× Warning! Note that elemental potentials taken from alloy descriptions may not work well for the pure species. This is particularly true if the elements were fit for compounds instead of being optimized separately. As with all interatomic potentials, please check to make sure that the performance is adequate for your problem.

× Updated! Potentials that share interactions are now listed as related models.

2008--Hepburn-D-J-Ackland-G-J--Fe-C

Citation: D.J. Hepburn, and G.J. Ackland (2008), "Metallic-covalent interatomic potential for carbon in iron", Physical Review B, 78(16), 165115. DOI: 10.1103/physrevb.78.165115.

Abstract: Existing interatomic potentials for the iron-carbon system suffer from qualitative flaws in describing even the simplest of defects. In contrast to more accurate first-principles calculations, all previous potentials show strong bonding of carbon to overcoordinated defects (e.g., self-interstitials, dislocation cores) and a failure to accurately reproduce the energetics of carbon-vacancy complexes. Thus any results from their application in molecular dynamics to more complex environments are unreliable. The problem arises from a fundamental error in potential design—the failure to describe short-ranged covalent bonding of the carbon p electrons. We describe a resolution to the problem and present an empirical potential based on insights from density-functional theory, showing covalent-type bonding for carbon. The potential correctly describes the interaction of carbon and iron across a wide range of defect environments. It has the embedded atom method form and hence appropriate for billion atom molecular-dynamics simulations.

LAMMPS pair_style eam/fs (2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1)

See Computed Properties
Notes: This file was implemented in the LAMMPS-compatible EAM/FS format by Sebastien Garruchet and posted with the permission of G.J. Ackland on 13 May 2009.
File(s):

Fe-C_Hepburn_Ackland.eam.fs

OpenKIM (MO_143977152728)

See Computed Properties
Notes: Listing found at https://openkim.org. This KIM potential is based on the files from 2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1.
Link(s):

KIM page EAM_Dynamo_HepburnAckland_2008_FeC__MO_143977152728_005

Implementation Information

This page displays computed properties for the 2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1 implementation of the 2008--Hepburn-D-J-Ackland-G-J--Fe-C 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

2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1/diatom

Click on plot to load interactive version

2008--Hepburn-D-J--Fe-C--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

2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1/EvsR.C

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.

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.
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.
The relaxed structures obtained from #2 are then evaluated using the spglib package to identify an ideal crystal unit cell based on the results.
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.
The cohesive energy, E_coh, is calculated from the measured potential energy per atom, E_pot$, 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 = oqmd-1214512
A15--beta-W = oqmd-1214957
A2--W--bcc = oqmd-1215135
A3'--alpha-La--double-hcp = oqmd-1215403
A3--Mg--hcp = oqmd-1215313
A4--C--dc = mp-66, oqmd-675640
A5--beta-Sn = oqmd-1215581
A6--In--bct = mp-1181996, oqmd-1215670
A7--alpha-As = mp-169, oqmd-594528
Ah--alpha-Po--sc = mp-998866, oqmd-636457, oqmd-1214601

