Study on melting of uranium dioxide

122 JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2017-0039 Mathematical and Physical Sci. 2017, Vol. 62, Iss. 8, pp. 122-126 This paper is available online at STUDY ON MELTING OF URANIUM DIOXIDE Tran Thuy Duong and Truong Minh Anh School of Nuclear Engineering and Environmental Physics, Hanoi University of Science and Technology Abstract. Determination of the melting point of fuel is essential for designing and operating nuclear reactors. We investigate the melting point of uranium dioxide by molecular dynamics simulation based on the change of the displacement of oxygen atoms, the radial distribution function, the density and the network structure of UO2 fuel. At the temperature of 2200K, the melting occurs at the surface of the fuel. The solid - liquid phase transition occurs mainly in the temperature range from 2800K to 3400K. We propose that the melting point of UO2 fuel is at the temperature of 3400K. Keywords: Melting point, uranium dioxide, phase transition, molecular dynamics simulation. 1. Introduction Understanding the thermal and mechanical properties of nuclear materials, especially nuclear fuel, is very important for the design and operation of reactors [1, 2]. In a loss of coolant accident, fuel melt down could occur and the design parameters of reactor components should be evaluated near the melting point [1]. However, experimental studies of high temperatures, pressures and radiation level are difficult and dangerous because all instruments have their limits of durability. Computer simulations are a way to avoid such complications as isolated processes can be simulated. To evaluate the thermal properties and transport phenomena of UO2, many molecular dynamics (MD) simulations have been performed [1-3, 10]. The aim of this paper is to determine the melting temperature for solid UO2 fuel in the nuclear reactor by using MD simulations. One approache for MD simulation for phase transition is using two atomic regions separated by an interface, where one region corresponds to the molten state while the other is associated with the crystal phase. The phase transition temperature of 3400-3600K for stoichiometric uranium dioxide was determined using this approach [4, 5, 10] and the obtained temperature was 300-500K higher than the experimental temperature of 3120K. Another method is based on an analysis of the radial distribution function of particle number density [5]. Maximums of this function correspond to coordination spheres in a crystal. As the temperature increases, the peak amplitude gradually decreases and the melting causes them to disorder. In particular, the peak number and the distance between them change, which describes the disordered atom system and we can determine the melting process. In this paper, we study the melting temperature of uranium dioxide based on the change of the displacement of oxygen atoms, the radial distribution function, the density and the network structure of fuel when the temperature increases. Received September 14, 2017. Accepted September 29, 2017. Contact Tran Thuy Duong, e-mail: duong.tranthuy@hust.edu.vn Study on melting of unanium dioxide 123 2. Content 2.1. Calculation method Based on the structure change from the crystalline to liquid phase, we determine the melting temperature of UO2. We apply the most popular interaction potential for the UO2 crystalline lattice as follows [5, 6, 8, 10] ( ) ( ) ( ) (1) Here the first term of Eq. (1) represents the Coulomb interaction. Other terms are short range interactions. The second term is the repulsive potential and the third is the van der Waals interaction. The fractional charge is specified for oxygen ions and is equal to 1.2. The charge for uranium ion is obtained by multiplying this value by two (2.4). The parameter f is equal to 0.0345 and rij is the distance between an ion i and another ion j. The other potential parameters were taken from [5, 6] and are listed in Table 1. Table 1. Parameters of the potential represented as [5] Uranium dioxide has flourite structure, where each U is surrounded by eight O nearest neighbors in a cubic arrangement. The MD cell in our simulation was constructed with an array of 7×7×7 supercells in three mutually orthogonal directions totalling 4116 ions. Periodic boundary conditions were applied. Depending on the task, computations were performed for a microcanonical NVE ensemble or a canonical NPT ensemble but both cases fulfilled isothermal conditions. To determine the phase transition temperature, we calculated the dependence of mean squared displacement, radial distribution function, density and structure cell on the temperature. 