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2003--Nord-J-Albe-K-Erhart-P-Nordlund-K--Ga-N

Citation: J. Nord, K. Albe, P. Erhart, and K. Nordlund (2003), "Modelling of compound semiconductors: analytical bond-order potential for gallium, nitrogen and gallium nitride", Journal of Physics: Condensed Matter, 15(32), 5649-5662. DOI: 10.1088/0953-8984/15/32/324.
Abstract: An analytical bond-order potential for GaN is presented that describes a wide range of structural properties of GaN as well as bonding and structure of the pure constituents. For the systematic fit of the potential parameters reference data are taken from total-energy calculations within the density functional theory if not available from experiments. Although long-range interactions are not explicitly included in the potential, the present model provides a good fit to different structural geometries including defects and high-pressure phases of GaN.

Related Models:
LAMMPS pair_style tersoff (2003--Nord-J--Ga-N--LAMMPS--ipr1)
See Computed Properties
Notes: This file was created and verified by Lucas Hale. The parameter values are comparable to those in the GaN.tersoff file in the August 22, 2018 LAMMPS distribution with this file using higher precision for the derived parameters. The parameter values are identical to the ones in the parameter file used by openKIM model MO_612061685362_001.
File(s):
OpenKIM (MO_612061685362)
See Computed Properties
Notes: Listing found at https://openkim.org. This KIM potential is based on a parameter file with identical parameter values as 2003--Nord-J--Ga-N--LAMMPS--ipr1.
Link(s):

Implementation Information

This page displays computed properties for the Tersoff_LAMMPS_NordAlbeErhart_2003_GaN__MO_612061685362_003 implementation of the 2003--Nord-J-Albe-K-Erhart-P-Nordlund-K--Ga-N 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

Tersoff_LAMMPS_NordAlbeErhart_2003_GaN__MO_612061685362_003/diatom

Click on plot to load interactive version

Tersoff_LAMMPS_NordAlbeErhart_2003_GaN__MO_612061685362_003/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

Tersoff_LAMMPS_NordAlbeErhart_2003_GaN__MO_612061685362_003/EvsR.Ga

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-1214526
A15--beta-W = oqmd-1214971, oqmd-1280429
A2--W--bcc = oqmd-1215149
A3'--alpha-La--double-hcp = oqmd-1215417
A3--Mg--hcp = oqmd-1215327
A4--C--dc = oqmd-1215506
A5--beta-Sn = oqmd-1215595
A6--In--bct = mp-140, oqmd-675527, oqmd-676193, oqmd-1215684

prototypemethodEcoh (eV/atom)Epot (eV/atom)a0 (Å)b0 (Å)c0 (Å)α (degrees)β (degrees)γ (degrees)
A2--W--bccdynamic-2.8414-2.84143.1443.1443.14490.090.090.0
mp-142dynamic-2.8328-2.83284.41137.40374.702890.090.090.0
oqmd-676227box-2.8224-2.82244.36357.59724.607790.090.090.0
mp-142box-2.8221-2.82214.36317.60014.606690.090.090.0
oqmd-1214704box-2.8218-2.82184.36217.60264.60590.090.090.0
oqmd-686543dynamic-2.8212-2.82127.15754.9294.551190.090.090.0
oqmd-8115dynamic-2.7894-2.78942.72427.52143.404990.090.090.0
oqmd-686543box-2.7841-2.78417.72964.63434.426890.090.090.0
mp-1067880box-2.7797-2.77977.76274.614.408490.090.090.0
oqmd-8115box-2.7689-2.76892.70337.45153.312390.090.090.0
oqmd-2814dynamic-2.7526-2.75265.82765.82765.827690.090.090.0
oqmd-2215box-2.7242-2.72428.76168.761615.710990.090.0120.0
A5--beta-Sndynamic-2.7118-2.71184.98954.98952.627690.090.090.0
Ah--alpha-Po--scdynamic-2.695-2.6952.59922.59922.599290.090.090.0
oqmd-1215862box-2.694-2.6943.67553.67554.504190.090.0120.0
A6--In--bctstatic-2.6773-2.67732.74892.74894.123690.090.090.0
A1--Cu--fccbox-2.6716-2.67163.97113.97113.971190.090.090.0
A3'--alpha-La--double-hcpbox-2.6627-2.66272.79622.79629.250290.090.0120.0
A3--Mg--hcpbox-2.6553-2.65532.78822.78824.650790.090.0120.0
A15--beta-Wbox-2.5402-2.54024.89434.89434.894390.090.090.0
A7--alpha-Asbox-2.5331-2.53313.93463.93467.190790.090.0120.0
A4--C--dcdynamic-2.4854-2.48545.53695.53695.536990.090.090.0
oqmd-1215951box-2.2268-2.22684.22644.22645.100290.090.0120.0

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:
1516.0531643.351643.350.00.0-0.0
1643.351516.0531643.350.00.0-0.0
1643.351643.351516.053-0.0-0.00.0
0.0-0.00.073.020.0-0.0
-0.00.0-0.0-0.073.020.0
-0.00.00.00.00.073.02

Phonon and Quasi-Harmonic Approximation Predictions

Phonon band structures and crystal properties estimated from quasi-harmonic approximation (QHA) calculations are displayed for select crystals. The calculations were performed using phonopy and LAMMPS. For the phonon calculations, 3x3 supercells of the potential-specific relaxed crystals were used. The QHA calculations were based on 11 strain states ranging from -0.05 to 0.05.

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

Notes and Disclaimers:

  • The thermodynamic properties estimated from QHA are based on the assumption that only volumetric changes affect the phonon behaviors as the temperature changes. This tends to give good predictions at lower temperatures but ignores anharmonic effects such as phonon coupling and vacancy formation that can be important at higher temperatures.
  • Note that direct molecular dynamics (MD) simulations using the same potentials will disagree with the thermodynamics properties listed here for the lowest temperatures. The MD results are purely classical in nature and therefore lack a zero-point energy, whereas the phonon calculations inherently provide a zero-point energy.
  • The structures explored here are taken from the dynamically relaxed structures above. Despite the rigorous relaxation method used, some of these structures prove to be unstable once internal deformations are added. The phonon results may reflect this and give bad band gap predictions for these unstable crystals.
  • All QHA calculations performed here use the same set of strains which might not be ideal for all crystals. Be sure to check the bulk modulus and Helmholtz vs. volume plots to verify if the QHA strained states are reasonable for each crystal of interest.
  • QHA results may not be available for all crystal structures that have phonon results. Missing QHA results indicates an issue either with the strained states or with the QHA calculation itself.
  • NIST disclaimer

Version Information:

  • 2023-03-14. Phonon and QHA plots added

Band Structures, Density of States, and QHA Verification Plots

Composition:
Prototype:
a0:
plot: