glue potential for Al-Pb system

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EAM_Dynamo_Landa_Wynblatt_AlPb__MO_699137396381_004

There is a newer version of this item. See EAM_Dynamo_LandaWynblattSiegel_2000_AlPb__MO_699137396381_005

Interatomic potential for Aluminum (Al), Lead (Pb).
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Title A single sentence description.	glue potential for Al-Pb system
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.	glue potential, Al, Pb, Al-Pb. Developed at Carnegie Mellon University to study the Al-Pb phase diagram and Pb/Al interfaces.
Species The supported atomic species.	Al, Pb
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None
Content Origin	http://www.ctcms.nist.gov/potentials/Pb.html

Contributor	Alexander I. Landa
Maintainer	Alexander I. Landa
Published on KIM	2018
How to Cite	Click here to download this citation in BibTeX format.
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_699137396381_004
Extended KIM ID 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.	EAM_Dynamo_Landa_Wynblatt_AlPb__MO_699137396381_004
Citable Link	https://openkim.org/cite/MO_699137396381_004
KIM Item Type 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).	Portable Model using Model Driver EAM_Dynamo__MD_120291908751_004
Driver	EAM_Dynamo__MD_120291908751_004
KIM API Version	1.6

Previous Version	EAM_Dynamo_Landa_Wynblatt_AlPb__MO_699137396381_003

Verification Check Dashboard

(Click here to learn more about Verification Checks)

Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configrations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
F The letter grade F was assigned because the normalized error in the computation was 2.00000e+00 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.	Results	Files
F The model is C^0 continuous. This means that the model has continuous energy, but a discontinuous first derivative.	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.	Results	Files
P 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.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
P No memory leak detected.	vc-memory-leak	informational	The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.	Results	Files
P 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.	Results	Files

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.

(No matching species)

Cohesive Energy Graph

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.

(No matching species)

Diamond Lattice Constant

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.

(No matching species)

Dislocation Core Energies

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.

(No matching species)

FCC Elastic Constants

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.

(No matching species)

FCC Lattice Constant

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.

(No matching species)

FCC Stacking Fault Energies

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.

(No matching species)

FCC Surface Energies

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.

(No matching species)

SC Lattice Constant

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.

(No matching species)

Cubic Crystal Basic Properties Table

Species: Al

Species: Pb

Tests

CohesiveEnergyVsLatticeConstant__TD_554653289799_001

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	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 bcc Aluminum	view	1615
Cohesive energy versus lattice constant curve for bcc Lead	view	1938
Cohesive energy versus lattice constant curve for diamond Aluminum	view	2010
Cohesive energy versus lattice constant curve for diamond Lead	view	1723
Cohesive energy versus lattice constant curve for fcc Aluminum	view	1723
Cohesive energy versus lattice constant curve for fcc Lead	view	1902
Cohesive energy versus lattice constant curve for sc Aluminum	view	1543
Cohesive energy versus lattice constant curve for sc Lead	view	1866

ElasticConstantsCubic__TD_011862047401_003

Elastic constants for cubic crystals at zero temperature

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2017
DOI: https://doi.org/

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	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)
Elastic constants for bcc Al at zero temperature	view	1148
Elastic constants for bcc Pb at zero temperature	view	1723
Elastic constants for fcc Al at zero temperature	view	1436
Elastic constants for fcc Pb at zero temperature	view	1400
Elastic constants for sc Al at zero temperature	view	1723
Elastic constants for sc Pb at zero temperature	view	1723

ElasticConstantsHexagonal__TD_612503193866_002

Elastic constants for hexagonal crystals at zero temperature

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2017
DOI: https://doi.org/

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)
Elastic constants for hcp Al at zero temperature		view	1651

Grain_Boundary_Symmetric_Tilt_Relaxed_Energy_vs_Angle_Cubic_Crystal__TD_410381120771_000

The relaxed energy as a function of tilt angle for a symmetric tilt grain boundary within a cubic crystal

Creators: Brandon Runnels
Contributor: brunnels
Publication Year: 2016
DOI: https://doi.org/

Compute grain boundary energy for a range of tilt angles given a crystal structure, tilt axis, and materials.

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)
The relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Al		view	60139090

LatticeConstantCubicEnergy__TD_475411767977_004

Equilibrium lattice constants for bulk cubic structures

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2018
DOI: https://doi.org/

Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.

