× 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.

2014--Liyanage-L-S-I-Kim-S-G-Houze-J-et-al--Fe-C

Citation: L.S.I. Liyanage, S.-G. Kim, J. Houze, S. Kim, M.A. Tschopp, M.I. Baskes, and M.F. Horstemeyer (2014), "Structural, elastic, and thermal properties of cementite (Fe3C) calculated using a modified embedded atom method", Physical Review B, 89(9), 094102. DOI: 10.1103/physrevb.89.094102.

Abstract: Structural, elastic, and thermal properties of cementite (Fe3C) were studied using a modified embedded atom method (MEAM) potential for iron-carbon (Fe-C) alloys. Previously developed Fe and C single-element potentials were used to develop a Fe-C alloy MEAM potential, using a statistics-based optimization scheme to reproduce structural and elastic properties of cementite, the interstitial energies of C in bcc Fe, and heat of formation of Fe-C alloys in L12 and B1 structures. The stability of cementite was investigated by molecular dynamics simulations at high temperatures. The nine single-crystal elastic constants for cementite were obtained by computing total energies for strained cells. Polycrystalline elastic moduli for cementite were calculated from the single-crystal elastic constants of cementite. The formation energies of (001), (010), and (100) surfaces of cementite were also calculated. The melting temperature and the variation of specific heat and volume with respect to temperature were investigated by performing a two-phase (solid/liquid) molecular dynamics simulation of cementite. The predictions of the potential are in good agreement with first-principles calculations and experiments.

LAMMPS pair_style meam (2014--Liyanage-L-S-I--Fe-C--LAMMPS--ipr2)

See Computed Properties
Notes: These files were contributed by Laalitha Liyanage (Central Michigan Univ., Univ. of North Texas) on 14 Apr. 2014.
File(s):

Fe3C_library_Liyanage_2014.meam
Fe3C_Liyanage_2014.meam

Implementation Information

This page displays computed properties for the 2014--Liyanage-L-S-I--Fe-C--LAMMPS--ipr2 implementation of the 2014--Liyanage-L-S-I-Kim-S-G-Houze-J-et-al--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

2014--Liyanage-L-S-I--Fe-C--LAMMPS--ipr2/diatom

Click on plot to load interactive version

2014--Liyanage-L-S-I--Fe-C--LAMMPS--ipr2/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

