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.

2014--Kang-K-H-Eun-T-Jun-M-C-Lee-B-J--Si-C

Citation: K.-H. Kang, T. Eun, M.-C. Jun, and B.-J. Lee (2014), "Governing factors for the formation of 4H or 6H-SiC polytype during SiC crystal growth: An atomistic computational approach", Journal of Crystal Growth 389, 120-133. DOI: 10.1016/j.jcrysgro.2013.12.007.

Abstract: The effects of various process variables on the formation of polytypes during SiC single crystal growths have been investigated using atomistic simulations based on an empirical potential (the second nearest-neighbor MEAM) and first-principles calculation. It is found out that the main role of process variables (temperature, surface type, growth rate, atmospheric condition, dopant type, etc.) is not to directly change the relative stability of SiC polytypes directly but to change the formation tendency of point defects. The biaxial local strain due to the formation of point defects is found to have an effect on the relative stability of SiC polytypes and is proposed in the present study as a governing factor that affects the selective growth of SiC polytypes. Based on the present local strain scheme, the competitive growth among SiC polytypes, especially the 4H and 6H-SiC, available in literatures can be reasonably explained by interpreting the effect of each process variable in terms of defect formation and the resultant local strain. Those results provide an insight into the selective growth of SiC polytypes and also help us obtain high quality SiC single crystals.

Related Models:
2007--Lee-B-J--Si

2016--Lee-E-Lee-K-R-Baskes-M-I-Lee-B-J--Si-O
LAMMPS pair_style meam (2014--Kang-K-H--Si-C--LAMMPS--ipr1)

See Computed Properties
Notes: These potential files were obtained from http://cmse.postech.ac.kr/home_2nnmeam, accessed Nov 9, 2020.
File(s):
library.meam
SiC.meam
OpenKIM (MO_145522277939)

See Computed Properties
Notes: Listing found at https://openkim.org.
Link(s):
KIM page MEAM_2NN_Fe_to_Ga__MO_145522277939_001

Implementation Information

This page displays computed properties for the 2014--Kang-K-H--Si-C--LAMMPS--ipr1 implementation of the 2014--Kang-K-H-Eun-T-Jun-M-C-Lee-B-J--Si-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--Kang-K-H--Si-C--LAMMPS--ipr1/diatom

