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MEAM_LAMMPS_DickelBaskesAslam_2018_MgAlZn__MO_093637366498_002

Interatomic potential for Aluminum (Al), Magnesium (Mg), Zinc (Zn).
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Title
A single sentence description.
MEAM potential for Mg–Al–Zn alloys developed by Dickel et al. (2018) v002
Citations

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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.
Because of its substantial c/a ratio, Zn has proven to be a problematic element to model using semi-empirical classical potentials. It has been shown, in particular, that for the modified embedded atom method (MEAM), a potential cannot simultaneously have an hcp ground state and c/a ratio greater than ideal. However, as an alloying element, practical Zn potentials can be generated by relaxing the condition that hcp be the lowest energy structure. A MEAM Zn potential is developed, which gives accurate material properties for the pure state and a MEAM ternary potential for the Mg-Al–Zn system, which will allow the atomistic modeling of a broad class of alloys containing Zn. Zn's effects in simple Mg–Zn results for this potential verifies the accuracy for the new potential in these systems.
Species
The supported atomic species.
Al, Mg, Zn
Disclaimer
A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.
None
Content Origin Files are provided by Doyl E Dickel (Mississippi State University) on Mar 6, 2021, and posted with his permission.
Contributor Yaser Afshar
Maintainer Yaser Afshar
Developer Doyl E. Dickel
Michael I. Baskes
Imran Aslam
Christopher D. Barrett
Published on KIM 2023
How to Cite

This Model originally published in [1] is archived in OpenKIM [2-5].

[1] Dickel DE, Baskes MI, Aslam I, Barrett CD. New interatomic potential for Mg–Al–Zn alloys with specific application to dilute Mg-based alloys. Modelling and Simulation in Materials Science and Engineering. 2018Apr;26(4):045010. doi:10.1088/1361-651x/aabaad — (Primary Source) A primary source is a reference directly related to the item documenting its development, as opposed to other sources that are provided as background information.

[2] Dickel DE, Baskes MI, Aslam I, Barrett CD. MEAM potential for Mg–Al–Zn alloys developed by Dickel et al. (2018) v002. OpenKIM; 2023. doi:10.25950/ca972fcb

[3] Afshar Y, Hütter S, Rudd RE, Stukowski A, Tipton WW, Trinkle DR, et al. The modified embedded atom method (MEAM) potential v002. OpenKIM; 2023. doi:10.25950/ee5eba52

[4] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6

[5] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a

Click here to download the above citation in BibTeX format.
Funding Not available
Short KIM ID
The unique KIM identifier code.
MO_093637366498_002
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.
MEAM_LAMMPS_DickelBaskesAslam_2018_MgAlZn__MO_093637366498_002
DOI 10.25950/ca972fcb
https://doi.org/10.25950/ca972fcb
https://commons.datacite.org/doi.org/10.25950/ca972fcb
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 MEAM_LAMMPS__MD_249792265679_002
DriverMEAM_LAMMPS__MD_249792265679_002
KIM API Version2.2
Potential Type meam
Previous Version MEAM_LAMMPS_DickelBaskesAslam_2018_MgAlZn__MO_093637366498_001

(Click here to learn more about Verification Checks)

Grade Name Category Brief Description Full Results Aux File(s)
P vc-species-supported-as-stated mandatory
The model supports all species it claims to support; see full description.
Results Files
P vc-periodicity-support mandatory
Periodic boundary conditions are handled correctly; see full description.
Results Files
P vc-permutation-symmetry mandatory
Total energy and forces are unchanged when swapping atoms of the same species; see full description.
Results Files
A vc-forces-numerical-derivative consistency
Forces computed by the model agree with numerical derivatives of the energy; see full description.
Results Files
F 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 vc-objectivity informational
Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.
Results Files
P 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 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 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
P vc-unit-conversion mandatory
The model is able to correctly convert its energy and/or forces to different unit sets; see full description.
Results Files


BCC Lattice Constant

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.

Species: Al
Species: Mg
Species: Zn


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.

Species: Mg
Species: Al
Species: Zn


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.

Species: Zn
Species: Mg
Species: Al


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.

