Gadolinium is now the most commonly used burnable poison in commercial reactors. Natural gadolinium consists of the isotopes 152, 154, 155, 156, 157, 158, and 160, with abundances of 0.2%, 2.18%, 14.8%, 20.47%, 15.65%, 24.84%, and 21.86%, respectively.1,2 Of these, 155Gd and 157Gd have extraordinarily high thermal neutron capture cross-sections of 61 000 and 254 000 barns, respectively (Figure 5). This means that gadolinia can effectively suppress the neutron multiplication factor at even a very low concentration.

However, gadolinia is usually concentrated spatially rather than dispersed to take advantage of spatial self­shielding3,4; when concentrated into a small number of fuel rods, for example, thermal neutrons entering the poisoned fuel rod are absorbed near the surface because of the high cross-section. 155Gd and 157Gd atoms near the center of the fuel rod see virtually zero thermal neutron flux, and are thereby shielded from neutron captures. Self-shielding thereby limits the initial multiplication effect of lumped gadolinium and extends the depletion time for 155Gd and 157Gd. Self-shielding has the effect that the initial reaction rate is proportional to the surface area, while the time to deplete the 155Gd and 157Gd is proportional to the ratio of surface area to volume. It allows the nuclear designer flexibility in controlling both the initial absorption effect and the depletion rate independently.

Gadolinium is usually incorporated in fuel assem­blies in the form of gadolinia/urania Gd2O3/UO2 fuel pellets, with properties only slightly different from those of conventional UO2 pellets and a virtu­ally identical manufacturing route. Figures 6 and 7 show typical distributions of Gd2O3/UO2 fuel rods in PWR and BWR fuel assemblies, respectively. Gadolinia rods offer the nuclear designer flexibility in choosing the optimal combination of initial reactiv­ity worth and poison depletion rate. There is a residual absorption penalty that, though less than that for dis­crete burnable poison rods, could in theory be reduced by using gadolinium enriched in 157Gd. Figure 8 shows the radial distribution of 157Gd atoms as a function of time. The self-shielding effect is evident in that the depletion proceeds from the outside in shells, usually likened to peeling an onion. 155Gd behaves similarly, though on a slower timescale because of its smaller cross-section.

Gadolinia is used routinely in the UK’s AGRs, but in a different form to that used in LWRs. AGR fuel elements incorporate discrete absorber cables containing gadolinia Gd2O3 powder in a stainless steel tube. These are located on a support structure within the outer graphite sleeve, with provision for up to three cables each at of the bottom, mid­dle, and top of the element, giving a maximum of nine cables per element. The complete AGR fuel assembly, called a stringer, consists of eight fuel elements stacked on top of one another, and at the interfaces between elements, the absence of fuel causes the thermal neutron flux and thermal power production to peak. This is because the thermal neutron flux is determined by the balance between the source of thermal neutrons slowing

down in the moderator and their removal by (prin­cipally) the nuclear fuel. Where fuel is absent, the balance shifts to produce a higher thermal flux. The gadolinia cables are used to counter this
deleterious axial heterogeneity, helping to reduce flux peaking in the axial gaps between fuel elements.

2.16.3.2

Erbium

Erbium is a less commonly used burnable poison mate­rial, but has been used in some commercial PWRs and is potentially useful for specialized applications. Natural erbium consists of the isotopes 162, 164, 166, 167, 168, and 170 with abundances of 0.14%, 1.61%, 33.6%, 22.95%, 26.8%, and 14.9%, respectively.2 The thermal neutron capture cross-sections are modest however, 167Er having the highest thermal cross­section of 700 barns and the others all less than 20 barns, which makes erbium characteristically slow to deplete in reactor and causes it to have a high residual absorption penalty. It is normally deployed in the form of erbia/urania Er2O3/UO2 fuel pellets in selected fuel rods.

Unlike boron, erbium acts as a resonant absorber, meaning that there are resonance peaks in the absorp­tion cross-section plotted against incident neutron kinetic energy (Figure 9). Erbium is therefore able to mimic the negative fuel temperature feedback mecha­nism due to resonance absorptions in 238U, which could theoretically be helpful in the so-called inert matrix fuel (IMF) designs currently being considered to irra­diate and destroy the minor actinides Np, Am, and Cm. Destruction of the minor actinides is more efficient if the fuel does not contain any 238U, which would gener­ate fresh 239Pu through fertile captures. IMF therefore uses matrix materials such as cerium, zirconium, and
yttria which dilute the nuclear materials, but which contribute little to neutron captures.