Interatomic Potentials Repository

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.

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.

Related Models:
2004--Ackland-G-J-Mendelev-M-I-Srolovitz-D-J-et-al--Fe-P

2005--Mendelev-M-I-Srolovitz-D-J-Ackland-G-J-Han-S--Al-Fe

2007--Mendelev-M-I-Han-S-Son-W-et-al--V-Fe

2014--Veiga-R-G-A-Becquart-C-S-Perez-M--Fe-C

2015--Eich-S-M-Beinke-D-Schmitz-G--Fe-Cr

2022--Bonny-G-Bakaev-A-Terentyev-D--Fe-C-Cr
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:

2025-07-02. All "mp-" reference structure calculations were re-relaxed using the updated Materials Project database rather than the original database structures. Also, a bug was fixed that caused the "static" relaxations to occasionally throw unnecessary errors. This was fixed and all affected calculations were reset and performed again.
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 = 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)
oqmd-1215848	dynamic	-3.1824	-3.1824	4.4394	4.4394	1.5495	90.0	90.0	120.0
mp-1182029	static	-3.1824	-3.1824	1.5495	3.5146	3.5003	90.0	100.4	90.0
oqmd-1215046	static	-3.1824	-3.1824	1.5495	3.5152	6.1458	90.1	92.5	90.5
mp-1197903	static	-3.0677	-3.0677	9.0913	10.5726	27.3253	98.3	96.3	105.1
mp-1018088	dynamic	-3.0544	-3.0544	4.6521	4.6521	4.6521	90.0	90.0	90.0
oqmd-590101	dynamic	-3.0513	-3.0513	2.849	2.849	7.8081	90.0	90.0	120.0
oqmd-1215937	static	-3.0513	-3.0513	2.849	2.849	7.3725	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-1040425	dynamic	-3.0513	-3.0513	2.849	2.849	19.9983	90.0	90.0	120.0
mp-990448	static	-3.0513	-3.0513	2.849	2.849	8.5238	90.0	90.0	120.0
mp-568363	dynamic	-3.0513	-3.0513	2.849	4.9347	8.1499	90.0	90.0	90.0
mp-937760	dynamic	-3.0513	-3.0513	2.849	4.9347	7.1733	90.0	90.0	90.0
mp-990424	static	-3.0513	-3.0513	2.849	2.849	24.8349	90.0	90.0	120.0
oqmd-1214690	static	-3.0513	-3.0513	2.849	4.9347	6.8126	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-169	static	-3.0513	-3.0513	4.9347	2.849	3.7634	90.0	111.5	90.0
mp-632329	static	-3.0513	-3.0513	4.9347	2.849	3.7364	90.0	94.2	90.0
oqmd-589491	dynamic	-3.0513	-3.0513	2.849	2.849	35.0839	90.0	90.0	120.0
mp-48	dynamic	-3.0513	-3.0513	2.849	2.849	7.8031	90.0	90.0	120.0
mp-997182	dynamic	-3.0513	-3.0513	2.849	2.849	12.0458	90.0	90.0	120.0
A7--alpha-As	dynamic	-3.0513	-3.0513	2.849	2.849	12.5456	90.0	90.0	120.0
A7--alpha-As	dynamic	-3.0513	-3.0513	2.849	2.849	11.6641	90.0	90.0	120.0
oqmd-590101	static	-3.0513	-3.0513	2.849	2.849	7.0022	90.0	90.0	120.0
mp-569304	static	-3.0513	-3.0513	2.849	2.849	33.9833	90.0	90.0	120.0
mp-606949	static	-3.0513	-3.0513	2.849	2.849	29.9058	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
mp-568286	static	-3.0513	-3.0513	2.849	4.9348	7.036	90.0	90.0	90.0
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
A7--alpha-As	static	-3.0513	-3.0513	2.849	2.849	10.4979	90.0	90.0	120.0
mp-568806	static	-3.0513	-3.0513	2.849	2.849	3.6562	90.0	90.0	120.0
mp-569416	static	-3.0513	-3.0513	2.849	2.849	55.5451	90.0	90.0	120.0
oqmd-610557	static	-3.0513	-3.0513	5.6977	7.0556	4.9345	90.0	90.0	90.0
mp-568410	dynamic	-3.051	-3.051	5.6949	7.1512	4.9338	90.0	90.0	90.0
mp-568410	static	-3.0508	-3.0508	5.6938	7.1766	4.9334	90.0	90.0	90.0
oqmd-610556	static	-3.0503	-3.0503	5.6888	7.257	4.932	90.0	90.0	90.0
mp-1096869	static	-3.0381	-3.0381	29.653	17.1265	3.5002	90.0	95.8	90.0
mp-1182684	static	-3.0188	-3.0188	12.7408	16.0344	18.7315	90.0	90.0	90.0
oqmd-1214868	static	-3.0086	-3.0086	7.6105	7.6105	7.6105	90.0	90.0	90.0
mp-1192619	static	-2.9979	-2.9979	10.4574	10.4574	10.4574	90.0	90.0	90.0
oqmd-1214779	static	-2.9944	-2.9944	10.0741	10.0741	10.0741	90.0	90.0	90.0
mp-1196857	static	-2.9922	-2.9922	12.4638	21.9697	6.035	90.0	90.0	90.0
mp-683919	dynamic	-2.9873	-2.9873	11.4963	19.2033	21.0308	90.0	90.0	90.0
mp-1245190	static	-2.982	-2.982	11.3796	12.1016	12.3137	88.7	88.7	86.0
mp-568028	dynamic	-2.9795	-2.9795	10.8086	16.7296	10.699	90.0	90.0	90.0
mp-568028	static	-2.9795	-2.9795	11.2698	16.255	10.699	90.0	90.0	90.0
mp-1147718	dynamic	-2.9795	-2.9795	11.2914	16.2713	10.6994	90.0	90.0	90.0
mp-1147718	static	-2.979	-2.979	11.7181	16.8737	11.5695	90.0	90.0	90.0
mp-1196583	dynamic	-2.979	-2.979	16.1214	16.1214	16.1214	90.0	90.0	90.0
oqmd-677227	static	-2.979	-2.979	16.1417	16.1417	16.1417	90.0	90.0	90.0
mp-1196583	static	-2.979	-2.979	16.3957	16.3957	16.3957	90.0	90.0	90.0
oqmd-603085	static	-2.979	-2.979	16.102	16.102	16.102	90.0	90.0	90.0
mp-667273	static	-2.979	-2.979	16.4661	16.4661	16.4661	90.0	90.0	90.0
mp-680372	dynamic	-2.9778	-2.9778	11.111	11.111	25.8592	90.0	90.0	120.0
mp-624889	static	-2.9698	-2.9698	5.3627	6.2727	6.0652	90.0	90.0	90.0
mp-624889	dynamic	-2.9698	-2.9698	5.3627	6.2727	6.0015	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
mp-683919	static	-2.9593	-2.9593	11.6881	19.502	20.132	90.0	90.0	90.0
oqmd-689315	static	-2.9593	-2.9593	11.6622	19.5326	20.1227	90.0	90.0	90.0
oqmd-610552	static	-2.9576	-2.9576	5.3106	6.1885	7.1128	90.0	90.0	90.0
mp-579909	dynamic	-2.9576	-2.9576	5.3106	6.1885	6.441	90.0	90.0	90.0
mp-579909	static	-2.9576	-2.9576	5.3105	6.1887	7.5754	90.0	90.0	90.0
mp-630227	dynamic	-2.9457	-2.9457	9.8194	10.6659	16.5109	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
oqmd-684627	static	-2.9133	-2.9133	10.1466	10.1466	17.4415	90.0	90.0	90.0
oqmd-595714	static	-2.9128	-2.9128	10.2253	10.3087	16.6213	90.0	90.0	90.0
mp-630227	static	-2.9126	-2.9126	10.2149	10.2161	17.9237	90.0	90.0	90.0
oqmd-614417	static	-2.8798	-2.8798	10.1288	10.1288	28.1671	90.0	90.0	120.0
mp-680372	static	-2.8793	-2.8793	10.1618	10.1618	29.5477	90.0	90.0	120.0
mp-683919	box	-2.8698	-2.8698	11.6022	20.0156	20.6251	90.0	90.0	90.0
oqmd-684315	static	-2.8567	-2.8567	11.7578	19.1999	10.8423	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-1205417	dynamic	-2.808	-2.808	13.3601	13.3601	7.7988	90.0	90.0	90.0
mp-1205417	static	-2.808	-2.808	13.4122	13.4122	7.7511	90.0	90.0	90.0
mp-1188817	dynamic	-2.7369	-2.7369	7.3016	7.3016	7.3016	90.0	90.0	90.0
