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Journal of Microscopy, Vol. 232, Pt 1 20 08, pp. 726

Received 12 December 2007; accepted 22 February 2008

Contribution of electron precession to the study of perovskites

displaying small symmetry departures from the ideal cubic ABO3

perovskite: applications to the LaGaO3 and LSGM perovskites

J . - P . M O R N I R O L I

, G . J . A U C H T E R L O NI E, J . D R E N N A N& J . Z O U

Laboratoire de Metallurgie Physique et Genie des Materiaux, UMR CNRS 8517, USTL, ENSCL,

Batiment C6, Cite Scientifique, 59500 Villeneuve dAscq, France

Centre for Microscopy and Microanalysis

School of Engineering, The University of Queensland, 4072, Queensland, Australia

Key words. Electron precession, LaGaO3, lanthanum gallate, LSGM crystal

structure, perovskite.

Summary

Electron microscopy and electron diffraction are well adapted

to the study of the fine-grained, faulted pure and doped

LaGaO3 and LSGM perovskites in which the latter is useful for

fuel cell components. Because these perovskites display small

symmetry departures from an ideal cubic ABO3 perovskite,

many conventional electron diffraction patterns look similar

and cannot be indexed without ambiguity.Electronprecession

can easily overcome this difficulty mainly because theintensity of the diffracted beams on the precession patterns

is integrated over a large deviation domain around the exact

Bragg condition. This integrated intensity can be trusted and

taken into account to identify the ideal symmetry of the

precession patterns (the symmetry which takes into account

both the position and the intensity of the diffracted beams).

In the present case of the LaGaO3 and LSGM perovskites,

the determination of the ideal symmetry of the precession

patterns is based on the observation of weak superlattice

reflections typical of the symmetry departures. It allows an

easy and sure identification of any zone axes as well as the

correct attribution of hkl indices to each of the diffracted

beams. Examples of applications of this analysis to the

characterizations of twins andto theidentificationof thespace

groups are given. This contribution of electron precession can

be easily extended to any other perovskites or to any crystals

displaying small symmetry departures.

Correspondence to: J.-P. Morniroli. Tel: 33320436937; fax: 33320434040;

e-mail: [email protected]

Introduction

There are many new materials, which are either in the

market place or under development, that are based upon

high-temperature electrochemical processes. Some examples

of these materials are batteries (Kao et al., 1992), catalysts

(Lahousse et al., 1998), epitaxial substrates (Christen et al.,

1997), gas separation membranes (Balachandran et al.,

1998), high-temperature electrodes (Kawada et al., 2006),

oxygen pumps (Yuan & Kroger, 1969), oxygen sensors(Weissbart & Ruka, 1961), radioactive waste containment

(Ringwood etal.,1979)and solidoxidefuelcells(Minh, 1993).

With such diverse categories of materials and applications

one can see the importance of these materials to our modern

technological society (Stlen et al., 2006). Some of these new

materials are based upon the ABO3 perovskite-type structure

whereseveralinnertransition(rareearth)elementgallatesare

isostructural with the archetypal ABO3 perovskite, GdFeO3.

With A- and/or B-site doping, these perovskite-based oxides

transform from insulators into conductors. Rather than being

electron conductorsthese oxides are eithermixed electron/ion

conductors orion conductors. Because ions aremuchlarger in

sizethanelectrons,their migrationpathwaysbecome far more

critical because these ions must jostle past cations in a solid

lattice. It is therefore important to study the basic migration

mechanisms for electronic, ionic and mixed conduction in

these complex ABO3 perovskite-type oxides.

The ABO3 perovskite-type structure is both geometrically

andchemicallystablegivingittheadvantageofgreatchemical

flexibility. That is, the ability of the lattice to accommodate

many different types of dopant atoms with both wide-ranging

atomic sizes and chemical valencies. Thus, in these doped

ABO3 perovskites one must correctly identify the crystal

C 2008 The AuthorsJournal compilation C 2008 The Royal Microscopical Society


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8 J . - P . M O R N I R O L I E T A L .

structure at bothroomand operatingtemperatures, especially

as at high temperatures, phase transitions occur which yield

the desired operating properties of these materials. Once the

crystal structure has been correctly identified, one can then

hopefully determine the anion conduction pathway through

the solid.The structure determination of these compounds using

X-ray patterns has been used routinely for many years;

for example see Wang et al. (1991). It indicates that some

perovskites adopt an ideal cubic aristotype structure but most

of them exhibit some small departures from this ideal cubic

symmetry leading to a lower symmetry to form orthorhombic,

rhombohedral, tetragonal or monoclinic structures.

However, as research moves into the nanoworld,

small and/or heavily faulted perovskite crystals are often

encountered that cannot be studied by X-ray or neutron

diffraction. The electron microscope is thus well adapted, not

only for imaging these fine-grained materials but also for

identifying or characterizing their crystallographic structureby means of electron diffraction. A major difficulty is then

encountered due to this symmetry lowering: that is many

zone axis diffraction patterns are very similar to each other

and cannot be indexed without ambiguity with conventional

electron diffraction. Nevertheless, the correct identification of

a zone axis pattern (ZAP) as well as the correct attribution

of hkl indices to each diffracted beam are required in many

material science fields, for example the characterization of

crystal defects (stacking faults, dislocations,twins. . .).Itisalso

required in electron crystallography in order to identify many

crystallographic features (the crystal system, the Bravais

lattice, the Laue class and the point and space groups).One solution to overcome this difficulty consists in

using convergent-beam electron diffraction or large-angle

convergent-beam electron diffraction which gives more

accurate andusefullinepatternsbutthesepatternscanbe very

complex and their interpretation is usually tedious and time

consuming. In addition, these methods require a specimen

of optimal thickness and, for the large-angle convergent-

beam electron diffraction technique, relatively large and non-

distorted crystals (Morniroli, 2002a). Recently, the electron

precession method, which was proposed by (Vincent &

Midgley, 1994) became commercially available and can be

fitted on most modern transmission electron microscopes. In

this technique (Fig. 1a), a parallel or a nearly parallel incident

beamisrapidlyrotatedbymeansofthepre-specimendeflection

coils of the microscope on the surface of a hollow cone whose

axis is directed along the optical axis and whose semi-angle

, in the range 0 to 3, is the precession angle. When a

[uvw] zone axis of the studied crystal is set as close as possible

along the optical axis, the diffraction pattern located in the

back focal plane is made of circles, which depending on the

precession angle, are more or less superimposed (Fig. 1b).