2014--Liyanage-L-S-I--Fe-C--LAMMPS--ipr2/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)
A4--C--dc	box	-7.37	-7.37	3.567	3.567	3.567	90.0	90.0	90.0
oqmd-599489	box	-7.37	-7.37	2.5214	2.5214	4.1214	90.0	90.0	120.0
mp-47	box	-7.37	-7.37	2.5214	2.5214	4.1217	90.0	90.0	120.0
mp-568806	box	-7.37	-7.37	2.5303	2.5303	4.2403	90.0	90.0	120.0
oqmd-610551	box	-7.37	-7.37	2.53	2.53	4.24	90.0	90.0	120.0
mp-937760	box	-7.3697	-7.3697	2.5303	4.3826	8.5033	90.0	90.0	90.0
oqmd-683819	box	-7.3697	-7.3697	2.5308	4.3817	8.5023	90.0	90.0	90.0
oqmd-683820	box	-7.3697	-7.3697	2.5308	4.3818	8.4995	90.0	90.0	90.0
oqmd-1214690	box	-7.3697	-7.3697	2.5316	4.3804	8.503	90.0	90.0	90.0
mp-568286	box	-7.3695	-7.3695	2.5295	4.384	8.3876	90.0	90.0	90.0
A7--alpha-As	box	-7.3688	-7.3688	2.5304	2.5304	12.7116	90.0	90.0	120.0
mp-48	box	-7.3688	-7.3688	2.5304	2.5304	8.4806	90.0	90.0	120.0
oqmd-590101	box	-7.3688	-7.3688	2.5303	2.5303	8.4803	90.0	90.0	120.0
mp-568363	box	-7.3687	-7.3687	2.5311	4.3815	9.0753	90.0	90.0	90.0
A7--alpha-As	box	-7.3686	-7.3686	2.5304	2.5304	12.6473	90.0	90.0	120.0
oqmd-589492	box	-7.3685	-7.3685	2.5304	2.5304	67.4915	90.0	90.0	120.0
mp-606949	box	-7.3685	-7.3685	2.5304	2.5304	36.2687	90.0	90.0	120.0
oqmd-589493	box	-7.3685	-7.3685	2.5304	2.5304	36.6955	90.0	90.0	120.0
mp-616440	box	-7.3679	-7.3679	2.5225	2.5225	16.4786	90.0	90.0	120.0
oqmd-637444	box	-7.3677	-7.3677	4.1322	4.1322	4.1322	90.0	90.0	90.0
oqmd-599492	box	-7.3675	-7.3675	2.5222	2.5222	16.4842	90.0	90.0	120.0
mp-611448	box	-7.3669	-7.3669	2.5225	2.5225	12.3619	90.0	90.0	120.0
oqmd-599491	box	-7.3667	-7.3667	2.5224	2.5224	12.3639	90.0	90.0	120.0
mp-569567	box	-7.3665	-7.3665	2.5231	2.5231	43.2494	90.0	90.0	120.0
oqmd-599493	box	-7.3661	-7.3661	2.5226	2.5226	30.9084	90.0	90.0	120.0
mp-569517	box	-7.3661	-7.3661	2.5227	2.5227	30.9061	90.0	90.0	120.0
mp-611426	box	-7.3658	-7.3658	2.5225	2.5225	8.2434	90.0	90.0	120.0
oqmd-599490	box	-7.365	-7.365	2.5226	2.5226	8.2435	90.0	90.0	120.0
mp-1188817	box	-7.2636	-7.2636	5.2504	5.2504	5.2504	90.0	90.0	90.0
oqmd-637443	box	-7.2634	-7.2634	5.2504	5.2504	5.2504	90.0	90.0	90.0
oqmd-637353	box	-7.2399	-7.2399	4.413	4.413	2.5028	90.0	90.0	90.0
mp-1008395	box	-7.2398	-7.2398	4.4131	4.4131	2.5027	90.0	90.0	90.0
mp-1078845	box	-7.2176	-7.2176	4.2721	8.8562	2.5292	90.0	90.0	90.0
mp-1080826	box	-7.0698	-7.0698	9.2032	2.581	4.2391	90.0	96.6	90.0
oqmd-637352	box	-7.0695	-7.0695	9.2065	2.5814	4.2375	90.0	96.6	90.0
oqmd-637130	box	-7.0636	-7.0636	9.1306	2.5787	4.2502	90.0	90.0	90.0
mp-1190171	box	-7.0628	-7.0628	9.1289	2.5787	4.2508	90.0	90.0	90.0
mp-1205283	dynamic	-7.0321	-7.0321	9.3922	12.6546	9.4801	90.0	90.0	90.0
oqmd-689315	dynamic	-7.0142	-7.0142	9.6815	15.8489	17.394	90.0	90.0	90.0
oqmd-610557	box	-6.981	-6.981	4.871	5.4058	4.6382	90.0	90.0	90.0
oqmd-610556	box	-6.9776	-6.9776	4.8684	5.4154	4.6403	90.0	90.0	90.0
mp-568410	box	-6.969	-6.969	4.8602	5.4419	4.6459	90.0	90.0	90.0
mp-1196583	dynamic	-6.9616	-6.9616	13.1799	13.1799	13.1799	90.0	90.0	90.0
mp-1244964	dynamic	-6.835	-6.835	9.9752	10.0791	10.6393	88.0	86.8	86.5
mp-1245190	dynamic	-6.8321	-6.8321	9.8042	10.1367	10.3145	91.4	94.5	90.5
mp-1147718	dynamic	-6.8127	-6.8127	10.1568	14.1067	8.6009	90.0	90.0	90.0
mp-1244913	dynamic	-6.8078	-6.8078	10.2059	10.2452	10.7332	93.4	92.7	92.3
oqmd-585286	box	-6.7242	-6.7242	5.0656	5.0656	5.0656	90.0	90.0	90.0