mp-630227	box	-2.7304	-2.7304	10.4226	10.5257	17.6059	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	-2.619	-2.619	10.6098	10.6098	28.0588	90.0	90.0	120.0
mp-1244964	box	-2.6177	-2.6177	11.4978	11.821	12.4693	90.7	94.4	92.3
mp-568028	box	-2.5896	-2.5896	9.0769	15.8991	11.2072	90.0	90.0	90.0
oqmd-637353	dynamic	-2.4916	-2.4916	4.8187	4.8187	2.7807	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	dynamic	-2.4588	-2.4588	4.6885	9.6374	2.7789	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
oqmd-599494	dynamic	-2.4569	-2.4569	2.7831	2.7831	48.0616	90.0	90.0	120.0
mp-569567	static	-2.4569	-2.4569	2.7832	2.7832	48.0582	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	static	-2.4557	-2.4557	2.782	2.782	13.7423	90.0	90.0	120.0
mp-611448	dynamic	-2.4557	-2.4557	2.7821	2.7821	13.742	90.0	90.0	120.0
mp-569517	dynamic	-2.4541	-2.4541	2.7806	2.7806	34.3908	90.0	90.0	120.0
mp-569517	static	-2.4541	-2.4541	2.7805	2.7805	34.3922	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
mp-570002	dynamic	-2.4456	-2.4456	5.3725	5.3725	5.3725	90.0	90.0	90.0
mp-47	dynamic	-2.4403	-2.4403	2.7682	2.7682	4.6247	90.0	90.0	120.0
oqmd-637130	static	-2.3865	-2.3865	9.8196	2.7921	4.6135	90.0	90.0	90.0
mp-1190171	dynamic	-2.3865	-2.3865	9.8196	2.7921	4.6135	90.0	90.0	90.0
mp-1080826	dynamic	-2.3848	-2.3848	9.9013	2.7925	4.6049	90.0	96.6	90.0
A6--In--bct	static	-2.3762	-2.3762	1.7067	1.7067	6.5714	90.0	90.0	90.0
oqmd-1216026	static	-2.3762	-2.3762	2.4137	2.4137	10.6485	90.0	92.7	90.0
A6--In--bct	dynamic	-2.3762	-2.3762	1.7067	1.7067	8.3485	90.0	90.0	90.0
mp-1056957	static	-2.3762	-2.3762	2.4137	2.4137	6.8874	90.0	90.0	90.0
mp-1097832	dynamic	-2.3762	-2.3762	2.4137	2.4137	9.8799	90.0	90.0	90.0
oqmd-1216026	dynamic	-2.3762	-2.3762	2.4137	2.4137	12.5976	90.0	90.3	90.0
oqmd-637352	box	-2.2449	-2.2449	9.8483	2.8006	4.6358	90.0	97.7	90.0
mp-1080826	box	-2.2393	-2.2393	9.8529	2.7993	4.6367	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	dynamic	-1.9535	-1.9535	4.8269	4.8269	4.8269	90.0	90.0	90.0
mp-1205283	box	-1.8547	-1.8547	10.1299	19.086	10.3755	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
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
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
mp-24	box	-0.8183	-0.8183	5.1849	5.1849	5.1849	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
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
oqmd-637443	box	-0.0	-0.0	12.298	12.298	12.298	90.0	90.0	90.0
mp-1188817	box	-0.0	-0.0	12.2901	12.2901	12.2901	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	11.5684	11.5684	11.5684	90.0	90.0	90.0
mp-1192619	box	-0.0	-0.0	24.797	24.797	24.797	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	static	-4.3051	-4.3051	4.6424	4.6424	14.3988	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)
oqmd-7999	static	-4.4866	-4.4866	10.4354	4.7981	4.5643	90.0	99.0	90.0
mp-2794	static	-4.4866	-4.4866	10.4354	4.798	4.5643	90.0	99.0	90.0
mp-645339	box	-4.0791	-4.0791	4.5516	4.7914	12.5295	90.0	103.4	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)
oqmd-319634	static	-3.6049	-3.6049	3.8231	3.8231	5.7253	90.0	90.0	120.0
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
oqmd-300376	static	-2.5014	-2.5014	2.53	2.53	11.5079	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	static	-1.4537	-1.4537	4.4388	4.4388	4.4388	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)
mp-18257	static	-4.5028	-4.5028	6.7125	6.7125	4.079	90.0	90.0	120.0
mp-21717	static	-4.4782	-4.4782	4.1261	6.7955	11.1748	90.0	90.0	90.0
oqmd-13852	static	-4.4633	-4.4633	6.4565	6.4565	4.7747	90.0	90.0	120.0
oqmd-13852	dynamic	-4.3699	-4.3699	6.5638	6.5638	4.7386	90.0	90.0	120.0
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	dynamic	-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
oqmd-13851	box	-4.5648	-4.5648	4.3203	4.872	2.61	90.0	90.0	90.0
mp-1102779	static	-4.3869	-4.3869	5.6511	2.4676	6.7184	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)
oqmd-7808	dynamic	-4.5122	-4.5122	4.4833	4.4833	4.6058	90.0	90.0	120.0
mp-13154	static	-4.5122	-4.5122	4.4829	4.4829	4.6073	90.0	90.0	120.0
oqmd-7808	static	-4.5122	-4.5122	4.4829	4.4829	4.6077	90.0	90.0	120.0
mp-13154	dynamic	-4.5122	-4.5122	4.483	4.483	4.607	90.0	90.0	120.0
oqmd-3494	static	-4.4223	-4.4223	4.7855	6.9405	4.191	90.0	90.0	90.0
mp-1182630	dynamic	-4.3841	-4.3841	5.0889	11.1678	2.8614	90.0	90.0	90.0
mp-510623	static	-4.3669	-4.3669	4.6179	6.5453	4.7902	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-1205444	static	-4.307	-4.307	7.5467	2.7573	14.3866	90.0	103.4	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
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-1205436	box	-3.4826	-3.4826	7.9474	7.9474	5.7125	90.0	90.0	90.0
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	static	-1.1319	-1.1319	14.3818	20.5229	14.6339	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-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-1078579	dynamic	-4.2232	-4.2232	5.919	2.7159	6.083	90.0	96.4	90.0
mp-1246	dynamic	-4.1772	-4.1772	3.8512	3.8512	3.8512	90.0	90.0	90.0
mp-1078579	static	-4.1391	-4.1391	5.9145	2.7454	6.0496	90.0	95.6	90.0
mp-1246	box	-3.9871	-3.9871	3.9166	3.9166	3.9166	90.0	90.0	90.0
mp-1070333	dynamic	-3.9659	-3.9659	6.1292	6.1292	2.4077	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
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	-3.8525	-3.8525	10.3946	10.691	10.7541	93.1	91.7	91.2
mp-1245108	static	-3.8435	-3.8435	10.3726	10.7237	10.7656	87.4	89.9	87.9
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	10.5221	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	static	-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	24007.680	24007.680	0.000	-0.000	-0.000
24007.680	23899.121	24007.680	0.000	-0.000	-0.000
24007.680	24007.680	23899.121	-0.000	-0.000	-0.000
0.000	0.000	0.000	-430.314	0.000	-0.000
0.000	0.000	0.000	-0.000	-430.314	-0.000
0.000	0.000	0.000	0.000	-0.000	-430.314