Click on plot to load interactive version

2014--Kang-K-H--Si-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

2014--Kang-K-H--Si-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)
A4--C--dc	dynamic	-7.37	-7.37	3.5565	3.5565	3.5565	90.0	90.0	90.0
oqmd-599492	dynamic	-7.3658	-7.3658	2.5098	2.5098	16.5018	90.0	90.0	120.0
oqmd-599494	dynamic	-7.3652	-7.3652	2.5091	2.5091	43.3426	90.0	90.0	120.0
oqmd-599491	dynamic	-7.3645	-7.3645	2.5083	2.5083	12.3931	90.0	90.0	120.0
mp-569517	dynamic	-7.3637	-7.3637	2.5073	2.5073	31.009	90.0	90.0	120.0
oqmd-599492	box	-7.3627	-7.3627	2.5075	2.5075	16.5454	90.0	90.0	120.0
mp-616440	box	-7.3625	-7.3625	2.5075	2.5075	16.5468	90.0	90.0	120.0
oqmd-599490	dynamic	-7.3625	-7.3625	2.5059	2.5059	8.2795	90.0	90.0	120.0
oqmd-599494	static	-7.3617	-7.3617	2.5065	2.5065	43.4745	90.0	90.0	120.0
mp-569567	box	-7.3615	-7.3615	2.5066	2.5066	43.4735	90.0	90.0	120.0
oqmd-599491	box	-7.3603	-7.3603	2.5054	2.5054	12.4354	90.0	90.0	120.0
mp-611448	box	-7.3602	-7.3602	2.5054	2.5054	12.4353	90.0	90.0	120.0
oqmd-599489	dynamic	-7.3597	-7.3597	2.5033	2.5033	4.1494	90.0	90.0	120.0
mp-569517	box	-7.3586	-7.3586	2.5039	2.5039	31.1346	90.0	90.0	120.0
oqmd-599493	box	-7.3582	-7.3582	2.5037	2.5037	31.1432	90.0	90.0	120.0
mp-611426	box	-7.3562	-7.3562	2.5019	2.5019	8.3196	90.0	90.0	120.0
oqmd-599490	box	-7.356	-7.356	2.5018	2.5018	8.3205	90.0	90.0	120.0
mp-47	box	-7.3477	-7.3477	2.4941	2.4941	4.191	90.0	90.0	120.0
oqmd-599489	box	-7.3474	-7.3474	2.494	2.494	4.1917	90.0	90.0	120.0
mp-1078845	dynamic	-7.2829	-7.2829	4.2567	8.7241	2.5013	90.0	90.0	90.0
mp-1078845	box	-7.2577	-7.2577	4.2661	8.8332	2.4788	90.0	90.0	90.0
oqmd-637353	dynamic	-7.2518	-7.2518	4.3993	4.3993	2.4801	90.0	90.0	90.0
mp-1008374	dynamic	-7.2345	-7.2345	2.5428	7.9145	2.5252	90.0	90.0	90.0
oqmd-637353	box	-7.2248	-7.2248	4.4381	4.4381	2.4464	90.0	90.0	90.0
mp-1008395	box	-7.2241	-7.2241	4.4387	4.4387	2.4459	90.0	90.0	90.0
mp-1008374	box	-7.2109	-7.2109	2.5046	8.076	2.502	90.0	90.0	90.0
oqmd-637352	dynamic	-7.2102	-7.2102	9.2134	2.5312	4.176	90.0	99.2	90.0
mp-1190171	dynamic	-7.2069	-7.2069	9.1075	2.5298	4.1764	90.0	90.0	90.0
mp-624889	static	-7.1679	-7.1679	4.6133	5.0353	4.3452	90.0	90.0	90.0
mp-1080826	box	-7.1652	-7.1652	9.1665	2.5469	4.1489	90.0	97.2	90.0
oqmd-637352	box	-7.1652	-7.1652	9.1651	2.5471	4.1486	90.0	97.2	90.0
oqmd-637130	box	-7.1617	-7.1617	9.072	2.5488	4.1493	90.0	90.0	90.0
mp-1190171	box	-7.1616	-7.1616	9.0732	2.5485	4.1499	90.0	90.0	90.0
mp-568806	dynamic	-7.1528	-7.1528	2.5172	2.5172	2.6807	90.0	90.0	120.0
A7--alpha-As	dynamic	-7.1451	-7.1451	2.5069	2.5069	8.821	90.0	90.0	120.0
oqmd-637443	dynamic	-7.1352	-7.1352	5.2175	5.2175	5.2175	90.0	90.0	90.0
mp-48	static	-7.1248	-7.1248	2.5119	2.5119	5.6242	90.0	90.0	120.0
oqmd-683820	dynamic	-7.1199	-7.1199	2.5367	4.3133	5.4679	90.0	90.0	90.0
oqmd-637443	box	-7.1126	-7.1126	5.2215	5.2215	5.2215	90.0	90.0	90.0
mp-1188817	box	-7.1091	-7.1091	5.2217	5.2217	5.2217	90.0	90.0	90.0
mp-1192619	dynamic	-7.1079	-7.1079	7.1108	7.1108	7.1108	90.0	90.0	90.0
oqmd-589492	static	-7.0952	-7.0952	2.511	2.511	42.5961	90.0	90.0	120.0
mp-569416	static	-7.0937	-7.0937	2.5106	2.5106	44.6894	90.0	90.0	120.0
mp-569304	static	-7.0613	-7.0613	2.5098	2.5098	28.5458	90.0	90.0	120.0
mp-569304	dynamic	-7.0613	-7.0613	2.5098	2.5098	32.3193	90.0	90.0	120.0
oqmd-589491	static	-7.0613	-7.0613	2.5098	2.5098	29.2224	90.0	90.0	120.0
oqmd-589491	dynamic	-7.0613	-7.0613	2.5098	2.5098	33.3056	90.0	90.0	120.0
oqmd-610557	box	-7.0508	-7.0508	4.7842	5.3113	4.469	90.0	90.0	90.0
oqmd-610556	box	-7.0489	-7.0489	4.7793	5.3221	4.469	90.0	90.0	90.0
mp-568410	box	-7.0467	-7.0467	4.7753	5.3291	4.4706	90.0	90.0	90.0
mp-1182684	dynamic	-7.0066	-7.0066	5.7919	7.4786	12.6068	90.0	90.0	90.0
mp-680372	dynamic	-6.9843	-6.9843	9.7493	9.7493	18.8242	90.0	90.0	120.0
oqmd-637444	static	-6.9788	-6.9788	4.1018	4.1018	4.1018	90.0	90.0	90.0
mp-1040425	dynamic	-6.9777	-6.9777	2.5119	2.5119	19.9989	90.0	90.0	120.0
mp-990448	static	-6.9777	-6.9777	2.5119	2.5119	8.5238	90.0	90.0	120.0
mp-1040425	static	-6.9777	-6.9777	2.5119	2.5119	19.9983	90.0	90.0	120.0
mp-997182	dynamic	-6.9777	-6.9777	2.5119	2.5119	12.046	90.0	90.0	120.0
mp-990448	dynamic	-6.9777	-6.9777	2.5119	2.5119	9.1562	90.0	90.0	120.0
mp-997182	static	-6.9777	-6.9777	2.5119	2.5119	12.0458	90.0	90.0	120.0
mp-683919	dynamic	-6.9305	-6.9305	8.8241	15.5066	16.8946	90.0	90.0	90.0
mp-1245190	dynamic	-6.9257	-6.9257	8.5	9.0069	9.3526	91.5	92.4	93.1
mp-630227	dynamic	-6.9136	-6.9136	8.522	9.1978	12.8065	90.0	90.0	90.0
oqmd-595714	dynamic	-6.9116	-6.9116	8.4974	8.9354	13.1162	90.0	90.0	90.0
mp-24	dynamic	-6.9025	-6.9025	4.4231	4.4231	4.4231	90.0	90.0	90.0
mp-667273	dynamic	-6.8779	-6.8779	12.9389	12.9389	12.9389	90.0	90.0	90.0
oqmd-603085	static	-6.8779	-6.8779	12.9354	12.9354	12.9354	90.0	90.0	90.0
mp-24	box	-6.8412	-6.8412	4.488	4.488	4.488	90.0	90.0	90.0
mp-1196583	dynamic	-6.8364	-6.8364	12.6489	12.6489	12.6489	90.0	90.0	90.0
mp-568028	static	-6.8301	-6.8301	7.9862	14.1585	9.5037	90.0	90.0	90.0
mp-680372	static	-6.8176	-6.8176	9.1952	9.1952	24.4296	90.0	90.0	120.0
oqmd-614417	static	-6.8176	-6.8176	9.2042	9.2042	24.4167	90.0	90.0	120.0
mp-1205283	static	-6.8137	-6.8137	8.7522	13.4098	9.2439	90.0	90.0	90.0
mp-1244964	dynamic	-6.812	-6.812	8.8821	9.7946	9.8286	96.5	94.6	90.8
oqmd-677227	dynamic	-6.8103	-6.8103	12.7209	12.7209	12.7209	90.0	90.0	90.0
mp-570002	dynamic	-6.8012	-6.8012	4.945	4.945	4.945	90.0	90.0	90.0
oqmd-595714	static	-6.7983	-6.7983	8.8095	9.1343	14.3225	90.0	90.0	90.0
mp-630227	static	-6.791	-6.791	8.9413	9.1406	14.4951	90.0	90.0	90.0
oqmd-614417	box	-6.7901	-6.7901	9.3537	9.3537	24.4938	90.0	90.0	120.0
oqmd-689315	static	-6.7817	-6.7817	9.4679	17.1777	18.174	90.0	90.0	90.0
mp-680372	box	-6.7804	-6.7804	9.4008	9.4008	25.4471	90.0	90.0	120.0
mp-683919	static	-6.7742	-6.7742	9.7817	16.9197	18.0337	90.0	90.0	90.0
mp-1147718	static	-6.7656	-6.7656	9.6004	14.0611	9.121	90.0	90.0	90.0
mp-1244913	dynamic	-6.7631	-6.7631	9.2632	9.3716	10.3318	87.1	83.7	83.2
oqmd-595714	box	-6.7563	-6.7563	9.2289	9.3986	14.7705	90.0	90.0	90.0
oqmd-684315	static	-6.753	-6.753	8.3596	14.2325	9.3692	90.0	90.0	90.0
mp-1197903	dynamic	-6.7489	-6.7489	5.7802	6.5295	18.8506	81.6	83.2	76.5
mp-683919	box	-6.7327	-6.7327	10.3536	17.8494	18.4291	90.0	90.0	90.0
mp-630227	box	-6.7244	-6.7244	9.3304	9.3821	15.7228	90.0	90.0	90.0
oqmd-684627	box	-6.7208	-6.7208	9.3422	9.3422	15.4406	90.0	90.0	90.0
oqmd-689315	box	-6.7203	-6.7203	10.2965	17.8589	18.455	90.0	90.0	90.0
mp-568028	box	-6.7034	-6.7034	8.5307	14.2988	9.7744	90.0	90.0	90.0
mp-667273	static	-6.7025	-6.7025	13.9731	13.9731	13.9731	90.0	90.0	90.0
mp-1147718	box	-6.6905	-6.6905	10.4526	14.9479	9.4628	90.0	90.0	90.0
oqmd-603085	box	-6.6758	-6.6758	14.265	14.265	14.265	90.0	90.0	90.0
mp-624889	box	-6.6564	-6.6564	4.8889	5.2723	5.6072	90.0	90.0	90.0
mp-667273	box	-6.656	-6.656	14.7629	14.7629	14.7629	90.0	90.0	90.0
oqmd-677227	box	-6.6508	-6.6508	14.478	14.478	14.478	90.0	90.0	90.0
mp-1196583	box	-6.6485	-6.6485	14.7055	14.7055	14.7055	90.0	90.0	90.0
oqmd-610552	box	-6.5971	-6.5971	4.7435	5.6558	6.3836	90.0	90.0	90.0
oqmd-585286	box	-6.5936	-6.5936	5.0095	5.0095	5.0095	90.0	90.0	90.0
mp-570002	box	-6.593	-6.593	5.0097	5.0097	5.0097	90.0	90.0	90.0
mp-579909	box	-6.5622	-6.5622	4.7359	5.6696	6.8531	90.0	90.0	90.0
mp-1244964	static	-6.5318	-6.5318	9.8896	10.0722	10.731	83.6	89.6	88.7
mp-1245190	static	-6.5253	-6.5253	9.8893	10.2274	10.2718	90.6	92.0	90.8
mp-1205283	box	-6.4674	-6.4674	10.2924	13.4878	9.2704	90.0	90.0	90.0
mp-1244913	static	-6.463	-6.463	10.0671	10.4165	10.5659	96.4	91.7	93.2
A7--alpha-As	box	-6.2603	-6.2603	2.5131	2.5131	6.3019	90.0	90.0	120.0
mp-1197903	static	-6.1526	-6.1526	5.6185	7.062	20.9171	87.3	89.7	84.2
oqmd-684315	box	-6.1444	-6.1444	10.2725	15.4593	9.4108	90.0	90.0	90.0
mp-1205417	static	-6.1381	-6.1381	13.8411	13.8411	3.7628	90.0	90.0	90.0
A3'--alpha-La--double-hcp	box	-6.1287	-6.1287	2.4469	2.4469	4.3316	90.0	90.0	120.0
mp-1095633	dynamic	-6.1087	-6.1087	6.7293	6.7293	6.6253	90.0	90.0	90.0
Ah--alpha-Po--sc	static	-6.0855	-6.0855	1.7874	1.7874	1.7874	90.0	90.0	90.0
A5--beta-Sn	box	-6.0713	-6.0713	3.441	3.441	1.8106	90.0	90.0	90.0
mp-1245190	box	-6.0652	-6.0652	10.7691	10.928	11.0842	88.1	89.8	87.3
mp-1244964	box	-5.952	-5.952	10.7419	11.0629	11.5295	90.5	95.1	93.1
A6--In--bct	static	-5.8883	-5.8883	1.6796	1.6796	5.4071	90.0	90.0	90.0
mp-1095534	box	-5.8169	-5.8169	10.6883	10.6883	2.3579	90.0	90.0	90.0
mp-1244913	box	-5.74	-5.74	11.2819	11.4335	11.8492	89.3	83.2	88.4
mp-1095633	box	-5.687	-5.687	6.3188	6.3188	8.1812	90.0	90.0	90.0
mp-1097832	static	-5.5377	-5.5377	2.3976	2.3976	9.8799	90.0	90.0	90.0
mp-1205417	box	-5.3481	-5.3481	13.1746	13.1746	7.644	90.0	90.0	90.0
A2--W--bcc	static	-5.3285	-5.3285	2.2637	2.2637	2.2637	90.0	90.0	90.0
mp-1197903	box	-5.2703	-5.2703	8.6703	11.4488	26.2794	100.4	94.2	108.0
A3--Mg--hcp	box	-5.2154	-5.2154	1.8733	1.8733	4.6758	90.0	90.0	120.0
A3--Mg--hcp	box	-5.0412	-5.0412	2.0684	2.0684	3.4018	90.0	90.0	120.0
A3'--alpha-La--double-hcp	box	-5.0396	-5.0396	2.071	2.071	6.7887	90.0	90.0	120.0
A1--Cu--fcc	box	-5.0379	-5.0379	2.9328	2.9328	2.9328	90.0	90.0	90.0
mp-1192619	box	-5.0217	-5.0217	10.1666	10.1666	10.1666	90.0	90.0	90.0
A15--beta-W	static	-4.9685	-4.9685	3.7219	3.7219	3.7219	90.0	90.0	90.0
oqmd-1214868	box	-4.4119	-4.4119	8.1298	8.1298	8.1298	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-1019097	dynamic	-6.6385	-6.6385	2.9595	2.9595	6.6255	90.0	90.0	90.0
mp-1019097	box	-6.6379	-6.6379	2.956	2.956	6.6441	90.0	90.0	90.0
mp-1102811	dynamic	-6.384	-6.384	4.712	4.712	4.712	90.0	90.0	90.0
C1--CaF2--fluorite	dynamic	-6.3672	-6.3672	4.7523	4.7523	4.7523	90.0	90.0	90.0
mp-1102811	box	-6.3305	-6.3305	4.7335	4.7335	4.7335	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)
A15--Cr3Si	static	-5.8625	-5.8625	3.9701	3.9701	3.9701	90.0	90.0	90.0
mp-972848	dynamic	-5.8614	-5.8614	3.1865	3.1865	6.1085	90.0	90.0	90.0
D0_3--BiF3	static	-5.841	-5.841	4.8923	4.8923	4.8923	90.0	90.0	90.0
L1_2--AuCu3	static	-5.7588	-5.7588	3.1671	3.1671	3.1671	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-1219306	box	-3.8501	-3.8501	9.5583	9.5583	9.574	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-1179504	dynamic	-5.0483	-5.0483	5.0899	10.9982	11.2908	106.1	90.4	90.2
mp-1202928	dynamic	-4.9899	-4.9899	4.9655	11.8656	12.6137	117.7	98.1	90.8
mp-1202928	static	-4.9222	-4.9222	4.8973	12.1568	12.1935	117.2	91.8	96.4
mp-1179504	static	-4.7761	-4.7761	5.1453	11.8592	12.8962	116.6	91.2	90.4
mp-1202928	box	-2.9882	-2.9882	5.4335	13.9941	14.5945	98.6	92.2	95.8

