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**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.

Plots of the cohesive energy vs interatomic spacing, *r*, are shown below for a number of crystal structures. The values were computed using the iprPy E_vs_r_scan calculation method. 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, 200 values of *r* are evaluated between 2.0 and 6.0 Å. 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:**

- 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.

Computed lattice constants and cohesive 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:
- 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.
- Structures in the Materials Project and OQMD DFT databases.

- All initial guesses are relaxed using three independent methods:
- "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 and a 3x3x3 supercell.
- "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.
- "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 a 10x10x10 supercell and nph integration with a 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 passed as inputs to the iprPy crystal_space_group calculation. This calculation uses 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.

**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:**

- 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:

Reference structure matches:

A1--Cu--fcc = mp-150, oqmd-7505

A2--W--bcc = mp-13, oqmd-8568

A3--Mg--hcp = mp-136, oqmd-51781

Ah--alpha-Po--sc = mp-568345

prototype | method | E_{coh} (eV) | a_{0} (Å) | b_{0} (Å) | c_{0} (Å) | α (degrees) | β (degrees) | γ (degrees) |
---|---|---|---|---|---|---|---|---|

A2--W--bcc | dynamic | -4.1341 | 2.8553 | 2.8553 | 2.8553 | 90.0 | 90.0 | 90.0 |

A15--beta-W | dynamic | -4.0609 | 4.5486 | 4.5486 | 4.5486 | 90.0 | 90.0 | 90.0 |

A3--Mg--hcp | dynamic | -4.0262 | 2.5933 | 2.5933 | 4.1653 | 90.0 | 90.0 | 120.0 |

A3'--alpha-La--double-hcp | dynamic | -4.0203 | 2.5901 | 2.5901 | 8.3838 | 90.0 | 90.0 | 120.0 |

A1--Cu--fcc | dynamic | -4.0149 | 3.6583 | 3.6583 | 3.6583 | 90.0 | 90.0 | 90.0 |

oqmd-21053 | dynamic | -3.9884 | 8.6347 | 8.6347 | 4.6087 | 90.0 | 90.0 | 90.0 |

oqmd-21053 | box | -3.9704 | 8.5495 | 8.5495 | 4.6465 | 90.0 | 90.0 | 90.0 |

A5--beta-Sn | static | -3.5654 | 4.2578 | 4.2578 | 2.4645 | 90.0 | 90.0 | 90.0 |

A7--alpha-As | box | -3.505 | 2.5468 | 2.5468 | 17.1341 | 90.0 | 90.0 | 120.0 |

Ah--alpha-Po--sc | static | -3.3816 | 2.2092 | 2.2092 | 2.2092 | 90.0 | 90.0 | 90.0 |

Ah--alpha-Po--sc | static | -3.2514 | 2.4931 | 2.4931 | 2.4931 | 90.0 | 90.0 | 90.0 |

Ah--alpha-Po--sc | box | -3.2501 | 2.4394 | 2.4394 | 2.4394 | 90.0 | 90.0 | 90.0 |

oqmd-21731 | box | -3.2501 | 2.4395 | 2.4395 | 7.3182 | 90.0 | 90.0 | 90.0 |

A4--C--dc | static | -2.892 | 5.4498 | 5.4498 | 5.4498 | 90.0 | 90.0 | 90.0 |

Date Created: October 5, 2010 | Last updated: October 02, 2018