23905.001	24013.559	24013.559	-0.000	0.000	-0.000
24013.559	23905.001	24013.559	-0.000	0.000	0.000
24013.560	24013.560	23905.001	-0.000	0.000	0.000
-0.000	-0.000	-0.000	-430.314	0.000	-0.000
-0.000	-0.000	-0.000	0.000	-430.314	0.000
-0.000	-0.000	-0.000	0.000	0.000	-430.314

23872.663	23981.221	23981.221	0.000	-0.000	-0.000
23981.221	23872.663	23981.221	-0.000	-0.000	-0.000
23981.221	23981.221	23872.663	-0.000	-0.000	0.000
0.002	0.002	0.002	-430.314	-0.000	0.000
0.002	0.002	0.002	-0.000	-430.314	-0.000
0.002	0.002	0.002	0.000	-0.000	-430.314

23931.459	24040.018	24040.018	0.000	0.000	-0.000
24040.018	23931.459	24040.018	-0.000	0.000	0.000
24040.018	24040.018	23931.459	0.000	0.000	0.000
-0.002	-0.002	-0.002	-430.314	0.000	0.000
-0.002	-0.002	-0.002	-0.000	-430.314	0.000
-0.002	-0.002	-0.002	0.000	0.000	-430.314

23663.423	23771.971	23771.971	-0.000	-0.000	-0.000
23771.971	23663.423	23771.971	0.000	-0.000	-0.000
23771.971	23771.971	23663.423	0.000	-0.000	-0.000
0.017	0.017	0.016	-430.314	-0.000	0.000
0.017	0.017	0.016	0.000	-430.314	-0.000
0.017	0.016	0.017	-0.000	-0.000	-430.314

24196.034	24304.603	24304.603	-0.000	0.000	0.000
24304.603	24196.034	24304.603	0.000	0.000	-0.000
24304.603	24304.603	24196.034	0.000	0.000	-0.000
-0.017	-0.017	-0.016	-430.314	0.000	0.000
-0.017	-0.017	-0.016	0.000	-430.314	0.000
-0.017	-0.016	-0.017	0.000	0.000	-430.314

0.002	0.001	0.001	-0.000	0.000	0.000
0.001	0.002	0.001	0.000	-0.000	0.000
0.001	0.001	0.002	-0.000	-0.000	0.000
-0.000	0.000	0.000	0.001	-0.000	-0.000
0.000	-0.000	0.000	-0.000	0.001	-0.000
0.000	0.000	-0.000	0.000	-0.000	0.001

0.002	0.001	0.001	0.000	0.000	0.000
0.001	0.002	0.001	0.000	0.000	0.000
0.001	0.001	0.002	-0.000	0.000	-0.000
0.000	-0.000	-0.000	0.001	-0.000	0.000
-0.000	0.000	-0.000	-0.000	0.001	-0.000
-0.000	-0.000	0.000	-0.000	-0.000	0.001

0.002	0.001	0.001	0.000	0.000	0.000
0.001	0.002	0.001	0.000	-0.000	0.000
0.001	0.001	0.002	-0.000	-0.000	0.000
-0.000	0.000	0.000	0.001	-0.000	-0.000
0.000	-0.000	0.000	-0.000	0.001	0.000
0.000	0.000	-0.000	0.000	0.000	0.001

0.002	0.001	0.001	-0.000	-0.000	-0.000
0.001	0.002	0.001	-0.000	0.000	0.000
0.001	0.001	0.002	-0.000	-0.000	-0.000
0.000	-0.000	-0.000	0.001	-0.000	0.000
-0.000	0.000	-0.000	-0.000	0.001	0.000
-0.000	-0.000	0.000	0.000	0.000	0.001

0.002	0.001	0.001	-0.000	-0.000	-0.000
0.001	0.002	0.001	-0.000	-0.000	-0.000
0.001	0.001	0.002	-0.000	-0.000	0.000
-0.000	0.000	0.000	0.001	0.000	0.000
0.000	-0.000	0.000	-0.000	0.001	0.000
0.000	0.000	-0.000	0.000	0.000	0.001

0.002	0.001	0.001	0.000	0.000	0.000
0.001	0.002	0.001	0.000	0.000	0.000
0.001	0.001	0.002	-0.000	-0.000	-0.000
0.000	-0.000	-0.000	0.001	-0.000	-0.000
-0.000	0.000	-0.000	-0.000	0.001	0.000
-0.000	-0.000	0.000	0.000	0.000	0.001

21287.231	19869.576	19869.576	-0.000	-0.000	0.000
19869.576	21287.231	19869.576	-0.000	0.000	0.000
19869.576	19869.576	21287.231	-0.000	-0.000	0.000
-0.000	-0.000	-0.000	-231.599	0.000	0.000
-0.000	-0.000	-0.000	0.000	-231.599	0.000
-0.000	-0.000	0.000	-0.000	0.000	-231.598

21284.639	19867.160	19867.160	0.000	0.000	-0.000
19867.160	21284.639	19867.160	0.000	-0.000	-0.000
19867.160	19867.160	21284.639	-0.000	0.000	-0.000
0.000	0.000	0.000	-231.599	-0.000	-0.000
0.000	0.000	0.000	0.000	-231.599	-0.000
0.000	0.000	-0.000	0.000	0.000	-231.599

21298.894	19880.446	19880.446	0.000	0.000	0.000
19880.446	21298.894	19880.446	0.000	-0.000	0.000
19880.446	19880.446	21298.894	0.000	-0.000	0.000
2146281115.847	2131145542.639	2124130910.142	1096023.601	753833.703	3903822.397
2128523644.933	2145540521.734	2123703768.940	1807848.460	-2697211.985	2272274.931
2127963114.950	2131932100.988	2146411578.995	59473.557	1438069.571	-4522363.354

21039.419	19973.227	19973.227	0.000	0.000	-0.000
19973.227	21039.419	19973.227	0.000	0.000	-0.000
19973.227	19973.227	21039.419	-0.000	0.000	-0.000
-2142408609.562	-2129513142.973	-2123605887.479	-1891364.394	1364114.592	-2894922.502
-2127751008.691	-2145545654.805	-2128022590.430	730666.435	-2779499.987	1789558.802
-2127869505.556	-2126086755.980	-2145445800.701	-2236071.095	3760864.477	-5340276.443

