Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional) Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional) Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional) Comprehensive nuclear materials 1 05 radiation induced effects on material properties of ceramics (mechanical and dimensional)
Trang 1Ceramics (Mechanical and Dimensional)
K E Sickafus
University of Tennessee, Knoxville, TN, USA
ß 2012 Elsevier Ltd All rights reserved.
1.05.2 Radiation Effects in Ceramics: A Case Study – a-Alumina Versus Spinel 124
1.05.2.3.3 Lattice registry and stacking faults I: (0001) Al2O3 129 1.05.2.3.4 Lattice registry and stacking faults II: {111} MgAl2O4 129 1.05.2.3.5 Lattice registry and stacking faults III: {1010} Al2O3 130 1.05.2.3.6 Lattice registry and stacking faults IV: {110} MgAl2O4 130
1.05.2.3.8 Unfaulting of faulted Frank loops II: {111} MgAl2O4 132 1.05.2.3.9 Unfaulting of faulted Frank loops III: {1010} Al2O3 132 1.05.2.3.10 Unfaulting of faulted Frank loops IV: {110} MgAl2O4 133 1.05.2.3.11 Unfaulting of faulted Frank loops V:experimental observations 133
1.05.3 Radiation Effects in Other Ceramics for Nuclear Applications 136
Abbreviations
dpa Displacements per atom
BF Bright-field
TEM Transmission electron microscopy
i Interstitial
SHI Swift heavy ion
PKA Primary knock-on atom
CVD Chemical vapor deposition
Ceramic materials are generally characterized by
high melting temperatures and high hardness values
Ceramics are typically much less malleable than
metals and not as electrically or thermally conduc-tive 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 electri-cal 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 cera-mics satisfy these requirements One of the purposes
of this chapter is to examine the fundamental mechanisms that lead to the relative radiation toler-ance 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 conse-quence, we lack a detailed understanding of atomic
123
Trang 2processes in ceramics exposed to radiation
Never-theless, progress has been made in recent decades in
understanding some of the differences between
radi-ation damage evolution in certain ceramic
com-pounds 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
magnesio-aluminate spinel (MgAl2O4) Under neutron
irradia-tion, 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
mechan-isms identified that help to explain the marked
dif-ference in the radiation damage response of these two
important ceramic materials The fundamental
prop-erties of point defects and radiation-induced defects
are discussed inChapter1.02, 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
irradia-tion condiirradia-tions used to produce a particular radiairradia-tion
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)
irradia-tion temperature, (3) irradiairradia-tion 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
alter-natively exhibiting damage susceptibility under
another set of conditions A good example of this is
MgAl2O4spinel Spinel is highly radiation tolerant in
a neutron irradiation environment but very
suscepti-ble 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 trans-formation; 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 differ-ent We examine these two radiation tolerance criteria through the course of this chapter
Versus Spinel 1.05.2.1 Introduction to Radiation Damage in Alumina and Spinel a-Al2O3and MgAl2O4are two of the most important engineering ceramics They are both highly refrac-tory oxides and are used as dielectrics in electrical applications (capacitors, etc.) Both a-Al2O3 and MgAl2O4 have been proposed as potential insulat-ing and optical ceramics for application in fusion reactors.1–3In a magnetically confined fusion device, these applications include (1) insulators for lightly shielded magnetic coils; (2) windows for radio-frequency heating systems; (3) ceramics for structural applications; (4) insulators for neutral beam injectors; (5) current breaks; and (6) direct converter insula-tors.3Such 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 electri-cal stresses A special concern is that under these extreme environments, ceramics such as a-Al2O3
and MgAl2O4must be mechanically stable and resis-tant to swelling and concomiresis-tant 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 1shows the results of one such study, where the high tem-perature, 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,4based 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
124 Radiation-Induced Effects on Material Properties of Ceramics
Trang 3displacements per atom (dpa) These dpa estimates
are based on the approximate equivalence (for
cera-mics) of 1 dpa per 1025n m2(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 from3 1026
to 2.5 1027
n m2 (3–200 dpa) On the contrary, a-Al2O3 irradiated
at temperatures between 925–1100 K exhibits
signifi-cant volume swelling, ranging from1 to 5% over
a fluence range of 1 1025
to 3 1026
n m2 (1–30 dpa) The purpose of the following discussion
is to reveal the reasons for the tremendous
dispar-ity 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-Al2O3following fast neutron
irra-diation at T ¼ 1050 K to a fluence of 3 1025n m2
(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 crystallo-graphic 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 mate-rial 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 MgAl2O4spinel 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 com-plexes (either vacancy loops or voids) However, the root cause of void formation is actually not the vacan-cies, 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 supersatu-ration of vacancies, that is, a condition in which the bulk vacancy concentration exceeds the complemen-tary 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
100 nm c
Figure 2 Bright-field transmission electron microscopy
image of voids formed in a-Al 2 O 3 irradiated at 1050 K to a
fluence of 3 10 25
n m2(3 dpa) (micrograph courtesy of Frank Clinard, Los Alamos National Laboratory).
Neutron fluence (n m -2)
Displacements per atom (dpa)
1
4
3
2
1
-1
0
10
100
MgAl2O4 a-Al 2 O 3
658–1100 K
1100 k
1025 k
925 k
1000
Figure 1 Volume swelling versus neutron fluence in
a-Al 2 O 3 alumina and MgAl 2 O 4 spinel.
Trang 4will 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
exces-sive concentration of vacancies, at which point the
v-defects will migrate locally and condense to form
voids (or vacancy loops or clusters) This entire
pro-cess, initiated by the supersaturation of vacancies,
causes the material to undergo macroscopic swelling,
and the material becomes susceptible to
microcrack-ing or failure by other mechanical mechanisms This,
indeed, is the fate suffered by a-Al2O3when 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.6When 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
diin-terstitials 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
supersatura-tion of vacancies and macroscopic swelling are
established
The defect situation just described can be
conve-niently summarized using chemical rate equations as
described in detail inChapter1.13, Radiation
Dam-age Theory Ineqn [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:
dC i ðtÞ
dt ¼ Pi ðAA! Aiþ VAÞ
Riv ðAiþ VA! AAÞ
Nðnucleation rate for interstitial loopsÞ
Gðgrowth rate for interstitial loopsÞ
½1a
dC v ðtÞ
dt ¼ Pv ðAA! Aiþ VAÞ
Riv ðAiþ VA! AAÞ ½1b
where Ci(t) and Cv(t) are the time-dependent
concen-trations of interstitials and vacancies, respectively;
Piand Pvare the production rates of interstitials and
vacancies, respectively (equal to the Frenkel pair
pro-duction rate); R 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; AAis an A atom
on an A lattice site; Aiis an interstitial A atom; and VAis
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 ineqn [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 con-dition for swelling
It is interesting to compare and contrast the neu-tron radiation damage behavior shown inFigure 1of alumina (a-Al2O3) and spinel (MgAl2O4) single crys-tals, 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 radiation-tolerant 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 annihila-tion mechanism in spinel so that a supersaturaannihila-tion of vacancies and concomitant swelling is avoided Indeed, it turns out that nucleation and growth of dislocation loops are far more pronounced in alu-mina 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 dislo-cation 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
126 Radiation-Induced Effects on Material Properties of Ceramics
Trang 5highly 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
struc-tural 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.10Therefore, 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=3 1011 f1010gh i (see, e.g., the review
by Kinoshita and Zinkle4) The first of these involves
precipitation on basal planes in the hexagonal
a-Al2O3structure, while the second is due to
precip-itation on m-type prism planes In MgAl2O4, similar
studies indicate that primitive interstitial dislocation
loops also have two characters: (1) 1/6h111i {111}
and (2) 1/4h110i {110}.4
Though the crystal struc-ture 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 tof1010g
alumina loops We will first compare and contrast
{111} spinel versus (0001) alumina loops and later
discuss {110} spinel versusf1010g alumina loops
Both spinel h111i {111} and alumina [0001]
(0001) interstitial dislocation loops involve insertion
of extra atomic layers perpendicular to theh111i 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
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.11Both structures can be described by a 24-layer stacking sequence along these directions Both spinel and alumina can be thought of as con-sisting 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 close-packed (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 inter-stices In spinel, cation interlayers alternate between
a pure Al kagome´ layer and a mixed MgAlMg, three-layer thick slab In alumina, each interthree-layer 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 1also shows the layer ‘blocks’ that have been found to comprise {111} and (0001) inter-stitial dislocation loops in spinel and alumina, respec-tively 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 1/6h111i 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 2, 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 elec-trostatic charge of 1 esu It has been proposed that this charge imbalance is overcome by partial inver-sion 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, (MgAl O )x
Trang 6Table 1 Layer stacking of {111} planes along h111i in cubic spinel and (0001) planes along [0001] in hexagonal alumina
(ABCABC-type O-stacking)
Layer composition
Frank loop Burgers vectors
(BCBC-type O-stacking)
Layer composition
Frank loop Burgers vectors t¼ tetrahedral
interstices
t ¼ tetrahedral interstices
o ¼ octahedral interstices
o ¼ octahedral interstices
1/6 <111>
¼ 4 layers (Al 3 O 4 )1þ
1/3 [0001]
¼ 4 layers (excluding empty tetrahedral layers) (Al 2 O 3 ) x
1/6 <111>
¼ 4 layers (Mg 2 AlO 4 )1
Trang 7Table 1indicates that an (0001) interstitial
dislo-cation loop in alumina consists of a four-layer block
(excluding the empty t layers) such that the
magni-tude 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
asso-ciated with interstitial dislocation loops along 3 in
alumina These dislocation loops consist simply of a
pair of Al layers interleaved with two O layers
1.05.2.3.3 Lattice registry and stacking
faults I: (0001) Al2O3
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
lat-erally 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 inTable 1(a1, a2, a3).11
Thus, the registry of cation/anion stacking in alumina
follows the sequence: a1B a2C a3B a1C a2B a3C
When extra pairs of Al and O layers are inserted
into the stacking sequence, a1B a2C a3B a1C a2B a3C,
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, Al2O3Al2O3, into the stacking
sequence described above We obtain:
a1 B a2C a3 B a1C a2 B a3C a1 B a2C a3 B
a1 C a2 B a3 C ðbeforeÞ
a1 B a2C a3 B a1C a2 B a3C a1 B a2C a1 B
a2 C a3 B a1 C a2 B a3 C ðafterÞ
a1 a2 a3 a1 a2 a3 a1 a2 j a1a2 a3 a1 a2 a3
ðafter; showing only cations and
showing stacking fault positionÞ ½2
Notice ineqn [2]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 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 dis-location loop formed by 1/3 [0001] block insertion in alumina is an intrinsic, cation-faulted, interstitial Frank loop This is also a sessile loop
1.05.2.3.4 Lattice registry and stacking faults II: {111} MgAl2O4
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 regis-tries labeled a, b, and c inTable 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 pro-jected onto one layer and labeled a0, b0, g0 With these definitions, the registry of cation/anion stacking in spinel follows the sequence: a C b0A g B a0C b A g0B
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 demon-strate 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:
a C b0A g B a0C b A g0 B a C b0 A g B
a0 C b A g0B ðbeforeÞ
a C b0A g B a0C b A g0 B b A a C b0A g B
a0
C b A g0B ðafterÞ
a C b0A g B a0C b A g0 B j b A j a C
b0 A g B a0 C b A g0B ðafter; showing
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 approach-ing the block from both the left and the right) Thus,
Trang 8the b A block actually contains two stacking faults, on
either side of the block The positions of these
stack-ing faults are denoted by vertical red lines ineqn [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 inTable 1, which uses a
mixed MgAlMg cation slab) We obtain:
a C b0 A g B a0 C b A g0B a C b0A g B a0C
b A g0 B ðbeforeÞ
a C b0 A g B a0 C b A g0B b0 A a C b0A g B
a0C b A g0 B ðafterÞ
a C b0
A g B a0 C b A g0B j b0A j a C
b0A g B a0C b A g0 B ðafter; showing
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
fault-ing for 1/3 [0001] (0001) loops in alumina and 1/6
h111i {111} loops in spinel Now, we must repeat
these considerations for 1=3 1011 f1010gh i prismatic
loops in alumina and 1/4h110i {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 1010ih direction normal to
the traces of the {1010} planes, the registry of the
{1010} planes varies between adjacent planes,
analo-gous 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
identi-cal 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, a1a2a3a1a2a3 Putting the
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=3 1010ih two-layer block, (Al2O3)x(Al2O3)x, is inserted into the stacking sequence, (a1B) (a2C) (a3B) (a1C) (a2B) (a3C), a stack-ing fault occurs as follows:
ða1BÞ ða2CÞ ða3BÞ ða1CÞ ða2BÞ ða3CÞ ða1BÞ
ða2CÞ ða3BÞ ða1CÞ ða2BÞ ða3CÞ ðbeforeÞ
ða1BÞ ða2CÞ ða3BÞ ða1CÞ ða2BÞ ða3CÞ ða1BÞ ða2CÞ
ða1BÞ ða2CÞ ða3BÞ ða1CÞ ða2BÞ ða3CÞ ðafterÞ
ða1BÞ ða2CÞ ða3BÞ ða1CÞ ða2BÞ ða3CÞ ða1BÞ ða2CÞ j
ða1BÞ ða2CÞ ða3BÞ ða1CÞ ða2BÞ ða3CÞ ðafter; showing stacking fault positionÞ ½5 Notice ineqn [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 ear-lier), the dislocation loop formed by 1=3 1010ih 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 1/4h110i {110} loops in spinel Spinel {110} planes alternate in composition, (AlO2)(MgAlO2)þ ., such that each layer is a mixed cation/anion layer To insert a charge-neutral interstitial slab alongh110i in spinel requires that we insert a {110} double-layer block, (AlO2)(MgAlO2)þ, that is, a stoichiometric MgAl2O4unit The thickness
of this slab isa/4 h110i, where a is the spinel cubic lattice parameter Along theh110i 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)þlayer We denote the Mg stacking sequence by a1a2a1a2 There are two Al atom patterns along h110i: (1) the first
130 Radiation-Induced Effects on Material Properties of Ceramics
Trang 9occurs in each (AlO2) 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)þlayer (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
fol-lows: (b0B) (a1b1C) (b0B) (a2b2C).
Now, as with the spinel {111} case described
earlier, when an extra 1/4 h110i two-layer block,
(AlO2)(MgAlO2)þ, is inserted into the spinel {110}
stacking sequence, (b0B) (a1b1C) (b0B) (a2b2C), a
stack-ing fault occurs as follows:
ðb0
BÞ ða1b1CÞ ðb0
BÞ ða2b2CÞ ðb0
BÞ ða1b1CÞ
ðb0
BÞ ða2b2CÞ ðbeforeÞ
ðb0BÞ ða1b1CÞ ðb0BÞ ða2b2CÞ ðb0BÞ ða1b1CÞ
ðb0BÞ ða1b1CÞ ðb0BÞ ða2b2CÞ ðafterÞ
ðb0BÞ ða1b1CÞ ðb0BÞ ða2b2CÞ ðb0BÞ ða1b1CÞ j
ðb0BÞ j ða1b1CÞ ðb0BÞ ða2b2CÞ ðafter;
showing stacking fault positionsÞ ½6
Notice ineqn [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 1/4h110i
two-layer block insertion in spinel is an extrinsic,
cation-faulted, sessile interstitial Frank loop
Figure 3shows an example of 1/4h110i interstitial
dislocation loops in spinel, produced by neutron
irra-diation.12The 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
pre-cautions outlined by Maher and Eyre.16These loops
were determined to be extrinsic, faulted 1/4 h110i
{110} interstitial dislocation loops It is evident in
Figure 3that 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
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 incre-mentally 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=3½1010 partial shear dislocation across the loop plane.6This is described
by the following dislocation reaction:
1
3½0001
faulted loop
þ 1
3½1010
partial shear
3½1011
unfaulted loop
ðbasalÞ ½7
c
500 nm c
Figure 3 Bright-field transmission electron microscopy (TEM) image of {110} faulted interstitial loops in MgAl 2 O 4
single crystal irradiated at 1100 K to a fluence of 1.9 10 26
n m2(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.
Trang 10This reaction is shown graphically inFigure 4 Note
that the magnitude of 1=3½1010 is approximately the
Al–Al (and O–O) first nearest-neighbor spacing in
Al2O3 When we pass a 1=3½1010 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 ineqn [2]and
assuming that the planes to the right are above the
ones on the left, we perform the 1=3½1010 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)
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]
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=3½1011, is a perfect lattice vector; therefore, the newly formed dislocation is a perfect dislocation The resultant 1=3½1011 (0001) dislocation is a mixed dis-location, 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
For this particular dislocation loop, it is thought that rather than unfaulting, 1/6h111i {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 pre-sumed 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.12Counter to this argument
is the idea that if a 1/6h111i {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 argu-ably be more stable However, {111} loops are never observed to grow very large (<100 nm) and are alto-gether absent in spinel samples irradiated at 1100 K.17 Therefore, it is likely that ‘disordered’ {111} intersti-tial 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=3½1010ð1010Þ 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
3½1010
faulted loop
þ 1
3½0001
partial shear
3½1011
unfaulted loop
ðprismaticÞ ½9 This reaction is symmetric with that shown in eqn [8] for unfaulting a (0001) basal loop in alumina The reaction ineqn [9]is shown graphically inFigure 4 When we pass a 1/3 [0001] shear through a 1=3½1010ð1010Þ dislocation loop, the cation planes beneath the loop assume new registries such that
in eqn [6], a1b1 and a2b2 commute as follows:
a1b1! a2b2! a1b1 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
1/3 [0001]
C
1/3 [1010]
1/3 [1011]
Figure 4 Alumina cation ‘honeycomb’ atom nets along
the c-axis in Al 2 O 3 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.
132 Radiation-Induced Effects on Material Properties of Ceramics