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Long-period shear structure in oxygen deficient La2CuO4−δ
Physica C 176 (1991) 575-595 North-Holland
Long-period shear structure in oxygen deficient La2CuO4_ G. Van Tendeloo a n d S. A m e l i n c k x University of Antwerp (RUCA), Groenenborgerlaan 171, B-2020 Antwerpen, Belgium Received 25 February 1991 Revised manuscript received 8 April 1991
A long-period shear structure of La2CuO4 has been determined using electron diffraction and high-resolution electron microscopy. The shear planes are formed by edge-sharing CuO6 octahedra; they are paralllel with the ( l l 1 )o planes of the orthorhombic basic structure. In successive domain strips the orthorhombic ao and Co axes are interchanged. The monoclinic shear structure has lattice parameters: am=0.66 nm; bin=0.76 nm; Cm= 2.66 rim; fl= 103°; its space group is P l 2 / c l above the T-~0 transition temperature ( 560 K) and P I c 1 below this temperature.
1.
Introduction
Among the many high-To superconducting materials known at present the first one studied was La2CuO4, as well in pure form as doped with strontium [ 1,2 ]. Although electron microscopy has been used extensively in the study of structural and microstructural aspects of oxide superconductors, the number of publications devoted to electron microscopic studies of La2CuO4 is surprisingly small as compared to that devoted to the 1-2-3 compounds, the bismuth compounds or the thallium compounds. Relevant results of the papers published so far are reviewed below. It is the purpose of this paper to report on a high-resolution electron microscopic study of defects in "stoichiometric" undoped La2CuO4 and in particular to show that oxygen deficient La2CuO4_6 exhibits a shear structure, the crystallographic shear planes being formed by edge-sharing CuO6 octahedra. The importance of the oxygen stoichiometry for the superconducting properties is well established.
with a body-centered unit cell with la, ol = [a2.o[ =up=0.38 nm and a long spacing of co=bo= 1.318 nm. Along the fourfold axis (cp) the layer sequence is: LaO-LaO-CuO2-LaO-LaO-CuO2. The copper ions are octahedrally coordinated by oxygen whereas the LaO-layers form two-layer sodiumchloride-like lamellae. The structure can thus be considered as a regular alternation of perovskite lamellae and sodiumchloride-like lamellae. The oxygen atoms at the apices of the CuO6 octahedra are simultaneously part of the LaO layers. The average structure is represented schematically in fig. 1 along two different zones: [ 100]p (fig. 1 ( a ) ) and [ 1 10]p (fig. 1 ( b ) ) . The room-temperature phase has orthorhombic symmetry with in-layer lattice parameters ao = 0.536 nm and Co=0.539 nm, i.e., approximately equal to apv/2. The long spacing bo-- 1.318 nm, i.e., twice the lamellae thickness is the same as that of the average structure. The exact space group is still somewhat in doubt; the most probable one is Cmca [4]. However, there is general agreement that the orthorhom-
2. Structural considerations ~!
The average structure of L a 2 C u O 4 , which occurs at temperatures exceeding 530 K, is of the K2NiF4 type [ 3-5 ]. It is a tri-perovskite-like structure, tetragonal
#1 A subscript p will be used for indices referred to the basic perovskite lattice whereas an index o is used for reference to the orthorhombic lattice, and m for reference to the monoclinic shear structure.
0921-4534/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
576
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2Cu04
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bicity is due to the cooperative tilting o f the cornerlinked CuO6 o c t a h e d r a in the perovskite lamellae [3,4]. The tilt scheme is represented in fig. 1 ( b ) . The CuO6 octahedra are tilted a p p r o x i m a t e l y 3 ° about an axis parallel with the ao-axis o f the o r t h o r h o m b i c unit cell. As a result o f the corner sharing within the layers o f octahedra successive rows parallel with the ao-direction are tilted in opposite sense. The CuO2 layers thus b e c o m e puckered. The tilts in successive bo-layers o f octahedra, indicated by curved arrows in fig. 1 ( b ) , are such that in a given Co-plane all tilts are in the same sense a n d in successive co-planes the tilts are in opposite sense. The tilting o f the octahedra is a c c o m p a n i e d by slight displacements o f the La-at-
oms as well, indicated by short straight arrows. On going through the T--,0 transition the tilting o f the octahedra may be initiated a r o u n d any one out o f two possible rotation axis, i.e., any one of the two aT axes o f the tetragonal phase can with equal a priori probability become the ao axis o f the o r t h o r h o m b i c structure. This m a y lead to the f o r m a t i o n o f out-ofphase boundaries, or d i s c o m m e n s u r a t i o n walls and twins with coherent ( 1 10)o planes. The occurrence o f such twins is d o c u m e n t e d in the literature. We discuss in the present p a p e r models for such interfaces. N e u t r o n diffraction studies c o m b i n e d with iod o m e t r i c titration of the oxygen content on powders and on twinned "single" crystals [ 6 - 8 ] have shown that the material m a y contain excess oxygen in the superconducting phase La2CuO4+a with fi~0.03. Specimens with up to 0 = 0 . 1 3 have been obtained as well [9]. F r o m neutron diffraction experiments on powder specimens o f La2CuO4+6 with 5 = 0.03 Jorgensen el al. [6] concluded that phase separation occurs on ageing below 320 K. One phase is stoichiometry non-superconducting La2CuO4; the other one is superconducting La2CuO4+6, i.e, oxygen-rich material. Similar results were o b t a i n e d by Zolliker et al. [9] using synchrotron radiation p o w d e r diffractometry. After ageing at 250 K the two phases were found to be present in roughly equal proportions. The powder diffraction patterns o f the two phases are not easy to unscramble since one o f the lattice p a r a m e ters is essentially c o m m o n to both phases. Recent high-resolution neutron diffraction experiments [6,8], as well as X-ray studies, lead to a model for the oxygen-rich phase. It was shown that the excess oxygen is i n c o r p o r a t e d in a site situated between the two LaO layers as shown schematically in fig. l ( a ) after ref. [6]. The insertion o f the excess oxygen results in small displacements o f the adjacent a t o m s a n d in particular in d e f o r m a t i o n and tilting o f the CuO6 octahedra. The apices A and B o f the two octahedra between which an oxygen is inserted are displaced as indicated by the arrows in fig. l ( a ) ; similar displacements occur in the plane perpendicular to the drawing. Davies and Tilley [10] have shown that a homologous series o f m i x e d layer c o m p o u n d s o f the type La,+ jCu,O3,+, can be prepared by choosing the appropriate LaO-CuO2 ratio. These c o m p o u n d s have
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LaeCu04_~
structures which are closely related to that of La2CuO4. Instead of a single perovskite layer they contain perovskite-like lamellae consisting of n-layers of CuO6 octahedra separated by bi-layer LaO lamellae having a sodiumchloride-like structure; the limiting oxygen layers of the perovskite lamellae being part of the sodiumchloride-like structure. Recently dislocations in La2_xSr~CuO4 were studied using diffraction contrast [ 11 ]. The Burgers vector of the dislocations was found to be [ ½, a, 0, lc]p, i.e., not a lattice vector. It was speculated that the dislocations should be bordering partials of faults implying that edge sharing of the CuO6 octahedra takes place along the interface.
577
3. Observations 3.1. Diffraction patterns 3.1.1. Basic structure
The diffraction pattern along the bo zone ( [ 010]o) reveals a quasi square rectangular lattice Which is consistent with the lattice parameters ao = 0.536 nm; Co=0.539 nm (fig. 2(a) ). Tilting away slightly from the bo-zone about the ao* direction the (01 i ) * section of reciprocal space is obtained (fig. 2 ( b ) ) . In this section the rectangle of strong spots is centered, whereas in the middle of the sides of the rectangle weak spots appear; some of the latter are not compatible with the space Cmca. It does not seem pos-
Fig. 2. Four sections of reciprocal space of the orthorhombic basic structure. (a) (010)* section, (b) (01 T)o* section, (c) ( 100)2 section, (d) (101 )o*section.
G. Van Tendeloo, S. Amelinckx I Long-period shear structure in La:Cu04_6
578
sible that they are generated by double diffraction. After 400 kV electron irradiation some of the weak spots disappear but the reciprocal lattice remains the same. Apparently some form of order is destroyed by the electron irradiation. Most probably oxygen atoms are involved since these are the most easily displaced atomic species present in the material. Presumably the tilt pattern looses its long range order. Figure 2(d) shows the ( i 0 1 ) * section of reciprocal space; it reveals the spacing do,o= 1.318 nm perpendicular to the layer planes. Finally fig. 2 (c) shows the ( 100)* section of reciprocal space. Again forbidden spots, such as 001, appear; however this spot could be generated by double diffraction. The reciprocal lattice, as deduced from the different sections of fig. 2, is represented in fig. 3; it is clear that some observed spots are not compatible with the space group Cmca. The reason for the occurrence of these "forbidden" reflections is not clear. An obvious reason that might be envisaged is the presence of twins within the area selected for the diffraction pattern. It is however doubtful that the presence of twins would not have been noted in the corresponding image. We therefore believe that the symmetry is destroyed by some small additional displacements leading to violation of the extinction conditions.
