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2007--Silva-A-C-Agren-J-Clavaguera-Mora-M-T-et-al--Al-Ni

Citation: A.C. Silva, J. Ågren, M.T. Clavaguera-Mora, D. Djurovic, T. Gomez-Acebo, B.-J. Lee, Z.-K. Liu, P. Miodownik, and H.J. Seifert (2007), "Applications of computational thermodynamics - the extension from phase equilibrium to phase transformations and other properties", Calphad, 31(1), 53-74. DOI: 10.1016/j.calphad.2006.02.006.
Abstract: Complex equilibria and phase transformations involving diffusion can now be calculated quickly and efficiently. Detailed examples are given for cases which involve varying degrees of non-equilibrium and therefore time-dependence. Despite very good agreement between such calculations and experimental results, many potential end-users are still not convinced that such techniques could be usefully applied to their own specific problems. Friendly graphic interface versions of calculating software are now generally available, so the authors conclude that the most likely source of the reluctance to use such tools lies in the formulation of relevant questions and the interpretation of the results. Although the potential impact of such tools was foreseen many years ago [M. Hillert, Calculation of phase equilibria, in: Conference on Phase Transformations, 1968], few changes in the relevant teaching curricula have taken into account the availability and power of such techniques.
This paper has therefore been designed not only as a collection of interesting problems, but also highlights the critical steps needed to achieve a solution. Each example includes a presentation of the "real" problem, any simplifications that are needed for its solution, the adopted thermodynamic formulation, and a critical evaluation of the results. The availability of such examples should facilitate changes in subject matter that will both make it easier for the next generation of students to use these tools, and at the same time reduce the time and effort currently needed to solve such problems by less efficient methods.
The first set of detailed examples includes the deoxidation of steel by aluminum; heat balance calculations associated with ladle additions to steel; the determination of conditions that avoid undesirable inclusions; the role of methane in sintering atmospheres; interface control during the physical vapour deposition of cemented carbide; oxidation of γ-TiAl materials; and simulation of the thermolysis of metallorganic precursors for Si-C-N ceramics and interface reaction of yttrium silicates with SiC-coated C/C-SiC composites for heat shield applications.
A second set of examples, more dependent on competitive nucleation and growth, includes segregation and carburization in multicomponent steels and features a series of sophisticated simulatons using DICTRA software.
Interfacial and strain energies become increasingly important in defining phase nucleation and morphology in such problems, but relatively little information is available compared to free energy and diffusion databases. The final section therefore demonstrates how computational thermodynamics, semi-empirical atomistic approaches and first-principles calculations are being used to aid filling this gap in our knowledge.

Related Models:
LAMMPS pair_style meam (2007--Silva-A-C--Al-Ni--LAMMPS--ipr1)
See Computed Properties
Notes: These potential files were obtained from http://cmse.postech.ac.kr/home_2nnmeam, accessed Nov 9, 2020.
File(s):

Implementation Information

This page displays computed properties for the 2007--Silva-A-C--Al-Ni--LAMMPS--ipr1 implementation of the 2007--Silva-A-C-Agren-J-Clavaguera-Mora-M-T-et-al--Al-Ni 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

2007--Silva-A-C--Al-Ni--LAMMPS--ipr1/diatom

Click on plot to load interactive version

2007--Silva-A-C--Al-Ni--LAMMPS--ipr1/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

2007--Silva-A-C--Al-Ni--LAMMPS--ipr1/EvsR.Al

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 = mp-134, oqmd-8100, oqmd-1214503
A15--beta-W = oqmd-1214948, oqmd-1280406
A2--W--bcc = mp-998860, oqmd-1215126
A3'--alpha-La--double-hcp = mp-1183144, oqmd-1215394
A3--Mg--hcp = oqmd-1215215, oqmd-1215304
A4--C--dc = oqmd-1215483
A5--beta-Sn = oqmd-1215572
A6--In--bct = oqmd-1215661

prototypemethodEcoh (eV/atom)Epot (eV/atom)a0 (Å)b0 (Å)c0 (Å)α (degrees)β (degrees)γ (degrees)
A1--Cu--fccdynamic-3.36-3.364.04474.04474.044790.090.090.0
A3'--alpha-La--double-hcpdynamic-3.3444-3.34442.84452.84459.475990.090.0120.0
A3--Mg--hcpdynamic-3.3305-3.33052.83262.83264.794690.090.0120.0
oqmd-1215037box-3.2724-3.27242.71784.85810.458490.090.090.0
mp-1245129dynamic-3.2687-3.268711.764211.788412.637791.590.4100.9
mp-1245152dynamic-3.2664-3.266411.524912.01812.495191.690.695.3
mp-1244953dynamic-3.2635-3.263512.087412.08912.301875.784.484.6
mp-1245067dynamic-3.2624-3.262411.678312.208112.412492.593.4101.1
mp-1245307dynamic-3.2613-3.261311.727711.935212.373491.892.292.2
oqmd-1214859dynamic-3.255-3.2556.99696.99696.996990.090.090.0
oqmd-1214859box-3.2525-3.25257.0027.0027.00290.090.090.0
A2--W--bccstatic-3.2417-3.24173.22693.22693.226990.090.090.0
A5--beta-Snstatic-3.2367-3.23675.13245.13242.625690.090.090.0
Ah--alpha-Po--scdynamic-3.2332-3.23322.60142.60142.601490.090.090.0
oqmd-1214770box-3.2302-3.23029.97159.97159.971590.090.090.0
mp-1244953box-3.2225-3.222511.96512.082112.281186.080.286.7
mp-1245129box-3.2206-3.220611.713412.027312.459693.591.696.6
mp-1245152box-3.2185-3.218511.890712.096912.205191.891.695.8
mp-1245307box-3.208-3.20811.986312.131912.137590.292.694.3
A15--beta-Wstatic-3.2034-3.20345.16485.16485.164890.090.090.0
mp-1245067box-3.1979-3.197911.930512.238412.286392.798.293.8
A7--alpha-Asbox-3.0979-3.09792.78222.782219.192290.090.0120.0
mp-1239196box-2.8656-2.86563.64843.648414.534290.090.090.0
oqmd-1215928box-2.7174-2.71744.59614.59614.831190.090.0120.0
A4--C--dcdynamic-2.4145-2.41456.29786.29786.297890.090.090.0

