## Abstract

U-Mo alloys are being developed as low enrichment uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) Program. In order to understand the fundamental diffusion behavior of this system, solid-to-solid pure U *vs* Mo diffusion couples were assembled and annealed at 923 K, 973 K, 1073 K, 1173 K, and 1273 K (650 °C, 700 °C, 800 °C, 900 °C, and 1000 °C) for various times. The interdiffusion microstructures and concentration profiles were examined* via* scanning electron microscopy and electron probe microanalysis, respectively. As the Mo concentration increased from 2 to 26 at. pct, the interdiffusion coefficient decreased, while the activation energy increased. A Kirkendall marker plane was clearly identified in each diffusion couple and utilized to determine intrinsic diffusion coefficients. Uranium intrinsically diffused 5-10 times faster than Mo. Molar excess Gibbs free energy of U-Mo alloy was applied to calculate the thermodynamic factor using ideal, regular, and subregular solution models. Based on the intrinsic diffusion coefficients and thermodynamic factors, Manning’s formalism was used to calculate the tracer diffusion coefficients, atomic mobilities, and vacancy wind parameters of U and Mo at the marker composition. The tracer diffusion coefficients and atomic mobilities of U were about five times larger than those of Mo, and the vacancy wind effect increased the intrinsic flux of U by approximately 30 pct.

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## References

Keiser D, Hayes S, Meyer M, Clark C. JOM 2003;55:55.

Snelgrove JL, Hofman GL, Meyer MK, Trybus CL, Wiencek TC. Nucl Eng Des 1997;178:119.

Lemoine P, Wachs D (2007) Advanced Nuclear Fuel Cycles and Systems, Boise, Idaho.

Meyer MK, Hofman GL, Hayes SL, Clark CR, Wiencek TC, Snelgrove JL, Strain RV, Kim KH. J Nucl Mater 2002;304:221.

Leenaers A, Van den Berghe S, Koonen E, Jarousse C, Huet F, Trotabas M, Boyard M, Guillot S, Sannen L, Verwerft M. J Nucl Mater 2004;335:39.

Perez E, Yao B, Keiser DD, Sohn YH. J Nucl Mater 2010;402:8.

Keiser DD, Jue JF, Yao B, Perez E, Sohn Y, Clark CR. J Nucl Mater 2011;412:90.

Yao B, Perez E, Keiser Jr DD, Jue J-F, Clark CR, Woolstenhulme N, Sohn Y. J Alloys Compd 2011;509:9487.

Perez E, Keiser D, Sohn Y. Metall Mater Trans A 2011;42:3071.

Leenaers A, Van den Berghe S, Van Renterghem W, Charollais F, Lemoine P, Jarousse C, Rohrmoser A, Petry W. J Nucl Mater 2011;412:41.

Liu X, Lu TC, Xing ZH, Qian DZ. Rare Metal Mat Eng 2011;40:1125.

Mazaudier F, Proye C, Hodaj F. J Nucl Mater 2008;377:476.

Komar C, Mirandou M, Aricó S, Balart S, Gribaudo L (2009) J Nucl Mater 395:162.

Kim Y, Hofman G, Ryu H, Hayes S. J Phase Equilib Diff 2006;27:614.

Ryu H, Park J, Kim C, Kim Y, Hofman G. J Phase Equilib Diff 2006;27:651.

Lundberg LB. J Nucl Mater 1989;167:64.

Adda Y, Philibert J. Compt. rend. 1958;246:113.

Adda Y, Kirianenko A. J Nucl Mater 1959;1:120.

Adda Y, Kirianenko A, Mairy C. J Nucl Mater 1959;1:300.

Adda Y, Kirianenko A. J Nucl Mater 1962;6:130.

Pavlinov L, Nakonechnikov A, Bykov V. Atomic Energy 1965;19:1495.

Fedorov GB, Smirnov EA, Zhomov FI, Gusev VN, Paraev SA. Atomic Energy 1971;31:1280.

Adda Y, Kirianenko A. J Nucl Mater 1962;6:135.

Manning J. Metall Mater Trans B 1970;1:499.

H. Mehrer, ed.:

*Diffusion in Solid*, Springer, Berlin, 2007.Loo FV. Prog Solid State Chem 1990;20:47.

