m17h

Natural Sciences Tripos Part III

MATERIALS SCIENCE

M17: Nuclear Materials (Lectures 18)

Dr J. H. Gwynne

Lent Term 2013-14

III

Name............................. College..........................

Part III Materials Science M17: Nuclear Materials Lent 2014

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INTRODUCTION

In existing technologies for nuclear power generation there are many performance, reliability

and safety issues centred on the materials in use. In particular, materials degradation is the

principal obstacle to extending the lifetime of an existing plant. In almost every case, materials

issues pose the greatest challenge in bringing next-generation reactor designs to fruition. Of

course, many of the challenges in nuclear power generation, however severe, are of a general

kind; examples are high temperatures and corrosive environments.

The focus of this part of the course will be the specific effects of radiation on structural

materials and in the reactor core. The effects of radiation can be dramatic: change in shape,

swelling by some tens of percent, hardening (more than five-fold), drastic embrittlement and

reduction in ductility, and accelerated corrosion effects such as environmentally induced

cracking.

Useful books

K.L. Murty & I. Charit, An Introduction to Nuclear Materials Wiley (2013)

B.R.T. Frost (ed.), Nuclear Materials (Vols 10A & 10B, Materials Science & Technology),

VCH (1994)

B.M. Ma, Nuclear Reactor Materials and Applications, Van Nostrand (1983)

G.S. Was, Fundamentals of Radiation Materials Science, Springer (2007)

Additional Resources

DoITPoMS TLP: Materials for nuclear power generation

http://www.doitpoms.ac.uk/tlplib/nuclear_materials/index.php

CES Edupack Nuclear Power Edition


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Contents

1. Introduction 5

1.1 Fundamentals 5

1.1.1 Notation 5

1.1.2 Binding energy 5

1.1.3 Types of radiation and radioactive decay 6

1.1.4 Exponential decay and half-life 7

1.1.5 Neutron classification 8

1.2 Nuclear Reactions 9

1.2.1 Interactions of neutrons with matter 10

1.2.1.1 Elastic and inelastic scattering 10

1.2.1.2 Neutron capture and activation 10

1.2.1.3 Fission 10

1.2.1.4 Neutron cross-section 12

1.2.2 Fusion 14

1.3 Nuclear Reactors 15

1.3.1 Components 15

1.3.2 General and specific materials considerations 16

1.3.3 Types of fission reactor 18

1.3.4 Generation I reactors: Magnox 19

1.3.5 Generation II reactors 20

1.3.5.1 Pressurised Water Reactor (PWR) 20

1.3.5.2 Boiling Water Reactor (BWR) 21

1.3.5.3 Advanced Gas-cooled Reactor (AGR) 21

1.3.5.4 Other types of Generation II reactor 22

1.3.6 Generation III and IV reactors 22

2. Radiation Damage 23

2.1 Introduction 23

2.2 Knock-on atoms and displacement cascades 23

2.3 Dislocation loops 25

2.4 Nucleation of cavities and voids 27

3. Nuclear fuels 28

3.1 Introduction 28

3.2 Metallic fuels 30

3.2.1 Uranium 30

3.2.1.1 Structure 30

3.2.1.2 Thermal expansion and thermal cycling growth 31

3.2.1.3 Thermal conductivity 32


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3.2.1.4 Mechanical properties 33

3.2.1.5 Corrosion 34

3.2.1.6 Irradiation growth 34

3.2.1.7 Irradiation swelling 35

3.2.1.8 Irradiation creep 37

3.2.2 Plutonium 38

3.2.3 Thorium 39

3.3 Ceramic fuels 40

3.3.1 UO2 41

3.3.1.1 Structure 42

3.3.1.2 Irradiation effects 43

3.3.2 Carbide and nitride fuels 46

4. Cladding 47

4.1 Introduction 47

4.2 Austenitic stainless steels 47

4.2.1 Helium production and void swelling 48

4.2.1.1 Minimising void swelling 52

4.2.2 Inverse Kirkendall effect 53

4.2.3 Dislocation densities 54

4.2.4 Creep 55

4.2.5 Mechanical properties 56

4.2.6 Summary 58

4.3 Ferritic alloys 59

4.4 Zirconium alloys 60

4.4.1 Structure 61

4.4.2 Effects of irradiation 61

4.4.2.1 Irradiation growth 62

4.4.2.2 Irradiation creep 63

4.4.2.3 Mechanical properties 63

4.4.2.4 Corrosion 64

5. Moderators 65

5.1 Introduction 65

5.2 Graphite 67

5.2.1 Structure 67

5.2.2 Effect of irradiation on properties 68

5.2.3 Wigner energy 69

5.3 Other solid moderators 70

5.3.1 ZrH 70

5.3.2 Beryllium 70

5.4 Liquid moderators 70


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6. Control rods 71

6.1 Introduction 71

6.2 Materials used for control rods 72

7. Corrosion of structural components 73

7.1 Introduction 73

7.2 Stress-corrosion cracking (SCC) 73

7.3 Irradiation-assisted stress-corrosion cracking (IASCC) 77

7.3.1 Irradiation effects: radiolysis of water 78

7.3.2 Irradiation effects: persistent effects 78

7.3.2.1 Stress 78

7.3.2.2 Segregation 78

7.3.2.3 Hardening 80

8. Summary of radiation damage and effects 81

Glossary 82

Abbreviations 84

Question sheet 1 85

Question sheet 2 87

Examples class 88


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1. Introduction

1.1 Fundamentals

1.1.1 Notation

A nuclide (any nucleus, any isotope of any element) can be represented as:

where: A is the mass number (number of nucleons, i.e. number of protons and neutrons)

Z is the atomic number (number of protons in the nuclide)

N is the neutron number

A = Z + N

The nuclide can be represented in various ways; for example can also be written as

, , or U-235.

1.1.2 Binding energy

Each nucleus has an associated binding energy. The total binding energy of a nucleus is the

energy released when a nucleus is assembled from individual nucleons: the greater the energy

release, the lower the potential energy of the nucleus. It is equivalent to the energy required to

split a nucleus into its component parts. Therefore the higher the binding energy, the more

stable the nucleus. If a nucleus is converted to another (or others) of higher binding energy, the

difference in the total binding energies of the nuclei is released as kinetic energy of the

resulting particles and gamma rays.

The graph below shows binding energy per nucleon as a function of atomic mass.


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1.1.3 Types of radiation and radioactive decay

Some large, unstable nuclei can become more stable by spontaneously undergoing radioactive

decay (others undergo fission, as well see in section 1.2).

Alpha radiation

An alpha particle is essentially a helium nucleus: two protons and two neutrons, or .

The most common source of alpha particles is the alpha decay of heavy atoms: when an atom

emits an alpha particle, its mass number decreases by four and its atomic number decreases by

two. This is an example of transmutation: the conversion of one chemical element or isotope

into another. For example, when undergoes alpha decay, it emits an alpha particle and

forms :

Beta radiation

Beta particles are high-energy, high-speed electrons ( ) or positrons ( ) emitted by certain

radioactive nuclei. The production of beta particles is known as beta decay, which also

involves transmutation.

If an unstable nucleus has an excess of neutrons, it may undergo decay, in which a neutron

is converted into a proton and an electron (and an antineutrino). An example is the decay of

into

:

Alternatively, if an unstable nucleus has an excess of protons, it may undergo decay, in

which a proton is converted into a neutron and a positron (and a neutrino). An example is the

decay of into

:

Gamma radiation

Gamma radiation, , is high-frequency (and therefore high-energy) electromagnetic radiation.

Gamma rays are produced during gamma decay, which occurs following alpha or beta decay.

The daughter nucleus is usually left in an excited state, so it can move to a lower energy state

by emitting a gamma ray.


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1.1.4 Exponential decay and half-life

Radioactive isotopes are subject to exponential decay (so long as the remaining number of

radioactive atoms is large): in a given sample, the number of radioactive atoms decreases at a

rate proportional to its current value:

where N(t) is the quantity of undecayed atoms after time t

is the decay constant

The solution to this differential equation is:

where N0 is the initial number of radioactive atoms

is the mean lifetime of the radioactive atom

and are related by

The half-life, , of a radioactive isotope is the length of time after which there is a 50%

chance that an atom will have undergone nuclear decay. It can also be thought of as the time

after which half the radioactive atoms will have decayed. It therefore follows that:

and can be related to the half-life by:

Therefore,

Note that N(t) can also be written as:

The half-life varies depending on the isotope, and is usually determined experimentally. Half-

lives can vary from 10-24

s to 10+30

s (54 orders of magnitude!). For a list of half-lives, see:

http://en.wikipedia.org/wiki/List_of_isotopes_by_half-life


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1.1.5 Neutron classification

So far, we have considered spontaneous decay. However, in a nuclear reactor, decay is

stimulated by neutron impact so it is useful to consider the way in which neutrons are classified.

This is usually done based on their kinetic energies. Typical values are given in the table below.

Category Energy

Cold neutrons 10 MeV

Generally, thermal neutrons are associated with a kinetic energy of ~0.025 eV (corresponding

to a speed of 2200 ms-1

).


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1.2 Nuclear Reactions

A nuclear reaction is the process in which two nuclei, or one nucleus and a subatomic particle,

collide to produce one or more nuclides that are different from the nuclide(s) that began the

process. A nuclear reaction therefore always involves transmutation. Nuclear reactions may

involve alpha particles, neutrons, protons, electrons or positrons.

The first study of a nuclear reaction was carried out by Ernest Rutherford in 1919. He was the

first person to deliberately transmute one element into another: he used alpha radiation to

convert nitrogen into oxygen through the following reaction:

An alpha particle is absorbed and a proton is emitted. This reaction can also be written in the

compact form:

Here is regarded as the target nuclide,

as the product nuclide. This experiment

showed Rutherford that hydrogen nuclei formed part of nitrogen nuclei (and therefore probably

other nuclei too) and led him to suggest that a hydrogen nucleus was possibly a fundamental

building block of all nuclei and perhaps also a new fundamental particle. He named it the

proton in 1920.

If a reaction like this is endothermic, then there is a threshold energy for it to be possible.

There is also the Coulomb barrier, which is the energy needed to overcome the electrostatic

repulsion of approaching positively charged nuclides.

Note that nuclear equations describe nuclear reactions without considering charges.


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1.2.1 Interactions of neutrons with matter

Most nuclear reactions that we will consider in this course involve neutrons interacting with

nuclei, we will now consider different ways in which this can happen.

1.2.1.1 Elastic and inelastic scattering

Elastic scattering refers to a collision between a neutron and a nucleus in which kinetic energy

and momentum are both conserved. In inelastic scattering, momentum is conserved but kinetic

energy is not: the neutron loses kinetic energy, resulting in the emission of gamma radiation.

Whether elastic or inelastic scattering occurs depends on factors such as the speed of the

neutron, and the neutron cross-section of the nucleus (see below).

Note that this is not a nuclear reaction as defined above, since scattering does not involve

transmutation.

1.2.1.2 Neutron capture and activation

If a nucleus captures a neutron, a heavier nucleus is formed, which may cause it to become

radioactive. This then makes the material more difficult to handle (repair, replace, recycle,

dispose of) safely. An example is cobalt, which is a common alloying addition. The usual

isotope is , but this is activated by neutron irradiation:

has a half-life of 5.3 years.

1.2.1.3 Fission

Nuclear fission was discovered experimentally in December 1938 by Otto Hahn and his

assistant Fritz Strassmann, and explained theoretically in January 1939 by Lise Meitner and her

nephew Otto Robert Frisch (Hahn won the 1944 Nobel prize in chemistry for the discovery of

nuclear fission). During fission, the nucleus of an atom splits into two lighter nuclei.

Only one naturally occurring nuclide shows spontaneous fission (and not very actively). One

possible fission reaction is:

Nuclear power generation relies on fission induced by incident neutrons. If a nucleus can

undergo fission regardless of the incident neutron energy (even if the probability of this


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occurring is low), the nucleus is referred to as fissile, whereas if there is a threshold energy

needed for fission to occur, the nucleus is referred to as fissionable. Examples of fissile nuclei

include , and .

The most commonly used fissile nuclide in thermal reactors is . When absorbs a

neutron, it leads to the formation of the unstable radionuclide , which immediately splits

into two smaller nuclei (typically of unequal mass), known as fission fragments. There are

many possible fission reactions, for example:

However, a neutron will not necessarily induce fission if it passes through the nucleus: for

example, fast neutrons are less likely to induce fission in than thermal neutrons the

faster a neutron is travelling, the less time it spends inside the nucleus and therefore the less

opportunity it has to induce fission.

The fission event must emit more than one neutron if the reaction is to be sustained (and

therefore to create a chain reaction). Each fission of generates an average of 2.4 neutrons,

and each fission of gives an average of 2.9 neutrons. Each fission event typically

releases about 200 MeV of energy, about 35% of which is converted to electrical energy in

power stations.

The fission products typically exhibit a decay series. For example , a fission product of the

above reaction, shows an isobaric (conserving mass number) decay series:

Neutron economy plays an important role in the design of nuclear reactors, since there are

several ways in which the released neutrons can be used up:

Fission of a fissile nucleus

Non-fission capture by the fuel or other components in the reactor core

Leakage of neutrons from the core

There is a certain minimum size of a chain reacting system, called the critical size, for which

the production of neutrons by fission just balances the loss of neutrons to the other processes,

and the reaction can be sustained independently. The associated mass is the critical mass. If


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more neutrons are lost than produced, the reactor is said to be subcritical, and if more are

produced than lost, the reactor is said to be supercritical.

Reactors can also be used to create (breed) fuel, the most common case being the production of

from fissionable using fast (E = 1 20 MeV) neutrons:

is then usable as a fissile fuel in thermal reactors.

1.2.1.4 Neutron cross-section

The likelihood of a nuclear reaction taking place is described using the appropriate cross-

section, . A cross-section is a measure of the degree to which a particular nuclide will interact

with neutrons of a particular energy and is roughly the effective projected area of the target

nuclide. In conjunction with the neutron flux (roughly equivalent to the number of neutrons

travelling through unit area in unit time), it enables calculation of the reaction rate (for example

to calculate the thermal power of a nuclear power plant). Cross-sections are usually quoted in

barns (1 barn (b) = 10-28

m2).

There are different neutron cross-sections, depending on the process being considered. For

example, the absorption cross-section, a, describes the likelihood of a neutron being absorbed

by a nuclide, whereas the scattering cross-section, s, describes the likelihood of a neutron

being scattered by a nucleus. The total absorption cross-section includes the fission cross-

section, f, and the capture cross-section (which is approximately equal to the cross-section for

neutron absorption followed by gamma emission, ). The total cross-section is the sum of the

individual cross-sections.


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The neutron cross-section depends on the target type, the type of nuclear reaction (scattering,

fission etc) and the kinetic energy of the species involved. To a lesser extent, it also depends on

the angle between the incident neutron and the target nuclide and the target nuclide temperature.

Note that represents the microscopic cross-section and is a property of a given nuclide,

whereas the macroscopic cross-section, , takes into account the number of those nuclides

present. For mixtures of isotopes and elements, the macroscopic cross-sections add.

The range of a neutron is the distance it travels before being stopped and is a function of the

neutron energy as well as the capture cross-section of the material through which the neutron is

moving.

For fission to be induced by thermal neutrons, the binding energy of the thermal neutron to the

fissile nuclide must exceed the energy required for the nuclide to split (the fission barrier).

Heavy nuclides show very different cross-sections for induced fission, f, and for neutron

absorption followed by gamma emission, :

Nuclide f (b) (b) Binding Energy (MeV) Fission Barrier (MeV)

3 x 10-6 737 4.8 7.5

530 48 6.8 6.0

586 99 6.5 5.7

3 x 10-6 2.7 4.8 5.8

752 269 6.5 5.0


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1.2.2 Fusion

Fusion will not be discussed in detail in this course, but it is worth including at this point for

completeness.