mp-570002	box	-6.7194	-6.7194	5.0679	5.0679	5.0679	90.0	90.0	90.0
mp-683919	box	-6.5329	-6.5329	11.1367	19.0488	19.6498	90.0	90.0	90.0
oqmd-614417	box	-6.5162	-6.5162	9.9248	9.9248	26.464	90.0	90.0	120.0
mp-680372	box	-6.5083	-6.5083	9.9467	9.9467	27.258	90.0	90.0	120.0
oqmd-689315	box	-6.495	-6.495	11.1499	19.0029	19.747	90.0	90.0	90.0
oqmd-595714	box	-6.4901	-6.4901	9.9254	9.9836	15.8863	90.0	90.0	90.0
mp-630227	box	-6.4779	-6.4779	9.9941	10.0174	16.6776	90.0	90.0	90.0
mp-1147718	box	-6.4515	-6.4515	11.2419	16.1546	10.1138	90.0	90.0	90.0
mp-579909	box	-6.4476	-6.4476	4.9565	6.2264	7.2725	90.0	90.0	90.0
oqmd-610552	box	-6.4475	-6.4475	4.9678	6.2077	6.8574	90.0	90.0	90.0
oqmd-603085	box	-6.4385	-6.4385	15.3775	15.3775	15.3775	90.0	90.0	90.0
mp-1196583	box	-6.4379	-6.4379	15.8391	15.8391	15.8391	90.0	90.0	90.0
mp-667273	box	-6.4329	-6.4329	15.5501	15.5501	15.5501	90.0	90.0	90.0
oqmd-684627	box	-6.4328	-6.4328	9.9711	9.9711	16.8172	90.0	90.0	90.0
mp-624889	box	-6.4262	-6.4262	5.2455	5.7187	6.0394	90.0	90.0	90.0
mp-568028	box	-6.4252	-6.4252	9.3805	15.0996	10.4631	90.0	90.0	90.0
oqmd-677227	box	-6.4039	-6.4039	15.6384	15.6384	15.6384	90.0	90.0	90.0
mp-1205283	box	-6.3412	-6.3412	11.0434	14.3701	9.8725	90.0	90.0	90.0
oqmd-1215848	dynamic	-6.1953	-6.1953	4.4156	4.4156	1.49	90.0	90.0	120.0
mp-1245190	box	-5.9741	-5.9741	11.6964	11.7503	11.9778	89.2	88.9	87.1
mp-24	box	-5.9418	-5.9418	4.8949	4.8949	4.8949	90.0	90.0	90.0
mp-1056957	box	-5.925	-5.925	2.4145	2.4141	8.5576	90.0	90.0	90.0
oqmd-1216026	box	-5.9247	-5.9247	2.4144	2.4144	13.0693	90.0	94.1	90.0
mp-1244964	box	-5.9214	-5.9214	11.5853	11.8478	12.3014	90.6	93.7	92.0
oqmd-684315	box	-5.9145	-5.9145	11.5146	16.6055	10.2222	90.0	90.0	90.0
mp-1244913	box	-5.7828	-5.7828	12.0233	12.3576	12.7333	91.1	95.3	91.3
A5--beta-Sn	box	-5.7488	-5.7488	3.814	3.814	1.6824	90.0	90.0	90.0
Ah--alpha-Po--sc	static	-5.7219	-5.7219	1.8348	1.8348	1.8348	90.0	90.0	90.0
mp-1182692	box	-5.5466	-5.5466	9.4986	12.2822	29.1644	95.6	94.2	111.9
mp-1192619	box	-5.511	-5.511	10.755	10.755	10.755	90.0	90.0	90.0
oqmd-1214779	box	-5.4909	-5.4909	10.291	10.291	10.291	90.0	90.0	90.0
mp-1203645	box	-5.4408	-5.4408	12.0913	7.4285	14.8211	90.0	105.6	90.0
mp-1095633	box	-5.3362	-5.3362	7.277	7.277	9.1404	90.0	90.0	90.0
A2--W--bcc	static	-5.2607	-5.2607	2.2749	2.2749	2.2749	90.0	90.0	90.0
A3--Mg--hcp	box	-5.2425	-5.2425	1.9115	1.9115	7.84	90.0	90.0	120.0
mp-1205417	box	-5.0702	-5.0702	15.1845	15.1845	8.7523	90.0	90.0	90.0
A15--beta-W	box	-4.8851	-4.8851	3.773	3.773	3.773	90.0	90.0	90.0
oqmd-1214868	box	-4.8118	-4.8118	8.4432	8.4432	8.4432	90.0	90.0	90.0
A3--Mg--hcp	box	-4.6847	-4.6847	2.1567	2.1567	3.5409	90.0	90.0	120.0
A3'--alpha-La--double-hcp	box	-4.683	-4.683	2.159	2.159	7.0706	90.0	90.0	120.0
A1--Cu--fcc	static	-4.6812	-4.6812	3.0567	3.0567	3.0567	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)
C1--CaF2--fluorite	static	-5.548	-5.548	4.4944	4.4944	4.4944	90.0	90.0	90.0
oqmd-1232084	box	-5.323	-5.323	4.3993	4.3993	2.66	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	box	-5.4814	-5.4814	4.7211	4.7211	12.871	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-645339	box	-5.114	-5.114	4.5027	4.987	11.4073	81.6	89.4	89.9
oqmd-7999	box	-5.1139	-5.1139	11.3393	4.5114	5.0062	90.0	98.4	90.0
oqmd-23087	box	-5.1136	-5.1136	4.5098	5.0043	11.3498	98.4	90.1	90.1

