cohesive-free-energy-hexagonal-crystal
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| cohesive-free-energy-hexagonal-crystal |
|---|---|
| Property Definition ID
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| tag:staff@noreply.openkim.org,2014-04-15:property/cohesive-free-energy-hexagonal-crystal |
| Title
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| Cohesive free energy of hexagonal crystal structure at a given temperature under stress-free boundary conditions |
| Description
A description about this Property Definition.
| Cohesive free energy of a hexagonal crystal at a given temperature under stress-free boundary conditions. |
| Contributor
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| karls |
| Maintainer
The user or organization who currently maintains this Property Definition.
| karls |
| Creation date
The date the Property Definition was "minted", based on its Tag URI.
| 2014-04-15 |
| Content on GitHub
The following content may be available on GitHub: Property Definition (an EDN file containing the Property Definition Keys listed below); Physics Validator (a script provided by the user for validating that an instance of the Property is physically valid); Property Documentation Wiki (the contents of the Wiki displayed at the bottom of this page).
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Property Definition Keys
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Required Optional
a
| type | float |
|---|---|
| has-unit | true |
| extent | [] |
| required | true |
| description | The average length of unit cell vectors <a> and <b> at the specified temperature under stress-free boundary conditions. The two associated directions must correspond to the first and second components of the entries of 'basis-atom-coordinates'. The triad (<a>,<b>,<c>) must form a right-handed system. |
basis-atom-coordinates
| type | float |
|---|---|
| has-unit | false |
| extent | [":" 3] |
| required | true |
| description | Fractional coordinates of the basis atoms in the conventional unit cell. If the unit cell vectors are denoted by <a>, <b>, and <c>, and the fractional coordinates of atom 'i' are [afrac_i, bfrac_i, cfrac_i], the value of 'basis-atom-coordinates' will be of the form [[afrac_1 bfrac_1 cfrac_1] [afrac_2 bfrac_2 cfrac_2] ... ]. All components of each basis atom should be between zero and one, inclusive of zero. |
c
| type | float |
|---|---|
| has-unit | true |
| extent | [] |
| required | true |
| description | The average length of unit cell vector <c> at the specified temperature under stress-free boundary conditions. The associated direction must correspond to the third component of the entries of 'basis-atom-coordinates'. The triad (<a>,<b>,<c>) must form a right-handed system. |
cohesive-free-energy
| type | float |
|---|---|
| has-unit | true |
| extent | [] |
| required | true |
| description | Cohesive free energy of the hexagonal crystal at the specified temperature under stress-free boundary conditions. |
species
| type | string |
|---|---|
| has-unit | false |
| extent | [":"] |
| required | true |
| description | The element symbols of the basis atoms. The order in which the species are specified must correspond to the order of the atoms listed in 'basis-atom-coordinates'. |
temperature
| type | float |
|---|---|
| has-unit | true |
| extent | [] |
| required | true |
| description | Temperature of the crystal. |
short-name
| type | string |
|---|---|
| has-unit | false |
| extent | [":"] |
| required | false |
| description | Short name defining the hexagonal crystal type. |
space-group
| type | string |
|---|---|
| has-unit | false |
| extent | [] |
| required | false |
| description | Hermann-Mauguin designation for the space group associated with the symmetry of the crystal (e.g. Immm, Fm-3m, P6_3/mmc). |
wyckoff-coordinates
| type | float |
|---|---|
| has-unit | false |
| extent | [":" 3] |
| required | false |
| description | Coordinates of the unique Wyckoff sites used in the fully symmetry-reduced description of the crystal, given as fractions of the lattice vectors. The order of elements in this array must correspond to the order of the entries listed in 'wyckoff-species' and 'wyckoff-multiplicity-and-letter'. |
wyckoff-multiplicity-and-letter
| type | string |
|---|---|
| has-unit | false |
| extent | [":"] |
| required | false |
| description | Multiplicity and standard letter of the unique Wyckoff sites used in the fully symmetry-reduced description of the crystal (e.g. 4a, 2b). Note that the sum of the Wyckoff multiplicities should equal the total number of elements in 'basis-atom-coordinates'. The order of elements in this array must correspond to the order of the entries listed in 'wyckoff-species' and 'wyckoff-coordinates'. |
wyckoff-species
| type | string |
|---|---|
| has-unit | false |
| extent | [":"] |
| required | false |
| description | The element symbol of the atomic species of the unique Wyckoff sites used in the fully symmetry-reduced description of the crystal. The order of the entries must correspond to the order of the entries in 'wyckoff-multiplicity-and-letter' and 'wyckoff-coordinates'. |
Property Documentation Wiki
Parameter Choices in the 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
Unfortunately, there appears to be an error in the unit conversion here. (There is also an indeterminacy associated with the “kcal” unit which can mean different things.) The kcal and erg values have led to two different values for epsilon being used in articles that cite [SW85].
(a) If the kcal number is selected (assuming that S&W meant the thermochemical kcal unit), then epsilon = 2.1682 eV. This can be seen from the following conversion (which uses NIST conversion factors):
(50 kcal_th/mol)/(6.02214129 mol^-1) = 8.30269461E-23 kcal_th
8.30269461E-23 kcal_th x 4.184E+03 (J/kcal_th) = 3.47384742E-19 J
3.47384742E-19 J x 6.24150934E+18 (eV/J) = 2.168205112 eV
(b) If the erg number is selected, then epsilon = 2.1672 eV, which follows from:
3.4723E-12 erg x 6.24150934E+11 (eV/erg) = 2.16723929 eV
As noted above, both values have been used in simulations that cite the original [SW85] paper. However, it appears that S&W intended to use the 50 kcal_th/mol value since they refer to this number more than once in the paper. (See for example discussion after Eqn. (8.1) in [SW85].) Therefore we argue that the appropriate choice is
epsilon = 8.30269461E-23 kcal_th
or in eV units (reduced to 5-digit significant digits):
epsilon = 2.1682 eV
Note that in the Si.sw parameterization for this potential distributed with LAMMPS, a value of epsilon=2.1683 is used, which appears to be due to slightly different unit conversion.
Another source of confusion is that in [SW85] the potential is fitted to an incorrect value for the cohesive energy of silicon. This is corrected by Balamane in a 1992 paper. See https://openkim.org/cite/MO_113686039439_004 for more details.
SW Functions
See the Stillinger-Weber Model driver page (linked above) for the definition of the model and its functions. The graphs below are for the Stillinger-Weber parametrization for silicon.
The graph of function \(f_2\) with the parameter values suggested by Stillinger and Weber (\(A=7.049556277\), \(B=0.6022245584\), \(p=4\), \(q=0\), \(a=1.80\)) is given in the following Figure:
The contour plot of the function \(h\) in \(f_3\) for \(\theta=\cos^{-1}(-0.25)=104.48^\circ\), as a function of \(r_{ij}\) and \(r_{ik}\) is given below:
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