# Revisiting thermodynamics and kinetic diffusivities of uranium–niobium with Bayesian uncertainty analysis

## Abstract

In this paper, thermodynamic and kinetic diffusivities of uranium–niobium (U–Nb) are re-assessed by means of the CALPHAD (CALculation of PHAse Diagram) methodology. In order to improve the consistency and reliability of the assessments, first-principles calculations are coupled with CALPHAD. In particular, heats of formation of γ -U–Nb are estimated and verified using various density-functional theory (DFT) approaches. These thermochemistry data are then used as constraints to guide the thermodynamic optimization process in such a way that the mutual-consistency between first-principles calculations and CALPHAD assessment is satisfactory. In addition, long-term aging experiments are conducted in order to generate new phase equilibria data at the γ _{2}/α+γ _{2} boundary. These data are meant to verify the thermodynamic model. Assessment results are generally in good agreement with experiments and previous calculations, without showing the artifacts that were observed in previous modeling. The mutual-consistent thermodynamic description is then used to evaluate atomic mobility and diffusivity of γ-U–Nb. Finally, Bayesian analysis is conducted to evaluate the uncertainty of the thermodynamic model and its impact on the system's phase stability.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

- OSTI Identifier:
- 1368005

- Alternate Identifier(s):
- OSTI ID: 1334151; OSTI ID: 1411073; OSTI ID: 1440946

- Report Number(s):
- LLNL-JRNL-703367; LA-UR-16-22697

Journal ID: ISSN 0364-5916

- Grant/Contract Number:
- AC52-07NA27344; AC52-06NA25396; DMR-1410983; CMMI-1534534; AC02-05CH11231

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Calphad

- Additional Journal Information:
- Journal Volume: 55; Journal Issue: P2; Journal ID: ISSN 0364-5916

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE; DFT; CALPHAD; Bayesian; uncertainty analysis; metallic fuels; U–Nb; thermodynamics; kinetic diffusivity; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY

### Citation Formats

```
Duong, Thien C., Hackenberg, Robert E., Landa, Alex, Honarmandi, Pejman, Talapatra, Anjana, Volz, Heather M., Llobet, Anna, Smith, Alice I., King, Graham, Bajaj, Saurabh, Ruban, Andrei, Vitos, Levente, Turchi, Patrice E. A., and Arróyave, Raymundo.
```*Revisiting thermodynamics and kinetic diffusivities of uranium–niobium with Bayesian uncertainty analysis*. United States: N. p., 2016.
Web. doi:10.1016/j.calphad.2016.09.006.

```
Duong, Thien C., Hackenberg, Robert E., Landa, Alex, Honarmandi, Pejman, Talapatra, Anjana, Volz, Heather M., Llobet, Anna, Smith, Alice I., King, Graham, Bajaj, Saurabh, Ruban, Andrei, Vitos, Levente, Turchi, Patrice E. A., & Arróyave, Raymundo.
```*Revisiting thermodynamics and kinetic diffusivities of uranium–niobium with Bayesian uncertainty analysis*. United States. doi:10.1016/j.calphad.2016.09.006.

```
Duong, Thien C., Hackenberg, Robert E., Landa, Alex, Honarmandi, Pejman, Talapatra, Anjana, Volz, Heather M., Llobet, Anna, Smith, Alice I., King, Graham, Bajaj, Saurabh, Ruban, Andrei, Vitos, Levente, Turchi, Patrice E. A., and Arróyave, Raymundo. Tue .
"Revisiting thermodynamics and kinetic diffusivities of uranium–niobium with Bayesian uncertainty analysis". United States.
doi:10.1016/j.calphad.2016.09.006. https://www.osti.gov/servlets/purl/1368005.
```

```
@article{osti_1368005,
```

title = {Revisiting thermodynamics and kinetic diffusivities of uranium–niobium with Bayesian uncertainty analysis},

author = {Duong, Thien C. and Hackenberg, Robert E. and Landa, Alex and Honarmandi, Pejman and Talapatra, Anjana and Volz, Heather M. and Llobet, Anna and Smith, Alice I. and King, Graham and Bajaj, Saurabh and Ruban, Andrei and Vitos, Levente and Turchi, Patrice E. A. and Arróyave, Raymundo},

abstractNote = {In this paper, thermodynamic and kinetic diffusivities of uranium–niobium (U–Nb) are re-assessed by means of the CALPHAD (CALculation of PHAse Diagram) methodology. In order to improve the consistency and reliability of the assessments, first-principles calculations are coupled with CALPHAD. In particular, heats of formation of γ -U–Nb are estimated and verified using various density-functional theory (DFT) approaches. These thermochemistry data are then used as constraints to guide the thermodynamic optimization process in such a way that the mutual-consistency between first-principles calculations and CALPHAD assessment is satisfactory. In addition, long-term aging experiments are conducted in order to generate new phase equilibria data at the γ2/α+γ2 boundary. These data are meant to verify the thermodynamic model. Assessment results are generally in good agreement with experiments and previous calculations, without showing the artifacts that were observed in previous modeling. The mutual-consistent thermodynamic description is then used to evaluate atomic mobility and diffusivity of γ-U–Nb. Finally, Bayesian analysis is conducted to evaluate the uncertainty of the thermodynamic model and its impact on the system's phase stability.},

doi = {10.1016/j.calphad.2016.09.006},

journal = {Calphad},

number = P2,

volume = 55,

place = {United States},

year = {Tue Sep 20 00:00:00 EDT 2016},

month = {Tue Sep 20 00:00:00 EDT 2016}

}