Energy is given off when a nucleus becomes stable (i.e. when it approaches the maximum on

the graph in section 1.1.2). Whilst moving from heavier nuclei towards this maximum requires

the nucleus to split apart (fission), moving from lighter nuclei towards the maximum requires

two nuclei to combine and form a heavier one (fusion). The energy release per mass of nuclide

is much higher for fusion than fission.

The reaction of most interest for power generation, yielding 17.6 MeV per event, and with a

Coulomb barrier of only 0.68 MeV is the fusion of deuterium and tritium:

There are, however, many technical challenges and no commercial fusion reactors currently

exist. It is unlikely that any will be set up for some years, but fusion for power generation is a

prominent research topic. Experimental reactors are in the process of being built, such as ITER

(International Thermonuclear Experimental Reactor), which is planned to be completed by

2018.


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1.3 Nuclear Reactors

1.3.1 Components

The main components of nuclear reactors will be discussed in more detail in subsequent

sections, but a summary is given here.

The fuel can be in metallic, alloy or ceramic form and is generally contained within tubes made

of a metallic alloy (cladding). The most commonly used fuels are enriched uranium (uranium

in which the percentage of has been increased), uranium oxides and plutonium oxides.

This cladding provides mechanical support to the fuel, prevents fission products from leaving

the fuel element and protects the fuel from corrosion caused by the coolant.

The fuel elements are typically arranged in a regular pattern (square, hexagonal etc) with the

moderator.

The moderator slows down neutrons to sustain the fission reaction with thermal neutrons.

The fuel-moderator assembly is surrounded by a reflector to direct neutrons towards the core

and to control neutron leakage (thereby improving neutron economy).

Outside, the reactor is surrounded by shielding that absorbs neutrons and gamma rays and

reduces the external radiation intensity to a tolerable level.

Control rods help to control the chain reaction by absorbing neutrons to maintain a steady

state of operation. Control rods are made from neutron-absorbing materials such as boron and

hafnium. There are usually two types of control rod in a nuclear reactor: rods for routine

control, which can be raised or lowered to increase or decrease the amount of heat being

generated, and safety rods, which can be lowered to shut the reactor down in an emergency.

The coolant removes the heat that is continually generated and is used to produce steam to

drive turbines for electricity generation. The coolant can be gas or liquid: examples include

light or heavy water, carbon dioxide, liquid metals and molten salts. A careful balance is

needed between the reduction in neutron economy due to the presence of the coolant and the

efficiency of heat removal.


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1.3.2 General and specific materials considerations

1.3.2.1 General Considerations

There are many important general materials considerations when choosing materials for use in

nuclear reactors.

Mechanical properties the materials used should be strong enough to bear the normal

loads that the structure would be subjected to and withstand internal or external stresses,

and ductile enough to avoid any catastrophic failure.

Ease of fabrication including forming, welding, machining etc.

Dimensional stability many components in power reactors are required to work at

high temperatures for extended times, so should be stable and creep-resistant.

Corrosion resistance many components are in close contact with reactor fluids (such

as coolants), so should be corrosion-resistant.

Heat transfer properties particularly relevant for the fuel and cladding materials. The

heat generated inside the fuel needs to be able to be conducted away efficiently.

Availability and cost

1.3.2.2. Specific Considerations

Of particular interest in this course is the effect of irradiation on the properties of the materials

used in nuclear reactors.

Neutron properties for example, the fuel cladding materials need a low neutron

absorption cross-section, whereas the control materials need a high neutron absorption

cross-section.

Susceptibility to induced radioactivity as described above, absorption of neutrons can

lead to the formation of different isotopes, which may be radioactive. Considerations

include the abundance of the isotopes, their half-lives and the type of radiation that they

produce. For example, isotopes with a short half-life that emit low energy radiation are

much less of a concern than those with a long half-life that emit high energy radiation.

Radiation stability as we will see in later sections, radiation damage can lead to a

variety of effects, including the formation of voids, embrittlement, creep and hardening.

The requirements of materials used for different components within a nuclear reactor are

summarised in the table below.


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Component Main requirements Possible materials

Cladding

material

Low neutron absorption

Stability under heat and radiation

Mechanical strength

Corrosion resistance

Good heat transfer properties

Al, Be, Mg, Zr

Stainless steels

Ni-based superalloys

Refractory metals (Mo, Nb, Ti,

W etc)

Moderators and

reflectors

Low neutron absoption

Large energy loss by neutron per

collision

High neutron scattering

Water (light or heavy)

Beryllium (or BeO)

Graphite

Control

materials

High neutron absorption

Adequate strength

Low mass (for rapid movement)



B, Cd, Hf, rare earths (Gd, Eu)

Coolants Low neutron absorption

Good heat transfer properties

Low pumping power (low Tm)


Low induced radioactivity


Gases (air, H2, He, CO2, H2O)

Liquid water (H2O and D2O)

Liquid metal (Na, Na-K, Bi)

Molten salts (-Cl, -OH, -F)

Organic liquids

Shielding

material

Capacity to slow down neutrons

Absorption of radiation

Absorption of neutrons

Light water

Concrete

Most control materials

Metals (Fe, Pb, Bi, Ta, W, Boral)


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1.3.3 Types of Fission Reactor

There are four generations of fission reactors:

Generation I these have now mostly been retired

Generation II these make up the majority of reactors still being used

Generation III these offer minor improvements to the generation II reactors

Generation IV these are futuristic designs that are currently being researched,

although commercial construction is unlikely before 2030.


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1.3.4 Generation I Reactors: Magnox

The worlds first nuclear power station to deliver electricity in commercial quantities was the

Calder Hall reactor in Sellafield, which had four Magnox reactors (and started operation in

1956).

Magnox reactors were used for the production of plutonium (for atomic weapons) as well as

for electricity generation, but they have all now been decommissioned (or are soon to be

decommissioned).

They used a graphite moderator, carbon dioxide as coolant, and natural (i.e. unenriched)

uranium as fuel. The cladding consisted of thin cylindrical tubes of a non-oxidising magnesium

alloy (the name Magnox comes from magnesium nonoxidising), typically Mg-0.8Al-

0.005Be. Mg has a low thermal neutron capture cross-section, and the alloy was creep-resistant,

resistant to corrosion by CO2 and (unlike pure Al) does not react with uranium. The Al

provided solid solution strengthening and Be improved oxidation resistance.

A schematic of a Magnox reactor is shown below. CO2 circulated under pressure through the

reactor core, heated up and was then sent to the steam generator to produce steam, which in

turn was used to drive a turbine.

Schematic of a Magnox reactor (from Wikimedia Commons, attribution: Emoscopes)

The disadvantages of this type of reactor include limited efficiency and power capacity due to

relatively low maximum operating temperature (345C) this maximum was imposed due to

concern about reaction of CO2 with graphite at higher temperatures.


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1.3.5 Generation II Reactors: 1960s onwards

Most commercial reactors operating today are Light Water Reactors (LWRs), of which there

are two main types: Boiling Water Reactors (BWRs) and Pressurised Water Reactors (PWRs).

PWRs make up 60% of the total currently operational reactors and BWRs account for another

21%. As the name suggests, they use water (normal light water as opposed to heavy water)

as the coolant and moderator.

1.3.5.1 Pressurised Water Reactor (PWR)

A PWR consists of two separate light water loops, primary and secondary, and is shown

schematically below.

The reactor core is located inside a reactor pressure vessel made of a low-alloy ferritic steel

(typical dimensions are 5 m diameter, 12 m height and 30 cm wall thickness). The pressure

vessel is internally lined with a reactor cladding of 308-type stainless steel or Inconel-617 to

provide corrosion resistance. The primary loop operates at a pressure of 15-16 MPa, so that the

water doesnt boil, even at temperatures of 320-350C.

The core contains an array of fuel elements with stacks of slightly enriched UO2 pellets clad in

Zircaloy-4. These cladding tubes are typically 10 mm in diameter and 0.7 mm in wall thickness.

About 200 fuel rods are bundled together to form a fuel element, and about 180 elements are

grouped to form an array creating the reactor core. The control rods are typically Ag-In-Cd or

B4C.

The primary loop is transported to a steam generator, where heat is transferred to the secondary

loop system, creating steam, which is used to drive a turbine. The steam generator is essentially

a heat exchanger containing thousands of tubes made from a nickel-bearing alloy or nickel-

based superalloy supported by carbon steel plates.

Schematic of a PWR (from Wikimedia Commons)


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1.3.5.2 Boiling Water Reactor (BWR)

A schematic of a BWR is shown below. The reactor pressure vessel in a BWR is similar to that

for a PWR. However, in a BWR, there is only one water loop. The water is at a lower pressure

than in a PWR (about 7 MPa), so that it boils in the reactor core - the normal steam temperature

is 290-330C.

The core consists of a fuel assembly comprising slightly enriched UO2 fuel clad with

recrystallised Zircaloy-2 cladding tubes (12.5 mm outer diameter). Typically, a BWR fuel

assembly would contain 62 fuel rods and 2 water rods in an 8 x 8 array.

The control material is generally B4C dispersed in 304-type stainless steel matrix, or hafnium,

and takes the form of blades arranged throughout the assembly in a cross-shape. Water passes

through the reactor core producing steam and is dried at the top of the reactor vessel.

Schematic of a BWR (from Wikimedia Commons)

1.3.5.3 Advanced Gas-cooled Reactor (AGR): this type of reactor was developed from the

Magnox design, but operates at a higher gas temperature to improve thermal efficiency. It was

designed such that the final steam conditions are identical to those in conventional coal-fired

power stations, meaning that the same design of turbo-generator plant could be used. It uses

slightly enriched uranium as the fuel, graphite as the moderator and carbon dioxide as the

coolant.

It has a better thermal efficiency than a PWR, but the reactor core is larger for the same power

output and the fuel is used less efficiently, which counters the thermal efficiency advantage.

The AGR is designed to be refuelled without being shut down first, but fuel assembly vibration

problems during refueling at full power meant that refueling is now only performed at lower

power or when shut down.


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1. Charge tubes

2. Control rods

3. Graphite moderator

4. Fuel assemblies

5. Concrete pressure vessel

and radiation shielding

6. Gas circulator

7. Water

8. Water circulator

9. Heat exchanger

10. Steam

Schematic of an AGR (from Wikimedia Commons)

1.3.5.4 Other types of Generation II reactor

CANDU (Canadian Deuterium Uranium) reactor: this is essentially a pressurised heavy

water reactor (PHWR). Instead of using enriched uranium as the fuel, it uses natural uranium,

meaning that there are fewer neutrons available to sustain the reaction. A more efficient

moderator is therefore needed, so heavy water is used because (deuterium) absorbs neutrons

less readily than (in light water). This type of reactor also allows refuelling without shutting

down.

Fast Breeder Reactor (FBR): production of fissile material actually occurs in the fuel of all

current commercial nuclear power reactors (towards the end of its life, a PWR fuel element

produces more power from fission of plutonium than uranium), but a breeder reactor is a

nuclear reactor in which more new fuel is produced than consumed during its operation. The

reactor converts fertile material (containing and ) into fissile material ( and

respectively).

The most common type of FBR is a Liquid Metal Fast Breeder Reactor (LMFBR), in which

liquid metal (usually Na) is used to transport the heat generated in the core. LMFBRs have a

high power density due to lack of a moderator and higher temperatures can be achieved,

leading to higher efficiency. However, Na must be carefully contained because it reacts readily

with oxygen and water, and also becomes radioactive as it passes through the reactor core.

1.3.6 Generation III and IV reactors

Generation III reactors are mainly advanced LWRs, which are designed to be safer, more

efficient, longer lasting and have a greater capacity. Generation IV reactors are futuristic

designs that will offer further improvements.


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2. Radiation Damage

2.1 Introduction

Radiation damage refers to microscopic defects produced in materials due to irradiation, and

results in changes to their physical, chemical and mechanical properties. The interaction of

high energy subatomic particles and radiation with crystal lattices can give rise to a variety of

defects, including vacancies and self-interstitials. The majority of radiation damage is caused

by neutrons and fission fragments: other types of radiation generally have insufficient energy

(or are not produced in large enough quantities) to cause major damage.

Radiation damage has been widely studied because of its importance in structural components

in and near the cores of nuclear reactors. Such components are subjected to extreme conditions

of various kinds, including high temperature, high stress and corrosion, but neutron irradiation

leads to specific types of damage.

Note that the term radiation effects is generally used to refer to the effects on the behaviour

or properties of materials in the aftermath of radiation damage. Radiation effects will be

covered in more detail in subsequent sections.

2.2 Knock-on atoms and displacement cascades

The key point is that the incident radiation is sufficiently energetic to displace atoms from their

equilibrium sites in the crystal structure, since the binding energy of lattice atoms is typically

small compared to the energy of the impinging particles.

This creates vacancies and self-interstitials (one vacancy and one interstitial constitute a

Frenkel pair). The damage follows the sequence:

1. An energetic incident particle (usually a fast neutron) strikes an atom in the crystal

2. The transfer of kinetic energy to the atom in the primary recoil is large enough to

displace it from its lattice site and it becomes a primary knock-on atom, or PKA,

leaving behind a vacant site

3. The PKA moves through the lattice, creating further knock-on atoms in a displacement

cascade

4. The PKA and other knock-on atoms eventually come to rest as interstitial atoms

A displacement cascade (also known as a displacement spike) is illustrated in the image below.

There is a high density of vacancies in the core, with the surrounding material rich in

interstitials.


- 24 -

The initial mean free path between collisions is of the order of 1 cm for fast neutrons but

decreases as energy is dissipated in successive collisions; the result is that displacement

cascades are concentrated in volumes 1 to 10 nm in diameter. Typical damage rates (measured

as displacements per atom per second, dpa s-1

) range from 10-9

dpa s-1

in thermal reactors to

10-5

dpa s-1

in the first wall of proposed fusion reactors.

The displacement energy is the minimum energy that must be transferred to a lattice atom in

order for it to be displaced from its lattice site. Generally, an average displacement energy of

25 eV is assumed, but the actual value depends on a variety of factors including the material

and its crystallographic structure, the trajectories of the knock-on atoms, and the thermal

energy of the atoms. Generally, higher melting point metals tend to have higher displacement

energies, as illustrated below.

Variation of displacement energy as a function of melting temperature (from Murty & Charit, 2013)


- 25 -

If the energy transferred by a knock-on atom to the struck lattice atom is less than the

displacement energy, the lattice atom will not be dislodged from its lattice site. It will instead

vibrate around an equilibrium position and the energy will be dissipated as heat.

Over the lifetime of a component, each atom could be displaced as many as 100 times. Clearly

such extreme conditions can have profound effects on the microstructure of the alloys involved.

These effects include dissolution of precipitates, changes in their morphology, and appearance

of non-equilibrium phases. In this course, we will focus on dislocations and formation of voids.

In principle, the vacancies and interstitials generated in displacement cascades might

recombine to restore the equilibrium structure. However, in practice, several factors can give a

substantial supersaturation of vacancies:

Self-interstitial atoms form stable clusters and are ultimately removed by dislocation

glide to other dislocations and grain boundaries; in effect, radiation damage has a bias

towards the production of vacancies.

Typically the vacancies and interstitials are created at a temperature high enough for

them to be mobile. The interstitials are more mobile, which is an additional factor

leaving the centres of displacement cascades vacancy-rich.

Dislocations, through the process known as climb, can act as sinks for vacancies and

interstitials, but the greater elastic strain around the latter again leads to their

preferential removal.

The supersaturation of vacancies leads to the appearance of new microstructural features.

2.3 Dislocation loops

Dislocation loops can form at lower temperatures (T < 0.2 Tm, where Tm is the absolute melting

temperature of the irradiated alloy). The displacement cascade illustrated in section 2.2 can be

thought of as a core of vacancies surrounded by a shell of interstitials. If the vacancy core or

the interstitial shell collapse (condense) onto a close-packed plane, dislocation loops can be

generated: collapse of the vacancy core results in a vacancy loop, whilst collapse of the

interstitial shell results in an interstitial loop.

In ccp metals, the stacking sequence of close-packed planes (the {111} planes) can be

described by ABCABCABC. Both types of dislocation loop disrupt the stacking sequence of

the planes, resulting in a stacking fault: vacancy condensation produces an intrinsic fault and

interstitial condensation produces an extrinsic fault.


