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II. - SHORT RANGE ORDER - SUPER IONIC
CONDUCTORSSTUDIES OF ORDERING USING
HIGH RESOLUTION ELECTRON MICROSCOPY
S. Iijima, J. Cowley
To cite this version:
11.
-
SHORT RANGE ORDER-SUPER
IONIC CONDUCTORS
STUDIES-OF ORDERING USING HIGH RESOLUTION ELECTRON MICROSCOPY
S. IIJIMA and J. M. COWLEY
Department of Physics, Arizona State University, Tempe, Arizona 85281 U.S.A.
Rbsumb. - Dans quelques cas favorables les images de microscopic tlectronique haute rtsolution
peuvent nous renseigner sur la disposition d'atomes relativement lourds aussi bien dans des cristaux parfaits que dans des solides desordonnts. L'information disponible est limitte B des projections 9
deux dimensions. I1 a t t t possible, dans ces limites, d'ttudier les problkmes de mise en ordre de cristaux dtsordonnts. Nous dtcrivons et interprttons les intensitts diffustes par des cristaux dtsor- donnts d'oxydes mixtes Nb-W ainsi que les ptriodicitts ihcommensurables au rtseau dans des cristaux de base Ta,O,, illustrant par cela les relations entre les donntes de la diffraction et les images. Abstract. - High resolution electron microscope images can provide us with the configurations of relatively heavy metal atoms in both perfect and disordered crystals directly in some favorable cases. The information available is limited to two-dimensional projections. Within this limitation, however, it has been possible to study ordering problems of disordered crystals. As examples we shall describe and interpret the diffuse scattering from disordered crystals of Nb-W oxides and incommen- surate lattice periodicities in Ta,O, based crystals, illustrating the relationships between diffraction data and the images.
Introduction. - Distributions of diffuse scattering intensity that arise from imperfections in crystals have long been a major means for the study of order and disorder phenomena in solids. A large number of studies have been done by use of X-ray or neutron diffraction techniques and undoubtedly these give the most quantitative results, although electron diffraction is used increasingly to detect and describe the nature of the disorder.
The recent development of high resolution.electron microscopy however has shown that the configurations of relatively heavy atoms in crystals can be determined by direct imaging in favorable cases [I]. This new technique has beeli used for imaging not only perfectly periodic regions of crystals but also non-periodic regions. The high resolution electron microscope images, information in direct space, combined with the. usual electron diffraction data allow us to make the interpretation of diffuse scattering more reliable since diffraction data are averaged over large-volumes of crystals.
-This opens up a new range of possibilities for the study of short-range-order and of ordering processes even though the method is still seriously limited to two-dimensional projections. As one of the present authors pointea out [2], there is the added compli- cation that dynamical diffraction'processes are impor- tant for all but the very light-atom materials. Hence the~wealth of detail in high -resolution images of three- dimensionally disordered crystals is,often difficult to interpret. However, careful comparison of the experi- mental-images and the theoretical calculation of image
intensities including full dynamical scattering effects makes it possible to some extent to study the nature of such three-dimensional disorders. This method has been applied to the study of the disorders in crystals of
(( GeNb,02, )) [3].
On the other hand images of two-dimensionally disordered crystals having linear and planar defects parallel to the incident beam can often be interpreted readily in spite of dynamical diffraction effects and can give valuable information on atomic ordering not obtainable by any other method. Various planar defects in some transition metal oxide systems have been studied and important roles of the defects in oxidation or reduction process of these materials were found [4-51. In particular, for the crystals of Nb,2-x0,, it has been found that the non-stoichio- metry of this crystal is accommodated by linear defects which take the form of chains of defect clusters of oxygen vacancies and niobium interstitial atoms. The formation and ordering processes of these clusters were observed directly at the atomic level of resolution and furthermore the diffuse scattering patterns caused .by the clusters were explained in terms of short range
order of the clusters [6-71.
In the present paper we shall deal with some disordered crystals of Nb,O,-WO, systems and Ta,O,-WO, systems and focus on the elucidation of relationships between electron diffraction patterns and high resolution images. For the former samples, the origin of the anomalous diffuse ring patterns appear- ing around some Bragg spots, which were first observed by Allpress in disordered crystal of 3 Nb20,-8 WO, [8],
C7-136 S. IIJIMA AND J. M. COWLEY
have been investigated by means of optical diffraction model experiments. For the latter materials, we shall discuss incommensurate lattice periodicities which are induced by deficiency of oxygen.
Theoretical background of electron microscopy.
-
HIGH RESOLUTION BRIGHT FIELD IMAGES OF CRYSTALS.
-
To interpret the high resolution electron microscope images of crystals, we are required to understand properly both the electron optics of the electron microscope and the electron diffraction phenomena inside the crystals. The former involves various elec- tron optical parameters, such as spherical aberration of the objective lens, chromatic aberration, the diver- gence angle of the incident electron beam, the objective aperture size, and the focus of the objective lens. These effects on the image intensities have been intensively studied at various laboratories and are fairly well understood [9].Treatment of electron scattering in crystals is the most important part for the study of image formation of crystals because the dynamical effects of scattered electron waves are usually significant. Here crystal thicknesses and alignment of crystal orientations are the most influential parameters for the image inten- sities. Rigorous calculations of amplitudes and phases of diffracted waves for perfect crystals have been developed at Melbourne and Arizona [lo]. The calcula- tions are based on the multi-slice formulation of electron diffraction theory due to Cowley and Moodie. Extension of these calculations to two-dimensionally disordered crystals has also been made by assuming an artificial superstructure cell which contains a suitably chosen portion of a disordered crystal [ll]. Accuracy of the image calculation can be determined by trun- cation of the number of the diffracted beams excited inside the crystals.
From the practical point of view, for the study of crystal defects it has been shown by detailed compari- son of experimental images and theoretical calcula- tions that if the images were obtained from the crystals having the thicknesses of less than roughly 50
A,
the image intensity distributions may often be interpreted as the ones to be expected under kinematical diffraction conditions, namely when there is a roughly linear relation between the density of scattering matter and image intensities [12]. This is the basis for the study of diffuse scattering from disordered crystals of 17 Nb,O,-49 WO,. This condition is also the basis for the use of o ~ t i c a l diffraction exwriments on the modelscopy, Cowley [14] suggested that thepretical interpre- tation of dark field images based on the weak phase object approximation is rarely valid and superposition of the defects or microdomains in the direction of the incident electron beam makes the interpretation difficult.
On the other hand, if the disorders occur two-dimen- sionally, so that the crystals remain perfectly periodic in the third direction, the ambiguity -arising from such superpositions effects can be eliminated. For this reason, the disordered crystalsof 17 Nb205-49 W 0 3 are ideal test objects to examine properties of the dark field images. Using these crystals we have investigated the limitation of information available from the dark field images. Methods for the theoretical calculation of the dark field images that have been developed in our laboratory will provide further confirmation of the interpretation.
ELECTRON MICRODIFFRACTION AND TRANSMISSION
ELECTRON MICROSCOPY. - In recent years techniques have been developed for obtaining diffraction patterns from very small .identifiable regions of electron microscope specimens. Patterns from -areas approach- ing 20
A
in diameter have been obtained using adap- tions of both the conventional transmission electron microscope [15] and the scanning transmission electron microscope 1161. With the latter type of instrument the selected areas may well be reduced to 5A
or less in the near future. By these means it should be possible to overcome the difficulty, inherent in -the standard selected area diffraction techniques, of obtaining direct correlation between the diffraction pattern and imageof a small region of an imperfect crystal.In studies of short range ordering it has already been shown [16] that diffraction patterns can be obtained from within individual microdomains. The extension of this method to even smaller regions should obviously be valuable. In cases &here the inter- pretation of image intensities from local atom confi- gurations is ambiguous the microdiffraction pattern should allow the structure to be resolved in greater detail.
KINEMATICAL AND PSEUDO-KINEMATICAL,SCATTERING FROM, DISORDERED CRYSTALS. - We review briefly
the kinematical approximation for the scattering from two-dimensionally disordered crystals and the pseudo- kinematical approximation which can provide some account of the dynamical scattering. effects for this
crystals having two-dimensional disorders. particular case.
DARK FIELD IMAGES OF DISORDERED CRYSTALS.
-
A high resolution image of a thin specimen obtainedThis technique has been widely applied as a-means to with the incident beam parallel to a principal axis can observe ordered microdomains in disordered crystals show the projection of the structure. The correspond- having short range order and microciystallites occur- ing kinematical amplitude distribution ,in the diffrac- ring in amorphous materials. Using only the diffuse tion pattern is given by the planar sectionaf the Fourier
transform function :
scattering which appear between sharp Bragg spots to
form th; image, the microdomains are visualized as F(uv0)
=
C
fi
exp { 2 ni(ux,+
vy,) } , (1)STUDIES OF ORDERING USING HIGH RESOLUTION ELECTRON MICROSCOPY C7-137
where the summation is taken over all atoms in the sample. For a thin crystal which is well-ordered in the beam direction the contributions of the n atoms superimposed in that direction
fik
may be combined to giveF(uv0) =
1
ji' exp { 2 ni(uxi+
vy,) } , (2)i
where
The kinematical diffraction intensity is then
=
C
C
A'
jj'* exp { 2 ziu(ri - r,) ) ,where u is written for the two dimensional reciprocal lattice vector and riand rjare vectors in the plane of the real space projection.
The selected area diffraction patterns usually obtained in transmission electron microscopes come from areas at least several thousand angstroms in diameter containing a large number of atoms. The diffracted intensity is then obtained from (3) by using the same sort of statistical averaging as for X-ray diffraction. At the other extreme, with high resolution electron microscopy it is possible to image separately the individual projected rows of atoms having scatter- ing factors
fj'
so that a direct correlation can be made with the ainplitude distribution (2) or the intensity distribution (3).As an intermediate stage, the microdiffraction devices now available with high resolution scanning transmission electron microscopes to obtain diffrac- tion patterns from regions of 10
A
or less in diameter will allow direct comparison of the diffraction pattern from a small group of atom peaks with the direct image.For systems having average periodic structures we can use Patterson function description of the disor- dered crystal [lo]. The projected potential can be written
where ( q(r) ) is the periodic average projected potential distribution and Aq(r) is the deviation from the average. The corresponding Patterson function is
and Fourier transforming gives
I
F(u)I2
=+
+
l2
( 5 ) where the first term on the right represents the sharp Bragg reflections from the average lattice and thesecond term is the diffuse background intensity. The diffuse intensity is therefore given by replacing the
fi'
andfj'
in (3) with the deviations from the average values, Af,' and Afj'.The kinematical approximation is normally valid only for very light atoms and very thin crystals. It can fail for even a single atomic layer of heavy atoms. However for sufficiently thin crystals (e.g. for less than 50
A
thickness, 100 keV electrons and 3A
reso- lution) a so-called column approximation can be applied. The wave function at a point in the exit fact of the crystal can be assumed to be influenced only by those atoms within a column running through the crystal in the beam direction and centered on the point. The radius of the column is given very approxi- mately by ( Z A ) ' / ~ where t is the crystal thickness. Then the scattering by each column of atoms will be charac- teristic of the type of atoms in the column even though it will not be given by the kinematical scattering factorfi'
but by a dynamical scattering factor 8: (see Cowley [26]) which in general will be complex and will have a different, broader, angular distribution as compared with,&'.
The diffuse scattering then will be given by
Idiff(uv) =
11
Ag: Agi* exp { 2 niu(ri - rj) }.
( 6 ) In this expression. the ri and rj will be the same as for the kinematical case. Since the differences between Agi and Afi' will be on a very small scale of distances, much smaller than the unit cell dimensions, the diffuse intensity given by (6) will differ from the kinematical intensity only over large distances in reciprocal space. Arguments suggested by Cowley and Iijima [12] and Fejes [18] agree with indications from computations that the relationship between dynamical and kinema- tical intensities in such cases, while not linear, will be nearly monotonic. Hence the local configurations of diffuse scattering will have very much the same form in the two cases even though the overall intensity variations, on a scale of distances much greater than the reciprocal lattice periodicity, may be very diffe- rent. Calculations which confirmed these conclusions were made by Fisher [19].In general the deviations from the average, Af' or Ag', will be equally often positive and negative. For favorable cases, such as those considered below, when the disorder occurs at a relatively small pro- portion of the sites within the unit cell, there will be large positive or negative deviations for these sites and small deviations elsewhere. Then the diffuse scattering can be found approximately by considering the deviations at these few sites only.
THE USE OF OPTICAL TRANSFORMS OF IMAGES. -
C7- 138 S. IIJIMA AND J. M. COWLEY
optical diffraction pattern will resemble the electron diffraction pattern from the corresponding part of the crystal.
In general dynamical diffraction effects will perturb the image intensity to the extent that, apart from the periodicities involved, the optical diffraction pattern intensity distribution may show very little correlation with the structure or with the electron diffraction intensities. However as we have seen. for sufficientlv thin crystals viewed in the proper orientation under appropriate imaging conditions, the image intensity, and hence the amplitude distribution of light trans- mitted through the photographic negative will give an approximate representation of the projected potential. Then the local details of the intensity distribution of the optical diffraction pattern will correlate closely with those of the electron diffraction pattern even if the large scale variations of intensity are different.
This method, or the equivalent use of a computer to obtain the Fourier transform, is particularly conve- nient for the comparison of diffraction patterns from image plates or from trial models, in the case of two dimensionally disordered crystals.
Experimental observations. - DISORDER I N CRYS- TALS WITH TETRAGONAL TUNGSTEN BRONZE TYPE STRUCTURE. - For the tetragonal tungsten bronze
type (hereafter abbreviated T.T.B. type) structures of ternary oxides of Nb205-WO,, two ordered structures, 4 Nb205-9 WO, [20] and 2 N b 2 0 5 . 7 WO, [21] are known. An idealized model of the 4 Nb205.9 WO, structure (viewed down the short c axis) is illustrated in figure la. The shaded squares represent oxygen- metal octahedra which are linked to each other by corner sharing. The unit cell consists of three T.T.B. type subcells (figure lb) and four of twelve pentagonal tunnels are filled regularly with oxygen-metal strings, resulting in a superstructure ( a = 12.251
A,
b= 36.621A
and c = 3.94A).
The electron diffraction pattern of the (hkO) reflections from an ordered region of this crystal is shown in figure 2a.PIC;. 1 . - (a) Idealized structure model of 4 Nb,O, .9 WO, crys- tal. Each hatched square represents an MO, octahedron, which shares its corner oxygen atoms with neighboring octahedra. Thc unit cell (outlined) consists of three tetragonal tungsten bronze cells (b) and one third of the pentagonal tunnels are filled with metal-oxygen strings parallel to e (filled circles). The double headed arrows A and B indicate pairs of filled pentagonal tunnels described
in the text.
For the crystals prepared with nonstoichiometric compositions (I7 Nb,05 .49 WO,), planar faults, such as twinning and out-of-phase domain boundaries. and interstitials were often observed [21, 221. The latter defect that we shall be concerned with below is a linear, or one-dimensional, defect extended in the c-direction and distributed in a perfectly continuous host lattice so that it can be regarded as an interstitial in the projection.
OBSERVATION OF DIFFUSE DIFFRACTION PATTERNS. - An electron diffraction pattern of the (hkO) reflections from the fragments having the interstitials shows unusual diffuse ring patterns around the sharp Bragg spots (figure 2b). The halves of the rings around
FIG. 2. - The (hkO) electron diffraction patterns (a) from an ordered crystal of 4 Nb,0,.9 WO,, (b) from a disordered crystal of 17 Nb,0,.48 WO, and (c) from the same crystal as in (b) but not in the exact [OOl] zone axes orientation. Diffused rings have been ana-
STUDIES O F ORDERING USING HIGH RESOLUTION ELECTRON MICROSCOPY C7-139
(+ 100) and (0
+
10) spots referring to the T.T.B. sublattice are missing as well as the ring around the (000). The disappearance of the rings is dependent on the crystal orientation. Tilt of the crystal away from the c axis with respect to the incident electron beam direction shows up the full rings (figure 2c). Analysis of these diffuse ring-patterns is obviously not easy but it will become feasible from the high resolution images.STRUCTURE IMAGES OF DISORDERED CRYSTALS. - A structure image corresponding to the region giving the diffuse rings shown in figure 2b is reproduced in figure 3b. Individual bright spots in the image were found to coincide with the empty square (small spots) or pentagonal tunnels (large spots) in the structure (see figure la). Although we cannot resolve individual metal-oxygen octahedra in this image, distributions of these tunnels allow us to draw adequately the arrange- ment of the metal atoms in the structure. Close exami- nation of the images showed that the host sublattice of T.T.B. type is perfectly periodic and disorder results from the interstitials of metal-oxygen strings in the pentagonal tunnels. It is noted that the ordered structure of 4 Nb205.9 WO, results from filling regularly one third of the tunnels in the host sublattice. An optical Fourier transform of the negatives of the image, figure 3a, shows the intensity distributions quite similar to those of the electron diffraction pattern shown in figure 2b (figure 36). The similarity indicates that the origin of the diffuse rings can be sought in the correlation among the positions of the filled pentagonal tunnels.
DARK FIELD IMAGES OF DISORDERED CRYSTALS. -
A dark image from the same region of a FIG, 3. - ( a ) Structure image from the disordered crystal that crystal as the bright field image of figure 3a shows gives diffused ring patterns as seen in figure 2b. Large and small
larger blobs than those in the bright field image. The bright spots in the image correspond to the positions of the empty pentagonal and square tunnels (see figure la). (b) Optical diffraction pattern from the same photographic negative as in figure 3a. (c) Daik field image corresponding exactly to the area shown in
figure 3a. The positions of the bright blobs coincide with the loca- tions where one set of the paired filled pentagonal tunnels occur
(A and B in figure la). (d) Optical diffraction pattern corres-
ponding to figure 3d.
number of the blobs is greatly decreased. To obtain the bright blobs the objective aperture was displaced by the beam-tilt method so as to be centered around the (110) spot (the position is indicated by a circle in the electron diffraction patterns of figure 2b). Because the aperture is smaller 'in size than that used for the biight field image.the resolution of the dark field image is poor. An optical diffraction pattern from the negative ofdigure 3c also shows the .ring patterns similar to the ones i n ' f i a r e 3b but a ring appears around the (000) spot (figure 3d), as in the electron diffraction patterns taken from the tilted crystal (figure 2c).
C7- 110 S. IIJIMA A N D J . M. COWLEY
appear all have an identical atom arrangement, or cluster of the atoms. This cluster occurs in the two different orientations in the ordered structure of 4 Nb,0, .9 WO,, and contains a pair of filled penta- gonal tunnels (shown by double arrows A and B in figure la). In the dark field images only one type of the cluster is imaged as a bright blob. This has been proved by the theoretical image. calculation [23]. Since the ring patterns were obtained from the optical diffraction pattern of the image, a correlation among the positions of the clusters must be responsible for the diffuse ring patterns. The smaller number of the spots makes it much easier to find the correlation than in the case of the bright field image.
OPTICAL TRANSFORM EXPERIMENTS. - The correla- tion function among the positions of the pairs of. the filled pentagonal tunnels can be described by optical transform experiments on simulated models for the disorders.
The perfectly periodic sublattice of the T.T.B. type will be represented by positions of the empty tunnels (indicated by open circles in figure 46) and can be regarded as an averaged lattice ( q(r) ) in equa- tion (4). Then the filled tunnels that were found directly from the image of figure 3a are represented by solid circles (figure 4a). This grating will correspond to an actual disordered structure, cp(r). The distri- bution of the filled tunnels is then a deviation from the averaged lattice, Aq(r) (figure 4c). Figures 4 are portions of the gratings used for optical diffraction
experiments. Fourier transform corresponding to the Ap(r) appears similar to that of the electron diffrac- tion patterns of figure 26. This confirms that the diffuse ring patterns are caused by the distribution of filled pentagonal tunnels. Therefore, the description of the optical grating of Ap(r) in terms of interatomic vectors among the filled tunnel positions gives the correlation function, so that basically it will be possible to determine the short range order parameters. In fact, an examination of the grating showed some prefe- rential ordering of the neighboring filled tunnels but the ordering appears much more complicated than that of disordered alloys with short range order.
The correlation was elucidated more intuitively by examining a distribution of the clusters, or pairs of the pentagonal tunnels, rather than the individual filled tunnels. The experiments on the dark field images suggested that the clusters which occur in two different orientations are equally responsible for the diffuse ring patterns. The positions of the clusters that were found directly from the image shown in figure 3a are illus- trated in figure 5a, where the two types of the clusters (A and B shown in figure la) are indicated by solid and open circles. The square grid may be referred to as the host lattice of the T.T.B. type. An optical diffrac- tion pattern from this grating (figure 5b) showed the ring patterns very similar to the electron diffraction pattern of figure 26 except for the appearances of the full rings near the (000) spots. Therefore, if we ignore this effect, we can analyze the ordering of the clusters in terms of short range order of the clusters.