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3. I. 2. M o d u l a t e d s t r u c t u r e
A long-period modulated superstructure was found in about 10% of the volume of the specimen. The most relevant zone of the diffraction pattern of this modulated structure is the [ 101 ] o zone (fig. 4 (a) ). The rows of closely spaced superstructure spots are oriented almost exactly along the [1 10]~ direction of the basic structure or the [ 111 ]* direction of the orthorhombic structure. They divide the distance between basic spots approximately in four equal intervals. However, the corresponding real space period is smaller than four times that of the basic structure; it is approximately 1.33 n m = ~ × 0 . 3 8 nm. It is clear that the intensities of the superstructure spots located close to the positions of basic spots are relatively the largest. To see this one should compare fig. 2(d) and 4(a) in parallel orientation. Such a behaviour is consistent with the assumption that the superstructure is a modulated structure of the basic La2CuO4 structure. The relationship between the diffraction patterns of the modulated structure and that of the basic structure is not a simple one. The superstructure spots in fig. 4(a) form very' nearly a centered rectangular arrangement as indicated in fig. 5. In reality the rectangle is somewhat deformed however. When rotating the specimen about an axis parallel with these rows of superstructure spots, i.e., parallel with [ 111 ]o the sequence of diffraction patterns of fig. 4 ( b - f ) is obtained with increasing tilting angle. The sections of reciprocal space obtained in this way are successively (a) ( i 0 1 ) * , (b) (514)*, (c) (g~13)*, (d) (312)*, (e) (211)* and finally (f) (i 10)*. These sections are represented in fig. 5. It is now clear that sequences of superlattice spots are associated with all basic spots; the repeat distance is twice that deduced from fig. 4(a), i.e., it is twice the separation of the interfaces, i.e., 2X 1.33 n m ~ 2 . 6 6 nm. Along the projection of fig. 4 (a) the projected interface separation is only 1.33 nm which is consistent with the observed extinctions along this zone. Note that in figs. 4 ( b - e ) the central row ool also exhibits the double period. This is due to double diffraction out of the non-central rows. The double diffraction spots are systematically weaker. Figure 6 shows the composite diffraction pattern of a crystal fragment containing an area exhibiting the modulated structure and an adjacent crystal area
G. Van Tendeloo, S. Amelinckx / Lon/z-,':~tod shear structure in LaeCuO4_a
579
Fig. 4. Six sections of reciprocal space of the long period shear structure. All sections are parallel with the dense rows of superstructure spots. The indices refer to the basic orthorhombic structure. (a) ( 101 )* section, (b) ( 51 4)* section, (c) (413 )* section, (d) ( 312 )* section, (e) (2 1 1 )* section, (f) (1 10)* section.
h a v i n g the basic structure. T h e r e l a t i o n s h i p b e t w e e n the two d i f f r a c t i o n p a t t e r n s is n o w i m m e d i a t e l y obvious. It is n o w d i r e c t l y o b s e r v a b l e that the m o s t in-
tense spots o f the m o d u l a t e d structure o c c u r close to the p o s i t i o n s o f basic spots. It is clear that also in those sections o f fig. 4 w h i c h c o n t a i n l o w - o r d e r basic
580
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2Cu04
two different orientations related by a m i r r o r operation with respect to the layer planes ( 0 1 0 ) . J
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Fig. 6. Diffraction pattern across a twin boundary showing the superposition of the ( 101 )o*section of one crystal, not exhibiting the long period, and the ( 101 )o* section of the twin, exhibiting the rows of superstructure spots.
spots, such as 4 ( e ) , the most intense superstructure spots occur close to these basic spots. The diffraction pattern o f fig. 6 reveals a small orientation difference between the bo-axis o f the basic structure and the corresponding lattice direction o f the m o d u l a t e d structure. Along the same zone ( i 01)o o f the basic structure the m o d u l a t e d structure has been found in
The basic o r t h o r h o m b i c structure has been imaged along different relevant zones. Figure 7 ( b ) shows the [ 0 1 0 ] o zone; it reveals the quasi tetragonal o r t h o r h o m b i c structure. The heavy a t o m columns are revealed as bright dots. The image along the ( 1 0 i )* section (fig. 8 ( a ) ) is particularly relevant since along this zone the heavy atoms form columns consisting all o f the same species; it thus reveals the stacking along the bo-direction. Even without c o m p u t e r simulation it is possible to find unambiguously the imaging code in thin parts o f the foil where the a t o m i c columns a p p e a r as black dots. In fig. 8 ( a ) the high resolution image is c o m p a r e d with a schematic representation o f the structure. The heavy atom columns o f lanthanum and copper can easily be recognized as dark dots by their characteristic geometrical configurations; as usual the oxygen atoms are not imaged under these conditions. In the thick parts the heavy a t o m columns a p p e a r as bright dots (fig. 9). The image o f fig. 9 was m a d e along the [ 100]o zone; it can be c o m p a r e d with the schematic representation o f the structure fig. 1 ( b ) . Careful e x a m i n a t i o n o f fig. 9 ( a ) shows that the vertical dot rows are perfectly straight, whereas the horizontal dot rows are slightly wavy. We believe that this is due to the tilts o f the rows o f o c t a h e d r a , which lead to small, observable displacements o f the heavy a t o m s as well. The rotation o f the octahedra is indicated by a curved arrow in fig. 1 ( b ) , whereas the corresponding displacements o f the La-atoms are shown by small straight arrows. 3.2.2. M o d u l a t e d structure
As a model for the m o d u l a t e d structure we propose a "shear structure" derived from the basic La2CuO4 structure. Using the imaging code established under identical conditions (i.e., in an adjacent region o f the same foil ) for the perfect structure in the thin part o f the foil, we can deduce an app r o x i m a t e model from the high resolution images along different zones, in particular from fig. 8 ( b ) . With respect to the layered structure the edge shar-
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2CuO~_a
581
Fig. 7. High-resolutionimagealong the [010 ]o zone exhibitingdislocations in the foil plane.
ing can take place according to two essentially different modes. If a family of edges, which are parallel with the layer planes, becomes common the Cp layers remain planar (fig. 10(c) ). In a view along the a2.pdirection the projected distance between the copper atom columns 1 and 4 in the shared octahedra is then ½ap. Within the layers the rows of heavy ions become staggered (fig. 10(d)). An essentially different situation occurs if a family of edges inclined with respect to the layer planes becomes shared (fig. 10(a) ). The layer planes then become stepped, the magnitude of the step being about one third of the interlayer spacing. The projected separation of the copper atom columns 1 and 4 in the edge sharing octahedra is now ½apx/'2. Within the layers the heavy atom rows
remain the same on both sides of the shear plane (fig. 10(b)). The observations of fig. 8(b) do not allow a straightforward and unambiguous distinction to be made on qualitative arguments only. The layer planes have indeed become stepped, but the steps are much smaller than those predicted by the model of fig. I 0 (a). On the other hand fig. 18 shows that the rows of heavy atoms have become staggered, although not exactly in anti-phase. The separation of the copper columns I and 4 in fig. 8(b) is found to be significantly closer to ½ap than to ½apv/2. As yet we have left the lanthanum ions out of our considerations. In both models the remaining lanthanum ions have to be accompanied somewhere in
582
G. Van Tendeloo, S. A m e l i n c k x / Long-period shear structure in L a 2 C u 0 4
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Fig. 8. (a) High-resolution image of the basic orthorhombic La2CuO4 structure along the a o zone -= [ 1 01 ]o. The heavy atom columns are imaged as dark dots; the oxygen atom columns are not imaged under the diffraction conditions used. This image can be compared with the schematic representation of the structure in fig. 1 (a); black dots indicate heavy ions, squares are the projections of the octahedra. (b) High-resolution image of the long period shear structure in La2CuO4_a along the [ 101 ]o zone (i.e., along the ap zone). The heavy atom columns are imaged as dark dots; the oxygen columns remain invisible. This image can be compared with the schematic representation of fig. 15, made along the same zone axis. The correspondence between black dots and atom columns is indicated.
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2CuO~_~
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Fig. 9. (a) High-resolution image along the [ 100]o zone. This image can be compared with the schematic representation along the same zone as in fig. 1(b). (b) High-resolutionimage along the (01 i )~ section. The interfaces are crystallographic shear planes along which the CuO6octahedra share edges.
the rectangle ABCD (fig. 8(b) ). Their presence causes the actual situation to deviate from the idealized models of either fig. 10(a) or 10(c). The compromise offering best overall correspondence with the observations of fig. 8(b) and 18 is to assume that the situation is best described by fig. 10(c), but that the presence of the lanthanum ions causes a local deformation of the layers in the shear plane, resulting in a small shift as represented schematically in fig. 15. In fig. 8 (b) the interfaces causing the long period (i.e., the crystallographic shear planes) are observed
583
edge on, and the perovskite cubes are viewed along the dense rows of heavy atoms, as can be deduced from the corresponding diffraction pattern (fig. 4(a) ). The high-resolution image shows that in one projected period, i.e., between two successive interfaces one observes linear sequences of four columns of copper atoms, indicated 1, 2, 3, 4 in figs. 8 (b) and 15, the separation of the columns being equal to ap = 0.38 nm. Where two such linear sequences meet a small offset in the bo-direction is observed; the line segment, joining the two copper columns at the ends of the sequences of four such as 1-4, being inclined with respect to the rest of the sequence. The projected separation of the two copper columns forming this short segment is only ~ ½ap. This behaviour is consistent with the assumption that edge sharing octahedra are presented along the interface. This is represented schematically in fig. 15; it implies that the displacement vector has a component perpendicular to the plane of the drawing as well; this is discussed further below. Within the rectangle ABCD (fig. 8 (b) ) formed by the projections of two close pairs of copper columns in the edge sharing octahedra, one distinguishes two further black dots, due to atom columns. These columns are also represented in fig. 15. The slightly smaller darkness of the dots marking these columns in fig. 8(b), as compared to that of the lanthanum columns of the perfect structure, suggests that they image incompletely occupied heavy atom columns. The observations do not allow to conclude whether they represent copper or lanthanum columns, but it seems reasonable to assimilate them with lanthanum columns, pushed out of their normal positions by the edge sharing CuO6 octahedra. In turn their presence presumably causes the small offset of the LaO layers, which is itself a consequence of the small tilt of these octahedra about their common edge. One lamella LaO-CuO2-LaO of the proposed structure is shown in projection along the normal to the plane of the lamellae in fig. 16. The displacement vector is close to R = ½[ i 10 ] p, when referred to the basic perovskite structure, i.e., ignoring the tilt of the octahedra. The projected repeat distance along this zone is then ~a~.p+ ½a2.p. Ignoring the tilt of the octahedra the model of fig. 15, viewed along the same zone a2.p as the diffraction pattern of fig. 6, has the unit mesh
584
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La:CuO4 ,~ I/2%~ i
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outlined by the dashed lines. The tilt of the octahedra doubles this repeat p e r i o d as represented in fig. 16. One o f the edges o f this projected unit mesh encloses the same small angle with the layer planes as that observed in the diffraction pattern o f fig. 6. The same angular difference can be observed in fig. 19 when looking u n d e r grazing incidence along the direction o f the layer planes. The average orientation in the m o d u l a t e d left part is slightly different from the orientation o f the layer planes in the u n m o d u lated part to the right. In deriving the tilts o f the octahedra in the different slabs it should be taken into account that along the interfaces the o c t a h e d r a share edges. Tilting a rigid o c t a h e d r o n about an axis parallel with the shared edge causes the tilts o f the coupled rigid oct a h e d r a to be opposite in sense. Tilting about an axis normal to the c o m m o n edge the coupling causes the two tilts to be in the same sense. As a result o f these rules the ao and Co axis o f the o r t h o r h o m b i c structures are in successive d o m a i n strips, as indicated in fig. 16 in which the sense o f tilting o f the octahedra
has been i n d i c a t e d by an arrow at the apical oxygen at the top o f the o c t a h e d r a facing the observer. This will be shown in section 4. Taking into account the tilt o f the octahedra does not affect the repeat period in the projection o f fig. 15 since viewing along any column the tilts are alternatingly in opposite senses and hence the average projection does not change. A view along the a~,p direction is shown in fig. t7. The image corresponding with section (1 1 0)* o f the reciprocal lattice (fig. 4 ( f ) ) is shown in fig. 18; it exhibits slabs o f perovskite structure separated by interfacial lamellae along which the stacking o f the perovskite lamellae becomes staggered as judged from the arrays o f bright dots. These images are somewhat similar to those o f the series o f homologous m i x e d layer c o m p o u n d s referred to a b o v e and described by Davies and Tilley [ 10 ]. However, in our images the pattern o f bright dots is not square but slightly parallelogram shaped. This form o f stacking o f the perovskite lamellae is consistent with the diffraction pattern o f fig. 4 ( f ) . In this foil, with a somewhat
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LaeCuO~_~ APB in (101)
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larger thickness, the heavy atom columns are imaged as bright dots under the diffraction conditions used. The lanthanum columns are imaged as the brightest dots, the copper columns as less bright dots. The geometry of the dots in fig. 18 can be compared with the schematic representation of fig. 16 taking into account that in this representation the octahedra were drawn as undeformed. Since the image of fig. 18 is a slightly oblique view of fig. 16 the square meshes are transformed into parallelograms. The zone used for imaging is (i 10)* indicated in figs. 5 and 4 ( f ) ; it contains rows of superstructure reflections but its zone axis is not quite parallel with the atom columns along the bo-axis, the viewing direction is parallel with the shear planes however. Nevertheless the correct topology of fig. 16 is reproduced in the observed image of fig. 18. However the slight inclination of the atom columns leads in the thicker parts of the wedge shaped foil to streaking of the dot pattern and even to the transformation of the bright dot rows into continuous lines with reinforcements. All these observations are consistent with the fact that this image is due to the same modulated structure as fig. 8, with fig. 4 ( f ) as the corresponding diffraction pattern. Note that the thickness of the perovskite lamellae in fig. 18 is not always constant; it shows some variability in block width as in fig. 12. Along the projection zone the lozenge-shaped pattern of bright dots is consistent with the model of fig. 16. It should be reminded that this image is related to that of fig. 8 (b) by a rotation about an axis normal to the shear planes. The bright dot pattern in fig. 18 is not related in a simple manner to dense columns in the structure, but the geometry allows to derive the number of unit cells in the successive slabs, as well as their geometrical arrangements. These are clearly consistent with the proposed model.
