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.

2020--Jeong-G-U-Lee-B-J--Pd-C

Citation: G.-U. Jeong, and B.-J. Lee (2020), "Interatomic potentials for Pt-C and Pd-C systems and a study of structure-adsorption relationship in large Pt/graphene system", Computational Materials Science 185, 109946. DOI: 10.1016/j.commatsci.2020.109946.

Abstract: Graphene-supported platinum (Pt) and palladium (Pd) nanoclusters have attracted attention as electrocatalysts for proton exchange membrane fuel cell (PEMFC) because of their high activity and resistance to CO poisoning. However, metal nanoparticles are weakly adsorbed to the graphene and easily migrate on the surface, causing sintering and loss of chemical activity. A thorough understanding of structure-adsorption relationship is important to design robust catalysts with high adsorption ability to stabilize metal nanoparticles, but this relationship is still not well understood, particularly in large scale systems (2–5 nm). Therefore, to investigate the structural evolution at atomic scale with atomistic simulations, we have developed interatomic potentials for the Pt-C and Pd-C binary systems, based on the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. These potentials reproduce various fundamental properties of the alloy systems in reasonable agreement with the experimental data and first-principles calculations. Molecular dynamics simulations employing the 2NN MEAM potential were carried out to analyse structural factors that have decisive effect on the adsorption energy, by changing the symmetry of the nanoparticles and the configuration of the nanoparticles adsorbed to graphene. These factors were characterized via coordination numbers, number of Pt atoms in contact with the graphene and adsorption site. The results of our study suggest avenues for stabilizing and immobilizing metal clusters on graphene in large systems.

Related Models:
2005--Lee-B-J-Lee-J-W--C

2006--Lee-B-J--Fe-C

2008--Kim-Y-M-Lee-B-J--Ti-C

2009--Kim-H-K-Jung-W-S-Lee-B-J--Fe-Ti-C

2010--Kim-H-K-Jung-W-S-Lee-B-J--Fe-Nb-C

2010--Kim-H-K-Jung-W-S-Lee-B-J--Nb-C

2020--Jeong-G-U-Lee-B-J--Pt-C
2003--Lee-B-J-Shim-J-H-Baskes-M-I--Pd

2013--Ko-W-S-Lee-B-J--V-Pd-Y

2018--Jeong-G-U-Park-C-S-Do-H-S-et-al--Pd-Al

2018--Jeong-G-U-Park-C-S-Do-H-S-et-al--Pd-Co

2018--Jeong-G-U-Park-C-S-Do-H-S-et-al--Pd-Cu

2018--Jeong-G-U-Park-C-S-Do-H-S-et-al--Pd-Fe

2018--Jeong-G-U-Park-C-S-Do-H-S-et-al--Pd-Mo

2018--Jeong-G-U-Park-C-S-Do-H-S-et-al--Pd-Ni

2018--Jeong-G-U-Park-C-S-Do-H-S-et-al--Pd-Ti
LAMMPS pair_style meam (2020--Jeong-G-U--Pd-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
PdC.meam

Implementation Information

This page displays computed properties for the 2020--Jeong-G-U--Pd-C--LAMMPS--ipr1 implementation of the 2020--Jeong-G-U-Lee-B-J--Pd-C potential. Computed values for other implementations can be seen by clicking on the links below:

2020--Jeong-G-U--Pd-C--LAMMPS--ipr1

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

2020--Jeong-G-U--Pd-C--LAMMPS--ipr1/diatom

Click on plot to load interactive version

2020--Jeong-G-U--Pd-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

2020--Jeong-G-U--Pd-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)
A7--alpha-As	dynamic	-7.4036	-7.4036	2.4546	2.4546	11.0545	90.0	90.0	120.0
mp-568806	dynamic	-7.3959	-7.3959	2.4556	2.4556	3.6684	90.0	90.0	120.0
oqmd-610551	box	-7.3958	-7.3958	2.4553	2.4553	3.6684	90.0	90.0	120.0
A7--alpha-As	box	-7.3902	-7.3902	2.4554	2.4554	10.9361	90.0	90.0	120.0
oqmd-1214690	dynamic	-7.3887	-7.3887	2.4574	4.2469	7.3637	90.0	90.0	90.0
oqmd-683820	box	-7.3887	-7.3887	2.4568	4.248	7.3653	90.0	90.0	90.0
oqmd-683819	box	-7.3887	-7.3887	2.4567	4.248	7.3655	90.0	90.0	90.0
oqmd-1214690	box	-7.3886	-7.3886	2.4563	4.2487	7.3664	90.0	90.0	90.0
mp-937760	box	-7.3886	-7.3886	2.4572	4.2472	7.3696	90.0	90.0	90.0
mp-48	static	-7.3882	-7.3882	2.4554	2.4554	7.269	90.0	90.0	120.0
oqmd-590101	box	-7.3882	-7.3882	2.4554	2.4554	7.269	90.0	90.0	120.0
mp-568286	box	-7.3881	-7.3881	2.456	4.2492	7.3852	90.0	90.0	90.0
oqmd-1215937	box	-7.388	-7.388	2.4554	2.4554	7.2691	90.0	90.0	120.0
mp-568363	box	-7.3852	-7.3852	2.4565	4.2482	7.5068	90.0	90.0	90.0
mp-569416	dynamic	-7.3781	-7.3781	2.454	2.454	57.2026	90.0	90.0	120.0
oqmd-589492	static	-7.3781	-7.3781	2.454	2.454	57.8366	90.0	90.0	120.0
oqmd-589492	dynamic	-7.3781	-7.3781	2.454	2.454	54.4312	90.0	90.0	120.0
mp-569416	static	-7.3781	-7.3781	2.454	2.454	57.7615	90.0	90.0	120.0
mp-569416	box	-7.375	-7.375	2.4545	2.4545	57.5676	90.0	90.0	120.0
oqmd-589492	box	-7.375	-7.375	2.4545	2.4545	57.7433	90.0	90.0	120.0
mp-606949	box	-7.3706	-7.3706	2.4542	2.4542	30.9086	90.0	90.0	120.0
oqmd-589493	box	-7.3706	-7.3706	2.4541	2.4541	31.3601	90.0	90.0	120.0
A4--C--dc	dynamic	-7.37	-7.37	3.5565	3.5565	3.5565	90.0	90.0	90.0
mp-569304	dynamic	-7.3682	-7.3682	2.453	2.453	34.4928	90.0	90.0	120.0
oqmd-589491	static	-7.3682	-7.3682	2.453	2.453	36.378	90.0	90.0	120.0
oqmd-589491	dynamic	-7.3682	-7.3682	2.453	2.453	33.5472	90.0	90.0	120.0
mp-569304	static	-7.3682	-7.3682	2.453	2.453	35.5363	90.0	90.0	120.0
oqmd-589491	box	-7.3627	-7.3627	2.4535	2.4535	35.9984	90.0	90.0	120.0
mp-569304	box	-7.3618	-7.3618	2.4536	2.4536	35.08	90.0	90.0	120.0
mp-616440	dynamic	-7.3595	-7.3595	2.5146	2.5146	16.4546	90.0	90.0	120.0
mp-569567	dynamic	-7.3582	-7.3582	2.5146	2.5146	43.2048	90.0	90.0	120.0
oqmd-599494	static	-7.3581	-7.3581	2.5142	2.5142	43.2164	90.0	90.0	120.0
mp-611448	dynamic	-7.3563	-7.3563	2.5145	2.5145	12.3486	90.0	90.0	120.0
mp-569517	dynamic	-7.3543	-7.3543	2.5143	2.5143	30.8852	90.0	90.0	120.0
oqmd-599492	box	-7.3517	-7.3517	2.5044	2.5044	16.6112	90.0	90.0	120.0
mp-616440	box	-7.3514	-7.3514	2.5042	2.5042	16.6142	90.0	90.0	120.0
oqmd-599490	dynamic	-7.3513	-7.3513	2.5141	2.5141	8.2416	90.0	90.0	120.0
mp-569567	box	-7.3492	-7.3492	2.5032	2.5032	43.6638	90.0	90.0	120.0
mp-611448	box	-7.3463	-7.3463	2.5018	2.5018	12.4936	90.0	90.0	120.0
oqmd-599489	dynamic	-7.3444	-7.3444	2.5135	2.5135	4.1264	90.0	90.0	120.0
mp-569517	box	-7.3426	-7.3426	2.5001	2.5001	31.2918	90.0	90.0	120.0
oqmd-599493	box	-7.3418	-7.3418	2.4998	2.4998	31.3055	90.0	90.0	120.0
mp-611426	box	-7.3375	-7.3375	2.498	2.498	8.3647	90.0	90.0	120.0
mp-1018088	static	-7.3341	-7.3341	4.0031	4.0031	4.0031	90.0	90.0	90.0
mp-997182	dynamic	-7.3335	-7.3335	2.4513	2.4513	12.0458	90.0	90.0	120.0
mp-1040425	dynamic	-7.3335	-7.3335	2.4513	2.4513	19.9983	90.0	90.0	120.0
mp-990448	dynamic	-7.3335	-7.3335	2.4513	2.4513	8.5238	90.0	90.0	120.0
mp-47	box	-7.3197	-7.3197	2.4908	2.4908	4.2157	90.0	90.0	120.0
oqmd-599489	box	-7.3192	-7.3192	2.4906	2.4906	4.2167	90.0	90.0	120.0
oqmd-637443	static	-7.2495	-7.2495	5.1722	5.1722	5.1722	90.0	90.0	90.0
mp-1096869	dynamic	-7.2471	-7.2471	25.4572	14.7005	7.4493	90.0	90.0	90.0
mp-1078845	dynamic	-7.2222	-7.2222	4.2586	8.966	2.463	90.0	90.0	90.0
mp-1008374	box	-7.1418	-7.1418	2.6678	7.8119	2.5224	90.0	90.0	90.0
oqmd-637443	box	-7.0941	-7.0941	5.2116	5.2116	5.2116	90.0	90.0	90.0
mp-1188817	box	-7.087	-7.087	5.2126	5.2126	5.2126	90.0	90.0	90.0
mp-1078845	box	-7.0853	-7.0853	4.3158	8.9323	2.4829	90.0	90.0	90.0
oqmd-610557	box	-7.0564	-7.0564	4.7365	5.6117	4.3375	90.0	90.0	90.0
oqmd-610556	box	-7.0533	-7.0533	4.7355	5.6117	4.3397	90.0	90.0	90.0
mp-568410	box	-7.0497	-7.0497	4.7356	5.6133	4.341	90.0	90.0	90.0
mp-1182684	dynamic	-7.0178	-7.0178	4.8782	9.4732	14.3132	90.0	90.0	90.0
oqmd-637353	box	-7.0125	-7.0125	4.4996	4.4996	2.4535	90.0	90.0	90.0
mp-1008395	box	-7.0095	-7.0095	4.5004	4.5004	2.4538	90.0	90.0	90.0
oqmd-689315	static	-6.9215	-6.9215	8.8931	17.5382	17.8329	90.0	90.0	90.0
mp-683919	static	-6.9215	-6.9215	8.8931	17.5398	17.8316	90.0	90.0	90.0
mp-1245190	dynamic	-6.8896	-6.8896	9.2987	9.4687	9.4808	90.6	94.8	90.1
mp-680372	dynamic	-6.8688	-6.8688	9.1328	9.1328	24.7083	90.0	90.0	120.0
oqmd-614417	static	-6.8688	-6.8688	9.1329	9.1329	24.713	90.0	90.0	120.0
mp-680372	static	-6.8688	-6.8688	9.136	9.136	24.8174	90.0	90.0	120.0
mp-683919	box	-6.8684	-6.8684	10.1639	17.5242	18.0335	90.0	90.0	90.0
oqmd-614417	dynamic	-6.8677	-6.8677	9.1327	9.1327	24.6267	90.0	90.0	120.0
mp-630227	static	-6.8529	-6.8529	9.0541	9.1263	14.823	90.0	90.0	90.0
oqmd-595714	static	-6.8529	-6.8529	9.0541	9.1262	14.8225	90.0	90.0	90.0
mp-1147718	dynamic	-6.8513	-6.8513	10.3519	13.117	9.0774	90.0	90.0	90.0
oqmd-684627	static	-6.85	-6.85	9.0944	9.0944	14.5032	90.0	90.0	90.0
oqmd-689315	box	-6.8468	-6.8468	10.0958	17.5905	18.0366	90.0	90.0	90.0
oqmd-603085	static	-6.8366	-6.8366	13.6553	13.6553	13.6553	90.0	90.0	90.0
mp-1205283	static	-6.8314	-6.8314	9.3275	13.2639	9.0536	90.0	90.0	90.0
oqmd-614417	box	-6.829	-6.829	9.2421	9.2421	24.2629	90.0	90.0	120.0
mp-568028	static	-6.8289	-6.8289	8.2405	14.0283	9.2605	90.0	90.0	90.0
mp-1080826	box	-6.8285	-6.8285	9.4175	2.5749	4.2133	90.0	98.2	90.0
oqmd-637352	box	-6.8269	-6.8269	9.4157	2.5753	4.2139	90.0	98.2	90.0
