Most nuclear power plants use uranium-235 as fuel. Under geological conditions, the thermodynamically stable species of uranium is the uranyl cation (UO2+), which is fairly soluble in water. As a result, uranium is present everywhere in the Earth’s crust, its concentration is relatively low, and the average concentration is about 3—5 ppm. Uranium can be extracted economically from rocks that have a concentration of uranium that is at least a couple of thousand parts per million. The most important uranium ore is uranium pitchblende, with mean uranium content about 0.5—0.8%. About 40% of the uranium of the Earth is in Australia.

The uranium is produced from the ore by crashing the ore into smaller pieces, and then concentrated the uranium containing ores by flotation. If uranium is pres­ent as U(IV), it is oxidized to U(VI) by air, or sometimes in a microbiological way. Then, the substance is leached by sulfuric acid. The formed uranyl sulfate complex, [UO2(SO4)2]2_, is separated by ion exchange resins or by extraction using an

238 235

organic solvent. Since natural uranium contains 99.3% U and only 0.7% 235U, and because 235U-enriched uranium compound is needed as fuel for nuclear reac­tors, the uranyl sulfate must be converted into a species that is appropriate for iso­tope enrichment. This species of uranium is UF6, the gas diffusion of which can be used for isotope enrichment. However, even uranium with a natural isotopic ratio can initiate fission chain reaction.

In addition to uranium, artificial fissile material such as Pu, Pu, and U (see Eqs. (6.22) and (6.23)) can be used as fuels. The fuel has to have a high cross section for thermal neutrons. Since the released energy is huge, the heat resistance of the compound of the fissile isotope is also important. The activation of the other atoms in the compound has to be avoided. These conditions are fulfilled by oxides. Usually, uranium dioxide (UO2), plutonium dioxide (PuO2), and thorium dioxide (ThO2) are used. In some reactors, uranium carbide (UC) has been tested. Mixed oxides, the so-called MOXs, are also produced from plutonium oxide and uranium oxide. For homogeneity, the oxides are co-precipitated from oxalate and then calcinated to oxide. MOX is used in light water reactors (as discussed in Section 2.1.1.2). One advantage of MOX fuel is that it provides a way to dispose of the surplus of weapons-grade plutonium, which otherwise would have to be disposed of as nuclear waste and would remain a nuclear proliferation risk. The characteristic properties of the most important fuels are shown in Figure 7.4.

Uranium dioxide is prepared as pellets and placed into rods made of zircon, zircalloy (zirconium with 1% niobium), or another metal. The rods are hermetically sealed and placed into the active zone of the reactor with the moderator. The seal should ideally be hermetic, but in reality, the fuel rods often have micro — and macro-ruptures through which the gaseous and soluble fission products can escape. A part of the gaseous fission products (Kr-85, Xe-133, and Xe-135 isotopes) is

emitted into the atmosphere. The gaseous molecules and compounds of iodine are filtered, usually by coal filters. The relative activities of the iodine isotopes with different half-lives give information on the size of the ruptures. The presence of iodine isotopes with short and long half-lives indicates the existence of macro — or micro-ruptures, respectively. Besides the gaseous fission products, the gaseous compounds of tritium and C-14 (see Section 7.3) are also released into the atmo­sphere. To decrease the emitted radioactivity, the gas emission is delayed or ignited and the products are condensed.

If the moderator (Section 7.1.1.2) and/or the coolant (Section 7.1.1.5) is water or heavy water, the soluble fission products (e. g., Cs-137, Cs-134, strontium, and iodine ions) can dissolve in them. For this reason, water is continuously purified by ion exchangers.

During the operation of nuclear reactors, the quantity of 235U continuously decreases; the fissile material is burning up. Most of the 235U present in the reactor undergoes fission reaction; however, a small part converts to 236U in an (n, Y) reaction. Similarly, the (n, Y) reaction of 238U produces transuranium elements,

ллл л -i

including 9Pu and Pu (Eq. (6.23)), which also undergoes fission reaction, increasing the power of the nuclear reactors. There are nuclear reactors specifically made to produce fissile plutonium isotopes, which are called “breeder reactors.”

The operation of the nuclear reactors is influenced by the fission products. Some of them (e. g., 135Xe and 149Sm) strongly absorb neutrons, decreasing the number of the neutrons and the reactivity. These fission products are called “reactor poisons.”

Since carbon compounds are present in any sphere of the Earth (atmosphere, hydro­sphere, lithosphere, or biosphere), the determination of the carbon isotope ratios obviously plays an important role in the study of the global carbon cycle. In addi­tion, the isotope analysis of other planets provides important information. For exam­ple, the 618O is the same in the rocks of the upper parts of the Earth’s crust and the Moon (618O = 5.5 6 0.2m), proving that the Earth and Moon share the same origin.

An important question in the global carbon cycle is the carbon isotope ratio of the Earth’s mantle. Because of the very high temperature, even isotope composition should be expected; however, there are significant differences in the isotope ratio of different minerals. Diamond and SiC mineral, for example, contain more 12C isotopes than magmatic minerals.

Deviation from the mean carbon isotope ratios refers to the major extinction event. Since the 13C/12C ratio of the biomass is lower than that of the sedimentary carbonate rocks, the sediments forming during the extinction events from the bio­mass show lower 13C/12C ratio than the mean value of the carbonate rocks. The 13C/12C can continue to decrease via the release of methane-hydrate bound to the deep-sea sediments, which is due to bacterial activity that prefers the light carbon isotope. During global warming, the methane-hydrate releases as carbon dioxide, increasing the carbon dioxide content of the atmosphere. The industrial carbon dioxide emission also decreases the 13C/12C ratio because of the burning of fossil fuel. All the above processes are in fact the consequence of biological isotope effects.

When the energy of the gamma photon (hv) is higher than the energy equivalent with the rest mass of two electrons (2m0c2), the gamma photon can transform into an electron and a positron when it passes the nuclear field. This process is called “pair formation,” the reverse process of annihilation (as discussed in Section 5.3.3). On the basis of the conservation of energy:

hv = m0c2 + Ee — + m0c2 + Ee+ (5.90)

where Ee — and Ee+ are the kinetic energy of the electron and the positron, respectively.

The cross section of the pair formation can be described as:

^ = KZ2f (Ey) (5.91)

where f(EY) is a factor depending on the energy of the gamma radiation, Z is the atomic number of the interacting substance (absorber), and K is constant. As seen, the cross section of the pair formation increases as the gamma energy and the atomic number increase.

Low- and intermediate-level radioactive wastes are buried in geological repositories. These repositories must isolate the nuclear waste from the biosphere as long as 100,000 years. For the storage of radioactive waste, the geological formations were used where water-soluble compounds have been accumulated for millions of years, such as salt mines, clay rocks, granite, and tuff. In these geological formations, fur­ther engineering barriers are constructed. The nuclear waste is placed into stainless steel or reinforced concrete containers and deposited inside the engineering barrier system. Only solid wastes are stored; liquid wastes are solidified by cementation or bitumen. The holes among the containers are filled with cement too.

There are some very important aspects to take into account when selecting a suitable environment for waste disposal. These are, for example, the hydrological properties of the geological environment, the corrosion and erosion of the engineer­ing barrier system, leaching, and migration of the radionuclide in the geological environment. In addition, the microbiological activity and the effects of radiolysis have to be considered.

Low — and intermediate-level radioactive wastes contain the technological wastes of nuclear energy production (clothing, paper, wood, ion exchange resins, plastics, contaminated tools, instruments, etc.). In the corrosion and microbiological degra­dation of these substances, gaseous compounds are released. The corrosion pro­duces hydrogen, while the microbiological processes transform the organic substances of the nuclear wastes into carbon dioxide or methane, depending on the redox conditions. The formation of carbon dioxide is less important because the anaerobic conditions are dominant in underground disposal. The gases can have unfavorable effects during storage. For example, the increasing pressure can push the radioactive gases and solutions into the environment. As a result of the cemen­tation, the pH of the pore solution is set above 12. This pH inhibits the corrosion of the containers and the microbiological activity, decreasing the rate of gas release.

