Moderator

¨     Introduction:

Nuclear reactors are based on the "fission" process for generating heat energy to produce electricity. Fission is a chain reaction process that needs to be controlled for smooth and safe operation of the reactor. (1)

The chemical which controls the speed of neutrons produced in a fission reaction is called moderator. Neutrons moving too fast are absorbed by other uranium atoms rather than fissioning them. The moderator slows the neutrons and increases the rate of fission (2). Different types of moderators are used in nuclear reactors like light water (roughly 75% of world’s reactors) , heavy water (20% of reactor), graphite (5% of reactor) beryllium etc.

Fission neutrons are produced at an average energy level of 2 MeV and immediately begin to slow down as the result of numerous scattering reactions with a variety of target nuclei. After a number of collisions with nuclei, the speed of a neutron is reduced to such an extent that it has approximately the same average kinetic energy as the atoms (or molecules) of the medium in which the neutron is undergoing elastic scattering. This energy, which is only a small fraction of an electron volt at ordinary temperatures (0.025 eV at 20(C), is frequently referred to as the thermal energy, since it depends upon the temperature.

Neutrons whose energies have been reduced to values in this region (< 1 eV) are designated thermal neutrons. The process of reducing the energy of a neutron to the thermal region by elastic scattering is referred to as thermalization, slowing down, or moderation. A good moderator reduces the speed of neutrons in a small number of collisions, but does not absorb them to any great extent. Slowing the neutrons in as few collisions as possible is desirable in order to reduce the amount of neutron leakage from the core and also to reduce the number of resonance absorptions in non-fuel materials.

The ideal moderating material (moderator) should have the following nuclear properties:

¨     large scattering cross section

¨     small absorption cross section

¨     large energy loss per collision

¨     should be cheap and abundant

¨     should be chemically stable

¨     moderator nuclei should have nearly same mass as that of neutron

Figure 1: Moderators

Is it always necessary?

Although moderators are necessary in most nuclear reactors this does not mean to say that all reactors require moderators. There is a special class of reactors known as fast reactors which do not use moderators but depend on the use of fast moving neutrons for causing fission. Even otherwise it must be remembered that fast moving neutrons have lesser probability of getting absorbed and causing fission but it does not mean that they are incapable of causing the fission reaction. A fast moving neutron travels with a speed which is nearly in the region of 10% of the speed of light, while a thermal neutron travels with a speed which is typically of the order of a few kilometers per second.

 There are also other categories of neutrons based on their energy levels such as slow neutrons, cold neutrons, ultra cold neutrons and so forth.

1.1  Reactor Moderators:

In a thermal nuclear reactor, the nucleus of a heavy fuel element such as uranium absorbs a slow-moving free neutron, becomes unstable, and then splits (fissions) into two smaller atoms (fission products). The fission process for ²³⁵U nuclei yields two fission products: two to three fast-moving free neutrons, plus an amount of energy primarily manifested in the kinetic energy of the recoiling fission products. The free neutrons are emitted with a kinetic energy of ~2 MeV each. Because more free neutrons are released from a uranium fission event than thermal neutrons are required to initiate the event, the reaction can become self sustaining a chain reaction under controlled conditions, thus liberating a tremendous amount of energy.

Figure 2: Graph between energy and  fission

                  cross-section.

The probability of further  fission events is determined by the fission cross section, which is dependent upon the speed (energy) of the incident neutrons. For thermal reactors, high-energy neutrons in the MeV-range are much less likely to cause further fission. (Note: It is not impossible for fast neutrons to cause fission, just much less likely.) The newly released fast neutrons, moving at roughly 10% of the speed of light, must be slowed down or "moderated," typically to speeds of a few kilometres per second, if they are to be likely to cause further fission in neighbouring ²³⁵U nuclei and hence continue the chain reaction. This speed happens to be equivalent to temperatures in the few hundred celsius range.

In all moderated reactors, some neutrons of all energy levels will produce fission, including fast neutrons. Some reactors are more fully thermalised than others; for example, in a CANDU reactor nearly all fission reactions are produced by thermal neutrons, while in a pressurized water reactor (PWR) a considerable portion of the fissions are produced by higher-energy neutrons. In the proposed water-cooled supercritical water reactor (SCWR), the proportion of fast fissions may exceed 50%, making it technically a fast neutron reactor.

