The Process of Nuclear Fission
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Abstract
The process of nuclear fission causes the formation of fission products. The source and quantity of byproducts of fission are explained to provide a foundation for a discussion of the effects of fission products. The swelling effect of both solid and gaseous byproducts of fission is explained and the negative effect that swelling has on fuel performance as well as its limiting affect on burnup is described. Finally, potential solutions to deal with the effects of fission products and subsequently allow for increased burnup are discussed.
Introduction
The quantity of fission products in a nuclear reactor is dependent on the amount of fission occurring, which is directly related to fuel burnup. Therefore it follows that increased fuel burnup causes a rise in the quantity of fission products. Fission product behavior negatively impacts fuel performance in a number of different ways. The negative impacts on fuel performance that fission byproducts have include fuel swelling, pressure and stress on the cladding, as well as decreased thermal performance of the fuel; all of which limit the amount of burnup a reactor can undergo. The neutralization, reduction, or removal of fission products and subsequently their associated negative effects will allow for higher burnup in nuclear reactors.
Source and Quantity of Fission Products
The total quantity of fission products present in the fuel can be determined by a direct mass balance relating the rate of production by fission (requires that the fission product yield be known) to the rate of loss by radioactive decay. In order to determine the overall fission product yield the contribution from beta decaying precursors to the independent yield of the isotopes must be accounted for. The independent fission yield (iy) is the probability per fission of directly forming a particle nuclide. The iy factors into the cumulative yield (cy) of an isotope (ZMA), where cy is the sum of the independent yields (with mass number z) plus contribution due to beta decay of the precursors in the mass chain. cy is given by the equation: . Another important factor in this discussion is the chain yield (yA), which is the cumulative yield from the last member of the change (the stable member) (i.e. yA= ). In simpler terms, the byproducts of fission (e.g. Sb-133, Te-135, etc.) undergo beta decay to form isotopes (e.g. Cs-133, Cs-135, etc.) that accumulate and adversely affect the cladding and fuel. It is important to note that the cladding and fuel are affected by the quantity of a particular chemical element released by fission (i.e. all the isotopes of a particular element behave the same in terms of their effects on the cladding and fuel). The concern, therefore, is the elemental yield (Yi) , which is the total quantity of a particular element (i) formed after irradiation time (tirr) to the number of heavy metal atoms that have fissioned. The Yi for a chemical element is given by the equation: where F is the fission rate per volume and Ni,A is the concentration of chemical element i resulting from the decay chain at mass number A. It is important to note that because two fission products are produced from every fission . Incorporating the yA and using the equation for Yi gives the Yi for a chemical element. The table below provides a summary of the elemental yields for the fission of U-235, Pu-239 and a typical LMFBR mixed oxide (i.e. 15% Pu-239 and 85% U-238).
The elemental yields can be collected into several groups that exhibit similar chemical and physical behavior in irradiated fuel. Said grouping of the elements is seen in the table below.
Group
Chemical Group Name
Elements
Noble Gas
Xe, Kr
Halogens
I, Br
Alkali Metals
Cs, Rb
Tellurium Group
Te, Se, Sb
Alkaline Earth
Sr, Ba
Noble Metals
Ru, Mo, Pd, Rh, Tc
Rare Earths
La, Nd, Eu, Y, Ce, Pr, Pm, Sm, Zr, Nb
From the above tables it is clear that both solid and gaseous fission products occur and each have different adverse effects that negatively impact the cladding and fuel.
Swelling Effect of the Solid Byproducts of Fission
Solid fission products, while not having as substantial an impact as gaseous byproducts of fission, negatively impact the cladding and fuel. Solid fission products are located in various areas of the fuel/fuel matrix. Examples include: Y, Zr, Nb, and Mo, which can be found in the oxide matrix of the fuel, while MN3 (where M=U and Pu and N=Rh and Pd) and Cs, Mo can be found in the grain boundaries of the cladding (i.e. located within other phases of the fuel [such as metallic inclusions]), etc. The two general categories of solid fission products are those that form soluble chemical compounds and those that do not . The solid fission products that form soluble chemical compounds do so based on their affinity for oxygen (e.g. Nb2O5, NbO2, etc.) and have minimal impact on the cladding and fuel (due to the chemical compounds solubility in the UO2 matrix). This is explained by looking at the dimensional changes of the fuel due to fission swelling. Swelling is the fractional increase in the volume of solid with respect to the initial volume of the as fabricated fuel and is given by the equation where VO is the volume of the fresh fuel and V is the volume after burnup, β. VO is given by the equation where VU and VPu are the volume per molecule of UO2 and PuO2. V is given by the equation . NU is given by the equation , NPu is given by the equation , and where Ni is the number of ith atom and vi is the volume of the ith atom. q is the ratio of Pu→ and β is the burnup→ . An equation that gives the change in volume to the fuel/fuel matrix due to solid fission products is arrived at in the form of . Using the equation that gives the change in volume to the fuel/fuel matrix due to solid fission products and partial volumes of each solid species it is calculated that for the fuel vU=40.93×10-24 cm3/molecule of UO2 and for soluble fission products vsoluble fp=40.93×10-24 cm3/molecule of UO2. Conclusion: The lattice constant of UO2 is effectively unchanged as a result of irradiation (i.e. solid byproducts of fission that form chemical compounds due to their affinity for oxygen have no noticeable impact on the UO2 matrix [i.e. no fuel swelling] due to their solubility in said matrix). Other solid fission products that do not form chemical