oqmd-595714	box	-6.8265	-6.8265	9.0922	9.2116	14.6616	90.0	90.0	90.0
mp-680372	box	-6.8262	-6.8262	9.2674	9.2674	25.2892	90.0	90.0	120.0
mp-667273	static	-6.8226	-6.8226	14.2353	14.2353	14.2353	90.0	90.0	90.0
oqmd-677227	dynamic	-6.8226	-6.8226	13.9442	13.9442	13.9442	90.0	90.0	90.0
mp-630227	box	-6.8127	-6.8127	9.0963	9.2025	15.6512	90.0	90.0	90.0
mp-1244964	dynamic	-6.812	-6.812	9.6206	9.7561	10.2231	93.0	92.8	95.0
oqmd-603085	box	-6.8083	-6.8083	13.9525	13.9525	13.9525	90.0	90.0	90.0
mp-1147718	box	-6.8058	-6.8058	10.2719	14.7116	9.2256	90.0	90.0	90.0
mp-1190171	box	-6.805	-6.805	9.3042	2.58	4.2181	90.0	90.0	90.0
oqmd-637130	box	-6.8039	-6.8039	9.3024	2.5804	4.2184	90.0	90.0	90.0
mp-667273	box	-6.8027	-6.8027	14.4166	14.4166	14.4166	90.0	90.0	90.0
mp-1197903	dynamic	-6.8009	-6.8009	6.3956	6.7196	18.3106	98.4	93.1	95.4
oqmd-677227	box	-6.7948	-6.7948	14.1406	14.1406	14.1406	90.0	90.0	90.0
mp-1196583	box	-6.7937	-6.7937	14.3577	14.3577	14.3577	90.0	90.0	90.0
oqmd-684627	box	-6.793	-6.793	9.176	9.176	15.276	90.0	90.0	90.0
mp-1244913	dynamic	-6.7758	-6.7758	8.7597	9.9136	11.0921	100.0	97.1	95.0
mp-624889	box	-6.678	-6.678	4.7327	5.1652	5.668	90.0	90.0	90.0
oqmd-610552	box	-6.5849	-6.5849	4.7338	5.2685	6.5227	90.0	90.0	90.0
mp-568028	box	-6.5807	-6.5807	8.6235	14.2731	9.6082	90.0	90.0	90.0
mp-579909	box	-6.5756	-6.5756	4.733	5.267	6.9465	90.0	90.0	90.0
mp-1192619	dynamic	-6.5706	-6.5706	7.8231	7.8231	7.8231	90.0	90.0	90.0
mp-1244964	static	-6.5359	-6.5359	9.4886	9.7803	10.8458	86.4	87.9	88.8
mp-1245190	static	-6.5097	-6.5097	9.5268	10.1664	10.175	88.8	88.4	85.8
oqmd-684315	static	-6.4499	-6.4499	9.2975	15.7255	8.9377	90.0	90.0	90.0
mp-1244913	static	-6.3907	-6.3907	9.5275	10.2571	10.3803	82.7	82.9	88.9
mp-570002	static	-6.2284	-6.2284	5.0331	5.0331	5.0331	90.0	90.0	90.0
mp-24	box	-5.9897	-5.9897	4.689	4.689	4.689	90.0	90.0	90.0
mp-1196857	static	-5.73	-5.73	6.254	18.177	5.337	90.0	90.0	90.0
mp-1205283	box	-5.7105	-5.7105	11.3543	13.4589	9.3143	90.0	90.0	90.0
mp-1056957	static	-5.6229	-5.6229	6.5479	3.1893	2.348	90.0	90.0	90.0
oqmd-585286	box	-5.4434	-5.4434	5.3564	5.3564	5.3564	90.0	90.0	90.0
mp-570002	box	-5.4423	-5.4423	5.3568	5.3568	5.3568	90.0	90.0	90.0
mp-1196857	box	-5.4349	-5.4349	8.7148	19.2545	6.2116	90.0	90.0	90.0
mp-1197903	static	-5.4148	-5.4148	7.305	15.6235	20.2063	76.4	88.4	77.3
oqmd-684315	box	-5.3916	-5.3916	10.6355	15.6983	9.6466	90.0	90.0	90.0
mp-1095633	dynamic	-4.7619	-4.7619	8.2091	8.2091	14.3	90.0	90.0	90.0
mp-1095633	static	-4.7619	-4.7619	7.8471	7.8471	14.2615	90.0	90.0	90.0
A7--alpha-As	box	-4.3092	-4.3092	2.8301	2.8301	7.2453	90.0	90.0	120.0
A3'--alpha-La--double-hcp	box	-3.9973	-3.9973	2.8086	2.8086	4.9645	90.0	90.0	120.0
A5--beta-Sn	static	-3.953	-3.953	3.8633	3.8633	2.1405	90.0	90.0	90.0
Ah--alpha-Po--sc	static	-3.8984	-3.8984	2.0684	2.0684	2.0684	90.0	90.0	90.0
mp-1095534	box	-3.7946	-3.7946	13.0965	13.0965	2.6067	90.0	90.0	90.0
A6--In--bct	static	-3.6933	-3.6933	2.0015	2.0015	6.2095	90.0	90.0	90.0
mp-1205417	box	-3.5761	-3.5761	17.3176	17.3176	10.1475	90.0	90.0	90.0
oqmd-1214868	static	-3.5069	-3.5069	9.5421	9.5421	9.5421	90.0	90.0	90.0
mp-1192619	box	-3.4108	-3.4108	13.1054	13.1054	13.1054	90.0	90.0	90.0
mp-1097832	static	-3.4035	-3.4035	2.9722	2.9722	9.8799	90.0	90.0	90.0
A2--W--bcc	static	-2.9173	-2.9173	2.6077	2.6077	2.6077	90.0	90.0	90.0
A3--Mg--hcp	box	-2.8568	-2.8568	2.2337	2.2337	5.7752	90.0	90.0	120.0
mp-1095633	box	-2.6964	-2.6964	16.8903	16.8903	3.8226	90.0	90.0	90.0
A3--Mg--hcp	box	-2.529	-2.529	2.3834	2.3834	3.9133	90.0	90.0	120.0
A3'--alpha-La--double-hcp	box	-2.5271	-2.5271	2.3863	2.3863	7.8152	90.0	90.0	120.0
A1--Cu--fcc	static	-2.5252	-2.5252	3.3791	3.3791	3.3791	90.0	90.0	90.0
A15--beta-W	static	-2.4762	-2.4762	4.3042	4.3042	4.3042	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	-5.7907	-5.7907	5.1179	5.1179	5.1179	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	-4.4601	-4.4601	5.5583	5.5583	5.5583	90.0	90.0	90.0
A15--Cr3Si	static	-4.3451	-4.3451	4.378	4.378	4.378	90.0	90.0	90.0
L1_2--AuCu3	static	-4.1449	-4.1449	3.4593	3.4593	3.4593	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)
B3--ZnS--cubic-zinc-blende	dynamic	-5.625	-5.625	4.919	4.919	4.919	90.0	90.0	90.0
B1--NaCl--rock-salt	static	-4.5687	-4.5687	4.5624	4.5624	4.5624	90.0	90.0	90.0
B2--CsCl	box	-3.9648	-3.9648	2.8116	2.8116	2.8116	90.0	90.0	90.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
C1--CaF2--fluorite	static	-3.8695	-3.8695	5.3108	5.3108	5.3108	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	static	-4.2149	-4.2149	3.8932	3.8932	3.8932	90.0	90.0	90.0
D0_3--BiF3	static	-4.0794	-4.0794	6.2552	6.2552	6.2552	90.0	90.0	90.0
A15--Cr3Si	static	-4.0075	-4.0075	5.0524	5.0524	5.0524	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)
A1--Cu--fcc	dynamic	-3.91	-3.91	3.8891	3.8891	3.8891	90.0	90.0	90.0
A3'--alpha-La--double-hcp	dynamic	-3.8998	-3.8998	2.745	2.745	9.0218	90.0	90.0	120.0
oqmd-1216074	dynamic	-3.8966	-3.8966	2.7435	2.7435	20.3279	90.0	90.0	120.0
oqmd-1216074	static	-3.8965	-3.8965	2.7435	2.7435	20.3284	90.0	90.0	120.0
A3--Mg--hcp	dynamic	-3.89	-3.89	2.7405	2.7405	4.53	90.0	90.0	120.0
oqmd-1215269	box	-3.8837	-3.8837	2.7207	4.7729	4.5454	90.0	90.0	90.0
oqmd-1214913	dynamic	-3.7823	-3.7823	6.7175	6.7175	6.7175	90.0	90.0	90.0
oqmd-1214913	box	-3.7777	-3.7777	6.7187	6.7187	6.7187	90.0	90.0	90.0
oqmd-1214824	dynamic	-3.7408	-3.7408	9.5665	9.5665	9.5665	90.0	90.0	90.0
A2--W--bcc	static	-3.7405	-3.7405	3.0439	3.0439	3.0439	90.0	90.0	90.0
A15--beta-W	dynamic	-3.7241	-3.7241	4.9586	4.9586	4.9586	90.0	90.0	90.0
oqmd-1214735	box	-3.5184	-3.5184	3.7463	9.2715	3.7458	90.0	90.0	90.0
Ah--alpha-Po--sc	dynamic	-3.4993	-3.4993	2.56	2.56	2.56	90.0	90.0	90.0
A5--beta-Sn	dynamic	-3.3904	-3.3904	4.996	4.996	2.5632	90.0	90.0	90.0
oqmd-1215982	dynamic	-2.9684	-2.9684	4.3679	4.3679	4.9796	90.0	90.0	120.0
A4--C--dc	static	-2.8004	-2.8004	5.8392	5.8392	5.8392	90.0	90.0	90.0
A15--beta-W	box	-1.0508	-1.0508	7.3204	7.3204	7.3204	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:

215.083	274.485	274.485	-0.000	-0.000	-0.000
274.485	215.083	274.485	-0.000	-0.000	-0.000
274.485	274.485	215.083	-0.000	-0.000	-0.000
0.000	-0.000	-0.000	-79.797	-0.000	-0.000
-0.000	0.000	-0.000	-0.000	-79.797	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-79.797

215.083	274.485	274.485	0.000	0.000	0.000
274.485	215.083	274.485	0.000	0.000	0.000
274.485	274.485	215.083	0.000	0.000	0.000
-0.000	-0.000	-0.000	-79.797	0.000	0.000
-0.000	-0.000	0.000	0.000	-79.797	0.000
0.000	0.000	-0.000	0.000	0.000	-79.797

215.083	274.485	274.485	0.000	0.000	0.000
274.485	215.083	274.485	0.000	0.000	0.000
274.485	274.485	215.083	0.000	0.000	0.000
-0.000	-0.000	-0.000	-79.797	0.000	0.000
-0.000	-0.000	-0.000	0.000	-79.797	0.000
-0.000	-0.000	-0.000	0.000	0.000	-79.797

215.084	274.486	274.486	-0.000	-0.000	-0.000
274.486	215.084	274.486	-0.000	-0.000	-0.000
274.486	274.486	215.084	-0.000	-0.000	-0.000
0.000	0.000	0.000	-79.797	-0.000	-0.000
0.000	0.000	0.000	-0.000	-79.797	-0.000
0.000	0.000	0.000	-0.000	-0.000	-79.797

215.082	274.484	274.484	0.000	0.000	0.000
274.484	215.082	274.484	0.000	0.000	0.000
274.484	274.484	215.082	0.000	0.000	0.000
-0.000	-0.000	-0.000	-79.797	0.000	0.000
-0.000	-0.000	-0.000	0.000	-79.797	0.000
-0.000	-0.000	-0.000	0.000	0.000	-79.797

57.181	313.286	313.286	0.000	-0.000	0.000
313.286	57.181	313.286	-0.000	-0.000	0.000
313.286	313.286	57.181	-0.000	0.000	0.000
-0.000	-0.000	-0.000	-340.730	0.000	-0.000
-0.000	-0.000	-0.000	-0.000	-340.730	-0.000
-0.000	-0.000	-0.000	-0.000	-0.000	-340.730

59.281	312.236	312.236	0.000	-0.000	0.000
312.236	59.281	312.236	0.000	-0.000	0.000
312.236	312.236	59.281	0.000	0.000	0.000
0.000	0.000	0.000	-340.730	0.000	0.000
0.000	0.000	0.000	0.000	-340.730	0.000
0.000	0.000	0.000	0.000	-0.000	-340.730

57.181	313.286	313.286	-0.000	0.000	0.000
313.286	57.181	313.286	0.000	-0.000	0.000
313.286	313.286	57.181	0.000	-0.000	0.000
-133966555.360	-144830668.631	-145699880.328	-11502603.916	2344633.080	-1669877.380
-139807217.050	-147797190.615	-142610063.657	-293088.989	-16714607.704	-3322061.838
-145240277.207	-135823162.647	-144305935.723	-1390171.253	-1073916.130	-13736942.532

57.181	313.286	313.286	0.000	0.000	-0.000
313.286	57.181	313.286	-0.000	0.000	-0.000
313.286	313.286	57.181	-0.000	0.000	-0.000
141235475.609	134855267.467	136776889.614	-12546859.673	-3013526.471	-726619.206
141072349.954	140728910.596	136279006.112	-5640796.654	-14727811.943	-390318.348
132312895.186	147085835.692	138915073.327	-5933087.010	1107754.213	-12144399.637

57.182	313.287	313.287	-0.000	-0.000	0.000
313.287	57.182	313.287	0.000	0.000	0.000
313.287	313.287	57.182	0.000	-0.000	0.000
-13860712.253	-14117641.230	-13964728.756	-1166485.596	552344.396	349585.551
-14183490.013	-14777745.027	-13892915.675	625965.622	-1274479.712	531527.138
-13603886.621	-13621368.779	-13295628.907	-434826.509	-470216.010	-1570280.383

