UNITED STATES DEPARTMENT OF COMMERCE

Alexander B. Trowbridge • Acting Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Nuclear Science and Technology

for Ceramists

Proceedings of a Symposium

April 7-12, 1966

Held under the auspices of the Ceramic Educational Council of the American

Ceramic Society, with the cooperation of the National Bureau of Standards, and

under the sponsorship of the Office of Naval Research. The symposium took place

at the 68th Annual Meeting of the American Ceramic Society in Washington, D.C.

National Bureau of Standards Miscellaneous Publication 285

Issued May 26, 1967

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price $1.75 (cloth)
Library of Congress Catalog Card Number: 67-60013
Contents

Introduction

1. Material Radiation Environment

Carl 0. Muehlhause

National Bureau of Standards

Washington, D. C.

2. Radiation Damage in Ceramics

Alan B. Lidiard

United Kingdom Atomic Energy Research Establishment

Harwell, Didcot, Berkshire, England

3. Physical Properties of Irradiated Ceramic Materials

Paul W. Levy

Brookhaven National Laboratory

Upton, L. I., New York

4. Chemical Problems Associated with Lattice Defects

R. J. Thorn and G. H. Winslow

Argonne National Laboratory

Argonne, Illinois

5. Nuclear Fuel Materials

D. W. Readey and J. H. Handwerk

Argonne National Laboratory

Argonne, Illinois

6. Reactor Materials Design

Don R. deHalas, W. D. Freshley and W. C. Morgan

Pacific Northwest Laboratories

Battelle Memorial Institute

Richland, Washington
Introduction

Our rapidly advancing technology continually presents demands to the materials scientist and engineer to make present materials do new things or to devise new materials. To meet these ever- expanding challenges, the ceramist must be able to bring to bear in his field the most advanced and sophisticated ideas and techniques available from other fields. To assist in this task, a series of Symposia was established through the joint efforts of the National Bureau of Standards, the American

Ceramic Society, and the Office of Naval Research. Additional support for the first two in the series was also provided by the Edward Orton, Jr. Ceramic Foundation,,

These symposia have all been held at Annual Meetings of the American Ceramic Society, under the auspices of the Ceramic Educational Council, joined in 1964 by the National Institute of Ceramic

Engineers. The first three Symposia were:

Mechanical Behavior of Crystalline Solids

New York, 1962

NBS Monograph 59

Microstructure of Ceramic Materials

Pittsburgh, Pennsylvania, 1963 NBS Miscellaneous Publication 257

Systems Engineering in Ceramics

Chicago, Illinois, 1964 NBS Miscellaneous Publication 267

One of the new technologies for which ceramics hold great promise is that of nuclear reactors. Among the material properties desirable in this technology are chemical inertness, the ability to operate at elevated temperatures, and dimensional stability under loads applied for long periods.

These general requirements suggest the potential usefulness of ceramics. Thus as nuclear reactor

technology grows and expands, important new uses for ceramics may be expected to appear.

The requirements placed upon nuclear materials are quite naturally related to the radiation envi- ronment. Materials are chosen to perform certain functions - as fuel, moderator, control, etc., and must operate under the intense bombardment from neutrons and other high-energy radiation. Direct

damage to the crystal structure by the radiation brings about changes in dimensions and in physical

properties. Chemical reactivities are altered, and thus the chemical stability of the materials and

the compatibility of one material with another are influenced. Successful development of nuclear

materials requires an understanding of the nuclear properties and reactions, the physical processes

involved in radiation damage, and the chemistry of materials under operating conditions of temperatures,

atmosphere, and loading.

The purpose of this Symposium is to provide an introductory survey of those properties involved

in the choice and use of materials. In the first chapter, Dr. C. 0. Muehlhause describes the radiation fields present in reactors and the features of these fields most important to the development of nuclear materials, touching upon the principal physical effects induced in materials by the radiation.

A. B. Lidiard, in the second chapter, discusses the solid state physics of radiation damage processes, with examples drawn partly from ceramics. The effects these processes have on physical properties is then described by P. Levy. Turning to chemical problems, R. J. Thorn and G. H. Winslow discuss the thermodynamics of non-stoichiometry , a particularly significant problem encountered with nuclear fuels.

Finally, in the last two chapters, D. W. Readey and J. H. Handwerk, and D. R. deHalas, W. C. Morgan,

and M. D. Freshley take up the problems encountered in the development of nuclear fuels on the one hand, and structural and moderator materials on the other, thus displaying the application of the basic

ideas presented in the first four chapters.

It is the hope of the editors that this volume may prove to be of value as an introductory survey

to the subject, and as a reference useful in the teaching of ceramic science. The editors would like

to take this opportunity to thank the authors for the generous contribution of time and energy represented by each paper.

Floyd A. Hummel, Chairman

Pennsylvania State University

Alan D. Franklin

National Bureau of Standards

Cyrus Klingsberg

Office of Naval Research

(Now at the National Academy of Sciences)

iv
Material Radiation Environment

C. 0. Muehlhause

Institute for Materials Research

National Bureau of Standards

Washington, D„ C. 20234

Abstract

Materials used in radiation systems are in general

restricted by a wide variety of boundary conditions. For

example, in reactor systems the materials are required not only to possess suitable nuclear properties, but also to display adequate stability against radiation damage. Ceramic

materials are important in this technology. Radiation fields

to which reactor materials are subjected are described, and

principal physical effects induced by the radiation are identified. The elucidation of these effects by materials sci- entists and engineers is important not only to nuclear tech- nology, but also to a general understanding of structure sen- sitivity of solids.

1
Material Radiation Environment

C. 0. Muehlhause

Except for a few scattered speculations and one experiment, work on the interaction of radiation

with bulk matter prior to the advent of atomic energy was confined to the effects on radiation by

matter, i.e., just the other way around from those considerations which will be given today. 1 refer

to the attenuation of radiation, the stopping of charged particles, the diffraction and scattering of radiation, and other similar considerations which come to mind when the radiation field intensities are

low. Large scale disruption of bulk matter by radiation was regarded as remote not only because the radiation densities were low, but also because it was recognized that most of the energy deposited by

charged particles induced transitory electronic and ionization changes from which the matter quickly

recovered. This is to say that nearly all of the energy lost by nuclear radiation quickly appears as thermal energy. If this were not so, we would have a formidable, if not impossible, technological

problem on our hands today. This will be illustrated with a few numbers.

Consider the case of fission wherein approximately 200 Mev of energy is released primarily via

the short range (~ 5u.) f ission products. This is a prime example of the enormous ratio, ~ 10s

, between

nuclear and chemical energies. Even if the fuel is alloyed or otherwise contained in a material having

100 times as many atoms and the energy to disrupt a lattice site is ~ 20 ev, one might only be able to burn one fuel atom in 10 s before the material integrity disappeared. Fortunately, this is not the case.

The high inherent energy ratio between nuclear and chemical processes should, however, constitute

a warning that if even a small fraction of the energy deposit goes into a permanent change in the bulk properties of matter, one could be faced with a serious problem in the engineering of nuclear

systems. This was first recognized and stated by E. P. Wigner in the early phases of the Manhattan

Project. Since then a large effort has been spent studying these phenomena in a wide variety of materials. Though much of the motivation has been technological in nature, the subject is of great

interest to solid state physicists, chemical physicists, metallurgists, ceramists and other materials

scientists who find the inducement of defects by radiation of singular importance to their understanding

of the structure sensitivity of solids. How and why this comes about will be indicated in other chapters. The purpose here will be to give some idea of the radiation environment prevailing in reactor

systems and some notion of the primary physical effects which accompany . that radiation.

We note first that the fission reactor is based upon the following nuclear process:

On

1 (slow) + 92 u23—

>

x + Y + vn(fast) +~ 200 Mev

X and Y represent the fission products, (Fig. 1) and v the average number of fast neutrons produced per fission. This number is ~ 2.5 and is the means by which the reaction is made self-sustaining. The fact

10 that the reaction is exothermic accounts for its ability to generate power. Approximately 3 x 10 - fissions per second are required to produce one watt.

Accompanying this reaction are some prompt y-rays. Other y-rays result from the decay of the fission products, X and Y, and also from neutron capture in other materials composing the reactor. Not all uranium absorptions lead to fission. On the average a little more than two neutrons (T|) are released per neutron absorbed, one of which is needed to sustain the reaction. The other neutron

is either absorbed in the control rods or some structural component, or else it leaks from the system.

In fact, the critical condition for steady power can be written:

Hfp = 1

"T|" is the average number of neutrons (fast) emitted per neutron absorbed (slow) in uranium; "f" is the fraction of neutrons absorbed in uranium compared with other materials; and "p" is the neutron non-leakage probability, a quantity dependent upon the size of the system.

The f -factor appearing above formally displays the requirement that materials comprising the reactor other than uranium fuel (i.e., moderator, structure, etc.) be of low neutron absorption. The

minimum allowable value for "f" is = 0.5.

A basic reactor system consists of a core of fuel assemblies, i.e., fuel elements containing

uranium; a coolant to remove the power or heat from the core; a moderator to slow the fast fission neutrons down to thermal energies (so that they may be reabsorbed by the fuel); control rods whose

position in the core maintains the critical condition (largely by adjusting "f" above); a reactor vessel

to contain the primary system; and a biological shield to reduce radiation levels to tolerance outside

the system.

2
Neutrons born at the instant of fission are fast. Their average energy is ~ 1 Mev, but the

distribution extends to ~ 10 Mev. (Fig. 2). In a thermal reactor it is necessary to slow them down by

noderation so that they may rereact with the fuel. The reason for this is that the probability for neutron

absorption generally varies inversely as the neutron velocity. Neutrons cannot be slowed down to an

average energy less than the thermal energy (~ 0.025 ev) of the moderator. At this energy (~ kT) they

are in thermal equilibrium with their environment. Roughly speaking then there are three principal

;neutron energy regions, i.e., parts to the energy spectrum, in which neutrons are found. These correspond to: the very fast or virgin fission neutrons, the intermediate or slowing down neutrons, and the thermal or slowed down neutrons.

The spectrum (Fig. 3) is, of course, continuous and varies in detail with the specific reactor

design. It also varies with, position inside a given reactor. For example, the average neutron energy

is highest near the fuel elements. The thermal portion is described by a Maxwell-Boltzman distribution,

lithe intermediate portion varies as ~ E

_1

, and the fast portion is like the fission spectrum of Fig. 2. The distance over which all of the transport, slowing down, and diffusion takes place varies from a few

feet to several tens of feet depending on the design and size of the core.

• Usually the uranium is either alloyed with another metal or embodied as an oxide in a metal to form

a cermet. This is then clad with a metal to form a plate or pin. A successful type of ceramic fuel

is U3 Og + Al clad with Al. The plates are assembled to form a so-called fuel element or assembly. Some

iappropriate number of these are in turn required to constitute the core. They are placed in a specific

geometrical array and individually cooled by the flow over their plates of some primary heat transfer

fluid. This might be gas, water, or even liquid metal. Between the assemblies and for some distance

beyond them is the moderator. This could be water, graphite, BeO, etc. Sometimes it is identical with

the coolant, e.g., water.

Also between the assemblies are located the control rods. These absorb slow neutrons and are automatically adjusted to guarantee the critical or steady state power condition. The absorption of the

rods is usually via one of the two following processes:

v 10 7 4

Qn (slow) +

5B j>3 Li +

2He + 2.8 Mev

On

1 (slow) + 43Cd

113

y UG

Cd llk

+ 8 Mev (y)

The first reaction produces new species (Li and He) and the second a heavier isotope plus y-rays.

Beyond the moderator region is the reactor vessel and perhaps an additional water cooled metal shield.

Finally, the entire system is contained by the biological shield, usually composed of concrete. This

last structure is one in which radiation damage is not controlling. Due to its poor thermal conductivity,

radiation levels must be kept low anyway to avoid excessive heating and an accompanying temperature rise

which would lead to a prohibitive thermal stress.

A general picture should now be evident to you in which we have a system composed of at least five

main components: the fuel assemblies, the core support structure, (usually steel grid plates), the moderator-coolant, the control rods, and the reactor vessel. All of these components are subject to various and intense radiations: fast neutrons, intermediate neutrons, slow neutrons, and y-rays with

their accompanying Compton electrons. In addition, the fuel proper is subject to fission product

bombardment. Also, the control rods, if composed of boron, are subject to alpha particle bombardment.

Requirements on the fuel are most severe. This is where the bulk of the power is generated and from which the heat must be transferred to the coolant. Proper fuel materials possess the following

characteristics: 1) high fuel content, 2) low parasitic neutron absorption, 3) high thermal conductivity,

4) high temperature stability, and 5) high radiation stability. Sometimes 2) is violated purposefully

to improve 1) by the addition to the fuel of so-called burnable poison (e.g., boron carbide, a ceramic).

This increases the life of the assembly by requiring a higher fuel loading. Ceramic fuels, though

lacking the conductivity of metallic fuels, can function at higher temperatures. They also offer the

advantage of being able to contain a higher fuel fraction than alloys.

Control rod materials are probably second in receiving intense radiation and are somewhat similar

to the fuel element problem in that a large fraction of their special material burns up and may also

generate foreign atoms.

The moderator-coolant receives intense radiation also, but this is usually a radiochemical

problem. If the fluid is water, for example, the disassociated molecules are either vented or made to recombine.

The core support and reactor vessel both receive considerable radiation exposure over the lifetime

of the system. These are expensive items, difficult to replace, and therefore should be designed to survive the life of the plant.

3
With this brief outline of the radiation conditions prevailing within a general reactor system, we will proceed to a more specific identification of the kinds of primary processes which these

radiations can induce. These are all nuclear in character. The secondary processes are the ones which

lead to the various and subtle solid state or chemical physics effects, and it is these which will be dealt with in greater detail in other chapters.

Before describing such things as neutron scattering, capture, transmutation and some of their consequences, it should be pointed out that the principal radiation effect is the inducement of power.

"Earlier it was stated that nearly all of the nuclear energy released is ultimately transformed by

ionization, electron-electron interaction, and electron-phonon interaction into thermal energy or heat. This is, of course, what one wants to happen in the fuel plates, but not also throughout the system.

About 85 percent of the total energy is released directly to the fuel plates and primary coolant. About j 10 percent of the energy is generated in the control rods and grid plates, and another 5 percent in the reactor vessel. The y-rays alone in the reactor core heat structural members at the rate of 1 to 10 watts per gm.

The inducement of power within the body or volume of structural members is a phenomenon not ordinarily encountered in engineering practice. It sets up additional thermal stresses which can limit

or even prohibit certain types of construction. For example, a high pressure - high temperature loop

contained by a cylindrical steel or other metal shell requires a certain wall thickness in the absence

of the radiation field. In the field an additional thermal stress is induced, thereby requiring a greater wall thickness. This in turn generates yet greater thermal stress and it may not be possible

to contain the loop by such a design at all.

The inducement of power by the radiation field in the various components can be analyzed at least initially, i.e., in a new clean system. This is to say that if the classic parameters of the materials

are known along with the nuclear cross sections, the initial performance of the materials can be predicted

The difficulties arise with time when the materials or their properties are changed by the radiation.

In the case of the pressure vessel cited above, it is evident one must know how the mechanical properties"

change with exposure in order to design a possible system. The situation with respect to creep, fatigue,

and thermal cycling is even more complex.

Let us now cite the primary radiation processes of importance. These are:

1. Slow neutron absorption.

This process was illustrated earlier in the examples of fission, n-alpha, and n-y capture. The process can either transform a nucleus into a different species or merely add to its atomic weight and emit y-rays. The rate at which this process or any nuclear process takes place is determined by the cross section of the nucleus, a, and the flux of the radiation, 0. The cross section is the effective

size of the nucleus for the process in question, and the flux is the number of bombarding particles,

in this case neutrons, pass ing through a unit area in a unit time. Thus, if there are N nuclei per

unit volume of cross section a in a flux 0, the rate at which the process takes place per unit volume

is given by Na0. Also, the meanlife for survival of the nucleus is given by (o~0) -1

.

In a typical power reactor thermal fluxes are ~ 10 13/cm3sec. B

10 which has a cross section of ~ 4-000 barns (1 barn = 10 _34 cm

3

) would have a meanlife in this flux of ~ 2.5 x 10 7 sec, or approximately

one year. The u

33S cross section is ~ 600 barns.

In the case of fuel atoms, such as uranium, the fission process leads to a variety of fission

products, some of which are gasses, e.g., Xe, Kr. In the case of boron- contain ing control rod materials

one of the reaction products is also a gas, namely He. These foreign atoms usually reside in interstitial

positions within the lattice and thereby alter the density and other bulk properties of the material.

The gases are particularly troublesome, especially in the case of ceramics. They can accumulate to form bubbles and generate a high internal pressure. This induces swelling, cracking, rupture, and leakage. This is perhaps the most serious radiation effect in fuel and control rod materials. Of course, the passage of these fissio or other fragments through the lattice also causes damage, but this appears

as a background effect in t .e presence of the other more serious one.

In the case of structural materials, neutron absorption usually results in producing a heavier

isotope and y-rays. For steel this is represented by: * /(slow)

26 Fe

5^_>26

Fe

57

where the * represents a highly excited state of Fe 57

. This promptly decays by cascade y-emission

according to:

Fe

57 -=—>Fe57

+ y (~ 8 Mev)

4
The emitted Y-rays cause the Fe

57 nucleus to recoil. The amount of energy Tv which can be transferred in this manner is given by:

Y A y where A is the atomic weight and Ey is the Y -ray energy emitted. If A ~ 50 and Ey ~ 2 Mev, Ty ~ 40 ev,

a quantity able to dislodge the atom from its site. The next process to be described is able to transfer

considerably more energy to such atoms.

2. Fast neutron scattering.

A billiard ball type elastic scattering takes place between neutrons and all nuclei, the cross section for this process being typically several barns. The recoil or knockon ion travels for a short

distance (~ lu. ) through the lattice. The maximum energy, TM , which can be transferred by this process

is given by:

T„ = 4A

E (A - if n where A is the atomic weight and E

n

is the bombarding neutron energy.

Tjvj results from a head on collision. In the case of iron and a 1 Mev neutron, T^ has the value ~ 70 Kev. The transferred energy, T, varies from zero (grazing incidence) to T^. If the scattering is isotropic, the differential probability distribution for transfer over this energy band is constant.

That is : dT

dp = —

M

If T ^ 25 ev the nucleus can be dislodged from the lattice. The passage of this ion through the

lattice creates both ionization and Frenkel pairs. This, however, is the subject of the other chapters.

Fast neutrons can also inelast ically scatter from materials like iron. This is a process in which

the neutron suffers a marked degredation in energy by exciting the nucleus to a higher state. For

iron:

*

Qn (fast) + 2g Fe -> 2 6 Fe +Qn ' (degraded)

and the subsequent prompt reaction:

*

„ £ Fe

56 ,Fe56

+ y (~ 800 Kev)

26 —> 26 which takes the iron back to its ground state by y-emission. The recoil energy from these two steps

is less than in the elastic case, but can be ~ ^n^» a s ignif icant fraction of the former case.

3. Electron scattering

Nuclear recoil from electron scattering is another possible process; however, due to the light

electron mass the recoil energy is small and of the same order as T^,, above.

4. Gamma ray transmutation.

For sufficiently high y-ray energies (resulting from fission product decay and neutron capture)

certain low binding nuclei can photo-disintegrate. For example, in beryllium or its oxide:

9 4 Y(~ 2 Mev) + ^Be__^2

2He + Q

n'

Fast neutrons can also induce this reaction. Again foreign atoms and, in particular gases, appear

in the matrix via this process.

These constitute the principal primary interactions. In a general way it can be seen that neutron

and y-radiation disassociates matter at the chemical level. Before closing this chapter three secondary

effects will be just briefly cited. These are:

1) In moderators such as graphite radiation scattering results not only in altered mechanical

properties, etc., but also in the inducement of stored energy. Graphite moderated power reactors must

be periodically annealed to relieve this condition.

2) Neutrons and y-rays cause chemical disassociation, a certain amount of which will back react

or anneal at the operating temperature.

3) Neutrons and y-rays can augment chemical combination by forming chemically active species

such as free radicals. This phenomenon can be put to use to fix nitrogen as in the so-called

5
chemonuclear systems. On the other hand it can operate to disadvantage by augmenting corrosion rates as in the graphite-moderated, sodium-cooled systems.

General References

R. Strumane, J. Nihoul, R. Gevers , and J. F. Kirchner and R. E. Bowman,

S. Amelinckx, The Interaction of Radiation Effects of Radiation on Materials

with Solids, North Holland Publishing Co. and Components , Reinhold Publishing

(Amsterdam, 1964) Co. (New York, 1964)

D. S. Billington and J. H. Crawford Jr., Reactor Material , Division of Radiation Damage in Solids , Princeton Technical Information, United States University Press (Princeton, 1961) Atomic Energy Commission

0

I0"5I I I I 70 90 110 130 150 170 MASS NUMBER

10' Figure 1. Fission Product Yield vs Mass

Figure 3. Reactor Neutron Spectrum

NEUTRON ENERGY, ev

6
Fundamentals of Radiation Damage in Ceramics

A. B. Lidiard

United Kingdom Atomic Energy Research Establishment

Harwell, Didcot, Berks., England

Abstract

Processes of radiation damage in ceramic materials of interest in nuclear technology are reviewed. These materials

include those used as fuels (e.g. U02 solid solutions) as fuel

coatings (e.g. SiC, A13 03 ) and as moderators (e.g. graphite,

BeO) . Radiation damage in these materials consists firstly of

the production of interstitial atoms and vacancies and, in fuels,

of the introduction of foreign atoms notably the fission products.

Secondly, at normal reactor temperatures the aggregation of these

defects into clusters occurs and in non-cubic materials this

leads to anisotropic changes in physical properties of the com- ponent, crystallites of which the most striking may be dimensional

changes (e.g. in graphite). In fuels the growth of bubbles of fission gas can also lead to important dimensional changes. The

theory of the growth of defect clusters will be described in relation to some of these problems.

Vi
I Fundamentals of Radiation Damage in Ceramics

A.B. Lidiard

1 . Introduction

Nuclear technology provides an interest in a variety of ceramic materials and requires us to study changes in their physical properties under reactor irradiation. However, these materials

do not form a coherent group from the point of view of solid state physics, but show a wide variety

of electronic and crystal structures. Examples are:

(i) carbides, nitrides, etc. of fissile elements, e.g. UC, UN; these have a metallic

electronic structure and a NaCl crystal lattice;

(ii) the stoichiometric oxides BeO, MgO, Al^^, ThO^, etc whicn are insulators;

(iii) non-stoichiometric oxides, e.g. U0

2» (U,Pu)C>2 which are semiconductors;

(iv) SiC, which is a semiconductor;

(v) graphite, which has a semi-metallic electronic structure.

The principle radiations to whicn these substances are subjected in a reactor are:

(i) neutrons, especially fission neutrons whose average energy is about 1.5 MeV (neutron

distributions are shown in Figures 2 and 3 on p. 20).

(ii) Y-rays, which can lead in turn to the production of Compton electrons and also cause photonuclear reactions;

(iii) (in fissile materials) fission fragments, which carry off most of the energy liberated

in fission (~ 200 MeV per U235 fission).

This variety of radiations and materials means that it is only at a rather general and qualitative

level that we can describe all the situations of interest. The important processes that we must

consider are the following.

(1) Atomic Displacements . Atoms are displayed from their normal lattice positions as a result

of receiving large amounts of kinetic energy - most frequently as a result of elastic collisions

with energetic neutrons or fission fragments. In such collisions the struck nucleus may receive energy up to a maximum ^max

given by

E =^^E , (1.1) max

(M+m)

2 n

where M = mass of the struck atom m = mass of the neutron (or fission fragment)

En

= energy of the incident neutron (or fission fragment)

„

This energy can be very high, e.g. for a C atom struck by a 1.5 MeV fission neutron E is 475 keV, and such a displaced atom ("primary") has the potentiality to displace many

other atoms ("secondaries") as it moves through the crystal. These displaced atoms eventually come

to rest in interstitial positions in the lattice; the existence of these "interstitials" and the corresponding vacant lattice sites ("vacancies") changes the physical properties of the solid - including those whicn are important in reactor design, e.g. thermal conductivity and physical

dimensions,,

(2) Introduction of Foreign Atoms , Foreign atoms are introduced into fissile materials in

greatest number as a result of the fission process itself. Figure 1 on p. 20 shows the distribution

of elements produced by the fission of U

235

. The rare gases Kr and Xe are especially important

because of their very low solubility in all solids.
In non-fissile materials transmutations occur as a result of nuclear reactions induced by the neutrons and many of these also lead to the production of insoluble rare gases, e.g.

(a) in BeO

followed by

(b) in MgO

Be

9 + n — 2n + 2 He ,

Be + n —> Li + H ,

7 4

Li + n — 2 He

Mg + n —» Ne + He ,

,. 25 ..22 „ 4

Mg + n —> Ne + He ;

(c) in all oxides

J6 _13 „ 4

0 + n —> C + He .

Since the solubility of these gases is invariably exceeded they may collect into bubbles at high

temperatures and cause swelling of the solid.

(3) Annealing Reactions. Interstitial atoms and vacancies can migrate through the lattice as

a result of thermal activation and can therefore recombine, with consequent removal of the damage.

Recombination can also occur when a new displacement sequence penetrates into a region of previous

damage. Thermally activated recombination means that less damage is retained at higher than at

low temperatures, while irradiation-induced recombination means that proportionally less damage

occurs at high doses than at low doses ("saturation").

(4) Clustering Reactions . Thermally activated motion of the interstitials and vacancies leads

not only to their mutual annihilation but also to the clustering of defects of like kind, e.g. interstitials may cluster together to form a new lattice plane. Such processes occur almost

universally at the temperatures of reactor operation and the study of their nucleation and growth is important. The nucleation and growth of rare gas bubbles and other precipitate phases may be equally

important at higher temperatures.

In this review we shall survey the elements of the quantitative description of these four major

processes, illustrating the principles as far as possible by examples in ceramic materials. Our

attention will be mainly on neutron damage; this will focus the discussion on the fundamentals of the

subject,, Even here we shall find large gaps in our knowledge and understanding of ceramic materials.

It does not therefore seem appropriate to elaborate greatly on the more complicated fission fragment

damage - even though tnis is of great importance in fuels. Where possible we shall try to indicate

the differences from neutron damage.

It is not our object to review knowledge of the effects of radiation upon physical properties nor

to discuss the principles behind different experimental methods of studying defects for which there are other sources, in particular the article by Levy on p. 2l[i]'.

2. The Displacement of Atoms

In passing through matter neutrons cause no direct ionisation or electronic excitation and collide

elastically with the nuclei with only very low cross-section (total elastic cross-sections cr typically ~ 10~24 cm2

). Since the number of nuclei per air* in a solid, N, is roughly 1022 it follows that the mean free path X = 1/facr is ~ 100 cm. Thus the primary displacements are well separated independent

events. The probability that an atom receives energy between E and E+dE as a result of a collision

between its nucleus and a neutron of energy En

is governed by the differential cross-section o"(En

,E) for this transfer. To a good approximation cr(En ,E) is generally independent of E up to Emax

-

beyond which it is zero, of course ("hard-sphere" collisions). This has the consequence

that the average energy of atoms struck by neutrons of energy En is Ejnax/2, which is very high for

fission neutrons. Each primary displaced atom of energy E therefore gives rise to a cascade of

collisions in the lattice, leading ultimately to v(E) displaced atoms altogether.

Figures in brackets indicate the literature references at the end of this paper,

9
2.1 Total number of displaced atoms

(a) The Collisions. It is a major part of our problem to calculate v(E) for each of the kinds | of atom making up the lattice. The greater part of the discussions of v(E)have however been made

for monatomic substances and we shall first describe the salient features of this simpler situation.

A useful and adequate simplification which is often made in approaching this problem is to treat the collisions between atoms as hard-sphere collisions - even though the actual potential of interaction

will not be inf initely hard but will be Coulombic at close distances of approach and something like

screened Coulombic or Born-Mayer (i.e. exponential) at larger distances. This hard-sphere approximation

is generally a fair one to use for collisions leading to large angular deflections if we equate the

classical distance of closest approach of two atoms in a head-on encounter to the sum of their

equivalent hard-sphere radii, i.e. to their diameter D when they are chemically the same. This means

that the effective diameter of an atom moving through the lattice is a function of its energy, D(E),

which decreases as its energy increases. A fast atom therefore sees a more open lattice than a slow one

For atoms of atomic weight, A, greater than about 50 the mean energy of a primary produced by

fission neutrons is low enough that, in subsequent collisions, the screening effect of the electrons

is always important,, All collisions are then effectively hard-sphere collisions. On the other

hand light atoms (A < 50) receive more energy from the neutrons and in the subsequent collisions the nuclei may penetrate right inside the screening electron cloud. The interaction potential is then

2 Coulombic, with the consequence that the cross-section for energy transfer E" is proportional to 1/(E') , so that low energy transfers are much more probable than the hard-sphere approximation would predict.

This causes an important difference in the distribution of defects, although for a special reason it turns out not to affect very much the total number of displacements 0 We shall therefore proceed first

on the basis that all collisions are hard-sphere collisions,,

Fission fragments are of sufficiently high initial energy (light ~ 95 MeV and heavy ~ 67 MeVj that

here too the collisions with the atoms of the solid are Coulombic, at least to begin with; as Figure 1 shows they become hard-sphere type when they have slowed down to ~ 160 keV (light) and ~ 400 keV (heavy).

This figure shows the energy at whicn the scattering becomes mainly Coulomb scattering as a function

of the atomic number of the colliding atoms. The boundary between Coulomb encounters and hard-sphere

encounters has been calculated using a screened Coulomb potential proposed by Bohr.

(b) The Displacement Energy. In terms of v(E) we can write down an expression for the displacemenl

cross-section cr defined so that

d'

No. of displaced atoms = (^N) x (neutron dose) , (2.1)

where N is the number of atoms per unit volume of solid and

f

00 Dose = (time of irradiation) x i 0(E

n) dEn

> (2.2)

o in wnicn <£(E r ) dE is the flux of neutrons having energies in the interval between E and E +dE . This

spectrum depends n

upon n

the reactor being used and oothe position of the specimen relative

nnnto the fuel

elements (an example is Figure 3 on p. 20) . The expression for cr is

E (E ) r max n

[E ) dE / v(E) cr(E ,E) dE n n

J E

n

O d / X o- = . (2.3)

d

(f 00 <p(E r ) dE

n n

In this expression we have introduced a lowest energy Ed which an atom must receive if it is to be

displaced from its normal lattice site; this energy is several times the sum of the thermodynamic

formation energies of interstitials and vacancies - the extra energy being dissipated as heat in the

displacement process. The cross-section cr(En

,E) may be taken as °total/En' To calculate v(E) we need the following:

(i) the fundamental displacement probability P(E) dE of an atom which has received energy

between E and E+dE;

(ii) a knowledge of the loss of energy by an energetic atom by ionisation.

10
A typical displacement probability may be as shown in Figure 2. There will be a lower threshold

corresponding to the direction of easiest displacement in the lattice. The function will then rise

in one or more steps corresponding to directions of more difficult displacement (more closely packed

crystal directions) before it approaches the asymptote P=1 at high energies. A much simpler model

than tnis is often used; P(E) is replaced by a simple step function

P(E) =0 E < E

d

,

P(E) =1 E > E

d

. (2.4)

For simple analytical calculations it is difficult to use more complex forms and we shall therefore

use (2.4) here,, Although some reasonable calculations of the energy Ed have now been made for

metals [2,3], this is best determined experimentally and this is generally done by electron

irradiation,, The small mass of the electron allows only low energy transfers. The energy of the electron beam can therefore be adjusted until a radiation damage threshold is found. In practice,

since P(E) is not generally a simple step function the exact value obtained may depend on the

sensitivity of the method used to study the radiation damage. An example of this occurs in graphite,

as shown by the following illustrative results.

TABLE I. Displacement Energies

1 Substance Displacement energy Method

C, graphite 33 eV threshold Sensitive chemical

method [4]

C, graphite 60 eV Electrical resistivity

change [5]

C, diamond 80 eV 7410 A* Colour centres [6]

SiC ~ 30 eV Change in carrier

concentration [ 7]

In compounds there is necessarily more than one displacement energy, but so far there are no examples of substances for which these have been determined. In AI2O3 there is a colour centre which absorbs at 6 eV. Electron irradiation experiments [&] lead to the conclusion that if

(as seems more likely) this is an oxygen defect then

E (0) = 40 eV, d

whereas if it is an Al defect then

Ed

(Al) = 22 eV .

Such uncertainties are at present characteristic of the materials we are interested in here and more

work needs to be done on the identification of defects and the determination of E^ parameters.

Errors in v(E) are in proportion to those in E^. In materials such as BeO, MgO, SiC, etc. where

the two kinds of atoms lie on equivalent sites we might expect their displacement energies to be

closely equal

(c) Ionisation. The third point we have to discuss before calculating v(E) is loss of energy

by ionisation and electronic excitation. This is unimportant at low energies where the electrons of the solid can follow the motion of the atom as it travels through,, At high energies, by contrast,

it is dominanto The energies of light atoms (say atomic weight < 50) displaced by fission neutrons

are such that ionisation losses are significant; this applies to all of the substances on our list0 Unfortunately, detailed knowledge of ionisation losses is not yery extensive,, Theoretical

expressions give order of magnitude agreement for 10 < E < 10 eV. The relation between the rates

of loss of energy by electronic excitation and by elastic collisions is shown schematically in

Figure 3. Electronic excitation rapidly dominates above a certain critical energy, E^, and is unimportant below it0 Commonly therefore one takes

v(E) = v(E

A

), E > E

i

. (2.5)

11
A crude, but often used, approximation is to take

E

i = M keV (2.6)

where M is the atomic weight of the moving atom. This relation between E and M results from

equating the dominant excitation frequency of the solid to the principal frequency associated with

the motion of the fast atom through it; the coefficient of proportionality, whicn strictly

is dependent upon the properties of the solid, turns out generally to be roughly 1 keV. For light

atoms under fast neutron irradiation, E > E .

.

max i A more satisfactory proceedure is to calculate both the rate of loss of energy in collisions

with the lattice and the rate of loss by ionisation as the primary is slowed down. This then gives

us the effective energy available for the production of displacements by the primary.

It is implicit in what we have just said that ionisation or electronic excitation per se will not lead to displacements of atoms from the lattice. While this is generally correct it is not true

of at least some alkali haiides and other alkali salts. Here there is no doubt that ionisation of

the solid leads to displacements of anions. The exact mechanism by which this occurs is still not

settled, but the various models proposed agree in not expecting the effect to be significant in

oxides. There is some indication that it may occur to a small extent in BeO [9]„

(d) The Calculation of v(E). With this simple model we can now determine the function v(E)

by a simple argument. We assume that after collision an atom continues through the lattice if its energy E > E

d

, otherwise not. Thus if an atom having energy < 2Ed collides with a stationary atom at least one of the pair has energy < Ej after collision and there is no multiplication in

the number of displaced atoms. Thus

v(E) = 1, E

d

< E < 2E

d

. (2.7)

When E > 2E^ we arrive at the following equation for v(E) based on the fact that after a collision

each of the two atoms gives rise to further displacements which on average total v(E). For hard

sphere collisions all energy transfers are equally probable and

E v(S') ^- + ( v(E-E') ^§1 ,

i.e. E v(E) = 2

J v(E') dE' ,

o

By (2.7) this gives

v(E) = E/2Ed

, E > 2E

d

. (2.8)

This result is due to Kinchin and Pease[l0]. Other formulations, either making slightly different

assumptions about the conditions for displacement or about the distribution of energy in the collisions

lead to closely similar results0

In fact this result (2.8) may even be good when the primary is so energetic that its collisions

with the atoms of the solid are no longer hard-sphere collisions but Coulomb collisions. The reason

is that by the nature of Coulomb collisions the primary then loses its energy principally in a series

of low angle collisions in each of which there is a relatively small transfer of energy. The

secondaries are on average energetic enough to produce further displacements, but are well within the range of hard-sphere encounters. The result is that the energy of the primary is spread out over a large number of secondaries each of which then produces more displacements in accordance with (2.8).

Since v(E) is linear in E we therefore arrive at the same total number of displacements as if we

had assumed (2.8) for the primary itself. This is especially fortunate in the present context since

at the high energies which light atoms may receive from fission neutrons the encounters are almost

entirely Coulombic.

12
Equation (2.8) has been widely used for the calculation of displacement cross-sections. An

example of its use together with (2.6) is that for graphite (E^ = 60 eV)

-21

cr = 0.677 x 10 x (equivalent Ni dose) d for a position in a hollow fuel element in the Harwell Pluto reactor [ll]. The equivalent Ni-dose is

a measure of the fast neutron flux in this reactor. A more careful treatment of the relative energy

losses by electronic excitation and by displacement (e„g. not completely omitting displacement

losses when E > E^) leads to a higher estimate [ll]

-21

o"^ a 1.313 x 10 x (equivalent Ni dose) .

Such results, although evaluated for a particular material and a particular neutron spectrum, are

typical. For order of magnitude estimates we may take it that this kind of calculation predicts

every atom to be displaced once by doses in the range 1020 - 102 ^.

This kind of simple cascade theory has not been developed for diatomic (or more complex solids)

except for a model solid of type AB in which Ed is the same for both atoms [l2]. As noted previously

we may expect this to be a fair model in some cases, e.g. for BeO and MgO. The total number of

displacements does not vary much with the ratio of masses of the two atoms. For example when the mass ratio parameter \ = 4 M \L/(M -tMj 2 is \ (heavier atom ~ 13 times the mass of the lighter)

the total number of displaced atoms1 Bis ~ 0.44 (E/E ) in place of (2.8). The difference between

the numbers of displaced atoms like and unlike the primary however increases more slowly than linearly with the energy of the primary. Thus primaries of very high energy effectively produce only displacements of their own kind. Since, in neutron irradiation, the mean primary energy is high this result implies that the numbers of displaced atoms of different kinds are in proportion to their neutron elastic scattering cross-sections.

2.2 Lattice Effects

It is known from work on radiation damage in metals (especially Cu and other noble metals) that

even where good threshold values E

d are known the expression (2.8) leads to overestimates of the number of displaced atoms [13]. It is generally believed that this is due to the neglect or the lattice structure in the calculation and, in particular, to the phenomenon of "channelling". It has been observed both experimentally and in computer simulations that a proportion of the fast displaced atoms become focussed into open channels through the lattice and that they then continue in these channels in fairly stable trajectories. An obvious example of a channel is obtained by looking along the c-axis of a wurtzite lattice, e.g. BeO. Atoms moving in these channels at velocities greater than phonon velocities lose energy by the generation of a phonon shock-wave- the energy received by the atoms of the lattice, although large, is then not large enough to cause' displacements (a few times 10 eV per plane).

Robinson and Oen [14] have developed the theory leading to (2.8) to include a probability P

that either of the two atoms involved in a collision becomes channelled afterwards. Channelled

atoms are assumed to produce no further displacements. Then in place of (2.8) they get

J-2P

V(E) --uh) -p]. (2.9)

In Cu P ~ 0.07 empirically. Nothing appears to be known about this quantity theoretically. It is assumed in the above calculation to be independent of E and this may be fair for a close-packed

lattice when collisions are hard-sphere collisions - the situation one is interested in for Cu. However, for light atoms struck by neutrons the subsequent collisions will generally be Coulomb

collisions and these give predominantly small angle deflections. It therefore seems unlikely that

P is significantly different from zero for many of the solids of interest here.

2.3 Distribution of Defects

The simple cascade theory of §2.1 can be developed to provide estimates of the range of an energetic atom and thus of the size of the region containing the defects produced by a given primary.

Such calculations have been done in the approximation of hard-sphere scattering but they are not independent of the potential of interaction between the atoms since the collision radius enters in

directly; this, as we have noted above depends on energy in a way fixed by the interaction

potential. Reasonable potentials exist and have been used. For example, the average Cu primary

13

257-304 0 - 67 -2
under fission neutron irradiation has an energy of 64 keV and in Cu metal this gives rise to a damaged

region about 250 X long; extension of the calculations to give the lateral spread leads to a width

about half this„ The atomic fraction of defects in this volume is thus about 2fo. These estimates

agree with the rate at which one observes saturation of irradiation damage at high doses due to the

overlap of separate damage regions 0

The channelling of the f ast atoms will undoubtedly lead to a more diffuse distribution than

calculated in this way; channelled atoms will come to rest (as interstitials) well outside the

damaged region, which will therefore contain an excess of vacancies. There are also low energy

processes - "replacement sequences" - leading to the same effect [15], Collision sequences propagate

coherently down close-packed rows of atoms as a result of either purely geometrical ("Silsbee")

focussing of successive collisions toward the axis or focussing assisted by the neighbouring rows of atoms. These are low energy effects because when the collision radii become too small (high energies)

the lattice effectively becomes too open to restrain the sequence of collisions along a row. These

maximum energies may be a few times the displacement energy E

d

« The point for the present discussion

is that for energies greater than E. (for the relevant direction) these sequences propagate as replacement sequences, each atom taking the place of the next one along the row. This process thus

also produces interstitials on the outside of the damaged region. Of course, in strongly ionic

compounds these replacement sequences can only propagate along rows of one kind of atom.

These features thus lead to a picture of neutron damage as consisting of relatively high defect

density with a diffuse distribution of interstitials on the outside. This is the commonly assumed

model which applies to materials of atomic number Z greater than about 25. However as we have

already seen the energies of light atoms displaced by fission neutrons are generally so high that

their collisions with atoms of the solid are primarily Coulomb, rather than hard-sphere, collisions.

The distribution of defects produced by a primary is then very different and consists not of a single

region of defects but of a greater number of clumps of a few interstitials and vacancies. One can make detailed predictions of the range of a primary and the mean size of these clumps once an interaction potential is assumed., We may contrast results for Ge(Z=32)with those for C(Z=6).Thus a 10 keV

Ge(about \ the mean energy of Ge primaries produced by 1 • 5 MeV fission neutrons) gives generally a single dense group of interstitials and vacancies ~ 200 A diameter [l6]. On the other hand a

100 keV C primary (again about ^ the mean energy of primaries produced by 1.5 MeV fission neutrons)

has a range ~ 2000 A and the secondary defects are produced in small groups of 10 or less, separated

by ~ 60A [17], In the example of a C primary it is not until it has slowed down to a few keV that

it enters the hard sphere range of collisions (Figure 1); its path will therefore end in a larger

group of defects0 For heavier atoms, e.g. Mg or Al, this final group will be larger. In the

corresponding situation which arises at the end of a fission fragment path it may be very large

indeed, containing several thousand defects,,

We can summarise the general picture thus:

(1) In ceramics containing only light atoms - most of those in our list - the defects resulting

from neutron irradiation are distributed in a large number of small groups. This is a mucn more

nearly random distribution than the usual picture of neutron damage in materials of medium and

high atomic weight.

(2) In ceramics containing both heavy and light atoms, say U0

2

, we expect the U primaries

to displace mainly the U atoms and so give large clusters of U-vacancies and U-interstitials.

Similarly the 0 primaries will displace mainly 0 atoms, but, lead to a mucn larger number of small groups of 0 interstitials and vacancies.

This picture of course applies to very low temperatures where the defects are frozen-in and cannot move after their production. Most experiments on these materials have, however, been done

at reactor temperature and above; some of the defects are then expected to be mobile as a result of

thermal activation. We must therefore consider the effect this has.

3. Annealing Processes

The picture of radiation damage which we have described in §2 only strictly applies at exceedingly low temperatures, where no thermally activated atomic migrations are possible. At

temperatures where these migrations can occur various annealing processes will go on, e.g. interstitial-vacancy recombination, the formation of small mobile clusters and eventually of large

immobile clusters. A basic knowledge of defect migration rates is needed to understand these processes and in this section we shall briefly discuss defect activation energies, since these are

the most important parameters determining these migration rates.

We shall elaborate on the following three features:

(i) the activation energies for interstitials are often less than those for the corresponding

vacancies (Table II).

14
(ii) activation energies are different for different electronic states and degrees of ionisation

of the same defect,,

(iii) close-pairs of vacancies and interstitials may recombine with very low activation energies.

TABLE II. Some Defect Migration Activation Energies

Substance

i Vacancy, Emy

1 Interstitial, E . ' mi Remarks

, ,

p..

1 o05 eV 0.71 eV E is mi

energy of

Stage III annealing

Ag 0„88 0.67 it Au 0.82 0.80 it

Graphite >2.5 ~0.5 r it!

Si 0.33 ~0 [18]

AgCl (Ag

+

) 0.33 (Ag+

) 0.15

AgBr (Ag

+

) 0.36 (Ag+

) 0.15

KC1 (Cl~) 0.95 (CI") -M3.07 [19,20] CaF

2 (F~) <0.9 (F_

) 1.7 n.b.E .>E mi mv

[21]

(i) Defect activation energies are known experimentally with varying degrees of certainty for

different substances. In the noble metals the vacancy activation energies are known accurately;

the interstitial activation energies are probably those characterising the famous annealing stage III, even though the evidence for this is still qualitative and subject to dispute. That the interstitial

in graphite has a lower activation energy than the vacancy is shown by the formation of interstitial

clusters - identified in the electron microscope - at lower temperatures than vacancy clusters. A

similar situation is observed also in some irradiated metals and oxides, thus confirming E .<E

, ' TO mi mv here too. For the Ag

+-ion defects in AgCl and AgBr both vacancy and interstitial activation energies are accurately known; even details of the mode of interstitial movement are known experimentally [22]. In the alkali halides - and by implication perhaps also in the alkaline earth oxides - calculations

predict [22],

E ~ E . for the cation defects mv mi

E > E . for the anion defects,, mv mi

The interstitial ions are predicted to move by a replacement /or interstitialcy mechanisms - as do the Ag

ions in AgBr and AgCl„ The anion interstitial in the alkali halides is predicted to move witn a low

activation energy and thus to anneal out at very low temperatures, e„g. below liquid N

2 temperature0

(ii) In insulators, of course, interstitials and vacancies can exist in various cnarge states

and the activation energy for migration may alter considerably when the centre is ionised or in an excited state. Thus in KC1 the F-centre appears less mobile than the empty anion vacancy, but the

activation energy for an F-centre in its first excited electronic state is very low indeed. On the

other hand the interstitial halogen atom - the so-called H-centre - migrates as easily as the

interstitial halogen ion. There is a considerable variety of possible behaviour with only a few

pointers to the general rules at the present time.

(iii) The processes of the recombination of close pairs of vacancies and interstitials may go with

very low activation energies. Indeed in many substances there are many positions of an interstitial

around a vacancy that are unstable, so that no activation is required for recombination. These unstable volumes determine the speed with which radiation damage saturates at very low temperatures.

In Cu, saturation measurements lead to an unstaDle volume of about 80 atomic volumes. Beyond these

unstable positions of the interstitial lie positions from which the activation energy is only

about 0.1 eV

Qcf. Table II) and from these positions thermally activated recombination takes place at or below ~ 50 K. The recombination of close pairs of anion vacancies and anion interstitials takes

place at even lower temperatures in KC1 and KBr. Again, of course, such processes depend on the charge states of the defects concerned; Coulomb forces between charged defects can easily be dominant.

15
These remarks and examples have been largely drawn from materials much more fully studied than

those of concern here. But it seems clear that even in ceramic materials we would expect processes involving interstitial-vacancy recombination and other rearrangements, e.g. formation of interstitial

pairs, at temperatures below room temperature. Some examples are:

2+

(1) BeO. We know from work on diffusion and ionic conductivity by Austermann [23] that the Be ion vacancy moves with an energy of ~ 1.5 eV. By analogy with the theoretical results for the

alkali halides we might assume that Be2+ interstitials move with roughly the same

Qactivation energy as the Be2+ vacancy, so that their migration will not be significant below, say, 200 C. On the other

hand by this same analogy 0

2~ interstitials may have an activation energy of not more than 0.5 eV and

they will consequently be mobile as low as ~ 200°K. The recombination of close interstitial-vacancy

pairs is expected at even lower temperatures ; indeed some recovery of thermal conductivity in

irradiated BeO is seen [25] between 100°K and 300°K (irradiation temperature ~ 1O0°K) . Further

evidence for the mobility of defects at low temperatures in BeO comes from the observation of defect

clusters in BeO after irradiation at reactor temperature In addition long wavelength (> say 5A) neutron scattering experiments [25] show that material irradiated at 150 C contains only a few per

cent of the predicted number of defects. (These experiments can give absolute values of the total

defect concentration when good estimates of the lattice distortion around the defects can be made).

Many more low temperature studies need to be made in order to understand the basic annealing processes

going onc

(2) MgO. In irradiated MgO a number of vacancy defect centres have been identified by optical

methods and spin resonance. These include:

(a) F-centres [27]

;

(b) aggregate centres having the same symmetry and probably the same structure as the M, R and N

centres in alkali halides [28];

(c) trapped hole centres [27],

However, with one possible exception [27] there appear to be no observations of interstitial centres

by these means, although large clusters formed at high temperatures have been identified as interstitial. There is very little information about activation energies or annealing processes in

this material, but again studies [28] of material irradiated at ~ 100°C show only a few per cent of

the defects expected from theory (using Ed ~ 25 eV) and there is little doubt that thermally

activated annealing occurs below room temperature.

(3) U0

2

« In U0

2 the interstitial oxygen ion migrates with an activation energy of ~ 1.3 eV, as

is known from a combination of oxygen diffusion studies and thermodynamic studies on non-stoichiometric uo 2+x* Owing to the difficulty of obtaining accurately stoichiometric material it has not so far

proved possible to study point defects optically in this substance. The electrical conductivity of U0„

is due to the migration of electron holes and in irradiated material the conductivity decreases, x

presumably

o as a result of the trapping of holes. A recovery stage, believed to be second order, occurs around 700 C with an activation energy of 2.3 eV. This temperature is much higher than the 100°C or so

to be expected if the interstitial oxygen ion were responsible (1.3 eV) and may correspond to the motion

of the uranium vacancy (which could also be a hole trap) . However, irradiation at reactor temperature

leads to the presence of defect clusters visible in the electron microscope and by annealing at higher

temperatures these have been identified as interstitial clusters without stacking fault, i.e. containing

both U and O in the correct proportion At the present time it does not seem easy to put the defect

clusters seen in the electron microscope in relation to point defects. There does not seem to be evidence for the different primary distributions of U and 0 defects expected in §2. This may be because one or more of the primary defects is mobile below reactor temperature [30].

(4) Graphite . Of the materials in our list, graphite is^undoubtedly the best understood [17], Here the vacancies do not become appreciably mobile until ~ 600 C whereas at room temperature the

interstitials are undoubtedly very mobile and form small clusters, both mobile and immobile. The mobile

interstitials which may be pairs or triplets, have an activation energy of 1.2 eV and nucleate larger

clusters. These grow on continued irradiation, forming extra discs between tne hexagonal layers. These

large clusters are visible in the electron microscope and they have been verified to be interstitial

layers by this means.

It is clear from these examples that in all the materials of interest here defect clusters are

formed in material irradiated at reactor temperature and above. Except in graphite, the basic

mechanisms by whicn these form and grow are so far largely unstudied; much of the necessary basic

knowledge about the point defects is missing. However it is clear that these clusters are an important

aspect of radiation damage and we shall therefore discuss them in further detail in the next section.

16
4. Defect Cluster Formation

The general pattern of clusters seen in neutron irradiated materials is that at lower temperatures

(reactor temperature and above) the density of clusters is high but their size is small. They are visible in the electron microscope, but not resolvable as more than dots. At higher temperatures of

irradiation their density is low but they are mucn bigger and their type - e.g. interstitials or vacancy, with or without stacking fault - may be determined. The total number of point defects retained in

the form of clusters after a given dose is less the higher the temperature of irradiation.

In anisotropic materials, e.g. graphite, BeO, U-metal f the collection of interstitial defects -

the more mobile - on to the basal plane of a crystal leads to a macroscopic growth in the perpendicular

direction. This does not saturate with dose so rapidly as properties dependent on point defects or

dislocation line length, e.g„ thermal conductivity. It is clear therefore that the nucleation and

growth of these clusters is important in practice and we make some remarks about these aspects. These

are mainly derived from a detailed study wnicn we have made for graphite [31] but are probanly of wider

application. We may, however, remark that the conditions of nucleation and growtn in other ceramic

systems have not yet been sufficiently well studied experimentally for this to be certain.

In tnis connection it should also be noted that ionic and charged defects can only cluster in the

correct stoichiometric proportions. On the other hand uncharged defects can cluster without

preserving stoichiometry, e.g. the clustering of F-centres to give M-, R-, N-centres and, ultimately,

metal particles in the alkali halides.

4. 1 Nucleation

In graphite this is known to be intrinsic or "homogeneous", i.e. the nuclei are formed by the random aggregation of the defects. The general characteristic of homogeneous nucleation is the temperature variation described above. At high temperatures the density of homogeneously formed nuclei

becomes lower than the density of impurity or boundary nucleation sites. A changeover to heterogeneous

nucleation at higher temperatures has also been observed in graphite.

Now tne density of homogeneously formed nuclei involves the mobility of the point defects which

form the cluster. In the early stages the rate of formation of nuclei must follow an equation

describing random encounters of the mobile defects, i.e.

-rr (nuclei) = (mobility constant) x c , (40 l)

where c is the concentration of mobile defects. Once formed, the nuclei grow as the irradiation

proceeds. The density of nuclei increases until a point is reached where a newly created defect is more likely to reach an existing cluster than it is to encounter another migrating defect. At this

point nucleation ceases and something closely approaching a steady state is established. As the

clusters grow their efficiency of collection of the defects increases and the steady-state concentration

of point defects falls, thus making the formation of further nuclei less and less probable as jthe irradiation proceeds. The density of nuclei arising in a solid (cubic) is proportional to D

-

^ where D

is the diffusion coefficient of the defect. In a strongly anisotropic material such as graphite in

which the defect migration is effectively two-dimensional the density of nuclei again is almost but

not exactly proportional to D~4. The nucleation of fission gas bubbles by the aggregation of fission

gas atoms is similar [32].

4.2 Growth

Since the interstitials execute a random walk through the lattice until they either disappear by

recombination with a vacancy or become attached to a cluster we can describe their concentration, c, by

a diffusion equation

|| = D V 2

c + G

o - r 6c, (4.2)

which contains the rate of generation by the radiation G and the interstitial-vacancy recombination

term T6c. Here r is the jump frequency of the interstitial (D a r) and 6 is the probability of

annihilation at any jump - proportional to the vacancy concentration and thus dependent on the time

(of irradiation). The boundary conditions to be observed are:

(i) c=0, at the cluster periphery at all t,

(ii) c=0, everywhere at t=0,

(iii) Vc=0, midway between clusters.

17
In graphite we have effectively a two-dimensional problem since the interstitials migrate much more

easily between the hexagonal layers than in the a-axis direction. Some general features of a detailed

study of the graphite problem are however worth noting,

(a) The solution for c is very flat over the greater part of the region between clusters. It

is therefore independent of their arrangement.

(b) The mean concentration of the mobile point defects is very low - due to the fine distribution

of sinks which the clusters represent. Thus in graphite at 200°C the mean spacing between clusters is only 800 A: as a result, after 5x10^ fast neutrons, the atomic fraction of mobile interstitials is

only ~ 10-

7. Hence the existence of sizeable radiation effects which cannot be accounted for by the clusters may imply the existence of small immobile clusters of interstitials in addition to the mobile

ones. This situation certainly occurs in graphite and probably in BeO and a number of other

substances as well.

(c) D is not important in determining the rate of growth of the clusters once nucleation is settled. This rather surprising result arises because once nucleation has stopped there is a nearly

steady state, the time dependence of c arising only through the (slow) growth of the defect cluster0 It is therefore a good approximation to put 3c/St — 0 in (4„2) whence, since D is proportional to f,

G

c = ^ x function of (8,r,t) . (4.3)

The rate of arrival of defects at the cluster is then

J. dS = - D(Vc) . dS (4.4)

clusters to depend on temperature as exp — ( Qg

J where Q

D

is the activation energy of D and

where J is the flux and £ is the cluster surface. Hence by (4.3) and (4.4) the cluster growth

is independent of D in this approximation. Of course, the total number of defects retained as clusters will be proportional to D

-^ through the density of nuclei.

The important parameters for the growth of clusters are G , the rate of introduction of defects,

and 8 their recombination probability. The former may be taken from the theory of §2.1; 8 varies

with dose. Since the vacancy concentration may saturate at high doses the rate of growth of

interstitial clusters may snow an increase at high doses. This effect occurs in graphite. There it

also appears that small vacancy clusters, even divacancies, may collapse and no longer act as sinks

for interstitials, but this may be a special property of this covalent structure.

The total number of defects retained as clusters at a given dose will therefore depend on temperature through the density of nuclei, which is proportional to D""$, and through the growth rate

i.e. 6. Roughly speaking then we may expect to find the total number of defects retained as

as exp

1 f%

is that for the annealing of 6.

4, 3 Gas Bubbles

The same general approach which we have taken above can be applied also to the growth of bubbles

of the insoluble gases formed in fission or by other reactions (§1). In general bubbles visible in

the electron microscope form at considerably higher temperatures than interstitial defect clusters - an effect probably due to the need for vacancies to migrate if the bubbles are to grow. Theories

of the influence of gas bubbles on the swelling of solid fuelds have been published [33] but the conditions for their validity do not seem to have been very throughly tested.

Experiments on the release of Xe fission gas from U0

2 can be used to obtain the Xe diffusion

coefficient [34], There seems little doubt that trapping of Xe occurs at defect clusters produced

by the irradiation, since the apparent diffusion coefficient falls by very large factors, ~ 10 , at high doses - an effect which has also been seen with the analogous system Ar in CaF„

(Ca44 + n —> At4' + a). However this seems to be another region where the work on defects visible

in the electron microscope is still waiting to be put in close correspondence with that on the point

defects, in this case the interstitial gas atoms.

5 0 Conclusion

In this article we have briefly reviewed a number of basic ideas in radiation damage with

special reference to ceramic materials of nuclear interest. These ideas have been extensively used up to now mainly for metals and require some elaboration for ceramic compounds. The work on metals,

however, also snows that experiments on ceramics are still at a rather early stage. Despite the

large amount done from a technological interest, basic studies on these substances are still very

18
incomplete and comparatively crude. In order to achieve proper understanding of radiation damage

in ceramics it is necessary to study irradiation effects at low temperatures especially using

methods susceptible to point defects (e.g. optical, electron spin resonance, thermal conductivity)

and to achieve an understanding of the formation of clusters in terms of point defects. Once the properties of point defects are determined with reasonable certainty (as e.g. the F-centre in MgO) these should then be employed to study defect reactions, especially the formation of small aggregates.

More careful work on diffusion and mass transport properties at high temperatures also needs doing.

Acknowl edgements

In the construction of this review I have benefited much from a number of discussions with

Dr. B. Henderson, Dr. A.M. Stoneham and Mr. R. S. Wilks and other colleagues at A.E.R. E.

References

[l] For more extensive accounts see (a)

D. S. Billington and J.H. Crawford,

Radiation Damage in Solids (University

Press, Princeton, 1961);

(b) D. S. Billington, Editor, Radiation

Damage in Solids (Italian Physical Society

and Academic Press, New York and London

1962); (c) R. Strumane et al, Editors,

The Interaction of Radiation with Solids

(Nortn Holland, Amsterdam, 1964)

C. Erginsoy, The Interaction of Radiation with

Solids, Editors R. Strumane et al (Nortn Holland, Amsterdam, 1 964) , p. 51.

H.H. Anderson and P. Sigmund, RisJJ Report

No. 103 (1965) C

G. Montet, G. Myers and F. Feates (to be

published)

M.W. Lucas and E.W.J. Mitcnell, Carbon,J_, 345 (1964).

E.W.J. Mitchell, Radiation Damage in Solids,

Editor D. S. Billington, (Academic Press, New York and London, 1962) p.518c

M.J. Moore and E.W.J. Mitchell,

7th International Conference on the Physics

of Semiconductors, Part 3, Radiation Damage

in Semiconductors (Dunod, Paris, 1965), p. 235.

E.W.J. Mitchell and P.D. Townsend, Disc. Far.

SoCo No. 31, p. 259 (1961). See also

W.D. Compton and G.W. Arnold, Ibid, p. 130.

R.S. Wilks and F.J. P. Clarke, J. Nucl. Materials, J4, 179 (1965).

G.H. Kinchin and R.S. Pease, Rep. Prog. Phys.,

J8, 1 (1955).

M.W. Thompson and S. B. Wright, J. Nucl. Materials, K5, 146 (1965).

E.M. Baroody, Phys. Rev. 112, 1571 (1958).

See e.g. D. K. Holmes, The Interaction of

Radiation with Solids, Editors Rc Strumane et al (Nortn Holland,

Amsterdam, 1964) p. 147.

14] M.T. Robinson and 0. S. Oen, Appl. Phys. Letts.

2, 83 (1963).

[15] See e.g. M.W. Thompson, The Interaction of Radiation witn Solids, Editors

R. Strumane et al (North Holland, Amsterdam,

1964) p. 84.

[16] M. Yoshida, J. Phys. Soc. Japan, JJ5, 44 (1961).

[17] J.H.W. Simmons, Radiation Damage in Graphite

(Pergamon, Oxford, 1965).

[18] G.D. Watkins, 7th International Conference

on the Physics of Semiconductors, Part 3, Radiation Damage in Semiconductors,

(Dunod, Paris, 1965) p. 97.

[19] R.G. Fuller, Phys. Rev. J42, 524 (1966).

[20] N. Itoh, B.S.H. Royce and R. Smoluchowski,

Phys. Rev. J_37, A1010 (1965).

[21] R.W. Ure, J. Chem. Phys. 26, 1363 (1957).

[22] See e.g. A.B. Lidiard, Handbuch der Physik,

20, 246 (1957).

[23] K. Tharmalingam, J. Phys. Chem. Solids, 25, 255 (1964).

[24] S.B. Austerman and J.W. Wagner, J. Amer.

Ceram. Soc. 49, 94 (1966).

[25] D. L. McDonald, Appl. Phys. Letts. 2, 175 (1963).

[26] D.G. Martin, Proc. Brit. Ceram. Soc. (in the press) c

[27] J.E. Wertz, G.S. Saville, L. Hall and

P. Auzins, Proc. Brit. Ceram. Soc., J_, 59 (1964).

[28] I. K. Ludlow and W.A. Runciman, Proc. Phys.

Soc. 86, 1081 (1965); I.K. Ludlow

Proc. Phys. Soc. 88 (in the press);

R.D. King and B. Henderson, Proc. Phys.

Soc. (in the press).

[29] B. S. Hickman and D.G. Walker, Phil. Mag.

_M, 1101, (1965).

[30] A.D. Whapham and B.E. Sheldon, Phil.

Mag. 12, 1179 (1965)„

[31] A.B. Lidiard and R. Perrin, Phil. Mag.

(in the press)

19
[32] G.W. Greenwood, A. J. E. Foreman and

D.E. Rimmer, J. Nucl. Materials, 4

305 (1959).

[33] R.S. Barnes ana R. S. Nelson, AERE Report

R.4952 (to be published in the

Proceedings of the Conference on Radiation

Effects in Solids held at Ashville,

North Carolina in September 1965).

[34] See e.g. Thermodynamic and Transport

Properties of U0

2 and Related Phases,

I.A.E.A. Technical Reports Series No. 39 (Vienna 1965) e

10"

10'

10

10

[

1 COULOMB COLLISIONS

HARD — SPHERE COLLISIONS

20 40 6O 80

ATOMIC NUMBER, Z

FIGIRE 1. The boundary between the region of

energy where the collisions are Coulomb

encounters and that where they are hard-sphere

collisions. The collisions are assumed to

take place between two equal atoms of atomic

number Z. This boundary line has been

calculated using the screened Coulomb potential

of Bohr in which the screening parameter is a smooth function of Z. In reality one expects

electron shell periodicity to cause this line

to be wavy and not exactly as shown here. The

boundary is in any case not sharp, (after

Billington and Crawford, Ref. 1 )

.

100 n.

30 40

ENERGY E

60

(eV)

io~ ioJ ENERGY OF MOVING ATOM

FIGURE 2. The integrated displacement probability

for an atom of energy E as calculated for

ffl-Fe (after Erginsoy, Ref 2).

FIGURE 3. Diagram showing the rates of loss

of energy per unit distance dE/dx by

(i) electronic excitation and ionisation,

( dE/dx) and (ii) elastic collisions,

(dE/dx) el* Scales for C atoms. For other

elements the diagram is schematic (after

Thompson and Wright, Ref.11).

20
Physical Properties of Irradiated Ceramic Materials

Paul W . Levy

Brookhaven National Laboratory

Upton, N. Y.

Abstract

Materials are subjected to two principal types or radiation effects

during reactor irradiation. First, there are ionization effects which re- sult from electron and (electronic) hole movement and trapping. Second,

there are displacement effects resulting from the movement of atoms. Reactor irradiation introduces vacancies, interstitials , and more complex de- fects consisting of combinations of these simple defects. Some of these

act as charge traps.

Numerous examples of radiation induced changes in the physical properties of ceramic materials can be cited. The most common phenomena associated with ionization effects is the coloring of glasses by irradiation.

Displacement effects occur when atoms are ejected from their lattice sites

by energetic electrons, gamma-rays, slow neutrons; fast neutrons (very

ef f eciently) ; and, rarely, by other radiations. Almost all of the fast neutron damage is caused by energetic lattice atom recoils which are cre- ated by elastic collisions with fast neutrons. As the recoil passes through

the lattice it produces numerous vacancies and interstitials along its tra- jectory.

Both the ionization effects and the formation of individual point

defects are illustrated by color-center studies on very pure fused silica.

The defect regions occurring along the trajectory of the lattice atom

recoil can be related to changes in the low temperature thermal conductivity in single crystal A13 03

. The collective effect of numerous damagecreating events, produced by long irradiations, result in a density decrease

in crystal quartz and density increase in fused silica.

In addition, the physical properties of materials are changed during

irradiation. During bombardment the defect concentration is increased and

this will, in turn, increase any defect-dependent diffusion processes. For

example, the diffusion of Be in BeO is greatly accelerated during reactor

irradiation.

21
Physical Properties of Irradiated Ceramic Materials

Paul W„ Levy

1. Introduction - Basic Radiation Damage Processes

When solids are exposed to nuclear radiations usually one or more of their physical properties

are changed. This simple fact is the basis for the branch of nuclear engineering concerned with

materials used in reactors or otherwise subjected to radiation,, Also, it is the reason for a large

basic physics and chemistry research effort to understand the fundamental mechanisms involved in these

changes. Most often the radiation induced effects are referred to as "radiation damage" and both the

engineering and basic investigations are referred to as "radiation damage research". This paper will

consider the effects of radiation on certain properties of a small number of ceramic materials that were

carefully selected to demonstrate the more important basic radiation processes. [1,2,3] ^ First, they were chosen to emphasize the difference between the ionizing processes and the atomic displacement

processes which occur in reactor radiation fields. Second, the choices demonstrate the difference be- tween three classes of radiation induced defects. These classes can be conveniently characterized since

they differ greatly in size. They are: 1) the point defects, which, at most, involve only a few atoms

or vacancies. 2) the totality of defects along the trajectory of a given recoil, sometimes called a spike and which the writer likes to call a Wigner region. And, 3) macroscopic changes, i.e., effects

which are measurable as a property of the entire damaged substance.

Before describing the "damaged" substance, consider first the radiation which produces "radiation

damage". The radiation field in a typical reactor may be divided into three components. One component

consists of neutrons with energies extending from a few MeV down to tenths of e'/'s„ The slow flux may

be as large or even larger than the fast flux, and is important when certain elements are present. A

second component is the electron flux. The electron energies also extend from a few MeV to less than an

eV. Lastly, there is the intense photon component which includes gamma rays, X-rays, and ultraviolet,

visible, and infra-red light. And again the energy range is from several MeV to a fraction of an eV. Each of the various radiation field components interacts with a crystal or glassy solid in a characteristic fashion. The fast neutrons and more energetic electrons are a primary source of radiation

damage since they can displace atoms from their normal lattice positions. Most often the neutron damage

will occur as a two step process. The initial step is an elastic, or rarely an inelastic, collision

between a fast neutron and a lattice atom. In ceramics, where the lattice atoms usually have relatively

low masses, a one MeV fast neutron will create recoiling lattice atoms in the 0.1 to 0.3 MeV range. The second step occurs as the recoiling atom literally "plows" through the lattice. It creates a large

number of vacancies and interstitials along its trajectory. The resulting damage region will be a straight or slightly curved oblate spheroid from 10 to 100 atom spacings wide and a few thousand atom

spacings in total length. Occasionally, the spike or damage region will be branched. In aluminum oxide,

for example, a one MeV neutron could produce a 0.2 MeV Al or 0 recoil that would form three or four

hundred vacancies, and a corresponding number of interstitials, in each spike or Wigner region. The

total number of spikes will be proportional to the total fast neutron flux and to the elastic scattering

cross section. Since the mean free path for typical reactor fast neutrons is several centimeters or more

the damage region will be quite uniformly distributed in centimeter size samples.

Many reactors have an appreciable slow or thermal neutron flux. In fact, some reactors have

facilities for irradiating samples with only slow neutrons. The slow neutron reactions can be a copious

source of lattice defects. In an (n,y) reaction a slow neutron is captured by the nucleus and one or more gamma rays are emitted. Conservation of momentum requires that when a gamma ray is emitted in one direction the nucleus recoils in the opposite direction. If the kinetic energy of the recoiling nucleus,

i.e. the recoil atom, exceeds the displacement energy it will eject itself from the lattice. Most often

this will create a single vacancy with a nearby interstitial. Also, slow neutrons will produce damage

by energetic nuclear reactions when the target contains certain elements. Examples are the Li (n,Q!)T^

and B^(n,Q!)Li^ reaction in which both the a particles and recoil nuclei are emitted with energies in

the MeV range. In this case the damage creating process is similar to that caused by nuclei recoiling

from elastic collisions with fast neutrons. The distribution of (n,y) and (n,a) reactions in the bombarded substance will depend on the total neutron absorption cross-section. If it is low, and the neutron mean free path is large compared to the sample size, the distribution of damage will be relatively uniform. If the cross-section is large, most of the reactions (damage) will occur at the surface and the reaction density (damage) will decrease

toward the sample center. Glasses containing boron or lithium are good examples of materials in which

1. Figures in brackets indicate the literature references at the end of this paper.

22
slow neutron produced damage is important,, Also, in these substances the damage tends to be greatest

near the surface and decreases toward the interior

The energetic electron and gamma-ray components will also displace atoms from the lattice. An in- cident fast electron will displace an atom from the lattice only if sufficient energy is transferred

in the collision. The minimum energy that must be imparted, the displacement energy, is approximately

25eV. To displace an oxygen atom the electron energy must exceed 0.16 MeV, and 0.25 MeV is required

to remove a silicon atom from the lattice.

Energetic gamma rays can produce displacements in two distinct ways. First, the gamma rays produce

fast electrons because of the Compton, and to a very slight extent photoelectric and pair production)

processes. Once formed, such electrons are indistinguishable from fast electrons produced in any other

way and can undergo elastic scattering with lattice atoms. Second, gamma rays may make (y,n) reactions

with a nucleus, i.e. a gamma ray is absorbed and a neutron is emitted by the nucleus. In this case, conservation of momentum requires that - when the neutron is emitted in one direction - the nucleus

recoils in the opposite direction. When the energy of the recoiling nucleus exceeds the displacement

energy it will eject itself from the lattice.

The electron displacement processes occur infrequently,, Once formed, the moving electron rapidly

loses energy by ionization and is quickly degraded below the energy required to displace an atom. In

reactors the (y,n) process is negligible even for the lightest elements. The flux of sufficiently

energetic gamma rays, and the reaction cross-section are both very small. The electron and gamma -ray processes create single vacancies and interstitials which are randomly distributed in the irradiated

material.

The second major process which occurs in the reactor radiation is ionization. A large fraction of the total ionization is produced by the lattice atom recoils as they "plow" through the lattice. In fact when the recoils are produced by reactor neutrons roughly half of the recoil energy is used up in producing ionization electrons and holes along the recoil trajectory. Superimposed on this is the ionization

provided by the reactor electron, and photon - mostly gamma-ray - radiation field. It is extremely

important to realize that the normal ionization process involves only electrons and (electronic) holes,

not the lattice atoms. The total number of ionization events which occur in most reactors is very

large; roughly one ion pair - per atom - per second.

A critical analysis of the different aspects of the ionization process indicates that it would not produce lattice defects. Yet, it is clear that 10 to 50 KeV X-rays produce F-centers, i.e. anion

vacancies, in the alkali halides and even ultra-violet light produces F centers in KI [4]. This is one, of many, radiation effects that is not understood at this time.

The defect properties of any irradiated material will be influenced by both the temperature during

irradiation and the subsequent thermal history. The ambient temperature in most reactors is usually

between 20 and 200 or 300 degrees C. Special irradiation facilities are available for irradiation

between liquid nitrogen temperature and more than 1000°C. During and immediately after the passage of

a recoiling lattice atom the closely surrounding lattice is in violent thermal agitation. Very roughly

half of the energy lost by the recoiling atom appears in the agitated region, usually called a thermal

spike. It may reach a temperature of several thousand degrees, but only for a period of less than

10"^ sec. Obviously thermal spikes will affect any temperature dependent processes. Vacancies, interstitials, and other defects will undergo accelerated diffusion. Electrons and holes will be released

from shallow traps, strains will be annealed, etc. Certainly thermal spikes will promote the diffusion

of induced defects, and annealing processes which are operative near the ambient reactor temperature

will tend toward completion. It would be convenient to attribute a spike -produced temperature increment,

to be added to the ambient temperature, to describe the effects of the thermal spikes. However, it appears that such a simple approach has a very limited, if any, utility.

2. Point Defects - Color Centers in Fused Silica.

The first radiation damage process to be considered in detail is the formation of color centers

in fused silica. [5,6] This example is included to illustrate several things. First, the production

of point defects by either neutrons or gamma rays. Second, the role of ionization in converting defects

to color centers. Third, to give an illustration, albeit an incomplete one, of the annealing of radiation damage. Fourth, to include some mention of point defects in glasses.

The absorption spectrum of irradiated Corning 7940 fused silica is shown in Fig. 1. This type of spectrum, i.e., the coloring of a solid by radiation, is definitely due to color centers. The classical

color center, the F-center, is an electron trapped on a negative ion vacancy in an alkali halide

crystal,, Other types of color centers are formed when electrons are trapped on more complicated

negative ion defects, when holes are trapped on positive ion defects, etc. Conceivably every combination of negative and positive ion defects can trap one or more charge carriers of proper sign and each

of these centers would have a characteristic absorption band. Once a band is identified with a par- ticular defect, color center measurements can become a useful tool for determining the concentrations

of that defect. However, it is important to realize that the defect alone usually does not give

rise to an absorption band. The band appears only when the appropriate carrier is trapped. Also, to

23
make precise concentration measurements it is essential that all, or a known fraction, of the defects

have been converted to color centers.

Color centers are also formed when charges are trapped by some of the impurities in the lattice.

The maximum intensity of an impurity- related band is fixed by the impurity concentration. This fact can be the basis for the identification of these bands. Under proper circumstances the defect-related

bands can be increased by exposure to radiation while the impurity band will remain constant. Absorption bands have been observed in a large variety of crystals, the number of bands varing

from one to more than ten. Very few of these bands have been correlated with specific defects. Thus,

as the number of correlations becomes larger color center measurements should become an increasingly

useful tool for studying defects.

The absorption spectrum of gamma-ray irradiated fused silica is very close to the spectrum obtained

by reactor irradiation. The rate of color center formation differs greatly. The reactor gamma-ray

component colors this material at about the rate as a comparable flux of Co gamma rays. Superimposed

on this is a large number of additional defects created by the reactor neutron component.

Color center formation in single crystal Al^O^ is entirely different [7], During gamma-ray irradiation 3 or 4 bands are formed. Reactor irradiation forms 6, 7, or 8, entirely different bands.

Furthermore, the bands induced by gamma rays reach maximum intensity at a dose of 3xl04R and remain

at this level for irradiations up to 10 9R. in the fused silica the gamma-ray coloring increases at a steadily decreasing rate up to 2xl08R and is increasing linearly above that dose. In reactor irradiated

Al^O, the bands increase linearly with dose after a slight amount of rapid initial growth. This linear

growth continues until more than 10 18 defects per cm3 have been created. Above this concentration the

formation rate decreases slowly with increasing defect concentration.

This fused silica and data is consistent with the following interpretation: Co^ gamma rays

do not create defects in Al^O^. At least, they do not produce defects that are stable at room tem- perature. The color centers produced by gamma rays are formed by carrier trapping on defects or impurities or both. There is a reasonable explanation for the absence of a color center increase at large doses. The displacement energy of both the Al and 0 atoms is higher than the maximum energy

that can be transferred from the most energetic Compton electrons created by the Co*^ gamma rays. The

fused silica situation is different. The displacement energy of either or both the 0 or Si atoms is below the maximum energy that can be imparted by the Compton electrons from Co^ gamma rays. Thus,

defects are formed in fused silica, but at a comparatively low rate. Once formed they are converted

to color centers by electron or hole capture. Obviously, the reactor radiations, particularly the

fast neutron component, are sufficiently energetic to produce defects in both materials.

This interpretation, especially the difference between the defect formation and charge trapping

processes, is supported by annealing studies on these materials [8]. When reactor colored A^O^ is heated, e.g. at 300°C for several hours, the optical absorption decreases during the first 20 minutes

and remains constant during the remainder of the heating period. If the crystal is then exposed to gamma rays, a relatively low dose will restore some, but not all, of the color removed. Additional

gamma-ray irradiation does not increase the color center density. A similar annealing procedure was applied to fused silica [9,10] to obtain the upper curve in Fig. 2. First, the sample was reactor irradiated until a convenient optical density level was attained.

Second, it is heated at 550°C for 40 minutes. Preliminary measurements had shown that this was the

shortest annealing time at this temperature (which was the lowest temperature) required to remove all

of the absorption bands with peaks below 6.2 eV. Next, it was irradiated with gamma rays. The upper

curve is the growth of the 5.82 eV peak as a function of gamma-ray dose. The lower curve in Fig. 2 shows the growth of the same peak in a sample that had not been previously exposed to radiation. Above 5xlO^R. the two curves are similarly shaped except that the top one is displaced upward by a relatively constant amount. Near the origin the upper curve increases very rapidly with increasing gamma-ray dose. When the optical density reaches 0.35 it &tarts to level

off and becomes nearly parallel to the lower curve. The extremely rapid increase near the origin can be attributed to charge trapping by existing defects. If defects were not present prior to irradiation the rapid increase would not occur. This annealing data also indicates that the heat treatment has removed

some defects and released all of the charges that were trapped on the remaining defects. When the sam- ple was subsequently exposed to gamma rays the remaining defects rapidly trapped charges. Continued

gamma-ray irradiation caused additional defects to be formed at the same rate observed in samples

exposed only to gamma rays.

3. The Damage Region Created by a Recoiling Lattice Atom

The next subject to discuss in detail is the region of damage, i.e., the spike or Wigner region,

created by an energetic recoiling lattice atom. Two things are to be emphasized. First, the fact that experimental data is available to substantially verify the descriptions of the spike region given above.

Second, the same example will illustrate how these regions influence the physical properties of an

24
insulator. The example chosen is the effect of fast neutron irradiation on the low temperature thermal

conductivity of single crystal A^O.., technically, synthetic sapphire or corundum. The work to be described was published by Berman, Foster and Rosenberg in 1954 [ll]. It is surprising that this is still an appropriate, if not the best, example that could be cited.

At room temperature the thermal conductivity of all insulators is almost entirely due to the transport of energy by lattice or phonon waves. The factors that limit the heat conductivity are usually

referred to as the thermal resistance. Above 20 or 30°K this resistance results from the interactions

of one phonon wave with all of the others. Usually, this thermal resistance is given by the expression

W

y

= A T-e

- 9/2T

where T= temperature in °K, 9 = Debye temperature, A and u are constants, the latter near unity. This

expression for the phonon-phonon interaction is usually written

W = A e

- e / 2T

U T Below 10 or 20°K the thermal resistance is the result of the interactions of the phonon waves with the sample boundary or surface, not with themselves. This contribution to the resistance will depend on

the shape and size of the sample. The usual expression for this part of the thermal resistance is given by W

B

= BT"

3

where B is a constant that depends on the shape and size of the sample.

The W and thermal resistance contributions must occur in all substances. Additional thermal

resistance will arise if the sample contains inclusions, lattice defects, impurities, etc., that can

scatter the phonon waves. Thus, the thermal resistance of a substance should be increased by any treatment that introduces additional scattering centers . If this added resistance is called W

R

the total thermal resistance is given by

T7 A -9/2T , B, W = - e + -3 + W

R Most often, heat conduction data is expressed as thermal conductivity, in units of Watts/cm/deg,

which is the reciprocal of the thermal resistance.

The thermal conductivity of single crystal Al.O^ both prior to irradiation and after a series of irradiations with fast neutrons is shown in Figs. 3 and 4. The first figure very clearly shows the de- crease in conductivity. The second figure relates the conductivity curves to the various terms in the thermal resistance expression. In the temperature range 1.5 to 10°K which corresponds to the straight

section on each curve the resistance is due to the boundary term W^, the radiation has decreased the conductivity in this range. Also, above 10°K the resistance due to the term W , has increased. From this data the radiation induced increase in thermal resistance W

R

has been computed. This is shown in Fig. 5. The next step is to use these curves to determine the size and shape of the radiation

induced defect region. The following simple expression for the thermal conductivity, K, is obtained

from elementary kinetic theory. K = t

113 cvl or W = — = —

3 K cvl where c = specific heat, v = velocity of the lattice waves, and 1 = mean free path, i.e. the average

distance between scattering points of the lattice waves. The radiation induced change in thermal

resistance, at any given temperature, is given by a similar expression

W

R

= 3 cvl

D

Where 1 is the mean free path for scattering by the defects. From the data in Fig. 5, and computing

the number of damage regions from the fast neutron scattering cross-section, the scattering power

(for phonons) of the damage regions can be estimated. In turn, from the scattering power, the size

of each damage region is obtained. The result obtained is approximately 1000 atoms, a number that agrees well with other determinations [1,2,3].

The shape of the spike or recoil damage region can also be inferred from Fig. 5. In determining

the size of the damage region, given above, it was assumed that the region was spherical. This is not consistent with the very nearly constant value of W

R

between, approximately, 20 and 40°K shown in

Fig. 5. The constant W in this temperature range is consistent with phonon scattering by long thin R

25
obstacles. The size of these regions, computed from the thermal resistance data, is roughly 100 angstroms in length by 10 angstroms in diameter. Again, these values are in accord with other estimates

of the recoil damage region dimensions.

Thermal conductivity is also influenced by exposure to purely ionizing radiation. When Al^O^ is exposed to gamma rays the thermal resistance is increased. This is shown in Fig. 6. The change is like that produced by fast neutron irradiation. However, it differs in one respect. The initial exposure produced all of the observed change. Additional exposure did not increase the resistance.

This is similar to the coloring of Al^O^ by gamma rays. An initial exposure of 3xl0^R produced

saturation coloration, i.e., additional irradiation did not produce an increase in color center concentration. These observations indicate that the gamma-ray created thermal resistance change is related to charge trapping. It is not clear why this should influence the conductivity. Furthermore,

the resistance increase is surprisingly large, it is approximately equal to the change produced by

the first neutron irradiation. It appears that additional work of this type on Al 0^ and other

materials could be very interesting.

4. Macroscopic Radiation Effects

The macroscopic or external properties of ceramics are affected by sufficiently large irradiations.

These macroscopic changes result from the cumulative effects of a large number of individual point

defects, of spikes, or both. The external physical dimensions which are often changed can be conve- niently and accurately measured. Small density changes are particularly easy to detect. A very good

example of this type of measurement is the work of Primak [12,13] and his co-authors who have systematically studied the irradiation induced dimensional changes in crystal quartz and fused or glassy

silica. This work will be briefly described to illustrate the macroscopic radiation effects.

Before doing this, the section on the basic radiation damage process must be expanded slightly.

To begin, consider the effect of an interstitial atom on the atoms that surround it in a crystal lat- tice. Intuitively one sees that the interstitial will push the surrounding atoms outward and a large

number of interstitials will tendtoexpand the crystal. Compare this withthe effect of a vacancy on the

lattice. There will be a tendency for the void produced by the removal of an atom to be partially

filled as the surrounding atoms tend to push in. A large number of vacancies would be expected to produce an overall contraction of the lattice. However, this picture is almost certainly too simple.

When an atom is removed from the lattice the attractive forces it exerts on the surrounding atoms are

no longer present to hold them together. Consequently the atoms nearest or next nearest tend to move

outward. These inward and outward movements will, at least partially, cancel and the total distortion

around a vacancy is relatively small. In fact, in some crystals it is not known if the distortion

around a vacancy expands or contracts the lattice. On the basis of these arguments, which are definitely oversimplified, it can be concluded that

radiation damage will cause most crystal lattices to expand. This conclusion is more readily understood by pointing out that the impinging radiation creates one interstitial atom for each vacancy

formed.

When glasses are subjected to atom-displacing radiation the effects of vacancy and interstitial

formation will be somewhat different. The glass network is less compact than the corresponding

crystal structure. For example, glassy silica is considerably less dense than crystal silica, i.e. quartz. The open spaces, or voids, in the network can accommodate interstitials and the lattice is strained very little or not at all. The displacement of a network modifier should have relatively

little effect on the network stability. In contrast, the displacement of a bridging oxygen or a silicon atom from the network will have a la"ger effect. In a loose structure the network could move

either in or out; this would depend on local forces.

The most common network- forming atoms are strong chemical reactants. In fact, this is the reason

for the strength of most glasses. This chemical reactivity should give rise to a strong tendency

for the reestablishment of the network after disruption by radiation. Thus the violent thermal

agitation, and perhaps even a short lived gas- like state, associated with the spike created by a recoil atom could be conducive to a network rearrangement. A priori , it cannot be said that this rearrange- ment will lead to a compacted or expanded lattice. It might be worth while to point out that this

radiation-induced lattice rearrangement might be characteristic of equilibrium temperature and pressure

conditions that are not attained in the usual glass forming equipment. If a glass which has been modified by radiation is subjected to the temperature and pressure conditions occurring when it was originally formed, it should revert to its previous state. Obviously, this does not apply to materials

like crystal quartz which, as is very well known, transforms to glassy quartz or fused silica when

heated to the melting point.

What happens when crystal quartz and fused silica are exposed to fast neutrons? Figure 7, taken

from the work of Primak et.al., [13] shows that the density of crystal quartz decreases with in- creasing exposure to fast neutrons. This indicates the lattice expansion tendencies predominate over the contraction tendencies. The opposite occurs with fused silica. This is shown in Fig. 8. The

density of the fused silica increases as the exposure to fast neutrons increases. This contraction

could result from the rearrangement of the network into a more dense lattice, Considering that fused

26
silica is all network former. Or, it could result from the following combination: the interstitials

do not expand the lattice since they find their way to the lattice voids and the vacancies permit the lattice to contract enough to produce an overall density increase. Other explanations for the radiation induced contraction can be given. At this time, the phenomena is not entirely understood.

As the quartz and fused silica are subjected to increasing doses of reactor radiations the dens approach one another. Fc same density or very nearly so.

2

sities approach one another. For exposure in excess of 10 or 10 nvt both materials acquire the

When the samples with small or moderate radiation induced density changes are heated the radiation

effect is reversed. The crystal quartz density increases and the fused silica decreases. Heating to

a sufficiently high temperature removes all the density changes. These annealing changes are shown in Figures 9 and 10. When the crystal quartz is heated the mobility of any vacancies or interstitials that are present

is greatly increased. If the interstitials are more mobile they will diffuse, in a random walk fashion,

until they encounter and combine with vacancies. In this way the lattice will be restored. Since

some interstitials may be more tightly trapped than others only a fraction may be mobile at a given

temperature. This is one possible explanation for the observation that prolonged heating well below

900 or 1000°C will anneal only part of this damage.

The processes contributing to the annealing of irradiated fused silica are not completely understood at this time. If the density change involves only defects annealing would occur in a manner

described above for crystal quartz. If the density involves network rearrangement then the annealing

processes are different and probably much more complicated.

A very interesting thing occurs upon annealing crystal quartz which has been very heavily irradiated until it has nearly the same density as highly irradiated fused silica. It does not revert to crystal quartz but becomes fused silica. It would appear that this nearly common density is characteristic of the state in which the atoms have undergone such a large number of displacements that both the original crystal lattice and the thermodynamically controlled glass structure have been transformed into

a common state. Upon heating the thermodynamics favor the glassy state and this is the state formed

during annealing. In some recent work Primak has shown that an additional complication occurs [14], in

that the density change is influenced by the presence of ionizing radiation. Obviously, this is an area for additional interesting work.

5. Radiation Enhanced Diffusion

The diffusion of atoms in a solid is a relatively slow process that is difficult to measure. In many materials the diffusion rate depends on the concentration of vacancies in the lattice and if this

is changed the diffusion rate is changed. The examples given in the preceding sections were chosen to emphasize both the different ways that radiation interacts with a solid and the different kinds of damage remaining in the lattice after irradiation. This required considerable discussion of the physical process that occurs during the short period that the bombarding particle is interacting with

the solid. The process which occurs during reactor irradiation that is most pertinent to a discussion

on diffusion is the creation of vacancies. Each incident particle will create some vacancies, the number depending on its mass and energy. Usually for each vacancy there will be a corresponding

interstitial. Both of these will diffuse in the solid. Each time that an interstitial encounters

a vacancy they will recombine and the respective concentrations will decrease. During irradiation the vacancy concentrations will depend on the radiation level. At low levels it will be linear with dose

but considerably less than linear at high levels.

The relation between radiation- induced vacancies and the diffusion process can be stated explicitly

in terms of the well-known diffusion equations. The general diffusion equation is usually written for

isotropic materials DV

2 [C] - ft [C] = 0

2 where [c] is the concentration of the defusing entity, t is the time, V is the Laplacian onerator,

and D is the diffusion coefficient. Very often the diffusion of atoms in solids occurs by way of the "vacancy mechanism". One of the atoms (next to a vacancy) jumps into the vacancy and both the atom

and vacancy have moved or "diffused". In this case the diffusion coefficient, D, in the above expres- sion is given by _ E y kT

D = D e m

, o

' where k and T have the usual meaning, E^ is the activation energy for vacancy migration; and

D = A[V ], o o where A is a constant and V the intrinsic vacancy concentration. During irradiation there will be an additional vacancy concentration which will depend on the dose rate; call this [V ] . Then D is K O

2?
o = A rV

o + V

and it is apparent that the diffusion constant D depends directly on the relative size of VQ and V^. The intrinsic vacancy concentration is dependent on the temperature, and is given by a relation of the form

-E f/kT V0 = Be

r/

,

where B is a constant and is the activation energy for vacancy formation. If at a high enough tem- perature V > V the radiation induced component of the diffusion is unimportant.

o R

Many examples of radiation-enhanced diffusion in metals and alloys can be found in the literature

[1,2] Only recently the preliminary results of a radiation-enhanced diffusion experiment in a ceramic

material were made available. 2 This is a study of the self diffusion of Be in BeO by de Bruin, Roman,

Watson, and Blood. [16] Classical tracer diffusion techniques were used. Be 7 tracer was deposited

on the surface of the samples. The samples were heated to various temperatures, or irradiated in a reactor at the same temperature. The diffusion which occurs during these treatments is determined from

the final distribution of tracer Be 7

. This is obtained by sectioning the sample and counting each

layer. Apparently, the diffusion occurs in the usual way since plots of log [Be 7

] versus the square of the penetration depth are linear.

A number of diffusion constant determinations are shown in Fig. 11. Each of the points refers to different radiation conditions and the straight line indicates how the diffusion constant of unirradiated

samples depends on temperature . Above 1200°C the radiation field does not increase the coefficient.

Apparently, above this temperature, the intrinsic vacancy concentration is large enough to control the diffusion rate. Between 1200° and 800°C the results are not easily understood. The data factitiously

suggests that the diffusion increases as the temperature is lowered. In this region the annealing of

,the radiation-induced defects is strongly temperature dependent. Also, the sample may be slightly

amorphous. It is apparent, upon reflection, that these and other effects can invalidate the simple vacancy diffusion model in this temperature range. Below 800°C the diffusion coefficients during

irradiation are comparable to those obtained at 1100 to 1400°C in samples not exposed to radiation.

This appears to be unmistakable evidence for a large amount of radiation -enhanced diffusion. It is conceivable that the observed increase is due to grain boundary diffusion, although de Bruin et al» believe it is not.

The effects of radiation on diffusion rates will undoubtedly be studied intensively in the future.

It will be particularly important in ceramic moderators and fuel elements.

2. The author is extremely grateful to Dr. H. J. de Bruin for making these results available

prior to publication; consequently, they are still subject to modification.

2b
References

[1] This and the following 2 references are

general books on radiation damage and

related subjects. G. J, Dienes and

G. H. Vineyard, Radiation Effects in Solids , Interscience, New York (1957).

[2] D. S. Billington and J. H. Crawford,

Radiation Damage in Solids , Princeton

Univ. Press., Princeton (1961).

[3] L. T. Chadderton, Radiation Damage in Crystals , Methuen, London (1965)

[4] T. P. P. Hall, D. Pooley, W. A. Runciman, P. T. Wedepohl, Proc. Phys.

Soc, 84, 719 (1964).

[5] J. H. Shulman and W. D. Compton,

Color Centers in Solids , Macmillian,

New York (1962). This is a general

treatment of color centers.

[6] P. W. Levy, to be published.

[7] P. W. Levy, Phys. Rev. 124 , 1226 (1961).

[8] P. W. Levy, Discussions Faraday

Soc. 31, 118 (1961)

[9 ] P . W . Levy , Chemical and Physical Effects

of High Energy Radiat ion on Inorganic

Substances , Amer. Soc. for Testing and

Materials, Philadelphia (1964) p. 3.

[10] P. W. Levy, to be published.

[11] R. Berman, E. L. Foster and H. M. Rosenberg, Defects in Crystalline Solids , The Physical Soc. London (1955) p. 321.

[12] W. Primak, L. H. Fuchs, and P. Day,

J. Amer. Cer. Soc, 38, 135 (1955).

[13] W. Primak, Phys. Rev. JL10, 1240 (1956).

[14] W. Primak and E. Edwards, Phys. Rev. 128 , 2580 (1962).

[15] M. Wittels and F. A. Sherrill, Phys. Rev.

93, 1117 (1954).

[16] H. J. de Bruin, D. Roman, G. M. Watson,

C. M. Blood, to be published.

257-304 0-67-3

29
ELECTRON- VOLTS

Figure 1, The color center spectrum produced

by irradiating relatively pure fused

silica. Very nearly the same spec- trum is obtained by either gammaray or reactor irradiation. The arrows indicate the peaks of the more

prominent absorption bands.

GROWTH OF 5.82 eV BAND IN FUSED SILICA EXPOSED TO Co 60 GAMMA- RAYS

0.6 r

0.5

in 0.4

<"0.3

0.2

0.1

Figure 2,

REACTOR IRRADIATED-HEATED TO 550°C THEN RECOLORED

5 10 15 20 25 GAMMA-RAY DOSE, IN UNITS OF I0

7 R

The growth of the 5.82 eV absorption

band in fused silica when exposed to

Co gamma rays . The upper curve

was obtained from a sample that had

been reactor -irradiated and then

heated for the shortest time and at the lowest temperature that would re- move the 5.82 eV band. The rapid

initial growth can be attributed to the coloring of reactor-induced de- fects that remained in the sample

after annealing. The lower curve was obtained from a pristine sample

which originally contained very few

uncolored defects.

Figure 3. The low temperature thermal conduc- tivity of synthetic sapphire,

A1„CL, before and after the indicated reactor irradiations. The

doses were 1.5, 8.9, 20.2, and

5 10 Temperature CK)100

Figure 4. The thermal conductivity data shown

in Fig. 3 plotted in a way that separates the linear low temperature

boundary scattering contributions,

the B/T term, from the non- linear

phonon-phonon contribution, the

(A/T) exp(-0/2T) term, that dominates at higher temperatures.

5C
Figure 6. The thermal conductivity of Al^O

before irradiation and after a

3 x 10 6 R Co60 gamma-ray dose.

ibii 1 1 1 —i r~\

Figure 7. The change in density of crystal

quartz exposed to reactor radiations.

Except for the "crosses" the various

points represent different kinds of physical measurements. The "crosses"

are independent X-ray measurements.

[15]

31
100 150 200 DAMAGING NEUTRONS ( I018 neutrons / cm* ( 3 4 5 6 7 6 ANNEALING TEMPERATURE ( I02 dag C)

Figure 8. The change in density of fused silica

exposed to reactor radiations. The

various points represent different

kinds of physical measurements. The

half open circles are data from a "fused silica" sample that had been

converted from crystal quartz by

irradiation.

Figure 9. The increase in density of a quartz

sample that had received a moderately heavy reactor irradiation,

after heating for approximately 30 minutes at each progressively higher

temperature point.

(B) is the density after irradiation

but before annealing.

(D) is the density of unirradiated

quartz

.

Figure 10. 23456789 ANNEALING TEMPERATURE ( I0e dag C)The decrease in density of a very heavily irradiated quartz sample

(solid circles) and fused silica

(open circles) after heating for

approximately 30 minutes at each of the progressively higher temperature

points

.

(B) indicates the densities after

irradiation but before

annealing.

(D) is the density of unirradiated

fused silica.

TEMPERATURE (100 »C)

15 14 13 12 II 10 9 8 7 6

u

<bto

01£

U.oo

s

1 o

COts

H'Oof

a.

10"'

10"'

r-f—i—i—

r

Dose > I Mev

1-5 x I0 l9 nvt 18

38

41

60 70 80 90 100

10.000/

T

110 120 130

Figure 11. Apparent diffusion coefficients for

the diffusion of Be (as radioactive -j N Be ) in polycrysta lline BeO during

the indicated reactor irradiations

at the temperatures shown. The data below 800°C ind icates that the presence of the radiation flux has

greatly enhanced the diffusion rate.

52
Chemical Problems Associated with Lattice-Defects.

Uranium Dioxide Phase

R. J. Thorn and G. H. Winslow

Argonne National Laboratory, Argonne, Illinois

1. Defects as Chemical Components

A. Thermodynamic Considerations

In most experiments and environments, a non-stoichiometric phase such as U02+x

behaves reproducibly as a binary system. It is bivariant so that the pressure is a unique function of composition and temperature only. Thus

p = p(x,T) . (1)

These statements are generally accepted as being so obvious that they suggest that any

thing which follows them is frivolous. Their acceptance, however, without some en- quiry tend to prejudice one in two important respects: Interesting experimental possibilities are excluded, and inconsistent relations are included in theoretical

analyses. It is significant in these respects to recognize that if the uranium dioxide

phase is to be described in terms of the defect-theory of non-stoichiometry, then one admits the real existence of other entities besides U and 0. In fact, it has been

demonstrated that the experimental results can be interpreted in terms of oxygen ions

at the interstitial positions near the centers of the fluorite unit cells [1] and the

necessary concomitant vacancies in the anionic sublattice. Recognition of the condition expressed by equation (l) and of the existence of what effectively amounts to more than two components is required if one desires to analyze thermodynamically the

non-stoichiometric phase. Yet a problem has been introduced. A clarification of this

problem is outlined below by employing symbols for the defects as chemical components

and by identifying conditions of restraint which in most experiments are an integral

part of the system.

For a phase such as ITC^.-^-, one accomplishes a thermodynamic analysis which is more complete than that usually presented for non-stoichiometric phases by recognizing

the following chemical symbols: U, 0, -, +, cs , as , and is_. Among these cs, as , and

is refer to cationic, anionic, and interstitial sites respectively. In writing chemical reactions involving these possible components, one requires that the symbols are conserved. Thus one writes for the essential equilibrium within the solid the reaction:

(0~ 2as) + is -> (0

-2

is) + as (2)

which differs from the frequently used convention by the requirement that each symbol

appears on each side of the equation. Of course, not all of the associated difficulties are solved by initiating the analysis thus, for to be rigorous one must rec- ognize the existence of all the components in all the phases. The appearance of the

components cs , as , and is_ in the gaseous phase may be rather unconventional but it is

a difficulty which creates no impossibilities and which is set aside herein. In the

situation being described the quantities (0 as) and (0 is) are similar to molecular

entities or atomic groupings within other molecular entities or domains to be cited

later. The reduction of the oxide can be represented by the reaction:

(0

_2as) |o

2 + as

-2

(3)

and a similar one for (0 is). Such reactions, however, are probably more hypothetical than real because the charge on a_s or _is undoubtedly relaxes practically

Figures in brackets indicate the literature references at the end of this paper.

33
instantly or never even develops in a real sense. Whatever the situation may be, the

general behavior suggests that thermodynamically this charge is so located that it

corresponds to well defined valence states for the cations. For instance, Thorn and

Winslow [2] have demonstrated that there exists a close parallel condition, for both

divalent and trivalent states in the case of the elements in the first transitional

row, between the energies in the oxides and those in aqueous solutions where one would expect the ions to be in well defined valencies. Consequently, one can represent the situation in UOg+x

by the equation:

2(U+5 cs) + as"2

-^ 2(U+

^cs) + as . (4)

The sum of reactions (3) and (4) represent more nearly than the individual reactions

the process actually occurring. However, because of other factors, one of which is

probably associated with localized charge-neutralization, the analysis must be car- ried at least one step further.

The seven possible components indicated by the symbols listed above suggest that

for a diphasic system there are seven degrees of freedom. However, in most experiments several conditions of restraint exist. Thus one recognizes the following re- lations among the numbers of the various symbols:

N+

= N_ , (5)

N = N , (6) cs u

v '

= '2N" , (7) as u '

v 1

N+4 + N

+5 = N„ , (8) u

N. = a.N . (9) xs 1 cs wy

Depending on whether a. is a prescribed function, there are four or five conditions

of restraint, and there" remain either three or two degrees of freedom.

B. Roles of Valence-States and Their Energies

For binary systems of anions and cations which are compounded from what might

be called Bravais "compounds", cs a as^, the primary contributions to the total

energies are the cohesive energies which can be evaluated in terms, of the Madelung

formulation. A single Madelung constant suffices for each structure. In these cases there exists only a single valence-state for the cation. In non-stoichiometric

phases, however, the presence of two valence-states for the cation introduces energies

which cannot be described in terms of single Madelung constants and consequently

features which simulate more nearly those corresponding to the conventional ternary

system than those for a binary. Towards a more complete thermodynamical analysis,

one must then recognize the existence of more complex structures which are variously

identified in terms of enlarged unit cells, super-structures, lattice molecules, co- operative effects, domains, etc. For the present purposes one can indicate

the situation by suggesting that the monophasic region is composed of subregions such

as

(U+4 cs)

a (u+5 cs)

b

(0" 2 is)

c (0- 2 as)

d as

e is ffJM(x) |]

-

Such units can serve as guides in further analyses which are directed towards the

following features, among others: (l) Recognition of the continuous transition from

one terminus to another of a monophasic region. (2) Recognition of defects as com- ponents or as conditions connecting Bravais "compounds". (3) Recognition of the

likelihood of local neutralization of electrical charge. (4) Introduction of a basis

for ternary systems generated from binary systems. The values of a, b, c, d, e, and

f can be evaluated from the conditions of restraint given above. Thus for one com- positional variable, 0/U = 2 + x, one finds that

b = (l?fe)a > (1°>

34
c =

'2a

i (l-2x)+4x-l

(11) 2(l-2x) d

'

d = (2+x)(a+b)-c , (12)

jand e = 2(a+b)-d . (13)

Depending on one's interest, any one of the letter-subscripts in the unit can be divided out to determine the size of M(x). Whatever one is accepted, the formula given

above implies that there must be at least one of each of the entities given and that

there exists a well defined configurational arrangement of the entitites in a real

material. Hence in most experiments there is only one variable, x, at the disposal

of the experimentalist and a corresponding number of adjustable parameters available

to the theorist. The quantities and M(x) are determined by the energetics of the

Situation. Thus one writes that a

1 = a± (x,T) , (14)

and

M = M(x,T) (15)

which are in a sense conditions of restraint also not at the disposal of the experimentalist. The number of "available" interstitial positions is fixed by the situation (x and T, x and p, or p and T) . When a small amount of oxygen is added to

stoichiometric uranium dioxide, the numbers of defects, as_ and (0 is), are small

at low temperature [3] and the size of the molecular unit is large if it is to contain at least one atom of each entity or it is small, i.e. comparable with a unit

cell, if the situation is imagined to consist of defects dispersed throughout a matrix. In this region it can be meaningful to approximate the description in terms

of point defects. However, as more oxygen is added the size of the molecular unit

decreases and its resemblance to the original structure of the Bravais-compound

cshasg becomes less. At some composition between 0 and 0.25 for x, the resemblance

to another Bravais-compound cshasg begins to appear in the form of the corresponding

molecular unit. Thereafter the second unit grows at the expense of the first one. At some point between the extremes there occurs the residues of a transition which

is usually manifested in the form of inflections on a plot of pressure vs. composition. Such are undoubtedly the sources for the obscured x-ray diffraction patterns

[h] for 0.08 < x < 0.13, for the non-reproducibility for the partial molar entropy

pointed out by Thorn and Winslow in this region [5], for the inflections observed by

Aukrust, Fj^rland, and Hagemark [6], and the turning point in a plot of the partial

molar entropy of oxygen vs. the partial molar enthalpy [7l- The similarities and

contrasts between this region and the diphasic region has been cited by Thorn and

Winslow [2]. In the latter case one phase is converted Into-, another; In the former

one domain or molecular unit is converted to another but no surface energies are involved .

As cited above, the observations by Thorn and Winslow [2] indicate that the

valence-states in the oxides of the elements in the first transitional row and the

corresponding states in aqueous solution are sufficiently equivalent that one can

represent, to the first order of approximation at least, the behavior of the oxides

in terms of valence-energies which appear to exist in aqueous solution. Hence it

fehould be possible to Identify formally, to evaluate accordingly well defined valencetenergies in solid oxides, and to develop therefrom a basis for solid state chemistry

in general. Towards a limited aspect of these ends, further comparisons between the

situations in oxides and in aqueous solutions are needed. An intercomparison among

the valence-energies associated with the hyper-stoichiometric side of the fluoritestructured dioxides of the elements near uranium is not possible because such have

not been measured in aqueous solution. An intercomparison is possible, however, for

the hypo-stoichiometric side. Consequently, to illustrate some of the factors involved, we cite the role of the trivalent and tetravalent states in some of these

compounds

In Table 1 is compiled a comparison among the valence-energies of some actinide,

and one rare earth, elements for which the electrode potentials in aqueous solution

have been reported [81. Therein one can observe the correlation between the increase

in the quantity AF|(lYr3 } aq) - AF^(M+ ,aq) and the increase in the partial pressure

of oxygen in equilibrium with an oxide having an arbitrarily selected composition.

This relation indicates that one can predict the relative stabilities of solid oxides
from the energies for the valence-states observed in aqueous solution. Having once recognized the potential uses of such approximations to the situation existing in the

solids, one can extend the description by recognizing that it is the relative ener- gies of lyf^S and of IT" which determine the properties. Hence within certain limits

imposed by the rigid parts of ionic electronic configurations, one can begin to treat

different elements as manifestations of different valence-energies of essentially one element. Thus it is possible to describe symbolically the^, general situation corre- sponding to the molecular unit given above by replacing U by or in general by

E. which is some numerical value for the i th energy in the +\ state and similarly

fir the U+5. and to indicate the relative amounts of each energy one introduces com- positional variables f^ and f,- for the valence energies E^ and Elp . Accordingly

one represents a multicomponent system by the formula:

f .E. +^) Vf.E.+5

^, . 0" 2 is) 0~ 2 as ,as is/L, v . 11 ja\ l_, j j /b /c> ,.d e f/M(x)

v i J A more complete investigation of this formalism should yield the basis for predicting

the behavior of ternary systems from the known behavior of binary systems and of the

energies of the appropriate valence states. For instance, one observes by inspecting

equation (4) that the more stable the lower valence-state is relative to the higher

valence-state the larger is the partial pressure of oxygen. Consequently, to stabilize, in this sense of a lower partial pressure of oxygen, a non-stoichiometric oxide

one adds a third chemical component having a more nearly positive value for the difference between the free energies of the valence-states than that for the host oxide.

Thus the addition of magnesium to the wiistite phase produces effectively a reduction of the phase [See 2].

2. Defect Theory of Non-Stoichiometry

A. Basic Elements

Because the primary interest in the system at hand is, as indicated by equation (l), to ascertain how the composition of the solid is determined by the pres- sure of a gaseous phase, the appropriate statistical thermodynamic analysis is one employing an open system. That is, one considers a system, solid U0o+X, containing

energy states Es and particles, not all of the various kinds of which are fixed, in

contact with a reservoir, the gas, having fixed chemical potentials, m^'s. Accordingly, one writes for the probability that the system is in state Es with + N2 + - - Nn particles of the various kinds:

P f S u 's) = CI e _P(Es r +pV-y ^iV (16) E ,N. <s lP ^i S) "E ,N. 's e b

4-< 1 1 K±OJ

s' 1 s' 1 1

In this expression (3 = ( kT) -1

. If this system were composed of entities corre- sponding to the seven symbols as independent components, then the probability of

the system would need to be normalized by summing over all seven components as well

as the energies. However, as cited above, not all of entities corresponding to the

symbols are independent because they are interrelated via equations (5) through (9).

Thus, in the case of the uranium dioxide phase, one recognizes, as stated above,

that the system is bivariant and consequently binary, i.e. there are only two N^'s.

Therefore, the construction of the appropriate partition function through the normalization of the probability must recognize this fact. For the purpose of describing

the non-stoichiometric phase, these two components can be selected, of course, in

several ways provided they are sufficiently independent to specify the composition

of the phase. The analysis which is usually effected is one which considers not U

and 0 as components but rather a_s_ and (0 is). When the corresponding probability

is normalized by equating the sum for P in equation (16) to unity one finds that

ePpV

- lit>,K) - y £

H

E ,„,„ e-^Vv (17)

e' n'.,n

s 1 v

s i' v in which is the number of interstitial sites occupied, Nv

is the number of anion

sites vacant, and >, 0 = e^o, commonly identified as the absolute activity for oxygen

In this formulation, however, the Nj_ and Nv are not independent. At constant ratio

of uranium to oxygen, oxygen ions can shift between lattice sites and interstitial

56
positions. Thus dN

y

= dN^ at constant x. And added oxygen is distributed between

lattice sites and interstitial positions. Thus (Nj_ - Nv )/Nu

= x. The more complete analysis of the system through the evaluation of the semigrand partition function T presents some logical problems which are not easily solved.

For instance, one should recognize that energy states available depends on composition somewhat in accordance with the molecularity cited above. Hence fi is a function

of Es as well as and Nv

. This fact implies that any interaction among the

entities precludes the possibility of random distribution of them. To date, however,

no general theory has been developed for the functional Q (E

s (N^, N )

) . Consequently,

an approximate evaluation has been acomplished by employing the elements of a ran- domized distribution in such a manner that it does not become catastrophically trivial or introduce several arbitrarily adjustable parameters. The functional Q. has

been evaluated [See 5 and 13] by calculating all the possible arrangements of Nj_ and

Nv and by including contributions of the defects to the vibrational part of the

partition function, and qv

. Thus, one writes that

(a.N ) ! (2N ) ! N. -N

n 1 u' v u

; _ i_ V h oi "

=

]\J tin M _M 'l I M I I 9M _M \ t Q i- %r iHa^-N.)! N

v !(2N

u -N

v

)! Q

i Qv

and following the usually presented arguments given by Heitler [14], one writes for

the energies:

2 2 E N E . . N. E

s

( Nl ,N

v

) = E

vN

v

- E.N. - -^_Y i^x_ (19)

u 1 u

in which

E is the energy required to remove an oxygen atom from an anion site to a position of rest in the gas.

Ej_ is the corresponding quantity for an oxygen atom on an interstitial site.

2 Evv/Zv

is the energy required to separate nearest neighboring pair of vacancies

2 Ej_j/Z. is the energy required to separate a nearest neighboring pair of oxygen ions on interstitial positions.

Defining the fraction of the sites vacant as

6 v = V2N

u

( 2°)

and the fraction of the interstitial sites occupied as

6

i = Va

iN

u '

( 21 )

and employing the usual procedures for maximization [13] , one obtains the results:

• 1-0 \ E 29 E v ^o = H-^fj - m + t- - J; ( in%)

E - 20

i E

ii 5

The absolute activity of oxygen is related to the partial pressure of diatomic

oxygen through the equation,

P o

2 = *

2kTQeD/RT

, (24;

in which Q is the partition function for molecular oxygen and D is its dissociation

energy.

37
B. Application to U02+x

The energies and the Debye or Einstein temperatures associated with q and q. in equations (22) and (23) have been evaluated [5] by a procedure which involves the

following items:

1. The value for the energy Ej_j_ was obtained by equating Ei:j/2R to the critical

temperature for the formation of U^0„ obtained by Roberts and Walter [15] . Thus

E. . = 5.56 kcal/mole

.

2. The value for E^ was obtained through an averaging procedure which employs the

measured relative partial molar free energy of oxygen. That is, equations (23) and

(24) can be employed to obtain

2E. + 4(x/a. )E. . = -F~ + 2Rljin x/(a. -x) | - Inq I + RT^n(kTQ) -f D , (25)

1 in 2 1 J from which one determines E.. . The value obtained is 93-95 kcal/mole.

3. The characteristic temperatures, 0j_ and e> v , used in the evaluation of q. and q as functions of the temperature were determined from

-Sq = S° + 2R-jin

i x/(a

i -x) 1 - £nq

i

- Tdinq

±/dT| (26)

and the Debye-Waller factors observed by Willis [16]. The results are 6. = 158.0°K

and e

v

= 542°K.

4. Values for Evv were obtained in two ways. The melting temperature, 2760°K, for

UO2 corresponds to Evv = 16.47 kcal/mole. A composition of U0]_ 38 a ^ 2200°K for the

lower phase boundary, UOg-U, [10,17] corresponds to Evv

= 16 . 87 'kcal/mole . The latter value was accepted.

5- A unique evaluation of Ev over the range of temperatures extending from 800 to

2400°K is not possible within the formulation developed to this stage, but this difficulty appears to yield significant additional information concerning the phase.

From a value, -170.53 kcal/mole, [10] for the relative partial molar free energy of

oxygen at 2200°K, one obtains Ev

= 209-67 kcal/mole. This value, however, is not

consistent with the relative partial molar free energy observed [18,19] at 1100°C.

An analysis of this difference suggests that a significant number of cationic vacancies in equilibrium at the higher temperature is frozen in at some intermediate

temperature and consequently these vacancies are not at equilibrium at the lower

temperatures. An analysis of the situation suggests that the fraction of uranium

sites vacant and frozen in is 3 x 10 in the experiment by Markin and Bones [18].

The effective value for E , is under these conditions, 134 • 7 kcal/mole.

The results of the analysis sketched above yields a fairly complete thermochemical description [19] of the uranium dioxide phase for 0 < x < 0.10 and 800 < T < 2400°K and for the lower phase boundary. Two illustrative examples of the agreement

between the experimental measurements and the analytical model are given in Figures

1 and 2.. In the first figure, the calculated relative partial molar free energies

are compared to the measured values at l400°K. In the second one, calculated and

measured lower phase boundaries are compared. There are, of course, places where the

model is inadequate, but these inadequacies reveal features which are not entirely

unanticipated. The possible role of the vacancies on the uranium sublattice has already been mentioned. Another insufficiency is displayed in Figure 3 in which a com- parison is presented between the calculated and' observed upper phase boundary. The

discrepancy between the two could be associated with a dependence of cc,j_ on x as prescribed by equation (l4). An attempt at this has been made by Hagemark [20], who

has suggested that the occupation of a site of the type used in this model prevents

the occupation of the twelve nearest neighboring sites of the same type. Thus he

writes that

a

i = 1 + \2x. * ( 27 )

On the other hand, Thorn and Winslow [5] have argued that a.j_ =1 up to x ~ 0.08 and
that ctj_ then changes to the value 1/4, given by equation (27) at x = 0.25, already

at x ~ 0.12.

The information concerning ctj_ which has been revealed by the analysis effected

by Thorn and Winslow illustrates the value of an analysis based on the concepts introduced in Section 1A and IB given above, especially with respect to the suggested

molecular units. It is expected that extensions of the significance of a.j_(x,T) could

be accomplished through mechanisms for structural changes which have been proposed

by Rees [21] or via long range ordering parameters (See for example Elcock [22] and

Green and Hurst [23]). It is particularly the latter which we choose to associate

with the molecular units or domains. In further analyses of the situation in the

uranium dioxide phase , one would be guided by such observations as those by Willis [1].

The energies E^ and E

y are identified with the reactions

(0~ 2 is) + 2(U+5 cs) =* 0(g) + 2(U+

^cs) + is (28)

and

(0" 2as) + 2(u+5 cs) =» 0(g) + 2(U+

cs) + as . (29)

The values obtained for these reactions are plausible ones. One would expect the potential energy for an oxygen ion on an interstitial position to be smaller than that

for a vacancy. Further the values are ordered in the expected manner relative to 6. and 9 V

. The direct significances of the energies Ej_j_ and Evv , however, are not so

1 readily identified with the actual processes occurring. The formalism presented

herein suggests that the phases which separate out at the phase boundaries are as- semblages of di-defects, (0~^is)2 and asg- The real phases are U^Oq and U respectively. A more complete investigation of this situation is obviously needed in terms

of domains which can be made to approach more closely the real phases

3. Kinetics at Equilibrium. Self -Diffusion

A. Basic Elements

Thermodynamic formalisms have been developed for two general types of transport

processes. They can be identified as (1) the transport in systems at equilibrium

and (2) reversible, coupled transport in systems removed from equilibrium. In both

cases the basic equation,

ldE,PdV_V ^r ^r ,_n

» dt ~ T dt +

T dt / , T dt ^^v) r

is applicable. The restricting conditions in the two cases are that (l) there is no net entropy produced in the first and (2) there is in the second. The first category

can be identified as local thermodynamic equilibrium in the following sense: Each

local region is considered to be at equilibrium in that an equilibrium equation of

state can be written for it, and the unidirectional transport of entities from one region to another is calculated on the basis of an imagined unidirectional gradient

rather than a net gradient. The equal flux in the opposite direction is ignored.

Most of the theoretical treatments of transport properties are of this type, modified

to account for relaxation, coupling, etc. which are introduced essentially after the

derivations. Self -diffusion of atomic species in solids, however, approaches very

closely a situation corresponding to local thermodynamic equilibrium. Consequently,

the investigation of self -diffusion constitutes a useful basis for initiating studies

of the inter-relationships between thermodynamic properties and atomic transport.

One should be able to derive meaningful thermodynamic quantities from measurements

of self -diffusion.

The factors which are considered to be significant for such processes have

been discussed by Rice [24], among others. Thus he writes for the self -diffusion

coefficient the equation:

D = |z<i 2>ve

d (l-0 d

)e

£/RT

, (31)

in which Z is the number of neighbors in the shell contained in the diffusioncomplex-unit, <i 2> is the mean squared jump-distance from defect to defect, 0 d is

the concentration of the defects involved, v is the weighted mean frequency of

39
vibration of the shell surrounding the diffusing atom, and U. is the energy needed to

expand the shell sufficiently so that the atom can jump.

In the analysis [3] of the self-diffusion of oxygen in U02

, x

it has been assumed

that the defects involved are the oxygen ions on interstitial sires. Accordingly,

one can solve [3] the equations given above to obtain the expression

o (E -E. ), 1 r , ? 8qi _ v 1

1 /? 1 e

i - 5 {

x' + lx2+1ie rt ; 1/2

|

, (32)

an approximation which is sufficiently exact to be applicable In the case at hand.

In this equation the quantity q./q varies slowly with temperature.

B. Application to U0 2+x

In the case of the uranium dioxide phase, it is possible to evaluate all the

quantities except in equation (31) by measurements which do not involve selfdiffusion.

1. The quantity :Z/2) <i > was evaluated by assuming that a diffusing atom jumps from

one interstitial position to another in the adjacent unit cell through a chain of

atoms. This mechanism is suggested on the basis of Willis's analysis of the neutron

diffraction. One imagines that the oxygen ion on an interstitial position itself

cannot initiate the jump because either all possible adjacent positions are either

blocked or there are too few vacancies. If, however, one of the four atoms surrounding the vacant interstitial position in the adjacent unit cell moves into the center

of the fluorite cell, then a chain of events can occur in which the vacancy moves "backwards" into the interstitial position initially occupied by the extra oxygen ion.

From the geometrical arrangement one deduces that .Z/2) <^ > = 22.4 x 10 cm .

2. The analysis by Rice suggests that the weighted mean frequency is determined

principally by the highest lattice frequency. Accordingly, the highest value observed

in the inelastic scattering of neutrons [25] was selected for v. The value is

18. 10 12 sec

-1

.

3- The value for E

y

- and consequently were determined from the analysis of

the thermochemica 1 properties. E

v

- E^ = 40.7 kcal/mole.

4. The energy was evaluated from the measurements by Auakem and Belle [26] for

values of x sufficiently large that the term 8(q./q )e ^v-M J/ RTj_ n equation (32) was negligible. The result is 29-7 kcal/mole. 1 v

A comparison between the values for the self-diffusion coefficient of oxygen in U02+x

measured by Auskern and Belle and the curves calculated from the model described

above is given in Figure 4. The agreement between the two appears to be within the

experimental errors. More accurate measurements are needed to examine the model

further

.

To compare self-diffusion in the three substances, U0 2 , Th02

, [27] CaF2 , [28]

(Figure 4), one notes the following items: (l) The partial pressure of oxygen (or

fluorine) and the facility with which the composition can be changed are reflected

essentially in Ey and/or E^ which are measures of the energies involved between the

two valence-states, +4 and +5, according to equations (28) and (29). (2) The extent

of the homogeneous region is determined primarily by E. . and E y. (3) It is (Ev-E^)

which, especially near stoichiometry, reflects the equilibrium distribution of the

anion between lattice and interstitial sites. (4) The energy Ug is a measure, in part

at least, of the elastic moduli. The three substances certainly differ considerably

with respect to items (l) and (2). The valencies in excess of +4 for thorium and +2

for calcium occur at energies which are much larger than the +5 state for uranium.

The values for (E

v

-Ej_) in the three cases, however, need not be very different. In

the dynamics of the lattices, thoria and urania should- be quite similar. The investigations of Willis [16,29] have demonstrated that the same kinds of displacements

of the anions occur in all three substances. Willis has also obtained very nearly

the same Debye temperatures for the first two substances. Consequently, one surmises

that in stoichiometric uranium dioxide and thorium dioxide the energies involved in + 1/2(E -E^) are very nearly the same. The actually reported values, 65.3 kcal/

mole and 65.8 kcal/mole respectively, for the activation energy for self-diffusion

2 of oxygen do agree. But the reported pre-exponential factors, 1/2 x 10-3 and 4.4 cm /

sec respectively, do not agree. If, however, one considers the experimental errors

40
and the difficulties associated with the reactions at the surfaces when particles of

different sizes, 2.65 n and 34.5 n respectively, are employed, one surmises that the

self-diffusion of oxygen in the two substances is very nearly the same so that both

the energies and the entropies in the two cases are comparable. Calcium fluoride on the other hand, appears to differ from these two substances. But such is to be expected because not only is the displacement observed by Willis different for CaF2

, but

also the elastic constants for it are smaller than those reported for uranium dioxide.

It may be significant to compare the change in slope of log D vs T at about T = 10~3 for calcium fluoride with the analysis given herein. In the model, a similar

change is predicted for the following reason: At low temperatures and sufficiently

large values of x, the occupation of the interstitial positions is effectively saturated; in equation (32) this corresponds to the condition wherein x > (8q^/q ) exp

[ (-E +E1 )/RT] . At high temperatures the occupation is accomplished by thermally

shifting the equilibrium: (0" 2 as) + is -4 (0 _2 is) + as, and the situation tends to approach that for x = 0. Such may be the source of the change in slope for calcium

fluoride

Since nitrogen probably dissolves interstitially rather than substitutional^ in

uranium dioxide, one anticipates that its diffusion is determined principally by the

energies associated with the lattice dynamics. The value reported [30] for the diffusion of nitrogen is 33-4 kcal/mole. The solubility of nitrogen is probably relatively small so that the fraction of the interstitial sites occupied by nitrogen is

probably much smaller than the fraction occupied by oxygen at stoichiometry . Consequently, one expects the observed rate of diffusion to be much smaller.

A detailed application of the results of this study to the technological aspects

of the transport of material in urania is obviously not yet possible. Nevertheless,

these studies should help to explain some of the problems of a basic nature which

have arisen In attempts to understand the processes involved in sintering. As one example we cite the following -. "As the volume diffusion coefficient for anions and

cations generally differ, it has been normal to assume that the movement of the ion

having the lower diffusion coefficient would be rate controlling. This assumption

has led to serious discrepancies between theory and experiment, with sintering being

more rapid than would be predicted from measured diffusion coefficients". The

"final explanation of this puzzling discrepancy in apparent-diffusion coefficients is one of the most important problems in sintering theory today" [31,19]- The experimental results in the case of uranium dioxide consistently demonstrate that the sintering occurs at temperatures such that the self-diffusion of oxygen is measurable

but such that the self-diffusion of uranium is not detectable. The former occurs at

temperatures near 1000°K; the latter requires temperatures in excess of 23CO°K to be

measurable. Further, one observes experimentally that the rate of sintering increases

with increasing oxygen dissolved in the solid phase. We surmise therefore that the

fault lies with a theory in which it is assumed that the rate is controlled by the

ion which moves more slowly. If successive steps are involved, then the slower one

is determining. However, it appears doubtful that the process of sintering does involve successively the diffusion of oxygen and uranium or vice versa. Rather, the

two occur simultaneously in parallel so that only the more mobile ions need to move. In this respect the analysis of the process by the methods of non-equilibrium thermodynamics serves to establish the criterion which resolves the apparent discrepancy,

for the equations derived therein [3] enable one to predict that the chemical interdiffusion is determined by the self-diffusion process having the larger coefficient.

More precise measurements of the sintering process are needed particularly in the

compositional range extending from 0 to 0.03 for x. At the present time one can hardly justify stating [32] otherwise than that for the former composition a rather

large activation energy is required, perhaps as large as 76 kcal/mole and for the

latter composition a value near 39 ± 4 kcal/mole is indicated, and that these are

not in disagreement with the analysis presented herein.

Acknowledgements

The author wishes to acknowledge the typing of the manuscript by Marianne Ryan

and Myrna Biasing and the preparing of the drawings by Ruth Lang.

This work was performed under the auspices of the U. S. Atomic Energy

Commission

41
References

[I] B. T. M. Willis, Nature 197 , 755

(1963); J. Phys. 25, 431 (1964).

[2] R. J. Thorn and G. H. Winslow, Advances in High Temperature Chemistry,

L. Eyring, e'd . , Academic Press,

Inc., New York, to appear.

[3] R. J. Thorn and G. H. Winslow, pp. 213-239, Vol. II, Thermodynamics

with Emphasis on Nuclear Materials

and Atomic Transport in Solids,

International Atomic Energy Agency,

Vienna, 1966.

[4] L. Lynds, W. A. Young, J. S. Mohl,

and G. G. Libowitz, pp. 58-65, Nonstoichiometric Compounds, R. Ward,

ed., American Chemical Society,

Washington, D. C, 1963-

[5] R. J. Thorn and G. H. Winslow, J. Chem. Phys. 44, 2632 (1966)

.

[6] E. Aukrust, T. F^rland, and K. Hagemark, pp. 713-22, Thermodynamics

of Nuclear Material, International

Atomic Energy Agency, Vienna, 1962.

[7] R. J. Thorn, unpublished manuscript.

[8] M. Purbaix, Atlas d'Equilibres

Electrochemiques, Gauthier-Villa rs and C ie

, Paris, 1963.

[9] R. J. Ackermann, E. G. Rauh, R. J. Thorn, and M. C. Cannon, J. Phys.

Chem. 67, 762 (1961).

[10] R. J. Ackermann, M. S. Chandrasekhariah, E. G. Rauh, Argonne National

Laboratory Report, ANL-7048, 1965-

[II] L. M. Atlas and G. J. Schleman, pp. 407-421, Vol. II, Thermodynamics

with Emphasis on Nuclear Materials

and Atomic Transport in Solids,

International Atomic Energy Agency,

Vienna, 1966.

[12] R. E. Ferguson, E. D. Guth, and L. Eyring, J. Am. Chem. Soc . , 76, 389O

(1954).

[13] See R. H. Fowler and E. A. Guggenheim,

Statistical Thermodynamics, Cambridge University Press, London,

1939.

[14] H. Heitler, Ann. d. Phys. 80, 629

(1926).

[15] L. E. J. Roberts and A. J. Walter,

J. Inorg. Nucl. Chem. 22, 213

(1961).

[16] B. T. M. Willis, Proc. Roy. Soc.

(London) A27_4, 134 (1963).

[17] A. E. Martin and R. K. Edwards, J. Phys. Chem. 69, 1788 (1965).

[18] T. L. Markin and R. J. Bones, U. K. Atomic Energy Research Establishment, Harwell, Rept. R4178, Part

2 (1962).

[19] See also, "Thermodynamic and Transport Properties of Uranium Dioxide," Tech. Rept. Ser. No. 39,

International Atomic Energy

Agency, Vienna, 1965. This report

contains a summary of the known

properties of the uranium dioxide

phase

.

[20] K. Hagemark, Institutt for Atomenergi, Norway, Kjeller Rept.

KR-67, 1964.

[21] A. L. G. Rees, Trans. Faraday Soc.

50, 335 (1954).

[22] E. Elock, Order-Disorder Phenomena,

Metheun, London, 1956.

[23] H. S. Green and C. A. Hurst, Order

Disorder Phenomena, Interscience

Publishers, New York, 1964.

[24] S. A. Rice, Phys. Rev. 112, 804

(1958).

[25] G. Dolling, R. A. Crowley, and

A. D. B. Woods, Can. J. Phys. 43,

1397 (1965).

[26] A. B. Auskern and J. Belle, J. Nucl.

Mater. 3, 267 (l96l).

[27] H. S. Edwards, A. F. Rosenberg, and

J. T. Bittel, Wright-Patterson

Air Force Base, Ohio, Rept. ASDTDR-63-635 (1963).

[28] H. Matzke, J. Nucl. Mater. 11, 344

(1964).

[29] B. T. M. Willis, Acta Cryst. 18,

75 (1965).

[30] H. M. Ferrari, J. Nucl. Mater. 12,

142 (1964).

[31] J. E. .Burke and R. L. Colbe, p. 199,

Vol. 3, Progress in Ceramic Science, Pergamon Press, 1963-

[32] See I. Amato, R. L. Colombo, and

A. M. J. Protti, J. Nucl. Mater.

11 , 229 (1964).
TABLE 1. Comparison of valence-energies of some actinide elements

[Element Relative stabilities of valence states

In aqueous | solution

Individual

values

Relative

to U

(kcal/mole ) ! (kcal/mole)

Partial pressure of O2

for MO 's) at 1600°C

l. 1

Th -69 to

U 14 0

Np -4 18

Pu -22 36

Am -50 64

Pr -66 80

« 10"18 atmb -22 c 5 x 10 atm

7.1 x 10 11 atmd

» 1 atm

References for Table 1:

a 23[3E(M+3) - 4E(M+1+ )]; E is the electrode potential given by Purbaix [7], which

is the negative of the electrode potential commonly used in the U.S.A.

b Ackermann et al. [9].

c Ackermann et al. [10].

d Atlas and Schlehman [11].

e Ferguson, Guth, and Eyring [12]
o Reference II o Reference 12 n Reference 13

jt Reference 14

Figure 3. Comparison of the locations of

the upper-phase boundary that would be

calculated from this model, using various

value of a±, with observed boundary.

See Ref. 5

O.OI 0 0.01 0.02 0.03 0.04 0.05 0.06 0.0? 0.08 0.09 OIO Oil

Figure 1. Comparison of relative partial

molar free energy calculated at l400°C

with observation. See Ref. 5
Nuclear Fuel Materials

D. W. Readey and J. H. Handwerk

Argonne National Laboratories

Argonne , Illinois

Abstract

Selection of a nuclear fuel material is dependent upon many com- promises of material properties consistent with demands of the power generating system. Those properties which dictate the use of a given

material for specific systems such as thermal and fast reactors, nu- clear rocket engines, and direct conversion devices, are reviewed.

Materials of interest are uranium, plutonium and thorium and their

compounds either alone or combined with each other or with non-fissile

materials. Technology at the present time is directed toward the utilization of primarily the oxides and carbides of fissile metals.

However, their nitrides, sulfides, and phosphides show promise as potential fuel materials but the properties of these compounds must

be more fully delineated before they can be considered for fuel pur- poses .

*5
Nuclear Fuel Materials

D, W. Readey and J. H. Handwerk

1. Introduction

Ceramic materials possess certain properties which make them attractive as fuel materials for nu- clear power generating systems. However, it should be pointed out at the outset that ceramics are not

the only materials being considered. On the contrary, the state of the art of reactor design is con- stantly changing and other fuels under consideration are: solid and liquid metals, molten salts, solu- tions, slurries, and even gases. Each of the reactor design concepts, utilizing the different fuel

types, has certain aspects which make some fuels more attractive than others.

To emphasize the property requirements for a nuclear fuel material, a summary of the physics, operation, and the environment encountered in nuclear power generating systems is presented. The properties

and the behavior in the reactor environment of some of the more important ceramic fuel materials is com- pared. In general, those aspects of material-environment interactions peculiar to a nuclear power gen- erating system are emphasized. Finally, the behavior of the actinide compounds which makes them interesting purely as materials is discussed. Throughout, the intent is not to give an exhaustive survey of all the design-environment-materials interactions but to emphasize the unique aspects of ceramic nuclear

fuel materials.

2. Nuclear Power Generating Systems

2.1. The Fission Process

When a fissionable nucleus, such as undergoes fission after absorption of a neutron, two new

nuclei are formed as fission products whose atomic weights are roughly half that of the fissioning nu- cleus. In addition, two or three neutrons, neutrinos, and p and y radiation are emitted with a total energy of some 205 MeV. About seventy percent of the energy is released as kinetic energy of the fission product nuclei which quickly dissipate their energy within a few microns. This large release of energy as heat in a small volume causes a great deal of radiation damage to the crystal lattice. To illustrate the magnitude of energy liberated, the fissioning of one gram of U

2 35 produces about one meg- awatt day of available energy [l].^

As the process proceeds, the fission products accumulate in the fuel and affect its properties.

Figure 1 gives a typical distribution of the yield of fission products from U235, which consist mainly

of Kr. Xe, Sr. Ba, Cs, I, Te, Zr, Mo, Ru, Ce and Nd [2].

2.2. Reactor Physics

In order for the process to continue, the neutrons released from a fissioning nucleus must be cap- tured by other nuclei which subsequently fission, and so on, creating a "chain reaction". However, if the neutrons produced do not produce further fissions, the chain reaction and heat generation ceases. Neutrons can be lost from the fission process either by leakage from the reactor core (that part of the reactor containing the fissionable material), or by capture by non-fissionable nuclei. To help reduce

the loss by leakage, a "reflector" material containing atoms of low atomic weight reflects neutrons back into the core via elastic nuclear collisions. To prevent loss by capture in non-fissionable nu- clei, structural materials are utilized in the core which have low capture cross sections (a measure

of the ability of a given nucleus to undergo the process in question) for neutrons. Therefore, a chain

reaction will be maintained only if the rate of neutron production equals the rate of leakage plus the rate of absorption. To maintain a steady state of neutron production and loss, materials which easily

absorb neutrons are inserted into the core via "control rods". Thus, a nuclear reactor can be defined

simply as an assembly of fissionable material arranged in such a way that a chain reaction is sustained

under control [l].

The neutrons emitted from a fissioning ^35 nucleus have mean energies of about 2 MeV. The cross section of U235 for fission is about 1.59 barns (l barn ~ 10~2^cm2

). Under these conditions, the critical mass (the minimum amount of fissionable material necessary for the sustained chain reaction) of pure

U235 metal is about 20 kg. However, for neutron energies on the order of thermal energy (0.025 eV), the fission cross section is 582 barns. To reduce neutron energies, "moderators" are used. These are

Figures in brackets indicate the literature references at the end of this paper.

46
materials which contain light nuclei and have lov capture cross sections which quickly reduce neutrons

to thermal energies by elastic collisions. The most efficient moderator is hydrogen. To illustrate the saving in the amount of fissionable material when thermal neutrons are utilized, which is of importance

from an engineering and economic standpoint, only about 0.8 kg. of 1)235 is sufficient for a critical

mass in a fully moderated and reflected U^S-HgO system [h]

From these considerations the origin of the terms "fast" and "thermal" reactors is obvious. A fast

reactor is one in which the neutrons are not moderated and have energies on the order of one MeV, whereas, a thermal reactor utilizes neutrons whose riean energies are on the order of 0.025 eV.

2.3- Reactor Sngineering

2.3.1. General

Regardless of the nuclear power generating system, be it a turbine, rocket engine, thermionic, or thermoelectric device, the primary objective is to extract heat from the fission process to produce

power. In the case of thermionic and thermoelectric systems, the heat is used directly for the generation of electricity. In a rocket propulsion system, the heat is transferred to the propellant gas which

doubles as the reactor coolant. However, the most common use of nuclear power is to heat a coolant me- dium from which the heat is extracted and used to operate a steam turbine for the generation of electrical power. A schematic diagram of a typical system of the latter type is shown in Figure 2. Since the reserves of fossil fuel are rapidly becoming depleted, there is no longer any question that electrical

power generation by nuclear energy is economically competitive. It is estimated that by I98O as much as 60,000 megawatts of electricity will be produced by nuclear power in the U. S. compared with only a few

thousand today [5]. By the year 2000, fully half the electrical power will be derived from the nucleus.

2.3-2. Breeding Fissionable Material

Although fossil fuel reserves are decreasing, the supply of readily fissionable isotopes present in the earth's crust is quite limited. In fact, rj235 i s unique, and its abundance is only 0.7% of all the naturally occurring uranium, with U238 comprising 99.2+%. Thus, if U

2 35 were the only fissionable isotope, there would be little hope for any long range economical power generation by nuclear fission.

However, two other fissionable isotopes, Pu239 and U233, can be produced from the relatively abundant

L'23o an(j Th232 ^y the following reactions:

U238 + n

l _ ^39 23 min

Hi + n Th233 23 min

Nr,239 + S" 2.3 days

Pa'2 33 + f

27 days

238 232 In this context, U and Th are referred to as "fertile" isotopes.

Since several neutrons are given off during each fission event and one of these is required to maintain the fission chain reaction, there are neutrons remaining which can produce other fissionable

nuclei by one of the above reactions. More specifically, the number of neutrons, T], emitted per neutron absorbed by the fissioning nucleus is given by: [6]

Pu239 + p

-

(1)

U'233

p

•n =

1 +

(2)

where n is the number of neutrons released during fission, and a and a are the cross sections of the fissile nucleus for capture and fission, respectively. Therefore, Tl-1 neutrons are available for

breeding. Table 1 compares the "H-l values for the three common fissile isotopes for both fast and thermal neutrons.

Since ten percent or more of the neutrons are lost via leakage or absorption, it is apparent that

only with fast reactors is it possible to breed more fissionable material than is consumed, the one possible exception is that of a u233_fueie a thermal reactor, which is marginal. There is another benefit to be gained from fast breeder reactors, namely, Tj23o an(j Th232 are more readily fissionable by

fast neutrons and contribute up to 25 percent of the power produced in a fast reactor compared to two percent for a thermal reactor. This enhanced fissioning and power generation is called "fast fission

bonus" [6]

47
TABLE 1. Neutrons Available for Breeding from U

23

^, Pu239 and U233

[6]

u

235 Pu239 u

233

Thermal Fast Thermal Fast Thermal Fast

n 2.J+7 2.51 2.91 2.97 2.51 2.55

0"^(barns ) 582 1-59 1.83 527 2.37

a (barns)

c 112 0.32 280 0.32 5^ 0.20

0.19 0.2 0.375 0.18 0.102 O.O85

H-i 1.07 1.09 1.12 1.53 1.28 1-35

Thus, for maximum utilization of the world's potential fissionable power resources, fast breeder

reactors are mandatory. At the present time, the Pu239_u23o cvc ie is economically preferable to the U233-Th232 cycle because of its higher breeding ratio, higher fast fission bonus, and smaller critical

mass requirements ["]]. However, future power needs can make the u233_Th232 CyCle economically feasible.

Ultimately, fast breeder reactors will also become economically more favorable than thermal reac- tors because of the value of the fissionable material produced. However, most of the reactors existing

and being built today are of the thermal type primarily because of the smaller fissionable material

requirements, and subsequent reactor size and cost, for a given power rating.

2.3.3- Reactor Operation, Environment and Fuel Materials

To economize on the size and cost of the reactor core, it is desirable to use fuel materials which

have a high fissile and fertile atom density. This is particularly true for fast reactors, such as a rocket engine, since the critical mass required is larger because of the smaller fission cross sections.

Also, the other nuclei or atoms in the reactor core, be they in the moderator, coolant, fuel or struc- tural members, should have a low neutron absorption cross section, again to economize on the critical

mass and size of the core.

The coolant in a power reactor extracts the heat generated in the fission process. In thermal re- actors the usual coolants are ordinary and heavy water, which also double as moderators, and CO2 gas

(in conjunction with graphite as moderator). For fast reactors, a non-moderating coolant with excellent heat transfer characteristics is required, hence, liquid sodium is most commonly used. To prevent

corrosion of the fuel material and release of radioactivity into the coolant, the fuel is normally en- cased in a cladding. The combination of fuel-cladding is usually referred to as the "fuel rod or plate". The common cladding materials, chosen because of their corrosion resistance and neutron trans- parency, are aluminum, magnesium, zirconium alloys, and stainless steels. A cladding and fuel combination must be selected to minimize reaction between them to prevent cladding failure, and release of radioactive material into the coolant. In spite of the cladding, it is still desirable to use a fuel

which reacts as little as possible with the coolant medium in case of cladding failure.

Coolant temperatures are usually limited to only a few hundred degrees centigrade because of struc- tural strength and corrosion problems. Therefore, to extract the maximum heat flux from a reactor, a large thermal gradient must exist within fuel rods. These gradients may be as high as 1000°c/cm for

some ceramic fuels. Hence, a high melting point and good thermal conductivity are of paramount impor- tance for a fuel material.

As the reactor operates, fission product accumulation, thermal cycling, and prolonged operation in the steep thermal gradient change the overall properties of fuel rods. This limits the amount of "burnup", or the amount of fission energy available in the fuel material actually used (commonly expressed in megawatt days per metric ton of fuel) before it must be removed from the reactor core. Since fuel cost

is an appreciable part of the cost of the power, generally the higher burnup, the lower the fuel cost. In fact, fuel costs decrease inversely proportional to burnup [8].

3. Properties of Ceramic Fuel Materials

3.1. General

Although ceramics possess many of the desired properties for a fuel, this does not necessarily im- ply that the fuel will be a massive, dense body. In some instances, this is the case, but in others the

46
ceramic is dispersed in a matrix of a metal or graphite or even another ceramic to give the overall fuel

rod improved properties, such as higher thermal or electrical conductivity, or lower work function. Also,

instead of relatively large dense pieces of fuel, some reactor designs utilize small, loosely compacted

particles to permit easy release of gaseous fission products. Therefore, it is difficult to generalize

processing and properties because of the multiplicity of reactor design concepts. Hence, an attempt will

be made to discuss only those processing techniques and properties which are unique to ceramic nuclear

fuel and are of reasonably general applicability.

From what has preceded, it is obvious that a nuclear fuel material must contain a certain percentage of the fissionable isotopes, U233, u

2 35, or Pu239. Usually about two percent is required for thermal reactors and about twenty percent or more for fast reactors with the rest the fertile lj23d and

Since the Pu239_ij23o "breeding cycle is presently of greatest interest, and plutonium is normally present

in minor concentrations, the discussion of properties will be concerned primarily with the uranium com- pounds. This is not to say that the properties of the other actinide compounds and their combination

with uranium compounds are not of interest. However, their properties and behavior are, in many re- spects, quite similar to those of the uranium compounds. Therefore, the uranium compounds are convenient vehicles for discussion and have also been the most thoroughly investigated.

3.2. Processing and Reprocessing

Some of the processing techniques utilized for ceramic nuclear fuels are quite conventional such as cold pressing and sintering. Others, such as arc melting and casting, are more unusual. Still others,

such as pyrolytic graphite coating of fuel particles, are exotic. However, there are two areas peculiar

to nuclear fuel materials worthy of special note: these are, (l) reprocessing the spent fuel to re- trieve unused and bred fuel, and (2) nuclear safety.

3.2.1. Reprocessing

Normally, less than ten atomic percent burnup (equivalent to about 100,000 MWD/metric ton) can be

sustained before a fuel rod must be removed from a reactor core because of degradation of its properties. To achieve maximum utilization, the unused and bred fissionable materials must be separated from the fission products and refabricated into new fuel rods. Many of the fission products are highly radioactive (the higher the burnup, the greater the radioactivity). Thus, reprocessing must wait until the

activity subsides or be carried out in a shielded, remote facility, which is an expensive operation.

Since fuel cost represents a sizeable fraction of the operating expenditures for a nuclear reactor, the expense of a remote reprocessing facility may override the cost of the large fuel inventory necessary

if conventional facilities are used. Such a remote reprocessing facility is shown in Figure 3- This

particular facility has been designed for reprocessing the metallic fuels for the EBR-II reactor. Re- processing of ceramic fuel materials is still in its infancy. Nevertheless, the ease of inexpensive

reprocessing is an important consideration in the selection of a fuel material for a given reactor application. Some of the reprocessing separation techniques under consideration are: solvent, extraction;

oxidation-reduction to remove volatile fission product oxides; vaporization of volatile actinide metal

chlorides and fluorides.

3.2.2. Nuclear Safety

During both processing and reprocessing fuel materials, there are two everpresent safety hazards:

(l) criticality, and (2) alpha particle activity of fissile and fertile nuclei.

235 o ,235 With regard to criticality, about 20 kg. of pure U metal and 0.8 kg. of IT in water, and even

less for Pu2 39 and U233, are necessary for a critical mass. Therefore, in any operation where there is any possibility, either intentional or accidental, of the fissionable material becoming intimately mixed

with a good moderator, such as water, a total amount of fissionable material considerably less than a critical mass must be used. This limits handling and storing procedures to relatively small quantities

of material, makes continuous processes difficult, and requires strict control, all of which contribute

to the expense of fissionable material.

All the common isotopes of uranium, thorium, and plutonium undergo radioactive decay by alpha emission, and to a much lesser extent, by spontaneous fission. Alpha particles are strongly absorbed by

most materials and can easily be protected against. However, since they are strongly absorbed, causing

a great deal of damage to the absorbing material, alpha emitters are particularly dangerous if they enter the human body. Uranium, plutonium and thorium compounds tend to concentrate in bone material

and. as a result, their maximum permissible body burden is set at a few tenths of a microcurie (l curie

= 3-7 x 10^0 disintegration/sec ) [9]. For most of the isotopes in question, this amounts to a few hundredths of a gram total body burden. However. Pu239 and u233 have much shorter half lives, and the per- missible body burden for them is only about 0.1 microgram. Therefore, much more stringent precautions

against inhalation, ingestion, and entrance through the skin must be taken and, as a result, work with

these isotopes must be carried out in gloveboxes. A typical glovebox enclosure for plutonium work is shown in Figure k. Gloveboxes give an added advantage in that many fuel materials react strongly with

air and atmospheric moisture and with an inert, dry atmosphere in the glovebox, oxidation and hydration

can be minimized.

49
3.3» Materials and Properties

3.3-1- General

Table 2 lists the properties of several uranium compounds -which are of primary interest for fuel

application. The list is by no means complete and is only meant to serve as an illustration of some materials being given major consideration and of representative property values. Other compounds such as aluminides, silic ides and beryllides are not listed since they are generally being given less attention,

and although the dicarbide is being considered for a dispersed fuel because of its compatibility with

graphite, it is not listed. The primary purpose of the list is to compare the properties of the oxide, UO , with the compounds having the sodium chloride structure.

TABLE 2. Typical Properties of Selected Uranium Compounds

(all values at room temperature unless specified)

U0

2 uc UN US UP

Crystal Structure CaF

2 NaCl NaCl NaCl NaCl

Density (gm/cc) 10. 96 [11]* 13. 63 [16] 14. 32 [11] 10.84[24] 10, 23 [24]

Uranium Density (gm/cc) 9.66 12.97 13.52 9-57 9.07

o" , thermal for second element

( barns

)

0.0002 0.0033 1.88 0.52 0.20

Lattice Parameter (A) 5A7I11] U.96D.6] 4.88[l6] 5-49f24] 5-59f24]

Melting Point (°C) 2730[10] 2500 [17] 2750[l4] 2450 [2k] 2240 [24]

Thermal Conductivity

(cal cm-1sec-l°C-1 ) 0.018-0. 028 [11] 0.05 [17] 0.035 [22] 0.026 [2k] 0.032 [24]

Electrical Resistivity (u.Q-cra) ~10n[l3] 70[l8] 160 [22] 179 [28] 325 [24]

-AFlog (kcal/mole) [14] 264. 6 24. 5 74.3 98.6 67[29]

Vapor Fressure (atm at 2000°K) ~10" 7 [12] ~io-10

[i9 ] ~10

_1+ [23] ~10

-8

[25] ~10" 6[29]

Thermal Expansion Coefficient

(io-6-c-i) 10.5D.3] 11.1 [19] 9-5 [22] 11.6[24] 8.6[27]

Young's Modulus (lO^psi) 31 [15] 30. 4 [20] 31 [11] 2k.2[26] 25.6[26]

Modulus of Rupture (psi) ~11,000[13] -15. 000 [21] Ik, 000 [26] 17,000[26]

Poisson's Ratio 0.30(15] 0.28M20] O.lfll]

*Reference

3-3«2. Nuclear Properties

A high uranium density is desirable for a reactor system so that the reactor core size and cost can be minimized. It is particularly important for fast breeder reactors in which neutron conserva- tion is important. Therefore, from this standpoint, UC and UN are most desirable for fast, reactor applications.

The other parameter which concerns the nuclear properties of these compounds is the thermal neu- tron absorption cross section, a , (thermal), for the second element. For a thermal reactor, one would

like this to be as small as pos sfble, for neutron economy. In this case, U02 and UC are the most

favorable, whereas, UN is the least. For fast reactors, this is of less importance because the differences in the cross sections decrease with neutron energy.

3 • 3 • 3 • Thermal and Chemical Stability

As was stated earlier, a high melting point is desirable in a fuel material in order to obtain a

50
large heat flux from the fuel element. All of the compounds in Table 2 have sufficiently high melting

points to be of interest as reactor fuels. In most cases, it is undesirable for melting to occur in the

fuel material for essentially two reasons. First, the major fraction of the fission products are gaseous

at these temperatures and melting releases the gases which had been trapped in the solid fuel, either as bubbles or in solid solution. Second, there is usually a significant volume change which takes place on melting which may cause swelling or even rupture of the cladding material. These problems, however, can be circumvented by leaving a certain amount of void volume within the fuel element to allow for fission

gas release and volume changes due to melting [30].

All of the compounds listed have sufficiently low vapor pressures at elevated temperature with, perhaps, the exception of UN. Naturally, the vapor pressure must be low to prevent swelling and rupture of the cladding material. Of course, this only becomes significant near atmospheric pressure. A low vapor pressure, however, is also desirable to prevent relocation of the fuel material within the

fuel element via an evaporation-condensation process under the influence of the steep thermal gradient.

Migration and segregation of fission products and fissile and fertile materials can also take place

by solid state diffusion and gas bubble migration under the influence of the temperature gradient [31]

This segregation of constituents can change considerably the overall properties of a fuel rod. One of the interesting effects of the temperature gradient extant in fuel materials is the observation of the

so-called "amoeba" effect [32]. For certain reactor designs, carbon-coated (to retain fission products)

UCg particles are dispersed in a graphite matrix. Under the influence of the temperature gradient, UCg

dissolves more carbon on the high temperature side of the particles and precipitates it on the cooler

side. As a result, the UCg migrates out of the carbon coating, up the temperature gradient, with a re- sulting microstructure which looks strikingly like an amoeba.

Compatibility between the fuel and cladding materials and corrosion resistance of the fuel in the

coolant medium if the cladding material should fail are also important. A complicating factor is that most of the ceramic fuels exhibit wide ranges of stoichiometry. Thus, the reactivity of the cladding

and coolant with the fuel depends strongly on fuel composition. As an example of the range of stoichiometry these materials can sustain, UOg has long been known to exist as a single phase up to about

UO2.25 above 1000°C [33]. Recently, however, it has been shown that UO2 may become hypostoichiometric

at temperatures above 1500°C and the single phase region extends down as far as UO^^g^ at 2l400°C [3^].

Figure 5 [35] gives the phase diagram of the plutonium-carbon system as a typical example of the non- stoichiometry range in the sodium chloride structure compounds.

Another factor worth noting is that accumulated fission products may change the activity of oxygen

or carbon, for example, in the fuel material and alter the compatibility and corrosion characteristics

of the fuel [36].

Therefore, the reactivity of a fuel material with its cladding and collant are dependent on a num- ber of variables which include temperature, composition of fuel, cladding and coolant, and burnup . Com- patibility of fuel and matrix materials is also an important consideration for dispersion type fuel

elements with matrices such as the graphite used in a nuclear rocket engine [37] and the tungsten considered for thermionic emission. [38] The very large number of possible combinations of materials, com- positions and environments precludes any detailed discussion of compatibility and corrosion. However,

the following somewhat limited observations can be made. Uranium dioxide is far less reactive in air,

water, steam and CO2 than are the non-oxides. [39] Therefore, the oxide is a good choice for thermal reactors which are generally water cooled. On the other hand, uranium carbide is relatively stable in

liquid sodium but its corrosion rate is strongly dependent on the oxygen content of the liquid metal. [39]

Also, if the carbide contains any excess carbon or the chemical activity of the carbon is high, there can be compatibility problems with carbide-forming cladding materials such as stainless steels and zirconium alloys.

3.3. h. Thermal Properties

3.3. 1+-1. Thermal Conductivity

As was pointed out earlier, all else being equal, the higher the heat flux from a fuel rod, the higher the power rating of the reactor. Therefore, the thermal conductivity of the fuel material is a property of primary importance. From Table 2 it is seen that UO2 has the lowest thermal conductivity

of all the compounds listed. Therefore, the higher the desired heat flux, as in a fast reactor, the less

desirable UO2 becomes compared to the other compounds.

The reason for the higher thermal conductivity of the sodium chloride structure compounds is that a

large fraction of heat is transported by electrons, whereas, thermal transport in UO2 is entirely by

phonons. Since the atomic weights of the metal and non-metal atoms in the actinide compounds are greatly

different, phonon conductivity is low because of the anharmonicity of the lattice vibrations [hO] . Figure 6 compares the thermal conductivity of UC with UO2 [ 21] . The electronic contribution to the thermal

conductivity for UC, kg

, was calculated from measured values of the electrical resistivity [21] with the

Wiedemann-Franz law,

51
where L is the Lorentz number, (L = 5.72 x 10 if k is in cal cm sec °C , T in °K, and p in ohmcm) T is the absolute temperature and, p, the electrical resistivity. It is seen that the phonon contribution to the thermal conductivity of UC is close to that for UO- and decreases with increasing temperature due to phonon-phonon scattering. Eventually, at some higher temperature, the electronic contribution will, for all practical purposes, equal the total thermal conductivity. For the other sodium chlo- ride type compounds, such as UN, [22] the behavior is similar. However, for UN, the total thermal con- ductivity increases with temperature parallel to the electronic contribution. This implies that the phonon contribution, which is larger for UN, is relatively insensitive to temperature. This behavior

parallels that of the transition metal monocarbides and nitrides which has recently been summarized by

Williams. [41] Williams explains the insensitivity of the phonon contribution by phonon scattering from

lattice defects, electrons and possible magnetic disorder on the metal sublattice. However, at higher

temperatures, the phonon contribution should be expected to decrease since phonon-phonon scattering will

eventually limit the phonon mean free path in the lattice.

Since solid fuel materials are generally polycrystalline bodies, there are interesting microstructural changes which have been observed to take place during operation with the steep temperature gradient.