The transmitted circle gives the transmitted intensity as a

function of the orientation of the incident beam during the

precession movement whereas each hkl diffracted circle gives

the diffracted intensity as a function of the orientation of the

incident beam with respect to the corresponding (hkl) lattice

planes.

This circle pattern is transformed into a spot pattern by

means of the post-specimen deflection coils which act in asynchronizedway andin opposite directionwith respect to the

pre-specimen deflection coils. The precession patterns, thus

observed on the microscope screen (Fig. 1c) look similar to

selected-areaelectrondiffractionpatternsbuttheydisplayfour

main advantages:

(1)The diffracted intensity of each hkl spot is integrated over

thecorresponding hklcircle present in theback focal plane,

i.e. along a large deviation domain on each side of the

exact Bragg conditions. As a matter of fact, this integrated

intensity is directly connected with the area located under

the rocking curve (the diffracted intensity as a function

of the deviation from the exact Bragg condition). As a

result, the integrated intensities are not very sensitiveto a slight crystal misorientation and a [uvw] zone axis

precession pattern always looks well aligned even if the

[uvw] crystal zone axis is not exactly located parallel with

the incident beam. This also means that the intensities of

the diffracted beams can be taken into account and trusted

when analysing a precession pattern. Thus, the ideal

symmetry of the precession patterns becomes available.

This symmetry takes into account both the position and

the intensity of the diffraction beams present on a pattern.

It can be observed for both the zero-order Laue zone

(ZOLZ) and the whole pattern (WP)1 reflections and it

is connected with the Laue class (Morniroli & Steeds,1992). As will be illustrated in Section 4, very small

differences of intensities can be observed on precession

patterns, which can be used to identify the presence or

the absence of symmetry elements and to surely infer this

ideal symmetry. It is a crucial and critically important

advantagewith respect to selected area-electron diffraction

patterns or microdiffraction patterns whose diffracted

intensities are extremely sensitive to slight misorientations

and usually only provide the net symmetry (the

symmetry which only considers the position of the

reflections).

(2)The precession patterns display a larger number of

reflections in the ZOLZ and in the high-order Laue zones

(HOLZs) than a selected-area diffraction pattern and

this number increases with an increase in precession

angle. This important property is very useful in electron

crystallography (Morniroli & Redjaimia, 2007; Morniroli

et al., 2007).

1AWPdisplaystheZOLZandatleastoneHOLZ.Throughoutthispaper,thenotations

for the ZOLZ and WP ideal symmetries will be in accordance with (Morniroli &

Steeds, 1992); they are underlined and given between parentheses for the ZOLZ.

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C O N T R I B U T I O N O F E L E C T R O N P R E C E S S I O N 9

Fig. 1. Schematic description of the electron precession technique. (a) Electron ray-path in the column of a transmission electron microscope. For the

sake of simplicity, only one hkl diffracted beam is drawn and the column contains only one intermediate lens and no projector lens. (b) Circle pattern

observed in the back focal plane of the objective lens. (c) Spot pattern observed on the microscope screen.

(3)During the precession movement, the incident beam is

never aligned along the zone axis where the strongest

dynamical interactions occur. Thus, the precession

patterns are less dynamical than the conventional

diffraction patterns.

(4)A few-beam behaviour is encountered with large

precession angles. Because the multiple diffraction paths

to the forbidden reflections are unlikely to occur when

this few-beam behaviour prevails, forbidden reflections

disappear or become very weak on large-angle precession

patterns. This property allows the identification of the

kinematical forbidden reflections (Morniroli & Redjaimia,

2007).

The purpose of this paper is to demonstrate that these

remarkable and useful precession features can be used

to identify, without ambiguity, any [uvw] zone axes and

to assign the correct hkl indices to the diffracted beams

of perovskite crystals displaying some small symmetry

departures. To illustrate this possibility, LaGaO3 perovskite

specimens were selected and observed. LaGaO3 perovskite is a



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1 0 J . - P . M O R N I R O L I E T A L .

Fig. 2. Description of the ideal cubic (a) and orthorhombic LaGaO3 (b) perovskites.

good example because both its room and high-temperatures

crystal structures exhibit a small departure from a cubic

symmetry to an orthorhombic and to a rhombohedral

symmetry, respectively. Some applications to the Sr and Mgdoped LaGaO3 perovskites (LSGM perovskites) will also be

given.

Description of the room temperature LaGaO3 crystal

structure

The ABO3 perovskite-type oxides consist of a trivalent

transition ion located in a A-site coupled with a trivalent

transition metal ion located in a B-site, which forms a BO 6octahedra (Glazer, 1972; Fig. 2a).

The arrangement of the BO6 octahedra in an ideal cubic

perovskite is shown in Fig. 2a. As reported by Marti et al.(1994), Slater etal. (1998)and Lerch etal.(2001),intheroom

temperature LaGaO3 perovskite, these octahedra are slightly

tilted and rotated (Fig. 2b). The corresponding structure is

then described by an orthorhombic unit cell with the space

group Pnma.

As a matter of fact, this pseudo-cubic LaGaO 3 perovskite

displays some very small symmetry departures from the ideal

cubicperovskite, whichmeans that its diffraction patterns will

be very close to cubic. To quantify this aspect, let us consider

a zone axis form of the ideal cubic perovskite. In the

general case,observedwhen u=v=wandnon-zero,thisform

contains48equivalent[uvw]directions(directionshavingthe

same parameter P[uvw] but different orientations because, in

the cubic crystal system, P[uvw] is not modified if the u, v, and

w signs are positive or negative and if the u, v and w indices

areinterchanged). Letus consider the case of the zone

axes. In the case of the Laue class m3m, it gives two types

of non-superimposable and mirror-related diffraction patterns

labelledA andB inFig. 3 where,forthesake of

simplicity, only the ZOLZ reflections are shown.

With the orthorhombic perovskite, the situation becomes

more complex because the 48 equivalent cubic

directions are transformed into six orthorhombic zone axis

forms : , , , , and

each of them containing eight equivalent directions

(in the orthorhombic crystal system, the parameter P[uvw] is

not modified if the u, v and w signs are positive or negative butthe u, v and w indices cannot be interchanged). As a result,

in the Laue class mmm, two sets of six different and mirror-

related diffraction patterns are obtained as shown in Fig. 3.

They differ from the cubic patterns by the presence of

weak extra reflections (to be more visible, they are magnified

10 times in Fig. 3),whichare located at twodifferent positions:

(1)In the middle of the small edge of the parallelograms

drawn with respect to the cubic reflections for the,

, and zone axis forms. Note that

the intensity of the extra reflections is different and typical

in each of these four patterns

(2)In the middle of both sides of the parallelograms as well

in the middle of the parallelograms for the two

and zone axis forms. The intensity of the extra

reflections is also typical of the zone axis.