A fast reactor uses no moderator, but relies on fission produced by unmoderated fast neutrons to sustain the chain reaction. In some fast reactor designs, up to 20% of fissions can come from direct fast neutron fission of uranium-238, an isotope which is not fissile at all with thermal neutrons.

Moderators are also used in non-reactor neutron sources, such as plutonium-beryllium and spallation sources.

1.2       Different moderators and their properties:

1.2.1   Graphite:

Historically, graphite has been a very popular neutron moderator, and is used in the majority of British reactors. However, the graphite used has to be highly pure to be effective. Graphite can be manufactured artificially using boron electrodes, and even a small amount of contamination from these electrodes can make the graphite unsuitable as a moderator since boron is a highly effective neutron absorber, and so it “poisons” the graphite by increasing the overall absorption cross section, Σa. It also has unique problems: it stores energy in metastable local defects when it is irradiated, particularly at lower temperatures. This so-called Wigner energy can be released suddenly when the graphite spontaneously returns to its stable phase, and this sudden rise in temperature is not desirable since it can cause further structural damage within the reactor. This means that graphite has to be annealed to remove the excess energy in its lattice in a controlled manner (4).

Figure 3: Nuclear reactor using graphite as a moderator (1)

It has satisfactory purity (99 percent pure, with ash content less than 300 ppm and boron less than about 2 ppm) available at reasonable price. It is thermally stable, but at elevated temperatures it can react with oxygen and carbon dioxide in the reactor decreasing the effectiveness. It can also form carbides (a compound composed of carbon with another element) after reacting with some metals and metal oxides. Despite being a non-metal, graphite has good heat conducting property, which is an important property of neutron moderators. The basic drawbacks of graphite in nuclear moderation are the chances of oxidation in presence of air, low strength and the low density. Its dimensions may change under the influence of radiations in the reactor (1).

Figure 4: Neclear reactor using graphite as a moderator (2)

1.2.2  Light Water:

Hydrogen is a good candidate for a neutron moderator because its mass is almost identical to that of the incident neutron, and so a single collision will reduce the speed of the neutron substantially. However, hydrogen also has a relatively high neutron absorption cross-section due to its tendency to form deuterium, and so light water is only suitable for enriched fuels which allow for a higher proportion of fast neutrons (4). Ordinary water is used in nuclear reactors as a moderator for a number of reasons. The low cost of water, easy availability and excellent slowing-down property makes it a fine neutron moderator. Ordinary water can be used as a moderator only if enriched uranium fuel is used. It can be employed as both, a moderator and a coolant in the nuclear reactor. The main drawbacks of ordinary water is its relatively low boiling point (1).

                 

          Figure 5: Nuclear reactor using light water as moderator

1.2.3    Heavy water:

Heavy water has similar benefits to light water, but because its water molecules already have deuterium atoms it has a low absorption cross section. Additionally, because of the high energy of the fast neutrons, an additional neutron might be knocked out of the deuterium atom when a collision occurs, thus increasing the number of neutrons present (4). Unlike ordinary water, it can perform satisfactorily with natural uranium fuel also; it yields highly enhanced neutron economy (unlike ordinary water, it absorbs the neutrons), allowing the reactor to operate without fuel enrichment facilities and generally enhancing the ability of the reactor. Unlike graphite moderator, it does not oxidize. Heavy water moderated nuclear reactors are smaller and require considerably less nuclear fuel.

The drawback associated with heavy water is the considerably higher cost than ordinary water (1).

Figure 6: Nuclear reactor using heavy water as moderator

1.2.4    Beryllium:

Beryllium-9 is favoured, because in addition to being a light element, on collision with a fast neutron, it can react as follows:

⁹Be + n → ⁸Be + 2n (4)

Beryllium is superior to graphite as a neutron moderator in nuclear reactors. Beryllium has been used in some reactors and beryllium oxide is proposed as a neutron moderator for high-temperature gas-cooled nuclear fission reactors. Beryllium is high in cost compared to graphite and heavy water, which often replace it.

The main problems with beryllium are its brittleness as a metallic phase and its toxicity, which make it less favoured as a moderator (1)

        

Figure 7: Beryllium as moderator

1.2.5    Zirconium Hydride:

 Zirconium hydride is not a usual material used as a moderator in nuclear reactors. When powdered, the material has poor thermal conductivity and hence requires special cooling provisions in high power reactors operating at high to moderate temperature. Zirconium hydride is employed in the "triga" reactor with enriched uranium as the fuel element (1).

1.2.6    Lithium Fluoride:

Lithium fluoride is commonly used in molten salt reactors. It is mixed with the molten metal and the fuel, and so its structural properties as a solid are not important (4).

1.2.7    Reflector:

As we know the reactor consists of the fission process which occurs when a thermal energy neutron is absorbed by the target nucleus leading to its division into two nuclei and emission of 2 or 3 neutrons apart from the heat energy. These neutrons fly randomly in all directions and are usually in the region of fast moving energy neutrons. The moderator is used to control the speed of these neutrons so that they act usefully in creating more fission, but many of these neutrons may simply get lost by flying off the reactor core and thus serving no useful purpose. This might hinder the progression of a chain reaction which is very necessary for the nuclear reactor.

In order to reduce this process of neutron loss the inner surface of the reactor core is surrounded by a material which helps to reflect these escaping neutrons back towards the core of the reactor and these materials are known as reflecting materials.

      Materials used as Reflectors:

There are a variety of materials which are used as a reflecting medium for neutrons and whatever material is used for the process, it must possess these properties:

1.Low absorption - this is necessary since if the reflecting material itself starts to absorb the very neutrons it is supposed to reflect back, then the purpose of installing the reflector material would itself be defeated and it would be better not to install any reflector at all.

2.High reflection - this is an obvious property and does not need any explanation for that is the very purpose for which the reflector exists in the core.

3.Radiation stability - since the reflector material will be exposed to high levels of radiation, it is but natural to assume that it should have a high stability towards radiation.

4.Resistance to Oxidation - the material should not get oxidized otherwise it will fail to serve the requisite purpose.

In actual practice there may not be a different material for moderator and reflector for the simple reason that most of the moderators also possess the above mentioned properties of a good reflector as well. Hence they serve the dual purpose of a reflector and a moderator as well. There light water, heavy water and carbon are mostly used as reflectors since they possess the above mentioned characteristics.

The use of a proper reflector helps to reduce the size of the reactor core for a given power output since the number of neutrons leaking are lesser and help to propagate the fission process instead. It also reduces the consumption of the fissile material (5).

Figure 8: Neutron Reflector

      1.2.8  Control Rods:

The rate of reaction in a nuclear reactor is controlled by control rods. Since the neutrons are responsible for the progress of chain reaction, suitable neutron      absorber are employed to achieve control of reaction rate. Cadmium and boron are frequently used materials. The control procedure involves the insertion or withdrawal of these materials, taken in the form of rods, into or from the reactor core. With the control rod fully inserted, enough neutrons are absorbed so that the average number of neutrons available to cause new fissions is less the one per fission reaction. As the rod is slowly withdrawn, the average number of available neutrons increases until it is just equal to one per reaction. At that time the reactor is said to be critical. During the operation, the position of the control rod is continually adjusted so that energy is released at a steady rate (6).

Figure 9: Control rods (1)

`

Figure 10: Control rods (2)

1.3         Logarithmic  Energy Decrement:

As we know that neutrons collide with nuclei number of times. A convenient measure of energy loss per collision is the logarithmic energy decrement. The average logarithmic energy decrement is the average decrease per collision in the logarithm of the neutron energy. This quantity is represented by the symbol Ɛ.  

