× Warning! Note that elemental potentials taken from alloy descriptions may not work well for the pure species. This is particularly true if the elements were fit for compounds instead of being optimized separately. As with all interatomic potentials, please check to make sure that the performance is adequate for your problem.

× Updated! Potentials that share interactions are now listed as related models.

2015--Purja-Pun-G-P-Darling-K-A-Kecskes-L-J-Mishin-Y--Cu-Ta

Citation: G.P. Purja Pun, K.A. Darling, L.J. Kecskes, and Y. Mishin (2015), "Angular-dependent interatomic potential for the Cu-Ta system and its application to structural stability of nano-crystalline alloys", Acta Materialia, 100, 377-391. DOI: 10.1016/j.actamat.2015.08.052.

Abstract: Atomistic computer simulations are capable of providing insights into physical mechanisms responsible for the extraordinary structural stability and strength of immiscible Cu–Ta alloys. To enable reliable simulations of these alloys, we have developed an angular-dependent potential (ADP) for the Cu–Ta system by fitting to a large database of first-principles and experimental data. This, in turn, required the development of a new ADP potential for elemental Ta, which accurately reproduces a wide range of properties of Ta and is transferable to severely deformed states and diverse atomic environments. The new Cu–Ta potential is applied for studying the kinetics of grain growth in nano-crystalline Cu–Ta alloys with different chemical compositions. Ta atoms form nanometer-scale clusters preferentially located at grain boundaries (GBs) and triple junctions. These clusters pin some of the GBs in place and cause a drastic decrease in grain growth by the Zener pinning mechanism. The results of the simulations are well consistent with experimental observations and suggest possible mechanisms of the stabilization effect of Ta.

Notes: This potential is meant to supplant the Hahibon 2008 Cu-Ta ADP potential by providing a refit of the Ta-Ta and Cu-Ta interactions.

LAMMPS pair_style adp (2015--Purja-Pun-G-P--Cu-Ta--LAMMPS--ipr1)

See Computed Properties
Notes: This file was provided by Yuri Mishin (George Mason University) on 11 Sep. 2015.
File(s): superseded

LAMMPS pair_style adp (2015--Purja-Pun-G-P--Cu-Ta--LAMMPS--ipr2)

See Computed Properties
Notes: This file was provided by Yuri Mishin (George Mason University) on 2 Nov. 2018. Ganga Purja Pun noted that the tabulated values are identical to the version above except that the short range behaviors (r < 0.5 Angstroms) for some functions have been fixed so that they now follow the correct trends.
File(s):

CuTa_LJ15_2014.adp.txt

Implementation Information

This page displays computed properties for the 2015--Purja-Pun-G-P--Cu-Ta--LAMMPS--ipr2 implementation of the 2015--Purja-Pun-G-P-Darling-K-A-Kecskes-L-J-Mishin-Y--Cu-Ta 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

2015--Purja-Pun-G-P--Cu-Ta--LAMMPS--ipr2/diatom

Click on plot to load interactive version

2015--Purja-Pun-G-P--Cu-Ta--LAMMPS--ipr2/diatom_short

Cohesive Energy vs. Interatomic Spacing

Plots of potential energy vs interatomic spacing, r, are shown below for a number of crystal structures. The structures are generated based on the ideal atomic positions and b/a and c/a lattice parameter ratios for a given crystal prototype. The size of the system is then uniformly scaled, and the energy calculated without relaxing the system. To obtain these plots, values of r are evaluated every 0.02 Å up to 6 Å.

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

Clicking on the image of a plot will open an interactive version of it in a new tab. The underlying data for the plots can be downloaded by clicking on the links above each plot.

Notes and Disclaimers:

These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
The minima identified by this calculation do not guarantee that the associated crystal structures will be stable since no relaxation is performed.
NIST disclaimer

Version Information:

2020-12-18. Descriptions, tables and plots updated to reflect that the energy values are the measuredper atom potential energy rather than cohesive energy as some potentials have non-zero isolated atom energies.
2019-02-04. Values regenerated with even r spacings of 0.02 Å, and now include values less than 2 Å when possible. Updated calculation method and parameters enhance compatibility with more potential styles.
2019-04-26. Results for hcp, double hcp, α-As and L1₀ prototypes regenerated from different unit cell representations. Only α-As results show noticable (>1e-5 eV) difference due to using a different coordinate for Wykoff site c position.
2018-06-13. Values for MEAM potentials corrected. Dynamic versions of the plots moved to separate pages to improve page loading. Cosmetic changes to how data is shown and updates to the documentation.
2017-01-11. Replaced png pictures with interactive Bokeh plots. Data regenerated with 200 values of r instead of 300.
2016-09-28. Plots for binary structures added. Data and plots for elemental structures regenerated. Data values match the values of the previous version. Data table formatting slightly changed to increase precision and ensure spaces between large values. Composition added to plot title and structure names made longer.
2016-04-07. Plots for elemental structures added.

Select a composition:

Download data

Click on plot to load interactive version

2015--Purja-Pun-G-P--Cu-Ta--LAMMPS--ipr2/EvsR.Cu

Crystal Structure Predictions

Computed lattice constants and cohesive/potential energies are displayed for a variety of crystal structures. The values displayed here are obtained using the following process.

Initial crystal structure guesses are taken from:
1. The iprPy E_vs_r_scan calculation results (shown above) by identifying all energy minima along the measured curves for a given crystal prototype + composition.
2. Structures in the Materials Project and OQMD DFT databases.
All initial guesses are relaxed using three independent methods using a 10x10x10 supercell:
1. "box": The system's lattice constants are adjusted to zero pressure without internal relaxations using the iprPy relax_box calculation with a strainrange of 1e-6.
2. "static": The system's lattice and atomic positions are statically relaxed using the iprPy relax_static calculation with a minimization force tolerance of 1e-10 eV/Angstrom.
3. "dynamic": The system's lattice and atomic positions are dynamically relaxed for 10000 timesteps of 0.01 ps using the iprPy relax_dynamic calculation with an nph integration plus Langevin thermostat. The final configuration is then used as input in running an iprPy relax_static calculation with a minimization force tolerance of 1e-10 eV/Angstrom.
The relaxed structures obtained from #2 are then evaluated using the spglib package to identify an ideal crystal unit cell based on the results.
The space group information of the ideal unit cells is compared to the space group information of the corresponding reference structures to identify which structures transformed upon relaxation. The structures that did not transform to a different structure are listed in the table(s) below. The "method" field indicates the most rigorous relaxation method where the structure did not transform. The space group information is also used to match the DFT reference structures to the used prototype, where possible.
The cohesive energy, E_coh, is calculated from the measured potential energy per atom, E_pot$, by subtracting the isolated energy averaged across all atoms in the unit cell. The isolated atom energies of each species model is obtained either by evaluating a single atom atomic configuration, or by identifying the first energy plateau from the diatom scan calculations for r > 2 Å.

The calculation methods used are implemented into iprPy as the following calculation styles

Notes and Disclaimers:

These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
The presence of any structures in this list does not guarantee that those structures are stable. Also, the lowest energy structure may not be included in this list.
Multiple values for the same crystal structure but different lattice constants are possible. This is because multiple energy minima are possible for a given structure and interatomic potential. Having multiple energy minima for a structure does not necessarily make the potential "bad" as unwanted configurations may be unstable or correspond to conditions that may not be relevant to the problem of interest (eg. very high strains).
NIST disclaimer

Version Information:

2022-05-27. The "box" method results have all been redone with an updated methodology more suited for non-orthogonal systems.
2020-12-18. Cohesive energies have been corrected by making them relative to the energies of the isolated atoms. The previous cohesive energy values are now listed as the potential energies.
2019-06-07. Structures with positive or near zero cohesive energies removed from the display tables. All values still present in the raw data files.
2019-04-26. Calculations now computed for each implementation. Results for hcp, double hcp, α-As and L1₀ prototypes regenerated from different unit cell representations.
2018-06-14. Methodology completely changed affecting how the information is displayed. Calculations involving MEAM potentials corrected.
2016-09-28. Values for simple compounds added. All identified energy minima for each structure are listed. The existing elemental data was regenerated. Most values are consistent with before, but some differences have been noted. Specifically, variations are seen with some values for potentials where the elastic constants don't vary smoothly near the equilibrium state. Additionally, the inclusion of some high-energy structures has changed based on new criteria for identifying when structures have relaxed to another structure.
2016-04-07. Values for elemental crystal structures added. Only values for the global energy minimum of each unique structure given.

Select a composition:

Download raw data (including filtered results)

Reference structure matches:
A1--Cu--fcc = mp-30, oqmd-592441, oqmd-593869, oqmd-594301, oqmd-594302, oqmd-594517, oqmd-594518, oqmd-594519, oqmd-594520, oqmd-598513, oqmd-635950, oqmd-1214520
A15--beta-W = oqmd-1214965
A2--W--bcc = mp-998890, oqmd-637373, oqmd-1215143
A3'--alpha-La--double-hcp = mp-989695, oqmd-1215411
A3--Mg--hcp = mp-989782, oqmd-1215321
A4--C--dc = oqmd-1215500
A5--beta-Sn = oqmd-1215589
A6--In--bct = mp-1010136, oqmd-1215678

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	-3.54	-3.54	3.615	3.615	3.615	90.0	90.0	90.0
A3'--alpha-La--double-hcp	dynamic	-3.5361	-3.5361	2.5561	2.5561	8.3374	90.0	90.0	120.0
oqmd-1216034	dynamic	-3.5348	-3.5348	2.5561	2.5561	18.7497	90.0	90.0	120.0
oqmd-1216034	box	-3.5347	-3.5347	2.5561	2.5561	18.7508	90.0	90.0	120.0
A3--Mg--hcp	dynamic	-3.5322	-3.5322	2.5561	2.5561	4.1624	90.0	90.0	120.0
oqmd-1215232	box	-3.5318	-3.5318	2.5459	4.4447	4.1632	90.0	90.0	90.0
A6--In--bct	box	-3.4951	-3.4951	2.941	2.941	2.7345	90.0	90.0	90.0
A2--W--bcc	static	-3.4945	-3.4945	2.8683	2.8683	2.8683	90.0	90.0	90.0
oqmd-1214876	static	-3.4715	-3.4715	6.2347	6.2347	6.2347	90.0	90.0	90.0
oqmd-1214876	box	-3.4711	-3.4711	6.2331	6.2331	6.2331	90.0	90.0	90.0
oqmd-1214787	dynamic	-3.4701	-3.4701	8.8814	8.8814	8.8814	90.0	90.0	90.0
oqmd-1214787	box	-3.47	-3.47	8.8815	8.8815	8.8815	90.0	90.0	90.0
A15--beta-W	dynamic	-3.4542	-3.4542	4.5959	4.5959	4.5959	90.0	90.0	90.0
mp-1059259	box	-3.4011	-3.4011	8.0257	2.4568	2.5149	90.0	90.1	90.0
mp-1120774	box	-3.3941	-3.3941	2.5394	2.5394	24.7603	90.0	90.0	120.0
oqmd-1215054	box	-3.3826	-3.3826	4.2653	9.0835	2.5763	90.0	90.0	90.0
oqmd-1214698	box	-3.3065	-3.3065	3.3449	8.5689	3.6207	90.0	90.0	90.0
oqmd-1277912	static	-3.2796	-3.2796	11.4263	11.4263	11.4263	90.0	90.0	90.0
oqmd-1277912	box	-3.2792	-3.2792	11.4233	11.4233	11.4233	90.0	90.0	90.0
A5--beta-Sn	static	-3.2295	-3.2295	4.6353	4.6353	2.4346	90.0	90.0	90.0
Ah--alpha-Po--sc	static	-3.1069	-3.1069	2.3928	2.3928	2.3928	90.0	90.0	90.0
A7--alpha-As	box	-2.7848	-2.7848	3.2256	3.2256	10.3067	90.0	90.0	120.0
oqmd-1215945	box	-2.754	-2.754	4.041	4.041	4.4818	90.0	90.0	120.0
A4--C--dc	box	-2.4192	-2.4192	5.3546	5.3546	5.3546	90.0	90.0	90.0
mp-1056079	static	-1.4842	-1.4842	11.8429	2.2852	22.7476	90.0	101.9	90.0
A1--Cu--fcc	box	-0.0	-0.0	7.8059	7.8059	7.8059	90.0	90.0	90.0
A3'--alpha-La--double-hcp	box	-0.0	-0.0	5.5196	5.5196	18.0269	90.0	90.0	120.0
A3--Mg--hcp	box	-0.0	-0.0	5.5196	5.5196	9.0134	90.0	90.0	120.0
A2--W--bcc	box	-0.0	-0.0	6.3735	6.3735	6.3735	90.0	90.0	90.0
A3--Mg--hcp	dynamic	-0.0	-0.0	5.52	5.52	9.0141	90.0	90.0	120.0
A3'--alpha-La--double-hcp	dynamic	-0.0	-0.0	5.52	5.52	18.0282	90.0	90.0	120.0
A1--Cu--fcc	dynamic	-0.0	-0.0	7.8065	7.8065	7.8065	90.0	90.0	90.0
A2--W--bcc	dynamic	-0.0	-0.0	6.3739	6.3739	6.3739	90.0	90.0	90.0
A4--C--dc	box	-0.0	-0.0	12.7469	12.7469	12.7469	90.0	90.0	90.0
Ah--alpha-Po--sc	dynamic	-0.0	-0.0	5.52	5.52	5.52	90.0	90.0	90.0
A6--In--bct	dynamic	-0.0	-0.0	5.52	5.52	8.28	90.0	90.0	90.0
A5--beta-Sn	dynamic	-0.0	-0.0	10.6448	10.6448	5.8547	90.0	90.0	90.0
A4--C--dc	dynamic	-0.0	-0.0	12.7479	12.7479	12.7479	90.0	90.0	90.0
A7--alpha-As	dynamic	-0.0	-0.0	8.2469	8.2469	22.9018	90.0	90.0	120.0
A15--beta-W	dynamic	-0.0	-0.0	11.04	11.04	11.04	90.0	90.0	90.0
A1--Cu--fcc	dynamic	-0.0	-0.0	7.9762	7.9762	7.9762	90.0	90.0	90.0
A3'--alpha-La--double-hcp	dynamic	-0.0	-0.0	5.64	5.64	18.4202	90.0	90.0	120.0
A3--Mg--hcp	dynamic	-0.0	-0.0	5.64	5.64	9.2101	90.0	90.0	120.0
A2--W--bcc	dynamic	-0.0	-0.0	6.5125	6.5125	6.5125	90.0	90.0	90.0
Ah--alpha-Po--sc	dynamic	-0.0	-0.0	5.64	5.64	5.64	90.0	90.0	90.0
A6--In--bct	dynamic	-0.0	-0.0	5.64	5.64	8.46	90.0	90.0	90.0
A4--C--dc	dynamic	-0.0	-0.0	13.025	13.025	13.025	90.0	90.0	90.0
A5--beta-Sn	dynamic	-0.0	-0.0	10.8762	10.8762	5.9819	90.0	90.0	90.0
A7--alpha-As	dynamic	-0.0	-0.0	8.4262	8.4262	23.3996	90.0	90.0	120.0
A15--beta-W	dynamic	-0.0	-0.0	11.28	11.28	11.28	90.0	90.0	90.0
A1--Cu--fcc	dynamic	-0.0	-0.0	8.1742	8.1742	8.1742	90.0	90.0	90.0
A3'--alpha-La--double-hcp	dynamic	-0.0	-0.0	5.78	5.78	18.8774	90.0	90.0	120.0
A3--Mg--hcp	dynamic	-0.0	-0.0	5.78	5.78	9.4387	90.0	90.0	120.0
A2--W--bcc	dynamic	-0.0	-0.0	6.6742	6.6742	6.6742	90.0	90.0	90.0
Ah--alpha-Po--sc	dynamic	-0.0	-0.0	5.78	5.78	5.78	90.0	90.0	90.0
A6--In--bct	dynamic	-0.0	-0.0	5.78	5.78	8.67	90.0	90.0	90.0
A4--C--dc	dynamic	-0.0	-0.0	13.3483	13.3483	13.3483	90.0	90.0	90.0
A5--beta-Sn	dynamic	-0.0	-0.0	11.1462	11.1462	6.1304	90.0	90.0	90.0
A7--alpha-As	dynamic	-0.0	-0.0	8.6354	8.6354	23.9805	90.0	90.0	120.0
A15--beta-W	dynamic	-0.0	-0.0	11.56	11.56	11.56	90.0	90.0	90.0
A1--Cu--fcc	dynamic	-0.0	-0.0	8.3439	8.3439	8.3439	90.0	90.0	90.0
A3'--alpha-La--double-hcp	dynamic	-0.0	-0.0	5.9	5.9	19.2693	90.0	90.0	120.0
A3--Mg--hcp	dynamic	-0.0	-0.0	5.9	5.9	9.6347	90.0	90.0	120.0
A2--W--bcc	dynamic	-0.0	-0.0	6.8127	6.8127	6.8127	90.0	90.0	90.0
Ah--alpha-Po--sc	dynamic	-0.0	-0.0	5.9	5.9	5.9	90.0	90.0	90.0
A6--In--bct	dynamic	-0.0	-0.0	5.9	5.9	8.85	90.0	90.0	90.0
A4--C--dc	dynamic	-0.0	-0.0	13.6255	13.6255	13.6255	90.0	90.0	90.0
A5--beta-Sn	dynamic	-0.0	-0.0	11.3776	11.3776	6.2577	90.0	90.0	90.0
A7--alpha-As	dynamic	-0.0	-0.0	8.8147	8.8147	24.4783	90.0	90.0	120.0
A15--beta-W	dynamic	-0.0	-0.0	11.8	11.8	11.8	90.0	90.0	90.0
A15--beta-W	box	0.0	0.0	11.8011	11.8011	11.8011	90.0	90.0	90.0
A5--beta-Sn	box	0.0	0.0	11.386	11.386	6.2051	90.0	90.0	90.0
Ah--alpha-Po--sc	box	0.0	0.0	5.9006	5.9006	5.9006	90.0	90.0	90.0
A3--Mg--hcp	box	0.0	0.0	5.9006	5.9006	9.6356	90.0	90.0	120.0
A3'--alpha-La--double-hcp	box	0.0	0.0	5.9006	5.9006	19.2712	90.0	90.0	120.0
A1--Cu--fcc	box	0.0	0.0	8.3447	8.3447	8.3447	90.0	90.0	90.0
A15--beta-W	box	0.0	0.0	11.5615	11.5615	11.5615	90.0	90.0	90.0
A5--beta-Sn	box	0.0	0.0	11.1474	11.1474	6.1334	90.0	90.0	90.0
A4--C--dc	box	0.0	0.0	13.3501	13.3501	13.3501	90.0	90.0	90.0
Ah--alpha-Po--sc	box	0.0	0.0	5.7807	5.7807	5.7807	90.0	90.0	90.0
A2--W--bcc	box	0.0	0.0	6.675	6.675	6.675	90.0	90.0	90.0
A1--Cu--fcc	box	0.0	0.0	8.1752	8.1752	8.1752	90.0	90.0	90.0
A3--Mg--hcp	box	0.0	0.0	5.7807	5.7807	9.4399	90.0	90.0	120.0
A15--beta-W	box	0.0	0.0	11.2858	11.2858	11.2858	90.0	90.0	90.0
A5--beta-Sn	box	0.0	0.0	10.8661	10.8661	6.0984	90.0	90.0	90.0
A4--C--dc	box	0.0	0.0	13.0317	13.0317	13.0317	90.0	90.0	90.0
Ah--alpha-Po--sc	box	0.0	0.0	5.6429	5.6429	5.6429	90.0	90.0	90.0
A2--W--bcc	box	0.0	0.0	6.5159	6.5159	6.5159	90.0	90.0	90.0
A3'--alpha-La--double-hcp	box	0.0	0.0	5.6429	5.6429	18.4296	90.0	90.0	120.0
A3--Mg--hcp	box	0.0	0.0	5.6429	5.6429	9.2148	90.0	90.0	120.0