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
B3--ZnS--cubic-zinc-blende	dynamic	-6.3753	-6.3753	4.3595	4.3595	4.3595	90.0	90.0	90.0
mp-570641	dynamic	-6.372	-6.372	3.0706	3.0706	60.8652	90.0	90.0	120.0
mp-567505	dynamic	-6.372	-6.372	3.0706	3.0706	20.2884	90.0	90.0	120.0
mp-582034	dynamic	-6.3715	-6.3715	3.0692	3.0692	53.3035	90.0	90.0	120.0
mp-568696	dynamic	-6.3715	-6.3715	3.0692	3.0692	35.5357	90.0	90.0	120.0
mp-582034	static	-6.3715	-6.3715	3.0691	3.0691	53.3049	90.0	90.0	120.0
mp-570804	dynamic	-6.3713	-6.3713	3.0683	3.0683	99.0435	90.0	90.0	120.0
mp-1204356	dynamic	-6.3712	-6.3712	3.068	3.068	144.7829	90.0	90.0	120.0
mp-7631	dynamic	-6.371	-6.371	3.0674	3.0674	15.2464	90.0	90.0	120.0
mp-571286	dynamic	-6.371	-6.371	3.0674	3.0674	91.4787	90.0	90.0	120.0
mp-571286	static	-6.371	-6.371	3.0674	3.0674	91.4798	90.0	90.0	120.0
mp-1200168	dynamic	-6.3709	-6.3709	3.067	3.067	221.1304	90.0	90.0	120.0
mp-1200168	static	-6.3709	-6.3709	3.0669	3.0669	221.134	90.0	90.0	120.0
mp-568619	dynamic	-6.3708	-6.3708	3.0672	3.0672	12.7079	90.0	90.0	120.0
mp-1200692	dynamic	-6.3708	-6.3708	3.0667	3.0667	129.6519	90.0	90.0	120.0
mp-1199063	dynamic	-6.3708	-6.3708	3.0665	3.0665	213.5644	90.0	90.0	120.0
mp-1199063	static	-6.3707	-6.3707	3.0664	3.0664	213.5768	90.0	90.0	120.0
mp-624397	dynamic	-6.3707	-6.3707	3.0663	3.0663	83.9124	90.0	90.0	120.0
mp-570985	dynamic	-6.3706	-6.3706	3.0661	3.0661	68.6658	90.0	90.0	120.0
mp-567551	dynamic	-6.3706	-6.3706	3.0659	3.0659	40.695	90.0	90.0	120.0
mp-571298	dynamic	-6.3704	-6.3704	3.0652	3.0652	99.2368	90.0	90.0	120.0
mp-571298	static	-6.3703	-6.3703	3.0652	3.0652	99.2407	90.0	90.0	120.0
mp-11713	dynamic	-6.3703	-6.3703	3.065	3.065	38.172	90.0	90.0	120.0
mp-1200848	dynamic	-6.3703	-6.3703	3.065	3.065	190.8601	90.0	90.0	120.0
mp-568656	dynamic	-6.3703	-6.3703	3.065	3.065	25.448	90.0	90.0	120.0
mp-1200848	static	-6.3703	-6.3703	3.065	3.065	190.8666	90.0	90.0	120.0
mp-570791	dynamic	-6.3701	-6.3701	3.0643	3.0643	48.3725	90.0	90.0	120.0
mp-567505	box	-6.37	-6.37	3.0755	3.0755	20.2149	90.0	90.0	120.0
mp-570690	dynamic	-6.3699	-6.3699	3.0635	3.0635	68.7725	90.0	90.0	120.0
mp-568735	dynamic	-6.3699	-6.3699	3.0635	3.0635	45.8483	90.0	90.0	120.0
mp-568735	static	-6.3699	-6.3699	3.0635	3.0635	45.849	90.0	90.0	120.0
mp-1197730	dynamic	-6.3696	-6.3696	3.0627	3.0627	129.9706	90.0	90.0	120.0
mp-11714	dynamic	-6.3694	-6.3694	3.0618	3.0618	10.1995	90.0	90.0	120.0
mp-568696	box	-6.3693	-6.3693	3.0747	3.0747	35.3933	90.0	90.0	120.0
mp-582034	box	-6.3693	-6.3693	3.0746	3.0746	53.0916	90.0	90.0	120.0
mp-9947	box	-6.3693	-6.3693	3.0747	3.0747	53.0897	90.0	90.0	120.0
mp-570641	box	-6.3693	-6.3693	3.0772	3.0772	60.5744	90.0	90.0	120.0
mp-1204356	box	-6.3687	-6.3687	3.0739	3.0739	144.1621	90.0	90.0	120.0
mp-571286	box	-6.3684	-6.3684	3.0735	3.0735	91.0726	90.0	90.0	120.0
mp-7631	box	-6.3684	-6.3684	3.0735	3.0735	15.1786	90.0	90.0	120.0
mp-570804	box	-6.3682	-6.3682	3.0753	3.0753	98.543	90.0	90.0	120.0
mp-1200692	box	-6.368	-6.368	3.073	3.073	129.0523	90.0	90.0	120.0
mp-570985	box	-6.3676	-6.3676	3.0726	3.0726	68.338	90.0	90.0	120.0
mp-567551	box	-6.3676	-6.3676	3.0725	3.0725	40.4996	90.0	90.0	120.0
mp-568619	box	-6.3671	-6.3671	3.0721	3.0721	12.6593	90.0	90.0	120.0
mp-1200168	box	-6.3671	-6.3671	3.0747	3.0747	219.8868	90.0	90.0	120.0
mp-568656	box	-6.3671	-6.3671	3.072	3.072	25.32	90.0	90.0	120.0
mp-11713	box	-6.367	-6.367	3.072	3.072	37.979	90.0	90.0	120.0
mp-571298	box	-6.3669	-6.3669	3.0717	3.0717	98.7615	90.0	90.0	120.0
mp-7140	dynamic	-6.3668	-6.3668	3.0549	3.0549	5.1222	90.0	90.0	120.0
mp-570791	box	-6.3667	-6.3667	3.0715	3.0715	48.1208	90.0	90.0	120.0
mp-624397	box	-6.3666	-6.3666	3.0743	3.0743	83.4213	90.0	90.0	120.0
mp-1199063	box	-6.3666	-6.3666	3.0744	3.0744	212.3367	90.0	90.0	120.0
mp-568735	box	-6.3662	-6.3662	3.071	3.071	45.6015	90.0	90.0	120.0
mp-1197730	box	-6.3657	-6.3657	3.0704	3.0704	129.246	90.0	90.0	120.0
mp-1200848	box	-6.3656	-6.3656	3.0734	3.0734	189.6979	90.0	90.0	120.0
mp-11714	box	-6.3651	-6.3651	3.0698	3.0698	10.1406	90.0	90.0	120.0
mp-570690	box	-6.3649	-6.3649	3.0724	3.0724	68.3292	90.0	90.0	120.0
mp-7140	box	-6.3568	-6.3568	3.061	3.061	5.0972	90.0	90.0	120.0
L1_0--AuCu	dynamic	-5.5438	-5.5438	2.5037	2.5037	2.913	90.0	90.0	90.0
B1--NaCl--rock-salt	static	-5.539	-5.539	4.3137	4.3137	4.3137	90.0	90.0	90.0
B2--CsCl	dynamic	-5.4475	-5.4475	2.582	2.582	2.582	90.0	90.0	90.0
L1_0--AuCu	box	-5.0239	-5.0239	2.8131	2.8131	2.3698	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	dynamic	-4.8869	-4.8869	4.8412	4.8412	4.8412	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)
D0_3--BiF3	static	-4.6255	-4.6255	5.7884	5.7884	5.7884	90.0	90.0	90.0
L1_2--AuCu3	static	-4.2939	-4.2939	3.6986	3.6986	3.6986	90.0	90.0	90.0
A15--Cr3Si	box	-4.1328	-4.1328	4.6984	4.6984	4.6984	90.0	90.0	90.0
A15--Cr3Si	static	-1.3056	-1.3056	6.5161	6.5161	6.5161	90.0	90.0	90.0
L1_2--AuCu3	box	-0.8529	-0.8529	5.6037	5.6037	5.6037	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)
A4--C--dc	dynamic	-4.63	-4.63	5.4271	5.4271	5.4271	90.0	90.0	90.0
mp-165	dynamic	-4.6275	-4.6275	3.8238	3.8238	6.3518	90.0	90.0	120.0
oqmd-22507	box	-4.6242	-4.6242	3.8363	6.631	6.3868	90.0	90.0	90.0
oqmd-717362	dynamic	-4.5841	-4.5841	14.6036	14.6036	14.6036	90.0	90.0	90.0
oqmd-717362	box	-4.5835	-4.5835	14.6054	14.6054	14.6054	90.0	90.0	90.0
mp-1203790	dynamic	-4.5803	-4.5803	10.3213	10.3213	16.8811	90.0	90.0	120.0
mp-1203790	box	-4.5797	-4.5797	10.3192	10.3192	16.8901	90.0	90.0	120.0
oqmd-717360	dynamic	-4.5611	-4.5611	10.139	10.139	10.139	90.0	90.0	90.0
oqmd-717360	box	-4.561	-4.561	10.1396	10.1396	10.1396	90.0	90.0	90.0
mp-1196961	dynamic	-4.545	-4.545	10.1144	10.1144	10.3198	90.0	90.0	120.0
mp-1196961	box	-4.5446	-4.5446	10.114	10.114	10.3184	90.0	90.0	120.0
mp-1204627	dynamic	-4.5034	-4.5034	16.6743	12.7698	9.9003	90.0	90.0	90.0
mp-1204627	box	-4.5001	-4.5001	16.7136	12.7567	9.9139	90.0	90.0	90.0
mp-1120747	dynamic	-4.4931	-4.4931	5.7518	5.7518	3.5832	90.0	90.0	120.0
oqmd-22407	dynamic	-4.4627	-4.4627	6.5444	6.5444	3.8943	90.0	90.0	90.0