The radiolysis of water (discussed in Section 13.4.2) also releases gases; how­ever, this reaction can be disregarded for the disposal of low — and intermediate- level nuclear waste.

2.1 Atomic Nuclei

2.1.1 Components of Nuclei

The atomic nuclei were discovered by the English physicist Ernest Rutherford on the basis of Ernest Mardsen’s experiments (Figure 2.1). In their experiments, Mardsen and Hans Geiger studied the backscattering of alpha rays (which were known to be positively charged) from a gold plate and observed that a very small portion of these particles (about 1 in 100,000) were scattered back at an angle of 180°. Since the backscattering of the positive alpha particles is directed by electrostatic forces, this is possible only if a very high portion of the positive charge of the atom is concentrated in very little volume. This small component of the atom is the atomic nucleus. The backscattered portion of the alpha parti­cles indicates that the radius of the nucleus is about 105 times smaller than the radius of the atom.

In addition to the positive charge, the mass of the atom is concentrated in the nucleus. The radius of the atomic nuclei (R) can be expressed approximately by Eq. (2.1):

R = R0 X A1/3 (2.1)

where A is the mass number and R0 is the radius of the nucleus of the hydrogen atom (~ 1.3 X 10_15 m). As a consequence of Eq. (2.1), the density of any atomic nucleus is approximately the same (p = 2 X 1017 kg/m3), independent of the iden­tity of the atoms. The mass of the nucleus is evenly distributed in the nucleus. This density then decreases quite abruptly to reach the density of the electron shell (which is very small—practically zero) at a distance of about 2.5 X 1015 m from the nucleus. Similarly, the charge density surrounding the nucleus decreases over the same distance to reach the charge density of the electron shell, which is comparatively very small due to the relatively large size of the electron shell (about 10_1° m).

The alpha backscattering experiments proved that the atomic nuclei have mass, charge, and well-defined geometric size. At the time of the alpha backscattering experiments, not much was known about neutrons. It was conceptualized that in order to neutralize the positive charge of the protons, electrons must be present in the nucleus. This model is called J. J. Thomson’s atomic model. According to this model, atomic

Nuclear and Radiochemistry. DOI: http://dx. doi. org/10.1016/B978-0-12-391430-9.00002-0

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nuclei should comprise protons and electrons. This model, however, can be disproved easily by the zero-point energy of the electron in the nucleus. Heisenberg’s uncertainty principle says that

where Дх and Дv are the uncertainty of the determination of the position and velocity, respectively; h is Planck’s constant; and m is the mass of the particle. The radius of the nucleus (R) can be substituted for Дх in the equation; if Дх > R, then the electron is outside the nucleus. From Eq. (2.2), Дv, and from here the energy of the electron, can be expressed as follows:

These calculations for the nucleus show that the zero-point energy of the electron is two orders of magnitude greater than the binding energy of nucleons (7—8 MeV/nucleon). Thus, if the electrons were restricted in the nucleus, their energy would be so high that they would leave it instantly. So, it is clearly proved that electrons cannot be present in the nucleus. Subsequently, in 1920, Rutherford conceptualized that the nucleus contains neutral particles that explain the difference between the charge and the mass of the nucleus. These particles were called “neutrons,” and they were experimentally demonstrated by James Chadwick in 1932 (Section 5.5.1).

Atomic nuclei consist of protons and neutrons. The number of protons is the atomic number (Z), and the sum of the number of protons (Z) and neutrons (N) is the mass number (A). The particles composing the nuclei are called “nucleons.”