21127.208	20064.506	20064.506	0.000	-0.000	0.000
20064.506	21127.208	20064.506	-0.000	0.000	0.000
20064.506	20064.506	21127.208	0.000	-0.000	0.000
213614216.593	212312254.390	212339724.714	-293857.802	431549.917	-23105.400
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	-0.000	0.000	-0.000
19864.581	20925.532	19864.581	0.000	-0.000	-0.000
19864.581	19864.581	20925.532	0.000	-0.000	-0.000
-214166980.196	-212497204.788	-212136722.697	42830.635	-83048.446	287745.942
-212317894.894	-213543333.045	-212380250.042	4883.391	-121427.142	-26864.942
-212880819.680	-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
6228680278.100	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

-6525752809.582	-6374483084.487	-6344052401.261	-5086387.141	11642585.859	-10720752.902
-6410641017.203	-6551317887.510	-6430082081.297	12940.163	-9088766.540	6527621.819
-6351213695.945	-6353405105.948	-6501693199.421	4452141.404	-8512307.184	-10865797.014
-6358405846.229	-6335122007.982	-6498411929.193	2277273.389	1406067.193	-7620645.718
-6824458601.447	-6904825622.251	-6708885623.833	-80981.446	-7789644.517	896183.067
-6924302092.561	-6993420731.887	-6990454833.613	-945821.112	-1036183.983	10254405.475

636249246.025	620651414.141	628760097.861	-9784.133	674348.666	-91428.124
631705264.678	639269063.864	623859225.781	243912.771	-552486.602	-666713.380
625401076.076	633971219.260	641761368.392	917381.706	-70882.511	-1239143.910
688741623.548	673346796.593	681937260.197	471934.041	232012.540	-1396284.262
691891261.720	693711190.223	705093059.644	846115.671	-374209.534	-97442.182
673101383.254	677561826.120	682240119.975	25479.631	979783.830	-178940.977

-642006273.710	-618770377.989	-617228905.213	-1506747.113	-1193041.898	27057.775
-620349706.261	-641334052.014	-617595171.139	-697037.048	-38474.009	-1105403.698
-619482029.413	-620424740.815	-641367977.488	315039.961	71721.259	93147.642
-652665584.421	-628318991.570	-627746414.206	-135998.537	-562525.137	-221192.401
-629838163.622	-651345302.050	-632948286.649	144970.622	510889.934	460943.036
-629823610.998	-631960640.667	-655005896.278	807238.157	-735210.910	-462595.435

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	29714.450	8253.659
66178619.832	64778885.478	64656554.366	49007.696	1616.858	18795.692
66419293.755	66317847.110	65660082.821	39292.850	1571.943	-14591.406
66588001.790	66737483.079	67299609.157	24167.263	-93338.788	18646.363

-64469620.885	-62672157.025	-62398699.133	-179898.977	99496.439	29395.243
-63141167.927	-64853637.571	-63048702.060	-56660.250	-6843.194	-43367.014
-62678901.797	-62734056.429	-64557339.435	68586.592	20571.825	52211.067
-68139688.279	-67357474.120	-67476692.587	-97769.116	4825.735	50692.630
-66482057.109	-66423951.174	-65793728.494	-119565.375	102056.889	-134197.444
-66346275.592	-67309956.154	-67083052.380	22741.030	-33478.447	11096.221

467092.752	55.111	55.111	-0.000	0.000	0.000
55.111	467092.752	55.111	0.000	0.000	-0.000
55.111	55.111	467092.752	0.000	-0.000	0.000
0.003	0.002	-0.003	55.026	0.000	0.000
0.001	0.005	-0.001	-0.000	55.027	0.000
0.002	-0.002	0.002	-0.000	-0.000	55.026

10286299.948	-4772398767.502	-4773570085.576	-0.017	-0.004	-0.015
-4502719280.653	-4521725737.469	-4512158286.220	-0.001	4.506	0.004
-4511710855.830	-4503507740.710	-4522257271.159	0.000	0.000	0.102
-0.002	-0.001	0.003	55.027	0.000	-0.000
-0.001	-0.005	0.002	0.000	55.027	-0.000
-0.001	0.003	-0.002	0.000	0.000	55.027

451366087.265	450185790.338	451516971.969	-0.000	-0.000	0.000
451611896.871	451537865.107	449715596.903	0.027	-0.002	-0.018
451569408.637	450133107.305	451350570.079	0.002	0.000	0.016
0.000	0.000	-0.023	55.026	-0.000	0.000
0.000	0.000	-0.023	0.000	55.026	0.000
0.000	-0.023	0.000	-0.000	-0.000	55.026

-451586865.382	-451356858.718	-450114901.207	-0.000	0.000	-0.000
-449638504.736	-451699450.727	-451478268.830	-0.011	-0.031	-0.001
-451567449.319	-449778896.125	-451568181.958	-0.000	0.002	-0.000
-0.000	-0.000	0.023	55.026	-0.000	0.000
-0.000	0.000	0.023	-0.000	55.026	-0.000
-0.000	0.023	-0.000	0.000	0.000	55.026

45144226.845	44992163.597	45161986.350	0.000	0.001	-0.000
45151675.961	45136741.416	45018802.429	-0.000	0.000	0.000
45157260.358	44997903.995	45147642.723	0.001	0.000	-0.001
0.000	-0.000	-0.233	55.111	0.000	0.000
-0.000	0.000	-0.234	-0.000	55.026	-0.000
-0.000	-0.233	0.000	0.000	0.000	55.111

-45162206.378	-45129103.641	-44996633.518	-0.001	0.000	-0.007
-45012630.855	-45150226.070	-45142293.064	-0.001	-0.002	-0.001
-45150164.597	-44979497.978	-45161224.499	0.004	-0.000	-0.002
-0.000	0.000	0.233	55.111	-0.000	0.000
0.000	0.000	0.234	-0.000	55.026	0.000
0.000	0.233	-0.000	0.000	-0.000	55.111

20817.630	21124.221	21124.221	-0.000	-0.000	-0.000
21124.221	20817.630	21124.221	-0.000	-0.000	-0.000
21124.221	21124.221	20817.630	-0.000	-0.000	-0.000
0.000	0.000	0.000	-469.267	0.000	-0.000
0.000	0.000	0.000	0.000	-469.267	-0.000
0.000	0.000	0.000	0.000	-0.000	-469.267

20829.536	21136.127	21136.127	0.000	0.000	0.000
21136.127	20829.536	21136.127	0.000	0.000	0.000
21136.127	21136.127	20829.536	-0.000	0.000	0.000
-0.000	-0.000	-0.000	-469.267	-0.000	0.000
-0.000	-0.000	-0.000	-0.000	-469.267	-0.000
-0.000	-0.000	-0.000	0.000	-0.000	-469.267

20764.053	21070.642	21070.642	0.000	0.000	-0.000
21070.642	20764.053	21070.642	0.000	-0.000	-0.000
21070.642	21070.642	20764.053	0.000	0.000	-0.000
0.001	0.002	0.002	-469.267	0.000	-0.000
0.002	0.001	0.002	0.000	-469.267	-0.000
0.002	0.002	0.001	0.000	0.000	-469.267

20883.113	21189.705	21189.705	-0.000	0.000	0.000
21189.705	20883.113	21189.705	0.000	0.000	0.000
21189.705	21189.705	20883.113	-0.000	-0.000	0.000
-0.001	-0.002	-0.002	-469.267	-0.000	0.000
-0.002	-0.001	-0.002	-0.000	-469.267	0.000
-0.002	-0.002	-0.001	-0.000	-0.000	-469.267