mp-1079297	dynamic	-4.4622	-4.4622	13.8076	3.8559	6.3331	90.0	97.6	90.0
mp-1079297	box	-4.4536	-4.4536	13.8565	3.8386	6.3549	90.0	97.0	90.0
oqmd-22408	box	-4.4528	-4.4528	13.8619	3.8391	6.3546	90.0	97.0	90.0
mp-999200	box	-4.4394	-4.4394	6.6346	6.6346	3.8166	90.0	90.0	90.0
oqmd-22407	box	-4.4378	-4.4378	6.6377	6.6377	3.8141	90.0	90.0	90.0
mp-1199894	dynamic	-4.4336	-4.4336	25.2619	15.1046	9.8008	90.0	94.5	90.0
mp-1201492	dynamic	-4.4314	-4.4314	17.4899	17.4899	17.4899	90.0	90.0	90.0
mp-1200830	dynamic	-4.4294	-4.4294	12.358	12.358	12.358	90.0	90.0	90.0
mp-1200830	static	-4.4294	-4.4294	12.3583	12.3583	12.3583	90.0	90.0	90.0
mp-1199894	box	-4.4255	-4.4255	25.2884	15.1253	9.8142	90.0	94.4	90.0
mp-1201492	box	-4.4254	-4.4254	17.5027	17.5027	17.5027	90.0	90.0	90.0
mp-1200830	box	-4.4168	-4.4168	12.3827	12.3827	12.3827	90.0	90.0	90.0
mp-971661	dynamic	-4.3884	-4.3884	10.0344	10.0344	10.0344	90.0	90.0	90.0
mp-1095269	dynamic	-4.3812	-4.3812	3.8436	10.7047	12.7517	90.0	90.0	90.0
mp-971661	box	-4.3799	-4.3799	10.0396	10.0396	10.0396	90.0	90.0	90.0
mp-1095269	box	-4.3702	-4.3702	3.8339	10.7548	12.7402	90.0	90.0	90.0
mp-1202745	dynamic	-4.3695	-4.3695	9.884	9.884	16.0823	90.0	90.0	120.0
mp-1202745	box	-4.3629	-4.3629	9.9036	9.9036	16.032	90.0	90.0	120.0
mp-1204046	dynamic	-4.3335	-4.3335	10.0837	10.0837	24.0961	90.0	90.0	90.0
mp-1204046	box	-4.3175	-4.3175	10.1016	10.1016	24.1008	90.0	90.0	90.0
mp-168	static	-4.3074	-4.3074	6.5642	6.5642	6.5642	90.0	90.0	90.0
Ah--alpha-Po--sc	static	-4.2928	-4.2928	2.6208	2.6208	2.6208	90.0	90.0	90.0
A7--alpha-As	box	-4.2928	-4.2928	3.7063	3.7063	9.0786	90.0	90.0	120.0
A5--beta-Sn	dynamic	-4.2826	-4.2826	5.0362	5.0362	2.5954	90.0	90.0	90.0
mp-168	box	-4.2489	-4.2489	6.6361	6.6361	6.6361	90.0	90.0	90.0
oqmd-3484	box	-4.2476	-4.2476	6.637	6.637	6.637	90.0	90.0	90.0
A7--alpha-As	box	-4.2199	-4.2199	3.7523	3.7523	8.9666	90.0	90.0	120.0
oqmd-7479	box	-4.2105	-4.2105	5.0644	5.1211	2.5671	90.0	90.0	90.0
oqmd-1214748	box	-4.2052	-4.2052	4.8696	7.6954	3.8566	90.0	90.0	90.0
mp-1079649	dynamic	-4.1899	-4.1899	8.156	5.1581	6.101	90.0	90.0	90.0
mp-1245041	dynamic	-4.1829	-4.1829	12.844	12.8502	13.101	72.7	71.7	75.3
mp-1001113	dynamic	-4.1791	-4.1791	3.6765	10.7158	3.3284	90.0	90.0	90.0
mp-1079649	box	-4.1678	-4.1678	8.177	5.158	6.0774	90.0	90.0	90.0
mp-1244990	dynamic	-4.1652	-4.1652	12.1511	12.4223	13.044	104.2	100.0	101.0
mp-1245242	dynamic	-4.1528	-4.1528	12.2566	12.6991	12.7086	79.9	82.6	82.1
mp-1244933	dynamic	-4.1527	-4.1527	12.3209	12.4535	12.761	79.2	77.8	73.4
mp-1245041	static	-4.1491	-4.1491	12.8145	12.9285	13.0697	72.8	70.9	74.6
mp-1244971	dynamic	-4.1427	-4.1427	11.6587	12.8086	13.2812	98.6	98.4	99.3
mp-1244933	static	-4.1405	-4.1405	12.3557	12.4808	12.6946	77.4	79.0	74.0
A2--W--bcc	static	-4.1378	-4.1378	3.1381	3.1381	3.1381	90.0	90.0	90.0
mp-1244971	static	-4.123	-4.123	11.582	12.9484	13.3476	97.3	98.3	100.1
mp-571520	box	-4.1167	-4.1167	9.4836	9.4836	5.7252	90.0	90.0	120.0
mp-1245242	static	-4.1134	-4.1134	12.3662	12.6072	12.7233	79.7	81.9	82.4
oqmd-691764	box	-4.1133	-4.1133	2.704	2.704	7.4962	90.0	90.0	120.0
oqmd-18985	box	-4.1113	-4.1113	9.4339	9.4339	5.7566	90.0	90.0	120.0
mp-644693	static	-4.1107	-4.1107	4.0749	5.2453	8.1448	87.0	86.6	71.9
oqmd-717361	dynamic	-4.109	-4.109	7.5376	7.5376	7.5376	90.0	90.0	90.0
mp-1244990	static	-4.1085	-4.1085	12.228	12.4549	12.8472	103.5	100.3	101.8
oqmd-78174	dynamic	-4.1069	-4.1069	8.6441	5.4039	5.4261	90.0	90.0	90.0
A3--Mg--hcp	dynamic	-4.0684	-4.0684	2.8168	2.8168	4.5884	90.0	90.0	120.0
mp-1094057	dynamic	-4.0664	-4.0664	2.8165	2.8165	20.6633	90.0	90.0	120.0
oqmd-1216087	dynamic	-4.0664	-4.0664	2.8165	2.8165	20.6636	90.0	90.0	120.0
oqmd-1216087	static	-4.0663	-4.0663	2.8166	2.8166	20.6623	90.0	90.0	120.0
mp-1094057	box	-4.066	-4.066	2.8165	2.8165	20.6649	90.0	90.0	120.0
A3'--alpha-La--double-hcp	dynamic	-4.0653	-4.0653	2.8164	2.8164	9.1871	90.0	90.0	120.0
A1--Cu--fcc	dynamic	-4.0623	-4.0623	3.9824	3.9824	3.9824	90.0	90.0	90.0
A6--In--bct	static	-4.06	-4.06	3.5741	3.5741	2.5684	90.0	90.0	90.0
oqmd-1214926	dynamic	-4.0583	-4.0583	7.0045	7.0045	7.0045	90.0	90.0	90.0
oqmd-10215	static	-4.043	-4.043	14.7874	14.7874	14.7874	90.0	90.0	90.0
mp-16220	static	-4.0429	-4.0429	14.786	14.786	14.786	90.0	90.0	90.0
mp-1072544	dynamic	-4.0246	-4.0246	6.6574	6.6574	6.6574	90.0	90.0	90.0
oqmd-1214926	box	-4.0183	-4.0183	6.9616	6.9616	6.9616	90.0	90.0	90.0
mp-1001113	box	-4.0106	-4.0106	3.1143	9.7766	4.3065	90.0	90.0	90.0
mp-1244971	box	-3.958	-3.958	11.7043	12.8505	13.4444	98.0	96.2	100.6
oqmd-78173	box	-3.9562	-3.9562	4.9369	5.1502	11.2654	90.0	90.0	90.0
mp-1244933	box	-3.9539	-3.9539	12.3712	12.524	12.6739	78.9	78.2	74.4
mp-1245242	box	-3.9522	-3.9522	12.4058	12.723	12.7575	79.7	82.1	81.0
mp-16220	box	-3.9517	-3.9517	14.7525	14.7525	14.7525	90.0	90.0	90.0
oqmd-10215	box	-3.9478	-3.9478	14.7407	14.7407	14.7407	90.0	90.0	90.0
oqmd-1214837	dynamic	-3.9382	-3.9382	10.4239	10.4239	10.4239	90.0	90.0	90.0
oqmd-1214837	box	-3.929	-3.929	10.428	10.428	10.428	90.0	90.0	90.0
mp-1244990	box	-3.8984	-3.8984	12.2234	12.4748	12.7812	104.0	100.2	100.8
mp-1120447	dynamic	-3.875	-3.875	5.0606	5.6083	6.8657	70.7	69.1	83.7
mp-676011	static	-3.8478	-3.8478	5.1714	5.3617	7.0865	71.2	71.5	64.3
oqmd-51152	static	-3.8391	-3.8391	2.6796	2.6796	2.6796	90.0	90.0	120.0
oqmd-1215104	box	-3.8387	-3.8387	5.359	9.2826	2.6795	90.0	90.0	90.0
mp-1268191	box	-3.828	-3.828	6.9613	6.9613	2.6446	90.0	90.0	120.0
mp-109	box	-3.7811	-3.7811	5.2594	5.2911	9.5416	90.0	90.0	90.0
oqmd-717361	box	-3.7183	-3.7183	7.4487	7.4487	7.4487	90.0	90.0	90.0
mp-1120447	box	-3.6795	-3.6795	5.2584	5.4418	6.7796	71.5	71.3	84.2
oqmd-1215995	box	-3.5927	-3.5927	3.9106	3.9106	7.929	90.0	90.0	120.0
A15--beta-W	static	-3.5444	-3.5444	5.0766	5.0766	5.0766	90.0	90.0	90.0
mp-1120747	box	-3.539	-3.539	5.4108	5.4108	4.2659	90.0	90.0	120.0
mp-1245041	box	-3.1921	-3.1921	9.9724	10.5191	12.4118	77.8	75.7	72.8
oqmd-78174	box	-1.8105	-1.8105	4.8602	12.7154	5.0695	90.0	90.0	90.0
A15--beta-W	static	-1.7733	-1.7733	6.4796	6.4796	6.4796	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:

507.401	520.007	520.007	-0.000	0.000	0.000
520.007	507.401	520.007	0.000	-0.000	-0.000
520.007	520.007	507.401	0.000	0.000	-0.000
0.000	0.000	0.000	-72.453	-0.000	-0.000
0.000	0.000	0.000	-0.000	-72.453	-0.000
0.000	0.000	0.000	-0.000	-0.000	-72.453

507.401	520.007	520.007	0.000	0.000	0.000
520.007	507.401	520.007	0.000	0.000	0.000
520.007	520.007	507.401	0.000	0.000	0.000
-0.000	-0.000	-0.000	-72.453	0.000	0.000
-0.000	-0.000	-0.000	0.000	-72.453	0.000
-0.000	-0.000	-0.000	0.000	0.000	-72.453

507.401	520.007	520.007	0.000	0.000	0.000
520.007	507.401	520.007	0.000	-0.000	-0.000
520.007	520.007	507.401	0.000	0.000	-0.000
0.000	0.000	0.000	-72.453	-0.000	-0.000
0.000	0.000	0.000	-0.000	-72.453	0.000
0.000	0.000	0.000	-0.000	0.000	-72.453

507.401	520.007	520.007	0.000	0.000	0.000
520.007	507.401	520.007	0.000	0.000	0.000
520.007	520.007	507.401	0.000	0.000	0.000
-0.000	-0.000	-0.000	-72.453	0.000	0.000
-0.000	-0.000	-0.000	0.000	-72.453	0.000
-0.000	-0.000	-0.000	0.000	0.000	-72.453

507.403	520.008	520.008	-0.000	-0.000	-0.000
520.008	507.403	520.008	0.000	-0.000	-0.000
520.008	520.008	507.403	-0.000	-0.000	-0.000
0.000	0.000	0.000	-72.453	-0.000	-0.000
0.000	0.000	0.000	-0.000	-72.453	-0.000
0.000	0.000	0.000	0.000	-0.000	-72.453

507.399	520.006	520.006	0.000	0.000	0.000
520.006	507.399	520.006	0.000	0.000	0.000
520.006	520.006	507.399	0.000	0.000	0.000
-0.000	-0.000	-0.000	-72.453	0.000	0.000
-0.000	-0.000	-0.000	0.000	-72.453	0.000
-0.000	-0.000	-0.000	0.000	0.000	-72.453

318.729	586.071	586.071	0.000	-0.000	0.000
586.071	318.729	586.071	0.000	0.000	-0.000
586.071	586.071	318.729	0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-403.895	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-403.895	0.000
-0.000	-0.000	-0.000	0.000	-0.000	-403.895

318.729	586.071	586.071	-0.000	-0.000	0.000
586.071	318.729	586.071	0.000	0.000	-0.000
586.071	586.071	318.729	0.000	0.000	-0.000
0.000	0.000	0.000	-403.895	0.000	-0.000
0.000	0.000	0.000	-0.000	-403.895	-0.000
0.000	0.000	0.000	0.000	-0.000	-403.895

318.488	586.192	586.192	-0.000	-0.000	0.000
586.192	318.488	586.192	-0.000	-0.000	0.000
586.192	586.192	318.488	-0.000	0.000	0.000
-0.000	-0.000	-0.000	-403.895	0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-403.895	0.000
-0.000	-0.000	-0.000	0.000	0.000	-403.895

318.729	586.071	586.071	-0.000	0.000	0.000
586.071	318.729	586.071	-0.000	0.000	-0.000
586.071	586.071	318.729	-0.000	0.000	-0.000
0.000	0.000	0.000	-403.895	0.000	-0.000
0.000	0.000	0.000	-0.000	-403.895	-0.000
0.000	0.000	0.000	-0.000	-0.000	-403.895