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:
114.33461.91661.916-0.00.0-0.0
61.916114.33461.916-0.00.00.0
61.91661.916114.3340.00.00.0
0.00.00.031.566-0.0-0.0
0.00.00.00.031.5660.0
0.00.00.00.00.031.566

Free Surface Formation Energy Predictions

Static free surface formation energies are displayed for select crystals. The values displayed here are obtained by taking a perfect periodic bulk crystal, slicing along a crystallographic plane, and using force minimization to statically relax the surfaces. The free surface formation energy is computed by comparing the energy of the defect system to the bulk system and dividing by the total surface area created by the cut.

The calculation method used is available as the iprPy surface_energy_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 calculation only performs straight cuts along crystallographic planes and static relaxations. Lower energy configurations may exist that require atomic restructuring of the surfaces.
  • Multiple values may be listed for a given plane followed by a number indicating different unique atomic planar cuts for the same theoretical plane.
  • NIST disclaimer

Version Information:

  • 2019-11-14. Calculations for the alternate #2 plane slices are now different from the #1 plane slices.
  • 2019-08-07. Data added.

Composition:
Prototype:
a0:

Download raw data

Surfaceγfs (mJ/m2)
(111)627.87
(332)724.83
(322)741.56
(221)778.28
(211)817.1
(331)832.7
(100)848.02
(321)885.5
(311)889.73
(110)917.4
(310)956.4
(320)964.24
(210)982.93

Point Defect Formation Energy Predictions

Static point defect formation energies, Ef, and elastic dipole tensors, pij, are displayed for select crystals. Relaxed defect configurations are obtained by taking a 12x12x12 supercell of a perfect periodic bulk crystal, inserting the point defect, and using force minimization to statically relax the atomic positions while keeping the system dimensions constant. Ef is computed by comparing the energy of the defect system to the same number of atoms in a perfect bulk crystal. pij is estimated as the difference in the system's global pressure with and without the defect multiplied by the system's volume.

Simple structural comparisons of the unrelaxed and relaxed defect configurations are used to help determine if the defect structure has relaxed to a different configuration. Relaxed structures that are identified as no longer consistent with the ideal defect definition are excluded from the table below. The only exception to this is if the lowest energy interstitial configuration does not coincide with a known ideal defect, its energies and pressure tensor are included under the listing "relaxed interstitial". The full list of calculation results including the transformed structures and the structural comparison values is included in the csv file available from the "Download raw data" link.

The calculation method used is available as the iprPy point_defect_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 changes in calculation methods, simulation software and implementations of the interatomic potentials.
  • The computed formation energy and elastic dipole tensor values are sensitive to the size of the system used. The 12x12x12 supercell size was selected as it should provide a decent approximation of the true bulk values.
  • The tests for identifying configuration relaxations are not guaranteed to be comprehensive or suitable for all point defect types. The table only shows the point defects that are consistent with the ideal configurations for that defect type, and the lowest energy interstitial.
  • The "relaxed interstitial" label indicates that the structure is not consistent with any of the known ideal interstitial configurations. No information is provided as to what that relaxed strucutre is, whether it is an unknown structure, a "near"-ideal defect, or a collapse to amorphous.
  • NIST disclaimer

Composition:
Prototype:
a0:

Download raw data

Point DefectEf (eV)p11 (eV)p22 (eV)p33 (eV)p12 (eV)p13 (eV)p23 (eV)
vacancy0.68-2.263-2.263-2.2630.00.00.0
1nn divacancy1.37-3.889-4.268-4.2680.00.0-0.076
2nn divacancy1.449-4.754-4.754-4.4970.00.00.0
crowdion interstitial2.513.93313.93314.1663.3040.00.0
110 dumbbell2.514.14913.93913.9390.00.03.309
100 dumbbell2.59315.98515.98511.6650.0-0.0-0.0
octahedral interstitial2.70614.08114.08114.0810.00.00.0
Date Created: October 5, 2010 | Last updated: December 14, 2022