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2018--Starikov-S-V-Kolotova-L-N-Kuksin-A-Y-et-al--U-Mo

Citation: S.V. Starikov, L.N. Kolotova, A.Y. Kuksin, D.E. Smirnova, and V.I. Tseplyaev (2018), "Atomistic simulation of cubic and tetragonal phases of U-Mo alloy: Structure and thermodynamic properties", Journal of Nuclear Materials, 499, 451-463. DOI: 10.1016/j.jnucmat.2017.11.047.
Abstract: We studied structure and thermodynamic properties of cubic and tetragonal phases of pure uranium and U-Mo alloys using atomistic simulations: molecular dynamics and density functional theory. The main attention was paid to the metastable γ0-phase that is formed in U-Mo alloys at low temperature. Structure of γ0-phase is similar to body-centered tetragonal (bct) lattice with displacement of a central atom in the basic cell along [001] direction. Such displacements have opposite orientations for part of the neighbouring basic cells. In this case, such ordering of the displacements can be designated as antiferro-displacement. Formation of such complex structure may be interpreted through forming of short U-U bonds. At heating, the tetragonal structure transforms into cubic γs-phase, still showing ordering of central atom displacements. With rise in temperature, γs-phase transforms to γ-phase with a quasi body-centered cubic (q-bcc) lattice. The local positions of uranium atoms in γ-phase correspond to γs-phase, however, orientations of the central atom displacements become disordered. Transition from γ0 to γ can be considered as antiferro-to paraelastic transition of order-disorder type. \n\nThis approach to the structure description of uranium alloy allows to explain a number of unusual features found in the experiments: anisotropy of lattice at low temperature; remarkably high self-diffusion mobility in γ-phase; decreasing of electrical resistivity at heating for some alloys. In addition, important part of this work is the development of new interatomic potential for U-Mo system made with taking into account details of studied structures.

See Computed Properties
Notes: These files were sent by S.V. Starikov (Joint Institute for High Temperatures, Russian Academy of Sciences) on 3 Dec. 2017 and posted with his permission.
File(s): superseded


See Computed Properties
Notes: This file was recieved by Sergei Starikov on August 2, 2018. He noted: "In the previous version, one function for Mo-Mo interaction had poor smoothing with r=r_cut. This "bug" led to the sake of the energy conservation during high-temperature (or long) calculations for pure Mo or U-Mo alloy. I made an additional check and found a small potential compilation issue leading to this energy drift. I fixed the file, so now it can be safely used with the time-step = 0.5 fs, even for long runs at high temperatures (the test was made for 1500K)."
File(s):

Implementation Information

This page displays computed properties for the 2018--Starikov-S-V--U-Mo--LAMMPS--ipr1 implementation of the 2018--Starikov-S-V-Kolotova-L-N-Kuksin-A-Y-et-al--U-Mo 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

2018--Starikov-S-V--U-Mo--LAMMPS--ipr1/diatom

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2018--Starikov-S-V--U-Mo--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

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2018--Starikov-S-V--U-Mo--LAMMPS--ipr1/EvsR.Mo

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.

  1. 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.
  2. 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.
  3. The relaxed structures obtained from #2 are then evaluated using the spglib package to identify an ideal crystal unit cell based on the results.
  4. 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.
  5. The cohesive energy, Ecoh, is calculated from the measured potential energy per atom, Epot$, 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-8637, oqmd-676152, oqmd-1214544
A15--beta-W = oqmd-1214989, oqmd-1280332
A2--W--bcc = mp-129, oqmd-676469, oqmd-1215167
A3'--alpha-La--double-hcp = mp-1066523, oqmd-1215435
A3--Mg--hcp = oqmd-1215345
A4--C--dc = oqmd-1215524
A5--beta-Sn = oqmd-1215613
A6--In--bct = oqmd-1215702