prototype	method	E_coh (eV/atom)	E_pot (eV/atom)	a₀ (Å)	b₀ (Å)	c₀ (Å)	α (degrees)	β (degrees)	γ (degrees)
C1--CaF2--fluorite	static	-296487.2486	-296487.2486	2.5403	2.5403	2.5403	90.0	90.0	90.0
C1--CaF2--fluorite	static	-4.1143	-4.1143	6.1132	6.1132	6.1132	90.0	90.0	90.0
oqmd-1232678	box	-3.4569	-3.4569	5.7995	5.7995	4.1496	90.0	90.0	90.0
C1--CaF2--fluorite	box	1221.4669	1221.4669	3.3438	3.3438	3.3438	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	-243364.3893	-243364.3893	1.8102	1.8102	1.8102	90.0	90.0	90.0
A15--Cr3Si	static	-243002.5273	-243002.5273	2.28	2.28	2.28	90.0	90.0	90.0
D0_3--BiF3	static	-242656.5978	-242656.5978	2.8637	2.8637	2.8637	90.0	90.0	90.0
oqmd-323408	box	-4.4836	-4.4836	5.5993	5.5993	4.3525	90.0	90.0	120.0
L1_2--AuCu3	static	-4.4404	-4.4404	3.9167	3.9167	3.9167	90.0	90.0	90.0
D0_3--BiF3	static	-4.377	-4.377	6.2654	6.2654	6.2654	90.0	90.0	90.0
A15--Cr3Si	static	-4.2461	-4.2461	4.9767	4.9767	4.9767	90.0	90.0	90.0
A15--Cr3Si	dynamic	-0.0	-0.0	11.04	11.04	11.04	90.0	90.0	90.0
A15--Cr3Si	dynamic	-0.0	-0.0	11.28	11.28	11.28	90.0	90.0	90.0
A15--Cr3Si	dynamic	-0.0	-0.0	11.56	11.56	11.56	90.0	90.0	90.0
A15--Cr3Si	dynamic	-0.0	-0.0	11.8	11.8	11.8	90.0	90.0	90.0
A15--Cr3Si	box	0.0	0.0	11.8011	11.8011	11.8011	90.0	90.0	90.0
A15--Cr3Si	box	0.0	0.0	11.5615	11.5615	11.5615	90.0	90.0	90.0
A15--Cr3Si	box	0.0	0.0	11.2858	11.2858	11.2858	90.0	90.0	90.0
A15--Cr3Si	box	285.972	285.972	3.017	3.017	3.017	90.0	90.0	90.0
D0_3--BiF3	box	289.7874	289.7874	3.7985	3.7985	3.7985	90.0	90.0	90.0
L1_2--AuCu3	box	294.9183	294.9183	2.3775	2.3775	2.3775	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_0--AuCu	static	-476423.3478	-476423.3478	1.2244	1.2244	1.6035	90.0	90.0	90.0
B2--CsCl	static	-471001.6532	-471001.6532	1.3395	1.3395	1.3395	90.0	90.0	90.0
B1--NaCl--rock-salt	static	-435252.193	-435252.193	2.12	2.12	2.12	90.0	90.0	90.0
B3--ZnS--cubic-zinc-blende	static	-262573.2871	-262573.2871	2.1246	2.1246	2.1246	90.0	90.0	90.0
B2--CsCl	dynamic	-5.7401	-5.7401	3.1762	3.1762	3.1762	90.0	90.0	90.0
oqmd-1220027	box	-5.6267	-5.6267	4.4702	3.0169	4.6616	90.0	90.0	90.0
oqmd-1229192	static	-5.6012	-5.6012	2.9479	2.9479	4.2775	90.0	90.0	120.0
B1--NaCl--rock-salt	static	-5.1242	-5.1242	5.1583	5.1583	5.1583	90.0	90.0	90.0
oqmd-1225706	box	-4.5446	-4.5446	4.4535	4.4535	5.1113	90.0	90.0	120.0
B3--ZnS--cubic-zinc-blende	box	-3.9501	-3.9501	5.9016	5.9016	5.9016	90.0	90.0	90.0
L1_0--AuCu	box	265.8811	265.8811	1.1285	1.1285	3.6015	90.0	90.0	90.0
B2--CsCl	box	1084.2364	1084.2364	1.7601	1.7601	1.7601	90.0	90.0	90.0
B1--NaCl--rock-salt	box	2547.6179	2547.6179	2.7429	2.7429	2.7429	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	-550678.6993	-550678.6993	2.3094	2.3094	2.3094	90.0	90.0	90.0
C1--CaF2--fluorite	dynamic	-5.9477	-5.9477	6.1788	6.1788	6.1788	90.0	90.0	90.0
oqmd-1240817	static	-3.2735	-3.2735	11.8402	11.8402	11.8402	90.0	90.0	90.0
C1--CaF2--fluorite	box	5102.9683	5102.9683	2.9479	2.9479	2.9479	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	-708759.7277	-708759.7277	1.5556	1.5556	1.5556	90.0	90.0	90.0
A15--Cr3Si	static	-706703.1564	-706703.1564	1.96	1.96	1.96	90.0	90.0	90.0