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
mp-1182029	static	-3.1824	-3.1824	1.5495	3.5003	3.5003	90.0	97.3	90.0
oqmd-1215848	dynamic	-3.1824	-3.1824	4.4394	4.4394	1.5495	90.0	90.0	120.0
mp-1182029	dynamic	-3.1824	-3.1824	1.5495	4.5135	4.4352	90.0	99.0	90.0
mp-1095633	dynamic	-3.067	-3.067	8.7339	8.7339	6.1205	90.0	90.0	90.0
mp-569304	dynamic	-3.0513	-3.0513	2.849	2.849	36.5932	90.0	90.0	120.0
mp-568286	dynamic	-3.0513	-3.0513	2.849	4.9347	8.2175	90.0	90.0	90.0
mp-937760	dynamic	-3.0513	-3.0513	2.849	4.9347	7.9811	90.0	90.0	90.0
mp-568363	dynamic	-3.0513	-3.0513	2.849	4.9347	8.4426	90.0	90.0	90.0
mp-990424	static	-3.0513	-3.0513	2.849	2.849	25.8284	90.0	90.0	120.0
mp-632329	dynamic	-3.0513	-3.0513	4.9347	2.849	3.9759	90.0	94.2	90.0
A7--alpha-As	static	-3.0513	-3.0513	2.849	2.849	12.061	90.0	90.0	120.0
A7--alpha-As	dynamic	-3.0513	-3.0513	2.849	2.849	12.5667	90.0	90.0	120.0
oqmd-1215937	dynamic	-3.0513	-3.0513	2.849	2.849	7.7553	90.0	90.0	120.0
mp-990424	dynamic	-3.0513	-3.0513	2.849	2.849	24.5525	90.0	90.0	120.0
mp-990448	dynamic	-3.0513	-3.0513	2.849	2.849	9.9991	90.0	90.0	120.0
mp-1040425	dynamic	-3.0513	-3.0513	2.849	2.849	19.9983	90.0	90.0	120.0
mp-568806	dynamic	-3.0513	-3.0513	2.849	2.849	3.83	90.0	90.0	120.0
mp-568286	static	-3.0513	-3.0513	4.9347	2.849	8.0283	90.0	90.0	90.0
mp-568363	static	-3.0513	-3.0513	4.9347	2.849	8.1499	90.0	90.0	90.0
oqmd-1214690	dynamic	-3.0513	-3.0513	2.849	4.9347	7.4626	90.0	90.0	90.0
mp-606949	dynamic	-3.0513	-3.0513	2.849	2.849	32.9151	90.0	90.0	120.0
mp-997182	dynamic	-3.0513	-3.0513	2.849	2.849	15.5268	90.0	90.0	120.0
mp-48	dynamic	-3.0513	-3.0513	2.849	2.849	7.9964	90.0	90.0	120.0
mp-997182	static	-3.0513	-3.0513	2.849	2.849	14.9976	90.0	90.0	120.0
mp-48	static	-3.0513	-3.0513	2.849	2.849	7.8031	90.0	90.0	120.0
mp-937760	static	-3.0513	-3.0513	2.849	4.9347	7.98	90.0	90.0	90.0
oqmd-590101	static	-3.0513	-3.0513	2.849	2.849	7.0022	90.0	90.0	120.0
mp-606949	static	-3.0513	-3.0513	2.849	2.849	31.983	90.0	90.0	120.0
oqmd-589493	static	-3.0513	-3.0513	2.849	2.849	30.4263	90.0	90.0	120.0
oqmd-610551	static	-3.0513	-3.0513	2.849	2.849	3.5023	90.0	90.0	120.0
oqmd-683819	static	-3.0513	-3.0513	2.849	4.9347	6.8177	90.0	90.0	90.0
oqmd-683820	static	-3.0513	-3.0513	2.849	4.9347	6.8106	90.0	90.0	90.0
mp-569416	static	-3.0513	-3.0513	2.849	2.849	57.2522	90.0	90.0	120.0
mp-1196583	static	-2.979	-2.979	16.3957	16.3957	16.3957	90.0	90.0	90.0
mp-667273	static	-2.979	-2.979	16.0947	16.0947	16.0947	90.0	90.0	90.0
mp-1196583	box	-2.9644	-2.9644	16.3945	16.3945	16.3945	90.0	90.0	90.0
oqmd-677227	box	-2.9217	-2.9217	16.156	16.156	16.156	90.0	90.0	90.0
mp-683919	box	-2.8698	-2.8698	11.6022	20.0156	20.6251	90.0	90.0	90.0
mp-1147718	box	-2.8308	-2.8308	11.6371	16.6982	10.6455	90.0	90.0	90.0
oqmd-689315	box	-2.8195	-2.8195	11.432	20.1422	20.7204	90.0	90.0	90.0
mp-630227	box	-2.7097	-2.7097	10.5727	10.5825	17.0777	90.0	90.0	90.0
oqmd-637443	static	-2.6818	-2.6818	5.816	5.816	5.816	90.0	90.0	90.0
mp-1244913	box	-2.6514	-2.6514	11.9391	12.0932	12.6009	91.3	95.4	92.3
mp-1245190	box	-2.6479	-2.6479	11.6879	11.8095	11.991	91.4	92.0	90.9
oqmd-614417	box	-2.6346	-2.6346	10.5919	10.5919	26.7628	90.0	90.0	120.0
mp-680372	box	-2.6202	-2.6202	10.6184	10.6184	27.5417	90.0	90.0	120.0
mp-1244964	box	-2.6177	-2.6177	11.4978	11.8211	12.4691	90.7	94.4	92.3
mp-568028	box	-2.5941	-2.5941	9.1367	15.9002	11.192	90.0	90.0	90.0
mp-1008395	static	-2.4916	-2.4916	4.8187	4.8187	2.7807	90.0	90.0	90.0
mp-1095534	box	-2.4682	-2.4682	11.2838	11.2838	6.6285	90.0	90.0	90.0
A4--C--dc	dynamic	-2.4646	-2.4646	3.9452	3.9452	3.9452	90.0	90.0	90.0
mp-1078845	static	-2.4588	-2.4588	4.6885	9.6374	2.7789	90.0	90.0	90.0
oqmd-599492	dynamic	-2.4579	-2.4579	2.7839	2.7839	18.2988	90.0	90.0	120.0
mp-569567	static	-2.4569	-2.4569	2.7831	2.7831	48.0612	90.0	90.0	120.0
mp-569567	dynamic	-2.4569	-2.4569	2.7831	2.7831	48.0629	90.0	90.0	120.0
oqmd-599494	static	-2.4557	-2.4557	2.7859	2.7859	47.9718	90.0	90.0	120.0
mp-611448	dynamic	-2.4557	-2.4557	2.782	2.782	13.7423	90.0	90.0	120.0