318.730	586.073	586.073	0.000	0.000	0.000
586.073	318.730	586.073	0.000	-0.000	0.000
586.073	586.073	318.730	-0.000	-0.000	0.000
-2183004.499	-1095739.322	-2990495.907	-282713.326	-136698.208	578359.702
-926443.753	-756522.236	-1547312.731	803160.952	82003.425	278965.321
-1559119.107	-1740150.864	-1972072.588	242465.908	498286.322	44740.915

318.487	586.190	586.190	0.000	0.000	-0.000
586.190	318.487	586.190	-0.000	0.000	-0.000
586.190	586.190	318.487	-0.000	-0.000	0.000
983337.720	2036983.188	2631537.300	-137571.101	-473701.554	15923.702
1377120.133	2243623.504	528295.240	-711005.903	367814.081	-352969.544
986145.670	2190758.803	1348519.210	-807785.298	-91871.607	-268374.264

2051.951	-201.955	-201.955	-0.000	-0.000	0.000
-201.955	2051.951	-201.955	-0.000	-0.000	0.000
-201.955	-201.955	2051.951	-0.000	-0.000	0.000
-0.000	0.000	-0.000	-273.640	-0.000	0.000
0.000	-0.000	-0.000	0.000	-273.640	0.000
0.000	-0.000	-0.000	-0.000	0.000	-273.640

2051.951	-201.955	-201.955	-0.000	0.000	-0.000
-201.955	2051.951	-201.955	-0.000	-0.000	-0.000
-201.955	-201.955	2051.951	-0.000	-0.000	-0.000
0.000	-0.000	0.000	-273.640	0.000	-0.000
-0.000	0.000	0.000	0.000	-273.640	0.000
-0.000	0.000	0.000	0.000	-0.000	-273.640

2051.952	-201.955	-201.955	-0.000	-0.000	0.000
-201.955	2051.952	-201.955	0.000	-0.000	-0.000
-201.955	-201.955	2051.952	0.000	0.000	0.000
-0.000	0.000	0.000	-273.640	-0.000	0.000
0.000	-0.000	0.000	-0.000	-273.640	0.000
0.000	0.000	-0.000	0.000	-0.000	-273.640

2051.950	-201.955	-201.955	-0.000	-0.000	-0.000
-201.955	2051.950	-201.955	-0.000	0.000	-0.000
-201.955	-201.955	2051.950	-0.000	-0.000	-0.000
0.000	-0.000	-0.000	-273.640	0.000	-0.000
-0.000	0.000	-0.000	-0.000	-273.640	-0.000
-0.000	-0.000	0.000	-0.000	-0.000	-273.640

2051.964	-201.954	-201.954	-0.000	0.000	0.000
-201.954	2051.964	-201.954	0.000	-0.000	-0.000
-201.954	-201.954	2051.964	-0.000	-0.000	0.000
-0.003	0.002	0.000	-273.640	0.000	0.000
0.002	-0.003	0.000	0.000	-273.640	0.000
0.002	0.000	-0.003	0.000	0.000	-273.640

2051.938	-201.956	-201.956	-0.000	-0.000	-0.000
-201.956	2051.938	-201.956	-0.000	0.000	-0.000
-201.956	-201.956	2051.938	-0.000	0.000	-0.000
0.003	-0.002	-0.000	-273.640	0.000	-0.000
-0.002	0.003	-0.000	-0.000	-273.640	-0.000
-0.002	-0.000	0.003	-0.000	0.000	-273.640

441.990	547.249	563.669	0.000	-0.000	-0.000
547.249	441.990	563.669	0.000	-0.000	-0.000
563.669	563.669	410.029	0.000	-0.000	-0.000
0.000	0.000	0.000	-39.490	-0.000	-0.000
0.000	0.000	0.000	-0.000	-39.490	-0.000
0.000	0.000	0.000	0.000	-0.000	-82.291

-944206210.739	-144883506.747	259633330.628	-15068094.912	20780043.571	3097947.071
547.249	441.990	563.669	-0.000	0.000	0.000
563.669	563.669	410.029	0.000	0.000	0.000
-0.000	-0.000	-0.000	-39.490	0.000	0.000
-0.000	-0.000	-0.000	-0.000	-39.490	0.000
-0.000	-0.000	-0.000	-0.000	0.000	-82.291

441.990	547.249	563.669	0.000	-0.000	-0.000
547.249	441.990	563.669	-0.000	-0.000	-0.000
563.669	563.669	410.029	0.000	-0.000	-0.000
0.000	0.000	-0.000	-39.490	-0.000	-0.000
0.000	0.000	-0.000	0.000	-39.490	-0.000
0.000	0.000	0.000	-0.000	-0.000	-82.291

441.990	547.249	563.669	-0.000	0.000	0.000
547.249	441.990	563.669	-0.000	0.000	0.000
563.669	563.669	410.029	0.000	-0.000	0.000
-0.000	-0.000	0.000	-39.490	0.000	0.000
-0.000	-0.000	0.000	-0.000	-39.490	-0.000
-0.000	-0.000	-0.000	-0.000	0.000	-82.291

441.992	547.251	563.671	0.000	-0.000	-0.000
547.250	441.992	563.671	0.000	-0.000	-0.000
563.671	563.671	410.031	0.000	-0.000	-0.000
0.000	0.000	-0.000	-39.490	0.000	-0.000
0.000	0.000	-0.000	0.000	-39.490	0.000
0.000	-0.000	0.000	0.000	-0.000	-52.629

-9123332.004	-2390878.666	3198372.580	-411624.490	-371726.444	46975.919
547.247	441.988	563.668	-0.000	-0.000	0.000
563.668	563.668	410.027	0.000	0.000	0.000
-0.000	-0.000	0.000	-39.490	-0.000	0.000
-0.000	-0.000	0.000	-0.000	-39.490	0.000
-0.000	0.000	-0.000	-0.000	0.000	-52.629

775.624	494.678	165.495	-0.000	0.000	0.000
602.405	667.897	165.495	-0.000	0.000	-0.000
165.496	165.496	1490.364	0.000	-0.000	0.000
0.000	0.000	-0.000	-17.251	0.000	-0.000
0.000	-0.000	-0.000	0.000	-17.251	0.000
0.000	0.000	-0.000	-0.000	0.000	32.746

775.624	494.678	165.495	0.000	0.000	-0.000
602.405	667.897	165.495	0.000	-0.000	-0.000
165.496	165.496	1490.364	-0.000	-0.000	-0.000
-0.000	-0.000	0.000	-17.251	-0.000	-0.000
-0.000	0.000	0.000	0.000	-17.251	-0.000
-0.000	-0.000	0.000	0.000	-0.000	32.746

775.624	494.678	165.495	-0.000	-0.000	-0.000
494.678	775.624	165.495	-0.000	-0.000	-0.000
165.495	165.495	1490.365	-0.000	-0.000	0.000
0.000	0.000	-0.000	-17.251	0.000	0.000
0.000	0.000	-0.000	-0.000	-17.251	0.000
0.000	0.001	-0.001	-0.000	0.000	32.746

667.894	602.406	165.496	0.000	-0.000	-0.000
602.404	667.896	165.496	0.000	-0.000	-0.000
165.496	165.496	1490.363	0.000	-0.000	0.000
-0.000	-0.000	0.000	-17.251	-0.000	-0.000
-0.000	-0.000	0.000	0.000	-17.251	-0.000
-0.000	-0.001	0.001	0.000	-0.000	32.746

775.626	494.678	165.497	-0.000	-0.000	0.000
602.408	667.907	165.492	-0.000	-0.000	0.000
165.494	165.494	1490.376	0.000	0.000	0.000
0.000	0.001	0.000	-17.251	0.000	-0.000
0.001	0.000	0.000	-0.000	-17.251	-0.000
0.004	0.007	-0.005	-0.000	-0.000	32.746

667.873	602.414	165.499	0.000	-0.000	-0.000
602.403	667.884	165.499	0.000	-0.000	-0.000
165.497	165.497	1490.352	0.000	-0.000	0.000
-0.000	-0.001	-0.000	-17.251	-0.000	0.000
-0.001	-0.000	-0.000	0.000	-17.251	-0.000
-0.004	-0.007	0.005	0.000	-0.000	32.746

663.968	776.960	100.791	0.000	-0.000	0.000
776.960	663.968	100.791	0.000	0.000	0.000
100.792	100.792	193.875	0.000	-0.000	0.000
0.000	0.000	-0.000	120.209	-0.000	-0.000
0.000	0.000	-0.000	0.000	120.209	0.000
-0.000	0.000	0.000	-0.000	0.000	-56.496

