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.

2002--Albe-K-Nordlund-K-Averback-R-S--Pt-C

Citation: K. Albe, K. Nordlund, and R.S. Averback (2002), "Modeling the metal-semiconductor interaction: Analytical bond-order potential for platinum-carbon", Physical Review B 65(19), 195124. DOI: 10.1103/physrevb.65.195124.

Abstract: We propose an analytical interatomic potential for modeling platinum, carbon, and the platinum-carbon interaction using a single functional form. The ansatz chosen for this potential makes use of the fact that chemical bonding in both covalent systems and d-transition metals can be described in terms of the Pauling bond order. By adopting Brenner’s original bond-order potential for carbon [Phys. Rev. B 42, 9458 (1990)] we devise an analytical expression that has an equivalent form for describing the C-C/Pt-Pt/Pt-C interactions. It resembles, in the case of the pure metal interaction, an embedded-atom scheme, but includes angularity. The potential consequently provides an excellent description of the properties of Pt including the elastic anisotropy ratio. The parameters for both the Pt-Pt interaction and the Pt-C interaction are systematically adjusted using a combination of experimental and theoretical data, the latter being generated by total-energy calculations based on density-functional theory. This approach offers good chemical accuracy in describing all types of interactions, and has a wide applicability for modeling metal-semiconductor systems.

Related Models:
OpenKIM (MO_500121566391)

See Computed Properties
Notes: Listing found at https://openkim.org.
Link(s):
KIM page Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_002
DOI 10.25950/e8e5efb7

Implementation Information

This page displays computed properties for the Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003 implementation of the 2002--Albe-K-Nordlund-K-Averback-R-S--Pt-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

Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003/diatom

Click on plot to load interactive version

Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003/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

Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003/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)
mp-569416	dynamic	-7.3756	-7.3756	2.5126	2.5126	54.7684	90.0	90.0	120.0
mp-568286	static	-7.3756	-7.3756	2.5126	4.352	7.0357	90.0	90.0	90.0
mp-568363	dynamic	-7.3756	-7.3756	2.5126	4.352	8.1526	90.0	90.0	90.0
mp-606949	dynamic	-7.3756	-7.3756	2.5126	2.5126	29.4946	90.0	90.0	120.0
mp-990424	static	-7.3756	-7.3756	2.5126	2.5126	24.1327	90.0	90.0	120.0
mp-568806	static	-7.3756	-7.3756	2.5126	2.5126	3.6541	90.0	90.0	120.0
mp-568363	static	-7.3756	-7.3756	2.5126	4.352	8.1499	90.0	90.0	90.0
oqmd-590101	dynamic	-7.3756	-7.3756	2.5126	2.5126	6.586	90.0	90.0	120.0
oqmd-589493	static	-7.3756	-7.3756	2.5126	2.5126	28.9536	90.0	90.0	120.0
mp-606949	static	-7.3756	-7.3756	2.5126	2.5126	29.4913	90.0	90.0	120.0
oqmd-590101	static	-7.3756	-7.3756	2.5126	2.5126	6.796	90.0	90.0	120.0
mp-1018088	dynamic	-7.3756	-7.3756	4.1031	4.1031	4.1031	90.0	90.0	90.0
mp-990424	dynamic	-7.3756	-7.3756	2.5126	2.5126	25.0011	90.0	90.0	120.0
oqmd-589492	dynamic	-7.3756	-7.3756	2.5126	2.5126	54.2295	90.0	90.0	120.0
oqmd-683819	static	-7.3756	-7.3756	2.5126	4.352	6.6497	90.0	90.0	90.0
mp-937760	dynamic	-7.3756	-7.3756	2.5126	4.352	7.1733	90.0	90.0	90.0
mp-569304	dynamic	-7.3756	-7.3756	2.5126	2.5126	33.9945	90.0	90.0	120.0
oqmd-1214690	static	-7.3756	-7.3756	2.5126	4.352	6.6767	90.0	90.0	90.0
mp-569304	static	-7.3756	-7.3756	2.5126	2.5126	33.1908	90.0	90.0	120.0
oqmd-683820	static	-7.3756	-7.3756	2.5126	4.352	6.7728	90.0	90.0	90.0
mp-632329	dynamic	-7.3756	-7.3756	4.352	2.5126	3.5549	90.0	94.3	90.0
oqmd-589491	dynamic	-7.3756	-7.3756	2.5126	2.5126	31.7117	90.0	90.0	120.0
mp-569416	static	-7.3756	-7.3756	2.5126	2.5126	54.6786	90.0	90.0	120.0
mp-1040425	static	-7.3756	-7.3756	2.5126	2.5126	19.9983	90.0	90.0	120.0
mp-632329	static	-7.3756	-7.3756	4.352	2.5126	3.7378	90.0	94.2	90.0
mp-1040425	dynamic	-7.3756	-7.3756	2.5126	2.5126	20.0161	90.0	90.0	120.0
mp-169	static	-7.3756	-7.3756	4.352	2.5126	3.7635	90.0	111.5	90.0
mp-990448	static	-7.3756	-7.3756	2.5126	2.5126	8.5238	90.0	90.0	120.0
mp-169	dynamic	-7.3756	-7.3756	4.352	2.5126	3.6167	90.0	113.0	90.0
mp-48	static	-7.3756	-7.3756	2.5126	2.5126	7.8031	90.0	90.0	120.0
A7--alpha-As	dynamic	-7.3756	-7.3756	2.5126	2.5126	9.7084	90.0	90.0	120.0
oqmd-589493	dynamic	-7.3756	-7.3756	2.5126	2.5126	29.4304	90.0	90.0	120.0
oqmd-1215937	dynamic	-7.3756	-7.3756	2.5126	2.5126	7.7484	90.0	90.0	120.0
mp-997182	static	-7.3756	-7.3756	2.5126	2.5126	12.0458	90.0	90.0	120.0
mp-48	dynamic	-7.3756	-7.3756	2.5126	2.5126	7.8102	90.0	90.0	120.0
mp-997182	dynamic	-7.3756	-7.3756	2.5126	2.5126	12.0464	90.0	90.0	120.0
oqmd-1215937	static	-7.3756	-7.3756	2.5126	2.5126	7.3725	90.0	90.0	120.0
oqmd-610551	static	-7.3756	-7.3756	2.5126	2.5126	3.501	90.0	90.0	120.0
oqmd-599493	dynamic	-7.3232	-7.3232	2.5157	2.5157	30.811	90.0	90.0	120.0
oqmd-599491	dynamic	-7.3232	-7.3232	2.5157	2.5157	12.3244	90.0	90.0	120.0
A4--C--dc	dynamic	-7.3232	-7.3232	3.5578	3.5578	3.5578	90.0	90.0	90.0
oqmd-599490	dynamic	-7.3232	-7.3232	2.5157	2.5157	8.2163	90.0	90.0	120.0
mp-616440	dynamic	-7.3232	-7.3232	2.5157	2.5157	16.4326	90.0	90.0	120.0
mp-569567	dynamic	-7.3232	-7.3232	2.5157	2.5157	43.1355	90.0	90.0	120.0
mp-47	dynamic	-7.3232	-7.3232	2.5157	2.5157	4.1081	90.0	90.0	120.0
oqmd-599489	box	-7.3232	-7.3232	2.5148	2.5148	4.111	90.0	90.0	120.0
mp-47	box	-7.3232	-7.3232	2.5146	2.5146	4.1117	90.0	90.0	120.0
oqmd-599492	box	-7.3225	-7.3225	2.5153	2.5153	16.439	90.0	90.0	120.0
mp-616440	box	-7.3223	-7.3223	2.5155	2.5155	16.4371	90.0	90.0	120.0
oqmd-599491	box	-7.3222	-7.3222	2.5154	2.5154	12.3291	90.0	90.0	120.0
mp-569567	box	-7.3222	-7.3222	2.5156	2.5156	43.1464	90.0	90.0	120.0
mp-611448	box	-7.3221	-7.3221	2.5155	2.5155	12.3284	90.0	90.0	120.0
oqmd-599493	box	-7.3221	-7.3221	2.5156	2.5156	30.8198	90.0	90.0	120.0
mp-569517	box	-7.322	-7.322	2.5154	2.5154	30.8231	90.0	90.0	120.0
mp-611426	box	-7.3219	-7.3219	2.5152	2.5152	8.2208	90.0	90.0	120.0
oqmd-599494	static	-7.3218	-7.3218	2.5143	2.5143	43.3601	90.0	90.0	120.0
oqmd-599490	box	-7.3217	-7.3217	2.5155	2.5155	8.2192	90.0	90.0	120.0
mp-1008374	dynamic	-7.3043	-7.3043	2.5106	7.8969	2.5253	90.0	90.0	90.0
mp-1096869	static	-7.3005	-7.3005	25.8707	15.1125	2.0001	90.0	90.4	90.0
mp-1008374	box	-7.2775	-7.2775	2.4171	8.1885	2.4772	90.0	90.0	90.0
mp-1078845	dynamic	-7.2343	-7.2343	4.2064	8.7443	2.5168	90.0	90.0	90.0
mp-1188817	dynamic	-7.2298	-7.2298	5.213	5.213	5.213	90.0	90.0	90.0
mp-1078845	box	-7.2293	-7.2293	4.2151	8.7548	2.5146	90.0	90.0	90.0
oqmd-610557	dynamic	-7.2291	-7.2291	4.7645	5.4067	4.399	90.0	90.0	90.0
oqmd-637443	box	-7.2258	-7.2258	5.2125	5.2125	5.2125	90.0	90.0	90.0
mp-1188817	box	-7.2232	-7.2232	5.212	5.212	5.212	90.0	90.0	90.0
oqmd-610557	box	-7.1976	-7.1976	4.7635	5.28	4.4774	90.0	90.0	90.0
oqmd-610556	box	-7.1973	-7.1973	4.7596	5.2908	4.4772	90.0	90.0	90.0
mp-568410	box	-7.1959	-7.1959	4.7547	5.2981	4.4796	90.0	90.0	90.0
oqmd-637353	dynamic	-7.1804	-7.1804	4.3857	4.3857	2.4889	90.0	90.0	90.0
mp-1008395	box	-7.1798	-7.1798	4.375	4.375	2.4992	90.0	90.0	90.0
oqmd-637353	box	-7.1797	-7.1797	4.374	4.374	2.5002	90.0	90.0	90.0
mp-1190171	dynamic	-7.1619	-7.1619	8.9566	2.5504	4.1366	90.0	90.0	90.0
mp-1080826	dynamic	-7.1592	-7.1592	9.023	2.5534	4.1327	90.0	96.6	90.0
oqmd-637130	box	-7.1537	-7.1537	8.9628	2.5285	4.1759	90.0	90.0	90.0
mp-1190171	box	-7.1534	-7.1534	8.9633	2.5282	4.1768	90.0	90.0	90.0
oqmd-637352	box	-7.1509	-7.1509	9.0349	2.5334	4.168	90.0	96.4	90.0
mp-1080826	box	-7.1503	-7.1503	9.0349	2.5334	4.169	90.0	96.4	90.0
mp-568028	dynamic	-7.0785	-7.0785	7.8724	13.9803	9.5902	90.0	90.0	90.0
oqmd-614417	dynamic	-7.0709	-7.0709	9.2677	9.2677	24.0606	90.0	90.0	120.0
mp-680372	dynamic	-7.0709	-7.0709	9.2677	9.2677	25.1577	90.0	90.0	120.0
mp-680372	static	-7.0709	-7.0709	9.2661	9.2661	25.6426	90.0	90.0	120.0
oqmd-614417	static	-7.0709	-7.0709	9.2643	9.2643	24.4517	90.0	90.0	120.0
mp-683919	dynamic	-7.0567	-7.0567	10.1855	17.5151	18.269	90.0	90.0	90.0
oqmd-689315	dynamic	-7.0567	-7.0567	10.0957	17.4513	18.269	90.0	90.0	90.0
mp-683919	static	-7.0567	-7.0567	10.3353	17.5914	18.2687	90.0	90.0	90.0
oqmd-689315	static	-7.0567	-7.0567	10.3097	17.5711	18.2676	90.0	90.0	90.0
mp-683919	box	-7.0446	-7.0446	10.3469	17.7474	18.3371	90.0	90.0	90.0
mp-630227	dynamic	-7.044	-7.044	9.1766	9.2384	15.5969	90.0	90.0	90.0
oqmd-595714	dynamic	-7.044	-7.044	9.1766	9.2384	14.4997	90.0	90.0	90.0
oqmd-595714	static	-7.044	-7.044	9.1766	9.2384	14.8315	90.0	90.0	90.0
mp-630227	static	-7.044	-7.044	9.1766	9.2384	15.892	90.0	90.0	90.0
oqmd-684627	dynamic	-7.0439	-7.0439	9.2076	9.2076	15.1815	90.0	90.0	90.0
oqmd-684627	static	-7.0439	-7.0439	9.2076	9.2076	15.47	90.0	90.0	90.0
oqmd-614417	box	-7.0361	-7.0361	9.3077	9.3077	24.536	90.0	90.0	120.0
mp-680372	box	-7.0318	-7.0318	9.3196	9.3196	25.718	90.0	90.0	120.0
oqmd-689315	box	-7.0241	-7.0241	10.3057	17.7167	18.3806	90.0	90.0	90.0
oqmd-595714	box	-7.0204	-7.0204	9.2472	9.3098	14.7342	90.0	90.0	90.0
mp-630227	box	-7.0184	-7.0184	9.2385	9.2933	15.8331	90.0	90.0	90.0
mp-1147718	dynamic	-7.015	-7.015	10.2697	14.7508	9.2333	90.0	90.0	90.0
mp-1147718	static	-7.015	-7.015	10.4038	14.9577	9.2333	90.0	90.0	90.0
oqmd-610552	dynamic	-7.0084	-7.0084	4.8225	5.5263	5.9101	90.0	90.0	90.0
mp-579909	dynamic	-7.0084	-7.0084	4.8225	5.5263	6.2826	90.0	90.0	90.0
mp-579909	static	-7.0084	-7.0084	4.8225	5.5263	6.554	90.0	90.0	90.0
mp-624889	static	-7.0084	-7.0084	4.8225	5.5263	5.3967	90.0	90.0	90.0
oqmd-610552	static	-7.0084	-7.0084	4.8225	5.5263	6.1536	90.0	90.0	90.0
mp-624889	dynamic	-7.0084	-7.0084	4.8225	5.5263	5.3939	90.0	90.0	90.0
mp-1147718	box	-6.9967	-6.9967	10.3996	14.9406	9.386	90.0	90.0	90.0
oqmd-684627	box	-6.9962	-6.9962	9.2679	9.2679	15.5177	90.0	90.0	90.0
mp-667273	dynamic	-6.9868	-6.9868	14.4015	14.4015	14.4015	90.0	90.0	90.0
oqmd-603085	dynamic	-6.9868	-6.9868	13.9524	13.9524	13.9524	90.0	90.0	90.0
oqmd-603085	static	-6.9868	-6.9868	14.1959	14.1959	14.1959	90.0	90.0	90.0
oqmd-677227	dynamic	-6.9868	-6.9868	14.1614	14.1614	14.1614	90.0	90.0	90.0
mp-1196583	dynamic	-6.9868	-6.9868	14.406	14.406	14.406	90.0	90.0	90.0
oqmd-677227	static	-6.9868	-6.9868	14.3922	14.3922	14.3922	90.0	90.0	90.0
mp-1196583	static	-6.9868	-6.9868	14.6187	14.6187	14.6187	90.0	90.0	90.0
mp-667273	static	-6.9867	-6.9867	14.6814	14.6814	14.6814	90.0	90.0	90.0
mp-1205283	dynamic	-6.9851	-6.9851	9.8032	12.6723	9.0586	90.0	90.0	90.0
oqmd-603085	box	-6.9809	-6.9809	14.1966	14.1966	14.1966	90.0	90.0	90.0
oqmd-610552	box	-6.9809	-6.9809	4.6334	5.7168	6.3224	90.0	90.0	90.0
mp-1196583	box	-6.9808	-6.9808	14.6196	14.6196	14.6196	90.0	90.0	90.0
mp-667273	box	-6.9794	-6.9794	14.6829	14.6829	14.6829	90.0	90.0	90.0
mp-624889	box	-6.979	-6.979	4.8538	5.2482	5.5835	90.0	90.0	90.0
mp-568028	box	-6.9772	-6.9772	8.4219	14.1475	9.7697	90.0	90.0	90.0
mp-579909	box	-6.977	-6.977	4.6189	5.734	6.7439	90.0	90.0	90.0
oqmd-677227	box	-6.9672	-6.9672	14.4015	14.4015	14.4015	90.0	90.0	90.0
mp-24	dynamic	-6.9293	-6.9293	4.3511	4.3511	4.3511	90.0	90.0	90.0
mp-1205283	static	-6.9007	-6.9007	9.1432	13.1732	9.2383	90.0	90.0	90.0
oqmd-684315	dynamic	-6.8663	-6.8663	8.0416	14.4115	9.6483	90.0	90.0	90.0
mp-1205283	box	-6.8012	-6.8012	10.0136	13.4554	9.1739	90.0	90.0	90.0
mp-1244964	dynamic	-6.7832	-6.7832	10.3585	10.4196	10.9246	84.0	87.2	88.0
mp-24	box	-6.7673	-6.7673	4.426	4.426	4.426	90.0	90.0	90.0
mp-1245190	dynamic	-6.7163	-6.7163	10.038	10.5559	10.659	90.7	92.8	91.0
mp-1244964	static	-6.7127	-6.7127	10.2087	10.468	11.1015	87.0	82.5	88.0
mp-570002	dynamic	-6.7095	-6.7095	4.9125	4.9125	4.9125	90.0	90.0	90.0
oqmd-585286	box	-6.6939	-6.6939	4.9207	4.9207	4.9207	90.0	90.0	90.0
mp-570002	box	-6.6938	-6.6938	4.9208	4.9208	4.9208	90.0	90.0	90.0
mp-1245190	static	-6.645	-6.645	10.1946	10.5996	10.6559	90.7	90.2	93.3
mp-1244913	dynamic	-6.5852	-6.5852	10.4913	10.6843	10.7597	88.1	87.5	85.2
mp-1244913	static	-6.5852	-6.5852	10.4914	10.6844	10.7598	88.1	87.5	85.2
mp-1245190	box	-6.4996	-6.4996	10.5568	10.694	10.7828	89.9	89.8	87.2
oqmd-684315	static	-6.4954	-6.4954	10.0654	16.0832	9.3255	90.0	90.0	90.0
mp-1244964	box	-6.4839	-6.4839	10.5301	10.5897	11.254	90.6	94.9	92.3
mp-1095534	dynamic	-6.3627	-6.3627	9.8319	9.8319	2.476	90.0	90.0	90.0
mp-1244913	box	-6.3386	-6.3386	10.8239	11.1024	11.2467	90.8	95.6	92.1
mp-1095633	static	-6.3307	-6.3307	6.562	6.562	7.1151	90.0	90.0	90.0
mp-1095633	dynamic	-6.3307	-6.3307	6.5619	6.5619	7.1153	90.0	90.0	90.0
mp-1205417	dynamic	-6.1677	-6.1677	12.0921	12.0921	7.0359	90.0	90.0	90.0
mp-1205417	static	-6.1677	-6.1677	12.1166	12.1166	7.0106	90.0	90.0	90.0
mp-1095534	box	-6.1411	-6.1411	10.1147	10.1147	2.4102	90.0	90.0	90.0
mp-1095633	box	-6.1148	-6.1148	6.4217	6.4217	7.444	90.0	90.0	90.0
oqmd-684315	box	-6.0757	-6.0757	10.7837	15.36	9.1602	90.0	90.0	90.0
oqmd-1216026	dynamic	-6.0535	-6.0535	2.2608	2.2608	9.1652	90.0	93.1	90.0
oqmd-1216026	static	-6.0535	-6.0535	2.2608	2.2608	9.1654	90.0	93.2	90.0
mp-1056957	static	-6.0535	-6.0535	2.2608	2.2608	6.5533	90.0	90.0	90.0
A6--In--bct	dynamic	-6.0535	-6.0535	1.5986	1.5986	6.3803	90.0	90.0	90.0
A6--In--bct	static	-6.0535	-6.0535	1.5986	1.5986	3.2998	90.0	90.0	90.0
mp-1056957	dynamic	-6.0535	-6.0535	2.2608	2.2608	6.5534	90.0	90.0	90.0
mp-1097832	dynamic	-6.0535	-6.0535	2.2608	2.2608	9.88	90.0	90.0	90.0
A6--In--bct	dynamic	-6.0535	-6.0535	1.5986	1.5986	6.5526	90.0	90.0	90.0
mp-1097832	static	-6.0535	-6.0535	2.2608	2.2608	9.8799	90.0	90.0	90.0
mp-1197903	dynamic	-6.051	-6.051	8.0395	10.7718	24.0974	100.3	96.9	97.8
oqmd-1215224	static	-6.0468	-6.0468	1.5987	3.1332	1.9999	90.0	113.6	90.0
mp-1197903	static	-6.0113	-6.0113	8.2462	10.829	23.5437	97.5	96.9	102.4
mp-1182029	static	-5.9965	-5.9965	1.3902	3.3843	3.3717	90.0	97.7	90.0
oqmd-1215046	static	-5.9965	-5.9965	1.3902	3.4437	5.8152	89.9	88.9	89.5
mp-1182029	dynamic	-5.9965	-5.9965	1.3902	3.3843	3.3618	90.0	96.6	90.0
oqmd-1215046	dynamic	-5.9965	-5.9965	1.3902	3.443	5.8142	89.9	90.0	89.5
oqmd-1215848	static	-5.9965	-5.9965	3.4043	3.4043	1.3902	90.0	90.0	120.0
mp-1196857	static	-5.9666	-5.9666	15.3434	19.9695	2.0027	90.0	90.0	90.0
mp-1196857	dynamic	-5.9666	-5.9666	9.1305	19.3729	5.9487	90.0	90.0	90.0
mp-1182684	static	-5.9486	-5.9486	11.3651	14.6754	16.1891	90.0	90.0	90.0
mp-1182684	dynamic	-5.9486	-5.9486	9.4881	11.0046	14.9372	90.0	90.0	90.0
mp-1205417	box	-5.8418	-5.8418	12.4343	12.4343	7.2079	90.0	90.0	90.0
mp-1197903	box	-5.7846	-5.7846	8.1382	9.6747	24.9875	96.5	97.0	104.9
mp-1182684	box	-5.7839	-5.7839	5.4926	11.3865	15.827	90.0	90.0	90.0
A7--alpha-As	box	-5.533	-5.533	2.5746	2.5746	5.5205	90.0	90.0	120.0
oqmd-1214779	dynamic	-5.5226	-5.5226	8.72	8.72	8.72	90.0	90.0	90.0
mp-1192619	static	-5.5226	-5.5226	9.4999	9.4999	9.4999	90.0	90.0	90.0
oqmd-1214779	static	-5.5226	-5.5226	9.1375	9.1375	9.1375	90.0	90.0	90.0
mp-1192619	dynamic	-5.5226	-5.5226	9.1039	9.1039	9.1039	90.0	90.0	90.0
mp-1192619	box	-5.4018	-5.4018	9.5196	9.5196	9.5196	90.0	90.0	90.0
oqmd-1214779	box	-5.3691	-5.3691	9.1276	9.1276	9.1276	90.0	90.0	90.0
Ah--alpha-Po--sc	static	-5.2423	-5.2423	1.7438	1.7438	1.7438	90.0	90.0	90.0
A5--beta-Sn	box	-5.0544	-5.0544	3.6223	3.6223	1.593	90.0	90.0	90.0
A15--beta-W	static	-4.5436	-4.5436	3.3144	3.3144	3.3144	90.0	90.0	90.0
A3'--alpha-La--double-hcp	box	-4.4127	-4.4127	2.6701	2.6701	3.6167	90.0	90.0	120.0
A2--W--bcc	box	-4.3388	-4.3388	2.0935	2.0935	2.0935	90.0	90.0	90.0
oqmd-1214868	dynamic	-3.7869	-3.7869	6.9139	6.9139	6.9139	90.0	90.0	90.0
oqmd-1214868	static	-3.7869	-3.7869	7.2223	7.2223	7.2223	90.0	90.0	90.0
oqmd-1214868	box	-3.7836	-3.7836	7.1759	7.1759	7.1759	90.0	90.0	90.0
A3--Mg--hcp	box	-3.6639	-3.6639	1.8633	1.8633	3.0434	90.0	90.0	120.0
A3'--alpha-La--double-hcp	box	-3.6634	-3.6634	1.8633	1.8633	6.0863	90.0	90.0	120.0
A1--Cu--fcc	box	-3.6629	-3.6629	2.6353	2.6353	2.6353	90.0	90.0	90.0
A2--W--bcc	dynamic	0.0	0.0	2.3664	2.3664	2.3664	90.0	90.0	90.0
A15--beta-W	box	0.0	0.0	4.0	4.0	4.0	90.0	90.0	90.0
A3'--alpha-La--double-hcp	dynamic	0.0	0.0	2.2767	2.2767	7.4282	90.0	90.0	120.0
A1--Cu--fcc	dynamic	0.0	0.0	3.0645	3.0645	3.0645	90.0	90.0	90.0
A3--Mg--hcp	dynamic	0.0	0.0	2.2759	2.2759	3.7088	90.0	90.0	120.0
A6--In--bct	dynamic	0.0	0.0	2.0345	2.0345	4.0653	90.0	90.0	90.0
A1--Cu--fcc	dynamic	0.0	0.0	3.2184	3.2184	3.2184	90.0	90.0	90.0
A2--W--bcc	dynamic	0.0	0.0	2.328	2.328	2.328	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	box	-4.525	-4.525	5.1754	5.1754	5.1754	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)
L1_2--AuCu3	box	-4.1433	-4.1433	3.2349	3.2349	3.2349	90.0	90.0	90.0
A15--Cr3Si	static	-3.8568	-3.8568	4.1836	4.1836	4.1836	90.0	90.0	90.0
D0_3--BiF3	static	-3.5302	-3.5302	5.2739	5.2739	5.2739	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
B1--NaCl--rock-salt	static	-5.5777	-5.5777	4.4131	4.4131	4.4131	90.0	90.0	90.0
B3--ZnS--cubic-zinc-blende	box	-4.8579	-4.8579	4.8837	4.8837	4.8837	90.0	90.0	90.0
B3--ZnS--cubic-zinc-blende	box	-4.6937	-4.6937	4.4997	4.4997	4.4997	90.0	90.0	90.0
B2--CsCl	static	-4.5065	-4.5065	2.9206	2.9206	2.9206	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	-4.9918	-4.9918	5.5843	5.5843	5.5843	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	-4.5556	-4.5556	6.0029	6.0029	6.0029	90.0	90.0	90.0
L1_2--AuCu3	box	-4.4103	-4.4103	3.7706	3.7706	3.7706	90.0	90.0	90.0
A15--Cr3Si	static	-4.181	-4.181	4.7782	4.7782	4.7782	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)
A3--Mg--hcp	dynamic	-5.7845	-5.7845	2.7804	2.7804	4.4866	90.0	90.0	120.0
oqmd-1216077	dynamic	-5.7794	-5.7794	2.7768	2.7768	20.2474	90.0	90.0	120.0
A3'--alpha-La--double-hcp	dynamic	-5.7769	-5.7769	2.775	2.775	9.0113	90.0	90.0	120.0
oqmd-1215272	box	-5.7702	-5.7702	2.7563	4.8388	4.5125	90.0	90.0	90.0
A1--Cu--fcc	dynamic	-5.7698	-5.7698	3.9174	3.9174	3.9174	90.0	90.0	90.0
oqmd-1214916	dynamic	-5.6975	-5.6975	6.7452	6.7452	6.7452	90.0	90.0	90.0
oqmd-1214916	box	-5.676	-5.676	6.7244	6.7244	6.7244	90.0	90.0	90.0
oqmd-1214827	dynamic	-5.6147	-5.6147	9.5415	9.5415	9.5415	90.0	90.0	90.0
oqmd-1214827	box	-5.5781	-5.5781	9.5559	9.5559	9.5559	90.0	90.0	90.0
A15--beta-W	dynamic	-5.5522	-5.5522	4.8984	4.8984	4.8984	90.0	90.0	90.0
A2--W--bcc	static	-5.5474	-5.5474	3.0535	3.0535	3.0535	90.0	90.0	90.0
oqmd-1215094	box	-5.4283	-5.4283	4.6729	10.1531	2.6911	90.0	90.0	90.0
oqmd-1214738	box	-5.2399	-5.2399	4.4386	6.9992	4.8186	90.0	90.0	90.0
A5--beta-Sn	box	-5.0178	-5.0178	4.9748	4.9748	2.5965	90.0	90.0	90.0
Ah--alpha-Po--sc	static	-4.8665	-4.8665	2.6197	2.6197	2.6197	90.0	90.0	90.0
A4--C--dc	box	-4.6621	-4.6621	5.8093	5.8093	5.8093	90.0	90.0	90.0
oqmd-1215985	box	-4.5971	-4.5971	4.3049	4.3049	5.3116	90.0	90.0	120.0

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:

11137.055	14806.352	14806.352	-0.000	-0.000	-0.000
14806.352	11137.055	14806.352	-0.000	-0.000	0.000
14806.353	14806.352	11137.055	0.000	0.000	-0.000
0.000	-0.000	-0.000	-2722.506	-0.000	-0.000
-0.000	0.000	-0.000	-0.000	-2722.506	0.000
-0.000	-0.000	0.000	0.000	0.000	-2722.506

11137.054	14806.352	14806.352	-0.000	-0.000	0.000
14806.352	11137.055	14806.352	-0.000	-0.000	0.000
14806.352	14806.352	11137.055	0.000	0.000	-0.000
-0.000	0.000	0.000	-2722.506	0.000	0.000
0.000	-0.000	0.000	0.000	-2722.506	-0.000
-0.000	0.000	-0.000	-0.000	-0.000	-2722.506

11137.059	14806.355	14806.355	0.000	0.000	0.000
14806.355	11137.059	14806.355	0.000	0.000	0.000
14806.355	14806.355	11137.059	0.000	0.000	0.000
0.002	0.001	0.001	-2722.506	0.000	-0.000
0.001	0.002	0.001	0.000	-2722.506	0.000
0.001	0.001	0.002	0.000	0.000	-2722.506

11137.051	14806.349	14806.349	-0.000	0.000	-0.000
14806.349	11137.051	14806.349	0.000	0.000	0.000
14806.349	14806.349	11137.051	0.000	0.000	0.000
-0.002	-0.001	-0.001	-2722.506	-0.000	0.000
-0.001	-0.002	-0.001	-0.000	-2722.506	-0.000
-0.001	-0.001	-0.002	-0.000	-0.000	-2722.506

11137.097	14806.382	14806.382	0.000	0.000	-0.000
14806.382	11137.097	14806.382	0.000	0.000	-0.000
14806.382	14806.382	11137.097	-0.000	-0.000	0.000
0.020	0.010	0.006	-2722.506	0.000	-0.000
0.010	0.020	0.006	0.000	-2722.506	0.000
0.010	0.006	0.020	0.000	0.000	-2722.506

11137.012	14806.323	14806.323	-0.000	-0.000	0.000
14806.323	11137.012	14806.323	-0.000	-0.000	-0.000
14806.323	14806.323	11137.012	-0.000	-0.000	-0.000
-0.020	-0.010	-0.006	-2722.506	-0.000	0.000
-0.010	-0.020	-0.006	-0.000	-2722.506	-0.000
-0.010	-0.006	-0.020	-0.000	-0.000	-2722.506

2102.109	5258.098	5258.098	-0.000	-0.000	-0.000
5258.098	2102.109	5258.098	-0.000	-0.000	-0.000
5258.098	5258.098	2102.109	0.000	0.000	-0.000
10561031547.718	11259548742.649	11334629598.704	-89280693.968	-140872654.440	-22682633.439
11239385536.521	10437185566.858	11218514443.359	-91695469.967	-37711999.257	-4084217.722
11394453982.048	11472603372.797	10571470699.930	-66657808.278	-273472872.948	-67775155.620