57.180	313.285	313.285	0.000	0.000	-0.000
313.285	57.180	313.285	-0.000	0.000	-0.000
313.285	313.285	57.180	0.000	0.000	-0.000
13337606.638	13595284.060	13190732.097	-1321492.799	-543689.159	-51361.166
13141195.745	13914656.024	13813607.211	392085.902	-1272997.222	-140426.347
13409001.212	14108440.445	12958928.323	193656.637	4916.791	-936039.754

1369.885	-242.672	-242.672	-0.000	-0.000	0.000
-242.672	1369.885	-242.672	-0.000	-0.000	-0.000
-242.672	-242.672	1369.885	-0.000	-0.000	0.000
-0.000	0.000	0.000	-244.296	0.000	0.000
0.000	-0.000	0.000	-0.000	-244.296	-0.000
0.000	0.000	-0.000	0.000	-0.000	-244.296

1369.885	-242.672	-242.672	0.000	0.000	-0.000
-242.672	1369.885	-242.672	0.000	0.000	-0.000
-242.672	-242.672	1369.885	0.000	0.000	-0.000
0.000	-0.000	-0.000	-244.296	0.000	0.000
-0.000	0.000	-0.000	0.000	-244.296	-0.000
-0.000	-0.000	0.000	0.000	0.000	-244.296

1369.886	-242.672	-242.672	0.000	-0.000	-0.000
-242.672	1369.886	-242.672	-0.000	0.000	-0.000
-242.672	-242.672	1369.886	0.000	0.000	-0.000
-0.000	0.000	0.000	-244.296	0.000	-0.000
0.000	-0.000	0.000	-0.000	-244.296	-0.000
0.000	0.000	-0.000	-0.000	0.000	-244.296

1369.884	-242.672	-242.672	0.000	0.000	0.000
-242.672	1369.884	-242.672	0.000	0.000	0.000
-242.672	-242.672	1369.884	0.000	0.000	0.000
0.000	-0.000	-0.000	-244.296	0.000	-0.000
-0.000	0.000	-0.000	0.000	-244.296	0.000
-0.000	-0.000	0.000	-0.000	0.000	-244.296

1369.893	-242.670	-242.670	0.000	-0.000	0.000
-242.670	1369.893	-242.670	-0.000	-0.000	-0.000
-242.670	-242.670	1369.893	-0.000	-0.000	0.000
-0.002	0.001	0.000	-244.296	0.000	0.000
0.001	-0.002	0.000	0.000	-244.296	0.000
0.001	0.000	-0.002	-0.000	-0.000	-244.296

1369.878	-242.673	-242.673	0.000	0.000	-0.000
-242.673	1369.878	-242.673	0.000	0.000	0.000
-242.673	-242.673	1369.878	0.000	0.000	0.000
0.002	-0.001	-0.000	-244.296	0.000	-0.000
-0.001	0.002	-0.000	0.000	-244.296	-0.000
-0.001	-0.000	0.002	0.000	0.000	-244.296

164.891	297.326	307.380	0.000	-0.000	-0.000
316.732	145.485	307.380	0.000	-0.000	-0.000
307.380	307.380	139.245	0.000	0.000	-0.000
0.000	-0.000	-0.000	-55.159	-0.000	-0.000
0.000	-0.000	-0.000	0.000	-55.159	-0.000
0.000	0.000	0.000	0.000	0.000	-66.217

164.891	297.326	307.380	-0.000	0.000	0.000
1388969716.779	1221774298.204	1074980197.274	50109774.771	54201488.540	34238145.075
307.380	307.380	139.245	-0.000	0.000	0.000
-0.000	0.000	0.000	-55.159	0.000	0.000
-0.000	0.000	0.000	-0.000	-55.159	-0.000
-0.000	-0.000	-0.000	-0.000	0.000	-66.217

164.891	297.326	307.380	-0.000	0.000	-0.000
297.326	164.891	307.380	-0.000	-0.000	0.000
307.380	307.380	139.245	0.000	0.000	-0.000
0.000	0.000	-0.000	-55.159	-0.000	-0.000
0.000	0.000	-0.000	0.000	-55.159	-0.000
0.000	-0.000	0.000	0.000	-0.000	-66.217

145.485	316.732	307.380	-0.000	0.000	0.000
316.732	145.485	307.380	-0.000	-0.000	0.000
307.380	307.380	139.245	0.000	-0.000	0.000
-0.000	-0.000	0.000	-55.159	0.000	0.000
-0.000	-0.000	0.000	-0.000	-55.159	-0.000
-0.000	0.000	-0.000	-0.000	-0.000	-66.217

-14736386.456	-11213270.799	-9377390.493	343311.993	-136752.950	272951.906
-15705071.076	-17954357.672	-10931024.707	-219188.474	161345.403	830217.105
307.381	307.381	139.246	0.000	0.000	-0.000
0.000	0.000	-0.000	-55.159	-0.000	-0.000
0.000	0.000	-0.000	0.000	-55.159	-0.000
-16704067.188	-15064568.922	-11167612.082	-113146.321	133590.785	-538676.809

15733529.081	17125179.579	10858495.862	367113.802	-32246.235	-958944.054
297.325	164.890	307.379	-0.000	0.000	-0.000
307.379	307.379	139.244	0.000	-0.000	0.000
-0.000	-0.000	0.000	-55.159	-0.000	0.000
-0.000	-0.000	0.000	-0.000	-55.159	0.000
16120645.372	15280289.188	10102244.210	-180899.867	-171776.410	-1596464.598

581.389	380.434	-0.637	-0.000	-0.000	0.000
429.073	532.750	-0.637	-0.000	-0.000	0.000
-0.637	-0.637	1064.200	-0.000	0.000	-0.000
0.000	0.000	0.000	-34.025	-0.000	0.000
0.000	0.000	0.000	-0.000	-34.025	0.000
0.000	0.000	0.000	0.000	0.000	51.839

581.389	380.434	-0.637	0.000	-0.000	-0.000
429.073	532.750	-0.637	-0.000	-0.000	-0.000
-0.637	-0.637	1064.200	0.000	-0.000	-0.000
0.000	-0.000	-0.000	-34.025	-0.000	-0.000
-0.000	-0.000	-0.000	0.000	-34.025	0.000
-0.000	-0.000	-0.000	0.000	0.000	51.839

532.751	429.072	-0.638	0.000	0.000	0.000
429.073	532.751	-0.638	0.000	0.000	0.000
-0.637	-0.637	1064.201	-0.000	0.000	0.000
0.000	0.000	-0.000	-34.025	0.000	-0.000
0.000	0.000	-0.000	-0.000	-34.025	0.000
0.000	0.000	-0.000	0.000	0.000	51.839

581.389	380.433	-0.638	0.000	-0.000	-0.000
429.073	532.749	-0.637	0.000	-0.000	-0.000
-0.637	-0.637	1064.199	0.000	-0.000	0.000
-0.000	-0.000	0.000	-34.025	-0.000	0.000
-0.000	-0.000	-0.000	0.000	-34.025	0.000
-0.000	-0.000	0.000	-0.000	-0.000	51.839

532.762	429.069	-0.638	-0.000	0.000	-0.000
429.074	532.757	-0.638	-0.000	0.000	0.000
-0.639	-0.639	1064.209	-0.000	0.000	0.000
0.000	0.001	-0.000	-34.025	0.000	0.000
0.001	0.000	-0.000	-0.000	-34.025	0.000
0.002	0.003	-0.002	0.000	0.000	51.839

581.387	380.433	-0.638	0.000	-0.000	0.000
429.072	532.743	-0.637	0.000	0.000	-0.000
-0.636	-0.636	1064.191	-0.000	0.000	-0.000
-0.000	-0.001	0.000	-34.025	-0.000	-0.000
-0.001	-0.000	0.000	0.000	-34.025	-0.000
-0.002	-0.003	0.002	-0.000	-0.000	51.839

247.582	358.616	-110.939	0.000	0.000	-0.000
364.969	241.229	-110.939	-0.000	0.000	-0.000
-110.938	-110.938	107.853	-0.000	0.000	-0.000
0.000	0.000	-0.000	134.909	0.000	0.000
0.000	0.000	-0.000	0.000	134.909	0.000
0.000	-0.000	0.000	0.000	0.000	-61.870

241.229	364.969	-110.939	-0.000	-0.000	0.000
358.616	247.582	-110.939	-0.000	-0.000	0.000
-110.938	-110.938	107.853	-0.000	-0.000	0.000
-0.000	-0.000	0.000	134.909	-0.000	0.000
-0.000	-0.000	0.000	-0.000	134.909	0.000
-0.000	0.000	0.000	-0.000	-0.000	-61.870

241.229	364.969	-110.939	0.000	0.000	0.000
364.969	241.229	-110.939	0.000	0.000	0.000
-110.938	-110.938	107.853	0.000	0.000	-0.000
0.000	0.000	-0.000	134.909	0.000	-0.000
0.000	0.000	-0.000	0.000	134.909	-0.000
0.000	0.000	-0.000	0.000	0.000	-55.517

241.229	364.969	-110.939	-0.000	-0.000	0.000
364.969	241.229	-110.939	0.000	-0.000	0.000
-110.938	-110.938	107.853	0.000	0.000	0.000
-0.000	-0.000	0.000	134.909	-0.000	0.000
-0.000	-0.000	0.000	-0.000	134.909	-0.000
-0.000	-0.000	0.000	-0.000	-0.000	-55.517

241.230	364.971	-110.939	0.000	0.000	-0.000
358.617	247.584	-110.939	0.000	0.000	-0.000
-110.938	-110.938	107.853	0.000	-0.000	-0.000
0.001	0.001	-0.001	134.909	0.000	0.000
0.001	0.001	-0.001	0.000	134.909	0.000
0.000	0.000	-0.000	0.000	0.000	-61.870

241.228	364.968	-110.939	-0.000	-0.000	0.000
364.968	241.228	-110.939	-0.000	-0.000	0.000
-110.938	-110.938	107.853	-0.000	-0.000	0.000
-0.001	-0.001	0.001	134.909	-0.000	0.000
-0.001	-0.001	0.001	0.000	134.909	-0.000
-0.000	-0.000	0.000	-0.000	-0.000	-61.870

122.505	345.611	306.855	0.000	0.000	0.000
345.611	122.505	306.855	0.000	0.000	0.000
306.855	306.855	130.403	0.000	0.000	0.000
-0.000	0.000	-0.000	-63.777	0.000	0.000
-0.000	0.000	-0.000	0.000	-63.777	-0.000
-1685916920.884	-1722900493.268	-1018863880.157	-23488394.016	-178440.361	-26241320.477

164.750	303.366	306.855	0.000	0.000	0.000
303.366	164.750	306.855	-0.000	-0.000	0.000
306.855	306.855	130.403	-0.000	-0.000	-0.000
0.000	-0.000	0.000	-63.777	-0.000	-0.000
0.000	-0.000	0.000	-0.000	-63.777	-0.000
1734099583.205	1662307426.343	978769921.614	-11245302.429	-20013806.145	-27730225.502

164.751	303.366	306.855	-0.000	-0.000	-0.000
-171022818.254	-174670960.653	-104309483.575	-1279046.950	-1614082.983	-1280530.356
306.855	306.855	130.403	0.000	0.000	0.000
0.000	0.000	-0.000	-63.777	0.000	0.000
-0.000	0.000	-0.000	0.000	-63.777	-0.000
0.000	-0.000	0.000	0.000	0.000	-69.308

164023626.792	186567504.324	102368150.176	1035187.770	-8624710.903	4407656.619
303.366	164.750	306.855	-0.000	-0.000	0.000
306.855	306.855	130.403	-0.000	-0.000	-0.000
-0.000	-0.000	0.000	-63.777	-0.000	-0.000
0.000	-0.000	0.000	-0.000	-63.777	-0.000
-0.000	0.000	-0.000	-0.000	-0.000	-69.308

-12962440.748	-11994476.289	-8726722.121	-92260.382	-347678.534	-382604.528
-17128198.539	-17436786.722	-10001120.409	-148866.232	176390.832	-551200.713
306.856	306.856	130.404	0.000	0.000	0.000
0.000	0.000	-0.000	-63.777	0.000	-0.000
0.000	0.000	-0.000	0.000	-63.777	0.000
-17863815.325	-15106816.758	-9785818.332	154027.164	58949.916	-337927.712

17551414.692	18088284.657	10287893.039	-91744.979	-276440.407	1077807.656
13376214.150	12212851.461	8403649.940	-197342.820	-114557.832	194808.923
306.854	306.854	130.402	-0.000	-0.000	-0.000
-0.000	-0.000	0.000	-63.777	-0.000	0.000
-0.000	-0.000	0.000	-0.000	-63.777	0.000
17977994.459	17254025.076	10074563.198	-310397.910	-356592.960	-1644842.747

1079.339	127.221	127.221	-0.000	-0.000	-0.000
127.221	1079.339	127.221	-0.000	-0.000	-0.000
127.221	127.221	1079.339	-0.000	-0.000	-0.000
0.000	0.000	0.000	622.673	-0.000	-0.000
0.000	0.000	0.000	-0.000	622.673	-0.000
0.000	0.000	0.000	-0.000	-0.000	622.673

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

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Plot:

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2020--Jeong-G-U--Pd-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:

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Surface	γ_fs (mJ/m²)
(0001) 2	218.03
(1011) 2	3906.01
(2112) 2	4267.59
(2131) 2	4329.24
(1121) 2	4336.42
(2241) 2	4351.68
(1120)	4353.73
(2241) 1	4659.22
(2132) 2	4682.12
(2130)	4728.11
(2112) 1	4868.01
(1121) 1	4948.70
(1012) 2	4986.53
(2132) 1	5069.24
(2021) 2	5273.23
(1010)	5280.18
(2131) 1	5509.03
(2021) 1	5938.65
(1012) 1	6242.33
(0001) 1	6562.27
(1011) 1	7848.31

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	1.503	-4.792	-4.792	-4.792	-0.000	0.000	0.000
1nn divacancy	3.005	-7.949	-8.607	-8.607	-0.000	-0.000	0.325
2nn divacancy	3.048	-10.124	-10.124	-9.816	-0.000	-0.000	-0.000
100 dumbbell	4.706	34.575	34.575	32.693	-0.000	0.000	0.000
octahedral interstitial	5.042	33.677	33.677	33.677	-0.000	-0.000	-0.000
crowdion interstitial	5.607	32.618	32.618	35.620	17.454	0.000	0.000
111 dumbbell	5.651	36.381	36.381	36.381	1.970	1.970	1.970
tetrahedral interstitial	6.682	36.236	36.236	36.236	-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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2020--Jeong-G-U--Pd-C--LAMMPS--ipr1/mdsolid.C.A4--C--dc.d5f8bcfa.a

Click on plot to load interactive version

2020--Jeong-G-U--Pd-C--LAMMPS--ipr1//mdsolid.C.A4--C--dc.d5f8bcfa.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:

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2020--Jeong-G-U--Pd-C--LAMMPS--ipr1/mdliquid.Pd.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:

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2020--Jeong-G-U--Pd-C--LAMMPS--ipr1/mdthermo.C.U

1079.342	127.221	127.221	-0.000	-0.000	-0.000
127.221	1079.342	127.221	-0.000	-0.000	-0.000
127.221	127.221	1079.342	-0.000	-0.000	-0.000
0.000	0.001	0.001	622.673	-0.000	-0.000
0.001	0.000	0.001	-0.000	622.673	-0.000
0.001	0.001	0.000	-0.000	-0.000	622.673

1079.336	127.220	127.220	0.000	0.000	0.000
127.220	1079.336	127.220	0.000	0.000	0.000
127.220	127.220	1079.336	0.000	0.000	0.000
-0.000	-0.001	-0.001	622.673	0.000	0.000
-0.001	-0.000	-0.001	0.000	622.673	0.000
-0.001	-0.001	-0.000	0.000	0.000	622.673

463.488	342.744	269.870	-0.000	0.000	0.000
342.745	463.488	269.870	-0.000	0.000	0.000
269.871	269.869	496.193	-0.000	0.000	0.000
0.001	-0.001	0.000	-1964.027	0.000	0.000
0.002	-0.002	0.000	-0.000	-1964.027	0.000
0.001	-0.001	0.000	-0.000	0.000	114.030

463.489	342.745	269.870	-0.000	0.000	0.000
342.745	463.489	269.870	-0.000	0.000	0.000
269.870	269.870	496.193	-0.000	0.000	0.000
-0.003	0.006	0.001	-1964.027	0.000	0.000
0.006	-0.003	0.001	-0.000	-1964.027	0.000
0.000	-0.000	-0.000	-0.000	0.000	114.030

463.492	342.746	269.871	-0.000	0.000	0.000
342.746	463.492	269.871	-0.000	0.000	0.000
269.871	269.871	496.197	-0.000	0.000	0.000
-0.029	0.058	0.008	-1964.026	0.000	0.000
0.058	-0.029	0.008	-0.000	-1964.026	0.000
-0.000	0.000	-0.000	-0.000	0.000	114.030

463.484	342.743	269.869	0.000	-0.000	0.000
342.743	463.484	269.869	0.000	0.000	-0.000
269.869	269.869	496.189	0.000	-0.000	-0.000
0.029	-0.058	-0.008	-1964.026	-0.000	-0.000
-0.058	0.029	-0.008	0.000	-1964.026	-0.000
0.000	-0.000	0.000	-0.000	-0.000	114.030

452.276	304.229	-72.915	0.000	-0.000	0.000
304.229	452.276	-72.915	0.000	-0.000	-0.000
-72.915	-72.915	126.682	0.000	0.000	-0.000
0.000	0.000	-0.000	327.873	-0.000	0.000
0.000	0.000	-0.000	0.000	327.873	-0.000
0.000	0.000	-0.000	0.000	0.000	97.018

452.277	304.229	-72.915	0.000	-0.000	-0.000
304.229	452.277	-72.915	0.000	-0.000	-0.000
-72.915	-72.915	126.682	0.000	-0.000	0.000
0.000	0.000	-0.000	327.873	-0.000	-0.000
0.000	0.000	-0.000	0.000	327.873	0.000
0.000	0.000	-0.000	0.000	-0.000	97.018

452.280	304.230	-72.915	0.000	-0.000	0.000
304.230	452.280	-72.915	0.000	0.000	-0.000
-72.915	-72.915	126.682	0.000	-0.000	0.000
0.002	0.002	-0.001	327.873	-0.000	0.000
0.002	0.002	-0.001	0.000	327.873	0.000
0.000	0.000	-0.000	0.000	-0.000	97.018

452.272	304.229	-72.915	-0.000	0.000	-0.000
304.229	452.272	-72.915	-0.000	0.000	0.000
-72.915	-72.915	126.681	-0.000	0.000	-0.000
-0.002	-0.002	0.001	327.873	0.000	0.000
-0.002	-0.002	0.001	-0.000	327.873	-0.000
-0.000	-0.000	0.000	-0.000	0.000	97.018

899.326	113.518	28.767	25.203	0.000	-0.000
113.518	899.326	28.767	-25.203	0.000	-0.000
9.857	9.857	51.050	0.000	0.000	-0.000
20.346	-20.346	-0.000	283.269	-0.000	-0.000
20.576	20.576	28.994	-0.000	283.046	27.637
-0.000	0.000	0.000	-0.000	20.346	551.319

1044.321	-58.317	9.857	20.346	-0.000	0.000
89.328	868.062	-10.303	-25.312	0.000	0.000
9.857	9.857	51.050	0.000	-0.000	0.000
1.852	-43.027	-29.010	283.205	0.000	0.000
-20.576	-20.576	-28.994	0.000	283.046	27.637
0.000	-0.000	-0.000	0.000	20.346	551.319

1044.322	-58.317	9.857	20.346	0.000	-0.000
11.607	975.348	10.526	-22.476	-0.000	-0.000
9.857	9.857	51.050	-0.000	0.000	0.000
29.209	-25.308	2.749	283.057	0.000	-0.000
-0.000	-0.000	0.000	-0.000	283.269	20.346
0.608	0.608	0.857	0.000	22.501	481.042