How to correctly identify these patterns?

With conventional electron diffraction (selected-area electron

diffraction or microdiffraction), the diffracted intensities

are too strongly modified by dynamical effects (multiple

diffraction) and/or by thickness variations and crystal

misorientationsinthediffractedarea,sothatonlythepositions

of the reflections and the net symmetry can be trusted. This

means that a zone axis cannot be surely identified among the

four , , and or between the

two and zone axis forms.

This is no longer the case with electron precession because

the intensity and the ideal symmetry can be taken into

account. Thus, the observation of the intensity of these typical

additional reflections is the basis of the zone axis identification

described in the present paper.

To this aim, we describe, the pseudo-cubic LaGaO3perovskite with respect to the ideal cubic perovskite and,

in analogy with the ordered structures commonly observed



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C O N T R I B U T I O N O F E L E C T R O N P R E C E S S I O N 1 1

Fig. 3. Description of the diffraction patterns produced by: the 48 equivalent zone axes from the ideal cubic perovskite the corresponding

,,,, and zone axes from the orthorhombicperovskite.For the sake of simplicity,only theZOLZreflections

are shown. To increase their visibility, the weak extra reflections are magnified 10 times.

in metal alloys, we consider the corresponding diffraction

patterns as made of fundamental reflections common to

the cubic and pseudo-cubic perovskites and of superlattice

reflections typical of the new periodicities and thus typical ofthe pseudo-cubic perovskite.

Figure 4 illustrates this analogy. In order to make a direct

comparison between the ideal and pseudo-cubic perovskites

and to describe the ZAPs with the same [uvw] indices, both

structures must be described by means of comparable unit

cells.For this reason, theidealcubicperovskite is notdescribed

by its conventional primitive cubic unit cell but by means

of a multiple tetragonal unit cell (Fig. 4a) whose contour

(Fig. 4b and c) is close to the orthorhombic LaGaO 3 unit cell

(Fig. 4a, b and c). The corresponding reciprocal lattices are

alsogivenin Fig.4d and d. Both reciprocal lattices display the

samefundamentalreciprocal nodeswhereas the pseudo-cubic

one displays additional superlattice nodes, which occur when

h+ l is odd or when h+ l is even and k odd.Throughout the present text, the subscripts c, t, and o will

refer to the cubic, multiple tetragonal and orthorhombic unit

cells, respectively.

In Fig. 5, the main zone axis diffraction patterns

(those which correspond to the six c, twelve cand eight c ZAPs of the ideal cubic perovskite) are

displayed and arranged on a stereographic projection so that

their mutual orientations are preserved. These patterns were

kinematically simulated by means of the electron diffraction

software (Morniroli, 2002b). The patterns fromthe idealcubic



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Fig. 4. Comparative descriptionof the ideal cubicand pseudo-cubic LaGaO3 perovskites. a, b, c, d Projection of thestructure (a), projection of thedirect

lattice (b), directlattice(c) andreciprocal lattice (d)of theidealcubic perovskite. a, b, c, d Projection of the structure (a), projection of thedirect lattice

(b), direct lattice (c) and reciprocal lattice (d) of the orthorhombic LaGaO3 perovskite.

perovskite (Fig. 5a) only display fundamental reflections.

One notices the absence of kinematical forbidden reflections

because the corresponding space group Pm3m does notcontain anyscrew axes orglideplanes. Asexpected, most ofthe

simulatedpatterns fromthe pseudo-cubic perovskites (Fig.5b)

display weak additional superlattice reflections. For the sake

of clarity, the intensity of these extra reflections is exaggerated

(their diameter is magnified 10 times). Some couples of

superlatticereflectionslocatedoneachsideofthemirrorsofthe

ideal cubic perovskite display a typical difference in intensity

connectedwith theloweringof symmetry (see, e.g. thecouples

of reflections (arrowed) on the [111]o, [111]o, [111]o and

[111]o ZAPs and located on each side of the pseudo-mirrors

m1 andm2). Some patterns also display kinematical forbidden

reflections connected with the glide planes and screw axes

of the Pnma space group of the orthorhombic perovskite.

With conventional electron diffraction (selected-area electron

diffraction or microdiffraction), the experimental observation

of these typical intensity differences between some couples of

superlattice reflections as wellas the identificationof forbidden

reflections is usually impossible due to multiple diffraction

paths connected with the strong dynamical behaviour of

electron diffraction. This is possible with electron precession

because the precession patterns are less dynamical and they

display, at least with large precession angle, a few-beam

behaviour.

Experimental procedures

Sample preparation for TEM observations

LaGaO3 perovskite specimens were prepared from powders of

99.99% pure La2O3 and Ga2O3. The powders were weighed

and mixed in a ball mill for 48 h in an alcohol slurry. They

were then calcined, ball milled for another 24 h and finally

sintered at 1200C in air for 12 h.

For LSGM, the raw powders capable of adsorbing H2O and

CO2 from the atmosphere were calcined at 1000C in air

and cooled in a dry, nitrogen atmosphere prior to weighing.

Powder milling was performed in a vibratory mill for 6 h

using stabilized zirconia in propan-2-ol. Milled powders were

dried in a vacuum oven at 6080C for 1012 h, and then

passed sequentially through 300-, 150- and 75-m stainless

steel sieves. After final sieving the powders were calcined at

the required temperature (10001200C) in air and then re-

milled. After passing through the 75-m sieve, the powder

was uniaxially pressed into either bar shapes for electrical

conductivity evaluation or pellets for phase assemblage and

microstructure characterization. The green specimens were

isostatically pressed then fired at 14001450C for 15 h in

air.

The resulting LaGaO3 and LSGM powders were pressed

into pellets at 200 kPa. Crushed pellets were mixed with a



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Fig. 5. Schematic description of the main zone axis

patterns for the ideal cubic (a) and pseudo-cubic (b)

LaGaO3 perovskites.Forthecubicunitcell,thesubscript

c refersto theconventionalcubic unitcell.The subscript

o is used for the indices of the orthorhombic LaGaO 3

unit cell. Mirrors present on the patterns are indicated

by bold lines and pseudo-mirrors by dotted lines.



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20-m aluminium powder with a ratio of about 10%

perovskite and 90% metal powder. A few tens of grams of

this powder mixture was then placed between two flat iron

sheets and laminated with a rolling mill at a pressure near the

maximum ofthe pressin orderto obtaina metalfoilof thickness

of about 50 m in which the crushed perovskite crystals areembedded.Three millimetre discs were thenpunched from the

foil with a Gatan disc punch (Gatan, Pleasanton, CA, USA).