D0_3--BiF3	dynamic	-6.7691	-6.7691	6.4389	6.4389	6.4389	90.0	90.0	90.0
L1_2--AuCu3	static	-6.7241	-6.7241	4.0452	4.0452	4.0452	90.0	90.0	90.0
oqmd-320515	box	-6.7151	-6.7151	5.7785	5.7785	4.5194	90.0	90.0	120.0
oqmd-302324	static	-6.7053	-6.7053	3.893	3.893	8.8636	90.0	90.0	90.0
oqmd-302324	box	-6.678	-6.678	4.1051	4.1051	7.8456	90.0	90.0	90.0
A15--Cr3Si	dynamic	-6.6748	-6.6748	5.2185	5.2185	5.2185	90.0	90.0	90.0
L1_2--AuCu3	box	1657.487	1657.487	2.0343	2.0343	2.0343	90.0	90.0	90.0
A15--Cr3Si	box	1717.517	1717.517	2.5627	2.5627	2.5627	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)
A7--alpha-As	static	-1000520.5298	-1000520.5298	1.1653	1.1653	3.2361	90.0	90.0	120.0
A3--Mg--hcp	static	-1000519.249	-1000519.249	0.96	0.96	1.5677	90.0	90.0	120.0
A3'--alpha-La--double-hcp	static	-1000519.2164	-1000519.2164	0.96	0.96	3.1353	90.0	90.0	120.0
A2--W--bcc	dynamic	-8.1	-8.1	3.304	3.304	3.304	90.0	90.0	90.0
oqmd-670903	dynamic	-8.0274	-8.0274	10.2655	10.2655	5.3993	90.0	90.0	90.0
A15--beta-W	dynamic	-8.0251	-8.0251	5.3482	5.3482	5.3482	90.0	90.0	90.0
mp-569794	box	-8.0236	-8.0236	10.2819	10.2819	5.3904	90.0	90.0	90.0
oqmd-670903	box	-8.0234	-8.0234	10.2824	10.2824	5.3901	90.0	90.0	90.0
oqmd-9754	box	-8.0233	-8.0233	10.2828	10.2828	5.39	90.0	90.0	90.0
mp-42	box	-8.0217	-8.0217	10.2814	10.2814	5.3907	90.0	90.0	90.0
A6--In--bct	static	-7.9858	-7.9858	2.846	2.846	4.5508	90.0	90.0	90.0
A1--Cu--fcc	static	-7.9757	-7.9757	4.2456	4.2456	4.2456	90.0	90.0	90.0
oqmd-1215286	box	-7.9717	-7.9717	2.8049	5.4224	4.7374	90.0	90.0	90.0
oqmd-1214841	dynamic	-7.9679	-7.9679	10.3189	10.3189	10.3189	90.0	90.0	90.0
A3'--alpha-La--double-hcp	box	-7.9622	-7.9622	2.9994	2.9994	9.736	90.0	90.0	120.0
oqmd-1214841	box	-7.9593	-7.9593	10.3279	10.3279	10.3279	90.0	90.0	90.0
A3--Mg--hcp	box	-7.9511	-7.9511	2.9989	2.9989	4.8007	90.0	90.0	120.0
oqmd-1214930	dynamic	-7.9375	-7.9375	7.2589	7.2589	7.2589	90.0	90.0	90.0
oqmd-1214930	box	-7.9305	-7.9305	7.261	7.261	7.261	90.0	90.0	90.0
oqmd-1215108	box	-7.6142	-7.6142	3.1586	4.6705	9.9671	90.0	90.0	90.0
oqmd-1214752	box	-7.5726	-7.5726	3.21	4.6592	9.9994	90.0	90.0	90.0
A5--beta-Sn	static	-7.3559	-7.3559	4.9384	4.9384	2.7686	90.0	90.0	90.0
oqmd-52302	box	-7.1559	-7.1559	5.1677	5.1677	2.5824	90.0	90.0	90.0
oqmd-9753	box	-7.1521	-7.1521	5.1689	5.1689	2.5825	90.0	90.0	90.0
A7--alpha-As	box	-7.0591	-7.0591	3.0359	3.0359	15.0939	90.0	90.0	120.0
Ah--alpha-Po--sc	static	-7.0363	-7.0363	2.592	2.592	2.592	90.0	90.0	90.0
oqmd-9752	box	-6.6862	-6.6862	10.3289	10.3289	4.913	90.0	90.0	90.0
mp-697196	box	-6.6843	-6.6843	10.339	10.339	4.9076	90.0	90.0	90.0
mp-1095086	static	-6.5118	-6.5118	4.9622	4.9622	8.7244	90.0	90.0	120.0
mp-1095086	box	-6.5093	-6.5093	4.9505	4.9505	8.7808	90.0	90.0	120.0
oqmd-1215999	box	-6.4919	-6.4919	4.3951	4.3951	4.8198	90.0	90.0	120.0
A4--C--dc	dynamic	-5.5255	-5.5255	4.5815	4.5815	4.5815	90.0	90.0	90.0
A4--C--dc	static	-5.1694	-5.1694	6.2362	6.2362	6.2362	90.0	90.0	90.0
oqmd-52301	box	-5.1454	-5.1454	12.5144	12.5144	3.0543	90.0	90.0	90.0
mp-1076923	static	-2.3947	-2.3947	22.6986	22.6986	2.6686	90.0	90.0	90.0
mp-1217805	static	-2.3947	-2.3947	30.7122	30.7132	2.6686	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:

169.897	122.621	122.621	-0.0	-0.0	-0.0
122.621	169.897	122.621	-0.0	-0.0	-0.0
122.621	122.621	169.897	0.0	0.0	-0.0
0.0	0.0	0.0	76.189	-0.0	-0.0
0.0	0.0	0.0	-0.0	76.189	-0.0
0.0	0.0	-0.0	-0.0	-0.0	76.189

169.896	122.621	122.621	0.0	0.0	-0.0
122.621	169.896	122.621	0.0	0.0	0.0
122.621	122.621	169.896	0.0	0.0	0.0
0.0	-0.0	-0.0	76.189	-0.0	0.0
-0.0	0.0	-0.0	-0.0	76.189	0.0
-0.0	-0.0	0.0	0.0	0.0	76.189

287.815	78.696	78.696	0.0	0.0	0.0
78.696	287.815	78.696	-0.0	-0.0	0.0
78.696	78.696	287.815	-0.0	-0.0	0.0
0.0	-0.0	0.0	27.611	-0.0	0.0
-0.0	0.0	0.0	0.0	27.611	0.0
-0.0	-0.0	0.0	0.0	0.0	27.611

289.215	77.997	77.997	-0.0	-0.0	-0.0
77.997	289.215	77.997	-0.0	0.0	-0.0
77.997	77.997	289.215	0.0	0.0	-0.0
-0.0	0.0	-0.0	27.611	0.0	-0.0
0.0	-0.0	-0.0	0.0	27.611	-0.0
0.0	0.0	-0.0	0.0	-0.0	27.611

287.816	78.696	78.696	0.0	0.0	0.0
78.696	287.816	78.696	-0.0	0.0	0.0
78.696	78.696	287.816	-0.0	-0.0	0.0
0.0	0.0	-0.0	12.076	-0.0	-0.0
0.0	0.0	-0.0	-0.0	12.076	0.0
0.0	-0.0	0.0	-0.0	0.0	12.076

289.216	77.997	77.997	0.0	0.0	0.0
77.997	289.216	77.997	0.0	-0.0	0.0
77.997	77.997	289.216	-0.0	0.0	0.0
0.0	0.0	-0.0	12.076	-0.0	0.0
0.0	0.0	-0.0	-0.0	12.076	0.0
0.0	-0.0	0.0	-0.0	-0.0	12.076

287.814	78.696	78.696	0.0	0.0	-0.0
78.696	287.814	78.696	0.0	0.0	0.0
78.696	78.696	287.814	0.0	0.0	-0.0
-0.0	-0.0	0.0	12.076	0.0	-0.0
-0.0	-0.0	0.0	0.0	12.076	-0.0
-0.0	0.0	-0.0	0.0	-0.0	12.076

120.973	134.991	134.991	-0.0	-0.0	-0.0
134.991	120.973	134.991	-0.0	0.0	-0.0
134.991	134.991	120.973	-0.0	0.0	-0.0
0.0	0.0	-0.0	87.711	0.0	0.0
0.0	0.0	-0.0	-0.0	87.711	0.0
0.0	0.0	-0.0	-0.0	0.0	87.711

120.974	134.992	134.992	-0.0	-0.0	0.0
134.992	120.974	134.992	-0.0	0.0	0.0
134.992	134.992	120.974	-0.0	0.0	0.0
0.0	0.0	0.0	87.711	0.0	0.0
0.0	0.0	0.0	-0.0	87.711	-0.0
0.0	0.0	0.0	-0.0	0.0	87.711

222.255	105.018	85.542	0.0	-0.0	0.0
120.289	206.984	85.542	0.0	0.0	0.0
85.542	85.542	226.754	0.0	-0.0	0.0
-0.0	0.0	-0.0	38.899	-0.0	0.0
-0.0	0.0	-0.0	0.0	38.899	0.0
-0.0	0.0	-0.0	0.0	-0.0	43.348

206.985	120.289	85.542	0.0	0.0	0.0
105.019	222.255	85.542	0.0	0.0	0.0
85.542	85.542	226.755	0.0	-0.0	0.0
0.0	-0.0	0.0	38.899	-0.0	0.0
-0.0	0.0	0.0	0.0	38.899	0.0
-0.0	0.0	0.0	0.0	-0.0	58.618

222.254	105.018	85.542	-0.0	0.0	-0.0
120.288	206.984	85.542	-0.0	0.0	-0.0
85.542	85.542	226.753	-0.0	0.0	-0.0
-0.0	0.0	-0.0	38.899	0.0	-0.0
0.0	-0.0	-0.0	-0.0	38.899	-0.0
0.0	-0.0	-0.0	-0.0	0.0	58.618

222.27	105.032	84.033	0.0	-0.0	0.0
120.721	206.582	84.033	-0.0	-0.0	-0.0
84.033	84.033	215.677	-0.0	-0.0	-0.0
-0.0	0.0	0.0	37.138	0.0	0.0
-0.0	0.0	0.0	-0.0	37.138	0.0
-0.0	0.0	0.0	0.0	-0.0	58.619

206.583	120.721	84.034	-0.0	0.0	0.0
120.721	206.582	84.034	-0.0	-0.0	-0.0
84.034	84.034	215.679	0.0	0.0	0.0
0.0	-0.0	0.0	37.138	0.0	-0.0
-0.0	0.0	0.0	-0.0	37.138	0.0
-0.0	0.0	-0.0	-0.0	-0.0	42.931

206.581	120.72	84.033	0.0	0.0	-0.0
120.72	206.581	84.033	0.0	-0.0	0.0
84.033	84.033	215.676	0.0	0.0	-0.0
-0.0	0.0	-0.0	37.138	-0.0	-0.0
0.0	-0.0	-0.0	-0.0	37.138	0.0
0.0	-0.0	0.0	0.0	0.0	42.931

45.509	65.54	65.54	0.0	-0.0	-0.0
65.54	45.509	65.54	-0.0	-0.0	-0.0
65.54	65.54	45.509	-0.0	-0.0	-0.0
-0.0	0.0	-0.0	-32.541	0.0	-0.0
-0.0	-0.0	-0.0	0.0	-32.541	-0.0
0.0	-0.0	-0.0	0.0	0.0	-32.541

45.51	65.54	65.54	0.0	-0.0	-0.0
65.54	45.51	65.54	0.0	-0.0	-0.0
65.54	65.54	45.51	0.0	-0.0	-0.0
-0.0	-0.0	-0.0	-32.541	-0.0	-0.0
-0.0	-0.0	-0.0	0.0	-32.541	-0.0
-0.0	-0.0	-0.0	0.0	0.0	-32.541

