¨ 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
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.
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).
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).
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).
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).
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)
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).
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).
`
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
Ei =
average initial neutron energy
Ef = 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, Ehigh, to any
lower energy, Elow, 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