Novel Synthesis and Applications of Metal, Metal Oxides (MOs), and Transition Metal Dichalcogenides (TMDs) for Energy, Sensing, and Memory Applications
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An Estimation of the Thermal Properties of PuRich Metallic Fuel
Abstract
Purich metallic fuel is promising for transuranic element burners. In this study, we calculated the thermal properties of Purich metallic fuel. The thermal conductivity was calculated by using both Nordheim’s rule and Wiedemann–Franz law. The thermal conductivity of Pu40Zr (14.3 Wm^{−1}·K^{−1} at 600 K) was much lower than that of U10Zr (23.5 Wm^{−1}·K^{−1} at 600 K), another candidate metallic fuel. This addresses the metallic fuel has much lower durability in accidental situations than UZr metallic fuel. Thus, we also calculated thermal conductivity of the Pu20U20Zr alloy. The result shows uranium addition to the PuZr alloy increased the thermal conductivity. In addition, we calculated the melting point of the Pu(0–80U)20Zr alloy and the result shows uranium addition increased melting point. This result suggests the accident tolerance of the Purich metallic fuel increases by adding uranium.
1. Introduction
Fast reactors can burn transuranic elements (TRUs; Pu, Np, Am, and Cm) effectively owing to their higher fissiontoneutroncapture ratio than lightwater reactors (LWRs). LWRs will be the dominant nuclear power plants for at least the next few decades. To burn the TRUs produced from LWRs, it is necessary to improve the TRU burning capability of fast reactors. Because uranium TRUfueled fast reactors also produce TRUs, the most effective approach is to use uraniumfree TRU fuel because this does not produce additional TRUs. Such a system could reduce the capacity of the TRU burner units and the associated fuel cycle facilities to about 1/5 and 1/8, respectively. There have been many studies on uraniumfree or fertilefree fuel systems [1–3]; however, difficulties remain, such as the requirement for new reprocessing technology. For example, reprocessing technology for producing TRUburning oxide fuel is required to separate actinides and lanthanides, which have similar chemical behavior [4]. In addition, the remote control technology for reprocessing needs modifications because of high radioactivity of minor actinides. By contrast, uraniumfree TRU metal could be reprocessed and fabricated based on pyroprocess and injectioncasting technologies without substantial modification [5].
In the United States, many studies concerning uraniumfree metal fuels have been carried out. Most notably, the US acceleratordriven transmutation of waste (ATW) program investigated an acceleratordriven transmutation system coupled with a subcritical fast reactor using uraniumfree metal fuel [6–9]. In such systems, thermal properties, such as the heat capacity, thermal conductivity, and melting temperatures of the fuel, are important for the design of the core structure of the burning reactor.
In our previous study, we estimated the melting temperature of TRUZr alloys [10] and the thermal properties of Purich alloys [11]. In the present study, we evaluate the thermal properties of Pu40Zr (Pu64at%Zr), a candidate material for TRU burners, and Pu20U20Zr (Pu15at%U40at%Zr) in a more relevant way.
2. Estimation of Thermal Properties
We calculated the heat capacity, thermal conductivity, and solidus and liquidus temperatures of the Pu40Zr and the PuUZr alloys because experimental work with plutonium is difficult to obtain approval in Japan. The heat capacity of alloys was estimated using the Neumann–Kopp law, which is equivalent to an additive law. Although the heat capacity varied considerably with phase changes, the estimated values for Pu40Zr and Pu20U20Zr alloys were similar if their phases were the same.
Generally, the thermal conductivity at high temperatures is calculated from the heat capacity, thermal diffusivity, and density. The heat capacity and density are often estimated from the Neumann–Kopp law and Vegard’s law. However, the thermal diffusivity is comparatively difficult to estimate because it varies significantly with composition, phase, and temperature. Another common way to estimate the thermal conductivity of metallic materials is to use the Wiedemann–Franz law, which multiplies the electrical conductivity, absolute temperature, and Lorentz number [12]. Unfortunately, however, the electrical conductivity of PuZr alloys had not been reported. Nordheim’s rule is a common way to estimate the electrical conductivity of element although its use is limited to alloys that form a solid solution. Fortunately, PuZr and PuUZr alloys are considered to form a bodycentered cubic (bcc) solid solution from related binary systems and the UPuZr ternary system [13, 14]. Therefore, the thermal conductivity of Pu40Zr and Pu20U20Zr alloys was estimated using both the Wiedemann–Franz law and Nordheim’s rule with the Nordheim coefficients.
Finally, we calculated the solidus and liquidus temperatures using ThermoCalc, which is based on the CALPHAD method. The phase diagrams of the UZr, PuZr, and UPu systems are available in the literature; thus, we calculated the liquidus and solidus temperatures by creating a pseudobinary system of the Pu(0–80U)20Zr alloy.
2.1. Heat Capacity
Figure 1 shows the data available in the literature for the UZr alloy [15] and the constituents: uranium, zirconium, and plutonium [16, 17]. There are anomalous peaks for the heat capacities of all three elements, which are caused by their phase transitions. The heat capacity of a compound can be estimated using the Neumann–Kopp (additive) law [18, 19]. Specifically, if a solid compound, M, is formed from elements A, B, and C by a chemical reaction:then the heat capacity of the compound is expressed by the heat capacity of each element as follows:
The heat capacity of the UZr alloy measured by Matsui et al. [20] was similar to that calculated using the Neumann–Kopp law. Therefore, it may be possible to use it to determine the heat capacities of PuZr and PuUZr alloys. Plutonium has many phase transitions, at which its heat capacity changes. For the PuZr system created by Kurata [21], the Pu40Zr alloy had two phases from room temperature to melting point, and the phasetransition temperature was approximately 902 K (Figure 2).
The lowtemperature phase is a facecentered cubic (fcc) structure, and the hightemperature phase is a bcc structure. Below 902 K, the heat capacity of plutonium in our calculation was determined by interpolation and/or extrapolation of the value for the β and δ (fcc) phases. Above 902 K, the heat capacity was determined by extrapolation of the ε (bcc) phase. The heat capacity of zirconium was determined in a similar manner. Figure 3 shows the estimated heat capacity for Pu40Zr and Pu20U20Zr alloys. For the Pu20U20Zr alloy, the phasetransition temperature was approximately 900 K, based on the available phase diagrams. The obtained fitting equations were as follows:
Although the phase transition temperature was different from the U50Zr alloy, the value of was not so different from it which has a similar ratio of zirconium with the Pu40Zr alloy.
2.2. Thermal Conductivity
Wiedemann–Franz law is known as a specific rule in metallic elements, which connect thermal conductivity with electrical conductivity [12]:where is the thermal conductivity (Wm^{−1}·K^{−1}), is the electrical conductivity , is the electrical resistivity , is the Lorentz number, and is the temperature (K). The Lorentz number is typically derived from the experimental measurement of thermal and electrical conductivity. However, it can also be derived from quantum mechanics, giving a value of , which is close to that of uranium, plutonium, and zirconium. Thus, we used this theoretical value of the Lorentz number in this study. For alloys form solid solution, Nordheim found that the electrical resistivity has a dependence, as follows [23]:where , , and are the electrical resistivity of the mixture and elements A and B, is the atomic fraction of element B, and is the Nordheim coefficient, which is an elementdependent parameter. For example, for the CuAu alloy, the Nordheim coefficient of CurichAu alloys and AurichCu alloys are different [24]. Thus, we treated the Nordheim coefficients of the UrichZr alloy and ZrrichU alloy separately in this paper.
From the Wiedemann–Franz law and Nordheim’s rule, the thermal conductivity is considered to have the same dependence as the electrical conductivity [25]:where , , and are the thermal conductivity (Wm^{−1}·K^{−1}) of the mixture and elements A and B, respectively, is the atomic fraction of element B, is the Nordheim coefficient, is the Lorentz number, and is the temperature. Because equation (5) only applies for binary alloys, we extended it to treat ternary alloys as a mixture of a binary alloy and third element as follows:where , , and are the thermal conductivity (Wm^{−1}·K^{−1}) of the ternary alloy, binary alloy, and third element C, respectively, and is the atomic fraction of element C. In our estimation, elements A, B, and C were U, Zr, and Pu, respectively, to obtain the Nordheim coefficients. To obtain the thermal conductivity of PuZr and PuUZr, elements A, B, and C were Pu, Zr, and U, respectively.
The thermal conductivity of UZr and UPuZr alloys were taken from the work of Takahashi et al. [26] and reports from the Argonne National Laboratory (ANL) [27, 28]. These values were fitted into the above equations to obtain the Nordheim coefficients and for UZr and UPuZr alloys as temperaturedependent linear functions. To derive these functions, we fitted the temperature dependences of the thermal conductivity of uranium, zirconium, and plutonium using the following equation from available data [29, 30]:
Obtained fitting parameters are shown in Table 1. We obtained the thermal conductivity of PuZr and PuUZr based on the assumption that their Nordheim coefficients were the same as those of UZr and UPuZr alloys. The Nordheim coefficients for UZr and UPuZr alloys are summarized in Table 2. In Figures 4 and 5, we compare the thermal conductivities obtained in the present study using the obtained Nordheim coefficients with those of the available data [26–28]. These show relatively close to measured thermal conductivity for both UZr and UPuZr alloys. For the U79Zr alloy, our correlation showed higher thermal conductivity than experimental data. However, if zirconium content is below 50 wt%, our correlation showed sufficiently agreed well. Obtained Nordheim coefficients were based on these experimental data. These experimental data were only available below 1173 K, and this is the temperature limitation in the present experiment. The Pu40Zr alloy had a significantly lower thermal conductivity than plutonium because of the effect of zirconium addition. However, the thermal conductivity of the Pu20U20Zr alloy was improved and it was close to that of plutonium because of the presence of uranium (Figure 6).


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2.3. Solidus and Liquidus Temperatures
Solidus and liquidus temperatures of the PuUZr alloy (Pu(0–80U)20Zr) were calculated by ThermoCalc [22] by creating a pseudobinary phase diagram. ThermoCalc is the calculation code based on the CALPHAD method, which creates phase diagrams and phase equilibria. A description of the CALPHAD method is provided elsewhere [31]. We used the database for the calculation to create UZr, PuZr, UPu, and UPuZr systems based on the most recent data of the Gibbs free energy reported by Kurata [13, 14] although the Purich region is not well understood in the UPuZr system. Verification of the database provided by Kurata is performed by D. E. Janney et al. [32]. There is no experimental data of the melting points for the PuUZr alloys, and thus, experimental measurement will be mandatory. To judge whether Purich metallic fuel can be used in fast reactors, the system should be evaluated. Our results are shown in Figure 7, and fitting was performed with uranium content as follows:where T_{liq} and T_{sol} are the liquidus and solidus temperatures, respectively, and W_{U} is the weight fraction of uranium. Accordingly, both T_{liq} and T_{sol} increase with increasing uranium content. We calculated T_{liq} and T_{sol} values of 1321.1 and 1530.5 K for the Pu20Zr alloy which were agreed well with the PuZr system [13]. We also calculated them of 1705.4 and 1788.9 K for the U20Zr alloy. These values were slightly lower than those for the U20Zr alloy calculated by the correlation produced by Ogata, as shown in Figure 7 [33, 34].
3. Conclusion
Ufree metallic alloy fuel has important advantages for use in TRU burners. Most importantly, we showed theoretically that the thermal conductivity of the Pu40Zr alloy was lower than that of the UZr alloys, which limits the core power. This addresses the metallic fuel has much lower durability in accidental situation than the UZr metallic fuel. To gain the safety margin, we also provided the estimation for the Purich metallic fuel with small amount of uranium addition. However, the addition of uranium to the PuZr alloy increased its thermal conductivity and solidus temperature. Despite these advantages, it should be noted that uranium addition could lead to lower efficiency in TRU burners.
Data Availability
No data were used to support this study.
Disclosure
Our previous work was presented in NuMat2018 at Seattle, entitled “An estimation of the thermal properties of Purich metallic fuel,” P1.008. This research was conducted as the Nuclear System Research and Development program under a contract with the Ministry of Education, Culture, Sports, Science and Technology (MEXT) in Japan during the fiscal year of 2014 to 2017. The title was “Innovative metallic fuel design and development of the production technology for TRU burning.”
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this study.
Acknowledgments
We thank Adam Brotchie, PhD, from Edanz Group (http://www.edanzediting.com/ac)for editing a draft of this manuscript.
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Copyright
Copyright © 2019 Naoya Odaira and Yuji Arita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.