- 26 -

Removal of a layer of atoms (i.e. following the formation of a vacancy loop) results in an

intrinsic (or single) fault in the stacking sequence, such as ABCAB/ABCABC (where /

indicates the missing plane of atoms). Insertion of an extra plane of atoms (following the

formation of an interstitial loop) produces an extrinsic (double) fault in the stacking sequence,

such as ABCAB/A/CABC.

The images below show an end-on view of a stack of close-packed planes in a crystalline metal:

(a) with a vacancy loop (intrinsic fault); (b) with an interstitial loop (extrinsic fault).

Dislocation loops (from Was, 2007)

In these dislocation loops, the Burgers vector is normal to the planes and of magnitude equal to

the interplanar spacing ( ). The dislocation is sessile (unable to glide).

The formation of vacancy-type and interstitial-type loops under irradiation is a major

contribution to the observed increase in dislocation density. The continuing evolution of

dislocation density under irradiation, however, involves many processes and is not susceptible

to analysis in terms of loop nucleation.


- 27 -

2.4 Nucleation of cavities and voids

Irradiation at higher temperatures (T > 0.2 Tm), leads to cavities or voids, the nucleation of

which is related to supersaturation not only of vacancies but also of dissolved helium atoms.

This helium arises from irradiation-induced transmutation reactions (of B, Ni and Fe)

accompanied by the emission of alpha particles: since alpha particles are positively charged,

they easily pick up electrons from the surrounding lattice and become elemental helium. The

rate of helium production is in the range of 0.512 atomic parts per million per dpa.

The precipitation of helium atoms results in the formation of small bubbles, which can

subsequently act as sinks for vacancies, thereby acting as a nucleation point for voids. The rate

of swelling is much greater than can be accounted for solely by the helium production rate, and

is mainly due to the condensation of vacancies.

Cavity nucleation under irradiation has the feature, not often encountered in metallurgical

precipitation, that the principal species (vacancies and helium atoms) are under continual

production; without this, cavities already produced would largely disappear on annealing.

From the first observations of cavity formation in 1967, it was recognised that this is a

particularly important form of radiation damage, leading to swelling and distortion of irradiated

components. At higher temperatures, it can cause hardening of irradiated alloys and associated

embrittlement and loss of ductility. The development of voids on grain boundaries from initial

helium bubbles also shortens creep life.


- 28 -

3. Nuclear fuels

3.1 Introduction

The basic requirements of a nuclear fuel (apart from being easily fissionable and preferably

fissile) are:

good thermal conductivity (to allow heat generated during fission to be removed)

ideally a high melting temperature (to be able to run as hot as possible without melting)

mechanical stability

The design and operation of a reactor depend on the behaviour of the fuel. The relative cost of

the fuel in nuclear power generation is low, so it is possible to expend resources on optimising

it.

There must be enough fuel in a reactor for the chain reaction to be self-sustaining. The total

mass of fuel would be supercritical (leading to a runaway reaction) if it were in monolithic

form (i.e. a single block), but it is sub-divided to permit moderation and control, and to allow

heat extraction from the fuel to be efficient enough to prevent it from melting. The fuel can be

in the form of plates or rods (mostly rods), and it is isolated from the coolant by cladding (see

section 4).

Typically, in a PWR, the fuel rods are 45 m long, and the cladding is 912 mm in diameter

and 0.60.8 mm thick. Fuel assemblies have 200300 rods and there are 150250 such

assemblies in the core, giving approximately 80100 tonnes of uranium in the reactor.

Westinghouse fuel sub-assemblies for a PWR (ca. 1978) (from Frost, 1994; Ma, 1983)


- 29 -

The linear heat generation rate (LHGR) is the heat generation rate (i.e. power) per unit length

of fuel rod (commonly expressed in kW/m) and is limited by the thermal conductivity of the

fuel and the need to avoid melting in the centre. Typical values are 1570 kW/m.

It is desirable to have the fuel rods inserted for longer in the reactor (so that they need to be

replaced less frequently) and to achieve greater burn-up (to allow more efficient use of the

fuel). Burn-up is a measure of how much energy is extracted from a primary nuclear fuel

source and is quoted as GW-days per tonne of U (or equivalent), GWd/t.

Generation II reactors were designed to achieve ~40 GWd/t. With newer fuel technology, and

particularly the use of nuclear poisons, these reactors are now capable of ~60 GWd/t.

Nuclear poisons (or neutron poisons) are neutron absorbers that are inserted into some reactors

to lower the high reactivity of the fresh fuel (the poisons are said to have negative reactivity): if

a reactor is designed to operate for a long period of time, more fuel than that needed for exact

criticality must be used, so neutron absorbers are added to control the reaction. The positive

reactivity from the excess fuel is balanced by the negative reactivity of the neutron absorber.

These nuclear poisons are often burnable, meaning that their effect wears off over the

lifetime of the fuel: ideally, the negative reactivity of the poison should decrease at the same

rate that the fuels excess positive reactivity is depleted. Examples include B4C-Al2O3,

borosilicate glass and Gd2O3.

Some more advanced designs are expected to achieve >90 GWd/t from higher-enriched fuel,

and eventually >200 GWd/t. Complete fission of all heavy metal in a breeder reactor, not just

fissile content but also any fissionable or fertile material, would yield ~1,000 GWd/t.

In a power station, high fuel burn-up is desirable for:

reducing the downtime needed for refuelling

reducing the number of fresh nuclear fuel elements required and spent nuclear fuel

elements generated while producing a given amount of energy

reducing the potential for diversion of plutonium from spent fuel for use in nuclear

weapons

It is also desirable that burn-up should be as uniform as possible both within individual fuel

elements and from one element to another. Materials issues, particularly in the fuel and in the

cladding severely restrict the burn-up that can safely be achieved.

At present 98% of all nuclear-generated electricity comes from oxide fuels, but for historical

and scientific reasons we first consider metallic fuels.


- 30 -

3.2 Metallic fuels

3.2.1 Uranium

Uranium is the basic nuclear fuel and is the basis for breeding new fuel. Pure uranium was used

in the earliest reactors (such as the Magnox reactors at Calder Hall). Metallic uranium and its

alloys are still used in teaching and research reactors for low-temperature operation, and are of

interest for some future designs of reactor.

In principle, metallic fuels have significant advantages:

high density of fissile or fissionable nuclides

good fabrication and machinability

excellent thermal conductivity

relative ease of reprocessing (through electrorefining)

Disadvantages include:

lower melting points

various irradiation instabilities

poor corrosion resistance in reactor fluids

compatibility issues with the cladding materials

Irradiation stability and corrosion resistance can, however, be improved through alloying.

Uranium makes up about 4 ppm of the Earths crust (making it more common than elements

such as silver and mercury) and the amount of economically recoverable uranium in the world

has been estimated to be about 5.5 million tonnes.

Natural uranium has 0.7% and 99.3% (and 0.006% ). It is found in a variety of

minerals, such as pitchblende (U3O8), and uraninite (UO2). The main producers of uranium are

Kazakhstan (27%), Canada (20%) and Australia (20%), although a sizeable portion of uranium

is also produced by reprocessing spent fuel rods.

3.2.1.1 Structure

Uranium has three crystalline polymorphs:

is orthorhombic (at RT: a = 2.852 , b = 5.865 , c = 4.945 )

is tetragonal (at 720C: a = 10.790 , c = 5.656 )

is cubic (bcc) (at 850C: a = 3.538 )


- 31 -

3.2.1.2 Thermal expansion and thermal cycling growth

In single-crystal form, -U is strongly anisotropic. The temperature dependence of its lattice

parameters is shown below. Note that the coefficient of thermal expansion (CTE) along the a

and c axes is positive, whereas that along the b axis is negative (i.e. as temperature increases, it

expands along the a and c directions but shrinks in the b direction).