4. Interpretation
(c) Fig. 11. Modelsfor planar defects. (a) Schematicrepresentation of the typeof anti-phase boundaryresulting fromthe phase transition T~0; the displacement vector is ½[001 ]o. (b) Schematic representation of a crystallographic shear plane resulting from edge sharing of the CuP6 octahedra. (c) Twin boundary resulting from the phase transition T~0.
4.1. Diffraction patterns
The diffraction pattern along (i 01 )* section could be indexed as shown in fig. 4(a) on the basis of a monoclinic unit cell. The unit cell parameters are approximately:
G. Van Tendeloo, S. A melinckx / Long-period shear structure in La2Cu04
586
Fig. 12. Low-magnification high-resolution image along the [ 101 ]o zone, exhibiting several singular crystallographic shear planes.
am = 0 . 6 6 n m ; bm = 0 . 7 6 n m ; c m =2.6 nm;~=
(am)(!0
102-103 ° .
T h e y are r e l a t e d to a l p , a2,p a n d Cp b y t h e r e l a t i o n
bm =
2
0
Cm
0
-- 2~
~a2.p], \a3,p/
@
©
Fig. 13. Crystallographic shear plane ending in partial dislocation: [ 101 ]o zone view.
Fig. 14. Schematic representation of the atomic configuration around a terminating shear plane (cf. fig. 13 ).
G. Van Tendeloo, S, A melinckx I Long-period shear structure in La2Cu04_6
0
c"3
~
t'3®
/
t
,,~
" ~,p
587
i
,
®-
a2,p
Fig. 15. Schematic view of the shear structure along the zone parallel with a2,p;the shear planes are formed by edge sharing CuO6 octahedra. The tilt of the octahedra has not been represented.
~oX,/Co
@
o
O
O
m
O Cm ID
£lm,pmi.
Fig. 16. Schematic view of one lamella of fig. 15 along the bo-=ep direction. The CuO~octahedra are represented as undeformed but the sense of the tilt is indicated by arrows. and in terms of the orthorhombic structure
where ~ is a small q u a n t i t y accounting for the offset in the bo direction of the shear planes. The following reflection conditions were ob-
served; the h o l reflections are only present for / = e v e n ; also the o o l reflections are only present for l = even, if double diffraction spots are ignored. Space groups compatible with these conditions are P l c l (no. 7) (point group m ) and P 1 2 / c l (no. 13) (point group 2 / m ) ,
588
G. Van Tendeloo, S. Amelinckx / Long-period shear structure m LaeCu04
,
r
,
i
i
',
a2 p
lp
p e r p e n d i c u l a r to the glide planes. We will show that the high-temperature phase, i.e, the shear structure in which the tilts o f the octahedra are ignored, belongs to the space group P 1 2 / c l , which reduces to the space group P l c l , when the tilts o f the octahedra are taken into account. One lamella o f the p r o p o s e d shear structure as suggested by the high resolution images is shown in fig. 16 in which also an outline o f the unit mesh (bm, Cm ) is indicated. The origin was chosen in a centre of s y m m e t r y o f the structure, still ignoring tilts o f octahedra. The structure is the same in all layers, the successive layers being stacked like in the normal tetragonal structure, the shear planes being shifted systematically over a distance ½ap in the [001 ] direction. This stacking ensures that within the d o m a i n strips the normal tetragonal structure is realized as suggested by the high resolution images.
Fig. 17. Schematic view along the a~,p direction of the shear structure of fig. 15, the tilts of the octahedra are indicated by arrows.
4.2. F o r m a t i o n o f the shear structure
the first space group being a subgroup o f the second. Both space groups have ( 0 1 0 ) glide planes with glide vector ½cm; the second has m o r e o v e r two fold axes
The superstructure could in principle be derived from the o r t h o r h o m b i c structure by the periodic introduction o f crystallographic shear planes. Taking
Fig. 18. Large area of shear structure viewed along the ( 110)* section. Under the diffraction conditions used th heavy atoms are imaged as bright dots. In the thick parts of the foil the bright dots degenerate into continuous bright lines, due to the slight inclination of the atom columns with respect to the viewing direction.
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LaeCuO4_a
this operation literally this would mean that within the successive domain strips the orthorhombic deformation would in all domain strips be in the same sense, i.e., within those strips the ao and Coaxis of the basic orthorhombic structure would be parallel. If this is accepted and if the octahedra are assumed to remain rigidly coupled along their corners within the domains and along their edges within the shear planes, it is straightforward to show that inevitably a triclinic structure results. However, this results is not compatible with the occurrence of systematic extinctions as observed in fig. 4 (a) and which indicate the presence of symmetry elements. The symmetry must thus at least be monoclinic, where such extinctions may occur. It therefore must be assumed that in reality the formation of the shear structure proceeds in two stages with two different characteristic temperatures. The formation' of the shear planes implies diffusion and therefore occurs at higher temperatures presumably exceeding the T ~ 0 transition temperature. The shear planes are thus assumed to be formed in the tetragonal phase. Only at lower temperatures the CuO6 octahedra become tilted and the room temperature shear structure is formed. This implies that now in principle the tilt axis of the octahedra can be different in successive domain strips, as proposed in our model, provided the sense of the tilts of octahedra remains correlated and consistent with corner and edge sharing. At this stage the space group is P12/cl and the point group is 2 / m of order 4. The lanthanum atoms of which the normal sites were lost as a result of the edge-sharing, will now order in the shear planes so as to minimize the Coulomb energy due to the uncompensated negative charges. An arrangement suggested by the high-resolution images (fig. 8 ( b ) ) , as well as by symmetry consideration, is represented in fig. 16, where the full and crossed dots reoresent the lanthanum atoms above and below the layers of CuO6 octahedra. In the view of fig. 8(b), these two sites give rise to the two dots within the rectangle ABCD. In a subsequent stage, at lower temperature, the T--.0 transitions occurs, presumably at a slightly different temperature from that in the unsheared structure, and the octahedra become tilted. We assume that within the domain strips the normal orthorhombic structure will be realized. The sense of tilting is indicated
589
by the short arrows in fig. 16. The arrows indicate the sense in which the apical oxygen, facing the observer, is displaced. It is reasonable to assume from size considerations that the lanthanum atoms in the shear planes will have a tendency to push apart the two apical oxygens on each side ot it. This imposes a sense on the tilt of the adjacent edge-sharing octahedra, which are considered as rigid. Due to this mutual coupling a tilt-scheme is imposed for the whole layer ofoctahedra. The tilt of the octahedra in the shear planes is unambiguously imposed by the edge sharing. The corner coupling leaves somewhat more freedom. The corner X of octahedron 2 (in fig. 16) for instance is forced to move upward (i.e., towards the observer) as a result of the tilt in the adjacent octahedron 1, which is part of the shear plane. This nevertheless leaves a choice for the tilt axis of octahedron 2; it can tilt either about the axis shown or about the perpendicular axis. Once this choice is made the rest of the tilt pattern follows. The observed monoclinic symmetry tells us that the correct choice is as indicated in fig. 16 since this leads to a monoclinic space group with a (010) glide plane and ½Cm glide vector, as required by the diffraction conditions. The alternative choice would lead to a triclinic unit cell. Once the tilt-scheme is fixed in one CuO-CuO2LaO layer the tilt-scheme in the other layers is determined if the known orthorhombic structure is to be generated within the domain strips. The superstructure thus finally consists of alternating strips of the two variants of the orthorhombic structure, which can be formed from a tetragonal single crystal, separated by a family of ( 1 1 1 )o edgesharing shear planes. The fact that strips of two variants of the orthorhombic structure occur in the shear structure strongly suggests the two-stage formation mechanism described.
5. Defects 5.1. Basic structure 5.1.1. Planar defects
The high-resolution image of fig. 9(b) along the ( 0 1 i ) * section reveals a quasi square dot pattern. The image exhibits planar interfaces along the ( 101 )o
590
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2Cu04_a
planes possibly resulting from the phase transition tetragonal to orthorhombic. Since the dot pattern is only shifted across the interface they must be translation interfaces. Independent of the imaging code the projected translation vector can be observed directly on the image; it is found to be either ½[001 ]o or ½[ 100]o. The vector ½[001 ]o is not acceptable as such since it is not a lattice vector of the tetragonal high-temperature phase. However, the vector ½[01 i ]o satisfies this condition. The interface, which results from the orthorhombic deformation is represented in fig. 11 (a) where the tilt of the octahedra is represented. The interface can be described as a conservative anti-phase boundary since its presence does not affect the composition of the crystal; the tilt of the octahedra, which is constant along a given (001)o plane and alternates in successive (001 )o planes, changes its sense where a [100]o row o f o c tahedra intersects the interface. The octahedra situated in the boundary will presumably be undeformed giving a certain width to the interface. Two crystallographically equivalent displacement vectors are indicated in fig. 11 (a). The displacement vector cannot be determined unambiguously in this way however; the relative displacement of the two dot patterns can also be interpreted as a displacement over ½[ 100]o. If this is the case a different model should apply, are represented in fig. 11 (b). We now can exclude that also a component of R perpendicular to the plane of the drawing should be present since R would then become ½[ 110 ] o which is a lattice vector in a C-centered unit cell and thus does not lead to a translation interface. The only solution is then that edge-sharing of the CuO6 octahedra occurs along a non-conservative interface. At this stage we cannot decide unambiguously which fault is being observed. However, in view of the fact that edge sharing is observed in the long period superstructure, to be discussed below, suggests that also in this case the second model is the more plausible one. Also the trace of the habit plane of the periodic shear planes observed in the superstructure is consistent with the traces of the isolated interfaces observed here along the [010] zone. The interface would be situated in a ( 111 )o plane rather than in ( 101 )o planes. Since the bo-parameter is large this plane only encloses a small angle with the normal to the layer plane and thus would be imaged as
a narrow line. In any case in fig. 9(b) the apparent width of the interface increases with increasing foil thickness, which confirms our assumption. In conclusion the interfaces are most probably isolated shear planes of the same type that give rise to the long-period modulated structure. Whereas anti-phase boundaries of the first type discussed here are likely to occur in samples which have undergone the T-~0 transition, in the annealed specimens the shear planes are more likely. When viewed along the (i 01)* section isolated planar interfaces in (111 )o planes are observed in fig. 12; they are most probably of the same type as those imaged in fig. 8. The interfaces can also adopt the "twin" orientation, i.e., they may be parallel with ( 11 i )o planes. However in any given area predominantly the same habit plane is adopted. Sometimes a single interface ends within the crystal; this necessarily gives rise to a dislocation (fig. 13). In fig. 14 we have analyzed schematically the atom configuration around such an ending interface, assuming the interface to be a crystallographic shear plane. Looking at the photograph of fig. 13 under grazing incidence along the dot rows parallel with the shear plane it is noted that these dot rows bend slightly inwards towards the shear plane. This observation demonstrates that the shear plane accommodates a deficiency of atoms. It is clear that the T-~0 phase transition can in a similar way give rise to twin boundaries with a coherent interface along the ( 101 )o plane. A model for a twin boundary is shown in fig. 11 (c).
5.1.2. Dislocations 5.1.2.1. Observations and their interpretation. Figure 7(a) shows a set of dislocations situated in the (010)o plane, imaged in a mixed contrast of lattice fringes and diffraction contrast. The structure image of the area around the dislocation is reproduced in fig. 7(b). One set of rows ( 1 ) of bright dots crosses the dislocation almost without being influenced, except for a small change in the orientation of the bright dot rows. In the core region these rows degenerate into continuous bright lines. The dislocation perturbs much more strongly the second set 2, and the core causes discontinuities and shifts in these dot rows.
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2Cu04_~
Such a behaviour is consistent with what one would expect for the image of a dislocation parallel with the (010) plane and with a Burgers vector parallel with the unperturbed dot rows, i.e., along the [ 100]o direction. The contrast features can intuitively be understood in terms of the atom column approximation (ACA) [ 12 ]. A relative displacement of two parts of the atom columns, above and below the glide plane, along the direction of the Burgers vector, will be imposed by the presence of the dislocation. If in all columns such displacements take place in the same plane, determined by the Burgers vector and the viewing direction (i.e., along the normal to the glide plane) the rows of bright dots parallel with that plane will form sharp but continuous bright lines. However the same displacements will much more strongly perturb the rows of atomic columns perpendicular to the Burgers vector and create discontinuous image shifts along the core. Rather than reasoning in terms of atomic columns one can also reason in terms of the wave theory of atomic image formation considering the images resuiting from the interference and superposition of a number of Fourier components or lattice fringes. We note that the Fourier components ng(n = integer) will not be perturbed by the presence of the dislocations if g.b=O. This expresses the condition that all displacements occur along the lattice planes perpendicular to g. Such planes are in fact not deformed by the presence of the dislocations and hence the corresponding set of lattice fringes remains unperturbed. The small orientation difference of the lattice fringes on both sides of the dislocation core is caused by the lattice tilt resulting from the edge component of a dislocation in a thin foil parallel with the surface roughly given by 0= b i t (t = thickness). Such a small lattice tilt causes a continuous shift of the position of the lattice fringes. 5.1.2.2. Model. The occurrence of a dislocation with a Burgers vector a [ 1 0 0 ] is somewhat unexpected, but can nevertheless be rationalized. On glide the layers of corner-sharing CuO6 octahedra will presumably remain unsheared, glide taking place between the two LaO layers forming a two-layer lamella of sodiumchloride-like structure. When ignoring the tilt of the octahedra, i.e., in the tetragonal phase, the shortest repeat in the plane is ½[ 101 ] o
591
and hence this would be a reasonable Burgers vector for a glide dislocation on a (010)o plane. However in the orthorhombic structure ½[ 101 ]o is not a lattice vector; such a dislocation thus generates a fault consisting of wrongly tilted octahedra. If the fault energy is sufficiently small, isolated partials might occur. However our observation suggests that the glide process apparently prefers a longer glide vector a [ 1 0 0 ] , avoiding in this way to generate a fault. Since a[ 100]o is a lattice vector such a dislocation is perfect. Glide now proceed along the [ 100 ]o "furrows" of the wavy layer of tilted CuO6 octahedra. An interpretation of the dislocations as the bordering partials of a shear plane seems improbable because of the strongly crystallographic orientation of the shear planes observed in the same specimens, on the one hand, and the rather random orientation of the dislocations in the (010)o plane in fig. 7(a) on the other hand [ 11 ]. 5.2. Defects in the modulated structure
As already mentioned, the modulated structure only occurs in a rather small volume fraction of the crystals. The shear plane separation is relatively constant; the smallest and most frequency observed one being ~ 1.33 nm as can be judged from figs. 19 and 20. However deviations from strict periodicity occur and apparently isolated shear planes occur occasionally as well (figs. 12 and 13). In view of the fact that according to our model the shear planes accommodate an oxygen deficiency the specimen must be slightly inhomogeneous and overall slightly oxygen deficient. The almost strict periodicity of the shear planes over large areas (fig. 20) can be understood by assuming that there is a repulsive interaction between parallel shear planes, the interaction being presumably mainly of an elastic nature with possibly a Coulomb contribution due to local charge imbalance along the interface Sometimes "hair-pin" shaped arrangements are observed, as for instance in fig. 19. Such arrangements were thought to play a role in the propagation of shear planes [ 13]. In fig. 19 the resolution, although not excellent, due to the relative thickness of the sample in that area, it is nevertheless sufficient to suggest a concrete model. The geometrical con-
592
G. Van Tendeloo, S. Amelinckx / Long-pertod shear structure in
La2CuO
4 6
Fig. 19. "Hairpin" shaped configuration of shear planes. In this rather thick part of the foil the lanthanum columns are imaged as bright dots. This image is analyzed in detail in the text and represented schematically in figs. 21 and 22.
figuration is represented schematically in fig. 21. It should first be noted that the geometry o f the rows of bright dots in the thick part o f fig. 20 suggests that these are the images o f l a n t h a n u m columns. The staggered arrangement o f the double rows o f these bright dots is consistent with the geometry o f the L a O - L a O layers in the structure a n d not with that o f the copper columns. At the tip o f the "hairp i n " three rows o f bright dots are presented in the correct arrangement to represent a three-layer lamellae o f LaO, i.e, one s u p p l e m e n t a r y layer o f LaO terminating on both ends at a shear plane. The atomic a r r a n g e m e n t o f the left end o f the tip is represented schematically in fig. 22 ( a ) . The offset p e r p e n d i c u l a r to the layer planes between the perovskite blocks I and II on both sides o f the shear plane is taken up by the s u p p l e m e n t a r y LaO layer, which simultane-
ously introduces a dislocation due to the insertion of one additional LaO layer. The upward curvature o f the lattice planes along the tip o f the " h a i r - p i n " is consistent with the presence of such a dislocation at both t e r m i n a t i o n s o f the s u p p l e m e n t a r y LaO layer. The right h a n d t e r m i n a t i o n o f the tip is blunted by the presence o f a small facet o f shear plane in the twin orientation. As a result the a t o m i c configuration of the tip at the right end is the m i r r o r image o f that at the left end (fig. 2 2 ( b ) ) . In fact the level difference between the perovskite layers in the right half o f fig. 22 is taken up (i.e., the gap is filled) in two steps. The first one is the f o r m a t i o n o f the twin as shown in fig. 2 2 ( b ) ; this results in the presence o f an extra layer o f thickness 2×~2bo, t e r m i n a t i n g at the intersection line o f the twinned shear planes A and B, i.e., a dislocation line, with this edge c o m p o n e n t (~b) o f
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LazCuO~_,~
593
Fig. 20. Large area of shear structure at somewhat lower magnification viewed along the [ 101 ]o zone.
j l /
Fig. 21. Schematic representation of the observed microstructure in fig. 20; the deformation of the (010)o layer planes is indicated schematically: D~, D2 and D3 represent dislocations.
the Burgers vector, is present along this line. The configuration around the line where the interface B intersects with the tip facet is now the mirror image of that present around the left end of the tip facet
and which is represented in fig. 22(a). Calling the Burgers vectors of the dislocations D~, D2 and D3 respectively b~, b2 and b 3 the following relations have to be satisfied for topological reasons: R~.e=bl.e; R2"e=b2.e and 2Rl-e=b3.e. Without the twin facet present the dislocations at the right end of the "hairpin" tip would have to have a Burgers vector b: + ha, which is presumably too large to be stable. The total energy can be lowered by the dissociation into two dislocations D2 and D 3. This dissociation is accompanied by the formation of a segment of shear planes D2D3 in twin orientation and by the shortening of the extra layer LaO between D~ and D2, as well as by reorientation of the right shear plane (fig. 21 ). The configuration at D 3 is elastically equivalent to a dislocation but there is no supplementary half plane. It is assumed that in the symmetrical position D 3 (fig. 22(b) ) there is no offset across the shear plane, the shared edge of the octahedra projects horizontally there.