FIG. 4. - Portions of the optical gratings constructed from the exper~menra~ lmages of figure >a arlu cnclr uprl~ar U I I ~ I ~ C L I U L I ~ C I L I C I L L S .
(a) Distribution of both occupied (solid circles) and empty (open circles) pentagonal tunnels, (b) that of the empty tunnels only and (c)
STUDIES O F ORDERING USING HIGH RESOLUTION ELECTRON MICROSCOPY C7-141
FIG. 5. - (a) Distribution of A- and B-type clusters, the positions of which were found directly from the image of figure 3a. The square grid lattice is referred, to as the host T.T.B. type. The clus- ters form domains having two different types of lattices (hatched and unhatched regions enclosed by lines). Each of these lattices is twinned and out of phase., (b) Optical diffraction pattern from the grating constructed by the positions of the clusters. Diffuse ring patterns are similar to these in electron diffraction pattern
(figure 2b).
The examination of the distribution of the clusters allowed us to draw some conclusions as follows. The unlike clusters of A and B tend to form pairs in certain direction with a constant separation. However, in the a axis direction of the T.T.B. lattice the like clusters tend to be neighbors. In some regions A and B clusters are ordered and form domains (enclosed by lines and unshaded in figure 5a). It will be found that actually the domains have an ordered structure of the 4 Nb20, .9 WO, type. The domains are often out-of-
phase. Two orientations for these domains (rotated by 900 with respect to each other) are seen and they are in the same twin relation as was often observed on a larger scale in the crystals having less disorder [21].
Beside the domains,of 4 Nb20, .9 WO, type there is another type of the domain having a square lattice (shaded). For these domains twin and out-of-phase relations are also common. We confirmed froni the optical diffraction experiments that the diffuse ring patterns were observed independently for,either type o'f domain bg$ were not observed if one set of the twinned* sets o f &main was removed. Therefore the twin relation in the domain structure seems to be substantially the origin for the diffuse ring patterns. Finally it is noted that almost-all clusters belong to one of the two types of the domains. In order to explain the short range order state in disordered alloys the microdomain models have quite often been proposed. The present observation will support the validity of this postulation to some extent although complicated disordered structure of the niobium- tungsten oxide crystals may not be compared directly with simple disordered alloys.
INCOMMENSURATE LATTICE PERIODICITIES. - Incom-
mensurate lattice periodicities of the superstructures have often been observed in disordered crystals ; for example, in Fe,-,O [24], ~ N b 0 , [25], magnesium germanate [26], TaS, [27] and many disordered alloys. Some of these superstructures appear as transitional states during phase transformation from one structure to another and many studies have been made, mostly on disordered alloys. Most observations have been made by diffraction methods and thus the nature of these superlattices was analyzed' on the basis of statistical distributions of some local lattice modula- tion [28].
On the other hand, the high resolution electron microscope images can provide directly the infor- mation on local structural variations occurring in crystals, so that this approach will allow us to study incommensurate lattices in terms of the direct space. An attempt has been made previously to investigate the lattice defects in wustite crystals [29] and distribu- tions of the defect clusters of oxygen vacancies, which cause the incommensurate superlattice periodicity, have been observed directly. However there was a difficulty in the interpretation of these images because of the three-dimensional distributions of the defects. In this section, we briefly describe some evidence on incommensurate superstructure lattice periodicities, due to the two-dimensional distributions, in crystals of Ta,O, and related structures. ,The details will be reported elsewhere.
Crystal structures of L-Nb20,, L-T~,O, and related compounds are based on the U0,-type structure and the stable phases in the system W0,-Ta20, form a homologous series, consisting of 8, 11, 13 and
'C7-142 S. IIJIMA AND J. M. COWLEY
FIG. 6. - Electron diffraction patterns. (a) The (hkO) and ( c ) the (Okl) reflections from crystals of 15 Ta,05.2 WO,, (b) the (hkO) and
( d ) the ( O k l ) reflections from crystals of L-Nb205. Incommensurate lattice periodicities are seen in the b axis direction of 15 Ta,05. 2 WO, and the c axis direction of L-Nb20,.