2102.108	5258.098	5258.098	0.000	0.000	0.000
5258.098	2102.108	5258.098	0.000	0.000	-0.000
5258.098	5258.098	2102.108	0.000	0.000	0.000
-11676463145.169	-11827735113.478	-11923369685.729	-781400596.904	-83154415.952	-29426740.117
-11645028494.940	-11933090478.884	-12014495984.307	-84527539.624	-810920050.753	-68056090.977
-11839098465.046	-11634963859.039	-11991357854.599	70018809.143	-97364317.832	-810527070.406

2102.111	5258.099	5258.099	-0.000	0.000	-0.000
5258.099	2102.111	5258.099	-0.000	-0.000	0.000
5258.099	5258.099	2102.111	-0.000	-0.000	-0.000
1115988597.671	1179053471.762	1168626741.498	-38732486.151	7153423.335	-3842788.641
1158795050.436	1152641210.085	1171442325.300	-4187541.070	-55525230.054	-21765465.173
1149934597.278	1149665904.626	1149420126.926	3192975.121	5937093.993	-39618541.192

2102.106	5258.097	5258.097	0.000	0.000	0.000
5258.097	2102.106	5258.097	0.000	0.000	0.000
5258.097	5258.097	2102.106	0.000	0.000	0.000
-1177575831.281	-1176683393.566	-1174102624.527	-82429002.135	-14030461.190	-2868336.732
-1178812379.588	-1217961041.630	-1173388073.039	324749.085	-85047475.077	-11826197.626
-1199279692.468	-1182217855.248	-1168608323.439	-12803604.384	6309208.147	-92446337.920

2102.135	5258.108	5258.108	-0.000	-0.000	-0.000
5258.108	2102.135	5258.108	-0.000	-0.000	-0.000
5258.108	5258.108	2102.135	-0.000	-0.000	-0.000
115461499.024	119512967.966	115626808.185	-6399956.235	923193.144	472127.711
119733704.414	114187232.088	117160295.913	790756.434	-5978757.619	556974.979
118287997.736	115481115.086	118202257.099	1244989.519	-1465161.113	-5388442.837

2102.082	5258.088	5258.088	0.000	0.000	0.000
5258.088	2102.082	5258.088	0.000	0.000	0.000
5258.088	5258.088	2102.082	0.000	0.000	0.000
-121477974.757	-119736510.616	-117208962.526	-7899412.764	-763115.739	-3219029.631
-119334027.537	-119577183.907	-117746837.364	-1618564.039	-8276057.470	-998173.291
-114325160.095	-118734531.649	-118720198.991	583222.199	1226497.961	-7639387.957

-2554.508	0.000	0.000	0.000	0.000
0.000	-2554.508	0.000	0.000	-0.000
0.000	0.000	-2554.508	-0.000	0.000
0.000	0.000	0.000	0.000	0.000
0.000	0.000	0.000	0.000	0.000
0.000	0.000	0.000	0.000	0.000

-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000

-2989.051	0.000	0.000	0.000	0.000
0.000	-2989.051	0.000	0.000	0.000
0.000	0.000	-2989.051	-0.000	-0.000
0.000	0.000	0.000	0.000	0.000
0.000	0.000	0.000	0.000	0.000
0.000	0.000	0.000	0.000	0.000

-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-0.000

6498.321	6389.851	6389.851	-0.000	0.000	-0.000
6389.851	6498.321	6389.851	-0.000	0.000	-0.000
6389.851	6389.851	6498.321	-0.000	0.000	-0.000
0.000	0.000	0.000	-2628.131	-0.000	-0.000
0.000	0.000	0.000	-0.000	-2628.131	-0.000
0.000	0.000	0.000	-0.000	-0.000	-2628.131

6498.321	6389.851	6389.851	-0.000	-0.000	-0.000
6389.851	6498.321	6389.851	-0.000	-0.000	-0.000
6389.851	6389.851	6498.321	-0.000	-0.000	-0.000
-0.000	-0.000	-0.000	-2628.131	0.000	0.000
-0.000	-0.000	-0.000	0.000	-2628.131	0.000
-0.000	-0.000	-0.000	0.000	0.000	-2628.131

6498.319	6389.851	6389.851	-0.000	0.000	-0.000
6389.851	6498.319	6389.851	-0.000	0.000	-0.000
6389.851	6389.851	6498.319	-0.000	-0.000	-0.000
0.001	0.001	0.000	-2628.131	-0.000	-0.000
0.001	0.001	0.000	0.000	-2628.131	0.000
0.001	0.000	0.001	0.000	0.000	-2628.131

6498.323	6389.851	6389.851	-0.000	-0.000	-0.000
6389.851	6498.323	6389.851	-0.000	-0.000	0.000
6389.851	6389.851	6498.323	0.000	-0.000	-0.000
-0.001	-0.001	-0.000	-2628.131	-0.000	0.000
-0.001	-0.001	-0.000	-0.000	-2628.131	0.000
-0.001	-0.000	-0.001	-0.000	-0.000	-2628.131

6498.305	6389.847	6389.847	-0.000	-0.000	-0.000
6389.847	6498.305	6389.847	-0.000	-0.000	-0.000
6389.847	6389.847	6498.305	-0.000	-0.000	-0.000
0.006	0.010	0.004	-2628.131	0.000	-0.000
0.010	0.006	0.004	0.000	-2628.131	0.000
0.010	0.004	0.006	0.000	0.000	-2628.131

6498.337	6389.855	6389.855	0.000	0.000	-0.000
6389.855	6498.337	6389.855	0.000	-0.000	0.000
6389.855	6389.855	6498.337	0.000	0.000	-0.000
-0.006	-0.010	-0.004	-2628.131	-0.000	0.000
-0.010	-0.006	-0.004	-0.000	-2628.131	-0.000
-0.010	-0.004	-0.006	-0.000	-0.000	-2628.131

10274.814	15085.825	15397.681	-0.000	-0.000	-0.000
15085.825	10274.814	15397.681	0.000	0.000	-0.000
15397.681	15397.681	9933.431	-0.000	-0.000	-0.001
0.000	-0.000	-0.000	-2215.951	-0.000	-0.000
0.000	-0.000	-0.000	-0.000	-2215.950	-0.000
6614627235.831	10035257939.075	-609745985.866	-819296.799	-7725740.670	91259115.917