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
D0_3--BiF3	static	-5.4377	-5.4377	4.5752	4.5752	4.5752	90.0	90.0	90.0
A15--Cr3Si	static	-5.1947	-5.1947	3.8896	3.8896	3.8896	90.0	90.0	90.0
L1_2--AuCu3	static	-4.9811	-4.9811	3.1017	3.1017	3.1017	90.0	90.0	90.0
A15--Cr3Si	static	-2.057	-2.057	7.3349	7.3349	7.3349	90.0	90.0	90.0
A15--Cr3Si	static	-0.1216	-0.1216	8.0498	8.0498	8.0498	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	-5.1712	-5.1712	6.8785	6.8785	4.3699	90.0	90.0	120.0
mp-21717	box	-5.1573	-5.1573	4.5147	6.793	11.5486	90.0	90.0	90.0
mp-18257	static	-5.1572	-5.1572	6.7859	6.7859	4.496	90.0	90.0	120.0
oqmd-42164	box	-5.1568	-5.1568	4.5143	6.796	11.5451	90.0	90.0	90.0
mp-18257	box	-5.1404	-5.1404	6.7698	6.7698	4.5299	90.0	90.0	120.0
oqmd-13852	box	-5.1403	-5.1403	6.7695	6.7695	4.5283	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-21378	box	-4.8305	-4.8305	10.4424	10.4424	10.4424	90.0	90.0	90.0
mp-1192884	box	-4.8298	-4.8298	10.442	10.442	10.442	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	dynamic	-5.8227	-5.8227	3.84	3.84	3.84	90.0	90.0	90.0
oqmd-1228598	dynamic	-5.658	-5.658	2.6387	2.6387	2.4663	90.0	90.0	120.0
B3--ZnS--cubic-zinc-blende	dynamic	-5.49	-5.49	4.119	4.119	4.119	90.0	90.0	90.0
oqmd-1225112	box	-5.4859	-5.4859	2.9501	2.9501	4.6406	90.0	90.0	120.0
B2--CsCl	static	-5.4323	-5.4323	2.4933	2.4933	2.4933	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-1871	box	-5.2467	-5.2467	4.3478	4.4013	2.7805	90.0	90.0	90.0
oqmd-13851	box	-5.243	-5.243	4.3511	4.3961	2.7809	90.0	90.0	90.0
mp-1102779	box	-5.192	-5.192	5.9416	2.6654	6.5308	90.0	90.0	90.0
C1--CaF2--fluorite	static	-5.022	-5.022	4.7801	4.7801	4.7801	90.0	90.0	90.0
oqmd-20513	box	-4.0341	-4.0341	3.9283	3.9283	2.4619	90.0	90.0	120.0
mp-568503	box	-4.0341	-4.0341	3.9283	3.9283	2.4619	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-510623	box	-4.9834	-4.9834	5.0632	6.7107	4.4557	90.0	90.0	90.0
oqmd-3494	box	-4.9816	-4.9816	5.0691	6.7063	4.452	90.0	90.0	90.0
mp-1182630	box	-4.9352	-4.9352	5.2744	11.0666	2.653	90.0	90.0	90.0
oqmd-7808	dynamic	-4.9027	-4.9027	4.5589	4.5589	4.4067	90.0	90.0	120.0
mp-1205436	box	-4.8911	-4.8911	8.4618	8.4618	4.2226	90.0	90.0	90.0
mp-13154	box	-4.8907	-4.8907	4.5394	4.5394	4.3963	90.0	90.0	120.0
oqmd-7808	box	-4.8882	-4.8882	4.5385	4.5385	4.3952	90.0	90.0	120.0
mp-1205444	box	-4.8543	-4.8543	8.0913	2.7517	14.5738	90.0	103.1	90.0
oqmd-41734	box	-4.8145	-4.8145	4.9719	7.0254	4.5951	90.0	90.0	90.0
mp-613523	box	-4.8127	-4.8127	4.9825	7.0265	4.5864	90.0	90.0	90.0
oqmd-321460	box	-4.5119	-4.5119	4.9203	4.9203	3.8337	90.0	90.0	120.0
oqmd-298554	static	-4.5063	-4.5063	3.5975	3.5975	6.2005	90.0	90.0	90.0
A15--Cr3Si	static	-4.4752	-4.4752	4.4145	4.4145	4.4145	90.0	90.0	90.0
D0_3--BiF3	static	-4.455	-4.455	5.4089	5.4089	5.4089	90.0	90.0	90.0
L1_2--AuCu3	static	-4.3897	-4.3897	3.4261	3.4261	3.4261	90.0	90.0	90.0
mp-1188724	static	-1.4816	-1.4816	14.3378	20.5229	13.5131	90.0	90.0	90.0
mp-1188724	dynamic	-1.4816	-1.4816	14.268	20.5229	11.8924	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	box	-4.7445	-4.7445	5.9848	2.7093	6.3635	90.0	100.4	90.0
mp-1070333	box	-4.6773	-4.6773	6.2725	6.2725	2.5629	90.0	90.0	90.0
oqmd-646134	box	-4.2898	-4.2898	3.8869	3.8869	3.8869	90.0	90.0	90.0
mp-1246	box	-4.2876	-4.2876	3.8887	3.8887	3.8887	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	-4.28	-4.28	2.851	2.851	2.851	90.0	90.0	90.0
A15--beta-W	dynamic	-4.1776	-4.1776	4.5826	4.5826	4.5826	90.0	90.0	90.0
A6--In--bct	box	-4.1732	-4.1732	2.526	2.526	3.668	90.0	90.0	90.0
A1--Cu--fcc	static	-4.173	-4.173	3.6041	3.6041	3.6041	90.0	90.0	90.0
A3'--alpha-La--double-hcp	box	-4.1708	-4.1708	2.5475	2.5475	8.3299	90.0	90.0	120.0
oqmd-1216039	box	-4.17	-4.17	2.5472	2.5472	18.7473	90.0	90.0	120.0
mp-1271693	box	-4.1692	-4.1692	2.5148	4.4671	4.1665	90.0	90.0	90.0
A3--Mg--hcp	box	-4.1686	-4.1686	2.5466	2.5466	4.1682	90.0	90.0	120.0
A3--Mg--hcp	box	-4.1686	-4.1686	2.5466	2.5466	4.1682	90.0	90.0	120.0
oqmd-1214792	box	-4.1657	-4.1657	8.8499	8.8499	8.8499	90.0	90.0	90.0
oqmd-1215237	box	-4.1593	-4.1593	2.4838	4.5028	4.189	90.0	90.0	90.0
oqmd-1214881	box	-4.1365	-4.1365	6.2138	6.2138	6.2138	90.0	90.0	90.0
mp-1245108	dynamic	-4.1281	-4.1281	10.2082	10.7033	11.0057	94.0	90.6	93.6
mp-1194030	box	-4.0714	-4.0714	8.5757	8.5757	4.6663	90.0	90.0	90.0
oqmd-21053	box	-4.0708	-4.0708	8.5805	8.5805	4.6629	90.0	90.0	90.0
mp-1245108	box	-4.0395	-4.0395	10.5546	10.598	10.9246	92.0	90.6	91.7
oqmd-1215059	box	-3.9533	-3.9533	2.5815	4.1622	9.0255	90.0	90.0	90.0
A5--beta-Sn	static	-3.6684	-3.6684	4.6094	4.6094	2.3953	90.0	90.0	90.0
mp-1096950	box	-3.6025	-3.6025	2.4603	2.4603	2.4052	90.0	90.0	120.0
Ah--alpha-Po--sc	static	-3.2146	-3.2146	2.3886	2.3886	2.3886	90.0	90.0	90.0
oqmd-21731	box	-3.2145	-3.2145	2.3886	2.3886	7.1662	90.0	90.0	90.0
oqmd-1215950	box	-2.971	-2.971	4.0228	4.5045	4.042	90.0	119.5	90.0
A7--alpha-As	box	-2.7873	-2.7873	3.4117	3.4117	9.5543	90.0	90.0	120.0
A4--C--dc	dynamic	-2.3739	-2.3739	5.4734	5.4734	5.4734	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:

348.229	438.966	438.966	0.0	0.0	0.0
438.966	348.229	438.966	0.0	0.0	0.0
438.966	438.966	348.229	0.0	0.0	0.0
0.0	0.0	-0.0	-81.748	0.0	0.0
-0.0	0.0	-0.0	0.0	-81.748	0.0
-0.0	-0.0	0.0	0.0	0.0	-81.748

-16.583	630.157	630.157	-0.0	-0.0	-0.0
630.157	-16.583	630.157	0.0	-0.0	-0.0
630.157	630.157	-16.583	0.0	-0.0	-0.0
-1610689970.767	-1392610573.698	-1340642106.484	-496597883.502	17287024.724	19297742.624
-1402437224.806	-1744236538.101	-1326908567.585	-14993773.658	-431430128.355	25918539.063
-1350927019.226	-1311966960.773	-1697238458.572	43060423.319	-18412320.485	-428030695.871

39.964	601.884	601.884	0.0	0.0	0.0
601.884	39.964	601.884	0.0	0.0	0.0
601.884	601.884	39.964	0.0	-0.0	0.0
1631299996.545	1354014977.47	1377402885.835	-419130321.313	-14999007.719	-50373912.829
1324543579.07	1511532294.042	1437297070.963	50061407.596	-433514823.514	-33415288.668
1469244855.43	1479725161.886	1662478696.857	-61397088.599	-8737876.835	-476146415.664

-16.583	630.158	630.158	-0.0	-0.0	-0.0
630.158	-16.583	630.158	-0.0	-0.0	-0.0
630.158	630.158	-16.583	-0.0	-0.0	-0.0
-152046376.558	-142800895.831	-126321451.544	-39815354.16	8820362.97	6469210.338
-113240941.712	-181073505.895	-140122663.701	3037034.368	-52588131.998	2661059.656
-143727111.912	-136980924.594	-172247766.655	1805216.3	3107252.904	-46765062.945

-16.583	630.157	630.157	-0.0	0.0	0.0
630.157	-16.583	630.157	-0.0	0.0	0.0
630.157	630.157	-16.583	0.0	0.0	0.0
160063328.405	133431215.427	147115711.568	-43231202.544	2333496.761	-4346212.256
144745382.699	160896087.42	143560821.704	-3759333.567	-35308812.551	948772.881
137064849.807	132719564.124	143348077.122	2478204.794	-2367692.722	-47400777.317

-16.585	630.159	630.159	-0.0	-0.0	-0.0
630.159	-16.585	630.159	0.0	-0.0	-0.0
630.159	630.159	-16.585	0.0	-0.0	-0.0
-16487180.761	-12723602.182	-14180384.218	-6036918.701	-714433.603	93415.616
-13169509.162	-17230584.963	-11995936.71	574737.773	-4900807.308	324736.487
-12726762.754	-14557180.44	-15590283.607	-372763.523	113852.857	-5396401.244

348.228	438.966	438.966	-0.0	0.0	0.0
438.966	348.228	438.966	0.0	-0.0	-0.0
438.966	438.966	348.228	-0.0	-0.0	-0.0
-0.0	-0.0	0.0	-81.748	-0.0	-0.0
-0.0	-0.0	0.0	-0.0	-81.748	0.0
-0.0	0.0	-0.0	-0.0	0.0	-81.748

348.23	438.967	438.967	0.0	0.0	0.0
438.967	348.23	438.967	0.0	0.0	0.0
438.967	438.967	348.23	0.0	0.0	0.0
0.0	0.0	-0.0	-81.748	0.0	0.0
0.0	0.0	-0.0	0.0	-81.748	-0.0
0.0	-0.0	0.0	0.0	-0.0	-81.748

348.228	438.965	438.965	-0.0	-0.0	-0.0
438.965	348.228	438.965	-0.0	-0.0	-0.0
438.965	438.965	348.228	-0.0	-0.0	-0.0
-0.0	-0.0	0.0	-81.748	-0.0	-0.0
-0.0	-0.0	0.0	-0.0	-81.748	0.0
-0.0	0.0	-0.0	-0.0	0.0	-81.748

-16.581	630.155	630.155	-0.0	0.0	0.0
630.155	-16.581	630.155	-0.0	0.0	0.0
630.155	630.155	-16.581	-0.0	0.0	0.0
15998969.679	13539997.681	15359528.909	-5691672.945	-217220.344	-288300.584
15255168.06	15490095.901	14126485.563	518202.679	-5881494.492	18101.603
13806456.001	14978852.315	15753071.346	-210139.467	184166.214	-5356657.562

519.735	440.143	440.143	-0.0	-0.0	-0.0
440.143	519.735	440.143	-0.0	-0.0	-0.0
440.143	440.143	519.735	-0.0	-0.0	-0.0
0.0	0.0	0.0	-97.738	-0.0	-0.0
0.0	0.0	0.0	-0.0	-97.738	-0.0
0.0	0.0	0.0	-0.0	0.0	-97.738

519.736	440.144	440.144	0.0	-0.0	-0.0
440.144	519.736	440.144	-0.0	0.0	-0.0
440.144	440.144	519.736	-0.0	0.0	-0.0
0.0	0.0	0.0	-97.738	0.0	-0.0
0.0	0.0	0.0	0.0	-97.738	0.0
0.0	0.0	0.0	0.0	-0.0	-97.738

519.734	440.141	440.141	0.0	0.0	0.0
440.141	519.734	440.141	0.0	0.0	0.0
440.141	440.141	519.734	0.0	0.0	0.0
-0.0	-0.0	-0.0	-97.738	-0.0	0.0
-0.0	-0.0	-0.0	-0.0	-97.738	0.0
-0.0	-0.0	-0.0	0.0	0.0	-97.738

314.747	453.45	463.203	-0.0	-0.0	0.0
965915065.962	-494999993.057	-3338388930.873	119214437.168	5272159.809	-53629583.923
463.203	463.203	292.331	0.0	-0.0	0.0
-0.0	0.0	-0.0	-62.129	-0.0	0.0
-0.0	0.0	-0.0	0.0	-62.129	0.0
0.0	0.0	0.0	-0.0	-0.0	-69.351

307.392	460.805	463.203	-0.0	0.0	-0.0
453.45	314.747	463.203	-0.0	0.0	-0.0
463.203	463.203	292.331	-0.0	0.0	-0.0
-0.0	-0.0	0.0	-62.129	0.0	-0.0
0.0	-0.0	0.0	-0.0	-62.129	-0.0
-0.0	-0.0	-0.0	0.0	0.0	-69.351

307.392	460.806	463.204	0.0	0.0	0.0
76680465.593	-48720134.291	-331810092.907	7789750.251	-3626722.077	2414091.208
463.204	463.204	292.331	0.0	-0.0	0.0
0.0	0.0	-0.0	-62.129	-0.0	0.0
0.0	0.0	-0.0	0.0	-62.129	0.0
0.0	0.0	0.0	0.0	0.0	-76.707

-82890272.773	51365762.836	350628154.063	-1874683.663	440782.24	-2669738.326
453.45	314.747	463.203	-0.0	0.0	0.0
463.203	463.203	292.331	-0.0	0.0	-0.0
-0.0	-0.0	0.0	-62.129	0.0	-0.0
-0.0	-0.0	0.0	-0.0	-62.129	0.0
-0.0	-0.0	-0.0	-0.0	0.0	-76.707

314.748	453.451	463.205	-0.0	-0.0	0.0
453.451	314.748	463.205	0.0	-0.0	0.0
463.205	463.205	292.333	0.0	-0.0	0.0
0.0	0.0	-0.0	-62.129	0.0	0.0
0.0	0.0	-0.0	0.0	-62.129	0.0
0.0	-0.0	0.0	-0.0	-0.0	-69.351

314.746	453.448	463.202	0.0	0.0	0.0
12769928.335	17470440.746	23777169.23	-491491.134	-205676.487	441574.636
463.202	463.202	292.33	-0.0	0.0	-0.0
-0.0	-0.0	0.0	-62.129	-0.0	-0.0
-0.0	-0.0	0.0	-0.0	-62.129	-0.0
-0.0	0.0	-0.0	-0.0	-0.0	-69.351

349.806	471.819	-0.025	-0.0	-0.0	0.0
471.805	349.819	-0.025	0.0	0.0	0.0
-0.025	-0.025	0.048	-0.0	0.0	-0.0
-0.0	-0.0	0.0	-6.336	-0.0	0.0
-0.0	-0.0	0.0	0.0	-6.336	0.0
-0.0	-0.0	0.0	0.0	-0.0	-61.006

349.821	471.807	-0.025	-0.0	-0.0	0.0
471.837	349.791	-0.025	0.0	-0.0	0.0
-0.025	-0.025	0.048	-0.0	-0.0	-0.0
0.0	-0.0	0.0	-6.336	0.0	0.0
-0.0	0.0	0.0	0.0	-6.336	0.0
0.0	-0.0	0.0	-0.0	0.0	-60.993

349.805	471.817	-0.025	-0.0	0.0	-0.0
471.834	349.788	-0.025	-0.0	0.0	-0.0
-0.025	-0.025	0.048	-0.0	-0.0	0.0
-0.0	0.0	-0.0	-6.336	-0.0	-0.0
0.0	-0.0	-0.0	-0.0	-6.336	-0.0
-0.0	0.0	-0.0	0.0	-0.0	-60.993

304.68	468.621	463.152	-0.0	-0.0	0.0
455.785	317.515	463.152	-0.0	0.0	-0.0
463.152	463.152	285.082	-0.0	-0.0	0.0
0.0	-0.0	-0.0	-66.665	-0.0	0.0
0.0	-0.0	-0.0	-0.0	-66.665	0.0
0.0	-0.0	0.0	-0.0	-0.0	-69.135

-133711862.989	-197145230.56	-250919788.132	4408937.898	-4937765.513	4799767.653
468.621	304.68	463.152	-0.0	-0.0	0.0
463.152	463.152	285.082	-0.0	-0.0	0.0
0.0	0.0	-0.0	-66.665	-0.0	0.0
0.0	0.0	-0.0	-0.0	-66.665	0.0
0.0	-0.0	0.0	-0.0	-0.0	-69.135