2.2. Results and discussion We investigated the mean squared displacement (MSD) of uranium and oxygen atoms in the temperature range of 300 to 3400K. The results are shown in Figure 1. At the temperature range of 500 to 3000K, our results are the same as in [1]. In the low temperature range from 300 to 1100 K, the MSD of the oxygen atoms is almost zero. As the temperature increases, the oxygen ions move around the lattice node at medium temperatures and move greater distances at 2600K. In the temperature region of 2800K to 3400K, the MSD is significantly different from that at the lower temperature range. This means that in this temperature range, the sample has been shifted to a liquid state. Moreover, the MSD of uranium atoms is insignificantly changed. This can be easily recognized because the atomic weigh of uranium is much larger than the atomic weigh of oxygen. So when the temperature is near the melting point, the oxygen atoms leave the crystal lattice easily. The change of position in the structure of oxygen atoms is more sensitive to temperature changes than that in uranium atoms. Therefore, in order to more accurately determine the melting Tran Thuy Duong, Truong Minh Anh 124 temperature range of UO2, we will calculate the radial distribution function of oxygen atoms in the sample. 500 1000 1500 2000 2500 3000 0 20 40 60 80 100 Oxygen Uranium M S D ( x 1 0 4 p m 2 ) T (K) Figure 1. Variation in mean square displacement (MSD) of oxygen and uranium ions in UO2 with temperature 2 4 6 8 10 12 14 16 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 g ( r) r (A) 1100K 2200K 2800K 3400K Figure 2. Radial distribution function (RDF) of oxygen atoms at different temperatures Figure 2 is the radial distribution function (RDF) of the O-O pair at different temperatures. Results show that when the temperature of sample reaches 2200K, the RDF of oxygen begins to change at long distances. It can be predicted that at this temperature, a small portion of the surface of the fuel has begun to melt but the interior of the fuel remains in a crystal state. As the temperature increases, this change is easier. At the temperature of 3400K, the RDF form of oxygen is like the RDF form of liquid. At this temperature, the sample is in a liquid state. This is the melting temperature of fuel. To further confirm our calculations, we also investigated the change of the density of fuel when the temperature increases from 300 to 3400K. The dependence of the density on temperature of fuel is shown in Figure 3. It can be seen that the graph is broken at temperature of 2800K. In the transition area from 2800 to 3400K, the density of fuel decreases sharply and goes Study on melting of unanium dioxide 125 up to the value of density of liquid UO2 measured by experiments [8]. Our result is in agreement with those reported in [9]. The change of the network structure of UO2 fuel with temperature is shown in Figure 4. At the temperature of 300K, the sample is in a crystalline state. As the temperature increases, the atoms shift away from the lattice nodes. At 3400K, the network structure of the sample is the chaotic structure of a liquid phase. This is evidence for a phase transition from crystal to liquid of UO2 fuel. Figure 3. Relationship between UO2 density and temperature 300K 2200K 2800K 3400K Figure 4. Network structure of UO2 at different temperatures 3. Conclusion Calculations for the dependence of the mean square displacement, the radial distribution function, the density and the network structure of UO2 on temperature show us the structural change. The change of parameters begins to appear from the temperature of 2200K and more clearly in the temperature range of 2800 to 3400K. At these temperatures, the phase transition from crystal to liquid begins and the material reaches a liquid state at 3400K. Our simulation sample has given a reasonably good value for the melting point. Our estimated value is between 3300 and 3400 K, which is near the experimental value of 3120 K. This shows that our sample gives a reasonable description for high-temperature UO2. Acknowledgements. This work was supported by Hanoi University of Science and Technology under grant number T2016-PC-184. 0 500 1000 1500 2000 2500 3000 7 8 9 10 11 d ( g /c m 3 ) T (K) Tran Thuy Duong, Truong Minh Anh 126 REFERENCES [1] Basak, C. B., A. K. Sengupta and H. S. Kamath, 2003. Classical molecular dynamics simulation of UO2 to predict thermophysical properties. Journal of Alloys and Compounds 360,1, pp. 210-216. [2] TatsumiArima, ShoYamasaki, Yaohiro Inagaki, KazuyaIdemitsu, 2006. Evaluation of thermal conductivity of hypostoichiometric (U, Pu)O2-x solid solution by molecular dynamics simulation at temperatures up to 2000K. Journal of alloys and compounds 415, 1, pp. 43-50. [3] S.I. Potashnikov, A.S. Boyarchenkov, K.A. 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