10274.813	15085.825	15397.681	0.000	0.000	0.000
-8739580825.084	-9813099790.663	-4619120858.546	27425318.726	-49362161.737	196272151.737
15397.680	15397.681	9933.429	-0.000	-0.000	0.001
-0.000	0.000	0.000	-2215.950	0.000	0.000
-0.000	0.000	-0.000	-0.000	-2215.951	0.000
-6940847666.533	-10321582427.174	582787862.015	1389161.069	-4325759.389	526827358.076

872452632.590	958752370.477	498524818.236	-92260.760	-1290869.100	-21928419.512
1276738653.743	373119857.705	-266464247.055	231529.929	648230.120	5071472.927
15397.684	15397.684	9933.437	-0.000	-0.000	-0.000
0.001	0.001	-0.000	-2215.950	0.000	0.000
0.001	0.001	-0.000	-0.000	-2215.950	-0.000
622352530.277	1024513657.450	-269031661.863	2317876.121	-2299220.458	-53640255.589

-1239194703.463	-381091955.100	290404312.337	-927084.751	-358864.971	-10669785.554
-870243765.342	-953390709.271	-487485994.638	2505911.427	2462718.608	20366150.402
15397.678	15397.678	9933.423	-0.000	-0.000	0.000
-0.001	-0.001	0.000	-2215.950	0.000	0.000
-0.001	-0.001	0.000	0.000	-2215.950	0.000
-661592538.878	-995216837.179	212792714.978	-1114776.189	-238504.881	26947966.272

86065412.421	89069222.796	51316105.354	-223679.755	16013.131	-2055396.276
120953082.497	38119958.911	-28691374.855	106573.931	82248.659	1586123.124
15397.715	15397.715	9933.502	0.000	0.000	-0.000
119430940.944	43704520.872	-23589303.090	53112.845	178409.074	763626.693
91675476.135	87453577.103	62023058.597	-294392.865	-40878.328	-286097.169
64033807.587	99409440.595	-33110849.084	-335006.524	-263361.271	-5006809.313

-121276308.924	-38241548.052	27979390.993	174677.312	8209.783	-582043.935
-86972849.742	-90204350.200	-51695814.078	-99698.531	643655.389	2112202.245
15397.647	15397.647	9933.358	0.000	0.000	0.000
-116618795.749	-44647139.536	23467888.071	-1179.222	-153190.797	-943416.356
-91199675.926	-94043342.925	-67688890.413	-485714.854	167930.122	553586.950
-63310642.463	-106544353.427	32130914.178	104207.466	159684.565	1449876.402

3422.776	2897.438	4330.115	-0.000	-0.000	-0.000
3512647702.614	6825350796.758	-5747196066.271	-10286201.474	12125301.354	-4770704.123
4190.266	4190.266	3505.342	-0.000	-0.000	0.000
0.000	0.000	-0.000	-1318.459	-0.000	0.000
0.000	0.000	-0.000	-0.000	-1318.459	0.000
5996990539.653	5267429635.991	-6769281421.168	-179982814.324	111931050.139	704011250.785

3422.776	2897.438	4330.115	0.000	0.000	0.000
2897.438	3422.776	4330.115	0.000	0.000	0.000
4190.266	4190.266	3505.343	0.000	0.000	-0.000
-0.000	-0.000	0.000	-1318.459	0.000	-0.000
-0.000	-0.000	0.000	0.000	-1318.459	-0.000
-5908031630.525	-5188219039.789	6791859165.635	162376744.147	100987867.499	725563625.460

308136553.123	399953510.059	-291358288.443	53985906.738	-2950599.891	-1949850.796
2897.438	3422.775	4330.114	-0.000	-0.000	0.000
4190.265	4190.265	3505.341	-0.000	-0.000	0.000
0.000	0.001	0.000	-1318.459	-0.000	0.000
0.001	0.000	0.000	-0.000	-1318.459	-0.000
595439473.627	519324040.847	-675544111.997	4971967.060	-3432746.005	69504037.181

-392357546.982	-672528136.266	608233617.111	-1015153.966	7039101.899	-896650.551
2897.439	3422.777	4330.115	0.000	0.000	-0.000
4190.267	4190.267	3505.345	0.000	0.000	-0.000
-0.000	-0.001	-0.000	-1318.459	0.000	-0.000
-0.001	-0.000	-0.000	0.000	-1318.459	0.000
-591782621.590	-506683303.385	681884585.663	-5028703.387	-2761095.224	75651877.442

3422.769	2897.432	4330.109	-0.000	-0.000	0.000
2897.431	3422.770	4330.109	-0.000	-0.000	-0.000
4190.256	4190.256	3505.321	-0.000	-0.000	0.000
0.009	0.003	0.001	-1318.459	-0.000	0.000
0.011	0.000	0.001	-0.000	-1318.459	0.000
59544792.066	52298566.967	-68349580.078	-183470.478	126617.405	6621029.869

-42628442.673	-66308460.777	61660467.297	84272.551	-441053.273	44029.315
-21887024.653	-30269263.436	15616148.739	-2992443.942	111747.334	18032.303
4190.277	4190.277	3505.364	0.000	0.000	-0.000
-0.009	-0.003	-0.001	-1318.459	0.000	-0.000
-0.011	-0.000	-0.001	0.000	-1318.459	-0.000
-59649054.589	-51493660.074	67898772.272	-59506.727	48694.738	7279005.800

10300.320	15069.404	15397.091	0.000	0.000	-0.000
12755949524.732	5268773794.790	-3963391508.343	21818416.073	-31082995.883	345759131.863
15397.091	15397.090	9913.656	0.000	0.001	-0.000
0.000	-0.000	-0.000	-2301.119	-0.000	-0.001
0.000	-0.000	0.000	0.000	-2301.119	-0.000
6784822483.623	9997330311.048	-3727047782.424	54705884.956	6592276.242	-640643265.452

10300.318	15069.403	15397.090	-0.000	-0.000	-0.000
15069.403	10300.318	15397.090	0.000	-0.000	0.001
15397.089	15397.090	9913.655	-0.000	-0.001	0.000
-0.000	0.000	-0.000	-2301.119	-0.000	0.001
-0.000	0.000	-0.000	-0.000	-2301.119	0.000
-7124502091.613	-9598889454.735	4224397408.276	-46627572.545	8316780.371	-133663027.605

860112146.269	1004712964.312	169950964.163	-81644.155	1815708.407	-10595282.012
1355161142.889	527620899.044	-348889273.152	2451807.401	-1370135.613	14415925.516
15397.094	15397.094	9913.663	0.000	0.000	-0.000
0.001	0.001	-0.000	-2301.119	0.000	-0.000
0.001	0.001	-0.000	0.000	-2301.119	-0.000
659436744.882	993985999.669	-377861213.431	-2966344.999	982389.654	-90391199.123