ThesethinfoilswereionbeamthinnedonaGatan600DuoMill

at room temperature for 2 h with both the upper and lower

Ar+ ion beams operated at 4 kV, with a 10 mA ion current

per gun and an angle of incidence of 10 both above and

below the foil, until the foil waselectron optically transparent.

These specimens have a much better quality than the crushed

specimens deposited on a carbon film where the transparent

areas are usually very small because they result from a

cleavage mechanism which produces some rapid variations

of the specimen thickness. On the contrary, the ion thinning

of the Al/perovskite foils produces relatively large electron-optically transparent areas with relatively small thickness

variations of the embedded crystals. Because aluminium is a

very malleable metal, these specimens are not brittle and can

be observed many times. In addition, aluminium is relatively

transparent to electrons meaning that there is no risk of

confusion with the studied perovskite crystals. Aluminium

is also a very good thermal conductor well adapted to high

temperature experiments up to 500C.

Transmission electron microscopy

Room temperature experiments on the perovskite sampleswere performed with a Philips CM30 TEM operated at

300 kV and equipped with the electron precession Spinning

Star equipment from Nanomegas (Brussels, Belgium). The

specimens observed in the present study are usually heavily

faulted and contain many twins. In order to avoid artefacts

due to these defects and to probe only defect free areas, the

precession patterns were obtained in microdiffraction mode.

In this mode, the electron beam is a nearly parallel electron

beam produced by a 10-m C2 condenser aperture. This beam

is focused on the specimen with a probe diameter of between

10 and 50 nm. All the precession patterns were recorded on a

1k 1k Gatan CCD camera.

An electron micrograph of a LaGaO3 grain coming from a

thin area of the sample is shown in Fig. 6. It shows typical

contrast connected with approximately 1020 nm domain

sizes.

Experimental results

All the ZAPs considered in the present study only display the

ZOLZ and therefore only give the ZOLZ ideal symmetry. The

main zone axes of the ideal cubic perovskite are described, i.e.

the c, c and c ZAPs.

Fig. 6. Typical electron micrograph of a LaGaO3 grain.

Identification of the [uvw] zone axis from precession patterns

c zone axes

As shown in the theoretically simulated patterns in

Fig. 7, the six equivalent c zone axes of the ideal cubic

perovskite with ideal (4 mm) symmetry (Fig. 7a) give, in the

orthorhombic perovskite, two different patterns:

(1)The [010]o and [010]o patterns (type A) with (2 mm)

symmetry. They display additional superlattice reflections

located in the centre of the square drawn with respect to

the fundamental reflections. Typical kinematical forbiddenreflections are also located along the two remaining

mirrors m3 and m4 (Fig. 7b).

(2)The [101]o, [101]o, [101]o and [101]o patterns (type B)

with (2 mm) symmetry where the additional reflections

are located along one of the edges of the square. Some

kinematical forbidden reflections are located along its

mirror m2 (Fig. 7c).

There is no special difficulty to identify these two A and

B types of zone axes by electron precession (Fig. 7b and

c) even with conventional electron diffraction (Fig. 7b

and c) because the position of the superlattice reflections

on both types are very different and cannot be modified

by multiple diffraction. One notices that the kinematical

forbidden reflections are clearly visible on all these patterns.

Nevertheless, we can use electron precession to detect

these forbidden reflections. As indicated in Section 1, the

kinematical forbidden reflections can be identified by using

a large precession angle (3 was found to be a good value);

with these experimental conditions, a few-beam behaviour

is observed during the precession movement of the incident

beam so that the probability of having multiple diffraction

paths to the forbidden reflections is unlikely to occur. With

these conditions, a forbidden reflection disappears or becomes



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Fig. 7. Electron diffraction patterns of the six c ZAPs for the pseudo-cubic perovskite. They are sorted into two types of patterns A and B.

a Kinematical simulated pattern, with (4 mm) symmetry, of the six equivalent c for the ideal cubic perovskite. b, b, b [010]o and [010]o

diffraction patterns with (2 mm) symmetry (type A). Kinematical simulated patterns (b), experimental precession pattern (b) and experimental selected-

area electron diffraction pattern (b ). The forbidden reflections are visible on the experimental patterns. c, c, c [101]o, [101]o, [101]o and [101]o

diffraction patterns with (2 mm) symmetry (type B). Kinematical simulated pattern (c), experimental precession pattern (c ) and experimental selected-

area electron diffraction pattern (c ). The forbidden reflections are visible on the experimental patterns. d, d Experimental precession pattern of type A

obtained with a 1 precession angle (d) and corresponding dynamical simulation performed with jEMS (d). The kinematical forbidden reflections (circled

reflections) are visible on both patterns. e, e Experimental precession pattern of type A obtained with a 3 precession angle (e) and corresponding

dynamicalsimulation performed withj EMS (e). Thekinematical forbiddenreflectionsare invisibleon both patterns.f, f Experimental precession pattern

of type B obtained with a 1 precession angle (f) and corresponding dynamical simulation performed with jEMS (f). The kinematical forbidden reflections

(circled reflections) are visible. g, g Experimental precession pattern of type B obtained with a 3 precession angle (g) and corresponding dynamical

simulation performed with jEMS (g). The kinematical forbidden reflections are invisible. Mirrors present on the simulated patterns are indicated by bold

lines.

very weak. This is what is observed on the patterns in

Fig. 7e and g, which correspond to the patterns with types

A and B. One notices that these patterns are in excellent

agreement with the corresponding dynamical simulations

(Fig. 7d, e, f and g) performed with the jEMS software

(Stadelmann, 1987, 2007).

c zone axes

The12equivalentc zoneaxesofthecubicperovskite

(Fig.8a), withsymmetry (2 mm),give fourdifferentdiffraction

patterns (Fig. 8be) in theorthorhombic LaGaO3 perovskites:

(1)The [001]o and [001]o patterns (type C) with (2 mm)

symmetry. The superlattice reflections are located on the

small edge of the rectangle drawn with respect to the

fundamental reflections. Some forbidden reflections are

located along the m2 mirror (Fig. 8b).

(2)The [111]o, [111]o, [111]o and [1 1 1]o patterns

(type D1) with (2) symmetry. Some superlattice

reflections are located along the diagonal d1 and

some forbidden reflections along the other diagonal d2(Fig. 8c).