20228.278	20534.854	20534.854	0.000	-0.000	-0.000
20534.854	20228.278	20534.854	-0.000	-0.000	-0.000
20534.854	20534.854	20228.278	0.000	-0.000	-0.000
0.015	0.016	0.015	-469.267	0.000	-0.000
0.016	0.015	0.015	0.000	-469.267	-0.000
0.016	0.015	0.015	0.000	0.000	-469.267

21418.877	21725.484	21725.484	0.000	-0.000	0.000
21725.484	21418.877	21725.484	-0.000	0.000	0.000
21725.484	21725.484	21418.877	-0.000	-0.000	0.000
-0.015	-0.016	-0.015	-469.267	-0.000	0.000
-0.016	-0.015	-0.015	-0.000	-469.267	0.000
-0.016	-0.015	-0.015	0.000	0.000	-469.267

530548.577	530375.562	530375.562	-0.000	-0.000	-0.000
530375.562	530548.577	530375.562	0.000	-0.000	-0.000
530375.563	530375.563	530548.577	-0.000	0.000	-0.000
0.078	0.078	0.078	-2271.223	-0.000	-0.000
0.078	0.078	0.078	-0.000	-2271.223	-0.000
0.078	0.078	0.078	-0.000	0.000	-2271.223

530567.821	530394.785	530394.785	0.000	0.000	0.000
530394.785	530567.821	530394.785	0.000	0.000	0.000
530394.785	530394.785	530567.820	0.000	0.000	0.000
-0.079	-0.079	-0.079	-2271.223	0.000	0.000
-0.079	-0.079	-0.079	0.000	-2271.223	0.000
-0.079	-0.079	-0.079	0.000	0.000	-2271.223

Phonon and Quasi-Harmonic Approximation Predictions

Phonon band structures and crystal properties estimated from quasi-harmonic approximation (QHA) calculations are displayed for select crystals. The calculations were performed using phonopy and LAMMPS. For the phonon calculations, 3x3 supercells of the potential-specific relaxed crystals were used. The QHA calculations were based on 11 strain states ranging from -0.05 to 0.05.

The calculation method used is available as the iprPy phonon calculation method.

Notes and Disclaimers:

The thermodynamic properties estimated from QHA are based on the assumption that only volumetric changes affect the phonon behaviors as the temperature changes. This tends to give good predictions at lower temperatures but ignores anharmonic effects such as phonon coupling and vacancy formation that can be important at higher temperatures.
Note that direct molecular dynamics (MD) simulations using the same potentials will disagree with the thermodynamics properties listed here for the lowest temperatures. The MD results are purely classical in nature and therefore lack a zero-point energy, whereas the phonon calculations inherently provide a zero-point energy.
The structures explored here are taken from the dynamically relaxed structures above. Despite the rigorous relaxation method used, some of these structures prove to be unstable once internal deformations are added. The phonon results may reflect this and give bad band gap predictions for these unstable crystals.
All QHA calculations performed here use the same set of strains which might not be ideal for all crystals. Be sure to check the bulk modulus and Helmholtz vs. volume plots to verify if the QHA strained states are reasonable for each crystal of interest.
QHA results may not be available for all crystal structures that have phonon results. Missing QHA results indicates an issue either with the strained states or with the QHA calculation itself.
NIST disclaimer

Version Information:

2023-03-14. Phonon and QHA plots added

Band Structures, Density of States, and QHA Verification Plots

Composition:

Prototype:

a₀:

plot:

Thermodynamic Predictions

Composition:

Plot:

Download data

Click on plot to load interactive version

2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1/phonon.C.G.png

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

Surface	γ_fs (mJ/m²)
(111) 2	-10603.33
(331) 2	-2160.53
(322)	-1614.45
(221)	-1498.26
(110)	-1202.51
(320)	-1195.04
(210)	-1153.18
(310)	-1136.74
(321)	-960.39
(211)	-956.24
(331) 1	-689.59
(311) 1	-596.45
(311) 2	266.17
(111) 1	493.74
(100)	1290.72

Stacking Fault Energy Predictions

Stacking fault energy plots and maps are displayed for select crystals. The values are computed by

Starting with a bulk crystal system
Creating a free surface along one of the system's periodic boundaries and using force minimization to relax it
The system is sliced in half along a crystallographic plane parallel to the free surface. One half of the system is shifted relative to the other
The atoms in the shifted system are allowed to relax only in the direction normal to the shifting plane
The stacking fault energy for a given shift is computed by comparing the energy of the system before and after applying the shift, and dividing by the area of the fault plane

The calculation method used is available as the iprPy stacking_fault_map_2D 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.
Values between the measured points are interpolated and therefore may not perfectly capture minima and maxima.
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:

2022-06-28. Table added for intrinsic and unstable energies, and ideal shear stresses. Plots (and table) now ordered by the associated planes.
2019-11-14. Calculations for the alternate #2 plane slices are now different from the #1 plane slices. The 1D plotting vectors have been changed to avoid duplicates. Minor improvements to how the 2D plots are displayed.
2019-08-07. Plots added.

Composition:

Prototype:

a₀:

plane:

Stacking fault energies in mJ/m² and ideal shears in GPa

E_usf a/2 [0 -1 1]	1070.59
τ_ideal a/2 [0 -1 1]	17.33

Download raw data

plot:

Point Defect Formation Energy Predictions

Static point defect formation energies, E_f, and elastic dipole tensors, p_ij, 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. E_f is computed by comparing the energy of the defect system to the same number of atoms in a perfect bulk crystal. p_ij 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 Defect	E_f (eV)	p₁₁ (eV)	p₂₂ (eV)	p₃₃ (eV)	p₁₂ (eV)	p₁₃ (eV)	p₂₃ (eV)
1nn divacancy	-2.057	129.257	129.257	129.257	-1.182	-1.182	-1.182
vacancy	-1.272	96.029	96.029	96.029	-0.000	-0.000	-0.000
relaxed interstitial	1.707	361.661	361.661	355.393	-4.579	2.067	2.067
100 dumbbell	2.099	263.823	263.823	269.204	0.000	0.000	0.000
bond centered interstitial	3.733	222.011	222.011	222.011	5.385	5.385	5.385

Dislocation Monopole Structures

Plots of the atomic structure of dislocation cores are shown here. The dislocations were constructed using dislocation monopole configurations in which a straight dislocation is created in the center of the system using anisotropic elasticity and the elastic constants computed above. A cylindrical region centered around the dislocation is allowed to relax while the remaining atoms are held fixed. The relaxation consists of 1 million NVT steps at 10 K followed by an energy/force minimization. The final plots show the atomic configuration near the center of the monopole system, and display differential displacement arrows and Nye tensor color maps that are both taken with respect to the Burgers vector direction.

These plots show a wide range of final structures, some corresponding to expected dislocation structures and others not. While the characterizations are dislocation-type dependent, some general classification guidelines are listed here.

Planar dislocations exist on a single slip plane, which results in a grouping of large differential displacement arrows between two atomic rows. All edge dislocations and some screw dislocations may be planar dislocations.
Non-planar dislocations are screw dislocations that are positioned at the intersection of more than one slip plane. This results in the differential displacement arrows circling the position of the dislocation core. These core structures often have rotational symmetry due to the intersecting planes.
The plotted atomic positions are also useful for characterizing the final configuration. For screw dislocations, the atomic projections should match projections in the bulk crystal if the crystal has not transformed. For edge dislocations, the projections should be the bulk projections with the extra half-plane of atoms directly above the dislocation core.
Images in which the atomic positions look correct but no large differential displacement arrows are observed are likely the result of the dislocation gliding out of view during relaxation.
Phase transformations are identified by large differential displacement arrows spread out in both plot directions, often across the whole image. Additionally, the atomic position projections will likely not correspond to what is expected.
Twins typically appear as a long line of large differential displacement arrows along a single plane. Note that twins can nucleate phase transformations so the distinction between the two is not always clear.