-1366085237.782	-526700334.164	369316724.598	50084.541	-1835090.079	-3932132.148
-863392526.409	-1017198016.241	-192863280.689	-2778904.403	1527706.083	11631483.652
15397.087	15397.087	9913.648	-0.000	-0.000	-0.000
-0.001	-0.001	0.000	-2301.119	-0.000	0.000
-0.001	-0.001	0.000	-0.000	-2301.119	0.000
-693422624.444	-920082148.060	419368105.955	1816583.197	-903078.921	-109329379.481

88480173.051	100782143.408	19967918.787	610937.024	172584.208	77311.099
126067830.622	54206829.020	-40421990.654	60000.008	203943.756	1142863.321
15397.124	15397.124	9913.727	-0.000	-0.000	-0.000
127984328.665	54421093.270	-37717062.209	271230.202	-730765.864	2150545.887
0.009	0.009	-0.001	0.000	-2301.119	-0.000
63428834.617	86623002.378	-38954088.189	499820.278	-523127.039	-6708458.354

-126849392.733	-55651621.957	38543194.956	249916.443	338497.197	-1507782.698
-88686355.728	-101754499.426	-19779641.528	150979.803	-38615.455	899533.649
15397.056	15397.056	9913.583	-0.000	-0.000	0.000
-129982291.621	-53595805.060	37114039.033	29151.522	-332344.828	-2638749.448
-0.009	-0.009	0.001	-0.000	-2301.119	0.000
-67943650.076	-86058445.444	45369444.751	-554797.965	-367865.131	-5078322.819

623.452	415.459	415.459	-0.000	-0.000	-0.000
415.459	623.452	415.459	-0.000	-0.000	-0.000
415.459	415.459	623.452	-0.000	-0.000	-0.000
0.000	0.000	0.000	385.883	-0.000	-0.000
0.000	0.000	0.000	-0.000	385.883	-0.000
0.000	0.000	0.000	-0.000	-0.000	385.883

623.452	415.459	415.459	0.000	0.000	0.000
415.459	623.452	415.459	0.000	0.000	0.000
415.459	415.459	623.452	0.000	0.000	0.000
-0.000	-0.000	-0.000	385.883	0.000	0.000
-0.000	-0.000	-0.000	0.000	385.883	0.000
-0.000	-0.000	-0.000	0.000	0.000	385.883

623.452	415.459	415.459	-0.000	-0.000	-0.000
415.459	623.452	415.459	-0.000	-0.000	-0.000
415.459	415.459	623.452	-0.000	-0.000	-0.000
0.000	-0.000	0.000	385.883	-0.000	-0.000
-0.000	0.000	0.000	-0.000	385.883	-0.000
-0.000	0.000	0.000	-0.000	-0.000	385.883

Phonon and Quasi-Harmonic Approximation Predictions

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

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

Notes and Disclaimers:

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

Version Information:

2023-03-14. Phonon and QHA plots added

Band Structures, Density of States, and QHA Verification Plots

Composition:

Prototype:

a₀:

plot:

Thermodynamic Predictions

Composition:

Plot:

Download data

Click on plot to load interactive version

Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003/phonon.C.G.png

Free Surface Formation Energy Predictions

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

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

Notes and Disclaimers:

These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
The calculation only performs straight cuts along crystallographic planes and static relaxations. Lower energy configurations may exist that require atomic restructuring of the surfaces.
Multiple values may be listed for a given plane followed by a number indicating different unique atomic planar cuts for the same theoretical plane.
NIST disclaimer

Version Information:

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

Composition:

Prototype:

a₀:

Download raw data

Surface	γ_fs (mJ/m²)
(322)	0.00
(310)	0.00
(320)	0.00
(100)	0.00
(110)	0.00
(331)	0.00
(111)	0.00
(311)	0.00
(211)	0.00
(332)	0.00
(321)	0.00
(221)	0.00
(210)	0.00

Point Defect Formation Energy Predictions

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

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

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

Notes and Disclaimers:

These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for changes in calculation methods, simulation software and implementations of the interatomic potentials.
The computed formation energy and elastic dipole tensor values are sensitive to the size of the system used. The 12x12x12 supercell size was selected as it should provide a decent approximation of the true bulk values.
The tests for identifying configuration relaxations are not guaranteed to be comprehensive or suitable for all point defect types. The table only shows the point defects that are consistent with the ideal configurations for that defect type, and the lowest energy interstitial.
The "relaxed interstitial" label indicates that the structure is not consistent with any of the known ideal interstitial configurations. No information is provided as to what that relaxed strucutre is, whether it is an unknown structure, a "near"-ideal defect, or a collapse to amorphous.
NIST disclaimer

Composition:

Prototype:

a₀:

Download raw data

Point Defect	E_f (eV)	p₁₁ (eV)	p₂₂ (eV)	p₃₃ (eV)	p₁₂ (eV)	p₁₃ (eV)	p₂₃ (eV)
110 dumbbell	-73.126	0.000	-0.000	-0.000	0.000	0.000	0.000
100 dumbbell	-34.454	-0.000	-0.000	-0.000	0.000	-0.000	0.000
111 dumbbell	-32.619	-0.000	-0.000	-0.000	0.000	0.000	0.000
octahedral interstitial	-20.116	-0.000	-0.000	-0.000	-0.000	0.000	0.000
tetrahedral interstitial	-18.852	-0.000	-0.000	-0.000	0.000	0.000	-0.000
1nn divacancy	0.000	-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
2nn divacancy	0.000	-0.000	-0.000	-0.000	-0.000	-0.000	-0.000
vacancy	0.000	-0.000	-0.000	-0.000	-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:

Download data

Click on plot to load interactive version

Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003/mdsolid.C.A1--Cu--fcc.6a2d0a26.a

Click on plot to load interactive version

Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003//mdsolid.C.A1--Cu--fcc.6a2d0a26.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

Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003/mdliquid.C.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

Tersoff_LAMMPS_AlbeNordlundAverback_2002_PtC__MO_500121566391_003/mdthermo.C.U

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-2.341	-2.340	-117.291	0.000	-19.178	432.597

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-69.203	-69.203	804.105	-0.000	-0.000	-0.000
-18.944	19.412	11.729	-64.962	-0.000	0.000
0.000	0.000	0.001	0.000	-57.394	-61.431
-0.000	-0.000	-0.000	0.000	-61.431	668.496