oqmd-599491	dynamic	-2.4557	-2.4557	2.782	2.782	13.7421	90.0	90.0	120.0
mp-611448	static	-2.4557	-2.4557	2.782	2.782	13.7426	90.0	90.0	120.0
mp-569517	static	-2.4541	-2.4541	2.7805	2.7805	34.3923	90.0	90.0	120.0
mp-569517	dynamic	-2.4541	-2.4541	2.7805	2.7805	34.3917	90.0	90.0	120.0
oqmd-599490	dynamic	-2.4516	-2.4516	2.7784	2.7784	9.185	90.0	90.0	120.0
oqmd-585286	dynamic	-2.4456	-2.4456	5.3725	5.3725	5.3725	90.0	90.0	90.0
oqmd-599489	dynamic	-2.4403	-2.4403	2.7682	2.7682	4.6247	90.0	90.0	120.0
mp-1080826	dynamic	-2.3848	-2.3848	9.9013	2.7925	4.6049	90.0	96.6	90.0
mp-1097832	static	-2.3762	-2.3762	2.4137	2.4137	9.8799	90.0	90.0	90.0
oqmd-637352	box	-2.2449	-2.2449	9.8483	2.8006	4.6358	90.0	97.7	90.0
mp-1080826	box	-2.2448	-2.2448	9.8497	2.7991	4.6383	90.0	97.7	90.0
A4--C--dc	static	-2.1515	-2.1515	5.2782	5.2782	5.2782	90.0	90.0	90.0
mp-24	static	-1.9535	-1.9535	4.8269	4.8269	4.8269	90.0	90.0	90.0
mp-24	box	-1.9363	-1.9363	4.8596	4.8596	4.8596	90.0	90.0	90.0
oqmd-684315	box	-1.8305	-1.8305	15.4385	15.8202	10.1949	90.0	90.0	90.0
mp-1205283	box	-1.8086	-1.8086	10.3338	19.0258	10.4108	90.0	90.0	90.0
Ah--alpha-Po--sc	static	-1.7288	-1.7288	2.2937	2.2937	2.2937	90.0	90.0	90.0
oqmd-610556	box	-1.6362	-1.6362	4.7282	5.5972	8.013	90.0	90.0	90.0
A7--alpha-As	box	-1.151	-1.151	2.4809	2.4809	7.0052	90.0	90.0	120.0
A15--beta-W	static	-1.0302	-1.0302	4.5377	4.5377	4.5377	90.0	90.0	90.0
A2--W--bcc	box	-0.9336	-0.9336	2.6546	2.6546	2.6546	90.0	90.0	90.0
mp-1078845	box	-0.8902	-0.8902	8.3481	12.3387	3.6423	90.0	90.0	90.0
A3'--alpha-La--double-hcp	box	-0.8388	-0.8388	2.5678	2.5678	4.0522	90.0	90.0	120.0
Ah--alpha-Po--sc	box	-0.829	-0.829	1.7897	1.7897	1.7897	90.0	90.0	90.0
A15--beta-W	static	-0.6191	-0.6191	4.1246	4.1246	4.1246	90.0	90.0	90.0
A3--Mg--hcp	box	-0.3992	-0.3992	1.895	1.895	6.65	90.0	90.0	120.0
A5--beta-Sn	box	-0.2964	-0.2964	3.4098	3.4098	1.854	90.0	90.0	90.0
A3--Mg--hcp	box	-0.0	-0.0	3.5003	3.5003	5.716	90.0	90.0	120.0
A1--Cu--fcc	box	-0.0	-0.0	4.9502	4.9502	4.9502	90.0	90.0	90.0
A6--In--bct	box	-0.0	-0.0	4.287	4.287	3.5003	90.0	90.0	90.0
A3--Mg--hcp	box	-0.0	-0.0	3.5007	3.5007	5.7159	90.0	90.0	120.0
A3'--alpha-La--double-hcp	box	-0.0	-0.0	3.5007	3.5007	11.4318	90.0	90.0	120.0
A2--W--bcc	box	-0.0	-0.0	4.0418	4.0418	4.0418	90.0	90.0	90.0
Ah--alpha-Po--sc	box	-0.0	-0.0	3.5003	3.5003	3.5003	90.0	90.0	90.0
A4--C--dc	box	-0.0	-0.0	8.0837	8.0837	8.0837	90.0	90.0	90.0
mp-1008395	box	-0.0	-0.0	9.7076	9.7076	5.8613	90.0	90.0	90.0
oqmd-599489	box	-0.0	-0.0	5.7121	5.7121	9.3467	90.0	90.0	120.0
oqmd-599490	box	-0.0	-0.0	5.709	5.709	18.8377	90.0	90.0	120.0
oqmd-599493	box	-0.0	-0.0	5.7086	5.7086	70.6921	90.0	90.0	120.0
mp-1188817	box	-0.0	-0.0	12.2955	12.2955	12.2955	90.0	90.0	90.0
oqmd-637443	box	-0.0	-0.0	12.298	12.298	12.298	90.0	90.0	90.0
oqmd-599492	box	-0.0	-0.0	5.7146	5.7146	37.5129	90.0	90.0	120.0
oqmd-599491	box	-0.0	-0.0	5.7143	5.7143	28.155	90.0	90.0	120.0
mp-570002	box	-0.0	-0.0	11.5635	11.5635	11.5635	90.0	90.0	90.0
A15--beta-W	static	0.4823	0.4823	3.4046	3.4046	3.4046	90.0	90.0	90.0
A1--Cu--fcc	static	0.5445	0.5445	2.6929	2.6929	2.6929	90.0	90.0	90.0
A2--W--bcc	static	0.5737	0.5737	2.136	2.136	2.136	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
oqmd-1232084	dynamic	-3.4535	-3.4535	4.7743	4.7743	2.5186	90.0	90.0	90.0
oqmd-1232084	box	-3.31	-3.31	4.8786	4.8786	2.4566	90.0	90.0	90.0
C1--CaF2--fluorite	dynamic	-3.1027	-3.1027	4.4409	4.4409	4.4409	90.0	90.0	90.0
C1--CaF2--fluorite	static	-2.6707	-2.6707	5.6392	5.6392	5.6392	90.0	90.0	90.0
C1--CaF2--fluorite	static	-2.57	-2.57	4.1384	4.1384	4.1384	90.0	90.0	90.0
C1--CaF2--fluorite	dynamic	-2.5013	-2.5013	4.5914	4.5914	4.5914	90.0	90.0	90.0
C1--CaF2--fluorite	dynamic	-2.4688	-2.4688	7.2421	7.2421	7.2421	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
oqmd-426162	dynamic	-4.6332	-4.6332	4.939	4.939	11.854	90.0	90.0	120.0
oqmd-426162	box	-4.181	-4.181	4.894	4.894	12.7505	90.0	90.0	120.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