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Fig. 8. Electron diffraction patterns of the twelve c ZAPs for the pseudo-cubic perovskite. They are sorted into four types of patterns C, D1, D 2

and E. a Kinematical simulated patterns of the twelve equivalent c, with (2 mm) symmetry, for the ideal cubic perovskite. b, b [001]o and

[001]o diffraction patterns with (2 mm) symmetry (type C). Kinematical simulated pattern (b) and experimental precession pattern (b). The forbiddenreflections are visible on theexperimental pattern. c [111]o, [111]o, [111]o and [1 1 1]o kinematical simulated patterns with (2) symmetry (typeD 1). d

[111]o, [111]o, [11 1]o and [111]o kinematical simulated patterns with (2) symmetry (typeD 2).e [100]o and [100]o kinematical simulatedpatterns

with (2 mm) symmetry (type E). f Experimental precession pattern performed with a 1 precession angle. It is in agreement with the types D1, D2 or E.

g, g Experimental precession patterns performed with 1(g) and 3 (g) precession angles. The absence of kinematical forbidden reflections along the

d1 diagonal in figure g (circled reflections)provesthat this pattern belongs to the D2 type. h,h

Experimental precession patterns performed with 1(g)

and 3 (g) precessionangles.This pattern belongs to the type E because no forbiddenreflectionsare identified on the 3 precession pattern. The bold lines

indicate mirrors.

(3)The [111]o, [1 11]o, [11 1]o and [1 1 1]o patterns (type

D2) with (2) symmetry. The superlattice and forbidden

reflections also are along the d1 and d2 diagonals but these

patterns are mirror related with respect to the patterns of

type D1 (Fig. 8d).(4)The [100]o and [100]o patterns (type E) with (2 mm)

symmetry. Some superlattice reflections are located along

boththe d1 and d2 diagonals. Forbidden reflections are not

present on these zone axes (Fig. 8e).

Type C patterns areeasily distinguished from thethreeother

types D1, D2 and E because the position of the superlattice

reflections on these patterns is typical. Thus, the experimental

precession pattern in Fig. 8b belongs to this type. On the

other hand, the types D1, D2 and E are very difficult to be

distinguished from each other by conventional methods, or in

lowangleprecessionpatternsbecausetheforbiddenreflections

will appear by multiple diffraction (Fig. 8f). Actually, they can

be distinguished by large-angle electron precession as shown

ontheexamplesinFig.8g,g ,h,andh. Large-angle precession

patterns prove that there are no forbidden reflections

in Fig. 8h, whereas kinematical forbidden reflections are

identified along the d1 diagonal in Fig. 8g. Therefore, the

precession patterns in 8g and 8h belong to the types D2 and

E, respectively.

Another way to make the distinction among the three E,

D1 and D2 patterns consists of tilting the specimen along

the m1 and m2 mirrors or pseudo-mirrors until some more

typical patterns are observed and to compare them with

the corresponding simulated patterns. The two sets of

experimentalpatternsshownin Fig. 9a andb were obtained in

that way. Each set display some strong differences connected

withthe positionsor the intensityof thesuperlattice reflections



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Fig. 9. Sets of electron precession patterns located along the m 1 and m2 mirrors around the c ZAPs. a, b Experimental precession patterns.

Some typical superlattice reflections are circled. c, d, e Corresponding simulated patterns located around the [100] o (or [100]o) (type E) (c), [111]o

(or [111]o, [111]o, [1 1 1]o) (type D1) (d) and [111] o (or [1 11]o, [11 1]o, [111]o) (type D2 (e). The arrows indicate some typical features. The bold anddotted lines indicate mirrors and pseudo-mirrors, respectively.

(see especially the circled superlattice reflections which prove

thepresenceoftwom 1 andm2 mirrorsinFig.9aandthelossof

these mirrors in Fig. 9b). The two sets are, in a unique way, in

perfect agreement with the corresponding simulated patterns

from type E and D1, respectively. Note that the simulated sets

of precession patterns also indicate a 2 mm,1 and1 WP ideal

symmetry for the types E, D1 and D2, respectively.

c ZAPs

The eight equivalent c ZAPs of the ideal cubic

perovskite (Fig. 10a) with (6 mm) symmetry give two types

of patterns in the orthorhombic perovskite:

(1)The [012]o, [012]o, [012]o and [01 2]o patterns (type F)

with (2 mm) symmetry (Fig. 10b).

(2)The [2 10]o, [2 10]o, [2 10]o and [210]o patterns (type G)

with (2 mm) symmetry (Fig. 10c).

Both types display forbidden reflections and very weak

superlattice reflections located at the same positions. They

also display the two same mirrors m1 and m4 meaning that

the four other m2, m3, m5 and m6 mirrors present in the

cubic perovskite are lost in the orthorhombic perovskite and

are only pseudo-mirrors. These two types of patterns are too

close to be easily identified even with electron precession.

To make the distinction between them, the solution consists

again in tilting the specimen along the m 1 mirror and the

two pseudo-mirrors m3 and m5 in order to reach some more

useful ZAPs like the ones shown in Fig. 10b, b , b and c,

c , c . The positions and the intensity of some superlattice

reflections present on these patterns is very typical of the types

F and G which can be identified without ambiguity in that

way (see, especially, the superlattice reflections indicated by

an arrow on the patterns b , b , c and c ). It is clear that

the experimental precession patterns shown in Fig. 10d and

d display superlattice reflections (marked with an arrow) in

agreement with type F patterns andin disagreement with type

G patterns. Note that the WP symmetry of the type F and G

patterns is m.

Identification of the otherc zone axes

Any otherc zone axes canalways be correctlyindexed

withrespecttothethreemainc,c andczone axes described above.



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Fig. 10. Electron diffraction patterns of the eight c ZAPs for the pseudo-cubic perovskite. They are sorted into two types of patterns F and G.

a Kinematical simulated patterns of eightequivalent c ZAPs forthe ideal cubic perovskite. They display a (6 mm) symmetry.b [012]o, [012]o,[012]o and [01 2]o kinematical simulated diffraction patterns with (2 mm) symmetry (type F). c [210] o, [210]o, [2 10]o and [210]o kinematical

simulated diffraction patterns (type G) with (2 mm) symmetry. b, b , b Simulated diffraction patterns obtained after a 19.4 specimen tilt along the

m1, m3 and m5 mirror and pseudo-mirrors of the pattern of type F. c, c , c Simulated diffraction patterns obtained after a 19.4 specimen tilt along

the m1, m3 and m5 mirror and pseudo-mirrors of the pattern of type G. d, d, d , d - Experimental precession patterns in agreement with the simulated

patterns b, b, b and b (type F). The bold and dotted lines indicate mirrors and pseudo-mirrors, respectively.

Interpretation of a o ZAP

To fully interpret a [uvw] zone axis diffraction pattern, hkl

indices must be attributed to each of the diffracted spots. This

attribution is not always an easy task with the pseudo-cubic

LaGaO3 perovskite due to symmetry lowering. For example,

let us consider the case of the [010]o (or [010]o) pattern (type

A) (Fig. 11a). The (4 mm) symmetry (mirrors m1, m2, m3 andm4)whichwouldbeobservedonthispatternfortheidealcubic

perovskite is decreasedto a (2 mm)symmetry(mirrorsm2 and

m4)forthepseudo-cubicLaGaO 3 perovskite.Asaresult,subtle

and very weak differences of intensities affect some couples of

superlattice reflections located on each side of the two pseudo-

mirrors m1 andm3. They arevisible on the theoretical pattern

in Fig. 11a (see, e.g. the couples of reflections marked with

an arrow), but they are too weak to be surely distinguished

on the corresponding experimental precession pattern. This

means that it is nearly impossible to make an experimental

distinction between two [010]o patterns rotated by 90. To

remove this ambiguity, the solution is to observe more typical

ZAPs located around the studied pattern (a solution already

describedearlier to make the distinction between thecandc zone axes).Thisisthe case with thethree patterns

shown in Fig. 11bd located at about 18.5 from [010]. A

clearly visible difference of intensity is observed between somecouples of superlattice reflections (see the circled reflections in

Fig. 11) located on each side of the pseudo-mirrors m 1 and

m3. These patterns are in agreement in a unique way

with the [131]o, [131]o and [131]o dynamical simulations in

Fig. 11b, c d (or [131]o, [13 1]o, [1 3 1]o if the pattern in

Fig. 11a is interpreted as being the [010] ZAP). Therefore, the

hklindicesofthe[010]o ZAP(or[010]o ZAP)canbeattributed

without ambiguity (Fig. 11a and a).

A second example concerns the [101]o ZAP (or [101]o,

[101]o and [1 0 1]o) (type B) (Fig. 12a). This pattern displays



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Fig. 11. Interpretation of the [010]o (or [010]o) zone axis pattern (type A). a, a [010]o (or [010]o) experimental (a) and simulated (a

) precession

patterns with (2 mm) symmetry. b, b [131]o (or [131]o) experimental (b) and simulated (b) precession patterns with (2) symmetry. c, c [131] o

(or [13 1]o) experimental (c) and simulated (c) precession patterns with (2) symmetry. d, d [131]o (or [1 3 1]o) experimental (d) and simulated (d

)

precession patterns with (2) symmetry. The bold and dotted lines indicate mirrors and pseudo-mirrors, respectively.

a (2 mm) symmetry with two mirrors m 1 and m3 whereas

it would display a (4 mm) symmetry (m 1, m2, m3 and m4mirrors) in the ideal cubic perovskite. As a matter of fact,

its WP symmetry is not (2 mm) but only m with a unique

mirror m1 meaning that two [101]o ZAPs rotated by 180

are different. This 180 ambiguity can be removed by tilting

the specimen around the [101]o and along the m1 mirror and

m3 pseudo-mirror in order to observe three more typical ZAPs

like the ones shown in Fig. 12bd. Again, a clear difference

of intensity among some couples of superlattice reflections

located on each sides of the pseudo-mirror m3 is visible (see

the circled and arrowed reflections in Fig. 12). Note that the

couples of superlattice reflections located on each side of the

m1 mirror display the same intensity. The comparison with

simulatedpatterns allows the unique attribution of the [313]o,

[201]o and [313]o indices to the experimental patterns b,

c and d, respectively. Thus, the correct hkl indices can be

assigned to the reflections of the [101]o pattern as shown in

Fig. 12a.

Applications

Identification of pertinent ZAPs for electron crystallography

The identification of both the Laue class and the possible

space groups of a crystal can be obtained, at microscopic

and nanoscopic levels, from observations of three features

available on conventional microdiffraction patterns:

(1)The net and ideal symmetries displayed by some specific

microdiffraction patterns provided the diffraction patterns

display at least one HOLZ. They are connected with the

crystal system and the Laue class.



14/20


Fig. 12. Interpretation of the [101] o (or [101]o, [101]o, [101]o) zone axis pattern (type B). a, a [101]o (or [101]o, [101]o, [101]o) experimental (a)

and simulated (a) precession patterns with (2 mm) symmetry. b, b [313]o (or [3 13]o, [31 3]o, [313]o) experimental (b) and simulated (b) precession

patterns with (2) symmetry. c, c [201]o (or [210]o, [201]o, [201]o) experimental (c) and simulated (c) precession patterns with (2 mm) symmetry. d,

d [313]o (or [313]o, [313]o, [3 13]o) experimental (d) and simulated (d) precession patterns with (2) symmetry. The bold and dotted lines indicate

mirrors and pseudo-mirrors, respectively.

(2)The shifts between the reflections located in the first-order

Laue zone (FOLZ) with respect to the ones located in the

ZOLZ. They are connected with the Bravais lattice.

(3)The periodicity differences between the reflections located

in the FOLZ and in the ZOLZ. They are connected with theglide planes.

A systematic method based on these features was proposed

by (Morniroli & Steeds, 1992) and was successfully applied

to various crystals (Redjaimia & Morniroli, 1994; Mateo

et al., 1997; Huve et al., 2000; Wei et al., 2000; Gomez-

Herrero et al., 2001; Ranjan et al., 2001; Meshi et al., 2002;

Quarez et al., 2003; Tarakina et al., 2003; Labidi et al., 2005;

Meshi et al., 2005).

Nevertheless, some experimental difficulties are

encountered with the ideal symmetry because its

identification requires a perfect alignment of the incident

beam along a zone axis. Other difficulties occur when the

studied crystal is not thin enough so that its patterns only

display a small number of reflections in the HOLZs. The

FOLZ/ZOLZ shifts and periodicity differences are then verydifficult to observe.

These difficulties are easily overcome with electron

precession mainly because the integrated intensities on the

precession patterns is directly connected with the ideal

symmetry and because the number of reflections present in

each of the Laue zones is larger than the one encountered on

conventional diffraction patterns.