Test	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 zero-temperature lattice constant for bcc Al	view	502
Equilibrium zero-temperature lattice constant for bcc Pb	view	646
Equilibrium zero-temperature lattice constant for diamond Al	view	790
Equilibrium zero-temperature lattice constant for diamond Pb	view	718
Equilibrium zero-temperature lattice constant for fcc Al	view	718
Equilibrium zero-temperature lattice constant for fcc Pb	view	502
Equilibrium zero-temperature lattice constant for sc Al	view	682
Equilibrium zero-temperature lattice constant for sc Pb	view	502

LatticeConstantHexagonalEnergy__TD_942334626465_003

Equilibrium lattice constants for hexagonal bulk structures

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2017
DOI: https://doi.org/

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)
Equilibrium lattice constants for hcp Al		view	4558

LinearThermalExpansionCoeffCubic__TD_522633393614_000

Linear thermal expansion coefficient of a cubic crystal structure at a given temperature and pressure v000

Creators: Mingjian Wen
Contributor: mjwen
Publication Year: 2016
DOI: https://doi.org/

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)
Linear thermal expansion coefficient of fcc Al at room temperature under zero pressure		view	5248551
Linear thermal expansion coefficient of fcc Pb at room temperature under zero pressure		view	1745856

PhononDispersionCurve__TD_530195868545_002

Phonon dispersion relations for fcc lattices

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2016
DOI: https://doi.org/

Calculates the phonon dispersion relations for fcc lattices and records the results as curves.

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)
Phonon dispersion relations for fcc Al		view	104652
Phonon dispersion relations for fcc Pb		view	116173

StackingFaultFccCrystal__TD_228501831190_000

Stacking and twinning fault energies for FCC crystals

Creators: Subrahmanyam Pattamatta
Contributor: SubrahmanyamPattamatta
Publication Year: 2018
DOI: https://doi.org/

Intrinsic and extrinsic stacking fault energies, unstable stacking fault energy, unstable twinning energy, stacking fault energy as a function of fractional displacement, and gamma surface for a monoatomic FCC 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)
Stacking and twinning fault energies for fcc Al		view	5061390
Stacking and twinning fault energies for fcc Pb		view	5941532

SurfaceTest__TD_955413365818_002

Broken-bond fit of high-symmetry surface energies in cubic crystal lattices

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2017
DOI: https://doi.org/

Calculates the surface energy of several high symmetry surfaces and produces a broken bond model fit. In latex form, the fit equations are given by:

E_{FCC} (\vec{n}) = p_1 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (2 ( |x+ 2y + z| + |x+2y-z| + |x-2y + z| + |x-2y-z| + |2x+y+z| + |2x+y-z| +|2x-y+z| +|2x-y-z| +|x+y+2z| +|x+y-2z| +|x-y+2z| +|x-y-2z| ) + c

E_{BCC} (\vec{n}) = p_1 (6 \left( | x+y+z| + |x+y-z| + |-x+y-z| + |x-y+z| \right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) +c.

In Python, these two fits take the form:
def BrokenBondFCC(params, index):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*(abs(x+2*y+z) + abs(x+2*y-z) +abs(x-2*y+z) +abs(x-2*y-z) + abs(2*x+y+z) +abs(2*x+y-z) +abs(2*x-y+z) +abs(2*x-y-z) + abs(x+y+2*z) +abs(x+y-2*z) +abs(x-y+2*z) +abs(x-y-2*z))+params[3]

def BrokenBondBCC(params, x, y, z):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*6*(abs(x+y+z) + abs(x-y-z) + abs(x-y+z) + abs(x+y-z)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[3]

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)
Broken-bond fit of high-symmetry surface energies in fcc Al		view	46584
Broken-bond fit of high-symmetry surface energies in fcc Pb		view	53726

VacancyFormationEnergyRelaxationVolume__TD_647413317626_000

Monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2018
DOI: https://doi.org/

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)
Monovacancy formation energy and relaxation volume for fcc Al		view	228936
Monovacancy formation energy and relaxation volume for fcc Pb		view	221902

VacancyFormationMigration__TD_554849987965_000

Vacancy formation and migration energies for cubic and hcp monoatomic crystals

Creators:
Contributor: jl2922
Publication Year: 2018
DOI: https://doi.org/

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)
Vacancy formation and migration energy for fcc Al		view	137419
Vacancy formation and migration energy for fcc Pb		view	382110

Errors

ElasticConstantsFirstStrainGradient__TD_361847723785_000

Test	Error Categories	Link to Error page
Classical and first strain gradient elastic constants for fcc aluminum	other	view

LatticeConstantHexagonalEnergy__TD_942334626465_003

Test	Error Categories	Link to Error page
Equilibrium lattice constants for hcp Pb	other	view

Files

LICENSE.CDDL
Makefile
alpb-setfl.eam.alloy
kimprovenance.edn
kimspec.edn

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Wiki

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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 $θ = \cos^{- 1} (- 0.25) = {104.48}^{\circ}$ , as a function of $r_{i j}$ and $r_{i k}$ is given below:

EAM_Dynamo_Landa_Wynblatt_AlPb__MO_699137396381_004

Verification Check Dashboard

Visualizers (in-page)

BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

Errors

Files

Download

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Wiki

Parameter Choices in the SW Potential

SW Functions