A three-body Stillinger-Weber (SW) Model (Parameterization) for Silicon modified by Balamane et al
Description
A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.
This Model implements the Stillinger-Weber (SW) potential for Si with a rescaled value of epsilon parameter used in the SW potential. The original epsilon value was
2.1682 eV. Balamane et al (1992) rescaled it to 2.315 eV so that experimental cohesive energy E_coh = 4.63 eV can be obtained. The original SW potential gives E_coh = 4.3364 eV. This version update is to make this model compatible with the model driver update to support multiple species. The functional form of the SW potential is written and there is a redifinition of parameters (e.g. A := A*epsilon). Besides, costheta_0 is updated from -0.3333333 to -0.3333333333333333 to give a better approximation of -1/3.
Species
The supported atomic species.
Si
Disclaimer
A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.
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.
Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).
The letter grade A was assigned because the normalized error in the computation was 1.36726e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.
vc-forces-numerical-derivative
consistency
Forces computed by the model agree with numerical derivatives of the energy; see full description.
The model is C^3 continuous. This means that the model has continuous energy and continuous derivatives at least up to order 3. (Derivatives beyond this order were not tested.)
vc-dimer-continuity-c1
informational
The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.
Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.
vc-objectivity
informational
Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.
All threads give identical results for tested case. Model appears to be thread safe.
vc-thread-safe
mandatory
The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.
This bar chart plot shows the mono-atomic body-centered cubic (bcc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This graph shows the cohesive energy versus volume-per-atom for the current mode for four mono-atomic cubic phases (body-centered cubic (bcc), face-centered cubic (fcc), simple cubic (sc), and diamond). The curve with the lowest minimum is the ground state of the crystal if stable. (The crystal structure is enforced in these calculations, so the phase may not be stable.) Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic face-centered diamond lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This graph shows the dislocation core energy of a cubic crystal at zero temperature and pressure for a specific set of dislocation core cutoff radii. After obtaining the total energy of the system from conjugate gradient minimizations, non-singular, isotropic and anisotropic elasticity are applied to obtain the dislocation core energy for each of these supercells with different dipole distances. Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic face-centered cubic (fcc) elastic constants predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic face-centered cubic (fcc) lattice constant predicted by the current model (shown in red) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This bar chart plot shows the intrinsic and extrinsic stacking fault energies as well as the unstable stacking and unstable twinning energies for face-centered cubic (fcc) predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic face-centered cubic (fcc) relaxed surface energies predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic simple cubic (sc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
Creators: Daniel Karls
Contributor: karls
Publication Year: 2016
DOI: https://doi.org/
Given an xyz file corresponding to a finite cluster of atoms, create a LAMMPS
file with the given positions/species and compute the total potential energy
and atomic forces.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Cohesive energy versus lattice constant curve for monoatomic cubic lattice
Creators: Daniel Karls
Contributor: karls
Publication Year: 2016
DOI: https://doi.org/
This Test Driver uses LAMMPS to compute the cohesive energy of a given monoatomic cubic
lattice (fcc, bcc, sc, or diamond) at a variety of lattice spacings. The lattice spacings
range from a_min (=a_min_frac*a_0) to a_max (=a_max_frac*a_0) where a_0, a_min_frac, and
a_max_frac are read from stdin (a_0 is typically approximately equal to the equilibrium lattice
constant). The precise scaling and number of lattice spacings sampled between a_min and a_0
(a_0 and a_max) is specified by two additional parameters passed from stdin: N_lower and
samplespacing_lower (N_upper and samplespacing_upper). Please see README.txt for further details.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Measures the cubic elastic constants for some common crystal types (fcc, bcc, sc) by calculating the hessian of the energy density with respect to strain. Error estimate is reported due to the numerical differentiation.
This version fixes the number of repeats in the species key.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Measures the hexagonal elastic constants for hcp structure by calculating the hessian of the energy density with respect to strain. Error estimate is reported due to the numerical differentiation.