45.509	65.539	65.539	-0.0	0.0	0.0
65.539	45.509	65.539	-0.0	-0.0	0.0
65.539	65.539	45.509	-0.0	0.0	-0.0
0.0	0.0	0.0	-32.541	-0.0	-0.0
0.0	0.0	0.0	-0.0	-32.541	0.0
0.0	0.0	0.0	-0.0	0.0	-32.541

-8.155	344.002	50.093	0.0	0.0	0.0
344.002	-8.155	50.093	0.0	0.0	0.0
50.093	50.093	258.536	0.0	0.0	0.0
-0.0	-0.0	-0.0	-21.51	0.0	-0.0
-0.0	-0.0	-0.0	0.0	-21.51	0.0
-0.0	-0.0	0.0	0.0	0.0	-23.283

309.871	25.976	50.093	0.0	0.0	0.0
25.976	309.871	50.093	0.0	0.0	0.0
50.093	50.093	258.536	0.0	0.0	0.0
-0.0	0.0	-0.0	-21.51	0.0	0.0
0.0	-0.0	-0.0	0.0	-21.51	0.0
-0.0	-0.0	-0.0	0.0	0.0	-23.283

-3938.303	4274.215	50.15	0.0	0.002	0.0
4274.235	-3938.324	50.15	0.002	0.001	0.0
50.093	50.093	258.538	0.0	0.0	0.0
-0.0	0.0	-0.0	-21.51	0.0	0.0
0.0	-0.0	-0.0	0.0	-21.51	-0.0
-0.0	-0.0	-0.0	-0.0	0.0	-23.283

-3937.949	4273.732	50.036	-0.0	-0.002	-0.0
4273.707	-3937.924	50.036	-0.002	-0.001	-0.0
50.093	50.093	258.534	-0.0	-0.0	-0.0
0.0	-0.0	0.0	-21.51	-0.0	0.0
-0.0	0.0	0.0	-0.0	-21.51	-0.0
0.0	0.0	0.0	0.0	0.0	-23.283

101.399	141.734	126.746	-0.0	0.0	0.0
141.734	101.399	126.746	0.0	-0.0	0.0
126.746	126.746	156.319	0.0	-0.0	0.0
-0.0	0.0	0.0	79.04	-0.0	0.0
-0.0	0.0	0.0	0.0	79.04	0.0
-0.0	0.0	0.0	0.0	0.0	94.103

101.4	141.734	126.746	0.0	0.0	0.0
141.734	101.4	126.746	-0.0	-0.0	0.0
126.746	126.746	156.32	0.0	-0.0	0.0
0.0	0.0	0.0	79.04	0.0	-0.0
0.0	0.0	0.0	0.0	79.04	0.0
0.0	0.0	0.0	0.0	0.0	94.103

39.521	14.988	62.085	-31.951	-0.0	0.0
14.988	39.521	62.085	31.951	-0.0	0.0
55.912	55.912	74.617	0.0	0.0	0.0
-31.951	31.951	-0.0	44.199	-0.0	0.0
0.0	0.0	-0.0	0.0	44.199	-31.951
0.0	0.0	0.0	0.0	-31.951	12.266

321.394	24.993	24.993	-0.0	-0.0	-0.0
24.993	321.394	24.993	0.0	-0.0	-0.0
24.993	24.993	321.394	0.0	0.0	0.0
-0.0	-0.0	-0.0	-19.951	-0.0	0.0
0.0	-0.0	-0.0	0.0	-19.951	-0.0
0.0	-0.0	-0.0	-0.0	-0.0	-19.951

321.394	24.994	24.994	0.0	0.0	0.0
24.994	321.394	24.994	0.0	0.0	-0.0
24.994	24.994	321.394	-0.0	0.0	-0.0
-0.0	0.0	-0.0	-19.951	-0.0	0.0
0.0	-0.0	-0.0	0.0	-19.951	-0.0
0.0	-0.0	-0.0	-0.0	-0.0	-19.951

321.397	24.994	24.994	0.0	-0.0	-0.0
24.994	321.397	24.994	0.0	-0.0	-0.0
24.994	24.994	321.397	0.0	0.0	-0.0
-0.0	0.0	-0.0	-19.951	-0.0	-0.0
0.0	-0.0	-0.0	-0.0	-19.951	-0.0
0.0	-0.0	-0.0	0.0	-0.0	-19.951

321.392	24.993	24.993	0.0	0.0	-0.0
24.993	321.392	24.993	0.0	0.0	0.0
24.993	24.993	321.392	0.0	0.0	0.0
0.0	-0.0	0.0	-19.951	0.0	-0.0
-0.0	0.0	0.0	0.0	-19.951	0.0
-0.0	0.0	0.0	-0.0	0.0	-19.951

0.0	0.0	0.0
0.0	10.803	-0.0
0.0	0.0	-0.0
0.0	-0.0	-0.0
0.0	0.0	-0.0
-0.0	0.0	0.0

207.715	71.748	115.609	0.0	1.451	-0.0
71.977	259.089	37.174	-0.0	0.454	-0.0
115.648	36.983	222.961	0.0	0.278	-0.0
0.0	-0.0	-0.0	-10.66	0.0	-0.455
1.121	0.279	0.265	0.0	62.321	-0.0
0.0	-0.0	-0.0	-0.343	0.0	-85.514