The 87Rb isotope has a long half-life (4.88 X 1010 years). This isotope emits negative beta radiation (as discussed in Section 4.4.2), producing an 87Sr isotope. Similarly to the ratio of 40K/40Ar, the age of geological formations can be determined by the ratio of 87Rb/87Sr. The problem with this approach, however, is that the source of an 87Sr isotope is not the decay of 87Rb alone; it was present at the time of the rock for­mation (t = 0). Thus, the quantity of Sr ( — N) can be expressed as:

Sr-87N = Sr-87Nt=0 + Rb-87N (eARb-87t — 1) (4.72)

where Sr-87Nt=0 is the quantity of Sr-87 at the time of the formation of the rock (at t = 0), Rb-87N is the quantity of Rb-87, ARb-87 is the decay constant of Rb-87,

and t is the age of the rock. Since the initial quantity of the Sr-87 is not known, for dating purposes, it also has to be determined. This problem is solved by incorporat­ing the quantity of Sr-86 into Eq. (4.72). Sr-86 is a stable isotope, the quantity of which does not change over time. By dividing Eq. (4.72) by the constant quantity of Sr-86 (Sr-86N), we obtain:

When the quantities of Sr-86, Sr-87, and Rb-87 are determined in different rocks or minerals with the same genetics, and the ratio of Sr-87N/Sr-86N is plotted as a function of Rb-87N/Sr-86N, a straight line is obtained. The slope of this straight line is (eARb-87t — 1), and the intercept is Sr_87Nt=0/Sr"86N, which shows the initial ratio of the strontium isotopes. The age can be determined from the slope of the straight line. The line is called an “isochron,” which means “similar age.” The method has been used to determine the age of igneous, metamorphic, and sedimentary rocks, and it is used frequently to date meteorites.

The positively charged irradiating particle has to pass through the Coulomb barrier of the target nucleus, so the energy of the irradiating particle has to be higher than the threshold energy, even in the case of exoergic reactions. The Coulomb barrier of light nuclei is always lower, so the nuclear reaction of the charged particles with light elements is more feasible. The maximal energy of the alpha particles is about 9 MeV, which is enough to overcome the Coulomb barrier of the light elements (e. g., (6.1) and (6.2) reactions). For most nuclear reactions with charged particles, however, the energy of the particles has to be amplified, i. e., the charged particles have to be accelerated. This has been done in van de Graaf generators, and more recently, linear accelerators and cyclotrons have been used (see Section 8.5.2).

The characteristic types of nuclear reactions with charged particles were shown in Table 6.1. They are presented here on the basis of irradiating particles.

The distribution of the isotope molecules is different in phases that are in thermo­dynamic equilibrium, including the liquid/gas, liquid/solid, and solid/gas phases. Similarly, the solubility of the isotope molecules is also different.

The isotope effects in the liquid/gas phases have been well studied. The effect can be characterized by the partial pressure of the isotope molecules:

where p and p’ are the partial pressure of the lighter and the heavier molecule, respectively, and є is the relative partial pressure. The degree of the isotope effect is usually low: є«1. Of course, the different partial pressures result in different boiling points (Table 3.2).

Usually, the partial pressure of the lighter molecules is greater. If not, an inverse isotope effect exists. Among the molecules in Table 3.2, methane shows an inverse isotope effect.

A well-known isotope effect in the solid/liquid phase is the ice/water system. The boiling point of 2H2O and 1H2O is different. As a result, the deuterium content of the icy seas is greater than the average deuterium content of the oceans.

The adsorption of the isotope molecules can also be different, a fact that is used in adsorption chromatography to separate isotopes. As the pressure and temperature decrease, the isotope effects increase, resulting in increased separation factors.

The different solubility of the isotope molecules have mainly been studied dur­ing the dissolution of light and heavy water in organic solvents. The inorganic salts and some organic compounds dissolve differently in light and heavy water.