The calculation method used is available as the iprPy dislocation_monopole calculation method.

Links are provided above the images allowing for users to download the final defect configuration and a corresponding defect-free configuration if they wish to further analyze the structures or use them for subsequent simulations.

Notes and Disclaimers:

While the general dislocation monopole method is universal to all dislocations, these calculations rely on dislocation-type specific atomic configuration sizes and differential displacement/Nye tensor settings. For the system size, the specific super cell multipliers vary based on the crystal and crystal vector orientations, but the sizes are always selected to minimize the length along the dislocation line and attempt to make the two other box dimensions similar. For the structure analysis tools, both are sensitive to the cutoff distance used to identify neighbors, and both have some method-specific parameters. Where known, the settings used here correspond to the most common ones used in literature.
For bcc dislocations, the differential displacement vectors shown here are "wrapped" in that if their magnitudes exceed b/2 then a value of b is added/subtracted to wrap the vector back around. This convention reveals the dislocation's structure and location without showing the slip history.
NIST disclaimer

Version Information:

2025-08-07. Plots first added.

Composition:

Type:

Nye tensor + differential displacement plot

Reference system: base.dump
Dislocation system: disl.dump

MD Solid Property Predictions

Plots of lattice and elastic constants are shown as a function of temperature. The 0K points were taken from the Crystal Structure Predictions and the Elastic Constants Predictions sections above for the unique crystal structures relaxed with the "dynamic" method. Starting from the 0 K relaxed crystal unit cells, supercell systems are created by replicating all three dimensions by the same multiplier to achieve at least 4000 atoms. The systems are then relaxed at 50 K and zero pressure using 1 million NPT steps. Lattice constants are estimated by averaging the measured box dimensions. Temperatures are iteratively increased by 50 K, with each subsequent relaxation calculation starting from the final atomic configuration at the previous temperature and relaxing for another 1 million steps.

The elastic constants are calculated using the deformation–fluctuation hybrid method. Starting from the final atomic configurations of the dynamic relaxations, the system is allowed to evolve at constant volume with a Langevin thermostat. The Born matrix is computed during this run by evaluating how the atomic forces would vary due to applied linear strain fields. The elastic constants can then be estimated using the averaged Born matrix values and the averaged stresses on the system.

The calculation methods used are available as the iprPy relax_dynamic and elastic_constants_dynamic calculation methods.

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:

The maximum temperature shown for a crystal either corresponds to the maximum value that has been computed so far, or the maximum value that the structure is believed to have remained untransformed. The unstable/transformation temperature identification is mostly automated and can miss transitions not associated with large discontinuities in property values with changing temperature.
For succinctness, the elastic constants displayed here are averaged according to the 0 K structure's crystal symmetry family. If the structures deviate from the expected symmetry at higher temperatures, the values may not be valid. Raw results are available for verification if requested.
NIST disclaimer

Version Information:

2025-08-07. Plots added.

Composition:

Prototype:

a₀:

Download data

Click on plot to load interactive version

2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1/mdsolid.C.A4--C--dc.2a03e9a4.a

Click on plot to load interactive version

2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1//mdsolid.C.A4--C--dc.2a03e9a4.Cij

MD Liquid Property Predictions

Plots of radial distribution functions at different temperatures and the temperature-dependent diffusion and viscosity are shown here for elemental liquids. Melt phases are constructed by starting with a 10x10x10 fcc super cell and relaxing with 50,000 NPT steps at zero pressure and a high melting temperature (3000 K for most potentials and elements). Following the melt, liquid structures are relaxed by running NPT for 10,000 steps over which the temperature is dropped by 50 K, then 50,000 NPT at the target temperature to estimate the equilibrium volume, followed by 20,000 NVT steps at the averaged equilibrium volume and target temperature. Structures from the NVT run are sampled to compute the radial distribution function of the liquid at the corresponding temperature.

The final relaxed configurations at each temperature explored are used as the initial configurations for the diffusion and viscosity calculations. For diffusion, the system is integrated for 100 runs of 2,000 NVT steps during which both the mean squared displacement (MSD) and the velocity auto correlation function (VACF) are computed. From these simulations, three estimates of diffusion are computed: one from the MSD of the full 200,000 step run, one in which the MSD is reset for each short run and then averaged, and one from the VACF computed for each short run and averaged. For viscosity, the Green-Kubo method is used which is evaluated during a 1 million step NVT run.

The calculation methods used are available as the iprPy relax_liquid_redo, diffusion_liquid, and viscosity_green_kubo calculation methods.

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:

The current liquid relaxation has some known issues, and therefore may be recalculated with an improved method later. Most notably, the unconstrained NPT relaxation may lead to one of the periodic dimensions becoming quite small which can negatively affect the simulations and property calculations. Additionally, the relaxations likely need to be longer to reduce the error associated with the measured volume and energy values.
Values are only displayed down to the last temperature currently calculated, or the last temperature at which the system is believed to remain liquid until the end of all simulations. The transformation temperature is estimated by looking at discontinuities in the measured property values and may incorrectly predict a phase to still be liquid if the discontinuities are small.
The three diffusion estimates provide a range of prediction values. For MSD, the longer the run the more likely it is that a small number of atoms will diffuse much farther than the rest, which skews the squared displacement higher.
NIST disclaimer

Version Information:

2025-08-07. Plots added. Data should be thought of as preliminary as results may be recalculated later.

Composition:

Download data

Property:

Click on plot to load interactive version

2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1/mdliquid.Fe.rdf

MD Thermodynamic Predictions

Plots of internal energy, Gibbs free energy, entropy, heat capacity and volume are shown here as a function of temperature for various crystal structures and liquid phases. The included crystal structures correspond to those in the Solid Structures vs. Temperature section, and the liquid phases to those in the Liquid Properties section. Internal energy and volume are taken from the associated structure relaxations mentioned in those previous sections. Constant pressure heat capacity is estimated using 3-point numerical derivatives of enthalpy versus temperature. Note that since all simulations done here are at 0 pressure, internal energy and enthalpy are equivalent.

The Gibbs energies of the phases are estimated using thermodynamic integration between the interatomic potential in question and a simpler model with known Gibbs free energy values. For solids, the reference model is an Einstein solid, while for liquids it is the Uhlenbeck-Ford potential. Besides a short run at the start of the solid calculations to estimate Einstein model spring constants, the two calculations proceed similarly. Starting with the final relaxation configurations, the systems are stabilized for 25,000 steps. Then, over the next 50,000 steps the potential is swapped out for the reference potential. The system is then stabilized for another 25,000 steps with the reference model before a reverse swap of 50,000 steps is performed. The simulation ends with one final 25,000 step stabilization period. From the simulation, the irreversible work of transformation is estimated and used to compute the absolute Gibbs free energy of the target phase and potential relative to the reference potential. Entropy is estimated as the difference in enthalpy and Gibbs free energy and divided by temperature.

The calculation methods used are available as the iprPy relax_dynamic, relax_liquid_redo, free_energy, and free_energy_liquid calculation methods.

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:

Good free energy estimates require that the initial and final phases before and after the thermodynamic integration remain the same. This is not an issue with the liquid calculations as the Uhlenbeck-Ford model always predicts a liquid, but may be an issue for the solid phase estimates. This is likely to be an issue for non-compact phases which the Einstein model is poor at representing.
NIST disclaimer

Version Information:

2025-08-07. Plots added.

Composition:

Property:

Download data

Click on plot to load interactive version

2008--Hepburn-D-J--Fe-C--LAMMPS--ipr1/mdthermo.C.U

530461.966	530289.046	530289.046	-0.000	-0.000	-0.000
530289.046	530461.966	530289.046	-0.000	-0.000	-0.000
530289.046	530289.046	530461.966	0.000	-0.000	-0.000
0.774	0.775	0.774	-2271.223	-0.000	-0.000
0.775	0.774	0.774	-0.000	-2271.223	-0.000
0.775	0.774	0.774	-0.000	-0.000	-2271.223

530654.427	530481.295	530481.295	0.000	0.000	0.000
530481.295	530654.427	530481.295	0.000	-0.000	0.000
530481.295	530481.295	530654.427	-0.000	-0.000	0.000
-0.774	-0.775	-0.774	-2271.223	0.000	0.000
-0.775	-0.774	-0.774	0.000	-2271.223	0.000
-0.775	-0.774	-0.774	0.000	0.000	-2271.223

529595.835	529423.868	529423.868	0.000	-0.000	-0.000
529423.868	529595.835	529423.868	-0.000	-0.000	-0.000
529423.868	529423.868	529595.835	0.000	0.000	-0.000
7.742	7.746	7.742	-2271.223	-0.000	-0.000
7.746	7.742	7.742	0.000	-2271.223	-0.000
7.746	7.742	7.742	0.000	-0.000	-2271.223

531520.444	531346.357	531346.357	-0.000	0.000	0.000
531346.357	531520.444	531346.357	0.000	-0.000	0.000
531346.357	531346.357	531520.444	0.000	0.000	0.000
-7.742	-7.746	-7.742	-2271.223	0.000	0.000
-7.746	-7.742	-7.742	0.000	-2271.223	0.000
-7.746	-7.742	-7.742	-0.000	0.000	-2271.223

14737847557.847	15512257330.790	14655207559.621	-6173176.639	3051047.850	8677916.764
11335.329	11315.230	12840.707	0.000	-0.000	-0.000
12840.273	12840.273	15406.843	0.000	0.000	-0.000
0.000	0.000	-0.000	-230.365	-0.000	-0.000
0.000	0.000	-0.000	-0.000	-230.366	-0.000
0.000	0.000	-0.000	0.000	-0.000	-10.050

-15485099809.060	-15301693090.982	-15082692694.717	-18650250.310	-2252076.712	-15346037.437
11337.795	11317.695	12843.939	-0.000	0.000	0.000
12844.511	12844.510	15412.397	0.000	0.000	0.000
-0.000	-0.000	-0.000	-230.365	0.000	0.000
-0.000	-0.000	-0.000	0.000	-230.365	0.000
-0.000	-0.000	0.000	-0.000	0.000	-10.050

1478228715.479	1550491884.780	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	0.000	-0.000	-0.000
0.001	0.001	0.001	-230.365	-0.000	-0.000
0.001	0.001	0.001	-0.000	-230.365	-0.000
1523397351.078	1496634280.540	1467833465.096	-1972569.281	-134393.293	-36628344.022

-1546442592.817	-1530288833.222	-1506145947.040	882862.459	-363426.053	-955398.968
-1480745650.916	-1553626634.311	-1469896921.048	-1270421.514	-2437925.852	-1042194.304
12863.578	12863.578	15437.393	-0.000	0.000	0.000
-0.001	-0.001	-0.001	-230.365	0.000	0.000
-0.001	-0.001	-0.001	0.000	-230.365	0.000
-1514976555.047	-1488394221.178	-1465671076.178	-2210330.232	-446551.272	-40699012.699

149609164.903	156267631.962	147397843.093	63040.943	80892.253	-98274.755
154657490.317	152982278.838	150586563.039	-40788.256	125629.149	166732.759
12630.533	12630.533	15131.887	-0.000	-0.000	-0.000
0.008	0.011	0.010	-230.365	-0.000	-0.000
0.045	-0.025	0.010	0.000	-230.365	-0.000
151503543.148	148331306.562	145926746.997	117678.599	-232723.791	-4109826.635

-154553876.162	-152845629.421	-150685775.406	112531.875	-21938.051	-92075.080
-149674635.679	-156071137.363	-147144611.183	35729.357	103188.422	-21139.809
12995.120	12995.120	15609.837	-0.000	0.000	0.000
-0.008	-0.011	-0.010	-230.365	0.000	0.000
-0.045	0.025	-0.010	0.000	-230.365	0.000
-153288819.612	-149156384.655	-146734944.609	-48974.800	-30720.046	-3164970.289

-7406.910	-7152.806	0.001	-0.000	-0.000	-0.000
1547007867.114	1416988719.444	1094389488.606	2667107.837	3498910.486	-21823189.243
1524244739.304	1412118289.761	1102085662.158	-285178.233	4662427.034	-25173057.425
1796758815.530	1763817688.820	1278841007.852	1043409.743	-726672.092	-10279691.079
1742395321.241	1740389881.824	1264902226.448	-3048767.183	-1496399.246	-9201185.033
1565109559.489	1475841316.690	1093197534.331	-3633657.770	-5327070.866	3413673.484

-1469389503.930	-1370556579.165	-1131703799.939	-7622593.556	-2597203.031	25771571.095
-1476673257.714	-1377424206.185	-1121890285.260	1141053.384	-206441.059	-25606535.426
-1527028043.440	-1449095906.045	-1086684797.719	3012560.403	-7954909.953	31782968.154
-1774683291.477	-1744095466.293	-1271841340.283	-1636619.964	-6048192.662	7122938.269
-1704225580.094	-1699770203.859	-1263633223.303	7206358.236	-2364189.908	13072157.734
-1495482766.966	-1412276485.373	-1058136244.044	10151144.965	-191341.289	7912251.688

156477851.727	146189475.502	112537390.629	-72917.851	30064.950	2282641.970
156980875.226	145394494.556	110846024.368	166243.070	-471581.161	-1483565.078
156845613.148	142914554.090	107341307.658	-170848.025	-34234.714	-1677525.979
179781841.178	177930260.064	126529703.824	-249499.973	-390158.399	42243.325
174164129.715	171002933.465	125007721.078	-247158.035	200791.812	-730153.131
147895375.729	142249167.291	106058713.028	9814.328	-46988.025	-3243936.513

-157569375.013	-146118346.238	-108047564.833	57195.654	213116.837	751495.685
-7145.621	-7399.723	0.001	-0.000	-0.000	0.000
-157411350.594	-142703010.095	-108420026.256	-99257.954	123595.805	1771705.733
-182440641.545	-178942943.201	-126191504.104	-263070.849	39277.030	-110938.916
-175955458.785	-173012929.423	-126450069.691	-243277.179	688627.215	-41495.681
-157937424.279	-143673897.780	-110455471.338	-95462.444	136497.855	1591493.504

15695752.601	14509400.819	10746415.629	-3010.478	-20729.261	-137733.284
15296374.422	14045130.248	11831844.651	2778.479	-50424.126	-40097.896
15695938.446	14274459.513	10882468.170	27921.128	4651.747	-251953.833
17831512.477	17388896.050	12674408.892	25117.500	8903.214	-91854.652
17654311.240	17552239.310	12543673.825	76670.945	30315.228	-15934.340
16047431.736	15307035.389	11229708.738	33704.993	7922.341	-161535.508