317.516	455.787	463.153	-0.0	-0.0	-0.0
455.787	317.517	463.153	0.0	-0.0	-0.0
463.153	463.153	285.084	-0.0	-0.0	0.0
0.0	0.0	-0.0	-66.665	-0.0	0.0
0.0	0.0	-0.0	-0.0	-66.665	-0.0
0.0	-0.0	0.0	-0.0	-0.0	-69.135

13512158.102	15574308.139	14447603.561	-556129.852	324691.465	-509205.46
455.784	317.514	463.151	0.0	0.0	0.0
463.151	463.151	285.081	0.0	0.0	-0.0
-0.0	-0.0	0.0	-66.665	0.0	-0.0
-0.0	-0.0	0.0	0.0	-66.665	-0.0
-0.0	0.0	-0.0	0.0	0.0	-69.135

630.405	350.326	350.326	0.0	0.0	-0.0
350.326	630.405	350.326	0.0	0.0	-0.0
350.326	350.326	630.405	0.0	0.0	-0.0
0.0	-0.0	0.0	619.389	0.0	-0.0
-0.0	0.0	0.0	0.0	619.389	-0.0
-0.0	0.0	0.0	0.0	0.0	619.389

630.406	350.327	350.327	-0.0	0.0	-0.0
350.327	630.406	350.327	0.0	-0.0	-0.0
350.327	350.327	630.406	0.0	0.0	-0.0
0.002	-0.001	-0.0	619.389	0.0	-0.0
-0.001	0.002	-0.0	0.0	619.389	-0.0
-0.001	-0.0	0.002	0.0	0.0	619.389

630.404	350.325	350.325	-0.0	-0.0	0.0
350.325	630.404	350.325	-0.0	0.0	0.0
350.325	350.325	630.404	-0.0	-0.0	0.0
-0.002	0.001	0.0	619.389	-0.0	0.0
0.001	-0.002	0.0	-0.0	619.389	0.0
0.001	0.0	-0.002	-0.0	-0.0	619.389

110.722	159.959	500.171	0.0	-0.0	0.0
159.959	110.722	500.171	0.0	-0.0	-0.0
500.171	500.171	1045.663	0.0	0.0	-0.0
-0.0	-0.0	-0.0	47.513	0.0	0.0
0.0	-0.0	-0.0	0.0	47.513	-0.0
0.0	-0.0	-0.0	0.0	0.0	24.633

110.723	159.959	500.171	0.0	0.0	-0.0
159.959	110.723	500.171	-0.0	-0.0	0.0
500.171	500.171	1045.663	0.0	0.0	-0.0
-0.0	-0.0	-0.0	47.513	0.0	-0.0
-0.0	-0.0	-0.0	0.0	47.513	-0.0
-0.0	0.0	-0.0	0.0	-0.0	24.633

110.724	159.959	500.173	0.0	-0.0	-0.0
159.959	110.724	500.173	-0.0	-0.0	-0.0
500.172	500.172	1045.668	0.0	0.0	0.0
-0.0	-0.0	-0.0	47.513	0.0	0.0
-0.0	-0.0	-0.0	0.0	47.513	-0.0
-0.0	0.0	-0.0	0.0	-0.0	24.633

110.72	159.959	500.169	-0.0	-0.0	0.0
159.959	110.72	500.169	-0.0	0.0	0.0
500.17	500.17	1045.657	-0.0	-0.0	-0.0
0.0	0.0	0.0	47.513	-0.0	0.0
0.0	0.0	0.0	-0.0	47.513	-0.0
0.0	-0.0	0.0	-0.0	-0.0	24.633

2557.943	-1767.216	-0.116	0.277	0.0	0.0
-1767.216	2557.943	-0.116	-0.277	0.0	0.0
-0.116	-0.116	1.167	-0.0	0.0	0.0
-2.281	-0.853	6.65	0.13	0.0	0.002
-0.0	0.0	0.0	-0.0	0.13	0.277
0.0	0.0	0.0	-0.0	0.277	2162.58

458.829	331.812	0.065	0.007	0.0	0.0
324.805	465.837	0.064	-0.008	0.0	0.0
-0.116	-0.116	1.167	-0.0	0.0	0.0
0.277	-0.277	0.0	0.13	0.0	0.0
-0.0	0.0	0.0	0.0	0.13	0.277
0.001	0.0	0.0	0.0	0.277	2162.58

747.978	43.062	-0.781	0.044	-0.0	-0.0
85.381	705.66	-0.785	-0.039	-0.0	-0.0
-0.116	-0.116	1.167	0.0	-0.0	-0.0
0.277	-0.277	-0.0	0.13	-0.0	-0.0
0.0	-0.0	-0.0	-0.0	0.13	0.277
-0.001	-0.0	-0.0	-0.0	0.277	2162.58