mp-2794	dynamic	-4.5066	-4.5066	11.6088	4.1953	4.7767	90.0	93.3	90.0
oqmd-7999	box	-3.3385	-3.3385	13.9186	3.3855	8.562	90.0	109.1	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
L1_2--AuCu3	static	-2.9594	-2.9594	2.6122	2.6122	2.6122	90.0	90.0	90.0
L1_2--AuCu3	dynamic	-2.7478	-2.7478	4.4447	4.4447	4.4447	90.0	90.0	90.0
A15--Cr3Si	dynamic	-2.7201	-2.7201	5.6214	5.6214	5.6214	90.0	90.0	90.0
L1_2--AuCu3	dynamic	-2.4976	-2.4976	3.5051	3.5051	3.5051	90.0	90.0	90.0
A15--Cr3Si	dynamic	-2.4236	-2.4236	4.4293	4.4293	4.4293	90.0	90.0	90.0
D0_3--BiF3	dynamic	-2.237	-2.237	5.9841	5.9841	5.9841	90.0	90.0	90.0
A15--Cr3Si	static	-2.2179	-2.2179	3.3409	3.3409	3.3409	90.0	90.0	90.0
A15--Cr3Si	static	-2.2061	-2.2061	3.4376	3.4376	3.4376	90.0	90.0	90.0
D0_3--BiF3	dynamic	-1.8304	-1.8304	7.2592	7.2592	7.2592	90.0	90.0	90.0
D0_3--BiF3	static	-1.7707	-1.7707	4.1713	4.1713	4.1713	90.0	90.0	90.0
A15--Cr3Si	dynamic	-1.6436	-1.6436	3.5434	3.5434	3.5434	90.0	90.0	90.0
D0_3--BiF3	static	-1.5823	-1.5823	4.9331	4.9331	4.9331	90.0	90.0	90.0
D0_3--BiF3	box	-1.4241	-1.4241	4.3488	4.3488	4.3488	90.0	90.0	90.0
L1_2--AuCu3	static	-1.2228	-1.2228	2.9305	2.9305	2.9305	90.0	90.0	90.0
L1_2--AuCu3	box	-1.2084	-1.2084	3.0336	3.0336	3.0336	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
oqmd-13852	dynamic	-4.3699	-4.3699	6.5638	6.5638	4.7386	90.0	90.0	120.0
mp-21717	box	-4.1432	-4.1432	4.5608	6.8389	10.6102	90.0	90.0	90.0
mp-18257	box	-4.1273	-4.1273	6.7754	6.7754	4.4913	90.0	90.0	120.0
oqmd-13852	box	-4.127	-4.127	6.7753	6.7753	4.4888	90.0	90.0	120.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
mp-1192884	box	-3.967	-3.967	10.0546	10.0546	10.0546	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
B1--NaCl--rock-salt	static	-4.5505	-4.5505	3.8414	3.8414	3.8414	90.0	90.0	90.0
oqmd-1228598	dynamic	-4.5502	-4.5502	2.5113	2.5113	2.525	90.0	90.0	120.0
B1--NaCl--rock-salt	static	-4.0963	-4.0963	3.5935	3.5935	3.5935	90.0	90.0	90.0
B2--CsCl	static	-3.9748	-3.9748	2.2216	2.2216	2.2216	90.0	90.0	90.0
oqmd-1228598	box	-3.9615	-3.9615	2.4922	2.4922	2.6717	90.0	90.0	120.0
oqmd-1225112	box	-3.8827	-3.8827	3.1685	3.1685	5.0131	90.0	90.0	120.0
oqmd-1219433	dynamic	-3.8365	-3.8365	2.9617	4.1642	2.6198	90.0	90.0	90.0
B3--ZnS--cubic-zinc-blende	static	-3.8	-3.8	4.4354	4.4354	4.4354	90.0	90.0	90.0
B3--ZnS--cubic-zinc-blende	static	-3.7876	-3.7876	4.132	4.132	4.132	90.0	90.0	90.0
B2--CsCl	dynamic	-3.7852	-3.7852	2.8172	2.8172	2.8172	90.0	90.0	90.0
B2--CsCl	dynamic	-3.414	-3.414	2.3056	2.3056	2.3056	90.0	90.0	90.0
B2--CsCl	box	-3.3677	-3.3677	2.2661	2.2661	2.2661	90.0	90.0	90.0
L1_0--AuCu	dynamic	-3.2576	-3.2576	2.639	2.639	5.0406	90.0	90.0	90.0
B1--NaCl--rock-salt	static	-3.0674	-3.0674	4.8369	4.8369	4.8369	90.0	90.0	90.0
L1_0--AuCu	box	-3.0141	-3.0141	4.055	4.055	2.5256	90.0	90.0	90.0
B2--CsCl	box	-2.6123	-2.6123	3.5957	3.5957	3.5957	90.0	90.0	90.0
B2--CsCl	static	-2.2782	-2.2782	2.0809	2.0809	2.0809	90.0	90.0	90.0
B3--ZnS--cubic-zinc-blende	static	-2.2309	-2.2309	5.5605	5.5605	5.5605	90.0	90.0	90.0
B1--NaCl--rock-salt	static	-2.0355	-2.0355	6.267	6.267	6.267	90.0	90.0	90.0
B3--ZnS--cubic-zinc-blende	dynamic	-1.8516	-1.8516	7.242	7.242	7.242	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
oqmd-13851	dynamic	-4.6589	-4.6589	4.5697	4.6783	2.5205	90.0	90.0	90.0
mp-1871	dynamic	-4.6589	-4.6589	4.5698	4.6782	2.5205	90.0	90.0	90.0
oqmd-13851	box	-4.5648	-4.5648	4.3203	4.872	2.61	90.0	90.0	90.0
mp-1102779	dynamic	-4.5474	-4.5474	6.4751	2.6071	6.0921	90.0	90.0	90.0
C1--CaF2--fluorite	dynamic	-4.2688	-4.2688	4.4411	4.4411	4.4411	90.0	90.0	90.0
mp-1102779	box	-3.9358	-3.9358	6.5987	2.4863	6.6847	90.0	90.0	90.0
C1--CaF2--fluorite	box	-3.7941	-3.7941	4.5463	4.5463	4.5463	90.0	90.0	90.0
C1--CaF2--fluorite	box	-3.7931	-3.7931	4.5342	4.5342	4.5342	90.0	90.0	90.0
mp-568503	dynamic	-3.5824	-3.5824	3.5547	3.5547	2.3704	90.0	90.0	120.0
C1--CaF2--fluorite	dynamic	-3.5192	-3.5192	5.5894	5.5894	5.5894	90.0	90.0	90.0
C1--CaF2--fluorite	static	-3.0787	-3.0787	4.1586	4.1586	4.1586	90.0	90.0	90.0