663.968	776.960	100.791	0.000	-0.000	-0.000
776.960	663.968	100.791	-0.000	0.000	-0.000
100.792	100.792	193.875	-0.000	-0.000	-0.000
-0.000	-0.000	0.000	120.209	-0.000	-0.000
-0.000	-0.000	0.000	-0.000	120.209	-0.000
0.000	-0.000	-0.000	-0.000	0.000	-56.496

668.339	772.590	100.791	-0.000	0.000	-0.000
772.590	668.339	100.791	0.000	-0.000	0.000
100.792	100.792	193.875	0.000	-0.000	0.000
0.000	0.000	-0.000	120.209	-0.000	0.000
0.000	0.000	-0.000	-0.000	120.209	0.000
0.000	0.000	-0.000	-0.000	-0.000	-52.125

663.968	776.960	100.791	0.000	-0.000	-0.000
772.589	668.338	100.791	-0.000	-0.000	0.000
100.792	100.792	193.875	0.000	0.000	-0.000
-0.000	-0.000	0.000	120.209	-0.000	-0.000
-0.000	-0.000	0.000	-0.000	120.209	-0.000
-0.000	-0.000	0.000	-0.000	-0.000	-52.125

663.971	776.962	100.791	0.000	-0.000	0.000
772.592	668.342	100.791	-0.000	-0.000	-0.000
100.793	100.793	193.876	-0.000	0.000	0.000
0.000	0.000	-0.002	120.209	-0.000	0.000
0.000	0.000	-0.002	-0.000	120.209	0.000
0.000	0.000	-0.000	-0.000	0.000	-52.125

668.336	772.587	100.791	-0.000	-0.000	-0.000
772.587	668.336	100.791	-0.000	0.000	0.000
100.791	100.791	193.874	-0.000	0.000	-0.000
-0.000	-0.000	0.002	120.209	-0.000	-0.000
-0.000	-0.000	0.002	0.000	120.209	-0.000
-0.000	-0.000	0.000	0.000	-0.000	-52.125

442.665	552.301	563.198	-0.000	-0.000	0.000
369386609.424	201511915.034	-303659314.912	17021373.592	-20024745.999	49451779.459
563.198	563.198	401.210	0.000	-0.000	-0.000
0.000	0.000	-0.000	-50.237	0.000	-0.000
0.000	0.000	-0.000	-0.000	-50.237	-0.000
0.000	0.000	0.000	-0.000	-0.000	-119.794

442.665	552.301	563.198	0.000	0.000	0.000
552.301	442.665	563.198	0.000	-0.000	0.000
563.198	563.198	401.210	0.000	0.000	0.000
-0.000	-0.000	-0.000	-50.237	0.000	0.000
-0.000	-0.000	0.000	0.000	-50.237	-0.000
-0.000	-0.000	-0.000	0.000	0.000	-119.794

1457431.041	-14505066.925	-45096678.263	-1865463.226	-3743185.298	9657452.876
617.277	377.689	563.199	-0.000	-0.000	-0.000
563.199	563.199	401.210	-0.000	-0.000	-0.000
0.000	0.000	-0.000	-50.237	-0.000	-0.000
0.000	0.000	-0.000	-0.000	-50.237	0.000
100336090.989	27404159.756	-28289526.059	-38343.847	-4477293.984	-4244745.964

442.665	552.301	563.198	0.000	0.000	0.000
552.301	442.665	563.198	0.000	0.000	0.000
563.198	563.198	401.210	0.000	0.000	0.000
-0.000	-0.000	0.000	-50.237	-0.000	0.000
-0.000	-0.000	0.000	0.000	-50.237	0.000
-95142802.726	-29364967.205	24848589.530	-153801.699	-2599178.039	-205633.969

2889162.523	-1092934.706	-3321480.093	-589827.317	-256752.958	550556.602
3245065.404	1942091.679	-2841357.622	-52944.639	679596.930	148629.129
563.200	563.200	401.212	-0.000	-0.000	-0.000
0.000	0.000	-0.000	-50.237	-0.000	-0.000
0.000	0.000	-0.000	-0.000	-50.237	-0.000
9473047.146	2172965.289	-2900907.912	14947.279	592888.293	-484261.579

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:

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plot:

Thermodynamic Predictions

Composition:

Plot:

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2014--Kang-K-H--Si-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:

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Surface	γ_fs (mJ/m²)
(111) 2	2512.09
(322)	3328.07
(331) 2	3430.90
(332)	3593.73
(211)	3757.48
(110)	3828.68
(321)	4058.29
(221)	4151.02
(311) 2	4385.04
(320)	4467.24
(311) 1	4529.33
(331) 1	4581.04
(210)	4810.01
(310)	4955.23
(100)	5296.50
(111) 1	8460.30

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:

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Point Defect	E_f (eV)	p₁₁ (eV)	p₂₂ (eV)	p₃₃ (eV)	p₁₂ (eV)	p₁₃ (eV)	p₂₃ (eV)
vacancy	2.409	0.777	0.777	0.777	0.000	0.000	0.000
1nn divacancy	4.148	3.161	3.161	3.161	2.402	2.402	2.402
100 dumbbell	6.285	20.910	20.910	34.632	0.000	0.000	0.000

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:

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2014--Kang-K-H--Si-C--LAMMPS--ipr1/mdsolid.C.A4--C--dc.a50571e0.a

Click on plot to load interactive version

2014--Kang-K-H--Si-C--LAMMPS--ipr1//mdsolid.C.A4--C--dc.a50571e0.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

2014--Kang-K-H--Si-C--LAMMPS--ipr1/mdliquid.Si.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

2014--Kang-K-H--Si-C--LAMMPS--ipr1/mdthermo.C.U

-4209144.434	-2471167.561	3426780.754	468344.845	29686.511	263393.939
552.299	442.663	563.197	-0.000	0.000	0.000
563.197	563.197	401.208	0.000	0.000	0.000
-0.000	-0.000	0.000	-50.237	-0.000	0.000
-0.000	-0.000	0.000	0.000	-50.237	-0.000
-9574579.317	-3210749.721	2104311.517	-77428.454	-79797.977	-429743.500

641.553	346.131	346.131	0.000	0.000	0.000
346.131	641.553	346.131	0.000	0.000	0.000
346.131	346.131	641.553	0.000	0.000	0.000
0.000	0.000	0.000	458.099	0.000	0.000
0.000	0.000	0.000	0.000	458.099	0.000
0.000	0.000	0.000	0.000	0.000	458.099

641.554	346.132	346.132	0.000	0.000	0.000
346.132	641.554	346.132	0.000	0.000	0.000
346.132	346.132	641.554	0.000	0.000	0.000
0.000	0.000	0.001	458.099	0.000	0.000
0.000	0.000	0.001	0.000	458.099	0.000
0.000	0.001	0.000	0.000	0.000	458.099

641.552	346.130	346.130	-0.000	-0.000	-0.000
346.130	641.552	346.130	-0.000	-0.000	-0.000
346.130	346.130	641.552	-0.000	-0.000	-0.000
-0.000	-0.000	-0.001	458.099	-0.000	-0.000
-0.000	-0.000	-0.001	-0.000	458.099	-0.000
-0.000	-0.001	-0.000	-0.000	-0.000	458.099

679.029	517.500	457.151	-0.000	0.000	-0.000
517.500	679.029	457.151	-0.000	0.000	-0.000
457.152	457.150	742.634	-0.000	0.000	-0.000
0.001	-0.001	0.000	93.447	-0.000	-0.000
0.001	-0.001	0.000	0.000	93.447	-0.000
0.001	-0.001	-0.000	-0.000	0.000	123.051

679.028	517.500	457.151	0.000	-0.000	0.000
517.500	679.028	457.151	0.000	-0.000	0.000
457.151	457.151	742.633	-0.000	-0.000	0.000
-0.000	-0.000	-0.000	93.447	0.000	0.000
-0.000	-0.000	-0.000	0.000	93.447	0.000
-0.000	0.000	0.000	-0.000	-0.000	123.051

679.033	517.501	457.152	-0.000	0.000	-0.000
517.501	679.033	457.152	0.000	-0.000	-0.000
457.152	457.152	742.638	-0.000	0.000	-0.000
0.003	0.002	0.004	93.447	-0.000	-0.000
0.002	0.003	0.004	-0.000	93.447	-0.000
-0.000	-0.000	-0.000	-0.000	0.000	123.051

679.024	517.498	457.150	0.000	0.000	0.000
517.498	679.024	457.150	0.000	-0.000	0.000
457.150	457.150	742.629	0.000	-0.000	0.000
-0.003	-0.002	-0.004	93.447	-0.000	-0.000
-0.002	-0.003	-0.004	0.000	93.447	0.000
0.000	0.000	0.000	-0.000	-0.000	123.051