Parida SC, Dash S, Singh Z, Prasad R, Venugopal V. J Phys Chem Solids 2001;62:585.

Brandes EA, Brook GB (1992)Smithells Metals Reference Book, 7th edn. Butterworth-Heinemann, Bodmin, U.K.

Berche A, Dupin N, Guéneau C, Rado C, Sundman B, Dumas JC. J Nucl Mater 2011;411:131.

Shewmon P (1989) Diffusion in Solids. Wiley, New York.

Ogata T, Akabori M, Itoh A, Ogawa T. J Nucl Mater 1996;232:125.

Hall LD. J. Chem. Phys. 1953;21:3.

Zhang X, Cui YF, Xu GL, Zhu WJ, Liu HS, Yin BY, Jin ZP. J Nucl Mater 2010;402:15.

Brewer L, Lamoreaux RH, Ferro R, Marazza R, Girgis K. Atomic energy review 1980;7:336.

Garg SP, Ackermann RJ. J Nucl Mater 1977;64:265.

Vamberskii YV, Udovskiy AL, Ivanov OS. J Nucl Mater 1973;46:192.

R.Gaskell D (2009) Introduction to the Thermodynamics of Materials, 4th edn. Taylor & Francis, New York.

## Acknowledgment

This study was supported by the U.S. Department of Energy, Office of Nuclear Materials Threat Reduction (NA-212), the National Nuclear Security Administration, under DOE-NE Idaho Operations Office Contract DE-AC07-05ID14517. Accordingly, the U.S. Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for the purpose of the U.S. Government.

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Manuscript submitted January 20, 2012.

## Appendix: Thermodynamic Description of γ(bcc) Phase in U-Mo System

### Appendix: Thermodynamic Description of γ(bcc) Phase in U-Mo System

Thermodynamic activity factors of U, \( a_{\rm U} , \) as a function of *N*
_{U} at a given temperature, were evaluated using the ideal solution, regular solution, and subregular solution models. The \( a_{\rm U} \) is related to *N*
_{U} by the activity coefficient γ_{U} as[37]:

In the ideal solution model, the interaction between U and Mo is ignored,[37] and the γ_{U} is unity. Therefore, \( a_{\rm U} \) is equal to *N*
_{U}.

In both the regular solution and subregular solution models, γ_{U} is not unity and can be derived from the molar excess Gibbs free energy, \( \Updelta G^{E} . \) This is expressed as[37]

where, Ω is a parameter in the regular solution model and is a function of *N*
_{Mo} or *N*
_{U} in the subregular solution model. \( \Updelta \bar{G}_{{\text{U \;or\; Mo}}}^{E} \) is the partial molar excess Gibbs free energy of U or Mo and is related to its respective γ as[37]

where, *R* is the molar gas constant with a value of 8.31 J/mol K, and *T* is the temperature in Kelvin.

The molar excess Gibbs free energy, \( \Updelta G^{\text{E}} , \) of U-Mo alloy (γ phase) in the temperature range from 838 K to 1557 K (565 °C to 1284 °C) is given by Parida[27] as

In the regular solution model, \( \Updelta G^{E} \) at a specific composition and temperature is calculated using Eq. [A4]. Then the value of \( \Updelta G^{\text{E}} \) is applied to determine Ω through Eq. [A2]. Finally, γ_{U} is obtained by substituting the value of Ω into Eq. [A3].

The subregular solution model can be more flexible than the regular solution model because it arbitrarily allows Ω to vary with composition as \( \Upomega = a + bN_{\rm U} \).[36] Thus, Eq. [A2] can derive to

where *a* and *b* can be determined through equating the corresponding terms in Eqs. [A4] and [A5] and can then be utilized to calculate the value of Ω to obtain γ_{U}. The value of in \( a_{\rm U} \) either the regular or subregular solution models is then simply determined by substituting γ_{U} into Eq. [A1].

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Huang, K., Keiser, D.D. & Sohn, Y. Interdiffusion, Intrinsic Diffusion, Atomic Mobility, and Vacancy Wind Effect in γ(bcc) Uranium-Molybdenum Alloy.
*Metall Mater Trans A* **44**, 738–746 (2013). https://doi.org/10.1007/s11661-012-1425-9

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DOI: https://doi.org/10.1007/s11661-012-1425-9