Species: Al
Species: Zn
Species: Mg


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.

Species: Mg
Species: Al
Species: Zn


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.

Species: Al


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.

Species: Al


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.

Species: Mg
Species: Zn
Species: Al


Cubic Crystal Basic Properties Table

Species: Al

Species: Mg

Species: Zn





Cohesive energy versus lattice constant curve for monoatomic cubic lattices v003

Creators:
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/64cb38c5

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)
Cohesive energy versus lattice constant curve for bcc Al v004 view 14074
Cohesive energy versus lattice constant curve for bcc Mg v004 view 12383
Cohesive energy versus lattice constant curve for bcc Zn v004 view 13268
Cohesive energy versus lattice constant curve for diamond Al v004 view 14064
Cohesive energy versus lattice constant curve for diamond Mg v004 view 15387
Cohesive energy versus lattice constant curve for diamond Zn v004 view 13517
Cohesive energy versus lattice constant curve for fcc Al v004 view 13328
Cohesive energy versus lattice constant curve for fcc Mg v004 view 14945
Cohesive energy versus lattice constant curve for fcc Zn v004 view 15313
Cohesive energy versus lattice constant curve for sc Al v004 view 14650
Cohesive energy versus lattice constant curve for sc Mg v004 view 13755
Cohesive energy versus lattice constant curve for sc Zn v004 view 15092


Elastic constants for cubic crystals at zero temperature and pressure v006

Creators: Junhao Li and Ellad Tadmor
Contributor: tadmor
Publication Year: 2019
DOI: https://doi.org/10.25950/5853fb8f

Computes the cubic elastic constants for some common crystal types (fcc, bcc, sc, diamond) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.
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 bcc Al at zero temperature v006 view 39147
Elastic constants for bcc Mg at zero temperature v006 view 45497
Elastic constants for bcc Zn at zero temperature v006 view 44099
Elastic constants for diamond Al at zero temperature v001 view 88639
Elastic constants for diamond Mg at zero temperature v001 view 160419
Elastic constants for diamond Zn at zero temperature v001 view 64123
Elastic constants for fcc Al at zero temperature v006 view 33508
Elastic constants for fcc Mg at zero temperature v006 view 65007
Elastic constants for fcc Zn at zero temperature v006 view 48516
Elastic constants for sc Al at zero temperature v006 view 49326
Elastic constants for sc Zn at zero temperature v006 view 54802


Equilibrium structure and energy for a crystal structure at zero temperature and pressure v001

Creators:
Contributor: ilia
Publication Year: 2023
DOI: https://doi.org/10.25950/e8a7ed84

Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.
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 crystal structure and energy for AlMg in AFLOW crystal prototype A12B17_cI58_217_g_acg v001 view 188395
Equilibrium crystal structure and energy for AlMg in AFLOW crystal prototype A14B13_cI54_229_ef_ah v001 view 255095
Equilibrium crystal structure and energy for MgZn in AFLOW crystal prototype A2B11_cP39_200_f_begik v001 view 193180
Equilibrium crystal structure and energy for AlMg in AFLOW crystal prototype A2B_tI24_141_2e_e v001 view 98136
Equilibrium crystal structure and energy for AlMg in AFLOW crystal prototype A30B23_hR53_148_5f_a2c3f v001 view 2663590
Equilibrium crystal structure and energy for AlMgZn in AFLOW crystal prototype A4B19C15_oC152_63_h_c3f2g2h_aefg2h v000 view 2245352
Equilibrium crystal structure and energy for AlMgZn in AFLOW crystal prototype A4B2C3_hP18_194_ef_f_h v000 view 55952
Equilibrium crystal structure and energy for MgZn in AFLOW crystal prototype A4B7_mC110_12_10i_ae8i4j v001 view 1070442
Equilibrium crystal structure and energy for AlMg in AFLOW crystal prototype A67B41_cP108_221_aeh2il_cfgm v001 view 773825
Equilibrium crystal structure and energy for Al in AFLOW crystal prototype A_cF4_225_a v001 view 62765
Equilibrium crystal structure and energy for Mg in AFLOW crystal prototype A_cF4_225_a v001 view 61473
Equilibrium crystal structure and energy for Al in AFLOW crystal prototype A_cI2_229_a v001 view 46603
Equilibrium crystal structure and energy for Mg in AFLOW crystal prototype A_cI2_229_a v001 view 71706
Equilibrium crystal structure and energy for Mg in AFLOW crystal prototype A_hP2_194_c v001 view 58381
Equilibrium crystal structure and energy for Zn in AFLOW crystal prototype A_hP2_194_c v001 view 67804
Equilibrium crystal structure and energy for MgZn in AFLOW crystal prototype AB2_hP12_194_f_ah v001 view 71559
Equilibrium crystal structure and energy for MgZn in AFLOW crystal prototype AB5_mC48_12_2i_ac5i2j v001 view 236984


Relaxed energy as a function of tilt angle for a symmetric tilt grain boundary within a cubic crystal v003

Creators:
Contributor: brunnels
Publication Year: 2022
DOI: https://doi.org/10.25950/2c59c9d6

Computes grain boundary energy for a range of tilt angles given a crystal structure, tilt axis, and material.
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)
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Al v003 view 49975766
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Al v001 view 76862499


Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure v007

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/2765e3bf

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)
Equilibrium zero-temperature lattice constant for bcc Al v007 view 16049
Equilibrium zero-temperature lattice constant for bcc Mg v007 view 16197
Equilibrium zero-temperature lattice constant for bcc Zn v007 view 17903
Equilibrium zero-temperature lattice constant for diamond Al v007 view 18559
Equilibrium zero-temperature lattice constant for diamond Mg v007 view 18037
Equilibrium zero-temperature lattice constant for diamond Zn v007 view 18738
Equilibrium zero-temperature lattice constant for fcc Al v007 view 26062
Equilibrium zero-temperature lattice constant for fcc Mg v007 view 19509
Equilibrium zero-temperature lattice constant for fcc Zn v007 view 19951
Equilibrium zero-temperature lattice constant for sc Al v007 view 15019
Equilibrium zero-temperature lattice constant for sc Mg v007 view 17067
Equilibrium zero-temperature lattice constant for sc Zn v007 view 18405


Equilibrium lattice constants for hexagonal bulk structures at zero temperature and pressure v005

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/c339ca32

Calculates lattice constant of hexagonal bulk structures at zero temperature and pressure by using simplex minimization to minimize the potential energy.
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 v005 view 420656
Equilibrium lattice constants for hcp Mg v005 view 501061
Equilibrium lattice constants for hcp Zn v005 view 501503


Phonon dispersion relations for an fcc lattice v004

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/64f4999b

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 v004 view 96973


Stacking and twinning fault energies of an fcc lattice at zero temperature and pressure v002

Creators:
Contributor: SubrahmanyamPattamatta
Publication Year: 2019
DOI: https://doi.org/10.25950/b4cfaf9a

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 v002 view 98907375


High-symmetry surface energies in cubic lattices and broken bond model v004

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/6c43a4e6

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 following 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 v004 view 176273


Monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/fca89cea

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 930416
Monovacancy formation energy and relaxation volume for hcp Mg view 834268
Monovacancy formation energy and relaxation volume for hcp Zn view 1035325


Vacancy formation and migration energies for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/c27ba3cd

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 2121816
Vacancy formation and migration energy for hcp Mg view 1119694
Vacancy formation and migration energy for hcp Zn view 4358775


ElasticConstantsCubic__TD_011862047401_006
Test Error Categories Link to Error page
Elastic constants for sc Mg at zero temperature v006 other view

ElasticConstantsHexagonal__TD_612503193866_004

EquilibriumCrystalStructure__TD_457028483760_001

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

LinearThermalExpansionCoeffCubic__TD_522633393614_001

PhononDispersionCurve__TD_530195868545_004
Test Error Categories Link to Error page
Phonon dispersion relations for fcc Al v004 other view

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004
Test Error Categories Link to Error page
Broken-bond fit of high-symmetry surface energies in fcc Al v004 other view




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