prototypemethodEcoh (eV/atom)Epot (eV/atom)a0 (Å)b0 (Å)c0 (Å)α (degrees)β (degrees)γ (degrees)
A2--W--bccdynamic-6.8803-6.88033.14913.14913.149190.090.090.0
oqmd-1214811dynamic-6.6737-6.67379.72459.72459.724590.090.090.0
oqmd-1214811box-6.6402-6.64029.71039.71039.710390.090.090.0
oqmd-1215256box-6.6258-6.62582.74635.2554.528790.090.090.0
A3--Mg--hcpbox-6.6018-6.60182.96382.96384.460290.090.0120.0
A15--beta-Wdynamic-6.5968-6.59684.99554.99554.995590.090.090.0
A6--In--bctstatic-6.5717-6.57172.68392.68394.512490.090.090.0
oqmd-1214900box-6.5642-6.56426.83726.83726.837290.090.090.0
A3'--alpha-La--double-hcpstatic-6.553-6.5532.85352.85359.090590.090.0120.0
mp-1181019box-6.5506-6.55064.99365.053610.260790.0100.190.0
mp-1181019static-6.5411-6.54115.00435.173210.083490.097.890.0
mp-1180307static-6.5308-6.53089.49613.06649.707990.0112.590.0
A1--Cu--fccstatic-6.5168-6.51683.98213.98213.982190.090.090.0
mp-1180307box-6.5086-6.50869.56853.0589.690690.0113.090.0
oqmd-1214633static-6.4955-6.49553.00473.00476.191190.090.0120.0
mp-1190217dynamic-6.4303-6.43037.71722.67613.55490.0101.290.0
mp-1190217static-6.4118-6.41187.77152.665213.499990.0101.190.0
mp-1190217box-6.411-6.4117.72162.66813.460990.0100.990.0
oqmd-1215078box-6.4108-6.41084.43959.79693.067790.090.090.0
A5--beta-Snbox-6.1286-6.12864.98334.98332.731290.090.090.0
mp-1056004static-5.9919-5.99192.80422.80422.510290.090.0120.0
oqmd-1214722static-5.8417-5.84174.37967.64294.384390.090.090.0
Ah--alpha-Po--scbox-5.7384-5.73842.54352.54352.543590.090.090.0
A7--alpha-Asstatic-5.6155-5.61553.57793.577910.074890.090.0120.0
oqmd-1215969static-5.6119-5.61194.30254.30254.459990.090.0120.0
A7--alpha-Asbox-5.5708-5.57083.69983.69989.379490.090.0120.0
A4--C--dcstatic-4.902-4.9025.64975.64975.649790.090.090.0
A7--alpha-Asstatic-4.7364-4.73643.13063.13067.5590.090.0120.0
A4--C--dcdynamic-4.3379-4.33794.13084.13084.130890.090.090.0
A3--Mg--hcpdynamic-1.7854-1.78541.81591.81592.837590.090.0120.0
A3'--alpha-La--double-hcpbox-1.7602-1.76021.85981.85986.076190.090.0120.0
A3'--alpha-La--double-hcpbox-1.7408-1.74081.81971.81976.007290.090.0120.0
A2--W--bccstatic-1.5806-1.58062.03142.03142.031490.090.090.0
A3--Mg--hcpbox-1.141-1.1415.42745.42748.862990.090.0120.0
A3'--alpha-La--double-hcpbox-1.141-1.1415.42745.427417.725890.090.0120.0
A1--Cu--fccdynamic-1.141-1.1417.67557.67557.675590.090.090.0
A15--beta-Wdynamic-0.9087-0.90879.24889.24889.248890.090.090.0
A2--W--bccdynamic-0.9033-0.90335.44355.44355.443590.090.090.0
A2--W--bccdynamic-0.8002-0.80026.26846.26846.268490.090.090.0
Ah--alpha-Po--scdynamic-0.616-0.6165.42915.42915.429190.090.090.0
A5--beta-Sndynamic-0.6159-0.615910.51410.5145.428690.090.090.0
A5--beta-Sndynamic-0.5237-0.52378.93078.93074.612190.090.090.0
A1--Cu--fccdynamic-0.5004-0.50046.69146.69146.691490.090.090.0
A3'--alpha-La--double-hcpbox-0.5004-0.50044.73164.731615.453290.090.0120.0
A3--Mg--hcpbox-0.5004-0.50044.73164.73167.726690.090.0120.0
A5--beta-Snbox-0.481-0.4819.0259.0254.343590.090.090.0
A6--In--bctbox-0.4775-0.47754.73564.73567.114590.090.090.0
A4--C--dcdynamic-0.4216-0.421612.539312.539312.539390.090.090.0
A15--beta-Wstatic-0.3984-0.39847.61547.61547.615490.090.090.0
Ah--alpha-Po--scdynamic-0.2592-0.25924.73324.73324.733290.090.090.0
A4--C--dcdynamic-0.1749-0.174910.93210.93210.93290.090.090.0
A1--Cu--fccdynamic-0.0976-0.09766.09026.09026.090290.090.090.0
A3--Mg--hcpdynamic-0.0976-0.09764.30644.30647.032390.090.0120.0
A3'--alpha-La--double-hcpbox-0.0976-0.09764.30644.306414.064690.090.0120.0

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:
195.719299.157299.1570.0-0.00.0
299.157195.719299.1570.00.00.0
299.157299.157195.7190.00.00.0
0.00.00.063.7430.00.0
0.00.00.0-0.063.7430.0
0.00.00.0-0.00.063.743

Phonon and Quasi-Harmonic Approximation Predictions

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

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

Notes and Disclaimers:

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

Version Information:

  • 2023-03-14. Phonon and QHA plots added

Band Structures, Density of States, and QHA Verification Plots

Composition:
Prototype:
a0:
plot: