Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional)

1.05 Radiation-Induced Effects on Material Properties of
Ceramics (Mechanical and Dimensional)
K. E. Sickafus
University of Tennessee, Knoxville, TN, USA

ß 2012 Elsevier Ltd. All rights reserved.

1.05.1.
1.05.2.
1.05.2.1
1.05.2.2
1.05.2.3
1.05.2.3.1
1.05.2.3.2
1.05.2.3.3
1.05.2.3.4
1.05.2.3.5
1.05.2.3.6
1.05.2.3.7
1.05.2.3.8
1.05.2.3.9
1.05.2.3.10
1.05.2.3.11
1.05.2.4
1.05.3.
1.05.3.1
1.05.3.2
1.05.3.3
1.05.3.4
1.05.4.
References

Introduction
Radiation Effects in Ceramics: A Case Study – a-Alumina Versus Spinel
Introduction to Radiation Damage in Alumina and Spinel
Point Defect Evolution and Vacancy Supersaturation
Dislocation Loop Formation in Spinel and Alumina
Introduction to atomic layer stacking
Charge on interstitial dislocations
Lattice registry and stacking faults I: (0001) Al2O3
Lattice registry and stacking faults II: {111} MgAl2O4
Lattice registry and stacking faults III: {1010} Al2O3
Lattice registry and stacking faults IV: {110} MgAl2O4
Unfaulting of faulted Frank loops I: (0001) Al2O3
Unfaulting of faulted Frank loops II: {111} MgAl2O4
Unfaulting of faulted Frank loops III: {1010} Al2O3
Unfaulting of faulted Frank loops IV: {110} MgAl2O4
Unfaulting of faulted Frank loops V: experimental observations
Amorphization in Spinel and Alumina
Radiation Effects in Other Ceramics for Nuclear Applications
Radiation Effects in Uranium Dioxide
Radiation Effects in Silicon Carbide
Radiation Effects in Graphite
Radiation Effects in Other Ceramics
Summary

Abbreviations
dpa
BF
TEM
i

v
ccp
hcp
SHI
PKA
CVD

Displacements per atom
Bright-field
Transmission electron microscopy
Interstitial
Vacancy
Cubic close-packed
Hexagonal close-packed
Swift heavy ion
Primary knock-on atom
Chemical vapor deposition

1.05.1. Introduction
Ceramic materials are generally characterized by
high melting temperatures and high hardness values.
Ceramics are typically much less malleable than

123
124
124
125
127
127
127

129
129
130
130
131
132
132
133
133
134
136
136
136
137
138
138
139

metals and not as electrically or thermally conductive. Nevertheless, ceramics are important materials
in fission reactors, namely, as constituents in nuclear
fuels, and are widely regarded as candidate materials
for fusion reactor applications, particularly as electrical insulators in plasma diagnostic systems. These
applications call for highly robust ceramics, materials
that can withstand high radiation doses, often under
very high-temperature conditions. Not many ceramics satisfy these requirements. One of the purposes
of this chapter is to examine the fundamental
mechanisms that lead to the relative radiation tolerance of a select few ceramic compounds, versus the
susceptibility to radiation damage exhibited by most
other ceramics.
Ceramics are, by definition, crystalline solids.

The atomic structures of ceramics are often highly
complex compared with those of metals. As a consequence, we lack a detailed understanding of atomic
123


124

Radiation-Induced Effects on Material Properties of Ceramics

processes in ceramics exposed to radiation. Nevertheless, progress has been made in recent decades in
understanding some of the differences between radiation damage evolution in certain ceramic compounds. In this chapter, we examine the radiation
damage response of a select few ceramic compounds
that have potential for engineering applications
in nuclear reactors. We begin by comparing and
contrasting the radiation damage response of two
particular (model) ceramics: a-alumina (Al2O3, also
known as corundum in polycrystalline form, or ruby
or sapphire in single crystal form) and magnesioaluminate spinel (MgAl2O4). Under neutron irradiation, alumina is highly susceptible to deleterious
microstructural evolution, which ultimately leads to
catastrophic swelling of the material. On the other
hand, spinel is very resistant to the microscopic
phenomena (particularly nucleation and growth of
voids) that lead to swelling under neutron irradiation.
We consider the atomic and microstructural mechanisms identified that help to explain the marked difference in the radiation damage response of these two
important ceramic materials. The fundamental properties of point defects and radiation-induced defects
are discussed in Chapter 1.02, Fundamental Point
Defect Properties in Ceramics, and the effects of
radiation on the electrical properties of ceramics
are presented in Chapter 4.22, Radiation Effects
on the Physical Properties of Dielectric Insulators

for Fusion Reactors.
It is important to be cognizant of the irradiation conditions used to produce a particular radiation
damage response. Microstructural evolution can vary
dramatically in a single compound, depending on
the following irradiation parameters: (1) irradiation
source–irradiation species and energies – these give
rise to the so-called ‘spectrum effects,’ (2) irradiation temperature, (3) irradiation particle flux, and
(4) irradiation elapsed time and particle fluence.
Throughout this chapter, we pay particular attention
to the variations in radiation damage effects due
to differences in irradiation parameters. A single
ceramic material can exhibit radiation tolerance
under one set of irradiation conditions, while alternatively exhibiting damage susceptibility under
another set of conditions. A good example of this is
MgAl2O4 spinel. Spinel is highly radiation tolerant in
a neutron irradiation environment but very susceptible to radiation-induced swelling when exposed to
swift heavy ion (SHI) irradiation.
Finally, it is important to note that radiation
tolerance refers to two distinctly different criteria:

(1) resistance to a crystal-to-amorphous phase transformation; and (2) resistance to dislocation and void
nucleation and growth. Both of these phenomena lead
(usually) to macroscopic swelling of the material, but
the causes of the swelling are completely different.
The irradiation damage conditions that produce these
two materials’ responses are also typically very different. We examine these two radiation tolerance criteria
through the course of this chapter.

1.05.2. Radiation Effects in
Ceramics: A Case Study – a-Alumina

Versus Spinel
1.05.2.1 Introduction to Radiation
Damage in Alumina and Spinel
a-Al2O3 and MgAl2O4 are two of the most important
engineering ceramics. They are both highly refractory oxides and are used as dielectrics in electrical
applications (capacitors, etc.). Both a-Al2O3 and
MgAl2O4 have been proposed as potential insulating and optical ceramics for application in fusion
reactors.1–3 In a magnetically confined fusion device,
these applications include (1) insulators for lightly
shielded magnetic coils; (2) windows for radiofrequency heating systems; (3) ceramics for structural
applications; (4) insulators for neutral beam injectors;
(5) current breaks; and (6) direct converter insulators.3 Such devices in a fusion reactor environment
will experience extreme environmental conditions,
including intense radiation fields, high heat fluxes
and heat gradients, and high mechanical and electrical stresses. A special concern is that under these
extreme environments, ceramics such as a-Al2O3
and MgAl2O4 must be mechanically stable and resistant to swelling and concomitant microcracking.
Over the last 30 years, many radiation damage
experiments have been performed on a-Al2O3 and
MgAl2O4 under high-temperature conditions by a
number of different research teams. Figure 1 shows
the results of one such study, where the high temperature, neutron irradiation damage responses of
a-Al2O3 and MgAl2O4 are compared. The plot in
Figure 1 was adapted from Figure 1 in an article
by Kinoshita and Zinkle,4 based on experimental data
obtained by Clinard et al. and Garner et al.5–8
The neutron (n) fluence on the lower abscissa
in Figure 1 refers to fission or fast neutrons, that
is, neutrons with energies greater than $0.1 MeV.
Figure 1 also shows the equivalent displacement

damage dose on the upper abscissa, in units of


Radiation-Induced Effects on Material Properties of Ceramics

5
4
Swelling (%)

Displacements per atom (dpa)
10
100

1

3

1000

a-Al2O3
1100 k
1025 k
925 k

2

MgAl2O4
658–1100 K

1

0
-1
1025

1026
1027
Neutron fluence (n m-2)

1028

Figure 1 Volume swelling versus neutron fluence in
a-Al2O3 alumina and MgAl2O4 spinel.

displacements per atom (dpa). These dpa estimates
are based on the approximate equivalence (for ceramics) of 1 dpa per 1025 n mÀ2 (En > 0.1 MeV).9
Figure 1 shows a stark contrast between the
radiation damage behavior, particularly the volume
swelling behavior, between a-Al2O3 and MgAl2O4.
Specifically, MgAl2O4 spinel exhibits no swelling
in the temperature range 658–1100 K, for neutron
fluences ranging from $3 Â 1026 to 2.5 Â 1027 n mÀ2
(3–200 dpa). On the contrary, a-Al2O3 irradiated
at temperatures between 925–1100 K exhibits significant volume swelling, ranging from $1 to 5% over
a fluence range of 1 Â 1025 to 3 Â 1026 n mÀ2
(1–30 dpa). The purpose of the following discussion
is to reveal the reasons for the tremendous disparity in radiation-induced volume swelling between
alumina and spinel.
Figure 2 shows a bright-field (BF) transmission
electron microscopy (TEM) image that reveals the
microstructure of a-Al2O3 following fast neutron irradiation at T ¼ 1050 K to a fluence of 3 Â 1025 n mÀ2

c

100 nm
Figure 2 Bright-field transmission electron microscopy
image of voids formed in a-Al2O3 irradiated at 1050 K to a
fluence of 3 Â 1025 n mÀ2 ($3 dpa) (micrograph courtesy of
Frank Clinard, Los Alamos National Laboratory).

125

($3 dpa). The micrograph reveals a high density of
small voids (2–10 nm diameter), arranged in rows
along the c-axis of the hexagonal unit cell for the
a-Al2O3. When voids are arrayed in special crystallographic arrangements, as in Figure 2, the overall
structure is referred to as a void lattice. Figure 2
shows the underlying explanation for the pronounced
volume swelling of a-Al2O3 shown in Figure 1,
namely the formation of a void lattice with increasing
neutron radiation dose. This phenomenon is well
known in many irradiated materials, both metals
and ceramics, and is referred to as void swelling.
Susceptibility to void swelling is a very undesirable
material trait and basically disqualifies such a material from use in extreme environments (in this case,
high temperature and high neutron radiation fields).
It should be noted that TEM micrographs (not shown
here) obtained from MgAl2O4 spinel irradiated under
similar conditions to those in Figure 2 show no
evidence of voids of any size.
1.05.2.2 Point Defect Evolution and

Vacancy Supersaturation
Voids are a consequence of a supersaturation of
vacancies in the lattice and the tendency of excess
vacancies to condense into higher-order defect complexes (either vacancy loops or voids). However, the
root cause of void formation is actually not the vacancies, but the interstitials. Each atomic displacement
event during irradiation produces a pair of defects
known as a Frenkel pair. The constituents of a
Frenkel pair are an interstitial (i) and a vacancy (v).
Interstitials are more mobile than vacancies at most
temperatures (at low-to-moderate temperatures, say
less than half the melting point (0.5Tm), vacancies are
essentially immobile in most materials), such that
i-defects freely migrate around the lattice, while
v-defects either remain stationary or move much
smaller distances than i-defects. Because i-defects
are highly mobile, they are able to diffuse to other
lattice imperfections, such as dislocations, grain
boundaries, and free surfaces, where they often are
readily absorbed. This situation leads to a supersaturation of vacancies, that is, a condition in which the
bulk vacancy concentration exceeds the complementary bulk interstitial concentration. This is a highly
undesirable circumstance for a material exposed
to displacive radiation damage conditions, because
the v-defect concentration will continue to grow
(unchecked) at approximately the Frenkel defect
production rate, while the i-defect concentration


126

Radiation-Induced Effects on Material Properties of Ceramics

will reach a steady-state concentration, determined
by interstitial mobility and by the concentration of
extended defects (extended defects presumably serve
as sinks for interstitial absorption). The v-defect
concentration will inevitably reach a critical stage
at which the lattice can no longer support the excessive concentration of vacancies, at which point the
v-defects will migrate locally and condense to form
voids (or vacancy loops or clusters). This entire process, initiated by the supersaturation of vacancies,
causes the material to undergo macroscopic swelling,
and the material becomes susceptible to microcracking or failure by other mechanical mechanisms. This,
indeed, is the fate suffered by a-Al2O3 when exposed
to a neutron (displacive) radiation environment.
It is interesting that a supersaturation of vacancies
can even be established in a material devoid of
extended defects, such as a high-quality single crystal
or a very large-grained polycrystalline material.
Single crystal a-Al2O3 (sapphire) is an example of
just such a material.6 When freely migrating i-defects
are unable to readily ‘find’ lattice imperfections such
as grain boundaries and dislocations, they instead
‘find’ one another. Interstitials can bind to form diinterstitials or higher-order aggregates. Eventually, a
new extended defect, produced by the condensation
of i-defects, becomes distinguishable as an interstitial
dislocation loop (also known as an interstitial Frank
loop). Once formed, such a lattice defect acts as a sink
for the absorption of additional freely migrating
i-defects. With this, the conditions for a supersaturation of vacancies and macroscopic swelling are
established.
The defect situation just described can be conveniently summarized using chemical rate equations as

described in detail in Chapter 1.13, Radiation Damage Theory. In eqn [1], we employ a simplified pair of
rate equations to show the time-dependent fate of
interstitials and vacancies produced under irradiation
for an imaginary single crystal of A atoms:
dCi ðt Þ
dt

¼ Pi ðAA ! Ai þ VA Þ
ÀRiÀv ðAi þ VA ! AA Þ
½1aŠ
ÀN ðnucleation rate for interstitial loopsÞ
ÀGðgrowth rate for interstitial loopsÞ
dCv ðt Þ
dt

¼ Pv
ÀRiÀv

ðAA ! Ai þ VA Þ
ðAi þ VA ! AA Þ

½1bŠ

where Ci(t) and Cv(t) are the time-dependent concentrations of interstitials and vacancies, respectively;
Pi and Pv are the production rates of interstitials and
vacancies, respectively (equal to the Frenkel pair production rate); Ri–v is the recombination rate of

interstitials and vacancies (i.e., the annihilation rate of
i and v point defects when they encounter one another
in the matrix); N and G are the nucleation and growth

rates, respectively, of interstitial loops; AA is an A atom
on an A lattice site; Ai is an interstitial A atom; and VA is
a vacant A lattice site (an A vacancy). (This equation
for vacancies assumes low or moderate temperatures,
such that vacancies are effectively immobile. Under
high-temperature irradiation conditions, we would
need to add nucleation and growth terms for voids,
vacancy loops, or vacancy clusters. Reactions with
preexisting defects are also ignored in eqn [1].) Note
in eqn [1] that i–v recombination, Ri–v, is a harmless
point defect annihilation mechanism (it restores,
locally, the perfect crystal lattice). On the contrary,
nucleation and growth (N and G) of interstitial loops
are harmful point defect annihilation mechanisms, in
the sense that these mechanisms leave behind
unpaired vacancies in the lattice, thus establishing a
supersaturation of vacancies, which is a necessary condition for swelling.
It is interesting to compare and contrast the neutron radiation damage behavior shown in Figure 1 of
alumina (a-Al2O3) and spinel (MgAl2O4) single crystals, in terms of the defect evolution described
in eqn [1]. Alumina must be described as a highly
radiation-susceptible material, due to its tendency
to succumb to radiation-induced swelling. Spinel,
on the other hand, is to be considered a radiationtolerant material, in view of its ability to resist
radiation-induced swelling. According to eqn [1],
we can speculate that mechanistically, nucleation
and growth of interstitial dislocation loops are much
more pronounced in alumina than in spinel. Also,
eqn [1] suggests that harmless i–v recombination
must be the most pronounced point defect annihilation mechanism in spinel so that a supersaturation of
vacancies and concomitant swelling is avoided.

Indeed, it turns out that nucleation and growth of
dislocation loops are far more pronounced in alumina than in spinel, as discussed in detail next. The
dislocation loop story described below is rich with
the complexities of dislocation crystallography and
dynamics. The unraveling of the mysteries of dislocation loop evolution in alumina versus spinel should
be considered one of the greatest achievements ever
in the field of radiation effects in ceramics, even
though this was accomplished some 30 years ago!
This story also illustrates the tremendous complexity
of radiation damage behavior in ceramic materials,
wherein point defects are created on both anion and
cation sublattices, and where the defects generated
often assume significant Coulombic charge states in


Radiation-Induced Effects on Material Properties of Ceramics

highly insulating ceramics (alumina and spinel are
large band gap insulators).
The earliest stages of the nucleation and growth of
interstitial dislocation loops are currently impossible
to interrogate experimentally. TEM has been used as
a very effective technique for examining the structural evolution of dislocation in irradiated solids but
only after the defect clusters have grown to diameters
of about 5 nm. Interestingly, important changes in
dislocation character probably occur in the early
stages of dislocation loop growth, when loop diameters
are only between 5 and 50 nm.10 Therefore, we must
speculate about the nature of nascent dislocation loops
produced under irradiation damage conditions.

1.05.2.3 Dislocation Loop Formation in
Spinel and Alumina
1.05.2.3.1 Introduction to atomic layer
stacking

Results of numerous neutron and electron irradiation
damage studies suggest that two types of interstitial
dislocation loops nucleate in a-Al2O3: (1) 1/3 [0001]
(0001); and (2) 1=3h1011if1010g (see, e.g., the review
by Kinoshita and Zinkle4). The first of these involves
precipitation on basal planes in the hexagonal
a-Al2O3 structure, while the second is due to precipitation on m-type prism planes. In MgAl2O4, similar
studies indicate that primitive interstitial dislocation
loops also have two characters: (1) 1/6 h111i {111}
and (2) 1/4 h110i {110}.4 Though the crystal structure of spinel is cubic, compared with that of alumina,
which is hexagonal, the nature of the dislocation loops
formed in spinel is similar to those in alumina: {111}
spinel loops are analogous to (0001) alumina loops;
likewise, {110} spinel loops are analogous to f1010g
alumina loops. We will first compare and contrast
{111} spinel versus (0001) alumina loops and later
discuss {110} spinel versus f1010g alumina loops.
Both spinel h111i {111} and alumina [0001]
(0001) interstitial dislocation loops involve insertion
of extra atomic layers perpendicular to the h111i and
[0001] directions, respectively. These layers are
either pure cation or pure anion layers. In both spinel
and alumina, anion layers along h111i and [0001]
directions, respectively (i.e., along the 3 direction
in both structures), are close packed (specifically,

they are fully dense, triangular atom nets), while the
cation layers contain ‘vacancies,’ which are necessary
to accommodate the cation deficiency (compared
with anion concentration) in both compounds (these
‘vacancies’ actually are interstices; they are ‘holes’
in the otherwise fully dense triangular atom nets

127

that make up each cation layer). Table 1 shows
the arrangement of cation and anion layers in spinel
and alumina, along h111i and [0001] directions,
respectively.11 Both structures can be described by a
24-layer stacking sequence along these directions.
Both spinel and alumina can be thought of as consisting of pseudo-close-packed anion sublattices, with
cation layers interleaved between the anion layers.
The anion sublattice in spinel is cubic close-packed
(ccp) with an ABCABC. . . layer stacking arrangement,
while alumina’s anion sublattice is hexagonal closepacked (hcp) with BCBCBC. . . layer stacking. In both
structures, between each pair of anion layers there
are three layers of interstices where cations may
reside: a tetrahedral (t) interstice layer, followed by
an octahedral (o) interstice layer, followed by another
t layer. In spinel, Mg cations reside on t layers, while
Al cations occupy the o layers. In alumina, all t layers
are empty and Al occupies 2/3 of the o layer interstices. In spinel, cation interlayers alternate between
a pure Al kagome´ layer and a mixed MgAlMg, threelayer thick slab. In alumina, each interlayer is pure Al
in a honeycomb arrangement.
1.05.2.3.2 Charge on interstitial dislocations

In addition to spinel and alumina layer stacking
sequences, Table 1 also shows the layer ‘blocks’ that
have been found to comprise {111} and (0001) interstitial dislocation loops in spinel and alumina, respectively. An interstitial loop in spinel is composed of
four layers such that the magnitude of the Burgers
vector, b, along h111i is 1/6 h111i. The composition
of each of these blocks has stoichiometry M3O4,
where M represents a cation (either Mg or Al) and
O is an oxygen anion. The upper 1/6 h111i block in
Table 1 has an actual composition of Al3O4, while
the lower 1/6 h111i block has a composition of
Mg2AlO4. If Mg and Al cations assume their formal
valences (2þ and 3þ, respectively), and O anions
are 2À, then the blocks described here are charged:
(Al3O4)1þand (Mg2AlO4)1–. This may result in an
untenable situation of excess Coulombic energy, as
each molecular unit in the block possesses an electrostatic charge of 1 esu. It has been proposed that
this charge imbalance is overcome by partial inversion of the cation layers in the 1/6 h111i blocks.12
(Inversion in spinel refers to exchanging Mg and Al
lattice positions such that some Mg cations reside on
o sites, while a similar number of Al cations move to
t sites.) If a random cation distribution is inserted into
either the upper or lower 1/6 h111i block shown in
Table 1, then the block becomes charge neutral, that
is, (MgAl2O4)x.


128

Layer #

24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0

Layer stacking of {111} planes along h111i in cubic spinel and (0001) planes along [0001] in hexagonal alumina
Layer height

23/24

22/24 (11/12)
21/24 (7/8)
20/24 (5/6)
19/24
18/24 (3/4)
17/24
16/24 (2/3)
15/24 (5/8)
14/24 (7/12)
13/24
12/24 (1/2)
11/24
10/24 (5/12)
9/24
8/24 (1/3)
7/24
6/24 (1/4)
5/24
4/24 (1/6)
3/24 (1/8)
2/24 (1/12)
1/24
0/24
–1/24

Spinel (MgAl2O4) {111}-layer stacking along h111i direction

Alumina (a-Al2O3) (0001)-layer stacking along [0001] direction

O ¼ oxygen

t ¼ tetrahedral
interstices
o ¼ octahedral
interstices

Layer registry
(ABCABC-type
O-stacking)

Layer
composition

O ¼ oxygen
t ¼ tetrahedral
interstices
o ¼ octahedral
interstices

t
O
t
o
t
O
t
o
t
O
t
o

t
O
t
o
t
O
t
o
t
O
t
o
t

C
B
A
C
B
A
C
B
A
C
B
A
C
B
A
C

B
A
C
B
A
C
B
A
C

–
O4
Mg1
Al1
Mg1
O4
–
Al3
–
O4
Mg1
Al1
Mg1
O4
–
Al3
–
O4
Mg1
Al1

Mg1
O4
–
Al3
–

Frank loop
Burgers vectors

1/6<111>
¼ 4 layers
(Al3O4)1þ

1/6<111>
¼ 4 layers
(Mg2AlO4)1À

t
O
t
o
t
O
t
o
t
O
t
o
t

O
t
o
t
O
t
o
t
O
t
o
t

Layer registry
(BCBC-type
O-stacking)

C
a3
B
a2
C
a1
B
a3
C
a2
B
a1

Layer
composition

–
O3
–
Al2
–
O3
–
Al2
–
O3
–
Al2
–
O3
–
Al2
–
O3
–
Al2
–
O3
–
Al2
–

Frank loop

Burgers vectors

1/3 [0001]
¼ 4 layers
(excluding
empty
tetrahedral
layers)
(Al2O3)x

Radiation-Induced Effects on Material Properties of Ceramics

Table 1


Radiation-Induced Effects on Material Properties of Ceramics

129

Table 1 indicates that an (0001) interstitial dislocation loop in alumina consists of a four-layer block
(excluding the empty t layers) such that the magnitude of the Burgers vector, b, along [0001] is 1/3
[0001]. The composition of each of these blocks is
Al2O3, which is charge neutral, that is, (Al2O3)x.
Thus, there are no Coulombic charge issues associated with interstitial dislocation loops along 3 in
alumina. These dislocation loops consist simply of a
pair of Al layers interleaved with two O layers.

specifically at the position of the red vertical line in
the last sequence. Kronberg13 refers to this as an
unsymmetrical electrostatic fault. This fault is seen

to be intrinsic and only in the cation sublattice; the
anion sublattice is undisturbed. In summary, the dislocation loop formed by 1/3 [0001] block insertion in
alumina is an intrinsic, cation-faulted, interstitial
Frank loop. This is also a sessile loop.

1.05.2.3.3 Lattice registry and stacking
faults I: (0001) Al2O3

Now, we consider the formation of an interstitial
dislocation loop along 3 in spinel. In spinel, O anion
layers are fully dense triangular atom nets stacked in
a ccp, ABCABC. . . geometry (A, B, and C are all distinct
layer registries). Between adjacent O layers, 3/4
dense Al and MgAlMg layers are inserted, with registries labeled a, b, and c in Table 1 (a cations have the
same registry as A anions; likewise, b same as B, c same
as C). For stacking fault layer stacking assessments
in spinel, it is conventional to simplify the layer
notation for the cations (see, e.g., Clinard et al.6).
The successive kagome´ Al layers are labeled a, b, g,
while the MgAlMg mixed atom slabs are each projected onto one layer and labeled a0 , b0 , g0 . With these
definitions, the registry of cation/anion stacking in
spinel follows the sequence: a C b0 A g B a0 C b A g0 B.
As with alumina, when extra pairs of cation and
anion layers are inserted into the spinel 3 stacking
sequence, a C b0 A g B a0 C b A g0 B, a fault in the
stacking sequence is introduced. One can demonstrate how this works by inserting a 1/6 h111i b A
block into the stacking sequence described above
(this is equivalent to the upper Burgers vector for
spinel shown in Table 1, which uses a kagome´ Al
cation layer). We obtain:

Next, we must consider the lattice registry of the
layer blocks inserted into alumina and spinel to
form interstitial dislocation loops along 3. Registry
refers to the relative translational displacements
between successive layers in a stack. In alumina,
O anion layers are fully dense triangular atom nets,
stacked in an hcp, BCBCBC. . . geometry. B and C
represent two distinct layer registries (displaced laterally with respect to one another). All the Al cation
layers occur within the same registry, labeled a in
Table 1 (a is displaced laterally relative to B and C).
These Al layers are 2/3 dense, relative to the fully
dense O layers, forming honeycomb atomic patterns.
The successive Al layers are differentiated by where
the cation ‘vacancies’ occur within each a layer.
There are three possibilities that occur sequentially,
hence the subscripted labels in Table 1 (a1, a2, a3).11
Thus, the registry of cation/anion stacking in alumina
follows the sequence: a1 B a2 C a3 B a1 C a2 B a3 C.
When extra pairs of Al and O layers are inserted
into the stacking sequence, a1 B a2 C a3 B a1 C a2 B a3 C,
a mistake in the stacking sequence is introduced.
In other words, the dislocation loop formed by the
block insertion is faulted (contains a stacking fault).
Let us see how this works by inserting a 1/3 [0001]
four-layer block, Al2ÁO3ÁAl2ÁO3, into the stacking
sequence described above. We obtain:
ðbeforeÞ

a C b0 A g B a0 C b A g0 B b A a C b0 A g B

b0 A g B a0 C b A g0 B ðafter; showing
stacking fault positionsÞ

a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a1 B
a2 C a3 B a1 C a2 B a3 C ðafterÞ
a1 a2 a3 a1 a2 a3 a1 a2 j a1 a2 a3 a1 a2 a3
ðafter; showing only cations and
showing stacking fault positionÞ

a C b 0 A g B a0 C b A g 0 B a C b 0 A g B
a0 C b A g0 B ðbeforeÞ
a0 C b A g0 B ðafterÞ
a C b 0 A g B a0 C b A g 0 B j b A j a C

a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a3 B
a1 C a2 B a3 C

1.05.2.3.4 Lattice registry and stacking
faults II: {111} MgAl2O4

½2Š

Notice in eqn [2] that after block insertion, the anion
sublattice is not faulted (BCBC. . . layer stacking is
preserved), whereas the cation sublattice is faulted,

½3Š

Notice in eqn [3] that after block insertion, both

the anion sublattice (CABCAB. . . stacking is not
preserved) and the cation sublattice are faulted.
Also, notice that the cation and anion stacking
sequences are faulted on both sides of the inserted
b A block (the layer sequences are broken approaching the block from both the left and the right). Thus,


130

Radiation-Induced Effects on Material Properties of Ceramics

the b A block actually contains two stacking faults, on
either side of the block. The positions of these stacking faults are denoted by vertical red lines in eqn [3].
The dislocation loop formed by 1/6 h111i block
insertion in spinel is an extrinsic, cationþanion
faulted, sessile interstitial Frank loop.
We can also consider inserting a 1/6 h111i b0 A
block into the spinel stacking sequence (i.e., the lower
spinel Burgers vector shown in Table 1, which uses a
mixed MgAlMg cation slab). We obtain:
a C b0 A g B a0 C b A g0 B a C b0 A g B a0 C

ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ða1 BÞ
ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ðbeforeÞ
ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ða1 BÞ ða2 CÞ

b A g0 B ðbeforeÞ
a C b0 A g B a0 C b A g0 B b0 A a C b0 A g B

ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ðafterÞ

ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ ða1 BÞ ða2 CÞ j

a0 C b A g0 B ðafterÞ
a C b 0 A g B a 0 C b A g 0 B j b0 A j a C
b0 A g B a0 C b A g0 B ðafter; showing
stacking fault positionsÞ

anion and cations together, we can write the {1010}
stacking sequence in alumina as (a1B) (a2C) (a3B) (a1C)
(a2B) (a3C).
Now, as with the basal plane story described
earlier, when an extra 1=3h1010i two-layer block,
(Al2O3)xÁ(Al2O3)x, is inserted into the stacking
sequence, (a1B) (a2C) (a3B) (a1C) (a2B) (a3C), a stacking fault occurs as follows:

ða1 BÞ ða2 CÞ ða3 BÞ ða1 CÞ ða2 BÞ ða3 CÞ
ðafter; showing stacking fault positionÞ
½4Š

Once again, both the anion and cation sublattices are
faulted, and we obtain an extrinsic, cationþanion
faulted, sessile interstitial Frank loop.
1.05.2.3.5 Lattice registry and stacking
faults III: {1010} Al2O3

So far we have considered Coulombic charge and faulting for 1/3 [0001] (0001) loops in alumina and 1/6
h111i {111} loops in spinel. Now, we must repeat
these considerations for 1=3h1011if1010g prismatic
loops in alumina and 1/4 h110i {110} loops in spinel.
We begin with alumina prismatic loops. Alumina

{1010} prism planes contain both Al and O in the
ratio 2:3, that is, identical to the Al2O3 compound
stoichiometry. Along the h1010i direction normal to
the traces of the {1010} planes, the registry of the
{1010} planes varies between adjacent planes, analogous to the registry shifts that occur between adjacent
(0001) basal planes in alumina (discussed earlier).
However, the patterns of Al atoms in all {1010} planes
are identical. Similarly, the O atom patterns are identical in all {1010} planes. The registry of the O atom
patterns between adjacent {1010} planes alternates
every other layer, analogous to the BCBC. . . stacking
of oxygen basal planes (Table 1, eqns [2–4]). On the
other hand, the registry of the Al cation patterns is
distinct from the O pattern registries (B and C), and
the registry of the Al patterns only repeats every fourth
layer. In other words, the stacking sequence of {1010}
plane Al atom patterns can be described using the same
nomenclature as in Table 1 and eqn [2] for (0001)
alumina planes, that is, a1 a2 a3 a1 a2 a3. . .. Putting the

½5Š

Notice in eqn [5] that after block insertion, the anion
sublattice is not faulted (BCBC. .. layer stacking is
preserved), whereas the cation sublattice is faulted,
specifically at the position of the red vertical line in
the last sequence. Similar to the case of basal plane
interstitial loop formation in alumina (discussed earlier), the dislocation loop formed by 1=3h1010i block
insertion in alumina is an intrinsic, cation-faulted,
sessile interstitial Frank loop.
1.05.2.3.6 Lattice registry and stacking

faults IV: {110} MgAl2O4

Next, we consider 1/4 h110i {110} loops in spinel.
Spinel {110} planes alternate in composition,
(AlO2)ÀÁ(MgAlO2)þ. . ., such that each layer is a
mixed cation/anion layer. To insert a charge-neutral
interstitial slab along h110i in spinel requires that we
insert a {110} double-layer block, (AlO2)ÀÁ(MgAlO2)þ,
that is, a stoichiometric MgAl2O4 unit. The thickness
of this slab is a/4 h110i, where a is the spinel cubic
lattice parameter. Along the h110i direction normal
to the traces of the {110} planes, the registry of
the {110} planes varies between adjacent planes,
analogous to the registry shifts that occur between
adjacent {111} planes in spinel (discussed earlier).
The O atom patterns are identical in all {110} planes,
but the registry of the O atom patterns between
adjacent {110} planes alternates every other layer,
analogous to the BCBC. . . stacking described earlier.
The Mg atom patterns are identical in each (MgAlO2)þ
layer, while the registry of the Mg atom patterns
alternates every other (MgAlO2)þ layer. We denote
the Mg stacking sequence by a1 a2 a1 a2 . . .. There
are two Al atom patterns along h110i: (1) the first


Radiation-Induced Effects on Material Properties of Ceramics

occurs in each (AlO2)À layer with no change in
registry between layers (we denote this Al pattern

by b0 ); and (2) the second occurs in each (MgAlO2)þ
layer, and the registry of these Al atom patterns
alternates every other (MgAlO2)þ layer (we denote
this Al stacking sequence by b1 b2 b1 b2 . . .).
Combining all these considerations, we can write
the {110} planar stacking sequence in spinel as follows: (b0 B) (a1b1C) (b0 B) (a2b2C).
Now, as with the spinel {111} case described
earlier, when an extra 1/4 h110i two-layer block,
(AlO2)ÀÁ(MgAlO2)þ, is inserted into the spinel {110}
stacking sequence, (b0 B) (a1b1C) (b0 B) (a2b2C), a stacking fault occurs as follows:

c

c
500 nm

ðb0 BÞ ða1 b1 CÞ ðb0 BÞ ða2 b2 CÞ ðb0 BÞ ða1 b1 CÞ
ðb0 BÞ ða2 b2 CÞ
0

ðbeforeÞ
0

0

ðb BÞ ða1 b1 CÞ ðb BÞ ða2 b2 CÞ ðb BÞ ða1 b1 CÞ
ðb0 BÞ ða1 b1 CÞ ðb0 BÞ ða2 b2 CÞ
0

0

ðafterÞ
0

ðb BÞ ða1 b1 CÞ ðb BÞ ða2 b2 CÞ ðb BÞ ða1 b1 CÞ j
ðb0 BÞ j ða1 b1 CÞ ðb0 BÞ ða2 b2 CÞ ðafter;
showing stacking fault positionsÞ

131

½6Š

Notice in eqn [6] that after block insertion, the anion
sublattice is not faulted (BCBC. . . layer stacking is
preserved), whereas the cation sublattice is faulted,
specifically at the positions of the red vertical lines in
the last sequence (the left-hand red line corresponds to
the cation fault position for cation planar registries
moving from right to left; likewise, the right-hand
red line corresponds to the cation fault position for
cation planar registries moving from left to right).
Thus, the dislocation loop formed by 1/4 h110i twolayer block insertion in spinel is an extrinsic, cationfaulted, sessile interstitial Frank loop.
Figure 3 shows an example of 1/4 h110i interstitial
dislocation loops in spinel, produced by neutron irradiation.12 The alternating black-white fringe contrast
within the loops is an indication of the presence of a
stacking fault within the perimeter of each loop. The
character of the {110} loops was determined by
Hobbs and Clinard using the TEM imaging methods
of Groves and Kelly,14,15 with attention to the precautions outlined by Maher and Eyre.16 These loops
were determined to be extrinsic, faulted 1/4 h110i

{110} interstitial dislocation loops. It is evident in
Figure 3 that the extrinsic fault associated with these
loops is not removed by internal shear, even when the
loops grow to significant sizes (>1 mm diameter).
This is the subject of our next topic of discussion,
namely, the unfaulting of faulted Frank loops.

Figure 3 Bright-field transmission electron microscopy
(TEM) image of {110} faulted interstitial loops in MgAl2O4
single crystal irradiated at 1100 K to a fluence of
1.9 Â 1026 n mÀ2 ($20 dpa). Reproduced from Hobbs, L. W.;
Clinard, F. W., Jr. J. Phys. 1980, 41(7), C6–232–236.
The surface normal to the TEM foil is along h111i. The
dislocation loops intersect the top and bottom surfaces
of the TEM foil, which gives them their ‘trapezoidal’ shapes.
The areas marked ‘C’ in the micrograph are regions
where a ‘double-layer’ loop has formed, that is, a second
Frank loop has condensed on planes adjacent to the
preexisting faulted loop.

1.05.2.3.7 Unfaulting of faulted Frank
loops I: (0001) Al2O3

In principle, faulted interstitial Frank loops can
unfault by dislocation shear reactions. This should
occur at a critical stage in interstitial loop growth,
when the energy of the faulted dislocation loop, with
a relatively small Burgers vector, becomes equal to
an equivalently sized, unfaulted dislocation loop,
with a larger Burgers vector. (In the absence of a

stacking fault, the energy of a dislocation scales as
b2, where b is the magnitude of the Burgers vector.)
From this critical point on, the energy cost to incrementally grow the size of a dislocation loop favors
the unfaulted loop, since there is no cost in energy
due to a stacking fault within the loop perimeter.
We examine first the unfaulting of 1/3 [0001] (0001)
loops in alumina.
To unfault a 1/3 [0001] (0001) dislocation loop in
alumina, we must propagate a 1=3½1010Š partial shear
dislocation across the loop plane.6 This is described
by the following dislocation reaction:
1
3½0001Š

þ 13½1010Š !

1
3½1011Š

faulted loop

partial shear

unfaulted loop

ðbasalÞ

½7Š

132

Radiation-Induced Effects on Material Properties of Ceramics

After propagating the partial shear through the loop,
we are left with an unfaulted layer stacking sequence.
The Burgers vector of the resultant dislocation loop,
1=3½1011Š, is a perfect lattice vector; therefore, the
newly formed dislocation is a perfect dislocation. The
resultant 1=3½1011Š (0001) dislocation is a mixed dislocation, in the sense that the Burgers vector is canted
(not normal) relative to the plane of the loop.
1.05.2.3.8 Unfaulting of faulted Frank
loops II: {111} MgAl2O4
C

1/3 [1011]

1/3 [0001]

1/3 [1010]
Figure 4 Alumina cation ‘honeycomb’ atom nets along
the c-axis in Al2O3 corundum (anion sublattice not shown
here). The black circles represent Al atoms. The gray
squares represent cation ‘vacancies.’ The diagram shows
the Burgers vectors involved in the partial shear unfaulting
reactions for interstitial dislocation loops in alumina.
Adapted from Howitt, D. G.; Mitchell, T. E. Philos. Mag. A
1981, 44(1), 229–238.

This reaction is shown graphically in Figure 4. Note

that the magnitude of 1=3½1010Š is approximately the
Al–Al (and O–O) first nearest-neighbor spacing in
Al2O3. When we pass a 1=3½1010Š shear through a 1/3
[0001] (0001) dislocation loop, the cation planes
beneath the loop assume new registries such that
in eqn [2], a1, a2, and a3 commute as follows:
a1 ! a3 ! a2 ! a1 . The anion layers beneath the
loop are left unchanged (B ! B, C ! C). Taking
the faulted (0001) stacking sequence in eqn [2] and
assuming that the planes to the right are above the
ones on the left, we perform the 1=3½1010Š partial
shear operation as follows:
a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 |C a1 B a2 C a3 B a1 C a2 B a3 C

(faulted)

C a3 B a1 C a2 B a3 C a1 B a2 C
a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C

(unfaulted)

[8]

For this particular dislocation loop, it is thought that
rather than unfaulting, 1/6 h111i {111} dislocations
simply dissolve back into the lattice, in favor of the
more stable 1/4 h110i {110} loops.12 As discussed
earlier, the 1/6 h111i {111} dislocation can be presumed to be relatively unstable because it possesses
both anion and cation faults, and in addition, it cannot
preserve stoichiometry or charge balance in either

normal or inverse spinel.12 Counter to this argument
is the idea that if a 1/6 h111i {111} dislocation loop
incorporates a partial inversion of its cation content,
then this loop could be made both stoichiometric
and charge neutral. Such a dislocation would arguably be more stable. However, {111} loops are never
observed to grow very large (<100 nm) and are altogether absent in spinel samples irradiated at 1100 K.17
Therefore, it is likely that ‘disordered’ {111} interstitial loops are not an important aspect of radiation
damage evolution in spinel.
1.05.2.3.9 Unfaulting of faulted Frank
loops III: {1010} Al2O3

To unfault a 1=3½1010Šð1010Þ dislocation loop in
alumina, we must propagate a 1/3 [0001] partial
shear dislocation across the loop plane.17 This is
described by the following dislocation reaction:
1
3½1010Š

þ 13½0001Š !

1
3½1011Š

faulted loop

partial shear

unfaulted loop

ðprismaticÞ

½9Š

This reaction is symmetric with that shown in eqn [8]
for unfaulting a (0001) basal loop in alumina. The
reaction in eqn [9] is shown graphically in Figure 4.
When we pass a 1/3 [0001] shear through a
1=3½1010Šð1010Þ dislocation loop, the cation planes
beneath the loop assume new registries such that
in eqn [6], a1b1 and a2b2 commute as follows:
a1 b1 ! a2 b2 ! a1 b1 . The anion layers beneath the
loop are left unchanged (B ! B, C ! C). In addition,
the Al-only cation layers are unchanged (b0 ! b0 ).
Taking the faulted (0001) stacking sequence in
eqn [2] and assuming that the planes to the right


Radiation-Induced Effects on Material Properties of Ceramics

133

are above the ones on the left, we perform the 1/3
[0001] partial shear operation as follows:

(bЈB) ( a1b1C) ( bЈB) ( a2b2C) (bЈB) ( a1b1C) |(bЈB)| (a1b1C ) (bЈB) ( a2b2C) (faulted)

(βЈB) ( α1β1C) ( βЈB) ( α2β2C) (βЈB) ( α1β1C) |(βЈB)| (α1β1C) ( βЈB) ( α2β2C) (faulted)

(bЈB) ( a1b1C) ( bЈB) ( a2b2C) (bЈB) ( a1b1C) (bЈB) (a2b2C ) ( bЈB) (a1b1C )

bЈB a2b2C bЈB a1b1C

(α2β2C) ( βЈB) ( α1β1C)
(βЈB) ( α1β1C) ( βЈB) ( α2β2C) (βЈB) ( α1β1C) (βЈB) (α2β2C) ( βЈB) ( α1β1C )

After propagating the partial shear through the loop, we
are left with an unfaulted layer stacking sequence. The
resultant dislocation loop, 1=3½1011Š, is a perfect dislocation. The resultant 1=3½1011Š (0001) dislocation is a
mixed dislocation, in the sense that the Burgers vector
is canted (not normal) relative to the plane of the loop.
1.05.2.3.10 Unfaulting of faulted Frank
loops IV: {110} MgAl2O4

To unfault a 1/4 [110] (110) dislocation loop in
spinel, we must propagate a 1=4½112Š partial shear
dislocation across the loop plane.12 This is described
by the following dislocation reaction:
1
4½110Š
faulted loop

þ

1
4½112Š

!

partial shear

1
2½101Š

½11Š

unfaulted loop

This reaction is shown graphically in Figure 5. When
we pass a 1=4½112Š shear through a 1/4 [110] (110)
dislocation loop, the atomic planes beneath the loop
assume new registries, such that in eqn [6], a1b1
and a2b2 commute as follows: a1 b1 ! a2 b2 ! a1 b1 .
The anion layers beneath the loop are left unchanged
(B ! B, C ! C). Also the Al b0 layers are left
unchanged (b0 ! b0 ). Taking the faulted (110) stacking sequence in eqn [6] and assuming that the planes
to the right are above the ones on the left, we perform
the 1=4½112Š partial shear operation as follows:

[0 0 1]

z

[1 0 0]

1/4 [112]

x
1/2[101]
a
[0 1 0]

y

[12]

(unfaulted)

[10]

1/4 [110]

Figure 5 Spinel unit cell showing the Burgers vectors
involved in the partial shear unfaulting reaction for interstitial
dislocation loops in spinel. The blue circles represent Mg
atoms (Al and O are not shown here).

(unfaulted)

After propagating the partial shear through the
loop, we are left with an unfaulted layer stacking
sequence. The Burgers vector of the resultant
dislocation loop, 1=2½101Š, is a perfect lattice vector;
therefore, the newly formed dislocation is a perfect dislocation (equal to the Mg–Mg first nearestneighbor spacing). The resultant 1=2½101Šð110Þ
dislocation is a mixed dislocation, in the sense that
the Burgers vector is canted (not normal) relative to
the plane of the loop.
1.05.2.3.11 Unfaulting of faulted Frank
loops V: experimental observations

Having examined the crystallography of unfaulting

reactions in alumina and spinel, it is interesting now
to compare and contrast what is experimentally
observed so far as dislocation loop evolution in irradiated Al2O3 versus MgAl2O4 is concerned. First, it is
observed that the 1/3 [0001] (0001) basal loops and
1=3h1010if1010g prismatic loops readily unfault
under irradiation, by the reactions shown in eqns
[7,8] and [9,10], respectively.6 These reactions occur
when the loops reach $50 nm diameter,10 and each
reaction produces an unfaulted loop with a 1=3h1011i
perfect Burgers vector. Once formed, these unfaulted
loops grow without bound until they intersect other
growing dislocation loops, ultimately forming a dislocation network. Such a dislocation network in neutron irradiated Al2O3 is shown in Figure 6.
Once the dislocation network in irradiated alumina is formed, it has been demonstrated that the
product dislocations within the network are free
to climb.6 The continuous climb of network dislocations in Al2O3 provides unsaturable sinks for Al and
O interstitials arriving in stoichiometric proportions.
All the conditions for a substantial supersaturation of
vacancies are now in place. Al and O interstitials are
readily absorbed at network dislocations, leaving
behind numerous unpaired Al and O vacancies in
the lattice. These unpaired vacancies inevitably condense to form voids. Under these conditions, void
swelling must be the anticipated radiation response
of the material.
Contrast the evolution described above for
alumina to the observed microstructural evolution
in spinel. The predominant 1/4 h110i {110}


134

Radiation-Induced Effects on Material Properties of Ceramics

100
10
0 nm

Figure 6 Weak-beam dark-field transmission electron
micrograph showing the dislocation network formed in
Al2O3 following neutron irradiation at 1015 K to a fluence of
3 Â 1025 n mÀ2 ($3 dpa). Reproduced from Clinard, F. W.,
Jr.; Hurley, G. F.; et al. J. Nucl. Mater. 1982, 108/109,
655–670.

dislocations in spinel do not unfault under most
experimental conditions tested to date.6 (Kinoshita
et al.51 observed unfaulted 1/2 h110i {110} perfect
loops in MgAl2O4 single crystals following neutron
irradiations in the JOYO fast breeder test reactor (fast
neutron fluences up to 6.5 Â 1025 n mÀ2 (equivalent
to 6.5 dpa), and temperatures between 673 and
873 K). Kinoshita et al.51 also proposed a growth process of loops in spinel as follows: 1/6 [111] (111)
1/4 [110] (111) 1/4 [110] (101) 1/4 [110] (110) 1/2
[110] (110). Notice that this sequence ends in an
unfaulted, perfect interstitial loop. This final loop
configuration should be a good sink for interstitials,
thus promoting a supersaturation of vacancies in the
lattice. However, in neutron irradiations of MgAl2O4
single crystals in the fast flux test facility (FFTF), no
evidence for 1/2 [110] (110) perfect dislocations was
found, for neutron fluences ranging from 2.2 Â 1026

to 2.17 Â 1027 n mÀ2 (equivalent to 22–217 dpa) in
the temperature range 658–1023 K.51 Therefore,
the proposed progression of spinel interstitial loop
characteristics described above has, to date, been
confirmed only under the JOYO irradiation conditions reported by Kinoshita et al.51) According to
Clinard et al.:6
Persistence of the 1/4 h110i {110} stacking fault
amounts to a failure of a 1=4h112i partial dislocation
to nucleate, sweep across the loop plane, and so
remove the fault.

The reason for this failure is paradoxical. Apparently,
stacking fault energy cannot be the reason. The stacking fault energy estimate for 1/4 h110i {110} stacking
faults in spinel, 180 mJ mÀ2,18 is similar to the energy
estimates for 1/3 [0001] (0001) and 1=3h1010if1010g
stacking faults in alumina (320 and 750 mJ mÀ2,
respectively).10 Therefore, there seems to be a reasonable ‘driving force’ available to favor unfaulting of
1/4 h110i {110} stacking faults in spinel. Perhaps the
explanation is simply that the magnitude of the partial shear vector required to unfault the faulted loops
is prohibitively large. In spinel, the magnitude of the
unfaulting 1=4h112i vector is $5 A˚, compared with
the 1/3 [0001] (4.32 A˚) and 1=3h1010i (2.74 A˚)
unfaulting vectors in alumina.
Whatever the reason, spinel 1/4 h110i {110}
stacking faults do not unfault, and this leads to void
swelling resistance and impressive inherent radiation
tolerance in spinel compared alumina. Hobbs and
Clinard summarize the situation as follows:
The absence of void swelling h in spinel i can be
attributed to the failure of the loops to unfault and

develop into dislocation networks; they therefore
remain less than perfect interstitial sinks since the
energy per added interstitial never drops below
the fault energy. Vacancy-interstitial recombination
thus remains the dominant mode of defect accommodation, and saturating defect kinetics inevitably ensue.

Therefore, in conclusion, the significant swelling of
Al2O3 alumina at high temperatures is attributable to
the unfaulting of interstitial dislocation loops and the
subsequent formation of dislocation networks, which
serve as efficient sinks for the absorption of interstitial atoms. This leaves behind a supersaturation of
lattice vacancies, that is, an excess of unpaired vacancies in the bulk of the Al2O3.
In irradiated MgAl2O4, only high-energy faulted
loops are available as sinks for interstitials. Therefore,
in this case, interstitial–vacancy (i–v) recombination
is the dominant mechanism for defect accommodation, and negligible swelling results.
1.05.2.4 Amorphization in Spinel and
Alumina
Another response of materials to irradiation, not
discussed up to now, is radiation-induced amorphization. Amorphization is a structural phase transformation from a crystalline solid to a solid that lacks any
long-range order. Typically, the material still maintains a certain degree of short-range order, but as far


Radiation-Induced Effects on Material Properties of Ceramics

as diffraction techniques can discern, any long-range,
crystalline order is destroyed following an amorphization transformation.
Amorphization is a metastable process in which
material is forced into a glass-like structure, which
under thermodynamic equilibrium would be a prohibited structure. Amorphization transformations are

most prevalent under ambient or low temperature
irradiation conditions, such that kinetic recovery
mechanisms are not effective at annihilating atomic
displacements produced by irradiation. Typically,
above a critical temperature, amorphization can be
avoided in an otherwise amorphizable material, due
to thermal recovery processes.
Amorphization transformations can occur under
both ballistic (displacive) and electronic (SHI) radiation damage conditions. Under ballistic conditions
and depending on the material, amorphization can
either occur within a single primary knock-on (PKA)
ion track (or other irradiating particle track), or proceed through the accumulation of defects due to
overlapping of damage tracks. Amorphization tends
to be detrimental to materials employed in radiation environments, because the crystal-to-amorphous
transformation is usually accompanied by significant
volume swelling, mechanical softening, and microcracking, to name but a few deleterious effects.
In ceramic materials, tendencies to radiationinduced amorphization are strongly dependent on
crystal structure and chemistry, with the vast majority
of ceramics exhibiting significant susceptibility to
amorphization. One of the key properties that has
been correlated quite well to amorphization resistance
is ionicity: highly ionic compounds tend to resist amorphization; highly covalent compounds tend to readily
succumb to amorphization at relatively low doses.19
Both spinel and alumina are relatively ionic compounds, but interestingly both can be amorphized by
both ballistic and electronic damage mechanisms.
Single crystal MgAl2O4 spinel was found to amorphize
under ballistic ion irradiation conditions at a peak
displacement damage level of 25 dpa (100 K irradiation temperature, 400 keV Xe2þions).20 A similar
result was obtained under in situ ion irradiation conditions (30 K irradiation temperature, 1.5 MeV Xeþ
ions).21 The critical temperature, Tc, for amorphization of spinel, has yet to be determined, but it is likely

to be well below room temperature. (Only below Tc
can the material be fully amorphized. Above Tc, kinetic
recovery dominates and the material is partially to
fully crystalline.) Single crystal a-Al2O3 (sapphire)
has been observed to amorphize by a ballistic damage

135

dose of about 3.8 dpa (20 K irradiation temperature,
1.5 MeV Xeþ ions, in situ).22 This is a significantly
smaller amorphization dose than that for spinel irradiated under similar conditions. The critical temperature, Tc, for amorphization of a-Al2O3 was estimated
to be about 170 K. In both alumina and spinel, the
radiation-induced amorphization transformation does
not occur by direct, ‘in-cascade’ amorphization but by
damage accumulation by overlapping cascades (damage tracks). Presumably, neither a-Al2O3 nor MgAl2O4
can be amorphized at ambient temperature or above
using displacive radiation damage conditions. However,
there is a report of amorphization of a-Al2O3 at a
ballistic damage dose of 3–7 keV per atom.23
Under SHI irradiation conditions, where electronic stopping predominates over nuclear stopping,
both alumina and spinel undergo amorphization
transformations, with significant concomitant volume
swelling. In both materials, the transformation does
not initiate until ion tracks are overlapped. In polycrystalline a-Al2O3, the threshold for amorphization
was found to be at an accumulated electronic energy
deposition of about 1.5 GGy (85 MeV I7þ ions at
ambient temperature; amorphization was found to a
depth of $4.5 mm, corresponding to energy deposition cross-sections ranging from $5 to 20 keV nmÀ1
per ion.24 In single crystal sapphire irradiated under
similar conditions (90.3 MeV 129Xe at room temperature), amorphization was found to initiate at the

sample surface at an accumulated electronic energy
deposition of about 0.3 GGy.25 These authors also
observed a correlation between swelling (as measured
by surface ‘pop-out’) and amorphization. However,
the swelling values obtained from their measurements are too large to be realistic (more than 50%
volume swelling). Nevertheless, the swelling associated with SHI radiation-induced amorphization
in alumina is substantial. Matzke26 observed $30%
free swelling in Al2O3 irradiated at $420 K with
72 MeV Iþ ions to fluences ranging from 1019 to
1021 ions mÀ2 (5–500 GGy at the sample surface).
In MgAl2O4, amorphization and significant
surface pop-out were observed in SHI irradiations
at 370 K using 72 MeV Iþ ions.27 The ion fluences
where pop-out was observed were 1 Â 1019 and
5 Â 1019 ions mÀ2 (5.3 and 27 GGy, respectively, at
the sample surface). The volumetric swelling associated with this crystal-to-amorphous phase transformation was estimated to be $35%.28 In summary,
huge volume changes appear to be associated with
SHI amorphization transformations in model ceramics such as spinel and alumina.


136

Radiation-Induced Effects on Material Properties of Ceramics

This concludes the comparison and contrast of
radiation damage effects in two model ceramic oxides, namely, a-Al2O3 alumina and MgAl2O4 spinel.
To make this chapter on radiation effects in nuclear
reactor relevant materials as comprehensive as possible, we offer in the following section some notes on
additional ceramic materials that are either important
currently in nuclear reactor applications or have

potential as advanced nuclear reactor materials with
respect to future applications. In particular, we consider three representative ceramic materials, namely,
urania, silicon carbide, and graphite.
Subsequent chapters treat these materials in
more detail: uranium dioxide (Chapter 2.02, Thermodynamic and Thermophysical Properties of the
Actinide Oxides; Chapter 2.17, Thermal Properties of Irradiated UO2 and MOX; and Chapter 2.18,
Radiation Effects in UO2), SiC (Chapter 2.12, Properties and Characteristics of SiC and SiC/SiC
Composites and Chapter 4.07, Radiation Effects in
SiC and SiC-SiC), and graphite (Chapter 2.10,
Graphite: Properties and Characteristics; Chapter
4.10, Radiation Effects in Graphite; Chapter 4.11,
Graphite in Gas-Cooled Reactors; and Chapter
4.18, Carbon as a Fusion Plasma-Facing Material).

1.05.3. Radiation Effects in Other
Ceramics for Nuclear Applications
In this section, we discuss briefly some important
radiation effects in a few ceramics that are used in
nuclear reactor applications. We will consider three
representative ceramic materials: (1) urania (UO2);
(2) silicon carbide (SiC); and (3) graphite (C). Unfortunately, we cannot provide a thorough review of the
radiation damage studies that have been performed
on many hundreds of other nonmetallic solids.
1.05.3.1
Dioxide

Radiation Effects in Uranium

UO2 is an important nuclear material because it is the
fuel form of choice for conventional light water reactors. Unfortunately, our knowledge of pure radiation

effects in UO2 is somewhat limited. This is because
235
U undergoes fission in a thermal neutron radiation
environment, and consequently, the radiation response
of UO2 is dictated by chemical evolutionary effects
rather than by conventional, point defect condensation
effects. Swelling in UO2 during service as a nuclear
fuel can be significant; several percent for some

percent burnup of heavy metal.29 This swelling is
primarily due to the accumulation of gaseous fission
products as well as to some degree, solid fission products. It is not believed that UO2 is susceptible to void
swelling (described in previous sections).
Under ballistic radiation damage conditions, UO2
exhibits polygonization, that is, a grain subdivision
process in which UO2 grains initially $10 mm diameter subdivide into 104 to 105 new small grains
of $0.2 mm size.30 These authors demonstrated that
polygonization is initiated at a critical ballistic damage dose, apparently independent of temperature.
In particular, irradiation of single crystal UO2 with
300 keV Xe ions at 77 K, 300 K, and 773 K, to a
fluence of 4 Â 1020 Xe mÀ2 or higher, produces the
polygonization transformation.30 However, these
authors concluded that this transformation cannot
be due to radiation damage alone but is probably
also related to the implanted impurity atoms (Xe),
which reach a concentration of 5–7% at the critical
fluence described above. Despite the polygonization
transformation in UO2, no amorphization transformation, induced by ballistic damage conditions, has
ever been observed.
Under SHI (electronic stopping) irradiation damage conditions, once again amorphization was not

observed (even with overlapped ion tracks), and the
SHI-induced swelling is negligible.31 These experiments included numerous ion species (Zn, Mo, Cd,
Sn, Xe, I, Pb, Au, and U) and energies ranging from
72 MeV to 2.7 GeV. Latent tracks were visible by
TEM for electronic stopping powers greater than
29 keV nmÀ1, but all tracks were crystalline. Lattice
parameter expansion and polygonization were also
observed.
1.05.3.2 Radiation Effects in Silicon
Carbide
SiC is an important engineering ceramic because of
its high-temperature stability, high thermal conductivity, and special electronic properties. It has been
proposed for use in nuclear applications including
structural components in fusion reactors, cladding
material for gas-cooled fission reactors, and as an
inert matrix for the transmutation of plutonium and
other transuranics.32 In high-temperature gas-cooled
reactors, SiC is the primary barrier material for
TRISO coated fuel particles.33 Also, SiC fiber, SiC
matrix (SiC/SiC) composites are attractive candidate
materials for first wall and blanket components in
fusion reactors.34


Radiation-Induced Effects on Material Properties of Ceramics

Only limited studies of elevated-temperature
microstructural evolution (dislocation loops, voids,
etc.), based on neutron or ion irradiations, have
been performed on SiC. In pyrolytic b-SiC (cubic,

3C), Price35 found small (2–5 nm diameter) {111}
Frank loops following neutron irradiation at 900  C
to 2.4 Â 1021 n cmÀ2 (E > 0.18 MeV) ($2.4 dpa). Yano
and Iseki36 found the same loops in b-SiC irradiated at 640  C to 1.0 Â 1023 n cmÀ2 (E > 0.10 MeV)
($100 dpa) and, using high-resolution TEM, determined these to be 1/3 h111i {111} interstitial Frank
loops. These loops are constructed by inserting a
single extra Si-C layer into the CABCAB Si-C stacking
sequence. This produces the sequence CAjC 0 B 0 jCAB,
where the prime denotes a p rotation of the tetrahedral unit (note that an adjacent Si-C layer is modified
by the insertion of the extra Si-C layer).
In 6H-type hexagonal a-SiC, Yano and Iseki36
found ‘black spot’ defects lying on (0001) planes
following neutron irradiation at 840  C to 1.7 Â 1021
n cmÀ2 (E > 0.10 MeV) ($1.7 dpa). They coarsened
these defects using high-temperature annealing and
determined the defects to be interstitial Frank loops.
The stacking sequence along (0001) in 6H a-SiC
is ABCA 0 B 0 C 0 . Yano and Iseki proposed that the
Frank loops are formed by a mechanism similar to
b-SiC (described above), wherein insertion of an
extra Si-C layer modifies an adjacent Si-C layer to
produce a sequence such as ABCjB 0A 0 jC 0 B 0 . Such a
defect is described as a 1/6 [0001] (0001) interstitial
Frank loop.
For low temperatures (150–800  C), small amounts
of swelling (0–2%) are observed in monolithic SiC
samples produced by chemical vapor deposition
(CVD).33 It should be noted that CVD-SiC is
cubic and highly faulted.37 This swelling saturates
at low damage levels (a few dpa) and the saturated

swelling is lower, the higher the temperature.
Much of this swelling is due to strain caused
by surviving interstitials formed during ballistic
damage cascades. As the irradiation temperature
approaches 1000  C, the surviving defect fraction
diminishes because interstitial mobility increases
with temperature and i–v recombination is enhanced.
Newsome et al.33 found swelling values of 1.9, 1.1, and
0.7% for neutron irradiations at 300, 500, and 800  C,
respectively.
Above 1000  C, neutron irradiation-induced void
formation in b-SiC was first observed by Price35
at 1250  C (4.3–7.4 dpa) and 1500  C (5.2–8.8 dpa).
Interestingly, no dislocation loops were observable
by TEM in these samples. Price35 postulated that

137

the interstitials may have been annihilated at stacking
faults. Alternatively, he suggested that interstitial
defects were present following irradiation, but they
were too small and the contrast too weak to detect
them. Nevertheless, at present it is not clear whether
void formation in SiC is due to vacancy supersaturation produced by a dislocation bias. In any case,
swelling of a few percent was observed for irradiations at temperatures greater than 1000  C, and
Price38 speculated that this swelling probably does
not saturate with dose.
At low temperatures ($60  C), Snead and Hay37
observed both a- and b-SiC to amorphize following
a total fast neutron fluence of 2.6 Â 1021 n cmÀ2

($2.6 dpa). This amorphization transformation was
accompanied by a large reduction in density
($10.8%), that is, volumetric swelling of nearly 11%.
Snead and Hay37 estimated that the critical temperature for amorphization (the temperature above which
amorphization is not possible) is $125  C (a lower
limit for the threshold amorphization temperature).
The critical temperature is dose rate dependent. In
the study above, the dose rate was $8 Â 10–7 dpa sÀ1.
In other electron and ion irradiation experiments with
dose rates of $1 Â 10–3 dpa sÀ1, researchers found
critical temperatures ranging from 20 to 70  C for
2 MeV electron irradiations,39–41 $150  C for energetic Si ions,42 and $220  C for 1.5 MeV Xe ions.43,44
1.05.3.3

Radiation Effects in Graphite

Graphite (C) is a very important material for nuclear
energy applications. Graphite is a moderator used to
thermalize neutrons in thermal gas and water-cooled
reactors in the United Kingdom and the Soviet
Union, respectively.45 Pyrolitic graphite is one of
the barrier coating materials used in TRISO coated
fuel particles.33 Graphite and carbon composites
are also used as plasma-facing materials in fusion
reactors.46 Numerous radiation effects studies have
been performed on graphite. Nevertheless, the behavior of graphite in a radiation damage environment
remains poorly understood. This is due primarily to
the fact that graphite comes in so many forms and is
produced in so many different ways, that in fact, the
structure and chemistry of graphite used in nuclear

applications is not a well-defined constant. Nevertheless, there are some aspects of the crystal structure of
graphite and the changes in this structure induced
by irradiation that are somewhat analogous to the
discussion of Al2O3 versus MgAl2O4, presented
earlier in this chapter.


138

Radiation-Induced Effects on Material Properties of Ceramics

Graphite is a hexagonal crystalline material, with
an ABAB. . . layer stacking arrangement of carbon
sheets. These carbon layers have obvious hexagonal
atom patterns in them. However, they are not fully
dense triangular atom nets, as would be the case in a
close-packed structure. They are so-called graphene
sheets, in which the atom pattern is a honeycomb
pattern, identical to the cation layer patterns in
Al2O3 (see Section 1.05.2.3.1). Each C atom is surrounded by three nearest-neighbor C atoms, and the
bonding linking each C atom with its neighbors is
characterized by sp2 hybridization. The bonding that
links adjacent graphene layers is weak, Van der
Waals-type bonding.
The interstitial dislocation loops that form in irradiated graphite, by the condensation of freely migrating interstitial point defects, form (not surprisingly)
on (0001) basal planes, between adjacent graphene
layers. In some of the earliest work on radiation
effects in graphite, this was described as follows47:
When subjected to bombardment with fission neutrons, primary collisions displace carbon atoms from
their normal sites in the layers, driving them to

sites between planes (interstitial or interlamellar
positions).

This loop nucleation is analogous to the (0001) basal
interstitial loops that form in Al2O3 during the initial
stages of irradiation (Section 1.05.2.3.1). However,
the basal loops in graphite do not grow to any significant size. Instead, the graphene layers adjacent to
interlamellar loop nuclei buckle, which causes a net
increase in the c-dimension of the hexagonal material
and a concomitant decrease in the a-dimension.48 This
buckling is believed to be due to sp3 bond formation
between C interstitials and C atoms in the graphene
planes.49,50 The overall macroscopic effect of c-axis
expansion and a-axis shrinkage is dimensional changes
of crystallites within the graphite. Macroscopic radiation damage effects in graphite are discussed in detail
in Chapter 4.10, Radiation Effects in Graphite.
1.05.3.4 Radiation Effects in Other
Ceramics
Numerous additional ceramics have been either used
or proposed for nuclear reactor materials applications. These include graphite (discussed in other
chapters in this volume) as well as carbides and
nitrides, such as ZrC and ZrN, which have higher
thermal conductivities than their sister oxide compound, ZrO2. Research into the radiation damage

properties of these materials is in its infancy, and
therefore, these compounds are not described in
further detail here.

1.05.4. Summary
The response of ceramic materials to radiation is especially complex because ceramics (with the exception

of graphite) are made up of anions and cations (sometimes several different cations) such that the atomic
defects that initiate radiation damage are different in
their size, chemistry, charge, mobility, and so on. Thus,
it is difficult to predict how the microstructure of a
ceramic will evolve under irradiation and, in turn, how
properties such as structural stability will change in
response to the radiation-induced microstructural
alterations. Nevertheless, we present a case study
(described below) wherein researchers have succeeded
in explaining the extraordinary differences between
the radiation responses of two important engineering
ceramics.
We devoted much of this chapter to comparing
and contrasting the high-temperature radiation damage response of two quite similar refractory, dielectric
ceramics: a-alumina (Al2O3) and magnesio-aluminate
spinel (MgAl2O4). Al2O3 is highly susceptible to
radiation-induced swelling, whereas MgAl2O4 is not.
The swelling of Al2O3 is due to excessive void formation in the crystal lattice. We considered in detail in
this chapter the atomic and microstructural mechanisms that help to explain why voids nucleate and grow
in Al2O3 to a very significant degree, whereas in
MgAl2O4, this problem is much less pronounced. We
showed that the reasons for the great differences
between the radiation damage behavior of Al2O3 and
MgAl2O4 have mainly to do with differences in the
way interstitial loops nucleate and grow in these two
oxides. The hope is that by understanding these differences, we will by analogy be able to understand the
radiation damage behavior of other ceramic materials.
In this chapter, we also examined two different
phenomena that lead to degradation in the mechanical properties of ceramics: (1) nucleation and growth
of interstitial dislocation loops and voids and (2)

crystal-to-amorphous phase transformations. Both
these phenomena cause macroscopic swelling of
materials. This ultimately leads to the failure of
materials because of unacceptable dimensional
changes, microcracking, excessive increases in hardness (or alternatively, softening in the case of amorphization), and so on.


Radiation-Induced Effects on Material Properties of Ceramics

We concluded this chapter with brief discussions
of a few ceramics additionally important for nuclear
energy applications, namely silicon carbide (SiC),
uranium dioxide (UO2), and graphite (C).

25.
26.
27.
28.

References
1.
2.
3.
4.
5.
6.
7.
8.
9.

10.
11.

12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.

Clinard, F. W. Ceramics International 1987, 13, 69–75.
Clinard, F. W.; Hurley, G. F.; et al. Res. Mech. 1983, 8,
207–234.
Clinard, F. W. J. J. Mater. Energy Syst. 1984, 6(2), 100–106.
Kinoshita, C.; Zinkle, S. J. J. Nucl. Mater. 1996, 233–237,
100–110.
Black, C. A.; Garner, F. A.; et al. J. Nucl. Mater. 1994,
212–215, 1096.
Clinard, F. W., Jr.; Hurley, G. F.; et al. J. Nucl. Mater. 1982,
108/109, 655–670.
Garner, F. A.; Hollenberg, G. W.; et al. J. Nucl. Mater.
1994, 212–215, 1087.
Parker, C. A.; Hobbs, L. W.; et al. J. Nucl. Mater. 1985,

133&134, 741–744.
Greenwood, L. R.; Smither, R. K. SPECTER: Neutron
Damage Calculations for Materials Under Irradiation;
ANL/FPP/TM; 1985; 197.
Howitt, D. G.; Mitchell, T. E. Philos. Mag. A 1981, 44(1),
229–238.
Sickafus, K. E.; Grimes, R. W.; et al. Layered Atom
Arrangements in Complex Materials; NM, Los Alamos
National Laboratory: Los Alamos, 2006.
Hobbs, L. W.; Clinard, F. W., Jr. J. Phys. 1980, 41(7),
C6–232–236.
Kronberg, M. L. Acta Metall. 1957, 5, 507–524.
Groves, G. W.; Kelly, A. Philos. Mag. 1961, 6, 1527–1529.
Groves, G. W.; Kelly, A. Philos. Mag. 1962, 7, 892.
Maher, D. M.; Eyre, B. L. Philos. Mag. 1971, 23, 409–438.
Clinard, F. W. J.; Hobbs, L. W.; et al. J. Nucl. Mater. 1982,
105, 248–256.
Welsch, G.; Hwang, L.; et al. Philos. Mag. 1974, 29, 1374.
Naguib, H. M.; Kelly, R. Radiat. Eff. 1975, 25, 1–12.
Yu, N.; Sickafus, K. E.; et al. Philos. Mag. Lett. 1994, 70(4),
235–240.
Sickafus, K. E.; Yu, N.; et al. J. Nucl. Mater. 2002, 304(2–3),
237–241.
Devanathan, R.; Weber, W. J.; et al. Nucl. Instrum. Meth.
Phys. Res. B 1998, 141, 366–377.
Burnett, P. J.; Page, T. F. Radiat. Eff. 1986, 97, 123–136.
Aruga, T.; Katano, Y.; et al. Nucl. Instrum. Meth. Phys. Res. B
2000, 166–167, 913–919.

29.

30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.

46.

47.

48.
49.
50.
51.

139

Kabir, A.; Meftah, A.; et al. Nucl. Instrum. Meth. Phys. Res. B

2008, 266, 2976–2980.
Matzke, H. Nucl. Instrum. Meth. Phys. Res. B 1996, 116,
121–125.
Sickafus, K. E.; Matzke, H.; et al. J. Nucl. Mater. 1999, 274,
66–77.
Zinkle, S. J.; Skuratov, V. A.; et al. Nucl. Instrum. Meth.
Phys. Res. B 2002, 191, 758–766.
Olander, D. R. Fundamental Aspects of Nuclear Reactor
Fuel Elements; Technical Information Center, Office of
Public Affairs, Energy Research and Development
Administration: Springfield, Virginia, 1976.
Matzke, H.; Turos, A.; et al. Nucl. Instrum. Meth. Phys.
Res. B 1994, 91(1–4), 294–300.
Matzke, H.; Lucuta, P. G.; et al. Nucl. Instrum. Meth. Phys.
Res. B 2000, 166–167, 920–926.
Jiang, W.; Weber, W. J. Phys. Rev. B 2001, 64, 125206.
Newsome, G.; Snead, L. L.; et al. J. Nucl. Mater. 2007,
371, 76–89.
Taguchi, T.; Igawa, N.; et al. J. Nucl. Mater. 2007,
367–370, 698–702.
Price, R. J. J. Nucl. Mater. 1973, 48, 47–57.
Yano, T.; Iseki, T. Philos. Mag. A 1990, 62(4), 421–430.
Snead, L. L.; Hay, J. C. J. Nucl. Mater. 1999, 273,
213–220.
Price, R. Nucl. Technol. 1977, 35, 320.
Inui, H.; Mori, H.; et al. Acta Metall. 1989, 37(5), 1337–1342.
Inui, H.; Mori, H.; et al. Philos. Mag. B 1990, 61(1), 107–124.
Inui, H.; Mori, H.; et al. Philos. Mag. B 1992, 66(6),
737–748.
Zinkle, S. J.; Snead, L. L. Nucl. Instrum. Meth. Phys. Res. B

Beam Interact. Mater. Atoms 1996, 116(1–4), 92–101.
Weber, W. J.; Wang, L. M. Nucl. Instrum. Meth. Phys. Res. B
1995, 106, 298–302.
Weber, W. J.; Wang, L. M.; et al. Nucl. Instrum. Meth.
Phys. Res. B 1996, 116, 322–326.
Burchell, T. D. In Carbon Materials for Advanced
Technologies; Burchell, T. D., Ed.; Elsevier Science:
Oxford, 1999.
Snead, L. L. In Carbon Materials for Advanced
Technologies; Burchell, T. D., Ed.; Elsevier Science:
Oxford, 1999; pp 389–427.
Billington, D. S.; Crawford, J. H. Radiation Damage in
Solids; Princeton University Press: Princeton, NY, 1961;
p 396.
Koike, J.; Pedraza, D. F. J. Mater. Res. 1994, 9,
1899–1907.
Wallace, P. R. Solid State Commun. 1966, 4, 521–524.
Jenkins 1973.
Kinoshita, C.; Fukumoto, K.-I.; et al. J. Nucl. Mater. 1995,
219, 143–151.