InthepresentcaseoftheorthorhombicLaGaO 3,thismethod

requires one to observe the three following ZAPs: o(patterns with type E), o (patterns with type A) and



15/20


Fig. 13. Identification of the LaGaO3 space group from electron precession patterns. a [100] o zone axis precession pattern. Only the ZOLZ reflections

are visible and can be characterized by mean of a centred rectangular unit cell with sides parallel to the m1 and m2 mirrors. b, c Electron precession

patterns obtained when the crystal is tilted a few degrees away from [100] o along the m1 and m2 mirrors. The FOLZ reflections are characterized by

means of a rectangular unit cell and some FOLZ reflections are located on the m 1 and m2 mirrors (circled reflections). d Theoretical [100] o ZAP

obtained in the case of a primitive orthorhombic lattice (oP) with a diagonal n glide plane parallel to the (100) lattice planes. The corresponding partial

extinction symbol is Pn.. .

o (patterns with type C). As mentioned previously,

there is no difficulty to identify the o and oZAPs because the corresponding patterns display typical

superlattice reflections. This is no longer the case with the

o ZAP (type E) which can be easily confused with the

patterns with the types D1 or D2. We have also indicated

previously howto identify this zone axis by using a large-angle

precession pattern or by specific specimen tilts.

The pattern in Fig. 13a was identified in this way.

Nevertheless, its FOLZ is not visible because the FOLZ radius

is too large for the acceptance angle of the microscope. To

observe it, the specimen is tilted a few degrees away from the

zone axis along the mirror m1 and m2 until some reflections

located in the FOLZ are observed as shown in Fig. 13b and c.Two useful features are visible on these misoriented patterns:

(1)Some reflections are located on the mirrors m 1 and m2(circled reflections); they reveal the absence of shift of the

FOLZ reflections with respect to the ZOLZ reflections in

agreement with a primitive P Bravais lattice.

(2)More reflections areobservedin theFOLZ than in theZOLZ.

This feature can be easily quantified by drawing, in the

FOLZ and in the ZOLZ, the smallest rectangular unit cell

describing the2D lattice ofreflections. Inthe FOLZ,this unit

cell is a rectangle whose sides are parallel to the m 1 and



16/20


m2 mirrors whereas in the ZOLZ the unit cell is a centred

rectanglewhosesidesaretwotimeslarger.ThisFOLZ/ZOLZ

periodicity difference is connected with the presence of a

glide plane perpendicular to the [100] zone axis, i.e. along

the (100) lattice planes.

Comparison with the theoretical pattern in Fig. 13d(Morniroli & Steeds, 1992) indicates that these features

correspond, in a unique way, to a n glide plane parallel to

the (100) lattice planes and to a partial extinction symbolPn..

(Hahn, 2002).

The same experiments performedalongthe twoother [010]

and[001]zone axes allow the identification of the Pnma space

group for the LaGaO3 structure.

Identification of a twin

Due to symmetry lowering, twinsare very frequentlyobserved

in perovskites andwere describedby many authors in the case

of LaGaO3 (Wang etal.,1991;Yao etal., 1991;Fink-Finowickiet al., 1992; Bdikin et al., 1993; Wang & Lu, 2006; Wang &

Lu, 2007).

The identification of the twin law, i.e. the identification

of a rotation axis [uvw] and a rotation angle around it,

can be inferred from diffraction patterns (Morniroli & Gaillot,

2000). In principle, two couples of parallel [uvw]A//[uvw]Bdirections coming from the two crystals A and B located on

each side of the studied twin need to be identified. It could

be two couples of [uvw] zone axes or one couple of zone

axes [uvw] and one couple of parallel lattice planes (hkl). The

knowledgeofthecorrect[uvw]orhklindicesarecrucialforthis

identification.Let us consider the diffraction pattern in Fig. 14a. It was

obtained when the electron beam is focused on a LaGaO3twin and it is made of the superimposition of a [010]o ZAP

(typeA)anda[101] o ZAP(typeB).Intheprevioussections,we

indicate that 90 and 180 ambiguities exist for these [010]oand [101]o patterns, respectively, and that these ambiguities

can be removed by observing, on some ZAPs located around

the [010]o and [101]o, some typical superlattice reflections

located on each side of the pseudo-mirrors present on the

patterns.

Actually, the patterns in Figs 11 and 12 were obtained

with the incident beam located on each side of the studied

twin. Both figures are arranged in a coherent way so as to

preserve their mutual orientation. The correct [uvw] and hkl

indices of these patterns were demonstrated in the previous

sections. From these patterns, many couples of parallel [uvw]

ZAPs can be obtained, for example [010]oA//[101]oB and

[131]oA//[201]oB, which give the following twin law: a 120

rotation around the common rotation axis [210]. This result

is obtained from the mathematical calculation described by

Morniroli& Gaillot, 2000. A schematicdescriptionof this twin

with {121} twin plane is given in Fig. 14b. It is in agreementwith previous studies.

Fig. 14. Characterization of a LaGaO3 twin. a Electron precession

pattern obtained when the incidentbeam is located onthe twin. Itis made

of the superimposition of the [010] o and [101]o ZAPs. b Schematic

description of the twin. The two lattices A and B on each side of the twin

plane (121)oA//(121)oB are rotated bya 120 angle around the common

direction [210]o.

Another way to obtain the same twin law is to consider

the pattern in Fig. 14a, where in addition to the couple of

parallelZAPs[010]oA//[101]oB italsogives(101)oA//(020)oB.

It is pointed out, that the correct interpretation of the [010]and [101] ZAPs is required to identify the actual twin law.

Especially, the 90 and 180 ambiguity for the [010]o and

[101]o ZAPs should be taken into account. If not, wrong

twin laws like 90 around [101] or 180 around [111] are

obtained.

Identification of the crystal structure at microscopic

and nanoscopic level

The comparison between experimental precession patterns

and simulated patterns allows an unambiguous crystal



17/20


Fig.15. Identificationof the LSGMspace group. a Experimental precessionpatterns located around ac ZAP.b, c Simulateddiffraction patterns

located around the[010]o (or[010]o)(a)and [101]o (or[101]o,[101]o, [101]o) (b)for theorthorhombic Imma space group.d, e, f Simulated diffraction

patterns located around the [010]o (or [010]o)(d), [101]o (or [101]o,) (e) and [101] o (or [101]o) (f) for the monoclinic I112/b space group. The mirrorsare indicated by a bold line and the pseudo-mirrors by a dotted line.

identification, especially if the weak superlattice reflections

are taken into account. In the case of LaGaO3 there is no

special difficulty because most of the authors agree with

the orthorhombic structure. As a matter of fact, all the

experimental patterns from our specimens are in perfect

agreement with this structure.

This is no longer the case with the LSGM perovskite. At

room temperature, two different structures based on X-ray

and neutron diffraction experiments were proposed:

(1)An orthorhombic structure with space group Imma (Lerch

et al., 2001).(2)A monoclinic structure with space group I112/b (Slater

et al., 1998).

Both of them are very close and only differ by some very

slight changes and by different loss of symmetry elements

(there is less symmetry elements in the monoclinic structure

than in the orthorhombic).

The identification of the real LSGM space group can be

obtained from a careful examination of the superlattice

reflections present on somediffraction patterns located around

a c ZAP (Fig. 15a). In this figure, it is clear that all

the couples of reflections (circled and arrowed spots) located

on each side of the m1, m2, m3 and m4 mirrors of the ideal

cubic structure display a clear difference of intensity, which

proves that these patterns do not contain any mirror. This

absence ofmirror isin agreement in a unique way with the

corresponding simulated patterns located around the [101]m(or [101]m) ZAP from the monoclinic I112/b space group

(Fig. 15e). It is in disagreement with all the other ctheoreticalpatternsfrom the two possiblespacegroups I112/b

and Imma. As a result, the LSGM space group is identified as

I112/b.

Discussion

This analysis is based on a qualitative observation of the

symmetry elements present on the precession patterns and

the deduction of the ZOLZ and WP ideal symmetry. Table 1

summarizes these ideal symmetries for the main zone axes

of the cubic perovskite as well as the resulting symmetries

in the orthorhombic perovskite. A 180 ambiguity occurs

with the patterns displaying an m or 1 symmetry. A special



18/20


Table 1. ZOLZ and WP ideal symmetries for the main zone axis patterns of the cubic and the orthorhombic LaGaO3 perovskites.

Ideal cubic LaGaO3 cs c c

perovskite Laue class m-3 m

Ideal symmetry

ZOLZ (6 mm) (4 mm) (2 mm)WP 3 m 4 mm 2 mm

Orthorhombic Type F Type G Type A Type B Type C Type D1 Type D2 Type E

LaGaO3 perovskite [012]o [210]o [010]o [101]o [001]o [1-11]o [111]o [100]o

Laue class [01-2]o [-210]o [0-10]o [-10-1]o [00-1]o [11-1]o [-1-11] o [-100]o

mmm [0-12]o [-2-10] o [-101] o [-111]o [1-1-1] o

[0-1-2]o [2-10]o [10-1] o [-1-1-1] o [-11-1] o

Ideal symmetry

ZOLZ (2 mm) (2 mm) (2 mm) (2 mm) (2 mm) (2) (2) (2 mm)

WP m m 2 mm very m 2 mm 1 1 2 mm

close to (4 mm)

4 mm s

180 ambiguity 90 ambiguity 180 ambiguity 180 ambiguity 180 ambiguity

90 ambiguity is observed for the [010] and [010] zone axes

because their corresponding 2 mm symmetry is very close to

4 mm.

The ideal symmetry is easily observed on the experimental

precession patterns. This is a major advantage with respect

to the conventional electron diffraction where only the less

useful net symmetry is usually inferred with surety. On most

patterns, only the ZOLZ reflections are considered to identify

the ZOLZ ideal symmetry and the WP ideal symmetry was

deduced from specific specimen tilt experiments. Another

way to get this WP symmetry is to consider the HOLZ

reflections.This approach is also possible but it is usually morecomplex to perform especially with high-symmetry zone axes

which have a HOLZ radius too large to be accepted by the

microscope.

Using electron precession to identify the zone axis could be

applied to any zone, but it is pertinent to use high-symmetry

patterns like c, c or c because these

patterns are easily recognizable and these zone axes can be

used as a starting point to reach any other less symmetrical

zone axes. The transition from one high-symmetry ZAP to

another one less symmetrical is easily made by observing

the Kikuchi lines which are visible on the corresponding

convergent-beam electron diffraction patterns.

Some experimental difficulties are connected with twins,

which are very frequent in these materials. These twins are

only visible for some particular crystal orientations and the

contrast differences between the two crystals located on each

side of the twin is usually weak. As a result, twin free areas

are not easy to locate and have a small size of about 0.1 m

so that the analysis requires very accurate positioning of the

incident beam.

Other limitations are connected with the possible tilt angles

of the specimen holder. The double tilt specimen holder used

in thepresent study allows45 and30 and tilt angles,

respectively. The required zone axes should be located within

these angular domains.

We indicate that the kinematical forbidden reflections

can be identified on large-angle precession patterns (about

3) because a few-beam behaviour prevails, which strongly

decreases the possibility of multiple diffraction. Nevertheless,

most of theprecessionpatterns given in thepresent paper were

obtained with a precession angle of about 1. The alignments

are then easy to perform even for very small spot sizes down

to 50 nm and the resulting patterns display a high quality.

With large precession angle (the maximum value is about 3

with our precession equipment) the perfect scan and descanalignments are more difficult to achieve and the resulting spot

size is larger due to spherical aberration so that it could be

difficult to focus the beam on a twin free area. Then, the

quality of large-angle precession patterns is usually poorer.

A microscope equipped with a spherical aberration corrector

should allow one to obtain larger precession angles without

decreasing the spot size.

Most of the simulated patterns given in the present paper

result from kinematical calculations, where the intensity of

the diffracted beams is connected with the square modulus

of the structure factor. These calculations are well adapted to

the weak superlattice reflections, which have a kinematical

behaviour especially at a large precession angle. The latestversion of the jEMS software from Pierre Stadelmann allows

one to simulate dynamical precession patterns. They were

particularlyusefultointerprettheeffectoftheprecessionangle

on the forbidden reflections on Fig. 7.

Conclusions

Electron precession is very useful for the analysis of these

pseudo-cubic perovskites. This property is mainly due to the

integrated intensity of the diffracted beams meaning that the

diffracted intensities can be taken into account and trusted.



19/20


The more useful ideal symmetry is available instead of the

net symmetry. Very small differences of intensity are also

detectable and are of very great help when dealing with the

identification of the presence or the absence of mirrors on

the precession patterns. The possibility of identifying, on large

precession patterns, the kinematical forbidden reflections dueto glide plane or screw axes is also very useful.

A method to identify any zone axis without ambiguity

is described and some applications of this method to the

characterization of twins and to the identification of the space

group are given.

This method is general and can be easily extended to other

perovskites or crystals displaying small symmetry departures

from a high symmetry.

Acknowledgements

We thank Justin Kimpton (RMIT) for supplying the LaGaO3

and LSGM; the French Embassy and the Australian Scienceand Technology (FEAST) program for J.-P.M. to travel to UQ

(October 2003, February 2006) and forG.J.A. to travel to Lille

(July 2005, July 2006) and The University of Queensland for

a UQ Travel grant for G.J.A. to Lille (July 2007).

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