C1--CaF2--fluorite	static	-2.0311	-2.0311	7.1293	7.1293	7.1293	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
mp-13154	static	-4.5122	-4.5122	4.4834	4.4834	4.6055	90.0	90.0	120.0
mp-13154	dynamic	-4.5122	-4.5122	4.4833	4.4833	4.6057	90.0	90.0	120.0
oqmd-7808	dynamic	-4.5122	-4.5122	4.4833	4.4833	4.6058	90.0	90.0	120.0
mp-1182630	dynamic	-4.3841	-4.3841	5.0889	11.1678	2.8614	90.0	90.0	90.0
mp-1205444	dynamic	-4.3839	-4.3839	7.5328	2.7384	14.02	90.0	102.0	90.0
mp-510623	dynamic	-4.3736	-4.3736	4.8077	6.6211	4.6645	90.0	90.0	90.0
oqmd-41734	box	-4.321	-4.321	5.1235	7.0183	4.6281	90.0	90.0	90.0
mp-1205436	dynamic	-4.3169	-4.3169	8.2496	8.2496	4.2979	90.0	90.0	90.0
mp-613523	box	-4.2951	-4.2951	5.111	7.0177	4.6221	90.0	90.0	90.0
mp-1182630	box	-4.2296	-4.2296	5.8542	10.8156	2.5432	90.0	90.0	90.0
mp-1205444	box	-4.1638	-4.1638	7.8195	2.7098	14.2921	90.0	103.5	90.0
mp-510623	box	-4.1145	-4.1145	4.7796	6.8672	4.5397	90.0	90.0	90.0
mp-1205436	box	-4.0763	-4.0763	7.6044	7.6044	4.7333	90.0	90.0	90.0
A15--Cr3Si	dynamic	-4.0367	-4.0367	4.3873	4.3873	4.3873	90.0	90.0	90.0
oqmd-321460	dynamic	-4.0247	-4.0247	4.9047	4.9047	4.0301	90.0	90.0	120.0
L1_2--AuCu3	dynamic	-4.012	-4.012	3.4679	3.4679	3.4679	90.0	90.0	90.0
oqmd-298554	static	-4.008	-4.008	3.4741	3.4741	6.8949	90.0	90.0	90.0
D0_3--BiF3	static	-3.7423	-3.7423	5.6935	5.6935	5.6935	90.0	90.0	90.0
mp-13154	box	-3.2778	-3.2778	4.3659	4.3659	7.727	90.0	90.0	120.0
L1_2--AuCu3	static	-3.0121	-3.0121	4.3065	4.3065	4.3065	90.0	90.0	90.0
A15--Cr3Si	static	-2.8222	-2.8222	5.4962	5.4962	5.4962	90.0	90.0	90.0
mp-1188724	dynamic	0.0	0.0	14.3274	20.5229	13.1372	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
mp-1078579	dynamic	-4.303	-4.303	5.4272	2.7389	6.2283	90.0	99.1	90.0
oqmd-646134	static	-4.2855	-4.2855	3.816	3.816	3.816	90.0	90.0	90.0
oqmd-646134	box	-4.2808	-4.2808	3.833	3.833	3.833	90.0	90.0	90.0
mp-1070333	dynamic	-4.1933	-4.1933	6.0969	6.0969	2.2922	90.0	90.0	90.0
mp-1246	box	-3.9871	-3.9871	3.9166	3.9166	3.9166	90.0	90.0	90.0
mp-1070333	box	-3.8131	-3.8131	6.2162	6.2162	2.3524	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
A2--W--bcc	dynamic	-4.013	-4.013	2.8553	2.8553	2.8553	90.0	90.0	90.0
A15--beta-W	dynamic	-3.928	-3.928	4.5347	4.5347	4.5347	90.0	90.0	90.0
oqmd-1214792	dynamic	-3.9198	-3.9198	8.8328	8.8328	8.8328	90.0	90.0	90.0
oqmd-1214792	box	-3.9145	-3.9145	8.8246	8.8246	8.8246	90.0	90.0	90.0
A3--Mg--hcp	dynamic	-3.8968	-3.8968	2.6054	2.6054	4.1676	90.0	90.0	120.0
oqmd-1216039	dynamic	-3.8953	-3.8953	2.5986	2.5986	18.8327	90.0	90.0	120.0
oqmd-1216039	box	-3.8952	-3.8952	2.5987	2.5987	18.8303	90.0	90.0	120.0
mp-1271693	box	-3.8949	-3.8949	2.5884	4.4884	4.2055	90.0	90.0	90.0
A3'--alpha-La--double-hcp	dynamic	-3.8945	-3.8945	2.5954	2.5954	8.3884	90.0	90.0	120.0
A1--Cu--fcc	dynamic	-3.8924	-3.8924	3.6584	3.6584	3.6584	90.0	90.0	90.0
A6--In--bct	box	-3.8918	-3.8918	2.6195	2.6195	3.5442	90.0	90.0	90.0
oqmd-1214881	static	-3.8859	-3.8859	6.1695	6.1695	6.1695	90.0	90.0	90.0
oqmd-1214881	box	-3.8854	-3.8854	6.1645	6.1645	6.1645	90.0	90.0	90.0
oqmd-1215237	box	-3.8796	-3.8796	2.5569	4.4126	4.316	90.0	90.0	90.0
mp-1194030	dynamic	-3.8538	-3.8538	8.6028	8.6028	4.6037	90.0	90.0	90.0
mp-1245108	dynamic	-3.8509	-3.8509	10.3495	10.7242	10.7971	92.4	90.8	90.9
oqmd-21053	box	-3.8417	-3.8417	8.5047	8.5047	4.6372	90.0	90.0	90.0
mp-1194030	box	-3.8359	-3.8359	8.4761	8.4761	4.6497	90.0	90.0	90.0
mp-1245108	box	-3.8015	-3.8015	10.522	10.5464	10.8796	90.4	91.7	91.8
oqmd-1215059	box	-3.7083	-3.7083	2.7056	4.0924	8.9398	90.0	90.0	90.0
A5--beta-Sn	static	-3.5209	-3.5209	4.6587	4.6587	2.4313	90.0	90.0	90.0
mp-1096950	box	-3.4462	-3.4462	2.5198	2.5198	2.4811	90.0	90.0	120.0
Ah--alpha-Po--sc	box	-3.3138	-3.3138	2.2375	2.2375	2.2375	90.0	90.0	90.0
oqmd-21731	box	-3.3137	-3.3137	2.2375	2.2375	6.7128	90.0	90.0	90.0
oqmd-1215950	box	-3.0729	-3.0729	3.8679	4.1397	3.882	90.0	119.6	90.0
A7--alpha-As	box	-2.9866	-2.9866	3.4218	3.4218	8.9702	90.0	90.0	120.0
A4--C--dc	static	-2.596	-2.596	5.4545	5.4545	5.4545	90.0	90.0	90.0

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:

23899.121	24007.68	24007.68	0.0	-0.0	-0.0
24007.68	23899.121	24007.68	0.0	-0.0	-0.0
24007.68	24007.68	23899.121	-0.0	-0.0	-0.0
0.0	0.0	0.0	-430.314	0.0	-0.0
0.0	0.0	0.0	-0.0	-430.314	-0.0
0.0	0.0	0.0	0.0	-0.0	-430.314

21298.894	19880.446	19880.446	0.0	0.0	0.0
19880.446	21298.894	19880.446	0.0	-0.0	0.0
19880.446	19880.446	21298.894	0.0	-0.0	0.0
2146281115.847	2131145542.639	2124130910.142	1096023.601	753833.703	3903822.397
2128523644.933	2145540521.734	2123703768.94	1807848.46	-2697211.985	2272274.931
2127963114.95	2131932100.988	2146411578.995	59473.557	1438069.571	-4522363.354

21039.419	19973.227	19973.227	0.0	0.0	-0.0
19973.227	21039.419	19973.227	0.0	0.0	-0.0
19973.227	19973.227	21039.419	-0.0	0.0	-0.0
-2142408609.562	-2129513142.973	-2123605887.479	-1891364.394	1364114.592	-2894922.502
-2127751008.691	-2145545654.805	-2128022590.43	730666.435	-2779499.987	1789558.802
-2127869505.556	-2126086755.98	-2145445800.701	-2236071.095	3760864.477	-5340276.443