975.826	9.730	9.538	22.439	-0.000	-0.000
9.931	975.947	9.766	-22.441	0.000	-0.000
9.454	9.454	50.482	-0.000	-0.000	-0.000
22.645	-22.234	0.290	283.208	0.000	-0.000
0.075	0.075	0.106	-0.003	283.187	23.020
0.206	0.206	0.290	0.000	22.440	483.039

975.378	9.348	8.958	22.441	0.000	0.000
10.192	975.441	9.598	-22.452	0.000	0.000
9.042	9.042	49.901	-0.000	-0.000	0.000
22.236	-22.647	-0.290	283.202	0.000	0.000
-0.075	-0.075	-0.106	0.003	283.187	23.020
-0.206	-0.206	-0.290	-0.000	22.440	483.039

984.104	9.407	10.641	22.944	-0.000	-0.000
9.778	984.339	11.004	-22.946	-0.000	-0.000
10.380	10.380	57.124	0.000	-0.000	0.000
22.960	-22.943	0.010	279.117	-0.000	-0.000
0.002	0.014	0.010	0.000	279.117	22.958
0.000	0.000	-0.000	0.000	20.982	555.715

984.298	9.786	10.984	22.947	0.000	0.000
9.347	984.044	10.569	-22.944	-0.000	0.000
9.829	9.787	56.438	-0.001	-0.000	0.001
20.982	-20.982	0.000	279.173	0.000	-0.000
-0.002	-0.014	-0.010	-0.000	279.117	22.958
0.000	-0.000	0.000	0.000	20.982	555.715

984.062	9.395	10.608	22.944	-0.000	-0.000
9.374	984.083	10.608	-22.944	0.000	-0.000
9.839	9.843	56.477	0.000	0.000	-0.000
20.982	-20.982	0.000	279.174	-0.000	0.000
0.000	0.001	0.001	-0.000	279.117	22.944
-0.000	0.000	-0.000	0.000	20.982	555.715

984.104	9.340	10.601	22.943	0.000	0.000
9.788	984.311	10.993	-22.947	0.000	0.000
9.837	9.833	56.470	-0.000	-0.000	0.000
20.982	-20.982	-0.000	279.173	0.000	-0.000
-0.000	-0.001	-0.001	0.000	279.117	22.944
0.000	-0.000	0.000	-0.000	20.982	555.715

983.496	10.606	10.993	22.970	-0.000	-0.000
9.573	984.532	10.995	-22.940	0.000	-0.000
10.380	10.380	57.124	0.000	-0.000	0.000
22.944	-22.944	0.000	279.120	-0.000	-0.000
-0.000	-0.000	0.000	-0.003	279.173	20.982
-0.000	0.001	0.000	0.000	22.944	487.354

2020--Jeong-G-U-Lee-B-J--Pd-C

C 7

Pd 9

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

984.302	9.794	10.994	22.947	-0.000	0.000
10.656	983.438	10.992	-22.971	0.000	0.000
10.380	10.380	57.123	0.000	0.000	-0.000
20.983	-20.982	-0.000	279.171	0.000	0.000
0.000	0.000	-0.000	0.003	279.173	20.982
0.000	-0.001	-0.000	-0.000	22.944	487.354

1055.923	-58.405	11.555	21.185	-0.000	-0.000
-58.405	1055.923	11.555	-21.185	-0.000	-0.000
10.625	10.625	58.971	0.000	0.000	-0.000
21.185	-21.185	0.000	277.647	0.000	-0.000
0.000	-0.000	0.000	-0.000	277.647	21.185
0.000	0.000	-0.000	0.000	21.185	557.164

987.296	10.027	11.444	23.090	0.000	0.000
9.946	987.378	11.445	-23.088	-0.000	0.000
10.625	10.625	58.971	0.000	0.000	-0.000
23.311	-23.242	0.039	277.589	0.000	0.000
-0.000	-0.000	0.000	-0.000	277.647	21.185
-0.000	0.000	-0.000	0.000	21.185	557.164

987.037	9.336	10.907	23.084	-0.000	-0.000
9.416	986.957	10.907	-23.086	-0.000	-0.000
10.625	10.625	58.971	0.000	0.000	0.000
21.185	-21.185	-0.000	277.647	-0.000	0.000
0.000	0.000	-0.000	0.000	277.647	21.185
0.000	-0.000	0.000	-0.000	21.185	557.164

1055.928	-58.406	11.555	21.185	-0.000	-0.000
9.960	987.310	11.413	-23.089	0.000	0.000
10.115	10.115	58.395	-0.000	-0.000	0.000
23.097	-23.075	0.013	277.597	0.000	0.000
0.003	0.003	0.004	-0.003	277.594	23.088
0.003	0.004	0.004	0.000	23.086	488.770

987.308	9.943	11.405	23.089	-0.000	-0.000
9.510	987.062	11.021	-23.086	-0.000	-0.000
10.093	10.093	58.369	0.000	0.000	-0.000
23.086	-23.092	-0.004	277.592	-0.000	-0.000
-0.003	-0.003	-0.004	0.003	277.594	23.088
-0.003	-0.004	-0.004	-0.000	23.086	488.770

-46.537	-121.625	1293.220	116.325	0.000	-0.000
-222.126	392.777	23.346	-19.753	-0.000	-0.000
-46.002	-46.001	83.044	0.000	-0.000	-0.000
-51.616	-314.303	1371.467	58.608	-0.000	-0.000
-0.000	0.000	0.000	-0.000	98.535	19.753
-0.000	0.000	0.000	0.000	19.753	307.451

277.515	-117.185	62.042	59.148	0.000	-0.000
-130.832	271.352	136.290	-57.810	-0.000	-0.000
50.932	50.932	-643.560	0.000	0.000	-0.000
55.924	-59.695	14.132	84.918	-0.000	-0.000
-0.627	-0.627	4.698	-0.000	84.859	57.976
-0.623	-0.624	4.680	0.000	57.833	201.021

392.774	-222.125	23.346	19.753	0.000	0.000
-117.452	280.473	51.933	-58.569	-0.000	0.000
54.690	54.690	-671.750	0.000	0.000	0.000
59.695	-55.925	-14.132	84.918	0.000	0.000
0.627	0.627	-4.698	0.000	84.859	57.976
0.623	0.624	-4.680	-0.000	57.833	201.021

455.330	265.111	265.111	0.000	-0.000	-0.000
265.111	455.330	265.111	0.000	-0.000	-0.000
265.111	265.111	455.330	-0.000	0.000	-0.000
-0.000	-0.000	0.000	86.073	0.000	-0.000
-0.000	-0.000	0.000	0.000	86.073	0.000
-0.000	0.000	-0.000	-0.000	-0.000	86.073