Cherenkov radiation (also spelled Cerenkov or (Cerenkov) is an electromagnetic radiation emitted when a beta particle passes through a dielectric medium at a speed greater than the velocity of light in that medium. It was discovered by Cherenkov in 1934, when he studied the radiation of radium salts in an aqueous solution. The experience was interpreted by I. M. Frank and I. E. Tamm. The gamma radiation of radium produces many secondary electrons with high energy (e. g., Compton electrons, discussed in Section 5.4.3), which pass through the medium (water) polarizing the molecules and arranging the dipoles. After passing the beta particle, the molecules rapidly revert to their ground state, emitting electromagnetic radiation. When the velocity of the beta particle (v) is greater than the velocity of light in the given medium (v > c/n, where c is the velocity of light in vacuum, n is the refractive index of the medium), there is an angle (0) where the waves of the electromagnetic radiation emitted at 0 and dt times interfere (Figure 5.12).

The angle of the interference is:

For example, with water (n = 1.337):

c 3 X 108 . о.

= m/s^2.2 X 108m/s

n 1.337 1 1

This velocity is equal to 0.26 MeV. Therefore, to have Cherenkov radiation, the beta particles must have at least 0.26 MeV. In practice, however, to be observed easily, beta energies must be above ~ 0.5 MeV.

Place of the light emission

Place of the light emission

The relation of the intensity (I(v)) and the frequency (f) of the Cherenkov radia­tion can be expressed as:

The maximal intensity is:

This means that the intensity is proportional to the frequency; therefore, the Cherenkov radiation is blue.

This interaction of the beta radiation can be applied to the direct measurement of the beta radiation by light detectors, for example, by photo multipliers. Cherenkov light can be observed in the nuclear reactors.

Another important part of nuclear reactors is the moderator. Its function is to slow down the fast neutrons emitted in the fission reaction by reducing the energy of neutrons to the level of thermal neutrons. Light elements are suitable moderators because they can effectively decrease the energy of the fast neutrons through inelastic collisions with neutrons. According to its atomic mass, hydrogen (1H) is expected to be the most effective moderator; however, a suitable moderator must also have a small cross section for neutron captures, which hydrogen does not have. Hydrogen can capture neutrons easily, transforming to deuterium. Deuterium is the most effective moderator, but it is rather expensive. The ratio of the modera­tor effect and the neutron capture can be expressed by the moderation ratio (given in Table 7.1).

Frequently used moderators are the following:

• Water (H2O), which is an effective moderator, absorbs part of the neutrons. A water­moderated reactor is shown in Figure 7.2.

• Heavy water (D2O), which is an effective moderator, absorbs only a few neutrons, but it is expensive.

• Graphite, which is a less-effective moderator than water, absorbs only a few neutrons. Its disadvantage is that it is flammable. In the first nuclear reactor, graphite was applied as the moderator.

• Beryllium and organic solvents are also suitable as moderators.

7.1.1.1 Moderator/Fuel Ratio

The moderator decreases the velocity of the neutrons, as discussed in Section 7.1.1.2. In addition, the moderator acts as a passive controller of the operation of the nuclear reactors.

All substances, including moderators, more or less absorb neutrons, inhibiting the fission chain reaction. Thus, if the reactor contains too much moderator, the degree of neutron absorption increases. However, if the quantity of the moderator is too low, the velocity of the neutrons does not decrease enough. As a result, the effective neutron multiplication factor versus the moderator/fuel plot function has maximum. Those reactors in which the moderator/fuel ratio is below the maximum are under-moderated, and those in which this ratio is above the maximum are over­moderated (Figure 7.5).

Under — and over-moderation play an important role in the safety operation of the reactors. The under-moderated reactors are safer because the decrease of the quantity of the moderator results in the decrease of the effective neutron multiplica­tion factor, stopping the reactor from entering a subcritical state. In over-moderated reactors, however, the decrease of the quantity of the moderator can increase the effective multiplication factor, and then the reactor can become supercritical (as happened in the Chernobyl accident, discussed in detail in Section 7.2).