768.720	606.328	5.574	0.000	-0.000	-0.000
606.328	768.720	5.574	-0.000	-0.000	0.000
5.574	5.574	164.734	-0.000	-0.000	-0.000
0.000	0.000	-0.000	500.253	-0.000	-0.000
0.000	0.000	-0.000	-0.000	500.253	-0.000
-0.000	-0.000	-0.000	0.000	-0.000	128.393

768.719	606.328	5.574	-0.000	0.000	0.000
606.328	768.719	5.574	0.000	0.000	0.000
5.574	5.574	164.734	0.000	0.000	0.000
-0.000	-0.000	0.000	500.253	0.000	0.000
-0.000	-0.000	0.000	0.000	500.253	0.000
0.000	0.000	0.000	-0.000	0.000	128.393

768.724	606.329	5.574	-0.000	-0.000	-0.000
606.329	768.724	5.574	-0.000	-0.000	0.000
5.575	5.575	164.735	0.000	-0.000	0.000
0.001	0.001	-0.002	500.253	-0.000	-0.000
0.001	0.001	-0.002	0.000	500.253	-0.000
-0.000	-0.000	-0.000	0.000	-0.000	128.393

768.715	606.326	5.574	0.000	0.000	-0.000
606.326	768.715	5.574	0.000	0.000	0.000
5.574	5.574	164.733	-0.000	-0.000	0.000
-0.001	-0.001	0.002	500.253	-0.000	0.000
-0.001	-0.001	0.002	-0.000	500.253	0.000
0.000	0.000	0.000	-0.000	0.000	128.393

905.672	374.286	220.158	-168.909	-0.000	-0.000
440.541	943.767	-275.699	139.658	-0.000	-0.000
145.767	145.767	1122.198	0.000	-0.000	-0.000
-73.434	201.839	-610.168	-388.905	-0.000	-0.000
64.203	64.203	-610.168	0.000	-388.906	-137.636
59.593	59.593	-566.362	-0.000	-139.882	251.721

834.927	441.403	237.398	-25.703	-0.000	-0.000
441.403	834.927	237.399	25.702	-0.000	-0.000
224.101	224.101	377.736	0.000	-0.000	-0.000
-19.883	31.517	-55.283	-621.457	-0.000	0.000
0.000	0.000	-0.000	-0.000	-323.935	-168.909
0.000	0.000	-0.000	-0.000	-168.909	265.693

905.671	374.286	220.158	-168.909	0.000	0.000
374.286	905.671	220.158	168.909	0.000	-0.000
212.476	212.476	488.212	-0.000	0.000	-0.000
-31.518	19.885	55.282	-621.455	0.000	0.000
-0.000	-0.000	0.000	0.000	-323.935	-168.909
-0.000	-0.000	0.000	0.000	-168.909	265.693

905.677	374.288	220.156	-168.909	-0.000	-0.000
388.702	860.416	366.730	106.922	-0.000	0.000
218.827	218.827	427.868	0.000	-0.000	0.000
-23.192	29.054	-27.842	-620.577	-0.000	0.000
0.001	0.002	-0.004	-0.000	-323.935	-168.909
2.902	2.902	-27.578	0.000	-27.561	197.656

828.528	435.000	298.207	-25.709	0.000	-0.000
435.003	828.524	298.209	25.701	0.000	-0.000
217.706	217.706	438.494	0.000	0.000	0.000
-26.296	25.131	5.527	-621.431	-0.000	-0.000
-0.001	-0.002	0.004	0.000	-323.935	-168.909
-2.902	-2.902	27.578	-0.000	-27.561	197.656

642.220	457.875	457.875	-0.000	-0.000	0.000
457.875	642.220	457.875	0.000	-0.000	-0.000
457.875	457.875	642.220	-0.000	0.000	-0.000
-0.000	-0.000	0.000	114.529	-0.000	-0.000
-0.000	-0.000	0.000	-0.000	114.529	0.000
-0.000	0.000	-0.000	-0.000	0.000	114.529

642.219	457.875	457.875	-0.000	-0.000	0.000
457.875	642.219	457.875	-0.000	0.000	-0.000
457.875	457.875	642.219	-0.000	-0.000	0.000
0.000	0.000	0.000	114.529	0.000	0.000
0.000	0.000	0.000	0.000	114.529	0.000
0.000	0.000	0.000	0.000	-0.000	114.529

642.224	457.876	457.876	-0.000	-0.000	0.000
457.876	642.224	457.876	0.000	-0.000	0.000
457.876	457.876	642.224	0.000	0.000	-0.000
-0.000	-0.000	-0.000	114.529	0.000	-0.000
-0.000	-0.000	-0.000	-0.000	114.529	0.000
-0.000	-0.000	-0.000	-0.000	-0.000	114.529

2014--Kang-K-H-Eun-T-Jun-M-C-Lee-B-J--Si-C

Si 2

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

Point Defect Formation Energy Predictions

Dislocation Monopole Structures

MD Solid Property Predictions

MD Liquid Property Predictions

MD Thermodynamic Predictions

642.215	457.874	457.874	-0.000	0.000	0.000
457.874	642.215	457.874	-0.000	0.000	0.000
457.874	457.874	642.215	0.000	-0.000	-0.000
0.000	0.000	0.000	114.529	-0.000	0.000
0.000	0.000	0.000	0.000	114.529	-0.000
0.000	0.000	0.000	0.000	-0.000	114.529

366.912	226.513	46.795	0.000	0.000	-0.000
195.933	859.355	247.166	0.000	-0.000	-0.000
38.880	269.304	1063.873	0.000	0.000	-0.000
-0.011	0.044	-0.034	412.703	0.000	0.000
-0.009	0.039	-0.030	0.000	80.009	-0.000
0.065	-0.262	0.199	0.000	0.000	121.416

366.930	226.437	46.856	-0.000	-0.000	0.000
224.633	779.609	288.356	-0.000	-0.000	0.000
38.898	269.228	1063.932	-0.000	-0.000	0.000
0.011	-0.044	0.034	412.703	0.000	0.000
0.009	-0.039	0.030	-0.000	80.009	0.000
-0.065	0.262	-0.199	-0.000	0.000	121.416

370.161	228.154	37.537	0.000	0.000	0.000
237.110	767.804	276.432	0.000	0.000	0.000
45.686	233.116	1096.184	-0.000	0.000	0.000
-0.001	0.002	-0.002	412.325	0.000	-0.000
-0.001	0.004	-0.003	0.000	80.009	-0.000
0.006	-0.026	0.020	0.000	0.000	121.415

370.159	228.151	37.545	-0.000	-0.000	0.000
237.111	767.798	276.437	-0.000	-0.000	0.000
43.412	262.381	1062.978	-0.000	0.000	0.000
0.001	-0.002	0.002	412.325	-0.000	0.000
0.001	-0.004	0.003	-0.000	80.009	0.000
-0.006	0.026	-0.020	0.000	0.000	121.415

366.922	226.476	46.825	0.000	0.000	-0.000
237.114	767.796	276.439	0.000	0.000	-0.000
43.412	262.385	1062.980	0.000	0.000	0.000
0.000	0.000	0.000	412.325	0.000	-0.000
-0.000	0.000	-0.001	0.000	80.009	-0.000
0.001	-0.003	0.002	-0.000	-0.000	121.415

366.920	226.474	46.825	-0.000	-0.000	-0.000
237.107	767.806	276.430	-0.000	0.000	0.000
43.411	262.385	1062.971	-0.000	-0.000	0.000
-0.000	-0.000	-0.000	412.325	-0.000	-0.000
0.000	-0.000	0.001	-0.000	80.009	0.000
-0.001	0.003	-0.002	0.000	0.000	121.415

375.136	231.071	41.420	0.000	-0.000	0.000
231.247	771.888	284.497	0.000	-0.000	-0.000
40.042	286.992	1036.427	0.000	0.000	0.000
0.034	-0.032	-0.036	422.649	0.000	0.000
0.055	-0.051	-0.059	-0.000	86.755	0.000
0.115	-0.337	0.163	-0.000	-0.000	101.801

374.990	231.275	41.493	0.000	-0.000	-0.000
231.100	772.093	284.570	-0.000	-0.000	-0.000
39.992	287.025	1036.498	0.000	0.000	-0.000
-0.034	0.032	0.036	422.649	0.000	-0.000
-0.055	0.051	0.059	0.000	86.755	-0.000
-0.115	0.337	-0.163	0.000	-0.000	101.801

377.886	231.340	34.964	-0.000	-0.000	0.000
189.807	875.515	247.956	0.000	-0.000	0.000
41.464	284.523	1036.332	-0.000	0.000	0.000
0.010	-0.016	-0.002	422.536	0.000	0.000
0.006	-0.005	-0.006	-0.000	86.755	0.000
0.011	-0.034	0.016	-0.000	-0.000	101.800