594
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LaeCu04_,~ (B) ,
i i
~
",\
i
/Uo {al
®
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/ @
i
/ Da
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u o
o
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/('
(b)
'(A)
Fig. 22. (a) Atomic arrangement around the dislocation D~ in fig. 21. (b) Atomic arrangement around the dislocation D 3 in fig. 2 I. The shear plane along ( 110)o changes abruptly its orientation into the "twin" orientation ( 1 T 0)o.
6. Conclusions
mechanism for shear structures, have been observed
[14]. Even though the material was prepared taking all precautions in order to achieve exact stoichiometry the material was found to be slightly oxygen deficient. As well isolated crystallographic shear planes, as one-dimensional periodic shear structures were observed. The oxygen deficiency is inhomogeneously distributed throughout the material as judged from the distribution of shear planes. The hairpin-shaped configuration of shear planes which was considered to be a characteristic feature of one of the proposed propagation mechanisms for shear planes [ 13 ], was observed and studied in detail with atomic resolution. Also single ending shear planes which play a role in an alternative formation
Acknowledgements This work has been performed in the framework of the Institute for Materials Science (IMS) of the University of Antwerp under an IUAP-contract with the Ministry of Science Policy. We are grateful to L. Pintschovius (Karlsruhe) and W. Weber (Dortmund, Karlsruhe) for providing the single crystal of LaCuO4. The authors also acknowledge stimulating discussions with J. Van Landuyt (RUCA), F. Weill (Bordeaux) and L. Pintschovius (Karlsruhe).
G. Van Tendeloo, S. Amelinckx /Long-period shear structure in La2CuO~_6
References [ 1 ] J.G. Bednorz and K.A. Muller, Z. Phys. B 64 (1986) 189. [ 2 ] J.G. Bednorz, M. Takashige and ICA. Miiller, Mat. Res. Bull. 22 (1987) 819. [3] B. Grande, H.K. Muller-Buschbaum and M. Schweizer, Z. Anorg. Alg. Chem. 428 (1977) 20. [4] J.M. Longo and P.M. Raccah, J. Solid State Chem. 6 ( 1973 ) 526. [5] C. Michel and B. Raveau, Rev. Chim. Mineral. 21 (1984) 407. [6] J.B. Jorgensen, B. Dabrowski, Shiyou Pei, D.G. Hinks, L. Soderholm, B. Monosin, J.E. Schirber, E.L. Venturini and D.S. Ginley, Phys. Rev. B 38 (1988) 11337. [7]P. Lightfoot, S. Pei, J.D. Jorgensen, X.X. Tang, A. Manthiram and J.B. Goodenough, Physica C 169 (1990) 65.
595
[8] C. Chaillout, S.W. Cheong, Z. Fisk, M.S. Lehmann, M. Marezio, B. Monosin and J.E. Schirber, Physica C 158 (1989) 183. [9] P.E. Zolliker, D.E. Cox, J.B. Parise, E.M. McCarron III and W.E. Farneth (preprint) [ 10] A.H. Davies and R.J.D. Tilley, Nature 326 (1987) 859. [ l l ] Prahibha L. Gai and E.M. McCarron III, Science 247 (1990) 553. [ 12 ] D. Van Dyck, J. Danckaert, W. Coene, E. Selderslaghs, D. Broddin, J. Van Landuyt and S. Amelinckx, in: Computer Simulations of Electron Microscope Diffraction and Images, eds. W. Krakow and O'Keefe (The Minerals, Metals and Materials Society, 1989) p. 107. [ 13 ] J. Van Landuyt and S. Amelinckx, J. Solid State Chem. 6 (1973) 222. [ 14 ] B.G. Hyde and L.H. Bursill, in: The Chemistry of Extended Defects in Non-Metallic Solids (North Holland, Amsterdam, 1970) p. 347.
Long-period shear structure in oxygen deficient La2CuO4_ G. Van Tendeloo a n d S. A m e l i n c k x University of Antwerp (RUCA), Groenenborgerlaan 171, B-2020 Antwerpen, Belgium Received 25 February 1991 Revised manuscript received 8 April 1991
A long-period shear structure of La2CuO4 has been determined using electron diffraction and high-resolution electron microscopy. The shear planes are formed by edge-sharing CuO6 octahedra; they are paralllel with the ( l l 1 )o planes of the orthorhombic basic structure. In successive domain strips the orthorhombic ao and Co axes are interchanged. The monoclinic shear structure has lattice parameters: am=0.66 nm; bin=0.76 nm; Cm= 2.66 rim; fl= 103°; its space group is P l 2 / c l above the T-~0 transition temperature ( 560 K) and P I c 1 below this temperature.
1.
Introduction
Among the many high-To superconducting materials known at present the first one studied was La2CuO4, as well in pure form as doped with strontium [ 1,2 ]. Although electron microscopy has been used extensively in the study of structural and microstructural aspects of oxide superconductors, the number of publications devoted to electron microscopic studies of La2CuO4 is surprisingly small as compared to that devoted to the 1-2-3 compounds, the bismuth compounds or the thallium compounds. Relevant results of the papers published so far are reviewed below. It is the purpose of this paper to report on a high-resolution electron microscopic study of defects in "stoichiometric" undoped La2CuO4 and in particular to show that oxygen deficient La2CuO4_6 exhibits a shear structure, the crystallographic shear planes being formed by edge-sharing CuO6 octahedra. The importance of the oxygen stoichiometry for the superconducting properties is well established.
with a body-centered unit cell with la, ol = [a2.o[ =up=0.38 nm and a long spacing of co=bo= 1.318 nm. Along the fourfold axis (cp) the layer sequence is: LaO-LaO-CuO2-LaO-LaO-CuO2. The copper ions are octahedrally coordinated by oxygen whereas the LaO-layers form two-layer sodiumchloride-like lamellae. The structure can thus be considered as a regular alternation of perovskite lamellae and sodiumchloride-like lamellae. The oxygen atoms at the apices of the CuO6 octahedra are simultaneously part of the LaO layers. The average structure is represented schematically in fig. 1 along two different zones: [ 100]p (fig. 1 ( a ) ) and [ 1 10]p (fig. 1 ( b ) ) . The room-temperature phase has orthorhombic symmetry with in-layer lattice parameters ao = 0.536 nm and Co=0.539 nm, i.e., approximately equal to apv/2. The long spacing bo-- 1.318 nm, i.e., twice the lamellae thickness is the same as that of the average structure. The exact space group is still somewhat in doubt; the most probable one is Cmca [4]. However, there is general agreement that the orthorhom-
2. Structural considerations ~!
The average structure of L a 2 C u O 4 , which occurs at temperatures exceeding 530 K, is of the K2NiF4 type [ 3-5 ]. It is a tri-perovskite-like structure, tetragonal
#1 A subscript p will be used for indices referred to the basic perovskite lattice whereas an index o is used for reference to the orthorhombic lattice, and m for reference to the monoclinic shear structure.
0921-4534/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
576
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2Cu04
~p =3 8 t
I' ,
c =%
(a)
/IN.
q
x
L
shear plane
Cu
[100 jp
..........
~'---"
i
=
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i i
i~,_ ~
i ~=
[110]p
(h)
Q
ap42
1/2
0,1
1/2
0,1
0
@
La
i --,I, '
co
ao
Fig. I. Schematic view of the La2CuO4structure. (a) Average (tetragonal) structure viewed along the ap direction. Excess oxygen can be incorporated at the site marked 0 hereby pushing the octahedra A and B outwards. (b) View along ao of the orthorhombic structure of La2CuO4; the tilt of the octahedra is indicated by curved arrows; the small straight arrows indicate schematically the La displacements.
bicity is due to the cooperative tilting o f the cornerlinked CuO6 o c t a h e d r a in the perovskite lamellae [3,4]. The tilt scheme is represented in fig. 1 ( b ) . The CuO6 octahedra are tilted a p p r o x i m a t e l y 3 ° about an axis parallel with the ao-axis o f the o r t h o r h o m b i c unit cell. As a result o f the corner sharing within the layers o f octahedra successive rows parallel with the ao-direction are tilted in opposite sense. The CuO2 layers thus b e c o m e puckered. The tilts in successive bo-layers o f octahedra, indicated by curved arrows in fig. 1 ( b ) , are such that in a given Co-plane all tilts are in the same sense a n d in successive co-planes the tilts are in opposite sense. The tilting o f the octahedra is a c c o m p a n i e d by slight displacements o f the La-at-
oms as well, indicated by short straight arrows. On going through the T--,0 transition the tilting o f the octahedra may be initiated a r o u n d any one out o f two possible rotation axis, i.e., any one of the two aT axes o f the tetragonal phase can with equal a priori probability become the ao axis o f the o r t h o r h o m b i c structure. This m a y lead to the f o r m a t i o n o f out-ofphase boundaries, or d i s c o m m e n s u r a t i o n walls and twins with coherent ( 1 10)o planes. The occurrence o f such twins is d o c u m e n t e d in the literature. We discuss in the present p a p e r models for such interfaces. N e u t r o n diffraction studies c o m b i n e d with iod o m e t r i c titration of the oxygen content on powders and on twinned "single" crystals [ 6 - 8 ] have shown that the material m a y contain excess oxygen in the superconducting phase La2CuO4+a with fi~0.03. Specimens with up to 0 = 0 . 1 3 have been obtained as well [9]. F r o m neutron diffraction experiments on powder specimens o f La2CuO4+6 with 5 = 0.03 Jorgensen el al. [6] concluded that phase separation occurs on ageing below 320 K. One phase is stoichiometry non-superconducting La2CuO4; the other one is superconducting La2CuO4+6, i.e, oxygen-rich material. Similar results were o b t a i n e d by Zolliker et al. [9] using synchrotron radiation p o w d e r diffractometry. After ageing at 250 K the two phases were found to be present in roughly equal proportions. The powder diffraction patterns o f the two phases are not easy to unscramble since one o f the lattice p a r a m e ters is essentially c o m m o n to both phases. Recent high-resolution neutron diffraction experiments [6,8], as well as X-ray studies, lead to a model for the oxygen-rich phase. It was shown that the excess oxygen is i n c o r p o r a t e d in a site situated between the two LaO layers as shown schematically in fig. l ( a ) after ref. [6]. The insertion o f the excess oxygen results in small displacements o f the adjacent a t o m s a n d in particular in d e f o r m a t i o n and tilting o f the CuO6 octahedra. The apices A and B o f the two octahedra between which an oxygen is inserted are displaced as indicated by the arrows in fig. l ( a ) ; similar displacements occur in the plane perpendicular to the drawing. Davies and Tilley [10] have shown that a homologous series o f m i x e d layer c o m p o u n d s o f the type La,+ jCu,O3,+, can be prepared by choosing the appropriate LaO-CuO2 ratio. These c o m p o u n d s have
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LaeCu04_~
structures which are closely related to that of La2CuO4. Instead of a single perovskite layer they contain perovskite-like lamellae consisting of n-layers of CuO6 octahedra separated by bi-layer LaO lamellae having a sodiumchloride-like structure; the limiting oxygen layers of the perovskite lamellae being part of the sodiumchloride-like structure. Recently dislocations in La2_xSr~CuO4 were studied using diffraction contrast [ 11 ]. The Burgers vector of the dislocations was found to be [ ½, a, 0, lc]p, i.e., not a lattice vector. It was speculated that the dislocations should be bordering partials of faults implying that edge sharing of the CuO6 octahedra takes place along the interface.
