POINT DEFECT STABILIZATION IN IONIC
CRYSTALS AT HIGH DEFECT CONCENTRATIONS
L. Hobbs
To cite this version:
L. Hobbs. POINT DEFECT STABILIZATION IN IONIC CRYSTALS AT HIGH DEFECT CONCENTRATIONS. Journal de Physique Colloques, 1976, 37 (C7), pp.C7-3-C7-26.
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JOURNAL DE PHYSIQUE
Colloque C7, supplément au n° 12, Tome 37, Décembre 1976, page C7-3
POINT DEFECT STABILIZATION IN IONIC CRYSTALS
AT HIGH DEFECT CONCENTRATIONS
L. W. HOBBS (*)
Materials Development Division, Atomic Energy Research Establishment,
Harwell, Oxfordshire 0 X 1 1 O R A , U. K.
Résumé. — Dans les cristaux ioniques, la stabilisation des défauts ponctuels diffère de celle dans
les métaux ou dans d'autres solides monatomiques, par la nécessité de conserver la stœchiométrie
(ou une stœchiométrie aménagée) et l'ordre. Dans ces solides, les défauts ponctuels primaires qu'ils
soient produits thermiquement, chimiquement, ou par irradiation, sont rarement présents ou
assemblés dans des proportions exactement stœchiométriques, et par conséquent pour de hautes
concentrations de défauts se produisent des structures de défauts secondaires étendues qui peuvent
être tout à fait distincts de celles formées dans des solides monatomiques. La non-stœchiométrie
peut être aménagée de plusieurs façons. Dans les oxydes de métaux de transition déficients en oxygène, les lacunes d'oxygène peuvent être effectivement éliminées par altération de la mode de liaison
des octaèdres initiais d'oxygène, engendrant des plans de cisaillement cristallographiques. Ce processus délocalise effectivement un changement de valence cationique. Dans les systèmes ayant un
défaut de cation ou un excès d'anion (par exemple Fei-zO, UO2+1, CaF2 : YF 3 ) l'adaptation peut
se faire par un changement localisé de valence cationique (et souvent de position) et par la formation
de complexes d'amas de défauts ponctuels (lacunes cationiques, interstitiels anioniques) ; ceux-ci
peuvent, lorsqu'ils se rassemblent, former des germes embryoniques pour une nouvelle phase de la
stœchiométrie altérée. Quand des changements de valence ne sont pas possibles, par exemple dans
les halogénures alcalins ou dans les oxydes et halogénures de terres alcalines non dopés, des
défauts de stœchiométrie étendus (tels que des boucles de dislocations) sont créés, mais ils doivent
s'accompagner d'autres formes plus stables de défauts ponctuels. L'agglomération de défauts
ponctuels de haute densité peut de plus conduire à la précipitation de phases élémentaires séparées, et aussi à la décomposition du solide.
Abstract. — Stabilization of point defects in ionic crystals differs from that in metals or other
monatomic solids in that there is the need to maintain both stoichiometry (or accommodate nonstoichiometry) and order. Primary point defects in these solids, whether produced thermally,
chemically, or by irradiation, seldom are present or aggregate in exactly stoichiometric proportions,
and in consequence at high defect concentrations extended secondary defect structures arise which
can be quite distinct from those formed in monatomic solids. Non-stoichiometry can be accommodated in several ways. In oxygen-deficient transition metal oxides, oxygen vacancies can be effectively
eliminated by alteration of the mode of linking metal-oxygen octahedra together, giving rise to
so-called crystallographic shear planes. This process effectively delocalizes a change in cation valency.
In cation deficient/anion excess systems (e. g. Fei-zO, U 0 2 « , CaF 2 : YF3), accommodation occurs
by a localized change in cation valency (and often position) and formation of point defect cluster
complexes (cation vacancies, anion interstitials) which when stacked together can form embryonic
nuclei for a new phase of altered stoichiometry. Where valency changes are not possible, for example
in alkali halides or undoped alkaline earth halides and oxides, stoichiometric extended defects
(such as dislocation loops) are generated, but these must be accompanied by other more stable forms
of point defect species. Aggregation of point defects at high density can additionally result in precipitation of separate elemental phases, and thus decomposition of the solid.
1. Introduction. — The science of point defects
in ionic solids has now become so exact, if not indeed
laboured, both in theory and in practice that it is
sometimes difficult to remember that only under
rather special circumstances is it possible to obtain
truly isolated point defects. What is more, it is now
quite clear that point defects alone cannot account
for a whole range of observed solid state phenomena,
,», „
. . .
„
,
.<•»,,„
.., . • ,
(*) Present address : Department of Metallurgy and Materials
Science, Case Western Reserve University Cleveland, Ohio
44106, u . S. A.
and an increasing variety of physical and chemical
properties of these solids is being ascribed to defect
interactions, defect clustering and extended defect
structures. It is also clear that, where defects are
formed in high density and as defect separations
diminish to atomic dimensions, traditional approaches
to point defects in dilute solution are seldom applicable
to the resulting defect aggregations. We can speak
of such defect associations as stabilizing point defects
which might otherwise combine with complementary
°
•. T
defects or diffuse out of the solid. In many cases,
association of defects leads to permanent structural
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1976702
C7-4
L. W. HOBBS
changes in a solid, so that the chemist's or metallurgist's
concept of phase becomes inextricably bound up
with the crystallographer's notion of periodic defect
arrangements in a solid.
Just as point defects in ionic solids differ from those
in metals o r semiconductors, so the nature of extended
defect structures differs correspondingly. It is comforting to the physicist's unified view of nature that many
of the same extended defects - for example dislocations - are found in metals, semiconductors, ionic
crystals and even organic molecular solids. But it
would be wrong to extrapolate from our experience
with any one of these systems to the detailed structure
of extended defects in another. Ionic crystals have
their own particular sets of rules which reflect both
the special character of the point defects and the nature
of the bonding between atoms peculiar to these solids.
The usual stabilization pattern is one where, at
significant defect concentrations, point defects transform into defect complexes, which in turn cluster
into larger aggregates and may occasion more extended
disorder. This sequence will be illustrated for six
different systems in sections 4-6.
2. Features peculiar to defect association in ionic
solids. - Before considering specific examples, it is
instructive to point out several general features of
defects in ionic crystals which govern the modes of
defect association and set ionic solids apart from
their metallic or covalent counterparts.
2. l POLYATOMICITY.
- Ionic crystals are by definition polyatomic, since the nature of the ionic bond
presupposes at least .two ion species of opposite
charge. This means we can define two (or more)
sublattices corresponding to each ion species, and
defects can occur on one, some or all of the ion sublattices. This is an important property which at once
distinguishes ionic solids from monatomic solids
such as metals or elemental semiconductors ; in order
to reproduce wholly analogous defect structures in
ionic solids it is necessary to accumulate equivalent
defects from all sublattices in stoichiometric proportion. This is rarely achieved.
It is furthermore usual for defects on different
sublattices to interact strongly, and frequently the
presence of defects on one sublattice induces disorder
on one or more of the other sublattices. This is because
defects in ionic lattices are strongly coupled to the
long-range Coulomb field of the host lattice, a feature
which suggests that point defects in ionic systems can
seldom be considered in isolation. Indeed, such
effects as polarization are well known to those who
calculate ionic defect properties [l]. Interactions
between defects on the same sublattice can be very
different for each sublattice and quite distinct from
the ionic bonding of the host solid ; for example,
anion-anion defect interactions are often covalent,
cation-cation defect interactions sometimes metallic.
2.2 CHARGEDDEFECTS AND VALENCE CHANGES. Ionic solids are most frequently insulators and electronic disorder cannot be readily delocalidze. It is
consequently possible for defects to acquire and
retain charge and to exist in several different charge
states. It is possible for excess charge to localize
even in the perfect lattice ; the self-trapped hole in
halides is an example. An ion vacancy is similarly
charged ; an anion vacancy, for example, is positivelycharged and can trap one or more electrons to alter
its charge state. Point defect charge states have a
large influence on mutual defect interactions and
defect mobilities, and therefore on defect aggregation.
The activation energy for migration of a neutral F
centre in KCl, for example, is 1.5 eV ; for the positively-charged empty anion vacancy 0.7 eV [2].
Extended defects can acquire charge as well ; dislocation cores are a well-documented case 131.
It is also possible for certain ions (usually cations)
to alter their charge state, thus their valency and
preferred coordination. The change may cause an
ion to alter its position in the lattice ; for example,
Fe2+ ions oxidized to Fe3" in ferrous oxide move
into interstitial sites (section 5.1). Such changes in
charge state can have additional consequences,
discussed below.
TO PRESERVE ELECTRICAL NEUTRALITY
2 . 3 NECESSITY
dominance of Coulombic binding
introduces the necessity to maintain overall electrical
neutrality throughout an ionic solid ; uncompensated
excess charge is costly thermodynamically and will
not persist in equilibrium. Therefore equilibrium
vacancy disorder exists as neutral Schottky multiplets,
and Frenkel pairs preserve overall neutrality ; for
the same reason, introduction of aliovalent ions
(intrinsic or impurity) results in generation of chargecompensating defects, often on other sublattices.
A corollary is that long-range ionic order must
be maintained ; electrostatic faults have very high
energies because the perturbation of the Coulomb
field is a dominant term in the disorder free energy [4].
The ionic lattice may even prefer ionically-charged
defects (which can be stabilized by the Coulomb
field) to neutral ones and effect the transformation ;
an example is accommodation of halogen interstitials
in alkali halides (section 6.2).
AND ORDER. - The
2.4 STOICHIOMETRY.
- The presence of more than
one atomic species in ionic solids engenders a complex
reciprocity between lattice defects and stoichiometry ;
defect structures may preserve existing stoichiometry
or may serve as vehicles for accommodating nonstoichiometry. As an example of the latter, the clustering of a point defect species of one type on a single
sublattice (for example, anion vacancies) can result
in a local non-stoichiometry in that element (in this
case a deficiency). Conversely, introducing an excess
(e. g. chemically or by implantation) or deficiency
POINT DEFECT STABILIZATION IN IONIC CRYSTALS AT HIGH DEFECT CONCENTRATIONS
(e. g. reduction) of one atomic species can lead to
the generation of various point and extended defect
structures in order to accommodate the impressed
non-stoichiometry. In the above example, an imposed
anion deficiency can lead to anion vacancy disorder ;
equally, an imposed cation excess could achieve the
same result. This reciprocity between defect structure
and stoichiometry is the single most striking feature
of defect stabilization in ionic lattices.
2.5 RADIATION-INDUCED
BIAS. - Irradiation is a
convenient and often technologically significant way
of introducing lattice defects at high concentrations.
In ionic solids, electronic excitations can be localized
and persist (as separated or associated electron-hole
pairs) for times sufficiently long that the lattice
becomes unstable and responds by effecting permanent
ion displacements, a process called radiolysis. In this
way, it is possible to create substantial disorder with
the (usually dominant) ionizing component of radiation ; since the mechanism is efficient in a large
number of ionic solids (halides, hydrides and azides
arc well-documented systems), it is possible to achieve
quickly large defect densities (displacement rates
can be as high as 1 dpa S-'). Radiolysis is a selective
process and usually involves initially only a single
sublattice (usually the anion one). This means that
the primary defect spectrum is biassed and, as discussed above, the imbalance can lead to local nonstoichiometry if the complementary products of
radiolysis aggregate separately.
For ionic solids which do not undergo radiolysis
(e. g. oxides), it is seldom the case that displacemcnt
cross sections for direct displacement are identical
for all sublattices. In extreme examples, it may prove
impractical to displace certain sublattices ;for example,
only oxygen ions can be displaced inU 0, by electrons
with energies < 3 MeV. Displacement rates will
therefore usually differ according to ion species (Fig. 1).
Nor in general will defect mobilities for each sublattice
be the same. Consequently, the primary defect spectrum may again become biassed, ant the secondary
defect structures stabilizing the damage may reflect
the non-stoichiometry of the initial disorder.
I
10'
'01
.
106
to5
PROTON ENERGY,
10'
C7-5
3. Techniques for observing extended defect structures. - Experimental techniques used to investigate
the nature of point defects in ionic solids viz. optical
absorption and luminescence, electrical conductivity,
paramagnetic resonance and so forth are in general
not very useful for characterizing the nature of larger
defect aggregates ; where they do provide information
(some examples are discussed in sections 4.2 and
6.2), it is usually information about only some of
the constituent defects and seldom reveals structural
characteristics of the aggregate. What interests us is
first structure on the atomic scale (e. g. ionic arrangements within a cluster) and next structure on the
scale of a few unit cells (e. g. morphology and arrangements of clusters). In either case, we must employ
radiation probes whose wavelengths are appreciably
less than the wavelength of light ; and we shall in
general be concerned with diffraction methods, though
other sorts of spectroscopy, e. g. y-ray spectroscopy
(such as Mossbauer effect) can also provide similar
or complementary information. We can employ
either indirect or direct methods ; indirect methods
integrate over a large number of similar defect structures, dircct methods evaluate single defect aggregates
and sometimes can resolve atomic arrangements
within aggregates. These two approaches are most
conveniently considered separately, although unified
treatments have appeared (see [5]).
3.1 INDIRECTMETHODS : X-RAY AND NEUTRON
- The elastically scattered intensity from
an assembly of N independent scattering centres is [6]
SCATTERING.
+ 11 (F, F,,,- < F,, > < F,, >) exp[ix.(rn - rn*)]The scattering vector x is defined by the difference
between scattered and incident wave vectors
x = (k' - k)
where k = 2 nA- l . For X-rays the wavelength
i is z 0.1 nm, while for thermal neutrons it lies
typically between 50 pm and 2 nm. F, are factors
describing thc scattering from the nth centre situated
at distance rn from an arbitrary origin. Dispersion
effects and polarization have been neglected in (l),
as have the effects of thermal vibrations, and the
scattering is presumed weak.
If the scattering centres are disordered or defective
but otherwise identical unit cells arranged on a basis
lattice, the first term of (1) represents (neglecting
form factors) the Bragg scattering
oV
FIG. 1. - Anionlcation displacement ratios in U 0 2 irradiated
with protons. Solid curves with, broken curves without mass
difference correction in secondary cascades. Ed(0) = 56 eV,
Ed(U) = 210 eV (Courtesy Mr. H. V. St. A. Hubbard).
Peaks in the intensity occur whenever
X
= g, where
L. W. HOBBS
C7-6
g is a reciprocal lattice vector defined by g.r, = 2 nn
for n integer ; this is simply a restatement of Bragg's
law. The average structure factor < F,,(x) > defines
the contents of the average unit cell
< F(x) > =
M
pmfm exp(i~.?,~).
< exp(- ix. U,)
>
m
(3)
where the sum extends over M atoms (or ions) contained in the unit cell. The f;, are atomic scattering
amplitudes, called atomic scattering factors for
X-rays where they depend on X, and coherent scattering lengths for neutrons where they are independent
of X. The contents of each unit cell may be defective
owing to atomic replacements or displacements ;
p , is the probability that the nzth site of the average
unit cell is occupied, and U,, is the static displacement
in the average unit
of atom m from the position
cell. The average in (3) containing U,, is analogous
to a thermal Debye-Waller factor, except that it
may not be possible to expand the exponential in
equivalent fashion because of the magnitude of
U, close to a defect. The effect of defects is to shift
the positions of the Bragg peaks, which now occur
for X.;, = 2 m, and to broaden them through the
static Debye-Waller term.
By measuring integrated intensities for a sufficiently
large number of reciprocal lattice points g, we can
and U, (see for example [7]).
determine (p,f;,,), im
It is not possible to determine pm and fm separately,
and this can lcad to ambiguity for disorder on more
than one sublattice. The local atomic arrangement of
defects cannot be deduced from the contents of the
average unit cell ; nor can evidence for clustering be
derived from Bragg intensities, unless new (interstitial)
sites appear in the average unit cell which were not
present in the defect-free crystal and the concentration
of defects is incompatible with the measured average
cell dimension if distributed uniformly. The information from Bragg intensities is therefore greatest in
those systems in which one atomic species alone
occupies new types of interstitial sites, e. g. Fe,-, 0
(section 5. l ) and UO, +, (section 6.1).
The second term in ( I ) represents the diffuselyscattered intensity. The three contributions to the
diffuse scattering are scattering from defects themselves
(Laue scattering), distortion scattering, and for polyatomic solids, short-range order scattering. For
small defect concentrations, the scattering from
neighbouring defects can be considered incoherent,
in which case the diffuse scattering is proportional
to the defect concentration c [8].
I,jiff(x) = cNM I FD(x) I2 .
(4)
The defect structurejactor F,(Ic) consists of two parts
The first term fD(x) is the scattering factor for the
defect itself. For vacancies involving atom m,
for interstitials fD =f;, exp(ix.ri), where ri is the
position of the interstitial within the unit cell. For
substitutional and interstitial impurities, the factors
are (j',- f,) and [f,exp(ix. r,)] respectively.
The second term of (5) is the scattering from the
distorted region around the defect. Putting X = g S,
we have for small s the scattering close to the reciprocal
lattice points [9]
+
where $4 is the Fourier transform of the elastic
displacement field due to the defect
U(S)= C exp(is. r,) u(rm).
m
The contribution from the third term of (6) is called
Huang [l01 scattering. For large defect concentrations,
the assumption in (4) that scattering from neighbouring defects is incoherent breaks down, and we must
consider correlations between defects for both terms
of (5). This procedure involves a large number of
correlations. Fortunately, at this stage defects usually
cluster and we may instead calculate scattering from
(isolated) defect clusters.
Diffuse scattering from single defects and simple
point defect clusters is discussed in further detail
by Peisl [13]. For a high density of clusters it is
necessary to further take into account correlations
between clusters, but a discussion of such shortrange order diffuse scattering is beyond the scope
of this review and is treated exhaustively elsewhere [5,
8, 14-17].
The diffuse scattering centred on g = 0 is small
angle scattering for which from (4) and (6)
The Fourier transform Gm(%-+ 0) is determined only
by displacements far away from the defects, and the
second term in (7) becomes - fm s(A V,/ V), where
iC
m
AV, is just the volume change due to the defect in
an infinite medium. For single interstitials, the two
terms of (7) may nearly cancel, whereas for vacancies
both terms are negative and add. Interstitial clusters
in polyatomic solids can, however, contribute appreciable scattered intensity, as can vacancy clusters,
dislocations and dislocation loops [18, 191.
Large regions with different scattering factor, for
example voids, vacancy aggregates, substitutional
inclusions, contribute largely through the f, term
POINT DEFECT STABILIZATION I N IONIC CRYSTALS AT HIGH DEFECT CONCENTRATIONS
in (7). The scattering in the forward direction for such
aggregates contains a form factor $ ( X , R), ignored
so far, which depends on aggregate size R and shape
[20-221. A significant complication in small-angle
scattering arises from the possibility of double- or
multiple-Bragg scattering back into the forward
direction, contributing terms involving ;;,,,(X # 0)
to (7) ; this can be avoided by utjlizing long-wavelength
neutrons with I > 2 g-' for the smallest g possible [23].
3 . 2 DIRECTMETHODS : TRANSMISSION ELECTRON
(TEM). - Electrons of high energy
(U E 10 keV t o 1 MeV) and mass m, can be considered as radiation with wave vector
Bragg-scattered plane waves g of the form considered
in (2).
If we collect all (or a sufficient number) of the
Bragg beams and Fourier transform them in the
objective lens of the microscope, we obtain a reconstructed image of the scattering material, but because
the phase information contained in (8) is lost when
intensities @F*are measured, we also lose information
on the spatial variation of v@). However, if we introwe produce in the image an
duce a small defocus
interference term
c,
MJCROSCOPY
k
=
2 nl-
=
2 rc J(2 m, ~ / h z -,j
with 1 ranging from 10 pm to < 1 pm. Such electrons
may be focussed by strong electromagnetic lenses
which perform the Fourier transforms of the diffracted
electron wave function [24]. This permits information
about the spatial distribution (X, y) of scattered
intensity (and sometimes phase) to be obtained.
Because of the small wavelengths, the Bragg angles
are small (- lo), and it is convenient to examine
materials in transmission. Inelastic scattering (involving energy loss) sets the practical limit for thickness
of material examined to t 5 1 pm because chromatic
aberration in the magnetic lenses limits resolution.
It is easier to consider the interaction of an electron
with the potential u(r) within a solid than with the
individual atoms ;one therefore solves the Schrodinger
equation for electrons of energy U moving in potential
v(r). For a crystal consisting of unit cells arranged
in a periodic lattice, the potential is periodic and can
be expanded in a Fourier series
with the periodicity of the lattice. The Fourier components v, are related to the individual atomic scattering factors through the structure factor
where C? is the volume of the unit cell.
Electrons are strongly scattered by the lattice
potential, thus dynamic interactions between Bragg
scattered electrons occur and dispersion is important,
unless we keep the volume of scattering material
small. In this case only, the crystal may be considered
a weak phase object 1251 and solutions to the Schrodinger equation are plane waves.
The limit for this approximation is t of order a few
unit cell thicknesses. A periodic potential gives
C7-7
[l - (4 nm. c/h2 k 2 ) iv2
1
V(X,y ) dz]
.
which from Poisson's equation is simply the projected
charge density of the lattice. Provided the lattice
is oriented along certain directions of high lattice
symmetry, a naive interpretation of the projected
charge density in terms of atomic structure (including
defects) may be possible [26].
For thicker crystals, we are restricted to investigating
more extended disorder. Because of the strong dynamic interactions of Bragg-scattered planc waves,
it is convenient in this case to consider electrons in
a crystal as sums of Bloch waves
Y(r)
~i;"exp[i(k(j) + g). r]
$"'
=
J
fl
where p") is the excitation of the jth Bloch wave
': ) and wave vector
with amplitude coefficients { C
kCJ'. ( C:) ), k'j', v, and .F are related through an
eigenvalue dispersion equation. These Bloch waves
propagate without scattering in the perfect crystal
and recombine at the exit surface to form Braggscattered plane waves. The effect of a defect is to
change the Bloch wave excitations (equivalent to
scattering one Bloch wave into another), either
through the effect of its displacement field on v(r)
(e. g. a dislocation) or through replacing some part
of the lattice with a region of different potential
(e. g. an inclusion). Usually images arc reconstructed
using a single Bragg-scattered beam, for example
the forward-scattered beam g = 0, with the crystal
oriented near to the Bragg position ( S E 0). In such
cases, only one Bloch wave, say j, usually contributes
appreciably to the intensity, and the defect contrast
AI(g = 0) is proportional to Re (A$")). For small
change AV in v(r), A$(') is given by perturbation theory
A$'"
= (2 nim, r/h2)
$"'(z)
I
1
b"'* Avb"' d r (9)
where the scattering from all other Bloch waves 1
into Bloch wave j is considered. For a displacement
field u(r) for example (9), becomes [27]
C7-8
L. W. HOBBS
which is analogous to (5) in X-ray and neutron
scattering. Examples of contrast from various types
of extended defects in ionic solids are given in sections
4-6 and elsewhere [28,29].
4. Anion-deficient/cation-excess systems. - The
inter-relationship between secondary defect structures
and non-stoichiometry can be illustrated by considering two different ways of accommodating a deficiency
of anions in a binary ionic solid. The first alters the
cationtanion ratio and thus necessarily the valency
while nonetheless maintaining cation coordination
geometry ; the second proceeds under a rigid valency
constraint and results in precipitation of the excess
(in this case cation) species.
SHEAR IN REDUCED TRAN4.1 CRYSTALLOGKAPHIC
OXIDES. - Many simple and mixed
transition metal oxides exhibit an astonishing range
of stable oxygen/metal ratios. For example, WO,
loses oxygen readily and can be reduced to a large
number of distinct phases, among them WO, (3.000),
W,~O,,, (2.950), w2,0,, (2.9171, w2,05, (2.900)
and W,,05, (2.885), the oxygen/metal ratio appearing
in brackets. The Nb205-TiO, mixed system exhibits
similar stable compositions N b 2 0 5 (2.500), 19
N b 2 0 5.Ti02 (2.487), 12 Nb205.Ti02 (2.480), 17
Nb205.3 TiO, (2.459), 22 Nb205.5 TiO, (2.449),
5 Nb205.2 TiO, (2.417), 2 Nb205.Ti02 (2.400)
and Nb205.Ti02 (2.333). The basic structural units
for both systems are (MO,) metal-oxygen octahedra
which, in the simplest case (the ReO, structure of
WO,) are linked together by sharing apexes. In reduced
compounds, the crystals must accommodate excess
anion vacancies, and these may be accommodated
structurally (Fig. 2) by altering the mode of octahedra
CS
Plane
CS
Plane
Slob o f
parent structur?
SITION METAL
FIG. 3a) Idealized WzoOja structure showing recurrent crystallographic shear planes separating slabs of unaltered WO3
structure. (Reproduced from ref. [32].) h) Crystallographic shear
planes in WzoOjs imaged by TEM. (Reproduced from ref. [28].)
in two dimensions, generating block structures (Fig. 4)
which are in turn joined to other blocks through
shared sites. Variations in block size and block
linkage provide still further possibilities for stable
oxygen/metal ratios. In addition, ordering of aliovalent cations can occur at the cation sites (e. g. in
the Nb205-Ti02 system [30]). A third topological
variant is rotary shear manifested in the complex
tunnel structures of the tungsten bronzes such as
FIG. 2. -Principle of crystallographic shear. Conversion of
a) apex-sharing [MO61 octahedra to edge-sharing, and b) edgeNb205-WO, (Fig. 5). Many of these structures are
sharing octahedra into face-sharing. ( ~ e p r o d u c e dfrom ref. [32].) only two-dimensional and can be i~nagedmore or less
directly by transmission electron microscopy as
linkage, e. g. from apex-sharing to edge-sharing along discussed in section 3.2 ; many beam images from
certain planes known as crystallographic shear pla- very thin (a few unit cells thick) crystal sections oriennes ( l ) , in this way eliminating sets of anion sites. The ted normal to the invariant axis display the projected
regular spacing of these defect planes (Fig. 3) thus lattice charge density and permit elucidation of
governs the overall oxygen/metal ratio. It is similarly structure, including more extended defects. Figure 4b,
possible for crystallographic shear to manifest itself for example, illustrates the 3 X 3 block structure of
VNb,O,, together with several interposed layers of
4 X 3 blocks (Wadsley [31] defects).
(L) This is not shear in the normal sense in that the displaceThe crystal chemistry of these transition metal
ment u must have a component normal to the shear plane in
oxide
structures has been expanded into a complex
order to eliminate material ; an analogy with intrinsic faults is
closer.
and sophisticated science, and several comprehensive
POINT DEFECT STABILIZATION IN IONIC CRYSTALS AT HIGH DEFEm CONCENTRATIONS
C7-9
FIG.5. - Idcalizcd tunnel structure of thc tungsten bronze
2 Nb205.7 WO3 (inset) and TEM image with unit cell indicated.
(Courtesy S. lijima, reproduced from ref. [34].)
4 . 2 F CENTREAGGREGATION I N HALIDES.- A
second mode of anion vacancy accommodation can
function under the rigid valency constraints imposed
by the alkali and alkaline earth halides. Anion vacancies in such systcms readily trap electrons to become
neutral F centres. These may be produced in thermodynamic excess by the process of additive coloratiol~
at high temperature under partial pressure of metal
vapour [35] followed by cooling, by electrolytic
coloration, or by radiolysis under ionizing radiation.
The maximum F centre concentrations achieved by
the three methods are typically dilute, of order 10-3.
In the case of additive coloration, the limit is set by
the vapour pressure of the alkali metal at the alkali
halides melting temperature, in the case of irradiation
at or below room temperature by F centre-interstitial
halogen recombination 1363.
The F centres arc, of course, in no scnse in equilibrium with the crystal and, given sufficient mobility
above room temperature, they either leave the crystal
or interact with each other and aggregate to form
regions of the crystal containing only metal cations
b>
FIG.4a) An idealized crystallographic shear 3 X 4 block structure. (Reproduced from ref. 1321.) b) 3 X 3 block structure of
VNb120zs incorporating two planes of 4 X 3 blocks (Wadsley
defects, arrowed) imaged by TEM. (Courtesy Dr. J. L. Hutchinson.)
reviews [32-341 are available ; we shall therefore not
pursue its complexjties further, other than to remark
that the general principles involved in the construction
of these crystallographic shear structures have application to many other ionic defect structures where
valency alterations are possible or mixed valency
phases present (see [34]). Some analogous processes
in cation deficient and anion excess systems are
discussed in sections 5 and 6.
;IG. 6. - Schematic F + alkali metal colloid transformation in
r,ocksalt structure alkali halides, leaving alkali atoms in the
f. c. c. positions of initial alkali ions.
L. W. HOBBS
C7- 10
and excess electrons. These regions transform (Fig. 6)
into precipitates of alkali (or alkaline earth) metal
whose sizes (1 nm-l pm) lie in the colloidal range.
The volume misfit with the matrix is, coincidentally,
very small, and because the alkali metal is readily
compressible relative to the stiffer surrounding matrix,
the accommodation strain in the matrix (Table I)
.,.
.
.
.
..
.
..I.
.
?W*
*-p'
TABLE1
Calculatrd A ccom~nodationStrain and Pressures for
hclusions BI Alkali Halides. Alkali Metal Colloids
from Aggregation oJ'F Centres, Halogen inclusionsfrom
Corldensatior~of Suhstitutional Molecular Centres.
X
-
L
L i F : Li
NaCl : Na
KC1 : K
KBr:K
K1 : K
1.1
- 1.6
0.7
-0.14
-1.7
E,
LiF:F,
NaCl : Cl,
KC1 : Cl,
KBr:Br,
KI:12
O/o
81.0
22.8
7.0
6.1
- 0.35
P'
m
-
33.6
13.8
3.2
2.3
0
.
is even smaller (- 1 % [37]). There is electron microscopical evidence [37-391 that the precipitates may
retain the face-centred cubic structure of the original
cation sites rather than assuming, in the case of alkali
halides, the normal body-centred cubic structure of
the alkali metal. Since thcy :¶re of colloidal size, these
inclusions scatter visible light, but additionally
excitation of surface plasmons in the free electron
metal [40-441 gives rise to optical absorption in
the visible region ; the two effects produce an optical
absorption band whose peak position is characteristic
of colloid size, width largely related to size distribution
and total integrated area proportional to the volume
fraction of metal [45, 461. These inclusions can be
observed by transmission electron microscopy by
virtue of their structure factor and absorption contrast, and are seen to nucleate preferentially along
dislocation lines (Fig. 7).
It has been customary to suppose chemical equilibrium to exist between F centres and colloids characterized by an equilibrium constant which embodies
the binding cnergy (-- 0.3 - 0.5 eV 147, 481) between
an F centre and a colloid ; but in no sense is this a
true thermodynamic equilibrium because the colloid
size is known to evolve with time [39, 491, and the
binding cnergy is a function of colloid radius through
Thomson's equation [50]. In fact, true thcrmodynamic equilibrium, in the absence of a surrounding
alkali metal atmosphere, corresponds to evaporation
of all F centres out of the crystal. Furthermore,
a size distribution of colloidal particles is always
present which can be measured, for example by replica
electron microscopy [39, 51, 521. The form and
evolution of the distribution suggest that two processes
are responsible for colloid growth : pairwise interaction [53] or coalescence [54] of neighbouring particles
via surface diffusion of F centres (or metal) around
3
,""
p,.
2
$5p
'r
.
*
%. .
*V,
, * " ,$,h
y"
, a
, ;.
d
-
200 nm
FIG.7. - Potassium colloidal inclusions nuclcating on dislocation lines in additively-coloured KC1 annealed 1 h at 673 K.
TEM at 15 K. (Reproduced from ref. [M].)
the metal/matrix interface, and diffusion-controlled
Ostwald [55, 561 ripening via transport of F centres
between distant particles through the matrix, most
likely along dislocations. The latter process is discussed
in detail by Jain and Hughes 1501. Ostwald ripening
leads to a distribution characteristically skewed
towards smaller sizes, while coalescence leads to a
zeroth-order logarithmic distribution skewed to higher
sizes. The evolution of potassium distributions in
KC1 at 423 K (Fig. 8) suggests that coalescence may
be initially important during nucleation and initial
precipitation, while Ostwald ripening dominates at
longer times. A further discovery is that, when large,
these metal particles acquire facetted shapes, and
both their shape and distribution ought to be taken
into account in interpreting optical data. A comprehensive treatment including shape docs not yet
exist, but Chassagne et al. [39] have succeeded in
reproducing observed optical absorption using size
distributions determined by replication and the Mie [57]
theory corrected for mean-free-path limitations [42,
58, 591.
F centres can be created by irradiation through a
remarkably efficient radiolysis process 160, 611. At
POINT DEFECT STABILIZATION IN IONIC CRYSTALS AT HIGH DEFECT CONCENTRATIONS
C7-l1
growth can be adequately modelled using the ratetheory approach [68] developed for void growth
in irradiated metals. They find growth proportional
to
for short times and eventually (dose)'.'
for long times. Under these conditions the (steady
state) F centre concentration saturates at a much
lower value and rather differently than at room
temperature. For all systems studied so far (NaCI [63] ;
LiF, NaF, KBr, K1 [ H ] ; CaF,, BaF,, SrF, [69])
there exists a temperature of maximum production
efficiency (Fig. 10) which in many cases is only
I
I--.
--
'
1
'
FIG.8. - Histograms of potassium colloid size distributions in
additivelycoloured KC1 annealed at 423 K. Solid line, 4 h ;
broken line, 12 h.
room temperature and below, the rate of stable F
centre production decreases with increasing irradiation dose ; the kinetics are governed by the immobility
(thus isolation) of F centres which serve as recombination sites for interstitials and whose concentration
10-3 [36]. Irradiating at
eventually saturates at
higher temperatures where F centres are mobile is
equivalent to irradiating metals in the regions where
voids are produced in that F centres can diffuse
directly to alkali metal colloid sinks. Since the interstitial halogen excess also diffuses to stable sinks
(see section 6.2), there is little recombination ; the
growth of the stabilized defect fraction is linear or
even supralinear (Fig. 9) with dose, and a large anion
deficiency - of order several O/ - can ultimately
be accommodated in the form of precipitated alkali
metal. The growth kinetics of these alkali metal
colloids can be followed by optical absorption [29,
62-64], transmission electron microscopy [29, 651
and small-angle scattering [66]. Jain and Lidiard [67]
have shown that the observed kinetics of colloid
-
FIG.9.- Supralinear growth of sodium colloid absorption
band at
portional
-
17 000 cm-l in NaCl irradiated at 423 K, and progrowth of additional bands at
25 500 and
37 000 cm-l. (Reproduced from ref. [63].)
TCW~EU4TURE 6
FIG.10. - Efficiency of alkali or alkaline earth metal colloid
formation in NaCl and alkaline earth fluorides, showing temperatures of maximum production efficiency. (Reproduced from
ref. 1621.)
FIG. 11. - Cubic inclusions, probably sodium metal, in NaCl
irradiated to 40 Grad at 423 K, revealed by Fresnel contrast
in TEM at 15 K.
C7-12
L. W. HOBBS
slightly removed from room temperature. The initial
rise is due to the onset of F centre mobility, but the
fall-off at higher temperatures (which corresponds to
thermal annealing of colloids produced at lower
temperature of irradiation (Fig. 28)) involves recombination of F centres and intcrstitials.
Optical absorption measurements [63] revcal three
absorption bands (Fig. 9) in NaCl growing in the
fixed intensity ratio 40 : l0 : 1. The most intense
corresponds to the fundamental colloid absorption,
j. e. using only the electrical dipole terms in the Mie
theory and the fundamental surface plasmon resonance. The origin of the second and third peaks is
unknown, but they could correspond to addition of
quadrupole terms and to higher order plasmon resonances in the metal. The data of Gyulai [73] in natural
rocksalt and of Smithard and Tran [46] in additivelycoloured NaCl show a weak subsidiary- peak correlating with the second band ; similar peaks have been
noted in glass : silver systems [44] and predicted in
KC1 : K 1581 for very small ( 5 nm) particles. That
these subsidiary bands have not been remarked on
previously is not surprising, since only with colloid
volume fraction approaching l "/, is there sufficient
optical density to make them readily visible. Electron
microscopy (Fig. 11) and small-angle neutron scattering (Fig. 12) reveal two additional features of
colloid behaviour (it is here assumed that what is
scattcring is alkali metal, though this has yet to be
definitively cstablished) ; when thc particles become
large they develop facets, just as do voids in metals,
and in at least one system (the alkaline earth fluorides,
CaF, and SrF, [69-72J) appear to establish an ordered
array (Fig. 13). The cubic shape suggests that the
subsidiary absorption bands may derive from nonspherical colloid morphology ; the effect of shape
for the case of small dielectric particles has been recently treated by Fuchs [74].
A
FIG. 13. - Ordered cubic array of inclusions (probably calcium
1 Trad near room
metal) in CaFz irradiated in the TEM to
temperature. (Reproduced from refs. [65], [69] and [71].)
-
Fro. 12. - Small-angle scattering of 1 nm thermal neutrons
from inclusions (probably sodium metal) in irradiated NaCI.
a) Guinier plots of absolute isotropically-averaged scattering
cross-sections for irradiation at 423 K ; b) anisotropic distribution of scattering along < 100 > directions for 100 Grad
irradiation at 473 K.
5. Cation-deficient systems. - In the case of alkali
metal colloids just considered, the system alkali
halide : alkali metal can be considered either anion
deficient or cation excess, the distinction being largely
academic because significant alterations of both
sublattices are in some measure involved. An heuristic
distinction can be made, however, between cation
POINT DEFECT STABILIZATION 1N IONlC CRYSTALS AT HIGH DEFECT CONCENTRATIONS
deficient systems (considered here) and anion excess
systems (considered in section 6) based on that sublattice which primarily takes part in the accommodation
of non-stoichiometry. We consider two modes of
accommodating cation vacancies, induced in the
first system by an intrinsic cation valency change, in
the second by introduction of aliovalent cation
impurities.
5.1 STRUCTURE
OF F E ~ - , O .-The
structure of
cation-deficient wustite and its further oxidation to
the higher oxides of iron (e. g. Fe304) is a classical
problem [75] of short-range order. The X-ray diflraction studies of Roth [76], Smuts 1771 and Koch et
Cohen [78], the neutron diffraction studies of Chectham
et al. [79] and the Mossbauer studies of Greenwood
and Howe [80] have indicated that hypo-stoichiometric
F e 0 has a cation-deficient NaCl structure additionally characterized by the presence of iron atoms in
tetrahedral interstitial sites and considerable cation
vacancy clustering. The simplest stable defect cluster
structure consistent with these features is the 4 : 1
cluster (Fig. 14) comprising a trivalent Fe3 interstitial
surrounded by four cation vacancies. Catlow [81, 821
has performed shell model calculations using the
Hades [l, 831 program for lattice defects in ionic
crystals on this and other cluster configurations ;
his results suggest that the 4 : 1 cluster forms exothermically and most likely constitutes the basic structural
unit for still larger defect clusters.
+
C7-13
clusters (i. e. an << 8 : 3 D cluster) for small defect
concentrations. Superstructure peaks observed in
X-ray and electron diffraction suggest that these
defect clusters are arranged in an array with periodicity
2.6 times the host unit cell spacing. For high defect
concentrations, Catlow proposes growth of spinel-like
corner-sharing aggregates (the << 16 : 5 aggregate,
Fig. 15) leading directly to nucleation of the inverse
spinel Fe304 structure.
U Catlop vacancy
Fe3+ ~ n t e r s t ~ t ~ a i
- --
FIG. 15. - (( 16 : 5 B aggregate in Fel-zO. This spinel-like
aggregate could be a precursor of the inverse spinel Fe304.
(Reproduced from ref. [82].)
The recent lattice-resolution transmission electron
microscopy results of Iijima [84] tend to confirm
this interpretation. He observes white dots (Fig. 16)
arranged in a regularly-twinned orthorhombic unit
cell with axes along < 100 > and clusters at positions
(X, y, Z ) = (0, 0, O), (-2, 0, - $), (0, 0, 3.) relative to
the host F e 0 structure. The $ a, spacing corresponds
to the superstructure peaks and suggests that these
image features represent defect clusters. Using this
spacing and the composition of Iijima's crystal
(Fe,.,,O), the number of vacancies per cluster is
about 5 , consistent with the c( 8 : 3 cluster suggested
by Catlow.
z Cation vacancy
Fe3+ ~nterstitial
Fro. 14. -Stack of three ((4 : 1 v clusters sharing common
cation vacancy-cation vacancy edges (an (( 8 : 3 cluster) in
Fe I - ~ O(Reproduced
.
from ref. [821.)
Such defect units can associate in ways entirely
anatogous to those considered in section 4.1 for [MO,]
structural units in transition metal oxides, the allowed
linkage modes being either corner sharing or edge
sharing (face sharing is not compatible with the
NaCl structure). These aggregation modes gradually
decrease the vacancylinterstitial ratio as is found
experimentally with increasing defect concentrations.
Catlow's results favour the further formation of small
(up to three) stacks of edge-sharing 4 : 1 defect
FIG. 16. - Ordered array of defect clusters in Feo.920 irnaged
by TEM, unit cell of array indicated. (Reproduced fromref. [84].)
5 . 2 SUZUKI-PHASE
PRECIPITATION IN
ALKALI HALlDES
DOPED WITH DIVALENT CATIONS. - Cation
vacancies
are created as charge compensators for the intro-
L. W. HOBBS
C7- 14
duction of substitutional divalent cation impurities
into alkali halides ; therefore doping with divalent
cations can be used as a means of introducing a
controlled concentration of (excess) extrinsic cation
vacancies. The contribution of such extrinsic vacancies
to electrical conductivity is, of course, well known [85].
In solid solutions MX : NX, the divalent impurity
ions and cation vacancies can remain dissociated or
exist as associated pairs ; at temperatures and con573 K
centrations below the solubility limit (below
in NaCl : Mn for example) these associated pairs may
cluster into dimers, trimers or higher aggregates [86-881.
Further aggregation leads to precipitation, in some
cases (e. g. NaCl : CaCI, [89, 901, NaCl : SrCI,,
NaCI : BaCI, [go]) as the divalent metal halide
NX,, in others (e. g. NaCI : CdCI,, NaCl : MnCI,,
LiF : MgF,) involving smaller divalent cations
(r2+/r+ < 1.2 [91]) as the Suzuki [92] phase
6 MX.NX,. The structure of the metastable Suzuki
phase (one-eighth of the unit cell is illustrated in
Fig. 17) has been established by X-ray diffraction [92951 and confirmed by recent point-ion model calculations [91]. It consists of an ordered array of divalent
metal cations and alkali metal cation vacancies on
alternate (200) NaCl planes, a structure which can
arise from successive additions of < 100 > type
impurity-vacancy dipoles anti-aligned along < 100 >
[88]. Significantly, HADES calculations (Catlow,
unpublished) indicate about equal energies for
dipoles in < 110 > orientation (nearest neighbour)
and the < 100 > orientation (intervening anion)
required here. The Suzuki phase is stabilized by
small anion displacements towards the divalent
cation [91, 951. Having a low surface energy and a
structure so similar to the matrix, this phase nucleates
readily.
-
- -~
,
,1
-'
Mn++
No'
Cl-
No* voconcy
FIG. 17. - Structure of the Suzuki phase 6 NaCI. MnC12. Oneeighth of a unit cell is shown. (Reproduced from ref. [97J.)
Suzuki phase precipitates have been observed
directly by optical microscopy [96, 971, replica electron
microscopy [96, 971, gold-decoration replication [961001 and most recently by direct transmission electron
microscopy [loll. The nlorphology (Fig. 18) is in the
FIG. 18. - Nearly-cubic Suzuki phase precipitates in
6 NaCI. MnC12, showing interface dislocation structure. TEM
at 15 K . (Reproduced from ref. [ l o l l . )
form of facetted cubes or rectangular parallelopipeds
with sides approximately parallel to { 100 } matrix
planes. The isotropic matrix misfit strains, calculated
using recently measured lattice parameters 195 ;
Lilley, private communication], are small (E 2: 0.1 ';/,
for 6 NaCl CdCI,, E 2: 0.2 % for 6 NaCl MnCI,)
assuming similar elastic properties for matrix and
precipitate ; this is confirmed by the TEM observations. Such misfits can be accommodated either
elastically or by sets of misfit dislocations of screw
character at the interface [102, 1031. Figure 18 in
fact shows what appear to be widely-spaced interface
dislocations, and cleavagc ledges corresponding to
intersection of a cleavage crack with misfit dislocations
of the appropriate spacing (about 60 nm for
6 NaCI. MnCI,) have been observed by gold-decoration replication [loo]. A combination of shear in
two equivalent directions gives rise also to a shear
distortion of the precipitate shape [l021 which can
be seen in figure 18.
The distributions of precipitate sizes has been determined by replication measurements [97] and significantly accords with that predicted for a surfacereaction limited Ostwald-ripening mechanism [50] ;
POINT DEFECT STABILIZATION IN IONIC CRYSTALS AT HIGH DEFECT CONCENTRATIONS
this is reasonable since condensation and redistribution of impurity-cation vacancy dipoles appear to
be favoured at or from geometrically specific sites
on the aggregate [92, 1041, and growth kinetics could
well be controlled by a relatively slow surface reaction.
C7-15
Anion vacancy
6. Anion-excess systems. - We finally consider two
modes of accommodating an excess of anion species,
the first in two systems capable of local cation valency
changes, either intrinsically or by additions of substitutional aliovalent cations, the second in a system
with, again, a rigidly imposed valency constraint.
6.1 ANIONEXCESS IN THE FLUORITE STRUCTURE. The fluorite structure, which forms the basis for both
UO, and alkaline earth fluorides, provides a nornlally
vacant octahedral site (Fig. 19) which may be easily
occupied by an anion interstitial charge-compensating
a nearest-neighbour oxidized lattice cation
(e. g. U4+ -+ U5+ in UO,)
or substitutional aliovalent impurity (e. g. Y3+
in CaF,). The resulting associated pairs and their
aggregates form the basis for accommodating considerable anion excess in the systems UO,+, for
0 < X < 0.25 and CaF, : M3+ to high dopant
concentrations (many X).
FIG. 20. - cc 2 : 2 : 2 D anion cluster in anlon-excess fluoritc
structure. (Reproduced from ref. [114].)
bonding between anion interstiiials. The resulting
c( 2 : 2 : 2
cluster (Fig. 20) is compatible with
occupation numbers deduced from neutron diffraction
results in both systems for dilute defect solutions and
with results in heavily-doped CaF, [115]. The next
larger aggregate arises from a substitutional interstitial
pair trimer which, when relaxed in analogous fashion,
results in the (( 4 : 3 : 2 )) cluster (Fig. 21). Still
larger aggregates in the alkaline earth fluorides are
unlikely due to the immobility of trivalent substitutional ions, but extended structures can form by
interaction of the terminal < 111 > interstitials in
neighbouring clusters. In UO,,,,
the 4 : 3 : 2
cluster forms a basis for the ordered structure of the
higher oxide U40, 11161.
FIG. 19. - Fluorite structure showing octahedral site available
for fluorine interstitial chargecompensating a trivalent substitutional cation impurity.
Experimental neutron diffraction data exist for
both these systems (Willis [l051 for UO,+., Cheetham
et al. [7, 1061, and Steele et al. [l071 for CaF, : Y),
while the local distortions accompanying the fluorine
interstitial in the systems CaF, : (YF,, TmF,, LaF,)
have been deduced by ENDOR measurements [1081101 and precision X-ray lattice parameter measurements [l 1l]. Catlow [l 12-1141 has looked in detail
at both systems with the HADES program, performing
shell-model calculations of several basic defect cluster
units suggested by the neutron diffraction results,
and estimating the interaction of neighbouring clusters.
The first cluster can form when two nearestneighbour substitutional cation-interstitial anion pairs
dimerize to form an aggregate which is stabilized by
a coupled lattice-interstitial relaxation, the interstitials
moving along < 110 > and lattice anions along
< 111 >. This structure requires a degree of covalent
FIG. 21. - 4 : 3 : 2 )) anion cluster in anion-excess fluorite
structure. This aggregate could be a precursor of U409 in
U02,.=.(~eproducedfrom ref. [l 131.)
It should be noted that there is no sharp plane of
demarcation between regions containing a high
density of interstitial disorder and the parent lattice ;
this may be the explanation for curious extended
defects (Fig. 22) observed by TEM in UO, +, [l 171,
the fault contrast from which wanes and vanishes
into perfect lattice without abrupt termination.
C7-16
L. W. HOBBS
More convincing shell model calculations have been
recently performed by Diller [l241 using HADES; both
calculations still point to the need to consider substantial delocalization onto nearest-neighbour anions.
The anisotropy of the elastic strain field surrounding
an H centre suggests that for certain mutual orientations there will be an attractive interaction between
H centres. Unlike Dienes et al. [125], Diller [l241 has
found two stable configurations for the di-H centre.
That associated H centre pairs are formed at high H
centre density appears well confirmed by the work
of Itoh and Saidoh [l261 who have shown that the H
optical absorption band saturates at the expense of
another band, the V, band, but what is not certain
is whether the V, absorption derives from di-H
centres in configurations of the sort investigated by
Diller, or whether the two neighbouring H centres
react immediately to form an interstitial halogen
molecule [X;]. The V, band resembles, more than H
centre absorption, the V, and V, bands produced
after further irradiation which are similar to bands
deriving from halogen molecules in solution 11271.
Possible configurations for the [X:] molecule are
the < 100 > body centre-body centre position investigated by White and Green [l281 and by Dienes et
al. [l251 and the [X;]! complex in which the molecule is bound to a lattice ion along < 11 1 >. We
adopt here Diller's convention that a superscript
outside the brackets enclosing the defect entity refers
to the defect charge relative to the lattice, and a
FIG.22. - Fringe contrast associated with defect structure in
U02Az revealed by TEM. The contrast does not terminate
abruptly but fades into the perfect lattice. (Reproduced from
ref. [l 171.)
6.2 ANIONINTERSTITIAL STABILIZATION IN ALKALI
- We conclude by considering excess anion
accommodation in an intrinsic system in which
changes in valency or coordination are not possible.