T-dependence of the lattice parameters of: (1) -U; (2) -U-15 at.% Pu (from Frost, 1994)

In polycrystalline samples, the anisotropic CTE causes problems when the temperature is

changed, since neighbouring grains (if unconstrained) would change shape in different ways on

heating or cooling. In a polycrystal, grains therefore exert stresses on each other and local

plastic flow, dislocation multiplication and hardening (and even failure of the material) can

occur.

If a polycrystal has grains in random orientations, no net shape change would be expected on

thermal cycling. However, rolled -U shows strong crystallographic texture (preferred grain

orientation), and textured polycrystals show thermal cycling growth. Note that growth in

this context means shape change at constant volume. The growth arises from relative

movement between neighbouring grains in different orientations combined with stress

relaxation in some of the grains by plastic deformation or creep.

The images below show the effect of thermal cycling growth in highly oriented fine-grained

-uranium between 50C and 500C for 1300 cycles (top) and 3000 cycles (bottom).


- 32 -

Effect of thermal cycling in uranium (from Murty & Charity, 2013)

Due to its greater symmetry, the gamma phase of uranium does not exhibit thermal cycling

growth, so gamma stabilising alloying additions such as Al, Mo and Mg can help avoid this

effect, as shown below. U-Mo alloys typically contain at least 6 wt% Mo in order to avoid

thermal cycling growth.

Thermal-cycling growth in uranium alloys (from Ma, 1983)

3.2.1.3 Thermal conductivity

A high thermal conductivity is required to allow heat to be removed from the fuel through the

cladding, to the coolant. The linear power rating of a fuel element is generally limited by the

thermal conductivity of the fuel, to avoid it melting. The figure below shows thermal

conductivity of annealed high-purity polycrystalline uranium as a function of temperature and

it can be seen that thermal conductivity increases as temperature increases (in practice, this is

limited by factors such as purity of the material).


- 33 -

Thermal conductivity of annealed uranium (from Murty & Charit, 2013)

3.2.1.4 Mechanical properties

Uranium is a relatively ductile metal and is therefore easy to work. A variety of fabrication

techniques can be used to process uranium, including: rolling, forging, casting, extrusion,

drawing, machining and powder metallurgy.

A typical stress-strain curve for uranium is shown below.

A typical stress-strain curve for uranium (from Ma, 1983)

It is worth noting that the mechanical properties depend on texture, fabrication history and heat

treatment. The tensile properties are also affected by impurities such as carbon, fission

products or alloying elements, and the strength also decreases dramatically with increasing

temperature.


- 34 -

3.2.1.5 Corrosion

Uranium reacts rapidly with most environments (air, oxygen, hydrogen, water etc). The UO2

surface layer that forms is not quite protective: at high temperatures, as the film thickens, it

cracks and crumbles, exposing fresh uranium underneath. Similarly, in water, the UO2 film

provides reasonable corrosion resistance at low temperatures (50-70C), but at higher

temperatures, the oxide becomes porous and the protection is lost.

Irradiation enhances corrosion, but this will be discussed in more detail in section 7.

3.2.1.6 Irradiation growth

Irradiation growth is a form of dimensional instability that occurs under irradiation without the

need for an applied stress, at relatively low temperatures (~300C). As in thermal cycling

growth, the volume of the material remains constant during irradiation growth (essentially,

material is moved from one place to another), so this is different to radiation swelling (see

section 3.2.1.7).

Under a neutron flux, even single crystals of -U show irradiation growth (although note that

-U does not, due to its isotropic nature). The growth is accompanied by hardening and

embrittlement, and arises from the generation of dislocation loops:

interstitial loops form on (010)

vacancy loops form on {110}

Interstitial and vacancy loops form on different planes because of the thermal spike and the

anisotropic CTE.

Consider the effect of heating an individual grain relative to its surroundings: it experiences

tension parallel to [010] (because the CTE in that direction is negative). Interstitial atoms will

then preferentially condense on (010), thereby giving an expansion to relieve the tensile stress

(analagous effects occur for vacancy loops on other planes). There is therefore a net expansion

parallel to [010].

If the material is polycrystalline, it will not show irradiation growth if there is no

crystallographic texture (individual grains would change shape but there would be no net shape

change), but irradiation growth will occur if it has preferred orientation.


- 35 -

Length changes for a uranium single crystal (from Frost, 1994)

3.2.1.7 Irradiation swelling

Irradiation swelling involves an increase in volume of a material as a result of irradiation.

There are two regimes of irradiation swelling:

At lower temperatures, swelling occurs because anisotropic irradiation growth causes

internal stresses, which can lead to cavitation (see section 2.4) and facilitates the

development of voids and therefore swelling.

At higher temperatures, fission gas bubbles (primarily and heavy, inert

gases) form in the phase.

Swelling rate of uranium phases in the burn-up range 0.20.5 at.% (from Frost (1994))


- 36 -

As illustrated below, voids in -U have a characteristic faceted shape, whilst those in cubic -U

are more rounded (due to the more isotropic nature of -U).

Pores in irradiated -U10Zr (wt%) (left) and in -U10Zr (right) (from Frost (1994))

As shown in the image below, the volume increases can be extreme!

Irradiation swelling of uranium and uranium alloys (from Ma (1983))


- 37 -

3.2.1.8 Irradiation creep

Creep rates can be accelerated by a factor of 10100 under irradiation, and the problem is

exacerbated by swelling. There are two slightly different types: radiation-induced creep and

radiation-enhanced creep, but both arise primarily because of vacancies.

Radiation-induced creep occurs at lower homologous temperatures than thermal creep. At

these lower temperatures, the vacancy concentration produced by atomic displacements due to

irradiation could be large enough to induce creep deformation under an applied stress. The

creep rate is proportional to the stress and the neutron flux.

Radiation-enhanced creep occurs at higher temperatures, at which thermal creep can also

occur. The addition of extra vacancies augments the vacancy concentration and enhances the

creep rate.

Note that irradiation affects both primary and secondary creep. In primary creep, the strain rate

is relatively high, but slows with increasing time - this is due to work hardening. The strain rate

becomes constant due to the balance between work hardening and annealing. This stage is

known as secondary or steady-state creep. Stress dependence of this rate depends on the creep

mechanism.


- 38 -

3.2.2 Plutonium

Plutonium can also be used as a nuclear fuel in nuclear reactors and in space applications.

is the major fissile isotope of plutonium and has a high fission cross-section. Plutonium

is only found naturally in trace quantities and is mainly produced artificially through the

transmutation of .

It can be recovered from spent fuel in thermal reactors, and depleted uranium can be kept

together with plutonium for fuels used in fast breeder reactors. Separated plutonium can also be

used in plutonium-burning reactors.

There are 6 phases of plutonium, which are only stable in limited temperature ranges. It is

monoclinic at room temperature, but also has orthorhombic, fcc, bct and bcc phases, and it also

readily undergoes martensitic transformations. It has a relatively low melting point of 640C.

Plutonium has a lower critical mass than uranium, and is also toxic and pyrophoric as well as

being very sensitive to corrosion. It is therefore difficult to work with, but a variety of

fabrication techniques can be used. Its mechanical properties depend on its phase (some phases

are very brittle, but others are relatively ductile), but also on impurity and defect concentrations.

Its properties therefore do not allow it to be used in pure form, so a variety of alloying

additions (Al, Ga, Mo, Th, Zr etc) are added. Zr is often added to increase the melting

temperature and to reduce interdiffusion with the stainless steel cladding. However, the

temperature gradient in alloy fuel rods leads to composition variation, driven by the Soret

effect (different atoms exhibit different responses to a temperature gradient).


- 39 -

3.2.3 Thorium

Thorium is another nuclear fuel that has not yet been used to its full potential. is a fertile

isotope that could produce fissile upon capturing a neutron, so is therefore an important

breeder material. is the only naturally-occurring isotope and has a half-life of 14 billion

years (!).

Thorium is far more abundant than uranium in nature: most rocks and sands contain minute

amounts of thorium, and monazite is a rare earth phosphate mineral, containing 67 wt%

thorium.

Thorium has two phases, both of which are cubic, and it has a melting point of ~1750C. Its

mechanical properties are sensitive to impurities, cold work and crystallographic texture, and it

is sensitive to corrosion (although much less so than plutonium). Its mechanical properties and

corrosion resistance can be improved by alloying.