577
3. Observations 3.1. Diffraction patterns 3.1.1. Basic structure
The diffraction pattern along the bo zone ( [ 010]o) reveals a quasi square rectangular lattice Which is consistent with the lattice parameters ao = 0.536 nm; Co=0.539 nm (fig. 2(a) ). Tilting away slightly from the bo-zone about the ao* direction the (01 i ) * section of reciprocal space is obtained (fig. 2 ( b ) ) . In this section the rectangle of strong spots is centered, whereas in the middle of the sides of the rectangle weak spots appear; some of the latter are not compatible with the space Cmca. It does not seem pos-
Fig. 2. Four sections of reciprocal space of the orthorhombic basic structure. (a) (010)* section, (b) (01 T)o* section, (c) ( 100)2 section, (d) (101 )o*section.
G. Van Tendeloo, S. Amelinckx I Long-period shear structure in La:Cu04_6
578
sible that they are generated by double diffraction. After 400 kV electron irradiation some of the weak spots disappear but the reciprocal lattice remains the same. Apparently some form of order is destroyed by the electron irradiation. Most probably oxygen atoms are involved since these are the most easily displaced atomic species present in the material. Presumably the tilt pattern looses its long range order. Figure 2(d) shows the ( i 0 1 ) * section of reciprocal space; it reveals the spacing do,o= 1.318 nm perpendicular to the layer planes. Finally fig. 2 (c) shows the ( 100)* section of reciprocal space. Again forbidden spots, such as 001, appear; however this spot could be generated by double diffraction. The reciprocal lattice, as deduced from the different sections of fig. 2, is represented in fig. 3; it is clear that some observed spots are not compatible with the space group Cmca. The reason for the occurrence of these "forbidden" reflections is not clear. An obvious reason that might be envisaged is the presence of twins within the area selected for the diffraction pattern. It is however doubtful that the presence of twins would not have been noted in the corresponding image. We therefore believe that the symmetry is destroyed by some small additional displacements leading to violation of the extinction conditions.
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3. I. 2. M o d u l a t e d s t r u c t u r e
A long-period modulated superstructure was found in about 10% of the volume of the specimen. The most relevant zone of the diffraction pattern of this modulated structure is the [ 101 ] o zone (fig. 4 (a) ). The rows of closely spaced superstructure spots are oriented almost exactly along the [1 10]~ direction of the basic structure or the [ 111 ]* direction of the orthorhombic structure. They divide the distance between basic spots approximately in four equal intervals. However, the corresponding real space period is smaller than four times that of the basic structure; it is approximately 1.33 n m = ~ × 0 . 3 8 nm. It is clear that the intensities of the superstructure spots located close to the positions of basic spots are relatively the largest. To see this one should compare fig. 2(d) and 4(a) in parallel orientation. Such a behaviour is consistent with the assumption that the superstructure is a modulated structure of the basic La2CuO4 structure. The relationship between the diffraction patterns of the modulated structure and that of the basic structure is not a simple one. The superstructure spots in fig. 4(a) form very' nearly a centered rectangular arrangement as indicated in fig. 5. In reality the rectangle is somewhat deformed however. When rotating the specimen about an axis parallel with these rows of superstructure spots, i.e., parallel with [ 111 ]o the sequence of diffraction patterns of fig. 4 ( b - f ) is obtained with increasing tilting angle. The sections of reciprocal space obtained in this way are successively (a) ( i 0 1 ) * , (b) (514)*, (c) (g~13)*, (d) (312)*, (e) (211)* and finally (f) (i 10)*. These sections are represented in fig. 5. It is now clear that sequences of superlattice spots are associated with all basic spots; the repeat distance is twice that deduced from fig. 4(a), i.e., it is twice the separation of the interfaces, i.e., 2X 1.33 n m ~ 2 . 6 6 nm. Along the projection of fig. 4 (a) the projected interface separation is only 1.33 nm which is consistent with the observed extinctions along this zone. Note that in figs. 4 ( b - e ) the central row ool also exhibits the double period. This is due to double diffraction out of the non-central rows. The double diffraction spots are systematically weaker. Figure 6 shows the composite diffraction pattern of a crystal fragment containing an area exhibiting the modulated structure and an adjacent crystal area
G. Van Tendeloo, S. Amelinckx / Lon/z-,':~tod shear structure in LaeCuO4_a
579
Fig. 4. Six sections of reciprocal space of the long period shear structure. All sections are parallel with the dense rows of superstructure spots. The indices refer to the basic orthorhombic structure. (a) ( 101 )* section, (b) ( 51 4)* section, (c) (413 )* section, (d) ( 312 )* section, (e) (2 1 1 )* section, (f) (1 10)* section.
h a v i n g the basic structure. T h e r e l a t i o n s h i p b e t w e e n the two d i f f r a c t i o n p a t t e r n s is n o w i m m e d i a t e l y obvious. It is n o w d i r e c t l y o b s e r v a b l e that the m o s t in-
tense spots o f the m o d u l a t e d structure o c c u r close to the p o s i t i o n s o f basic spots. It is clear that also in those sections o f fig. 4 w h i c h c o n t a i n l o w - o r d e r basic
580
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2Cu04
two different orientations related by a m i r r o r operation with respect to the layer planes ( 0 1 0 ) . J
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\ 3.2. High-resolution images 3.2.1. Basic structure
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Fig. 5. Reciprocal lattice of the basic structure in relation to the different sections of the reciprocal space of the modulated structure.
Fig. 6. Diffraction pattern across a twin boundary showing the superposition of the ( 101 )o*section of one crystal, not exhibiting the long period, and the ( 101 )o* section of the twin, exhibiting the rows of superstructure spots.
spots, such as 4 ( e ) , the most intense superstructure spots occur close to these basic spots. The diffraction pattern o f fig. 6 reveals a small orientation difference between the bo-axis o f the basic structure and the corresponding lattice direction o f the m o d u l a t e d structure. Along the same zone ( i 01)o o f the basic structure the m o d u l a t e d structure has been found in
The basic o r t h o r h o m b i c structure has been imaged along different relevant zones. Figure 7 ( b ) shows the [ 0 1 0 ] o zone; it reveals the quasi tetragonal o r t h o r h o m b i c structure. The heavy a t o m columns are revealed as bright dots. The image along the ( 1 0 i )* section (fig. 8 ( a ) ) is particularly relevant since along this zone the heavy atoms form columns consisting all o f the same species; it thus reveals the stacking along the bo-direction. Even without c o m p u t e r simulation it is possible to find unambiguously the imaging code in thin parts o f the foil where the a t o m i c columns a p p e a r as black dots. In fig. 8 ( a ) the high resolution image is c o m p a r e d with a schematic representation o f the structure. The heavy atom columns o f lanthanum and copper can easily be recognized as dark dots by their characteristic geometrical configurations; as usual the oxygen atoms are not imaged under these conditions. In the thick parts the heavy a t o m columns a p p e a r as bright dots (fig. 9). The image o f fig. 9 was m a d e along the [ 100]o zone; it can be c o m p a r e d with the schematic representation o f the structure fig. 1 ( b ) . Careful e x a m i n a t i o n o f fig. 9 ( a ) shows that the vertical dot rows are perfectly straight, whereas the horizontal dot rows are slightly wavy. We believe that this is due to the tilts o f the rows o f o c t a h e d r a , which lead to small, observable displacements o f the heavy a t o m s as well. The rotation o f the octahedra is indicated by a curved arrow in fig. 1 ( b ) , whereas the corresponding displacements o f the La-atoms are shown by small straight arrows. 3.2.2. M o d u l a t e d structure
As a model for the m o d u l a t e d structure we propose a "shear structure" derived from the basic La2CuO4 structure. Using the imaging code established under identical conditions (i.e., in an adjacent region o f the same foil ) for the perfect structure in the thin part o f the foil, we can deduce an app r o x i m a t e model from the high resolution images along different zones, in particular from fig. 8 ( b ) . With respect to the layered structure the edge shar-
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2CuO~_a
581
Fig. 7. High-resolutionimagealong the [010 ]o zone exhibitingdislocations in the foil plane.
ing can take place according to two essentially different modes. If a family of edges, which are parallel with the layer planes, becomes common the Cp layers remain planar (fig. 10(c) ). In a view along the a2.pdirection the projected distance between the copper atom columns 1 and 4 in the shared octahedra is then ½ap. Within the layers the rows of heavy ions become staggered (fig. 10(d)). An essentially different situation occurs if a family of edges inclined with respect to the layer planes becomes shared (fig. 10(a) ). The layer planes then become stepped, the magnitude of the step being about one third of the interlayer spacing. The projected separation of the copper atom columns 1 and 4 in the edge sharing octahedra is now ½apx/'2. Within the layers the heavy atom rows
remain the same on both sides of the shear plane (fig. 10(b)). The observations of fig. 8(b) do not allow a straightforward and unambiguous distinction to be made on qualitative arguments only. The layer planes have indeed become stepped, but the steps are much smaller than those predicted by the model of fig. I 0 (a). On the other hand fig. 18 shows that the rows of heavy atoms have become staggered, although not exactly in anti-phase. The separation of the copper columns I and 4 in fig. 8(b) is found to be significantly closer to ½ap than to ½apv/2. As yet we have left the lanthanum ions out of our considerations. In both models the remaining lanthanum ions have to be accompanied somewhere in
582
G. Van Tendeloo, S. A m e l i n c k x / Long-period shear structure in L a 2 C u 0 4
~
Fig. 8. (a) High-resolution image of the basic orthorhombic La2CuO4 structure along the a o zone -= [ 1 01 ]o. The heavy atom columns are imaged as dark dots; the oxygen atom columns are not imaged under the diffraction conditions used. This image can be compared with the schematic representation of the structure in fig. 1 (a); black dots indicate heavy ions, squares are the projections of the octahedra. (b) High-resolution image of the long period shear structure in La2CuO4_a along the [ 101 ]o zone (i.e., along the ap zone). The heavy atom columns are imaged as dark dots; the oxygen columns remain invisible. This image can be compared with the schematic representation of fig. 15, made along the same zone axis. The correspondence between black dots and atom columns is indicated.
