I. INTRODUCTION
Recently, demand for Pd, Nd, Dy, and other rare metals is increased because they are used for many rapidly-progressing technologies such as clean energy devices. As a result, in Japan, which relies on the import of them from other countries, supply risks of them have increased. Thus, a stable supply of these rare elements is strongly desired.
It is known that platinum group metals (PGMs), rare earth (RE), and other useful elements are contained in spent nuclear fuels (SNF) of nuclear reactors as fission products (FPs). They are defined nuclear rare metals (NRMs) in the concept of the Advanced ORIENT cycle [1], shown in the upper part of Fig. 1, in which these materials are actively retrieved from SNF by chemical partitioning to use as precious resources. Most of these elements, however, have very high or long-life radioactivity which prevents them to be considered as resources.
The nuclear transmutation process has a possibility of decreasing the amount of radioactive nuclides, as well as to change an element to another one, eventually leading to a stable isotope by such a process:
The Après ORIENT research program [2] shown in the lower part of Fig. 1 was initiated in FY2011 aiming at creating stable, highly-valuable elements (i.e. secondary NRMs) by nuclear transmutation from FPs contained in SNF of nuclear reactors. The present investigation was carried out as a fundamental study to embody the Après ORIENT research program to clarify characteristics of creation of elements by nuclear transmutation.
II. CALCULATION METHOD
A burnup calculation was performed to analyze the nuclear transmutation rate from FPs. In this study, nuclear reactors were assumed as sources of intense neutron flux and neutron capture reactions by reactor neutrons were considered as a method of creation of NRMs by nuclear transmutation. After a nucleus captures a neutron, it may eventually undergo β- decay and, therefore, is transformed into another element having one proton more than before. Hence, stable highly-valuable rare metal elements (i.e. secondary NRMs) will be created by (n, γ) reaction, succeeded by β- decay of FPs which are generally characterized by high radioactivity. Such a process can be written as
The burnup calculation was carried out with the ORLIBJ40 package [4], which is a combination of ORIGEN2.2 code [5] as burnup calculation code and 1-group cross section library based on JENDL-4.0 [6]. In ORLIBJ40, the irradiation geometry is assumed to be homogeneous, which may not be realistic. This point will be improved in our future work by employing 3-dimensional Monte-Carlo simulators.
The flowchart of computation adopted in this study is shown in Fig. 2. It is assumed to irradiate a target element by neutrons in LWR such as PWR, FBR such as MONJU (a sodium cooled prototype fast breeder reactor in Japan). The computation scheme consists of the following 7 steps:
STEP 1: A burnup calculation is performed with the condition that a PWR is operated for 1125 days to reach 45000 MWd/tHM. The fuel is assumed to be fresh with an enrichment of 235U by 4.7%. A 1-group cross section library PWR47J40.LIB [7] is used in this calculation.
STEP 2: A decay calculation of the spent nuclear fuels during a cooling period of 5 years is carried out. Yields of elements contained in FPs after the cooling are shown in Fig. 3.
STEP 3: Amount and isotopic composition of each element are analyzed as an initial condition of the target ZFP element for neutron irradiation in the following steps.
STEP 4: Input data of each target ZFP element is prepared for a burnup calculation of a ZFP assumed to have been obtained by perfect mutual element separation (amount and isotopic composition of which is determined in STEP 3). Then, the ZFP is also assumed to have been reloaded in a core region of a PWR or a blanket region of MONJU at the time of the mutual element separation. Isotopic composition of the nuclear fuel of each reactor core is shown in Table 1. Isotopic composition of reloaded Ru and Rh are shown in Table 2 as examples of reloaded a ZFP.
| Mass number | LWR (PWR) (%) | FBR (MONJU) (%) | |
|---|---|---|---|
| U | 235 | 4.7 | 0.24 |
| 238 | 95.3 | 80.76 | |
| Pu | 238 | - | 0.57 |
| 239 | - | 10.07 | |
| 240 | - | 4.75 | |
| 241 | - | 2.28 | |
| 242 | - | 1.33 |
| 44Ru | 45Rh | ||||
|---|---|---|---|---|---|
| Mass number | Weight (g) | Half-life | Mass number | Weight (g) | Half-life |
| 98 | 1.20E-07 | Stable | 101 | 3.54E-10 | 3.3 years |
| 99 | 2.35E-02 | Stable | 102 | 3.22E-06 | 207 days |
| 100 | 1.42E+02 | Stable | *102m | 5.51E-08 | 3.742 years |
| 101 | 1.05E+03 | Stable | 103 | 6.13E+02 | Stable |
| 102 | 1.07E+03 | Stable | 106 | 6.17E-06 | 30.07 sec |
| 103 | 5.41E-13 | 39.26 days | |||
| 104 | 7.21E+02 | Stable | |||
| 106 | 6.59E+00 | 371.8 days | |||
STEP 5: A burnup calculation is performed corresponding to operation of each reactor for 1125 days with the following conditions:
PWR; neutron flux: 3.29×1014 /(cm2 s), with a 1-group cross section library as PWR47J40.LIB.