          

        Ɛ = ln - ln

         _{Ɛ = ln}

_where:

_Ɛ = average logarithmic energy decrement

E_{i =} average initial neutron energy

E_f = average final neutron energy

  The symbol Ɛ is commonly called the average logarithmic                                energy decrement because of the fact that a neutron loses, on the average, a fixed fraction of its energy per scattering collision. Since the fraction of energy retained by a neutron in a single elastic collision is a constant for a given material, Ɛ is also a constant. Because it is a constant for each type of material and does not depend upon the initial neutron energy, Ɛ is a convenient quantity for assessing the moderating ability of a material. The values for the lighter nuclei are tabulated in a variety of sources. The following commonly used approximation may be used when a tabulated value is not available.

                 Ɛ =

This approximation is relatively accurate for mass numbers (A) greater than 10, but for some low values of A it may be in error by over three percent.

Since Ɛ represents the average logarithmic energy loss per collision, the total number of collisions necessary for a neutron to lose a given amount of energy may be determined by dividing into the difference of the natural logarithms of the energy range in question. The number of collisions (N) to travel from any energy, E_high, to any lower energy, E_low, can be calculated as shown below.

N =

    = ln

    1.4  Macroscopic Slowing Down Power:

Although the logarithmic energy decrement is a convenient measure of the ability of a material to slow neutrons, it does not measure all necessary properties of a moderator. A better measure of the capabilities of a material is the macroscopic slowing down power. The macroscopic slowing down power (MSDP) is the product of the logarithmic energy decrement and the macroscopic cross section for scattering in the material. Following equation illustrates how to calculate macroscopic slowing down power:

MSDP = Ɛ

1.5 Moderating Ratio:

Macroscopic slowing down power indicates how rapidly a neutron will slow down in the material in question, but it still does not fully explain the effectiveness of the material as a moderator. An element such as boron has a high logarithmic energy decrement and a good slowing down power, but it is a poor moderator because of its high probability of absorbing neutrons. The most complete measure of the effectiveness of a moderator is the moderating ratio. The moderating ratio is the ratio of the macroscopic slowing down power to the macroscopic cross section for absorption. The higher the moderating ratio, the more effectively the material performs as a moderator. Following shows how to calculate moderating ratio of a material:

                        

                                   MR =  

Moderating properties of different materials are compared in following Table (3):

Material	Ɛ	Number of collisions to Thermalize	Macroscopic Slowing Down Power	Moderating Ratio
	0.927	19	1.425	62
	0.510	35	0.177	4830
Helium	0.427	42	9 *	51
Beryllium	0.207	86	0.154	126
Boron	0.171	105	0.092	0.00086
Carbon	0.158	114	0.083	216

1.6    The Moderating Coefficient.

1.6.1 Moderator Temperature Coefficient:

The moderator temperature coefficient, αmod, determines the rate of change of reactivity with moderator temperature. This coefficient determines the ultimate response of a reactor to fuel and coolant temperature change. It is desirable to have a negative moderator temperature coefficient because of its self-regulating effect. In thermal reactors when the moderator temperature is increased

1. the physical density of the moderator liquid is changed due to thermal expansions, and

2. thermal cross sections change.

The increased temperature of the moderator in water moderated reactors will cause the neutron flux to move toward higher neutron energies. This is an especially promoted effect when absorption cross section does not follow a 1/υ dependence. Thus, the presence of, for example, 238U at higher temperatures will increase parasitic absorptions and thus tend to keep the coefficient negative. The change in the neutron spectrum at increased moderator temperature has effect on reactivity which is more pronounced in the presence of poisons such as 135Xe and 149Sm because of their resonances placed at very low neutron energies (around 0.1 eV). The moderator expands at increased temperature which causes a reduction in the density of atoms present; therefore the efficiency of the moderator is reduced. The magnitude and sign of the moderator temperature coefficient depends on the moderator-to-fuel ratio in such a manner that if

• reactor is under-moderated the coefficient will be negative.

1.6.2  Moderator Pressure Coefficient:

The moderator pressure coefficient of reactivity is defined as the change in reactivity due to a change in system pressure. The reactivity is changed due to the effect of pressure on the moderator density. When the pressure is increased, the moderator density is increased which, in turn, increases the moderator-to-fuel ratio in the core. In the case of an under-moderated core, the increase in moderator-to-fuel ratio will result in a positive reactivity insertion. In water moderated reactors, this coefficient is much smaller than the temperature coefficient of reactivity