This version fixes the number of repeats in the species key and the coordinate of the 2nd atom in the normed basis.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
LammpsExample2: energy-volume curve for monoatomic cubic lattice
Creators: Daniel Karls
Contributor: karls
Publication Year: 2014
DOI: https://doi.org/
This example Test Driver illustrates the use of LAMMPS in the openkim-pipeline
to compute an energy-volume curve (more specifically, a cohesive energy-lattice
constant curve) for a given cubic lattice (fcc, bcc, sc, diamond) of a single given
species. The curve is computed for lattice constants ranging from a_min to a_max,
with most samples being about a_0 (a_min, a_max, and a_0 are specified via stdin.
a_0 is typically approximately equal to the equilibrium lattice constant.). The precise
scaling of sample points going from a_min to a_0 and from a_0 to a_max is specified
by two separate parameters passed from stdin. Please see README.txt for further
details.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Calculates lattice constant by minimizing energy function.
This version fixes the output format problems in species and stress, and adds support for PURE and OPBC neighbor lists. The cell used for calculation is switched from a hexagonal one to an orthorhombic one to comply with the requirement of OPBC.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
This test driver is used to test lattice invariance shear in a cubic crystal based on cb-kim code. Initial guess of lattice parameter, shear direction vector, shear plane normal vector, relaxation optional key need to be set as input. The output will be first PK stress, stiffness matrix, cohesive energy, and displacement of shuffle (if relaxation optional key is true)
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
This Test Driver uses LAMMPS to compute the linear thermal expansion coefficient at a finite temperature under a given pressure for cubic lattice (fcc, bcc, sc, diamond) of a single given species.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Potential energy and atomic forces of periodic, non-orthogonal cell of atoms
Creators: Daniel Karls
Contributor: karls
Publication Year: 2014
DOI: https://doi.org/
Given an extended xyz file corresponding to a non-orthogonal periodic box of
atoms, create a LAMMPS file with the given positions/species and compute the
total potential energy and atomic forces.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Computes the monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Computes the monovacancy formation and migration energies for cubic and hcp monoatomic crystals.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Parameter Choices in Balamane et al. Rescaled SW Potential
In the original Stillinger-Weber paper (SW85: PRB 31:5262, 1985) it is stated that in order to obtain the correct “atomization energy” (cohesive energy) the following choice for epsilon must be made (see Eqn. (2.9) in [SW85]):
epsilon = 50 kcal/mol = 3.4723E-12 erg/atom
There are some unit conversion issues related to this data (see https://openkim.org/cite/MO_405512056662_003). However, a more fundamental problem is that in [SW85] the potential is fitted to an incorrect value for the cohesive energy of silicon. Using Eqn. (2.8) in [SW85], the cohesive energy corresponding to epsilon = 2.1682 eV (corresponding to 50 kcal/mol) is
E_coh = 2.168205112 eV x 1.999993 = 4.33639505 eV
However, the accepted experimental value for E_coh for silicon in the diamond structure is 4.63 eV. (See for example, B. Farid and R. W. Godby, “Cohesive energies of crystals”, Phys. Rev. B, vol 43, 14248-24250, 1991).
This discrepancy led Balamane, Halicioglu and Tiller in their review article of silicon potentials (H. Balamane, T. Halicioglu and W. A. Tiller, “Comparative study of silicon empirical interatomic potentials”, Phys. Rev. B, vol. 46, 2250-2279, 1992) to rescale the SW epsilon parameter to 2.315 eV which reproduces the experimental cohesive energy.
It is important to realize that the rescaled potential is completely different from the original SW potential. It will have different forces, different elastic constants, different activated processes, etc. Only equlibrium structures will be the same. Unfortunately, Balamane et al. did not state in their article that this rescaling was performed which has led to some confusion. (The fact that a rescaling was done was mentioned in an earlier article by the authors, Balamane et al., Phys. Rev. B, vol 40, 9999-10001. See last paragraph on p.9999.)
Balamane et al.’s rescaled SW potential may have merit, but it should not be confused with the original SW potential, which should use epsilon = 2.1682 eV (see https://openkim.org/cite/MO_405512056662_003)
Three_Body_Stillinger_Weber_Balamane_Si__MO_113686039439_002