21127.208	20064.506	20064.506	0.0	-0.0	0.0
20064.506	21127.208	20064.506	-0.0	0.0	0.0
20064.506	20064.506	21127.208	0.0	-0.0	0.0
213614216.593	212312254.39	212339724.714	-293857.802	431549.917	-23105.4
212806617.453	214358782.845	213330595.148	-571270.654	-357955.422	83068.909
212173565.527	213034163.619	214069175.031	-110578.866	30062.661	-78467.377

20925.532	19864.581	19864.581	-0.0	0.0	-0.0
19864.581	20925.532	19864.581	0.0	-0.0	-0.0
19864.581	19864.581	20925.532	0.0	-0.0	-0.0
-214166980.196	-212497204.788	-212136722.697	42830.635	-83048.446	287745.942
-212317894.894	-213543333.045	-212380250.042	4883.391	-121427.142	-26864.942
-212880819.68	-213523630.949	-214227344.773	115770.924	142928.449	-132722.011

6384623026.305	6243383239.831	6291047276.141	14026112.493	-4858494.187	-15722314.359
6318793360.497	6376688306.666	6247822149.728	2682562.701	12727998.295	-26131488.507
6228680278.1	6306993602.844	6373606722.984	-2439227.799	-7874345.201	-3130932.961
6247102044.181	6215999740.448	6364181323.571	383969.561	-3357887.405	9184089.933
6552520189.359	6662312783.105	6605911450.791	-10701354.875	-927194.381	-2429942.347
6541357223.243	6580201189.073	6629826497.752	-3337434.545	8579635.297	3793208.301

23905.001	24013.559	24013.559	-0.0	0.0	-0.0
24013.559	23905.001	24013.559	-0.0	0.0	0.0
24013.56	24013.56	23905.001	-0.0	0.0	0.0
-0.0	-0.0	-0.0	-430.314	0.0	-0.0
-0.0	-0.0	-0.0	0.0	-430.314	0.0
-0.0	-0.0	-0.0	0.0	0.0	-430.314