-7342.867	-7088.782	0.001	0.000	0.000	0.000
-13299027.399	-12679833.801	-11483351.500	-55879.288	26804.672	-87131.277
-15334606.077	-14259038.837	-10994316.461	-34548.445	-8281.441	398630.107
-17687656.625	-17068891.226	-12892512.193	-22673.565	-72043.112	3322.476
-17206692.084	-17320019.280	-12544813.147	17483.717	34219.860	68582.482
-15780416.478	-14857767.009	-10837068.094	-41348.991	170821.598	78094.225

5905.755	5735.746	5735.746	0.000	0.000	0.000
5735.746	5905.755	5735.746	-0.000	0.000	0.000
5735.746	5735.746	5905.755	-0.000	-0.000	0.000
-0.000	-0.000	-0.000	174.308	0.000	0.000
-0.000	-0.000	-0.000	0.000	174.308	0.000
-0.000	-0.000	-0.000	0.000	0.000	174.308

5907.531	5737.521	5737.521	-0.000	-0.000	-0.000
5737.522	5907.531	5737.521	0.000	-0.000	-0.000
5737.522	5737.521	5907.531	0.000	-0.000	-0.000
0.000	0.000	0.000	174.308	-0.000	-0.000
0.000	0.000	0.000	-0.000	174.308	-0.000
0.000	0.000	0.000	-0.000	-0.000	174.308

5941.372	5771.364	5771.364	0.000	-0.000	0.000
5771.364	5941.372	5771.364	0.000	0.000	0.000
5771.364	5771.364	5941.372	0.000	0.000	0.000
-0.000	-0.000	-0.000	174.308	0.000	0.000
-0.000	-0.000	-0.000	0.000	174.308	0.000
-0.000	-0.000	-0.000	0.000	0.000	174.308

5915.521	5745.511	5745.511	-0.000	-0.000	-0.000
5745.511	5915.521	5745.511	-0.000	-0.000	-0.000
5745.511	5745.511	5915.521	-0.000	-0.000	-0.000
0.000	0.000	0.000	174.308	-0.000	-0.000
0.000	0.000	0.000	-0.000	174.308	-0.000
0.000	0.000	0.000	-0.000	-0.000	174.308

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

Fe 6

Implementation Information

Diatom Energy vs. Interatomic Spacing

Cohesive Energy vs. Interatomic Spacing

Crystal Structure Predictions

Elastic Constants Predictions

Phonon and Quasi-Harmonic Approximation Predictions

Band Structures, Density of States, and QHA Verification Plots

Thermodynamic Predictions

Free Surface Formation Energy Predictions

Stacking Fault Energy Predictions

Point Defect Formation Energy Predictions

Dislocation Monopole Structures

MD Solid Property Predictions

MD Liquid Property Predictions

MD Thermodynamic Predictions

5998.314	5828.317	5828.317	0.000	0.000	0.000
5828.317	5998.314	5828.317	-0.000	0.000	0.000
5828.317	5828.317	5998.314	-0.000	0.000	0.000
-0.003	-0.004	-0.003	174.308	0.000	0.000
-0.004	-0.003	-0.003	0.000	174.308	0.000
-0.004	-0.003	-0.003	0.000	0.000	174.308

5995.423	5825.402	5825.402	-0.000	-0.000	-0.000
5825.402	5995.423	5825.402	-0.000	-0.000	-0.000
5825.402	5825.402	5995.423	-0.000	-0.000	-0.000
0.003	0.004	0.003	174.308	-0.000	-0.000
0.004	0.003	0.003	-0.000	174.308	-0.000
0.004	0.003	0.003	-0.000	-0.000	174.308

107653.994	107653.996	107653.996	-0.000	-0.000	0.000
107653.996	107653.994	107653.996	-0.000	-0.000	0.000
107653.996	107653.996	107653.993	-0.000	-0.000	-0.000
901670499.137	840422140.399	849003206.218	-9946255.358	-2488604.525	-935413.461
847562571.577	907531061.261	849948536.789	4140652.574	-12370860.990	-3626729.832
833820763.739	837412095.893	915154303.287	-3255305.152	-5893254.009	-11355944.437

107658.888	107658.886	107658.886	0.000	0.000	0.000
107658.886	107658.888	107658.886	0.000	0.000	0.000
107658.886	107658.886	107658.888	0.000	0.000	0.000
-893952172.741	-844696267.548	-839291184.035	-12563398.815	2941132.199	7033499.911
-841090850.560	-892815678.007	-844867596.242	4528829.431	-12263184.500	10110161.290
-842963575.053	-847658613.996	-888703245.765	1641243.881	3862851.433	-6324697.202

107631.954	107631.975	107631.975	-0.000	-0.000	0.000
107631.975	107631.954	107631.975	-0.000	-0.000	0.000
107631.975	107631.975	107631.954	-0.000	-0.000	-0.000
89844185.978	84227085.988	84972589.594	354335.746	-147753.556	-157533.654
84070271.106	90258247.157	85259459.302	-216495.409	-10821.569	252489.308
87853983.835	88638559.355	90570774.157	67348.143	113758.598	-161642.764

107680.928	107680.906	107680.906	0.000	0.000	-0.000
107680.906	107680.928	107680.906	0.000	0.000	-0.000
107680.906	107680.906	107680.928	0.000	0.000	0.000
-90264751.957	-87614583.419	-87728167.837	313428.845	243736.572	68017.136
-87177007.387	-88386307.729	-87308471.106	324012.259	788083.947	31816.146
-87545775.429	-87384685.340	-87847412.681	294561.436	-13043.721	691636.182

107411.560	107411.775	107411.775	0.000	-0.000	0.000
107411.775	107411.560	107411.775	-0.000	0.000	0.000
107411.775	107411.775	107411.560	-0.000	-0.000	0.000
13930264.120	13930452.969	13930453.071	51290.845	-0.000	-0.000
13930452.969	13930264.120	13930453.071	-0.000	51290.845	-0.000
13930452.969	13930453.072	13930264.120	-0.000	-0.000	51290.845

107901.299	107901.083	107901.083	0.000	0.000	-0.000
107901.083	107901.299	107901.083	0.000	0.000	-0.000
107901.083	107901.083	107901.299	0.000	0.000	0.000
-13930264.153	-13930453.002	-13930453.105	51290.848	0.000	0.000
-13930453.002	-13930264.153	-13930453.105	0.000	51290.848	0.000
-13930452.992	-13930453.095	-13930264.143	0.000	0.000	51290.847

12459.723	12992.430	12543.948	-0.000	-0.000	0.000
12992.430	12459.723	12543.948	-0.000	0.000	-0.000
12543.948	12543.948	11043.567	-0.000	-0.000	0.000
17656074149.070	17974752402.725	17870935883.445	8468626.145	37626802.370	21005239.672
18032425604.310	17668119410.043	17795360760.464	-33120671.945	2874698.273	-30765988.270
-0.000	-0.000	-0.000	-0.000	0.000	239.594

12459.720	12992.429	12543.946	0.000	0.000	0.000
12992.429	12459.720	12543.946	0.000	0.000	-0.000
12543.946	12543.946	11043.565	0.000	0.000	-0.000
-17563704800.868	-18025292355.183	-17829036105.179	8442120.043	19511917.891	7044980.898
-17989660370.271	-17673251945.493	-17801476564.431	-5522129.350	46246070.727	11090456.495
0.000	0.000	0.000	0.000	0.000	239.594