The fate of the anion interstitial in irradiated alkali
halides has been a mystery ever since it was first
established [l181 that radiolysis of these solids led
to production of anion Frenkel pairs. It is less well
remembered that earlier classic work by Mollwo [l 191
and subsequent Japanese work [l201 concerned
itself with incorporation of a substantial chemicallyinduced halogen excess, certain parallels existing
between the two cases since aggregation of interstitial
halogen leads to local regions of excess halogen
content.
It is now well known that the form of the primary
interstitial product of radiolysis, the H centre, is an
X; molecular ion situated on a single halogen lattice
site ; it arises from crowdion translation of the V,
part of the dissociating self-trapped exciton [60, 1211.
Calculations of H centre configurations and stability
were made using a point-ion model 1122, 1231 but
yielded incorrect predictions for molecular orientation.
HALIDES.
m
x
Z
MOLECULE
D
VACANCY
a)
FIG. 23. -Two halogen molecular defects in anionexcess
rock-salt structure. a) [Xq]!- defect ; b) [~jl!-- defect, rightangled configuration. (Reproduced from ref. [124].)
POINT DEFECT STABILIZATION IN IONIC CRYSTALS AT HIGH DEFECT CONCENTRATIONS
FIG. 24. - Evolution of interstitial dislocation loop distributions in NaCl irradiated at room temperature : U ) 200 Mrad,
b) 500 Mrad, c) 2 Grad. Dccrease in loop density is due to
coalescence. TEM at 15 K. (~eproduccdfrom ref. [37].)
C7-17
L. W. HOBBS
C7-18
subscript to the lattice site if any ((-) anion, ( f )
cation) occupied by the defect. Diller'sresults(TableI1)
suggest that in some cases [X;]?
has the lower
formation energy. In both cases the large increase
in elastic distortion energy is offset by the large
molecular binding energy ( - 2.5 eV per chlorine
molecule).
An important alternative site for the molecules
is an associated anion-cation vacancy pair, occupation
of which leads to an [X:]+- defect (Fig. 23a).
Formation of this defect in the perfect lattices involves
ejection of an anion and a cation interstitial, a process
Hobbs et al. [l291 first proposed as the source of
perfect prismatic interstitial dislocation loops and
the climb of existing dislocations observed in irradiated
alkali halides (Fig. 24). The contribution of the
elastic energy (line energy) of the dislocation per
interstitial ion pair absorbed to thc formation encrgy
of [X:]+- defects is negligible for large loops, so
formation of these defects constitutes a highly exothermic process [l301 (Table 11). Diller has calculated
that dislocation loops could nucleate with as few
as four [X:] molecules displacing ion pairs. The
[X:], - molecular defect can bind with a lattice ion
to form an X,- molecule ion in a trivacancy, i. e.
[X,-]: --, a defect proposed some time ago by
Zaleskiewicz and Christy [l31 1 for the V, centre.
Two sterically different alternatives are possible ;
Diller has found the right-angled configuration
(Fig. 23b) to be the more stable and with lower
formation energies than [X;]: - defects at least in
chlorides (Table 11). Similar structures must arise
after chemical additions of excess halogen under
high pressure (-- 5 MPa) of halogen gas [37, 1321.
The same V bands are produced as in irradiated crystals (Fig. 25a) and dislocation loops are observed
(Fig. 25b). The proportionality of the V band absorption with pressure of the (diatomic) halogen gas [l 19J
indicates that the absorbed halogen is accommodated
in molecular form.
Dislocation loops are extremely good sinks for
halogen interstitials, the long range strain-fields from
large loops effective out to a radius of some 150 nm
in attracting mobile interstitials at room temperature [37]. These loops are responsible for many
observed changes in macroscopic properties after
irradiation, e. g. irradiation hardening [37, 133, 1341,
decreased thermal conductivity [l 35, 1361, lattice
parameter changes 1137, 1381 and volume expansion [139]. A large portion of the diffuse X-ray
scattering [140, 1411 is also attributable to loops.
With increasing dose, the density ofzloops decreases
continuously (Fig. 24) through coalescence of neighbouring loops ; this process is undoubtedly assisted
by thermally-activated glide and self-climb [l421
of interacting loops which proceeds via a vacancy
mechanism and thus explains the rather different
loop distributions for liquid-nitrogen and room tem-
Formation energies (eV) for defect configurations stabilizing
lzalogen excess in NaCl relative to two isolated halogen atonfs at infinity
Two separated H centres
1.68
[cl:] body centre-body centre interstitial molecule along < 100 >. (Molecular binding energy
- 2.51 eV)
1.58
[Cl;
.!l
along < 111 > centred on Cl- site
1.08
[~l:]? - substitutional molecules in existing vacancy pair
- 0.57
[Cl;]., - - substitutional molecule utilizing existing vacancy pair, right-angled configuration
- 0.59
Line Energy Contribution
per Interstitial Pair
for N Anion-Cation
Interstitial Pairs
Condensed in a
Dislocation Loop
of Radius r,
N
r l , nm
&IN
10
102
lo3
104
1OS
0.6
1.9
6.0
19
60
1.85
0.9 1
0.39
0.16
0.06
-
POINT DEFECT STABILIZATION I N IONIC CRYSTALS AT HIGH DEFECT CONCENTRATIONS
6
,u
C7-19
0'08
0 CL
4
:
ooc
0
700
?LOO
3
7OC
lLC0
FIG. 26. - Evolution of interstitial loop 'Sire distributions in
NaCl irradiated to 4 Grad at about 323 K and annealed for
increasing times at 623 K. (Reproduced from ref. (1241.)
the sort discussed by Jain and Hughes [50]. Consequently, there may be no correlation between the
final distribution of interstitial loops and the distribution of molecular centres of the form [X:]+originally responsible for loop nucleation. The high
defect densities, achieved by irradiating at elevated
temperatures under conditions where F centres are
also stabilized in large aggregate sinks (section 4.2),
lead to enormous loop growth and thus repeated
intersections to form dense dislocation networks
(Fig. 27).
Annealing crystals heavily-irradiated at or below
about 423 K results in two-stage recovery (Fig. 28) 1631.
The first stage beginning about 473 K results in a
large reduction in anion vacancy centre concentration
(aggregated in the form of alkali metal colloids)
accompanied by corresponding changes in the V
bands. Observations at lower F centre concentrations
show this stage to be accompanied by thermoluminescence [l431 and stored energy [I441 release,
and there is little doubt that this stage corresponds to
vacancy-interstitial recombination, possibly from
mobile F centres (evaporated from alkali colloids)
FIG. 25. - Incorporation of excess iodine in K1 heated 1 000 s encountering dispersed molecular centres. The end
under 5 M N m-= pressure of I2 vapour at 773 K. a ) Optical
products oT this recombination stage should thus
absorption spectrum showing V2 and V3 bands which transform
on annealing at (48 K to a band corresponding to free rnolec~~lar be anion-cation vacancy pairs which are complcmentary to the interstitial dislocation loops ; an interiodinc ; 0) Dislocation loops formed in the as-coloured crystal
revealed by TEM at 15 K. The result of annealing is shown in
mediate step is notably the formation of paramafigure 30b. (Reproduced from ref. [132].)
gnetic V, centres (VK centres trapped next to cation
vacancies [145]). There is no corresponding altcration
in
the distribution of interstitial dislocation loops
perature irradiations. Annealing above room temperature further coarsens the loop structure ; the shape during this first stage, however ; these do not anneal
of the observed distribution (Fig. 26) confirms that until a second stage well above 700 K, presumably
the coarsening process is coalescence by glide and through absorption of vacancy pairs, with an addiself-climb rather than by vacdncy bulk diffusion of tional release of stored energy [144].
C7-20
L. W. HOBBS
FIG.27. - Dislocation network formation in NaCl irradiated at 423 K to
(a) 4 Grad, ( b )40 Grad. TEM at 15 K. (Reproduced from ref. [37].)
l
0 AREA LiNDER COY.OI0
lARB!lRARY
34x0
UNITS)
!
A PEAK OPTICAL DENSITY OF
25.5m cm-' BAh.0
!
ANNEALING
-
TEMPERATURE, K
-
FIG.28. - Annealing of sodium colloid band at 17 000 cm-*
and band at
25 500 cm-' in NaCl irradiated at 423 K. (Reproduced from ref. [63].)
Not all vacancy centres are removed in the first
stage in heavily-irradiated crystals ; about 30 0/,
remain (Fig. 2 8 ) in the form of alkali metal collojds
which undergo ripening, just as in additively-coloured
crystals, and finally anneal out only above 600 K [63].
This suggests that a substantial fraction of interstitial
centres is unavailable for recombination, most likely
because they are firmly clustered. In crystals containing a chemical excess of halogen (and thus no complementary anion vacancies), the first annealing stage
does not exist ; instead, the V,/V, bands evolve into
a band at longer wavelength (Fig. 2 5 a ) which corresponds to absorption by free molecular halogen,
suggesting that aggregation of molecular centres of
the form [X,]: - can prccipitate halogen from solid
solution. This is reasonable considering that the
[X,]: - defects represent fully substitutional halogen,
i. e. substitutional on both sublattices.
Thc internal pressure and matrix accommodation
strain for such precipitated inclusions, assuming no
additional condensation of vacancy pairs, can be
calculated 1371 (Table I). Unstrained inclusions are
expected for iodine in KI, and these are observed
by transmission electron microscopy (Fig. 29a) in
annealed crystals of K1 additively-coloured with
excess iodine. Highly-strained inclusions are expected
for chlorine in KC1 or NaCl and fluorine in LiF.
Thin foils of KCI, NaCl and LiF [37, 146-1481 irradiated in the electron microscope all develop such
strained inclusions (Fig. 296) ; the measured accommodation strains for KC1 (- 7 "/,) agree well with the
POINT DEFECT STABILIZATION IN IONIC CRYSTALS AT HIGH DEFECT CONCENTRATIONS
FIG. 29. -Two forms of presumed halogen precipitation
in halogen-excess alkali halides (a) unstrained inclusions in
K1 : 12, same material as figure 25 annealed 30 m at 648 K.
TEM at 15 K. (b) Strained inclusions in KC1 heavily-irradiated in the TEM slightly above room temperature, the
measured accommodation strain being about 7 "/,. (Reproduced from ref. [71].)
C7-21
L. W. HOBBS
(7-22
FIG. 30. - Dislocation loops and dislocation network in CaF2 irradiated to :
a) 40 Grad at 333 K, b)
1 Trad just above room temperature. T E M at 15 K. (Reproduced from ref. [69].)
-
calculated strains in table I. This result suggests that
the ultimate mode of accommodating excess halogen
in alkali halides is halogen precipitation, though
the mechanism is by no means a straightforward
one and involves several intermediate defect structures.
Parallel observations (Fig. 30) have been made in
heavily-irradiated alkaline-earth fluorides [62, 691,
and Catlow (private communication) has calculated
that substitutional incorporation of molecular fluorine is energetically feasible in these systems. Thus it
may be possible to accommodate an intrinsic anion
excess in the fluorite structure in a different way to
that outlined in section 6.1.
7. Conclusions. - An intimate relationship clearly
exists between accommodation of non-stoichiometry
and extended point-defect aggregate structures in
polyatomic ionic solids. Such structures can be resolved
and identified by powerful direct methods involving
diffraction phenomena, and these methods will be
increasingly utilized to elucidate the response of
ionic lattices to high defect concentrations. The
ability to utilize a wide range of additional techniques
in ionic solids (optical absorption, paramagnetic
resonance, ionic conductivity, etc.) provides a unique
advantage in relating the structure and properties
of individual point defects to the modes of their
eventual stabilization.
Acknowleggments. - The author is indebted to
Drs. C. R. A. Catlow, G. Chassagne, A. K. Cheetham,
K. M. Diller, M. Hirai, A. E. Hughes, S. C . Jain,
A. B. Lidiard, M. J. Norgett, V. M. Orera, M. Saidoh,
J. P. Stott, M. J. Yacaman, to Mr. D. Llewelyn
and to Mrs. U. Jain for discussions relating to their
work.
POINT DEFECT STABILIZATION IN IONIC CRYSTALS AT HIGH DEFECT CONCENTRATlONS
C7-23
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DISCUSSION
F. B ~ N I ~ R
-EDislocations
.
are defects which are
not in thermodynamical equilibrium. The content of
the dissolved iodine gas in K1 which accumulates in
dislocation loops should then depend not only on the
external pressure of iodine but, also, on the time the
sample is submitted at the iodine pressure ?
L. W. HOBBS.- It is not clear at what stage dislocation loops form during the additive coloration with
halogen, nor is it clear what state the excess halogen
is in at the coloration temperature. The loops may
nucleate at temperatures below the initial coloration
temperature during cooling or at room temperature
following quenching.
L. SLIFKIN.
- It's amusing that the same defect
which you have described in Fe, -,O is also found in
AgCl doped with Fe3+. When the Fe2+ is converted
,
into an interstitial si'e, evicts 3 addito ~ e ~it +jumps
tional silver ions, and is thercby surrounded by a
tetrahedron of cation vacancies.
L. W. HOBBS.- It is comforting, though not surprising, that some of the same forms of point defect
accommodation are found in several ionic systems,
and gives us confidence that extended defect structures elucidated for one system can often be generalized
G. GUILLOT.
- What is your own opinion on the
physical mecanism of the first stage annealing of dislocation loops ? What is the mobile entity ?
L. W. HOBBS.- The interstitial dislocation loops
in irradiated NaCl exhibit only a single stage of annealing at about 523 K. At lower temperatures they may
alter their distribution by coalescence via a glide and
self-climb mechanism ; their shrinkage above 523 K
must be due to absorption of cation-anion vacancy
pairs.
The V bands, however, anneal independently of
the loops at much lower temperatures, presumably
through recombination of F centres and halogen
molecular centres. My own feeling is that this occurs
when F centres become mobile but at temperatures
above which large F centre aggregates (alkali metal
colloids) are no longer stable and re-emit F centres.
The apparent formation of halogen inclusions suggests
however that halogen molecular species may also be
mobile at these or somewhat higher temperatures, so
a clear-cut decision cannot be made.
H. PEISL.- In order to make your observations
you have to use extremely thin samples. How much are
the defect reactions and the structure of the extended
defects influenced by the nearly two surfaces ? How
sure can one be that the same defects are created in
bulk crystals ?
L. W. HOBBS.- In order to answer your question,
it is necessary to consider separately two different sorts
of observation. For the highest resolution studies,
for example lattice resolution of crystallographic
shear structures, one must use extremely thin specimens,
of order 10 nm or less, both because the projected
charge density approximation breaks down and
because chromatic aberration reduces resolution for
thicker foils. For such thin specimens, the effects of
nearby surfaces can clearly be large, although the oxide
materials used for such studies are strong and less
likely to be affected by elastic image forces than some
materials.
For observations at lower resolution, say for studies
of point defect clusters such as inclusions or dislocation loops by normal diffraction. Contrast, much
thicker specimens can be used, up to several pm
in some cases for the 1 MV electron microscope.
The principle concerns in this case are the relaxation
of elastic stresses provided by the surfaces (which
can lead to loss or rearrangement of dislocation
structures) and loss of mobile point defects to surface
sinks. Extended defect structures produced in situ
in thin foils, for example by irradiation damage, thermal decomposition or chemical reaction (e. g. oxida-
0-26
L.
W. HOBBS
tion, reduction) can be unrepresentative of bulk
structures and therefore suspect. A case in point is
the large strained inclusions formed in microscopeirradiated alkali halides which may owe their appearance to the stress-relief provided by nearby foil
surfaces. For extended defects produced in bulk
material subsequently thinned, surface effects are less
likely to influence defect structure, and in many
cases steps can be taken to immobilize structures
arising in bulk samples before thinning.
H. MATZKE.- Would it be possible at the present
state of knowledge, to say something about the
thermal stability of the ordered defects shear structures
or clusters, and is anyone working on this problem ?
Obviously, with increased temperature, the clusters,
etc... might dissociate : knowledge on thermal stability, dissociation energies, etc... would be important,
e.g. to letter understand high temperature kinetic
processes.
L. W. HOBBS.- Many people are concerned about
the metastability of their observed defect structures.
Crystallographic shear structures in transition metal
oxides, for example, are quenched in from high temperatures and specific P,,, and it would be indeed
interesting to investigate the thermal stability of such
defects. I don't know whether anyone is working on
this particular problem, but I doubt whether such a
study would shed much light on the high temperature
kinetic processes responsible for their initial formation. J. B. Cohen's group (M. Hayakawa, M. Morinaga
and J. B. Cohen in Defects and Transport in Oxides,
ed. M . S . Seltzer and R. I. Jaffee (Plenum Press,
New York) 1974, p. 177) have studied short-range
order in Fe, -,O at temperature and found it resembles
that in the quenched specimens previously studied
by Koch and Cohen. There have been some theoretical
studies of the stability of ordered void arrays in metals,
and we have been studying for some time the annealing
behaviour of all defect aggregates observed in halides.