23872.663	23981.221	23981.221	0.0	-0.0	-0.0
23981.221	23872.663	23981.221	-0.0	-0.0	-0.0
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23931.459	24040.018	24040.018	0.0	0.0	-0.0
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23663.423	23771.971	23771.971	-0.0	-0.0	-0.0
23771.971	23663.423	23771.971	0.0	-0.0	-0.0
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24196.034	24304.603	24304.603	-0.0	0.0	0.0
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0.002	0.001	0.001	-0.0	0.0	0.0
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21287.231	19869.576	19869.576	-0.0	-0.0	0.0
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21284.639	19867.16	19867.16	0.0	0.0	-0.0
19867.16	21284.639	19867.16	0.0	-0.0	-0.0
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636249246.025	620651414.141	628760097.861	-9784.133	674348.666	-91428.124
631705264.678	639269063.864	623859225.781	243912.771	-552486.602	-666713.38
625401076.076	633971219.26	641761368.392	917381.706	-70882.511	-1239143.91
688741623.548	673346796.593	681937260.197	471934.041	232012.54	-1396284.262
691891261.72	693711190.223	705093059.644	846115.671	-374209.534	-97442.182
673101383.254	677561826.12	682240119.975	25479.631	979783.83	-178940.977

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63938123.455	62270781.067	63037149.486	120813.834	-44954.051	21149.662
62900988.046	63644158.068	62231747.121	-15210.849	-2440.368	-31957.731
62436845.474	63008609.583	63760913.938	-15311.242	29714.45	8253.659
66178619.832	64778885.478	64656554.366	49007.696	1616.858	18795.692
66419293.755	66317847.11	65660082.821	39292.85	1571.943	-14591.406
66588001.79	66737483.079	67299609.157	24167.263	-93338.788	18646.363

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467092.752	55.111	55.111	-0.0	0.0	0.0
55.111	467092.752	55.111	0.0	0.0	-0.0
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45144226.845	44992163.597	45161986.35	0.0	0.001	-0.0
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20817.63	21124.221	21124.221	-0.0	-0.0	-0.0
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20829.536	21136.127	21136.127	0.0	0.0	0.0
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20764.053	21070.642	21070.642	0.0	0.0	-0.0
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20883.113	21189.705	21189.705	-0.0	0.0	0.0
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20228.278	20534.854	20534.854	0.0	-0.0	-0.0
20534.854	20228.278	20534.854	-0.0	-0.0	-0.0
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0.015	0.016	0.015	-469.267	0.0	-0.0
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21418.877	21725.484	21725.484	0.0	-0.0	0.0
21725.484	21418.877	21725.484	-0.0	0.0	0.0
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530548.577	530375.562	530375.562	-0.0	-0.0	-0.0
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530567.821	530394.785	530394.785	0.0	0.0	0.0
530394.785	530567.821	530394.785	0.0	0.0	0.0
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530461.966	530289.046	530289.046	-0.0	-0.0	-0.0
530289.046	530461.966	530289.046	-0.0	-0.0	-0.0
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0.774	0.775	0.774	-2271.223	-0.0	-0.0
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530654.427	530481.295	530481.295	0.0	0.0	0.0
530481.295	530654.427	530481.295	0.0	-0.0	0.0
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529595.835	529423.868	529423.868	0.0	-0.0	-0.0
529423.868	529595.835	529423.868	-0.0	-0.0	-0.0
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7.742	7.746	7.742	-2271.223	-0.0	-0.0
7.746	7.742	7.742	0.0	-2271.223	-0.0
7.746	7.742	7.742	0.0	-0.0	-2271.223

531520.444	531346.357	531346.357	-0.0	0.0	0.0
531346.357	531520.444	531346.357	0.0	-0.0	0.0
531346.357	531346.357	531520.444	0.0	0.0	0.0
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14737847557.847	15512257330.79	14655207559.621	-6173176.639	3051047.85	8677916.764
11335.329	11315.23	12840.707	0.0	-0.0	-0.0
12840.273	12840.273	15406.843	0.0	0.0	-0.0
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11337.795	11317.695	12843.939	-0.0	0.0	0.0
12844.511	12844.51	15412.397	0.0	0.0	0.0
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1478228715.479	1550491884.78	1466639853.015	839559.527	2544071.971	2272589.985
1546354725.999	1530570340.439	1505336990.593	-1209130.821	-46751.262	267490.138
12821.206	12821.206	15381.847	0.0	-0.0	-0.0
0.001	0.001	0.001	-230.365	-0.0	-0.0
0.001	0.001	0.001	-0.0	-230.365	-0.0
1523397351.078	1496634280.54	1467833465.096	-1972569.281	-134393.293	-36628344.022