The commercial use of thorium has a number of obstacles to overcome: a large amount of

R&D and testing are still needed and the costs of fuel fabrication and reprocessing are

high. also becomes contaminated with , which decays to daughter nuclides that are

high-energy gamma-emitters (and therefore difficult to handle), such as .


- 40 -

3.3 Ceramic fuels

The essential requirements remain that there should be a sufficient number density of fissile

atoms (and we would like to avoid high levels of U enrichment), and that the other nuclides

(non-fissile components) should have a low mass number and small neutron absorption

coefficient.

Potential advantages of ceramics:

good irradiation stability (no phase transitions)

higher fuel and plant operating temperature (higher melting temperature than metals)

excellent corrosion resistance

low thermal expansion coefficients

Disadvantages of ceramics:

brittle, low fracture strength

poor thermal conductivity, as illustrated below (especially UO2)

poor heat transfer to cladding (no metallurgical bond)

Thermal conductivities of major nuclear fuels (from Frost, 1994)

The three main ceramic nuclear fuels are UO2, UC and UN, although UO2 is most commonly

used (largely for historical reasons).


- 41 -

3.3.1 UO2

UO2 is a precursor to U metal and was first used as a blanket fuel, resistant to high-temperature

water (a blanket fuel is a layer of material containing fertile isotopes that is placed around the

reactor core as a reflector or absorber, but which is also used to breed additional fissionable

material). However, it is now very well studied, and has been in reliable use as a nuclear fuel

for nearly 50 years.

In UO2 fuel, either natural or slightly enriched uranium (0.7 4% ) can be used. If enriched

uranium is used, it is good practice to vary the enrichment across the core, as illustrated below.

This is because irradiation is usually non-uniform and tends to be higher in the centre of a fuel

rod, so having a varying enrichment can allow burn-up to occur more evenly.

Plan of the fuel sub-assembly and reactor core for a PWR (from Frost, 1994)

Note that Fast Breeder Reactors use a mixed oxide, MOX: (U0.75Pu0.25)O2. The oxides UO2 and

PuO2 show complete mutual solubility:

Solidus and liquidus lines in the UO2-PuO2 equilibrium phase diagram (from Frost, 1994)


- 42 -

A high density is desirable to ensure a high density of fissile or fissionable atoms, and good

thermal conductivity. However, some residual porosity is useful to retain fission product gases

and to allow densification on heating to offset irradiation swelling.

UO2 can be processed by conventional ceramic powder sintering into bulk shapes such as

pellets, rods and tubes with densities typically 9397% of the theoretical density (a lower

density of 85% is used for Fast Breeder Reactors, to allow greater burn-up). Pellets are usually

used (see image below), since it is difficult to manufacture a whole fuel rod from a ceramic.

Sintering must be performed in an inert (or reducing) atmosphere, because sintering in air can

lead to the formation of other uranium oxides such as U3O8 the different densities of the

various oxide phases causes problems during sintering.

3.3.1.1 Structure

UO2 has the CaF2 structure (fcc, a = 5.47 ): the calcium ions occupy the face-centred lattice

sites whilst the oxygen anions sit in tetrahedral interstices. The large octahedral interstice in the

centre of the unit cell is empty and can therefore accommodate fission products. This is

important for radiation stability (since it prevents the products from diffusing elsewhere and

forming voids).


- 43 -

UO2 shows no polymorphic phase changes on heating and its melting temperature (2865C) is

much higher than that of uranium metal. UO2 does restructure by grain growth and void

migration, especially above 1700C.

It has a low tensile strength of approximately 35 MPa and a Youngs modulus of

approximately 170 GPa. It rapidly loses strength and becomes ductile above 11001400C (the

transition temperature depending on strain rate and grain size), but exhibits cracking on reactor

start-up and shut-down. This cracking occurs primarily due to thermal stresses rather than due

to irradiation effects.

The image below shows crack distribution in a fuel pellet, with a superposed strength vs

temperature curve for (U, Pu)O2. The pellet is ductile in the centre, where the temperature is

highest, but becomes brittle closer to the edges, where the temperature is lower.

3.3.1.2 Irradiation effects

Upon irradiation, gas release can occur:

Xe and Kr (insoluble fission products)

Cs, I, Br, Te (volatile fission products)

The amount of gas released depends on a variety of factors, including porosity, irradiation time

and irradiation temperature. The centre temperature of the rod in thermal reactors is typically

restricted to ~1400C (note that in FBRs the temperature may initially be higher to promote gas

release.)

Irradiation swelling of UO2 is low, as illustrated below.


- 44 -

Irradiation swelling: (a) in U metal in a Magnox reactor; (b) in UO2 in a PWR (from Frost, 1994)

Failure of oxide fuel rods occurs mainly due to pellet-cladding mechanical interaction (PCI).

This can be alleviated by:

leaving sufficient space between the fuel and cladding (but note that this can affect the

efficiency of heat transfer)

using graphite as a liner to provide lubrication

using smaller diameter rods at lower LHGR

On increasing the LHGR, expansion and cracking of UO2 fuel pellets

can strain the cladding, as illustrated here (from Frost, 1994).

UO2 can deviate significantly from stoichiometry. This is an important issue affecting

properties and possible burn-up. As fuel is burned, the oxygen:metal ratio increases (because

not quite all the oxygen released can combine with fission products). It is good practice to start

with hypostoichiometric fuel (where oxygen:metal 1.97) as oxygen release is detrimental

for the cladding.

Thermal conductivity of perfectly dense (U0.8Pu0.2)O2- (from Frost, 1994)


- 45 -

In the ceramic UO2, transport (i.e. diffusion) rates are low (compared to those in metallic U),

but the movement of grain boundaries during grain growth sweeps gas from grain interiors to

grain boundaries, where the bubbles then coarsen by diffusion of gas atoms along the grain

boundaries, as shown below.

Gas bubbles on grain boundaries in UO2 tested in an AGR (from Frost, 1994)

Bubbles start from residual porosity in the sintered pellets and then migrate up the temperature

gradient in the fuel rod. UO3 is the main volatile species.

The migration of bubbles up the temperature gradient

generates a void along the central axis of the fuel pellet.

This image shows thermal restructuring in a 7.5 mm

diameter 94% dense fuel pellet of (U, Pu)O2, tested in a

FBR at a LHGR of 45 kW/m and a burn-up of 40 GWd/t.

Grain growth, cracking and a central void can be seen (from

Frost, 1994).

In MOX fuel rods, similar processes transport U from the centre to the surface, leaving the

centre Pu-rich.


- 46 -

3.3.2 Carbide and nitride fuels

There are many carbides and nitrides of U (UC, U2C3, U2C, UN, U2N3, UN3), but those of

interest for use as fuels are UC and UN, which show complete mutual solubility.

UC and UN both have the NaCl structure:

UC: a = 4.961 , Tm = 2780 K

UN: a = 4.889 , Tm = 3120 K

They are widely recognised as intrinsically better fuels for the future, in particular as advanced

fuels for FBRs. They would permit moderate LHGR (~70 kW/m), high burn-up (>150 GWd/t),

and efficient operation as they have a higher density of metallic atoms than UO2.

UC has been used in thermal and FBRs, and has been more extensively studied than UN, but

UN is of particular interest for easier reprocessing (important for the FBR fuel cycle).

The carbide and nitride fuels show similar irradiation effects to UO2, but they have greater

stability and better thermal conductivity, thus permitting higher LHGR and greater burn-up.


- 47 -

4. Cladding

4.1 Introduction

The cladding must:

isolate the fuel from the coolant (this requires chemical stability and mechanical

integrity)

have a low neutron absorption cross-section (to allow neutrons to pass through the

cladding without being absorbed)

be corrosion-resistant, and in general be compatible with the fuel and coolant

conduct heat well (to allow heat to be transferred from the fuel, through the cladding, to

the coolant: heat transfer from fuel to cladding should also be considered, as well as

heat transfer through the cladding)

have a melting point well above the operating temperature of the reactor (note that new

designs of reactor may well have higher operating temperatures)

have adequate strength and ductility, especially to withstand swelling of the fuel

have high stability under irradiation

have a low induced radioactivity (to facilitate recycling after use)

The cladding is one of the most critical components in a reactor, and its performance

(especially irradiation growth and corrosion resistance) is often the key factor limiting

attainable burn-up.