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2CuO~_~
i
Fig. 9. (a) High-resolution image along the [ 100]o zone. This image can be compared with the schematic representation along the same zone as in fig. 1(b). (b) High-resolutionimage along the (01 i )~ section. The interfaces are crystallographic shear planes along which the CuO6octahedra share edges.
the rectangle ABCD (fig. 8(b) ). Their presence causes the actual situation to deviate from the idealized models of either fig. 10(a) or 10(c). The compromise offering best overall correspondence with the observations of fig. 8(b) and 18 is to assume that the situation is best described by fig. 10(c), but that the presence of the lanthanum ions causes a local deformation of the layers in the shear plane, resulting in a small shift as represented schematically in fig. 15. In fig. 8 (b) the interfaces causing the long period (i.e., the crystallographic shear planes) are observed
583
edge on, and the perovskite cubes are viewed along the dense rows of heavy atoms, as can be deduced from the corresponding diffraction pattern (fig. 4(a) ). The high-resolution image shows that in one projected period, i.e., between two successive interfaces one observes linear sequences of four columns of copper atoms, indicated 1, 2, 3, 4 in figs. 8 (b) and 15, the separation of the columns being equal to ap = 0.38 nm. Where two such linear sequences meet a small offset in the bo-direction is observed; the line segment, joining the two copper columns at the ends of the sequences of four such as 1-4, being inclined with respect to the rest of the sequence. The projected separation of the two copper columns forming this short segment is only ~ ½ap. This behaviour is consistent with the assumption that edge sharing octahedra are presented along the interface. This is represented schematically in fig. 15; it implies that the displacement vector has a component perpendicular to the plane of the drawing as well; this is discussed further below. Within the rectangle ABCD (fig. 8 (b) ) formed by the projections of two close pairs of copper columns in the edge sharing octahedra, one distinguishes two further black dots, due to atom columns. These columns are also represented in fig. 15. The slightly smaller darkness of the dots marking these columns in fig. 8(b), as compared to that of the lanthanum columns of the perfect structure, suggests that they image incompletely occupied heavy atom columns. The observations do not allow to conclude whether they represent copper or lanthanum columns, but it seems reasonable to assimilate them with lanthanum columns, pushed out of their normal positions by the edge sharing CuO6 octahedra. In turn their presence presumably causes the small offset of the LaO layers, which is itself a consequence of the small tilt of these octahedra about their common edge. One lamella LaO-CuO2-LaO of the proposed structure is shown in projection along the normal to the plane of the lamellae in fig. 16. The displacement vector is close to R = ½[ i 10 ] p, when referred to the basic perovskite structure, i.e., ignoring the tilt of the octahedra. The projected repeat distance along this zone is then ~a~.p+ ½a2.p. Ignoring the tilt of the octahedra the model of fig. 15, viewed along the same zone a2.p as the diffraction pattern of fig. 6, has the unit mesh
584
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La:CuO4 ,~ I/2%~ i
0
0
i
0
0
0
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o',5/Z2;
(c)
(a)
o
i ,0 ,,0
(b)
(d) Fig. 10. Schematic representation of shear planes resulting from edge sharing C u O 6 octahedra. (a) An inclined edge is shared: the projected separation as viewed along a2.p is i ap~ 2. (b) View along cp of the same configuration as in (a). (c) Edges parallel with the layer plane are shared. The projected separation along a2.p is ~apl. (d) Horizontal view along cp of the same layers as (c).
outlined by the dashed lines. The tilt of the octahedra doubles this repeat p e r i o d as represented in fig. 16. One o f the edges o f this projected unit mesh encloses the same small angle with the layer planes as that observed in the diffraction pattern o f fig. 6. The same angular difference can be observed in fig. 19 when looking u n d e r grazing incidence along the direction o f the layer planes. The average orientation in the m o d u l a t e d left part is slightly different from the orientation o f the layer planes in the u n m o d u lated part to the right. In deriving the tilts o f the octahedra in the different slabs it should be taken into account that along the interfaces the o c t a h e d r a share edges. Tilting a rigid o c t a h e d r o n about an axis parallel with the shared edge causes the tilts o f the coupled rigid oct a h e d r a to be opposite in sense. Tilting about an axis normal to the c o m m o n edge the coupling causes the two tilts to be in the same sense. As a result o f these rules the ao and Co axis o f the o r t h o r h o m b i c structures are in successive d o m a i n strips, as indicated in fig. 16 in which the sense o f tilting o f the octahedra
has been i n d i c a t e d by an arrow at the apical oxygen at the top o f the o c t a h e d r a facing the observer. This will be shown in section 4. Taking into account the tilt o f the octahedra does not affect the repeat period in the projection o f fig. 15 since viewing along any column the tilts are alternatingly in opposite senses and hence the average projection does not change. A view along the a~,p direction is shown in fig. t7. The image corresponding with section (1 1 0)* o f the reciprocal lattice (fig. 4 ( f ) ) is shown in fig. 18; it exhibits slabs o f perovskite structure separated by interfacial lamellae along which the stacking o f the perovskite lamellae becomes staggered as judged from the arrays o f bright dots. These images are somewhat similar to those o f the series o f homologous m i x e d layer c o m p o u n d s referred to a b o v e and described by Davies and Tilley [ 10 ]. However, in our images the pattern o f bright dots is not square but slightly parallelogram shaped. This form o f stacking o f the perovskite lamellae is consistent with the diffraction pattern o f fig. 4 ( f ) . In this foil, with a somewhat
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LaeCuO~_~ APB in (101)
1
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CRYSTALLOGRAPHIC SHEAR PLANE
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585
larger thickness, the heavy atom columns are imaged as bright dots under the diffraction conditions used. The lanthanum columns are imaged as the brightest dots, the copper columns as less bright dots. The geometry of the dots in fig. 18 can be compared with the schematic representation of fig. 16 taking into account that in this representation the octahedra were drawn as undeformed. Since the image of fig. 18 is a slightly oblique view of fig. 16 the square meshes are transformed into parallelograms. The zone used for imaging is (i 10)* indicated in figs. 5 and 4 ( f ) ; it contains rows of superstructure reflections but its zone axis is not quite parallel with the atom columns along the bo-axis, the viewing direction is parallel with the shear planes however. Nevertheless the correct topology of fig. 16 is reproduced in the observed image of fig. 18. However the slight inclination of the atom columns leads in the thicker parts of the wedge shaped foil to streaking of the dot pattern and even to the transformation of the bright dot rows into continuous lines with reinforcements. All these observations are consistent with the fact that this image is due to the same modulated structure as fig. 8, with fig. 4 ( f ) as the corresponding diffraction pattern. Note that the thickness of the perovskite lamellae in fig. 18 is not always constant; it shows some variability in block width as in fig. 12. Along the projection zone the lozenge-shaped pattern of bright dots is consistent with the model of fig. 16. It should be reminded that this image is related to that of fig. 8 (b) by a rotation about an axis normal to the shear planes. The bright dot pattern in fig. 18 is not related in a simple manner to dense columns in the structure, but the geometry allows to derive the number of unit cells in the successive slabs, as well as their geometrical arrangements. These are clearly consistent with the proposed model.
4. Interpretation
(c) Fig. 11. Modelsfor planar defects. (a) Schematicrepresentation of the typeof anti-phase boundaryresulting fromthe phase transition T~0; the displacement vector is ½[001 ]o. (b) Schematic representation of a crystallographic shear plane resulting from edge sharing of the CuP6 octahedra. (c) Twin boundary resulting from the phase transition T~0.
4.1. Diffraction patterns
The diffraction pattern along (i 01 )* section could be indexed as shown in fig. 4(a) on the basis of a monoclinic unit cell. The unit cell parameters are approximately:
G. Van Tendeloo, S. A melinckx / Long-period shear structure in La2Cu04
586
Fig. 12. Low-magnification high-resolution image along the [ 101 ]o zone, exhibiting several singular crystallographic shear planes.
am = 0 . 6 6 n m ; bm = 0 . 7 6 n m ; c m =2.6 nm;~=
(am)(!0
102-103 ° .
T h e y are r e l a t e d to a l p , a2,p a n d Cp b y t h e r e l a t i o n
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Fig. 13. Crystallographic shear plane ending in partial dislocation: [ 101 ]o zone view.
Fig. 14. Schematic representation of the atomic configuration around a terminating shear plane (cf. fig. 13 ).
G. Van Tendeloo, S, A melinckx I Long-period shear structure in La2Cu04_6
0
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~oX,/Co
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Fig. 16. Schematic view of one lamella of fig. 15 along the bo-=ep direction. The CuO~octahedra are represented as undeformed but the sense of the tilt is indicated by arrows. and in terms of the orthorhombic structure
where ~ is a small q u a n t i t y accounting for the offset in the bo direction of the shear planes. The following reflection conditions were ob-
served; the h o l reflections are only present for / = e v e n ; also the o o l reflections are only present for l = even, if double diffraction spots are ignored. Space groups compatible with these conditions are P l c l (no. 7) (point group m ) and P 1 2 / c l (no. 13) (point group 2 / m ) ,
588
G. Van Tendeloo, S. Amelinckx / Long-period shear structure m LaeCu04
,
r
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lp
p e r p e n d i c u l a r to the glide planes. We will show that the high-temperature phase, i.e, the shear structure in which the tilts o f the octahedra are ignored, belongs to the space group P 1 2 / c l , which reduces to the space group P l c l , when the tilts o f the octahedra are taken into account. One lamella o f the p r o p o s e d shear structure as suggested by the high resolution images is shown in fig. 16 in which also an outline o f the unit mesh (bm, Cm ) is indicated. The origin was chosen in a centre of s y m m e t r y o f the structure, still ignoring tilts o f octahedra. The structure is the same in all layers, the successive layers being stacked like in the normal tetragonal structure, the shear planes being shifted systematically over a distance ½ap in the [001 ] direction. This stacking ensures that within the d o m a i n strips the normal tetragonal structure is realized as suggested by the high resolution images.