MONJU; neutron flux: 2.70×1015 /(cm2 s), with a 1-group cross section library as MONJMXRDJ40.LIB [7].
STEP 6: A decay calculation is carried out corresponding to a cooling period of 5 years.
STEP 7: Analysis of the amount and isotopic composition of the Z+1NRM element created from the ZFP is performed.
III. RESULTS AND DISCUSSION
A. Comparison of the "creation rate" of a Z+1NRM element
In order to discuss transmutation efficiency quantitatively, "creation rate" of a Z+1NRM element was defined as
Actually, this quantity indicates a yearly-average of the transmutation rate for an irradiation period of 1125 days (3.08 years). Then, comparison of creation rates of each Z+1NRM element calculated by Eq. (3), as shown in Fig. 4. The creation rate of 45Rh represents the calculated result for 45Rh created from transmutation of reloaded 44Ru contained in FPs. It turned out that high creation rates appeared in valuable elements such as PGMs (44Ru: 8.03%/year (FBR), 46Pd: 20.6%/year (LWR)) and middle or heavy RE elements (for example, 64Gd: 23.4%/year (LWR), 66Dy: 17.1%/year (FBR)). Overall, there is a tendency in many elements having small creation rates (less than 1%/year) such as 39Y, that the creation rate by FBR is higher than that by LWR, depending on the difference in the amount of neutron flux. On the contrary, some elements with high creation rates (more than 10%/year) such as 50Sn, show the opposite results regardless of the difference in the neutron flux. Therefore, it can be concluded that both transmutation systems have certain advantages and disadvantages and it should be carefully chosen which system to use to create a certain Z+1NRM. Incidentally, if proper moderators were applied in the transmutation region of FBR, higher creation rates could be obtained for any Z+1NRM element.
It is also clear in Fig. 4 that there is a difference in these creation rates according to even-oddness of atomic numbers Z’ (=Z+1). In addition, it is shown that these elements with even Z’ have higher creation rates than those with odd Z’. For example, the creation rate of 46Pd from 45Rh is higher than those of both sides, that is, 45Rh from 44Ru and 47Ag from 46Pd. It is generally known that nuclei with an even number of protons are more stable than those with an odd number of protons. Therefore, the difference in each creation rate of Z+1NRM is considered to be based on the difference in the stability of the nucleus due to even-odd effects.
B. Introduction of "average 1-group neutron capture cross section"
The transmutation rate of a nuclide can be approximately represented to be directly proportional to the neutron capture cross section of the nuclide and neutron flux, such as
Naively, the creation rate of a Z+1NRM element might be represented in the same way. However, the cross section of a ZFP element does not exist because a cross section is a physical quantity associated with a nucleus but not an element. In the present study, the "average 1-group neutron capture cross section" of a ZFP element was introduced, and was defined as
⟨cZ⟩: average 1-group neutron capture cross section of element Z;
σcZi: 1-group neutron capture cross section of isotope i of element Z;
mZi: weight of isotope i of element Z in FP.
Figure 5 shows average 1-group neutron capture cross sections of each target ZFP element. It turns out that the structure of these average 1-group neutron capture cross sections of each target ZFP element (Fig. 5) has a clear correlation with that of those creation rates of each Z+1NRM element (Fig. 4). In addition, it is noticed that there are two valleys minimizing cross sections (around Sr and Ce). This structure is considered to be formed by the presence of N=50 and 82 "neutron magic numbers" in this mass region, as indicated in Table 3.
| Neutron magic number | N = 50 | N = 82 |
|---|---|---|
| Kr 86 | Xe 136 | |
| Rb 87 | Cs 137* | |
| The nuclide which exists in target | Sr 88 | Ba 138 |
| ZFP elements reloaded | Y 89 | La 139 |
| Zr 90 | Ce 140 | |
| Nb 91* | Pr 141 | |
| Mo 92 | Nd 142 |
C. Relation of creation rates of Z+1NRM elements with average 1-group neutron capture cross sections of target ZFP elements
Figure 6(a) shows creation rates of even Z’ (=Z+1) NRMs as a function of average 1-group neutron capture cross sections of target FPs having an odd Z. Fig. 6(b) shows similar data for even Z target FPs leading to odd Z’ NMRs. Because FBR (MONJU) had a larger neutron flux than LWR (PWR), creation rates by FBR were higher than those by LWR. In addition, the larger the average 1-group neutron capture cross section of each target ZFP element was, the higher the creation rate of each _Z+1NRM element was. Thus, a clear correlation was established between creation rates and average 1-group neutron capture cross sections. In the case of the creation of NRMs with even Z’, the creation rate of a _Z+1NRM element was approximately proportional to the 0.78th power of the average 1-group neutron capture cross section of the target ZFP element, as
In addition, deviation from this trend is rather small. On the other hand, in the creation of NRMs with an odd Z’, the creation rate of a _Z+1NRM element was roughly proportional to the 0.63th power of the average 1-group neutron capture cross section of the corresponding target ZFP element, as
However, this case is characterized with a large dispersion from the average trend. Reasons for the difference in the powers and dispersion will be discussed in the following section.
