.680190.090.090.0
A15--beta-Wstatic-1.5736-1.57363.59163.59163.591690.090.090.0
A2--W--bccstatic-1.4589-1.45892.23992.23992.239990.090.090.0

Elastic Constants Predictions

Static elastic constants are displayed for the unique structures identified in Crystal Structure Predictions above. The values displayed here are obtained by measuring the change in virial stresses due to applying small strains to the relaxed crystals. The initial structure and the strained states are all relaxed using force minimization.

The calculation method used is available as the iprPy elastic_constants_static calculation method.

Notes and Disclaimers:

  • These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
  • The presence of any structures in this list does not guarantee that those structures are stable.
  • The elastic constants have been computed for a variety of strains, and in some cases for slightly different lattice constant values. The static nature of this calculation can give poor predictions if the evaluated states straddle a functional discontinuity in the potential's third derivative. Be sure to compare the elastic constants for the different strains (positive and negative).
  • NIST disclaimer

Version Information:

  • 2019-08-07. Data added.

Composition:
Prototype:
a0:
strain:

Download raw data

Cij in GPa:
6574088160.4436154760578.6714553238081.875-150973542.584146716602.82732388603.618
4571883839.1576322323524.7886346553287.01446332878.06-26022139.682-49785081.131
6056506945.2114500163400.2936586954841.795159466441.23154924615.15965858352.178
-0.00.0-0.0-10.4880.00.0
0.00.00.00.0-10.4880.0
0.00.00.00.00.0-10.488