The crystal of 15 Ta205.2 WO,, which is iso- structural with that of L-Nb,O, according to X-ray study [31], has an orthorhombic unit cell with a = 6.2, b = 29.3, c = 3.9
A
and the b spacing is nearly 8 times that of the U0,-type subcell 1321. Electron diffraction patterns of L-Nb205 and 15 Ta20,.2 WO, crystals showing the (hkO) spots and the (Okl) spots are shown in figures 6a-d. The b spacing of L-Nb,O, is exactly 8 times of that of the subcell, while a small deviation in b spacing for 15 Ta,05 .2 WO, can be recognized. The spacing varied slightly from specimen to specimen as has been often observed, not only in the 8 subcell type but also in ail the other phases. We also confirmed .a slight rotation of rows of the superstructure spots around each pseudo-hexagonal sublattice spot (withstrong intensity) that has been reported by Spiridelis et al. [33].
An electron micrograph from a crystal of 15 T a 2 0 5 .2 WO, in the same orientation as figure 6a shows many dark bands running nearly parallel to the a-axis direction (Fig. 7a). These bands were not observed in the images of L-Nb,O,. The spacing varies continuously approximately from 60
A
to 250A.
In some regions (arrowed) the bands are arr?yed regu- larly, resulting in a superstructure. Spatial distribu- tions of these bands are in accordance with all the observations in the electron diffraction patterns. ASTUDIES O F ORDERING USING HIGH RESOLUTION ELECTRON MICROSCOPY C7-143
The periodicity of this superstructure is about
6.7 x c of the host lattice. This nonintegral multi- plicity is clearly demonstrated in the high resolution images (figure 8), where the dark rods having various lengths (1
-
4) x c appear parallel to the c-axis direction. The average distance between the positions of neighboring rods along a line parallel to the c-axis is 6.7 x c, which agrees with the observation on the electron diffraction pattern. The statistical distribution of the rods can be seen more clearly in the optical diffraction pattern (inset), which appears identicala> with the electron pattern.
FIG. 7. -(a) Relatively lower magnification image of a crystal of 15 Ta,0,.2 W 0 3 in the [OOI] orientation. The dark bands
appear in a pseudo periodic manner in nearly perpendicular direc- tions to b axis. The spacing varies continuously and in some regions the bands are arrayed regularly (arrowed), resulting in a super- structure. (b) High 'resolution image of the dark bands shows
that they result from intergrowth of slabs having a width of 1.2 x b
of the host lattice. The width corresponds to one unit cell of the 'IG. *. - Structure image of a crysta1 of L-Nb205 in the [loo]
11 sub-cell p o ~ y m o r p ~ , Therefore the distribution of the dark orientation corresponding to the electron diffraction pattern of bands is considered as the compositional modulation of the host figure 6d. The dark rods having various lengths appear ~arallel
lattice. to the-c-axis direction. The statistical distribution of the rods (see optical diffraction pattern of the inset) gives rise to the incom-
mensurate superstructure latt~ce per~od~cit~es.
unit cell of the 11 subcell type (indicated by X). There- fore the regions where the bands are ordered have a different structure from the host lattice, in this case the 19 subcell type, causing a periodic compositional modulation in the 8 subcell type of 15 Ta205.2 WO,.
More remarkable incommensurate lattice perio- dicity was found in. the c-axis direction of L-Nb205 crystal. The electron diffraction pattern of figure 6d
showed that this crystal has a superstructure in the c-axis direction and is different from that of 15 Ta205.2 WO,, contrary to previous sugges- tions [31]. However very weak diffuse patterns are seen at the positions where the superstructure spots appear in the crystal of L-Nb205.
The dark rods appear to arise from distortion planes where, according to the X-ray studies, the straight chains of edge-sharing, regular pentagon of the U0,-type subcell are folded [32]. The folding intro- duces some distortion of the pentagons and also reductions in their coordination numbers. Therefore the incommensurate lattice periodicities would be a consequence of rather long range interaction of the local distortions of the host lattice in the c-axis direction.
Acknowledgments. - This work was supported by
S. IIJIMA AND J. M. COWLEY
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