These changes significantly affect the overall thermal conductivity of the fuel elements. For example,

the gaseous fission products produce lenticular voids in U02, [30] with their short axes parallel to the

direction of the heat flux. These voids are very effective in reducing the thermal conductivity. On the

other hand, due to the migration of these voids up the thermal gradient, large columnar grains are formed [30] in UOg whose long axes are parallel to the direction of the heat flux. Figure J [k2] shows an example of this columnar grain growth in UOo- It has been shown that photon conduction becomes the

primary heat transfer process in single crystal UO2 at temperatures above 1000°C [hj>]. Hence, it would

be expected that the columnar grain structure would behave similarly to single crystal UO2 and the ther- mal conductivity would increase at elevated temperatures. Whether or not this actually occurs is still open to question. [30]

Figure 8 [hk] is an example of some of the micro- and macro- structural changes which take place

during irradiation and illustrates the effect of increasing the overall thermal conductivity of the fuel material. Note the columnar grain growth and the large central void formation in the sample on the left. The central void has been formed by the migration of fission gas bubbles up the teiaperature gradient.

In both cases, there is severe cracking of the fuel material with penetration of the lead bonding

(light phase) into the cracks.

3.3-^.2. Thermal Shock Resistance

During the operation of a reactor, the fuel material is subjected to thermal cycling and thermal

shock resistance is important to inhibit cracking and disintegration of the fuel. Cracking and disintegration is undesirable because: (l) a redistribution of fuel material may occur producing swelling or rupture of the cladding; (2) the surface area of the fuel increases, enhancing the release of gaseous fission products; and (3) the overall thermal conductivity of the fuel element decreases.

If the thermal stress resistance, R, is defined as: [hO]

k S (1-uO

where, k = thermal conductivity

S = fracture strength

(j, = Poisson's ratio

E = Young's modulus

cc = thermal expansion coefficient

then roughly speaking UO2 should exhibit the lowest thermal shock resistance of all materials listed in Table II becau se , while all other, parameters are similar, the thermal conductivity is lowest for UO 2

• However, several of these properties such as S are strongly dependent upon microstructure , which varies

with operating conditions, hence it is difficult to make predictions as to the thermal shock resistance

of a given material under the environmental conditions present during reactor operation.

3.3- 5. Mechanical Properties

As was pointed out above, there is little difference in the room temperature mechanical properties

52
of these compounds and they depend strongly on microstructure. The creep behavior of fuel materials at elevated temperature is of importance since the pressure of fission product gases in voids can cause de- formation of the fuel and concomitant swelling and possible rupture of the cladding. Here again, creep

rate depends greatly on the microstructure and its changes within the reactor environment.

The creep rate is also dependent on composition. For example, the creep rate of UO2 increases with

increasing hyperstoichiometry while the activation energy decreases [h$] . There is a reasonable correlation between the activation energies for creep and for uranium self diffusion in U02- Hence, on this

basis and the fact that the strain rate is linear with stress, creep in UO2 has been associated with the

Nabarro-Herring mechanism. Recent constant strain rate experiments [26] on U02 have shown the nucleation and growth of grain boundary voids in tensile regions. This behavior is consistent with the NabarroHerring diffusional creep mechanism.

For the sodium chloride compounds, the slip system is the same as the fee metals, (ill) <110>, but

slip is an activated process and apparently only slightly dependent on stoichiometry [21]. Creep in UC,

[21,1)6] UN, [k6] US and UP [26] is probably limited by an activated nonconservative dislocation motion

[21] but the situation is not at all clear at the present.

3.3.6. Electrical Properties

The electrical properties of fuel materials are of primary importance when being used in a thermionic power system. Here, a high electrical conductivity and low work function are necessary. However, any deficiencies can be circumvented by dispersing the fuel in a matrix possessing the desired properties

such as tungsten.

k. Bonding and Electronic Structure

In this section a short discussion of the defect and electronic structure, and the bonding of the actinide nuclear fuel compounds will be given, again concentrating on the compounds of uranium as being

representative. As will be seen, the situation is quite complex, and due to the lack of sufficient

experimental and theoretical information, much of the discussion is tentative and even speculative.

The type of bonding in the actinide compounds is doubtless complex since it involves combinations

of s, d and f electrons of the metal and s and p electrons of the nonmetal. The number of valence electrons available varies from eight for ThC to fourteen for PuS. The type of bonding certainly affects

the electrical and magnetic properties, the defect structure and degree of nonstoichiometry in these

compounds

h. 1. Dioxides

The dioxides are different from the sodium chloride type compounds in that they have high room tem- perature electrical resistivities and are semiconductors, that is, they possess a positive temperature

coefficient of resistivity. Uranium dioxide exhibits both hyper- and hypostoichiometric deviations from

the ideal UO2.00 composition. Neutron diffraction results indicate that hyperstoichiometric VOq contains oxygen interstitials P+7] • No information is available concerning the defect structure of hypostoichiometric U02- A recent study of electrical conductivity and Hall mobility concludes that electronic con- duction in U02

tallies place by a "hopping electron" or small polaron mechanism [h8]. It should also be

pointed out that UO2 undergoes an antiferromagnetic transition at 28°K [^9].

Plutonium dioxide is known to deviate only hypostoichiometr ically from the ideal Pu02 composition.

In this case, the electrical properties and stoichiometry changes are consistent with a hopping electron

mechanism and oxygen vacancies in the lattice [50].

In many respects, the dioxides behave quite similarly to the semiconducting transition metal oxides

such as NiO and TiC>2, etc. and, hence, their bonding can be considered to be a mixture of covalent and,

primarily, ionic.

k. 2. Sodium Chloride Type Compounds

The NaCl type compounds, in general, exhibit semimetallic behavior in that they have positive tem- perature coefficients of resistance and high room temperature resistivities. In this respect, they are

quite similar to the transition metal monocarbides and nitrides such as TiC and TiN. Certainly, the bond type in these compounds is not at all clear. In Table 3 are listed observed and calculated lattice

parameters. From this table, it appears that US can be considered either covalent or ionic whereas the carbides definitely appear to be more covalent. That a certain degree of covalent bonding exists in

these compounds is evidenced by their magnetic transitions. Table k lists the known magnetic transitions of the uranium compounds.

Another indication of the bond type and similarity to the transition metal monocarbides and nitrides

is the deformation behavior of these compounds. For example, it has been shown that the slip system of UC at high temperatures is (ill), <110> [21] which is the same as the transition metal compounds but

55
TABLE 3 • Calculated and Observed Lattice Parameters of NaCl-Type Compounds

Covalent [51] Ionic [52]

Metal Non- metal

Observed

Lattice

Parameter

(A)

Metal

Radius

(A)

Non- metal

Radius

(A)

Calculated

Lattice

Parameter

(A)

a /a

0' c

Cation

Radius

(A)

Anion

Radius

(A)

Calculated

Lattice Parameter

(a)

a /a

0' c

Th

UPu

S

S

S

5.68

5.^9

5-5^

1.80

1.55

1.53(a)

1.03

1.03

1.03

5.66

5.16

5-12

1.004 I.06

1.06

0.99

0.93

1.8k

1.8k

5.11

5-5>+

1.112 0.990

Th

U

Pu

NN

N

5.16

k.89

it. 91

1.80

1.55

1.53(a)

0.71

0.71

0.71

5.02 4.52

k.k8

1.03

1.08

1.09

0.99

0.93

1.71

1.71

5 AO

5.28

0.955

0.925

Th

U

Pu

PP

P

5.82

5-59

5.67

1.80

1-55

1.53(a)

0.93

0.93

0.93

5.U6 k.96

k.92

1.05

1.13

1.15

0.99

0.93

2.12

2.12

6.22

6.10

0.938

0.918

Th

UPu

C

C

c

5-3^

k.96

h.97

1.80

1.55

1.53(a)

0.77

0.77

0.77

5.1k

k.6k

k.6o

i.bk

1.07

1.08

0.99

0.93

2.60

2.60

7.18

7.06

0.71+3 0.705

TABLE k. Magnetic Transitions of Uranium Compounds

C ompound Transition Type Temperature (°K) Reference

US ferromagnetic 178 52

UN ant iferromagnetic 50 53

UP antiferromagnetic 130 52

UC none

quite different from the (110), <110> glide in the alkali halides [5k].

Although information on the defect structure of these compounds when they deviate from stoichiometry is lacking, it is generally felt that hypostoichiometry implies nonmetal vacancies and hyperstoich

iometry. nonmetal Interstitials

.

In order to relate nonstoichiometry and electrical properties to bonding in these materials, it is tempting to carry the analogy between the actinide and transition metal sodium chloride compounds further. For example, Denker [55] discusses the nonstoichiometry and defect structure of TiC, TiN and T10

on the basis of an electronic density of states curve vhich contains both bonding and antibonding over- lapping bands. His argument is essentially as follows. Titanium monoxide exhibits a wide range of

stoichiometry from Ti0n.8 to Ti01.2- At stoichiometry, both the titanium and oxygen sublattices have

about fifteen percent vacant sites and, throughout the range of composition, the number of valence

electrons per titanium site always remains about 8.5. Stoichiometric TiO would have ten valence elec- trons per metal atom site, four from titanium and six from the oxygen. A density of states curve similar to that considered by Denker is shown in Figure 9- To arrive at this type of density of states

curve, ionic and covalent bonding between metal and nonmetal were considered as well as covalent interaction between metal-metal and nonmetal-nonmetal atoms. Below the minimum in the density of states

5k
curve, the electronic levels are largely all bonding levels whereas above the minimum, they are largely

antibonding . If all the lattice sites were filled in the stoichiometric TiO, the Fermi level would

occur at the indicated position deep within the antibonding band. Therefore, to stabilize the rock salt structure, about fifteen percent vacancies are permitted, dropping the Fermi level down to about the minimum in the density of states curve, near the bottom of the antibonding band, a decrease in the free

energy of about 1.75 eV per molecule or 40.3 kCal per mole of TiO. Denker then calculates that the energy to form fifteen percent vacancies is about 0.62 eV per molecule or 14.4 kCal per mole of TiO.

Hence, the sodium chloride structure can be stabilized and the free energy at absolute zero lowered by

a net of about 1.1 eV per molecule or 25.9 kCal per mole if fifteen percent vacancies are allowed to exist in the structure.

Denker also points out that for TiC, the bonding band is not quite filled. Therefore, he postulates, that increasing the number of valence electrons by adding TiN in solid solution to fill the bonding band, will produce a material with the highest stability and melting point in the TiC-TiN system.

It is interesting to speculate that similar occurrences for the actinide metal compounds are pos- sible since their behavior parallels the transition metal compounds in so many other ways. Postulating

a density of states curve for these materials, similar to that in Figure 9, it would no doubt be even

more complex because of the f electron contributions. Also, the number of valence electrons can vary from eight for ThC to fourteen for PuS . Therefore, with this type of model and the large variation in

the number of valence electrons in these compounds, a number of interesting possibilities arise.

1. Widely varying degree of nonstoichiometry from compound to compound,

2. large defect concentrations on both sublattices near stoichiometry

3. possibility of semiconductivity where bands do not overlap and the lower ones are filled,

4. wide variations in stability, deviations from stoichiometry and electrical properties with

solid solution.

Evidence that the actinide compounds behave in this manner is shown by the maxima in melting points

found in the UP-US [24] and UC-US [56] systems in line with Denker's suggestion of maximum stability

with filled bonding bands.

5. Conclusion

Nuclear ceramic fuel materials have certain desirable properties which make them attractive for use

in nuclear power generating systems. Although a great deal of information has been generated on the properties of these materials, because of the complex interactions between the fuel and its reactor en- vironment, much more needs to be done. From a fundamental standpoint, the actinide compounds are ex- citing vehicles for the study of solid state phenomena because of their apparent similarities, yet also

their vast differences which arise from their complex electronic structure and bonding.

These are materials in which there is a strong correlation between the understanding of the basic

physical phenomena and their engineering usefulness. Some of the areas of further study which would

yield a better understanding of the materials themselves and provide useful design data are:

1. The chemical potentials of the various constituents in the materials as a function of composition and temperature,

2. mechanism of fission product retention in the solid state,

3. atomic diffusion in chemical and thermal gradients,

4. fission gas void formation and migration,

5. the effect of thermal gradients on microstructural changes such as grain growth,

6. variations in all of the above with solid solutions between various fuel compounds and fission

products

Certainly ceramic nuclear fuel materials merit a good deal of consideration since it can be estimated that in the not too distant future the value of the annual production of plutonium metal alone,

will exceed one billion dollars [5]. Therefore, it does not take a great deal of imagination to foresee that the nuclear fuel industry will make a sizeable contribution to the gross national product

within a few short years.

Acknowledgments

Thanks are extended to Mr. J. E. Schumar for his helpful comments and enlightening discussions.

This work was performed under the auspices of the United States Atomic Energy Commission.

55
References

[l] A. Glasner, Introduction to Nuclear Science , p. 90, Van Nostrand, Princeton, N. J. (1961).

[2] H. Soodak, editor, Reactor Handbook, 2nd Ed., Vol. Ill, Part A. Physics , p. 10, Interscience. New York (I962).

[3] ibid. p. 275.

[U] ibid. p. 285.

[5] Plutonium Survey, I963 . Edison Electric In- stitute. New York (1963 )

•

[6] R. G. Palmer and A. Piatt. Fast Reactors , p. 3. Temple Press, London (196I).

[7] F. J. Leitz, p. 105, Fast Reactor Technology , Report No. ANS-100, American Nuclear Society (1965).

[8] R. B. Gordon, Nuclear Fuel Elements , ed. by

H. H. Hausner and J. F. Schumar, p. 20,

Reinhold, New York (1959).

[9] Maximum Permissible Body Burdens and Maximum

Permissible Concentrations of Radionuclides

in Air and Water for Occupational Exposure . National Bureau of Standards Handbook 69

(1959) .

[10] T. D. Chikalla, J. Am. Cer. Soc. , h6 323

(1963).

[ll] G. F. Burdi, editor, Snap Technology Handbook, Vol. Ill, Refractory Fuels and Cladding , Report No. NAA-SR-8617. Vol. Ill,

April (I965).

[12] R. J. Ackermann and R. J. Thorn, Paper No. SM-66/80, Thermodynamic

s

(Proceedings of

the IAEC Symposium on Thermodynamics with

Emphasis on Nuclear Materials and Atomic

Transport in Solids, Vienna, July 22-27,

1965). Vol. I, p. 2^3. Int. Atomic Energy

Agency, Vienna (1966).

[13] J. Belle, editor, Uranium Dioxide: Properties and Nuclear Applications , Chapter 5, Physical Properties of Uranium Dioxide,"

p. 173. Naval Reactors, Division of Reactor

Development, USAEC (1961).

[ih] M. H. Rand and 0. Kubaschewski . The Thermo

chemical Properties of Uranium Compounds , Oliver and Boyd, Edinburgh (1963).

[15] S. M. Lang, "Properties of High Temperature

Ceramics and Cermets, Elasticity and Density at Room Temperatures," U. S. National

Bureau of Standards, Monograph 6, March

(1960) .

[l6] N. R. Gardner, Nuclear Reactor Fuel Elements,

Metallurgy and Fabrication , A. R. Kaufman,

ed., p. 191+ , Interscience, New York (1962).

[17] A. Strasser, Nuclear Eng

.

, August (i960).

[18] J. A. Leary, R. L. Thomas, A. E. Ogard, and

G . C . Wonn , Carbides in Nuclear Energy , Vol . I

.

, p. 365, Macmillan, London (I96U).

[19] M. A. De Crescente and A. D. Miller, ibid,

p. 3^2.

[20] L. J. Graham and R. Chang, Compounds of In- terest in Nuclear Reactor Technology , p

.

f+09, Nuclear Metallurgy, Vol. X, AIME, IMD Special Report No. 13 (1964).

[21] S. C. Carniglia, p.i+03 of Ref. 18.

[22] E. 0. Speidel and D. L. Keller, "Fabrication

and Properties of Hot-Pressed Uranium

Mononitride , " Report No. BMI-1633, May

(1963).

[23] J. Bugl and A. A. Bauer, p. 215 of Ref. 20.

[2k] Y. Baskin and P. D. Shalek, p. 1+57, Ref. 20.

[25] E. D. Cater, R. J. Thorn, and R. R. Walters,

p. 237, Ref. 20.

[26] C. R. Tottle, "Mechanical Properties of Uranium Compounds," Report No. ANL-707O,

November (1965).

[27] "Reactor Development Program Progress Re- port," Report No. ANL-7017, February

(1965).

[28] P. D. Shalek, J. Am. Cer. Soc , hG, 155

(1963).

[29] K. A. Gingerich and P. K. Lee, J. Chem.

Phys. , hO 3520 (1961+).

[30] T. J. Paskar, D. R. Dehalas, D. L. Keller,

and L. A. Neimark, Proc. 3rd Intern. Conf. on the Peaceful Uses of Atomic Energy, Geneva , August 31-September 9, 196U7pA72

Vol. 11, United Nations, New York (1965).

[31] I. D. Thomas, Current Trends in Nuclear

Power , proceedings of a symposium held at Tucson, Arizona, February 26-March 12,

1962, p. 52, published by Argonne National

Laboratory (1962).

[32] W. V. Goeddel, Materials and Fuels for HighTemperature Nuclear Energy Applications , M. T. Simnad and L. R. Zumwalt, eds . , p. 130, MIT Press, Cambridge, Mass. (196I+).

[33] H. R. Hoekstra, p. 229 of Ref. 13.

[3h] A. E. Martin and R. K. Edwards, J. Phys.

Chem. , 69, 1788 (I965).

[35] R. N. R. Mulford, et al. , Plutonium, I960 , p . 301 , Cleaver-Hume , London (1961).

[36] M. H. Rand and L. E. J. Roberts, Paper No. SM-66/29, Ref. 12, Vol. I, p. 3.

36
[37] R> W. Spence, International Science and

Technology , No. 1+3, p. 58, July (1965).

[38] A. F. Weinberg, L. Young, and R. G. Hudson,

p. 73 of Ref. 32.

[39] see Ref. 11.

[1+0] W. D. Kingery, Introduction to Ceramics , John Wiley and Sons, New York (i960).

[1+1] W. S. Williams, J. Am. Cer. Soc

1+9, I56

(1966).

[1+2] L. A. Neimark and J. H. Kittel, "The Irradiation of Aluminum Alloy-Clad Thoria-Urania

Pellets," Report No. ANL-6538, June (196U).

[1+3] J. L. Daniel, J. Matolich, Jr., and H. W. Deem, "Thermal Conductivity of UO2,"

Report No. HW-699I+5, September (1962).

[1+1+] L. A. Neimark, J. H. Kittel, and C. L. Hoenig, "Irradiation of Metal-FiberReinforced Thoria-Urania," Report No. ANL-6397, December (1961).

[1+5] W. M. Armstrong and W. R. Irvine, J. Nucl. Maters. , 12 26l (I96I+).

[1+6] M. H. Fossler, F. J. Huegel, and M. A. De Crescente, "Compressive Creep of UC and

UN." Report No. PWAC-1+82, Pt. 1, October

(1965) .

[1+7] B. T. M. Willis, Nature , 197 755 (1963).

[1+8] P. Nagels, et al. , J. Appl. Phys. , 35 1175

(196M.

[1+9] p. 212 of Ref. 13.

[50] L. M. Atlas, private communication.

[51] F. Costa and R. R. Conte, p. 3 of Ref. 20.

[52] M. Allbutt, A. R. Junleison, R. M. Dell,

ibid, p. 65.

[53] P. Costa, R. Lallement, F. Anselin and D. Rossignol, p. 83 of Ref. 20.

[5h] W. S. Williams, Science , 152, p. 31+, April

(1966) .

[55] S. P. Denker, p.51 of Ref. 20.

[56] P. D. Shalek and G. D. White, p. 266 of Ref.

18.

40 60 80 100 120 140 160 180 MASS NUMBER

FIGURE 1. Fission product yield from U

235

[3].

57
CONTROL ROOM

SHIELD

REACTOR CORE

HEAT EXCHANGER

SUPPLY TANK

TURBO-GENERATOR

STEAM BOILER

RECEIVING TANK

ELECTROMAGNETIC PUMP'

FIGURE 2. Schematic diagram of a typical liquid-metal-cooled reactor power generating system.

FIGURE 3. Interior view of the remote reprocessing facility for the EBR-II reactor showing the equip- ment used for pyrometallurgical reprocessing of the metallic fuel. Operating personnel are behind

the wall (biological shield) running from the left to the rear of the photograph.

5&
FIGURE k. Plutonium metallography glovebox in- stallation at Argonne National Laboratory il- lustrating a typical glovebox facility.

0.06

'o

0-05

— 0.04-

CT 0.03 - O

O

zo

o

<

orI

0.02

0.01

0 200 400 600 800 1000 1200 TEMPERATURE, °C

2500

2000

£ 1500

1000

500

WEIGHT PERCENT CARBON

0 0 6 1.2 2.1 3 2 4.8 70 10.5 16.7 311 1 l l I

LIQUID+ PuC 2

i

1 1 r

/ LIQUID +C

T"

z"1

I 2050°-^ | Pu C 2+ C

Pu 2 C3 +PuC 2 —y~ "

LIQUID

'LIQUID

/ Pu2

+C 3

/ 1654°

'

1\

j^PuC2

I rl7.52!

PuC

LIQUID + PuC

630°± 2° 2E:

,'PuC

. 480° € * C

122° ff+C

+PuC

Pu2 C 3 + C

-Pu 2 C 3

J L 0 10 20 30 40 . 50 60 70 80 90 100

Pu ATOMIC PERCENT CARBON C

FIGURE 6. Comparison of the thermal conductivity

of UO2 and UC; kip, k^, and k

g are the total,

phonon, and electronic thermal conductivities

of UC respectively. Note the large electronic

contribution in UC which increases with increasing temperature.

FIGURE 5. Plutonium-carbon phase diagram [35]

illustrating typical deviation from stoichiometry of the sodium chloride type compounds. FIGURE 7. Longitudinal section through U02 -25.6

w/o Th02 pellet showing columnar grain growth

(dark) and molten area (gray) after 28,500

MWD/metric ton burnup . [42]

59
Unfibered

k tie =86 w/cm

20,000 Mwd/T

Th02

- lOw/o U02

10 w/o Mo Fibers

k tie = 115 w/cm

20,000 Mwd/T

Th02

- 30 w/o U02

FIGURE 8. Effect of increasing the overall thermal conductivity (measured by kdO) of an irradiated

oxide fuel rod by insertion of molybdenum fibers. Note the large central void and columnar grain

growth in the sample on the left produced by fission gas migration up the thermal gradient. The

light areas are the lead bonding phase which has penetrated cracks formed in the fuel by thermal

cycling [hk].

!

p

-6 -5 -4-3-2-1 0 I 2 3 ENERGY , eV

FIGURE 9- Density of electronic states curve in the transition metal monocarbides , nitrides and

oxides. The position marked "10" would be the Fermi level in TiO if both sublattices were

full. The position marked "8.5" indicates the Fermi level in stoichiometric TiO with fifteen

percent vacancies in both sublattices. The top

of the bonding band falls at about the minimum

in the density of states curve; above the mini- mum the states are largely antibonding [55]-

60
Reactor Materials Design

D. R. de Halas, W. C. Morgan, and M. D. Freshley

Battelle Northwest

Richland, Washington

Abstract

Design problems in the use of graphite as structural and moderator materials in a nuclear reactor are discussed „ The type

of graphite to be used is controlled by the service temperature

and type of atmosphere. Dimensional stability under irradiation

is controlled by graphite structure. Effects of radiation damage,

service temperature and atmosphere on the use of beryllium oxide

are outlined. A summary of the several types of irradiation

damage to nuclear control materials are given. Engineering aspects

of ceramic fuel element design are used as a basis for discussion

of materials coupling problems in reactor design. Stresses intror

duced by changes in the core often cause clad failure. Compatibility between the core and clad material, and effects of impurities in the core as acting on the clad, are also important. Ser- vice conditions affect the choice of materials, due to effects

on performance of failed fuel elements, corrosion, and fission

gas release.

61
Reactor Materials Design

D. R. de Halas, W. C. Morgan, M. D. Freshley

1. Introduction

This paper covers four independent subjects: graphite, beryllium oxide, ceramic control materials,

and the design of ceramic fuel elements. The first three sections cover the properties of nonfuel

ceramic materials used in reactor design and discuss limits of application and design considerations

for use in these materials. The fourth section discusses the influence of the properties of ceramic

fuel materials on the design of nuclear reactor fuel elements.

2. Graphite

Introduction

The choice of graphite as a moderator material in the first nuclear reactors was predicted on the large ratio of neutron scattering cross-section to absorption cross section, the availability of large amounts of material at relatively low costs, and the ease of forming and machining to the shapes and sizes required for construction. These "traditional" reasons are still valid and govern the choice of graphite over other materials for certain applications, but other special properties are becoming more important in specific designs. The high strength-to-weight ratio, increased strength at elevated tem- peratures and wide range of available thermal conductivities, are examples of some of the special pro- perties of artificial graphites.

Artificial carbons and graphites are aggregates of, approximately randomly oriented graphite cry- stallites, which are literally glued together with nongraphitic carbon atoms. Graphite crystals are composed of hexagonal planes of carbon atoms, stacked in an A-B-A- sequence as shown in Figure 1, with

rather weak bonding between the planes. Thus, the physical properties of the crystals are very anisotropic, as is shown in Table I. The physical properties of the artificial aggregate can be varied

over a wide range depending on the choice of raw materials and processing conditions, which control the alignment of crystallites, the bulk density, and the amount of nongraphitic carbon.

TABLE I. Physical Properties of Crystals

Single Crystal

a-direction c-direction

Coefficient of Thermal Expansion

0-500 ° C (x 10" 6 per ° C) 500-1000 ° C (x 10" 6 per ° C) -0.5 +0.8

28.2

29.4

Electrical Resistivity (ohm-cm) 4 x

10" 5 0.3

Thermal Conductivity (watts/cm °C) 4.0 0.8

Limitations on Use

As with any material some of the properties impose limitations on the environments in which gra- phite can be used. The reaction of graphite with oxidizing gases has perhaps received the most attention. The amount of oxidation which is considered permissible in a given application is usually limi- ted by reduction of strength rather than the gross amount of graphite removed. The loss of strength

with oxidation is disproportionally large for graphite; for example, a homogeneous weight loss of 10% may result in 50% reduction in compressive strength. Oxidation rates are of course dependent on con- trollable properties, such as porosity and impurity content, but as a general rule, reaction rates are considered excessive above about 300 °C in air and 600 °C in CO2 • The problems associated with oxidation can be eliminated by the use of nonoxidizing gas atmospheres, such as helium or nitrogen, or pro- tective coatings, such as pyrolytic carbon or silicon carbide. Coatings must of course be chemically

stable in contact with graphite at the operating temperatures, but even more important, the coating

62
and artificial graphite grade must be carefully chosen to eliminate any significant mismatch in thermal

expansion coefficients or dimensional changes under irradiation.

The design of nuclear reactors often requires that structural or cladding materials operate in contact with graphite for long periods of time. The choice of materials for such applications, espe- cially at elevated temperatures, must be carefully made since most metals and their oxides react with

carbon far below their melting point. In this regard, it is fortuitous that the oxides of thorium,

uranium, and plutonium do not react with graphite below about 1800 °C; and likewise the oxides of aluminum, beryllium, magnesium, and zirconium are usable over about the same temperature range.

One of the most important phenomena associated with graphite is the fairly large dimensional

changes which are produced during neutron irradiation. Irradiation of graphite crystals results in an expansion in the direction perpendicular to the basal planes and contraction in the direction parallel

to the planes. However, the behavior of the artificial graphites is dependent not only on the changes

occurring in the crystallites, but also on the changes in the nongraphitic portions of the aggregate.

In general artificial graphite bodies initially contract in all directions when irradiated at temperatures above 300 °C; at higher exposures contraction ceases and the aggregate begins to expand. The

contraction rates and other phenomena depend on the type of graphite and the irradiation temperature.

These effects will be discussed in more detail in a following section of this paper.

Examples of Usage and Reactor Design

The prime use of graphite in reactors has been as the neutron moderator. Some typical graphite

moderated reactor designs are listed in Table II, the listing is not meant to include all reactors, but

represents different types which have evolved.

TABLE II. Graphite Moderated Reactor Types

i Coolant

Horizontal Channels

i

Air

Water

! co

2 He

Reactors X-10 (ORNL) BGRR Windscale Reactors (UK)

Hanford Production Reactors

NPR

G-2 and G-3 (French)

UHTREX (Los Alamos)

Vertical Channels Water APS (USSR)

Urals Power Station Reactors (USSR)

C0

2 Calder Hall Reactors (UK)

Tokai Mura (Japan)

AGR (UK)

He EGCR (ORNL)

Dragon (UK-EURATOM)

; . Peach Bottom

Sodium Hallam

Molten Salt MSRE (ORNL)

Pebble-Bed He PBR (West Germany)

PBRE (ORNL)

The first reactors were built of graphite bars stacked in horizontal layers. This arrangement

allows the fuel and coolant tubes to be solidly supported by the graphite moderator, but distortion

of the stack at high exposures can result in maintenance or fueling problems.

One of the most unusual graphite moderated reactors ever conceived is the Ultra High Temperature

Reactor Experiment (UHTREX). The core consists of 24 wedge-shaped graphite blocks; each a 40- inch

high block containing 13 radial fuel channels. The blocks are keyed together, producing a cylinder

70 inches in diameter with a 12-inch diameter axial hole, and pinned to a graphite base disk. The

entire core can be rotated to charge fuel elements and discharge them through the central hole. The

unclad fuel elements consist of graphite tubes impregnated with uranium oxide. Fuel temperatures of

63
1820 °C and exit helium coolant temperatures of 1315 °C are expected during operation.

One means of reducing the distortion problem is to turn the stack on end as was done with the Calder Hall Reactors. As variation of this configuration one can interlock the bars with keys, as was

done at Takai Mura, use monolithic multihole columns as in the EGCR, or position the fuel channels

between bars as in the Hallam Reactor. All of these configurations reduce the effect of graphite distortion; in addition, means can be provided in the design for periodic replacement of the moderator if the distortion is expected to become excessive.

Another alternative is to make the moderator replaceable with the fuel, as a monolithic fueled

column as in the Peach Bottom and Dragon Reactors, as fueled segmented blocks as in the Colorado Reactor types.

The Dragon and Peach Bottom Reactors both make extensive use of graphite in their designs. Both

are helium cooled and are fueled with U-Th carbides in graphite-clad elements. Maximum graphite tem- peratures of about 1650 °C are expected at coolant outlet temperatures of 730 - 750 °C. The main

differences in the two reactor designs are in the arrangement of the replaceable fuel-moderator ele- ments and in the methods used to scavenge fission products which are released from the fuel.

The Pebble Bed Reactors are of another unusual design. The uranium or thorium oxides or carbide

fuels are contained in graphite spheres, which werve the dual purpose of containing the fission pro- ducts and acting as moderator.

In the Molten Salt Reactor Experiment (MSRE) at Oak Ridge, the fuel is a solution of fluorides of uranium, thorium, hiJ , beryllium, and zirconium, circulated through channels in the graphite moderator.

This design provides a possibility of reducing fuel costs and shut-down time for a power- generating

reactor.

Graphite is useful for reactor shielding either in purified form as a neutron reflector, or as a neutron absorber by adding a neutron poison such as boron„ Porous carbon or carbon felt is an excellent material for heat shielding if protected from fast neutrons or if the design allows large dimensional changes in these parts.

Dimensional Changes During Irradiation

To understand the effects of neutron irradiation on artificial graphite, it is helpful to consider

how the material is made. The normal nuclear grade graphites are composed of small particles of a ground petroleum coke filler; about half of the particles, by weight, are less than 0.1 millimeter on

a side, each containing literally millions of graphitic carbon crystallites. The filler particles are mixed with about 25 weight-percent coal-tar pitch, which binds the particles together, then the mass

is extruded to the desired shape. During the extrusion process, flow of the mass through the dies

generally aligns the long axis of the particles parallel to the axis of extrusion. Since the basal

planes of the crystallites are generally oriented parallel to the long axis of the filler particles,

this results in a preferred orientation of crystallites within the bar and a higher degree of orientation near the surface of the bar.

After extrusion, the bars are baked to pyrolyze the binder pitch, then heated in a graphitizing

furnace to a temperature between 2400 and 3000 °C. Some shrinkage and cracking occurs during the heating and the crystallites grow in perfection.

During the period of cooling-down from graphitization temperature, the anisotropy of the thermal

expansion coefficients results in generation of internal stresses in the temperature range below about

1800 °C These stresses are partially relieved by formation of microscopic cracks, called Mrozowskicracks, parallel to the crystallite basal planes.

Thus, the resultant body is composed primarily of graphitic crystallites, but contains some non- graphitic bonding carbon, some residual internal stresses, and a system of cracks parallel to the cry- stallite basal planes.

During neutron irradiation, the volume change of the crystallites is always positive; the expan- sion in the "c-direction" is larger than the contraction in the "a-direction" by a factor which varies

from about 10 at room temperature to about 2.5 at 650 °C. The dimensional changes of an artificial

graphite are dependent not only on the changes of the constituent crystallites but also on how much

of these changes are transmitted to the aggregate, how much is absorbed in closure of the internal

cracks or in deformation of nongraphitic portions of the aggregate, and on the effect of the changes

in internal stresses. Typical behavior of a graphite under irradiation is illustrated in Figure 2.

The general features of the dimensional change resulting from exposure to neutron irradiation for

graphites have been postulated to result from the following phenomena:

64
(1) Low-exposure transverse expansion due to relief of internal stresses.

(2) "Linear contraction" dependent on "a-direction" contraction, with much of the "c-direction"

expansion being absorbed in closure of cracks.

(3) Transmission of "c-direction" expansion to the aggregate and re-orientation of crystallites within

the body, after closure of the cracks.

Two other phenomena, associated with irradiation- induced dimensional changes, can be of prime

importance to reactor designers, arising from the effects of external stress and of sample size.

Externally applied stresses produce significant creep rates in artificial graphites during irradiation. For example, compressive stresses of only a few hundred psi are required to increase the apparent con- traction rates by a factor of 2. The steady-state creep is apparently accommodated in the inter-crystalline boding regions since the crystalline dimensional changes do not appear to be affected by the applied stresses.

It has been observed that the dimensional change rates of large bars of graphite are about 2.5 times the rates obtained on small samples. Two effects have been postulated to explain this observation:

(1) in large bars, a "skin" of highly oriented graphite exists due to the effect of the extrusion process; this skin may contract at a more rapid rate than the interior graphite, thus producing

stresses which accelerate the contraction

(2) in smaller samples, cracks, which intercept the surface, may partially relieve the internal

stresses generated between crystallites.

3. Beryllium Oxide

Introduction

Beryllium oxide has always been an attractive material for thermal nuclear reactors even prior to the demonstration of criticality at Stagg Field, Chicago. Its principal attributes are good moderating

characteristics, relatively high thermal conductivity, and relative inertness. The interest in beryllium oxide is still high for advanced reactor applications where It is the aim to increase efficiency

by using higher temperatures.

The applications for beryllium oxide fall in two categories; those in which it is used only as a moderator, and those in which it is used as a fuel matrix material. In the latter applications, it also acts as a moderator material.

Use as a Moderator

Extensive investigations in the United States and Europe have delineated the limitations and the applications of beryllium oxide. Under certain power reactor conditions the BeO can be physically

degraded due to the neutronic production of helium gas in the lattice and the effects of fast neutrons

on the cry stallographic structure of the BeO. If irradiations are carried out at too low a temperature

the BeO is subject to physical disintegration by microcracking „ Factors that influence the radiation

degradation of BeO include grain size, impurities or additives, and if it is used as a fuel material,

the extent of fuel loading.

The resistance of BeO to neutron irradiation degradation improves as the temperature is increased

above 500 °C. At the present time there are only limited data concerning the effects of irradiation

above ~ 1100 °C. It appears that for certain reactor applications BeO may possess suitable radiation

integrity starting in the range from 700 to 1000 °C.

Use as a Fuel Matrix

Fueled BeO can take many forms. Much of the work has been done with spherical U0£ particles, of maybe 200 to 300 u, diameter, enclosed by BeO. Figure 3 shows a micrograph of such a fuel structure. Similar structures have been made using U0

2 "Th02 and even UC2 or UC

2 -ThC

2 particles.

When BeO is used as a fuel matrix one of its principal requisites is good retention of fission

products. In general, the amount of fission products released from a BeO matrix has been 2 to 3 orders

of magnitude higher than reactor designers prefer. The higher amounts released appear to result from

the porosity of the matrix even though greater than 987„ of theoretical density has been achieved. Poor fission product retention has been one reason for a lessening of interest in BeO as a fuel material.

65
However, recent work at General Atomic has shown that Improvements In the fabrication tecnniques

for BeO have markedly Improved fission product retention at temperatures as high as 1400°C. Values that are quite close to those that are desired are now obtained. The improved retention characteristics are due mainly to closing of pores in the BeO matrix by the production of a material having a density of > 99.37= of the theoretical value. The high density appears to be related to two factors: the current availability of more highly sinterable grades of BeO powder; and development of the technique of hot

pressing during sintering. This latter technique is excellent for overcoming the limitations of less sinterable powders and reducing variability from batch to batch of the same powder. The resulting

structures have a grain size of 5 u. or less which probably not only enhances fission product retention

but also reduces the effects of radiation on physical degradation. To date the results on these im- proved materials are preliminary, but high exposure irradiations have been started.

Cost

The cost of material and its fabrication has always been greater for BeO than for graphite. This

has placed some limitations on the competitive position of BeO as a solid moderator material. However,

due to recent demands of the aerospace and electronics industries, BeO can now be obtained in large

quantities for approximately $10/lb. This compares with the cost of $20/lb. five years ago. This

reduced cost aids in making fueled BeO competitive with other high temperature fuel systems, particularly coated particles. The recent improvements in fabrication methods have reduced the cost of fueled BeO compacts so much that there Is now a much less pronounced differential between coated particle fuels

and fueled BeO than there used to be.

4. Ceramic Control Materials

Control materials are used in nuclear reactors to absorb neutrons and control reactivity. Their

primary requirement, therefore, is that they have a high absorption cross section for neutrons. The very fact that control materials have high cross sections means that they are highly susceptible to reaction and potential damage from neutrons.

Control materials have been used in reactors in forms of alloys (for example, cadmium- indium- silver

alloy), as dispersions (for example, B^C in aluminum), or as pure ceramic (for example, B^C) . The pure

ceramic materials have little structural strength and must be supported by the control rod components. A basic design might consist of encapsulated doughnut- shaped ceramic wafers strung on a water cooled

tube. Alternately, the control rod could be fabricated by vibrational compaction of sized ceramic powder.

Desirable properties of control materials include:

"high cross section for neutron cross- section

,

"dimensional stability at high temperature,

"good radiation damage resistance,

"ease of fabrication,

mechanical stability,

"decay after neutron absorption to a daughter material also possessing a high cross section for neutron absorption.

Common forms in which ceramic control materials are used are listed in Table III.

66
TABLE III. Common Ceramic Control Materials

Material

Me 1 t 1 ng Point

Macroscopic

Cross Section May be Used

B.C 2450 °C

j ojiO cm \d f4j»o cm ) 4

\ 4. in stainless steel L in graphite

H£0

2 2.9 cm"

1 <

Gd

2 0

3 2330 0 C -1 ! I 1134.4 cm

in Zr, Ti, EU2°3 2050 0 C 116.8 cm"

1 ^ stainless steel

Sm

2 03

i

2300 °C 141.1 cm"

1

, , 1

A prime consideration in the use of control materials Is damage by neutrons. The damage principally falls into two categories; characterized by (n, a) and (n, y) reactions.

Examples: Types of Reaction

(n, a)

„10 ' .B + n

7 4

_> 3Li +2He

(n, »)

151 ' Eu + n

63 o 63

„ 152 Eu + y

63Eu

152

64

Gd 152 + &

The (n, a) reactions with thermal neutrons are generally limited to the light elements. The damage

to the control material is principally caused by the products of this reaction. In the case of boron,

the lithium atom that is formed has a larger atomic radius than the boron and causes lattice strain as

it accumulates. However, the principal cause for damage is the helium atoms. At the higher temperatures these diffuse and agglomerate into small bubbles. With continued burnup, the pressure in the bubbles becomes considerable and causes appreciable swelling of the boron (B^C) . Damage is also produced

in the crystal lattice by displacements resulting from collisions with recoil atoms. However, these displacements, creating interstitial atoms and vacancy clusters in the lattice, tend to be annealed out

at higher temperatures.

The (n, y) tyP e °f reaction is generally much less damaging to control materials. First of all, there is no helium generated. Also, the ionic radius of the product tends to be similar to that of the parent, so that there is less lattice distortion.

The means of controlling the damage lie in the design of the control rods. A particulate ceramic

such as B^C may be dispersed in a metal. The metal matrix acts first to provide restraint on the swel- ling of the ceramic particles. It also acts to lower the temperature of the ceramic phase, thereby

reducing helium atom agglomeration and swelling. It is also possible to allow for swelling of the par- ticles by using a low density particle in a dense metal matrix. Use of vibrationally compacted powder

with a gas plenum for helium collection would also circumvent Irradiation damage.

It is worthwhile to mention that the choice of control materials in fast reactors is much more

limited than for thermal reactors. The control materials must have a high cross section for neutron

absorption at high energies and this essentially limits the choice to the lighter elements, in particular, boron. Thus, in spite of the problems created by the (n, a) reaction in boron, these problems will

have to be overcome by clever design and materials development. It is likely that much more effort will

67
be needed in the development of improved dispersion- type boron-based control materials.

5. Design of Ceramic Fuel Elements

Introduction

Although several kinds of ceramic systems hold promise as fuel for power reactors, oxides, car- bides, and cermets have received the most attention and are being investigated most actively. Each

fuel system has advantages and disadvantages and, ultimately, the service conditions dictate the choice

of material. Fissile materials include Uranium, Thorium, and Plutonium with uranium receiving most attention. Recently, however, the use of plutonium as enrichment has received more emphasis and hence

mixtures of uranium with plutonium, either for the oxide or carbide systems, are being investigated

more earnestly.

Many factors must be considered in the design of reactor fuel elements and one of the complicating

considerations is that the properties of the fuel material are continually changing throughout its reactor lifetime. The primary fuel design considerations are dimensional stability and compatibility

and reactions between core and cladding and coolant, fuel relocation, solid and gaseous fission product

accommodation, fission product and plutonium migration, fuel swelling and thermal expansion, among

others. All of the ceramic fuel materials are prone to the same kinds of irradiation effects and the basic problems are essentially the same for each fuel type.

A satisfactory fuel design must provide structural integrity of the fuel for long operating lifetimes in the reactor environment and hence, the fuel material and its cladding must be considered as an integral unit.

Oxide Fuel Design

Dramatic structural changes occur during irradiation of high specific power oxide fuel elements.

The postirradiation structure of oxide fuels is relatively insensitive to the fabrication technique,

whether involving pelletizing or the use of packed particles. Sintering, grain growth, and densification of oxide fuels occur in the reactor at fuel temperatures above 1600 °C. This sintering and den- sification of the fuel causes the formation of a void in the thermal center of the fuel region. The

densif ication process causes radial redistribution of the fuel. At fuel temperatures above melting,

axial displacement or slumping of the oxide- fuel has been observed. The degree of slumping depends upon the fuel geometry (rod diameter), the operating conditions, and the initial bulk fuel density.

These structural changes within the reactor affect the thermal conductivity of the fuel, altering

the temperature profiles as irradiation proceeds.

Adequate accessible porosity must be provided within the fuel rods to accommodate swelling due to the accumulation of fission products and the thermal expansion of the fuel material. Fuel swelling is due to the combined effects of retained fission products and thermal expansion. At high burnup , UCU

fuel changes im composition due to the accumulation of massive amounts (over 20%) of fission products,

which causes swelling. The volume of UO2 irradiated at relatively low temperatures increases 0.7% per

10^0 fissions/cm-^. This expansion rate is not attained until the initial porosity of the fuel is occupied. The thermal volume expansion of UO2 from room temperature to the melting temperature is 15% and

it experiences an additional increase of 10% in passing through the melting transition. Hence, a total

volume increase of about 25% must be accommodated between room temperature and the fully molten condition. The effects of these large volume increases are particularly important in areas of a fuel rod

which may have increased bulk density due to slumping or axial fuel relocation. Swelling in these

regions then would cause interaction between the fuel and the cladding, and deformation or failure of the cladding.

Fuel rod swelling is reduced by using annular pellets or low density powder in the range of 80 to 85% of the theoretical density. However, the void space provided to accommodate swelling increases the potential for fuel redistribution.

Since approximately 30% of the fission products formed during the fission process are gases which

may be released from the fuel at high operating temperatures, the fuel must be designed to accommodate

the release of gases without allowing excessive pressure buildup within the rod to stress the cladding.

Fission gas release values as high as 88% have been measured in UO2-PUO2 fuel rods operating under high

power generating conditions. A reasonable fission gas release model for oxide fuels assumes 100% gas release from the fuel volume operating at temperatures above 1800°C and approximately 10% release for

that fuel volume operating below this temperature. Excessive internal pressures within the fuel rod

are avoided by the provision of adequate void space to accommodate the release of gases. Another solu- tion to the problem of excessive pressure buildup that is receiving attention for high burnup fuels is the continual venting of the gases from the rod during operation through such devices as porous plugs.

68
Fuel property measurements made outside the reactor for nonirradiated ceramic fuel specimens should

not be considered completely indicative of the performance capability of that fuel. The most important

example of this is the differences in UO2 thermal conductivity that are measured in and out of the reactor. These differences are apparently related to the oxygen potential within a completely canned fuel

element, the magnitude of the thermal gradients, and at low temperatures, irradiation damage. Fuel

composition also effects thermal conductivity. High 0:U ratios, in particular, seem to adversely affect

heat transfer rates.

Interactions Between Fuel and Cladding

Cladding strains are caused by external (coolant) pressures. This effect becomes important in the large diameter tubular elements and rods clad with thin-walled collapsible cladding. Thermal cycling

of collapsed cladding would probably lead to early fatigue failure in the reactor. Cladding strain pro- duced by thermal expansion of the fuel can rapidly limit fuel element performance.

Fuel-cladding interactions at high burnup are also affected by the chemical and radiation cladding

material. In some cases, impurities in the oxide fuel material, such as water, carbon compounds, and halogens have a dramatic effect on the compatibility between the core and the cladding. Hydrocarbon

impurities in the ceramic fuel' can cause massive hydriding and subsequent rupture in the Zircaloy

cladding in a relatively short period of time. The failure of some Zircaloy-clad rods after irradiation

is characterized by a tree- like corrosion penetration from the inner surface of the cladding, a small crack, and no metallographically discernible zirconium hydride. Failures of this type have been tenta- tively attributed to fission product iodine attack on the Zircaloy. If such a failure mechanism is real, then fuel element exposure would be limited by fission product iodine buildup and temperature.

These failures have been isolated cases and there is no statistical evidence that such a limit may be a real one.

Behavior of Fuel After Penetration of the Cladding

Penetration of cladding need not in itself limit the useful life of an oxide or ceramic fuel ele- ment and in fact, satisfactory failure behavior is an important fuel design consideration. Operating

experience in several power reactors, test reactors, and experimental reactors has shown that fission

product loss from the failed fuel rods can be accommodated without creating intolerable operating pro- blems o Irradiations of oxide fuel rods containing intentional defects have shown that fission product

activity bursts generally occur after changes in reactor power level. Steady-state release of fission

products has been sufficiently low to cause no concern. One of the major concerns associated with the

operation of oxide fuel rods with defects is the possibility that extensive fuel washout may occur as

a result of waterlogging. This problem has been of particular concern for packed particle fuels which

are more susceptible to the intake of water; however, operating experience with regard to lack of fuel

washout has been very favorable.

Carbide Fuel Design

Uranium carbide or mixtures of uranium carbide and plutonium carbide fuels have application in liquid-metal-cooled thermal and fast reactors. In common with oxides, the carbides have the advantage

of high melting point and good dimensional stability.

The thermal conductivity of the carbides is 4 to 10 times higher than that of uranium dioxide or mi^ed oxide fuel. The power generation rate limit may therefore be higher for carbides than for lower

conductivity fuel materials. There are several ways to take advantage of this property with fewer,

larger diameter fuel rods, higher specific power operation, and lower fuel temperatures to decrease

fuel redistribution, swelling, and fission gas release.

The disadvantages peculiar to carbides are based on their thermodynamically reactive nature. The

carbide fuels are less compatible with cladding materials than are the oxides. The poor oxidation

resistance of carbides requires that they be handled in low oxygen and low moisture content atmospheres.

Stoichiometry control is particularly important in carbide fuels. For example, free uranium or free- metal may cause enhanced fission gas release.

One of the most successful cladding materials for carbides is stainless steel, either type 304 or

316, since it is readily available and compatible with the sodium coolant. Medium nickel content alloys

such as Hastelloy-X or Incoloy have higher strength but their compatibility with carbide is unknown.

High nickel alloys such as Nimonic or Inconel-X are not compatible. Refractory alloys based on niobium,

vanadium, molybdenum, and tantalum are reasonably compatible with the carbide but are likely to be

unstable with respect to the coolant. Reaction with sodium is sensitive to impurities in the sodium. In order to take advantage of the high thermal conductivity of carbides, sodium bonding of the carbides

to stainless steel cladding has been intensively investigated. However, this poses carburization pro- blems with hyperstoichiometric fuel. Sodium helps reduce the higher carbides in the fuel and transfer, the carbon to the stainless steel at temperatures as low as 650 °C. With hypostoichiometric UC fuel

69
sodium causes reactions to occur between free uranium and stainless steel cladding at temperatures of

760 to 870 °C.

One of the major problems to be solved for carbides as well as oxides is the accommodation of fuel

swelling at high burnups without disruption of the cladding and without excessive fuel temperatures. Even the small diametral increases of 0.6% per percent burnup of fissile atoms amount to sufficiently

large changes at 10 atomic percent burnup to put the cladding under severe strain.

Cermet Fuel Design

Cermet type fuels are utilized in small compact reactors operating at high specific power. A Pu02~ stainless steel cermet is being considered as the driver fuel for the Fast Test Reactor. One of the major reasons for the selection of the cermet as a reference fuel for the FTR is the large thermal ex- pansion characteristic which produces strong, prompt negative temperature and power coefficients of reactivity.

Cermet type fuels disperse the fissionable ceramic phase as discrete particles in a continuous

matrix of nonfissile material. To minimize radiation damage and provide metallic properties, the matrix

should predominate in volume and exist as a continuous phase surrounding the fissile particles. The

matrix metal, in effect, acts as a structural material in the fuel element.

A prime objective is to concentrate the irradiation damage in the dispersed phase and in a highly

localized region surrounding the dispersed fissile particle, leaving a fission-product-free region of matrix metal around the zone of damage. The design of an ideal dispersion fuel includes a dispersed

particle size large compared to the fission product range, uniform dispersion of particles in the metal

matrix, a continuous matrix of maximum possible volume fraction, and high fissile particle density.

Other areas to be considered in cermet fuel design are the combined effects of residual stress,

thermal stress, pressure from fission gases, volume expansion of the ceramic fuel particles, and fast flux irradiation damage to the matrix and cladding.

Because of the reduced fissionable atom density in cermet type fuels, the specific damage to individual particles is very great. With high density ceramic fuel particles tightly held in a dense

matrix, very high fission gas pressures can result as the burnup become appreciable. It has been pro- posed to use low density fuel particles in a high density matrix to provide void space for the accommo- dation of fission gases generated during the irradiation process. The use of low density particles

would also provide expansion space for swelling resulting from the accumulation of fission products

within the particle at the very high burnups.

6. Acknowledgments

The authors would like to acknowledge the assistance of R. J. Lobsinger and J. B. Burnham of this

Laboratory in the preparation of the information on ceramic control materials.

R. A. Meyer of General Atomic kindly furnished the up-to-date information on the status of beryllium oxide technology used in preparation of that section of this report.

This paper includes work performed by Battelle Northwest for the United States Atomic Energy

Commission under Contract AT(45-1) - 1830.

7. Selected References

R. E. Nightingale, Nuclear Graphite , M. T. Simnad and L. R. Zu:.walt,

Academic Press (New York, 1962) Materials and Fuels for High-Temperature

Nuclear Energy Applications , MIT Press (Cambridge, Mass., 1964)

70
U. S. GOVERNMENT PRINTING OFFICE : 1967

O - 257-304