Calculation of steady-state dynamical phase diagram in U-Mo binary system under irradiation

doi:10.1016/j.jnucmat.2020.152698

Journal of Nuclear Materials

Volume 544, February 2021, 152698

https://doi.org/10.1016/j.jnucmat.2020.152698 Get rights and content

Highlights

•
irradiation-enhanced diffusion and irradiation-induced ballistic mixing are considered in the effective free energy.
•
The steady-state dynamical phase diagram of U-Mo binary system under irradiation is calculated.
•
Under irradiation, the high-temperature stable γ(U,Mo) phase can be stabilized near room temperature.

Abstract

The steady-state dynamical phase diagram of U-Mo system under irradiation is studied by the thermodynamic model and effective free energy model. In the effective free energy model, we consider the irradiation-enhanced diffusion and ballistic mixing caused by recoil implantation and cascade collision. The effective free energy and diffusivity of each phase in U-Mo binary system at different temperatures were calculated. The dynamical phase diagrams of U-Mo alloys under different irradiation intensities were calculated and the differences between the dynamical phase diagram and thermodynamic equilibrium phase diagram was discussed. The calculated results show that, due to the irradiation-induced ballistic mixing, the high-temperature stable γ(U,Mo) phase can be stabilized near room temperature, which agree well with the experimental reports.

Introduction

Metallic uranium alloys are being developed as candidate fuels for future high performance nuclear power reactors. The isotropic body-centered cubic (bcc) γ phase is expected to be more resistant to thermal recycling and irradiation damage than non-isotropic α phase [1]. Uranium alloys with the addition of molybdenum in γU phase(containing from 15.1 to 21.6 at% molybdenum) exhibit good mechanical strength, thermal conductivity, increased corrosion resistance and irradiation performance [2], [3], [4]. Generally, U-Mo alloys are inevitably subject to the extreme environments of intense irradiation during its application, which is considered as thermodynamically nonequilibrium state and produce a range of phase transformations and microstructural alterations [5]. These evolutions can significantly affect the physical and mechanical properties of uranium alloys.

An in-reactor study of U-Mo alloys have been reported by Bleiberg et al. [6]. Their experimental results show that, at temperature range of 70-200°C, the alloys reverted to the metastable high-temperature γ phase during irradiation. This phenomena cannot be explained by the thermodynamic equilibrium phase diagram(TEPD) of U-Mo binary system [7]. As show in Fig. 1, stable γ(U,Mo) phase region only exist at high temperatures and experiences an eutectoid decomposition below 828K from the γ(U,Mo) phase into αU and MoU₂ phase. It is reported that irradiation-induced ballistic mixing could stabilize solid solution phases and order-disorder transition in intermetallic compounds [8]. However, the effects of irradiation on the phase boundary and alloy solubility are still not clear. Therefore, as a promising fuel materials, detailed investigations of the phase stability of U-Mo alloys are necessary to be carried out.

As is well known, the thermodynamic properties and phase relationships of alloying system under thermodynamic equilibrium can be described by thermodynamic models. However, the U-Mo alloys are inevitably subject to irradiation during its application. Hence, the phase relationships of U-Mo alloys under irradiation cannot be simply explained by referring to the thermodynamic properties or the thermodynamic equilibrium phase diagrams. Previous studies have showed that irradiation impacted alloys through two main mechanisms: irradiation-induced mixing and irradiation-enhanced diffusion [9]. Martin [10] studied the influence of ballistic mixing on diffusion and proposed a macroscopic, continuum-based model, in which an effective free energy functional was defined by adding the extra diffusion term to the Cahn-Hilliard equations. In their model, the ballistic effects were mainly caused by recoil implantation and cascade collision [9,10]. The effective free energy model has been successfully used for the steady-state dynamical phase diagram calculation of U-Nb system under irradiation [11].

The purpose of this paper is to study the influence of irradiation intensity, irradiation temperature and irradiation-induced defect on the diffusion coefficient and the effective free energy. By applying the effective free energy model and the thermodynamic model, we calculate the steady-state dynamical phase diagram of U-Mo binary system under irradiation and compare the calculated results with thermodynamic equilibrium phase diagram.

Section snippets

Thermodynamic modeling

In U-Mo binary system, the Gibbs free energies of the solution phases (αU, βU, γ(U,Mo), (Mo)) were described by the sub-regular solution model. The molar Gibbs free energy of each solution phase in the U-Mo system is given as follows: $F = \sum_{i = U, M o}^{0} G_{i}^{φ} c_{i} + R T \sum_{i = U, M o} c_{i} \ln c_{i} + c_{U} c_{M o} \sum_{j = 0}^{n}^{j} L_{U, M o}^{φ} {(c_{U} - c_{M o})}^{j}$ where $^{0} G_{i}^{φ}$ is the Gibbs free energy of the pure element i in the φ phase, which is taken from the SGTE database compiled by Dinsdale [12]. R is the gas constant and T is the absolute temperature. The c_i is

Irradiation-enhanced diffusion

In this work, the formation energy and migration energy of vacancy for the MoU₂ phase were calculated by first-principles methods, all calculations are performed with the Vienna Ab-initio Simulation Package (VASP) code [20,21] of projector-augmented wave (PAW) method [22]. The generalized gradient approximation with the Perdew-Burke-Ernzerhofscheme [23] is adopted for the exchange-correlation potential. The diffusion barriers for a vacancy inside MoU₂ crystal are calculated using the climbing

Discussion

Our present calculations have shown the effect of irradiation-induced point defects(i.e., vacancy and interstitial) concentrations on the irradiation-enhanced diffusion coefficient and the effective free energy of the various potential phases of the U-Mo system. The calculated results indicate that the vacancy concentration and the diffusion coefficient increases with the decrease of dislocation density(ρ_d) under irradiation. However, due to the self-diffusion coefficients were mutually offset

Conclusions

By coupling the effective free energy model and the thermodynamic model, the steady-state dynamical phase diagram of U-Mo binary system under irradiation was calculated and the differences between the steady-state dynamical phase diagram and the conventional thermodynamic equilibrium phase diagram were discussed. It is found that the irradiation has little effect on the phase equilibria in U-Mo binary system at high temperatures. Under irradiation, the γ(U,Mo) phase can be stabilized at lower

Author contributions

Yong Lu: Conceptualization, modelling; Zheng Jiang: Writing; Linyang Li: Calculation, Programming; Cuiping Wang: Supervision; Xingjun Liu: Conceptualization, Reviewing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to thank the financial support for this research by National Key R&D Program of China (2017YFB0702401), Natural Science Foundation of Fujian Province(2019J01033) and the Fundamental Research Funds for the Central Universities (20720170038).

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As an example of thermomechanical treatment, it has been found that stress-assisted phase transformation could be realized as well as the pronounced properties (e.g., superplasticity) through the thermomechanical coupled process [22,61,62]. In addition, the recent computational results from the effective free energy and the thermodynamic modeling show that γ-U phase can be stabilized at lower temperatures due to the irradiation-induced ballistic mixing [15,16]. The aforementioned treatment strategies as well as radiation effects provide possible opportunities for tuning the PTW.
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View full text

Calculation of steady-state dynamical phase diagram in U-Mo binary system under irradiation

Highlights

Abstract

Introduction

Section snippets

Thermodynamic modeling

Irradiation-enhanced diffusion

Discussion

Conclusions

Author contributions

Declaration of Competing Interest

Acknowledgements

Phys. Chem. Solids.

Alloy. Comp.

J. Nucl. Mater.

J. Nucl. Mater.

Calphad

Acta. Metall.

Prog. Mater. Sci

Mater. Sci. Eng. A

J. Nucl. Mater.

J. Nucl. Mater.

J. Non-Cryst. Solids.

J. Nucl. Mater

Acta Mater

J. Nucl. Mater.

Interaction of uranium-molybdenum fuel with an aluminum matrix with deep burnup

At. Energy