D. Classification of the difference in the even-odd effect of atomic number
Table 4 summarizes the difference the even-odd effect has an atomic number Z’ (=Z+1) from created NRMs. In the case of creation of NRMs with even atomic number Z’ (ex. 46Pd), target FPs (45Rh) have an odd atomic number Z, and they have only 1 or 2 stable isotopes (45Rh: 1). That is, if an isotope (45Rh) captures a neutron, it can decay easily, as in Fig. 7. Additionally, the _Z+1NRM element (46Pd), created by β- decay of an isotope of the target ZFP element capturing a neutron, has so many stable isotopes (46Pd: 6) that it hardly causes additional transmutation to another element (ex. 46Pd→ 47Ag). Fig. 8 shows the time variation of the weight of isotopes of target 45Rh in the case of irradiation by LWR. It turns out that because a majority of isotopes of target 45Rh are almost all 103Rh, 103Rh is mainly transmuted and decreased, as
| Atomic number of created Z+1NRM | ||
|---|---|---|
| Even [ex. Pd] | Odd [ex. Rh] | |
| The number of stable isotopes of Target ZFP | 1 or 2 (It is easy to change elements.) [Rh:1] | Many (It is hard to change elements.) [Ru:7] |
| The number of stable isotopes of Created Z+1NRM | Many (Created elements are stable.) [Pd:6] | 1 or 2 (Created elements are unstable.) [Rh:1] |
| The dispersion from the average trend | Small | Large |
In addition, Fig. 9 shows the time variation of the weight of isotopes of 46Pd created from target 45Rh in the case of irradiation by LWR. It turns out that many isotopes of 46Pd, which are heavier than 104Pd (that is, the nuclide had captured more neutron after reaction as Eq. (8)), remain after cooling without decay because they are stable (Fig. 7).
On the other hand, in the case of the creation of NRMs with odd atomic number Z’ (ex. 45Rh), target FPs (44Ru) have an even atomic number Z and many stable isotopes (44Ru: 7). That is, even if an isotope (44Ru) captures a neutron, it cannot decay easily because it probably changes another stable isotope, such as in Fig. 10. Fig. 11 shows the time variation of the weight of isotopes of target 44Ru in the case of irradiation by LWR. It turns out that 102Ru, which has a possibility of creation of 103Rh, is the only stable isotope of 45Rh by (n, γ) reaction and β- decay, as
had not decreased, but increased. It suggests that not 102Ru, but 101Ru had mainly captured many neutrons and more nuclei of 102Rh had been created by (n, γ) reaction of 101Ru, then decreased them such as
Thus, it turns out that the creation rate of 45Rh was not high (Fig. 4) because target 44Ru had been wasting many neutrons by other reactions not involved in the creation of 45Rh. In addition, Fig. 12 shows the time variation of the weight of isotopes of 45Rh created from target 44Ru in the case of irradiation by LWR. It turns out that all created isotopes of 45Rh except 103Rh had decayed, although they had been created (Fig. 10). Therefore, many neutrons must be captured before they reach a β--unstable isotope which finally undergoes β- decay. In this case, the creation rate of a _Z+1NRM element is not directly affected by a single neutron capture process, but is affected by the number of neutron capture reactions to reach to the β--unstable isotope of the target ZFP element. Since the number of stable isotopes varies from element to element, the dispersion from the average trend is expected to be larger in the latter case.
IV. CONCLUSION
A burnup calculation has been performed in order to analyze the process which aims at creating highly-valuable stable elements (i.e. secondary nuclear rare metals; NRMs) from fission products (FPs) by using a neutron capture reaction, followed by β- decay. As a result, high rates of creation of _Z+1NRM elements were obtained for platinum group metals (44Ru: 8.03%/year (FBR), 46Pd: 20.6%/year (LWR)) and middle or heavy rare earth elements (ex. 64Gd: 23.4%/year (LWR), 66Dy: 17.1%/year (FBR)). It was found that creation rates of NRMs with even atomic number Z’ (=Z+1) were generally high, but those of NRMs with odd Z’ were comparatively low. Having introduced average 1-group neutron capture cross sections of target ZFP elements, correlation with creation rates of _Z+1NRM elements was analyzed and the following rules were established: the creation rate of a NRM element with even (odd) atomic number Z’ was approximately proportional to the 0.78th (0.63th) power of the average 1-group neutron capture cross section of the corresponding target FP element with odd (even) atomic number Z. It was also found that the dispersion from the average trend was much larger in the case of creation of NRMs with odd Z’ than in the case of creation of ones with even Z’. These differences could be attributed to the even-odd effect of average 1-group neutron capture cross sections and the number of stable isotopes. Based on the methodologies established and results obtained in this work, a design optimization of a reactor core and condition of neutron irradiation is going to be performed as a future work in order to increase the creation rate of NRMs.
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