The most commonly used cladding materials are stainless steels (for more extreme conditions

in FBRs) and zirconium alloys (in thermal reactors).

4.2 Austenitic stainless steels

Austenitic (or ) stainless steels have an fcc structure. In low carbon steels, austenite is only

stable above the eutectoid temperature (730C), but different alloying additions can stabilise

austenite to lower temperatures.

Austenitic stainless steels are the cladding materials of choice in FBRs where operating

conditions are particularly severe:

irradiation can give as much as 100 dpa in total

liquid-metal temperatures: 250C to 700C


- 48 -

The most commonly used austenitic stainless steels are 304 and 316, typical compositions of

which are tabulated below.

Fe C Cr Ni Mo Mn Si P S

304 balance


- 49 -

Due to their small size, helium atoms can easily diffuse interstitially and form bubbles.

However, voids that form under irradiation are much larger than can be explained only by the

production of helium: as described in section 2, helium bubbles act as sinks for vacancies and

therefore act as nucleation sites for voids.

Austenitic stainless steels show good dimensional stability under irradiation, until the onset of

void swelling. The figure below schematically shows void swelling behaviour as a function of

radiation dose, illustrating the different stages of void swelling. The initial incubation period

represents the neutron dose required to produce sufficient helium to make void nucleation

possible: this incubation period depends on a variety of factors, including temperature,

composition and microstructure.

Void swelling behaviour (from Murty & Charit, 2013)

After the incubation and transient period (which is highly variable and depends on many

factors linked to the distribution of solute elements), the swelling enters steady state. The

steady state swelling rate in austenitic stainless steels is typically ~1% per dpa (in comparison,

the rate in ferritic steels is 0.1% per dpa), although the rate is lower at both high and low

temperatures. This is illustrated in the figure below, which schematically shows the three

regimes of steady-state swelling rate in 316 stainless steel.

(from Frost, 1994)


- 50 -

In region I (at low temperatures) direct recombination of vacancies and interstitials can occur

(due to lower mobilities at lower temperatures): the swelling rate is therefore low but increases

with increasing temperature (as mobility increases).

In region II, the steady state swelling rate is high, and can only be explained by an excess of

vacancies.

In region III (at higher temperatures), the swelling rate decreases with increasing temperature,

since the rate of vacancy emission from voids is greater than the flux of vacancies joining the

voids.

Under neutron irradiation the maximum total swelling reported for an austenitic stainless steel

is 88% (at 510C), although the largest reported swelling is 260% for irradiation by 140 keV

protons at 625C!

The images below show void swelling at different temperatures in 316 stainless steel at

~1.41027

neutrons/m2 (En > 0.1 MeV), equivalent to ~70 dpa (from Frost, 1994).


- 51 -

The image below shows swelling (~10% linear, 33% by volume) of a 316 stainless steel

cladding tube (not containing fuel) irradiated at 1.51027

neutrons/m2 (En > 0.1 MeV),

equivalent to ~75 dpa, at 510C. Note that all relative proportions are preserved during

swelling (from Frost, 1994).

The swelling of the cladding can be quite variable, as illustrated in the left-hand image (a)

below. This shows the top of a bundle of fuel rods irradiated to 2.1x1027

n/m2 (E > 0.1 MeV):

the rods vary in length as a function of gradients in dose, non-uniformity of composition and

variations in crystallographic texture (as a result of processing).

In comparison, the right-hand image (b) shows an undistorted fuel-rod assembly manufactured

using a non-swelling cladding (see below) that has been irradiated at 1.9x1027

n/m2 (E > 0.1

MeV) (from Frost, 1994).


- 52 -

4.2.1.1 Minimising void swelling

The transient period before the onset of steady state swelling can be prolonged by balanced

solute additions and appropriate thermomechanical treatments.

P and Si are particularly useful additions, since these form precipitates, the surfaces of which

act as vacancy sinks, which reduces the vacancy supersaturation.

This effect is illustrated below and shows that the degree of cold work and solute additions can

change the amount of swelling in 316 stainless steel irradiated at 500C (from Frost, 1994).

Swelling is accelerated by stress, as illustrated

in this graph, which shows the effect of stress

on the swelling of two modified 316 stainless

steels, irradiated as pressurised tubes (from

Frost, 1994).


- 53 -

4.2.2 Inverse Kirkendall effect

The Kirkendall effect (discovered in 1947) is the motion of

the boundary layer between two metals, that occurs as a

result of the difference in diffusion rates of the metal atoms

(see IB course A).

In the Kirkendall experiment two blocks of metal (A and B)

are joined together with inert markers (fine molybdenum

wires) at the interface to form a diffusion couple.

If the diffusivity of A atoms is higher than the diffusivity of

B atoms, there is a net flux of atoms to the right while the

inert markers remain stationary.

The situation can also be viewed in terms of vacancies. The equilibrium number of vacancies

in A is low and in B it is high. The vacancy flux is therefore higher from B to A than A to B.

The inverse Kirkendall effect arises when a flux of vacancies drives an opposite flux of more

mobile atoms. Voids act as sinks for vacancies, so the flux of vacancies towards voids is in fact

a flux of atoms away from voids. Faster-diffusing species exchange places more often with the

vacancies than slow-diffusing species. The fast-diffusing solutes are therefore depleted at sinks

while the concentrations of the slow-diffusing species increase.

In austenitic stainless steels, different elements have different diffusivities:

The more mobile Cr and Fe atoms diffuse away from voids to such an extent that the matrix

away from the voids converts to phase ferrite (bcc) and only the regions close to the voids

retain the original austenite phase. This occurs because nickel (which is itself fcc) is an

austenite stabiliser whereas chromium (which is bcc) is a ferrite stabiliser.


- 54 -

4.2.3 Dislocation densities

Typical dislocation densities in austenitic stainless steels are given below:

Annealed: 1012 m-2

Cold-worked: 1015 to 1016 m-2

Irradiated: (6 3) x 1014 m-2 (at steady state)

The figure below shows dislocation density as a function of irradiation dose in annealed and

cold-worked austenitic stainless steels, irradiated at 500C (from Frost, 1994).

The irradiation drives the dislocation density to the same steady-state value, independent of the

starting value.

This steady-state arises due to a balance between irradiation causing an increase in dislocation

density (as discussed in section 2), whilst also causing an increase in mobility (due to heating

of the material and therefore annealing), which enables dislocations to be removed and

therefore decreases the dislocation density: at steady-state, dislocations are generated at the

same rate as they are removed, meaning that the dislocation density reaches a constant value.

In an annealed sample, the initial dislocation density is low, so irradiation leads to an overall

increase in dislocation density. However, in a cold-worked sample, the initial dislocation

density is already high, so the effect of increased mobility means that dislocations are removed

faster than they are created (until steady state is reached), so that there is an overall decrease in

dislocation density.

The absolute value of the steady-state depends on a variety of factors including temperature

and neutron energy. The higher the temperature, the more effective the annealing-out of

damage, so the lower the steady state dislocation density.


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4.2.4 Creep

Irradiation accelerates creep by orders of

magnitude, as seen in this graph, which shows the

influence of neutron irradiation on creep rate of an

annealed steel (from Frost, 1994). Components can

be readily designed to avoid normal thermal creep,

so irradiation creep is the main issue. There is a

complex interaction of displacement rate and

temperature, and it is difficult to do in-reactor

experiments.

Here, the effect of irradiation on creep can be seen.

The graph shows results from uniaxial tensile tests

of 20% cold-worked 316 stainless steel during

thermal ageing and neutron irradiation (from Frost,

1994).

Additionally, creep is accelerated by swelling.

This graph shows the correlation of irradiation

creep coefficients with swelling rates for annealed

304L stainless steel (from Frost, 1994).


- 56 -

4.2.5 Mechanical properties

Irradiation induces hardening and loss of

ductility, due to the increased dislocation

density.

This graph shows the effects of neutron

irradiation to 12.5 dpa at 450C on the

m17h

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