Fig. 17. Schematic view along the a~,p direction of the shear structure of fig. 15, the tilts of the octahedra are indicated by arrows.
4.2. F o r m a t i o n o f the shear structure
the first space group being a subgroup o f the second. Both space groups have ( 0 1 0 ) glide planes with glide vector ½cm; the second has m o r e o v e r two fold axes
The superstructure could in principle be derived from the o r t h o r h o m b i c structure by the periodic introduction o f crystallographic shear planes. Taking
Fig. 18. Large area of shear structure viewed along the ( 110)* section. Under the diffraction conditions used th heavy atoms are imaged as bright dots. In the thick parts of the foil the bright dots degenerate into continuous bright lines, due to the slight inclination of the atom columns with respect to the viewing direction.
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LaeCuO4_a
this operation literally this would mean that within the successive domain strips the orthorhombic deformation would in all domain strips be in the same sense, i.e., within those strips the ao and Coaxis of the basic orthorhombic structure would be parallel. If this is accepted and if the octahedra are assumed to remain rigidly coupled along their corners within the domains and along their edges within the shear planes, it is straightforward to show that inevitably a triclinic structure results. However, this results is not compatible with the occurrence of systematic extinctions as observed in fig. 4 (a) and which indicate the presence of symmetry elements. The symmetry must thus at least be monoclinic, where such extinctions may occur. It therefore must be assumed that in reality the formation of the shear structure proceeds in two stages with two different characteristic temperatures. The formation' of the shear planes implies diffusion and therefore occurs at higher temperatures presumably exceeding the T ~ 0 transition temperature. The shear planes are thus assumed to be formed in the tetragonal phase. Only at lower temperatures the CuO6 octahedra become tilted and the room temperature shear structure is formed. This implies that now in principle the tilt axis of the octahedra can be different in successive domain strips, as proposed in our model, provided the sense of the tilts of octahedra remains correlated and consistent with corner and edge sharing. At this stage the space group is P12/cl and the point group is 2 / m of order 4. The lanthanum atoms of which the normal sites were lost as a result of the edge-sharing, will now order in the shear planes so as to minimize the Coulomb energy due to the uncompensated negative charges. An arrangement suggested by the high-resolution images (fig. 8 ( b ) ) , as well as by symmetry consideration, is represented in fig. 16, where the full and crossed dots reoresent the lanthanum atoms above and below the layers of CuO6 octahedra. In the view of fig. 8(b), these two sites give rise to the two dots within the rectangle ABCD. In a subsequent stage, at lower temperature, the T--.0 transitions occurs, presumably at a slightly different temperature from that in the unsheared structure, and the octahedra become tilted. We assume that within the domain strips the normal orthorhombic structure will be realized. The sense of tilting is indicated
589
by the short arrows in fig. 16. The arrows indicate the sense in which the apical oxygen, facing the observer, is displaced. It is reasonable to assume from size considerations that the lanthanum atoms in the shear planes will have a tendency to push apart the two apical oxygens on each side ot it. This imposes a sense on the tilt of the adjacent edge-sharing octahedra, which are considered as rigid. Due to this mutual coupling a tilt-scheme is imposed for the whole layer ofoctahedra. The tilt of the octahedra in the shear planes is unambiguously imposed by the edge sharing. The corner coupling leaves somewhat more freedom. The corner X of octahedron 2 (in fig. 16) for instance is forced to move upward (i.e., towards the observer) as a result of the tilt in the adjacent octahedron 1, which is part of the shear plane. This nevertheless leaves a choice for the tilt axis of octahedron 2; it can tilt either about the axis shown or about the perpendicular axis. Once this choice is made the rest of the tilt pattern follows. The observed monoclinic symmetry tells us that the correct choice is as indicated in fig. 16 since this leads to a monoclinic space group with a (010) glide plane and ½Cm glide vector, as required by the diffraction conditions. The alternative choice would lead to a triclinic unit cell. Once the tilt-scheme is fixed in one CuO-CuO2LaO layer the tilt-scheme in the other layers is determined if the known orthorhombic structure is to be generated within the domain strips. The superstructure thus finally consists of alternating strips of the two variants of the orthorhombic structure, which can be formed from a tetragonal single crystal, separated by a family of ( 1 1 1 )o edgesharing shear planes. The fact that strips of two variants of the orthorhombic structure occur in the shear structure strongly suggests the two-stage formation mechanism described.
5. Defects 5.1. Basic structure 5.1.1. Planar defects
The high-resolution image of fig. 9(b) along the ( 0 1 i ) * section reveals a quasi square dot pattern. The image exhibits planar interfaces along the ( 101 )o
590
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2Cu04_a
planes possibly resulting from the phase transition tetragonal to orthorhombic. Since the dot pattern is only shifted across the interface they must be translation interfaces. Independent of the imaging code the projected translation vector can be observed directly on the image; it is found to be either ½[001 ]o or ½[ 100]o. The vector ½[001 ]o is not acceptable as such since it is not a lattice vector of the tetragonal high-temperature phase. However, the vector ½[01 i ]o satisfies this condition. The interface, which results from the orthorhombic deformation is represented in fig. 11 (a) where the tilt of the octahedra is represented. The interface can be described as a conservative anti-phase boundary since its presence does not affect the composition of the crystal; the tilt of the octahedra, which is constant along a given (001)o plane and alternates in successive (001 )o planes, changes its sense where a [100]o row o f o c tahedra intersects the interface. The octahedra situated in the boundary will presumably be undeformed giving a certain width to the interface. Two crystallographically equivalent displacement vectors are indicated in fig. 11 (a). The displacement vector cannot be determined unambiguously in this way however; the relative displacement of the two dot patterns can also be interpreted as a displacement over ½[ 100]o. If this is the case a different model should apply, are represented in fig. 11 (b). We now can exclude that also a component of R perpendicular to the plane of the drawing should be present since R would then become ½[ 110 ] o which is a lattice vector in a C-centered unit cell and thus does not lead to a translation interface. The only solution is then that edge-sharing of the CuO6 octahedra occurs along a non-conservative interface. At this stage we cannot decide unambiguously which fault is being observed. However, in view of the fact that edge sharing is observed in the long period superstructure, to be discussed below, suggests that also in this case the second model is the more plausible one. Also the trace of the habit plane of the periodic shear planes observed in the superstructure is consistent with the traces of the isolated interfaces observed here along the [010] zone. The interface would be situated in a ( 111 )o plane rather than in ( 101 )o planes. Since the bo-parameter is large this plane only encloses a small angle with the normal to the layer plane and thus would be imaged as
a narrow line. In any case in fig. 9(b) the apparent width of the interface increases with increasing foil thickness, which confirms our assumption. In conclusion the interfaces are most probably isolated shear planes of the same type that give rise to the long-period modulated structure. Whereas anti-phase boundaries of the first type discussed here are likely to occur in samples which have undergone the T-~0 transition, in the annealed specimens the shear planes are more likely. When viewed along the (i 01)* section isolated planar interfaces in (111 )o planes are observed in fig. 12; they are most probably of the same type as those imaged in fig. 8. The interfaces can also adopt the "twin" orientation, i.e., they may be parallel with ( 11 i )o planes. However in any given area predominantly the same habit plane is adopted. Sometimes a single interface ends within the crystal; this necessarily gives rise to a dislocation (fig. 13). In fig. 14 we have analyzed schematically the atom configuration around such an ending interface, assuming the interface to be a crystallographic shear plane. Looking at the photograph of fig. 13 under grazing incidence along the dot rows parallel with the shear plane it is noted that these dot rows bend slightly inwards towards the shear plane. This observation demonstrates that the shear plane accommodates a deficiency of atoms. It is clear that the T-~0 phase transition can in a similar way give rise to twin boundaries with a coherent interface along the ( 101 )o plane. A model for a twin boundary is shown in fig. 11 (c).
5.1.2. Dislocations 5.1.2.1. Observations and their interpretation. Figure 7(a) shows a set of dislocations situated in the (010)o plane, imaged in a mixed contrast of lattice fringes and diffraction contrast. The structure image of the area around the dislocation is reproduced in fig. 7(b). One set of rows ( 1 ) of bright dots crosses the dislocation almost without being influenced, except for a small change in the orientation of the bright dot rows. In the core region these rows degenerate into continuous bright lines. The dislocation perturbs much more strongly the second set 2, and the core causes discontinuities and shifts in these dot rows.
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in La2Cu04_~
Such a behaviour is consistent with what one would expect for the image of a dislocation parallel with the (010) plane and with a Burgers vector parallel with the unperturbed dot rows, i.e., along the [ 100]o direction. The contrast features can intuitively be understood in terms of the atom column approximation (ACA) [ 12 ]. A relative displacement of two parts of the atom columns, above and below the glide plane, along the direction of the Burgers vector, will be imposed by the presence of the dislocation. If in all columns such displacements take place in the same plane, determined by the Burgers vector and the viewing direction (i.e., along the normal to the glide plane) the rows of bright dots parallel with that plane will form sharp but continuous bright lines. However the same displacements will much more strongly perturb the rows of atomic columns perpendicular to the Burgers vector and create discontinuous image shifts along the core. Rather than reasoning in terms of atomic columns one can also reason in terms of the wave theory of atomic image formation considering the images resuiting from the interference and superposition of a number of Fourier components or lattice fringes. We note that the Fourier components ng(n = integer) will not be perturbed by the presence of the dislocations if g.b=O. This expresses the condition that all displacements occur along the lattice planes perpendicular to g. Such planes are in fact not deformed by the presence of the dislocations and hence the corresponding set of lattice fringes remains unperturbed. The small orientation difference of the lattice fringes on both sides of the dislocation core is caused by the lattice tilt resulting from the edge component of a dislocation in a thin foil parallel with the surface roughly given by 0= b i t (t = thickness). Such a small lattice tilt causes a continuous shift of the position of the lattice fringes. 5.1.2.2. Model. The occurrence of a dislocation with a Burgers vector a [ 1 0 0 ] is somewhat unexpected, but can nevertheless be rationalized. On glide the layers of corner-sharing CuO6 octahedra will presumably remain unsheared, glide taking place between the two LaO layers forming a two-layer lamella of sodiumchloride-like structure. When ignoring the tilt of the octahedra, i.e., in the tetragonal phase, the shortest repeat in the plane is ½[ 101 ] o
591
and hence this would be a reasonable Burgers vector for a glide dislocation on a (010)o plane. However in the orthorhombic structure ½[ 101 ]o is not a lattice vector; such a dislocation thus generates a fault consisting of wrongly tilted octahedra. If the fault energy is sufficiently small, isolated partials might occur. However our observation suggests that the glide process apparently prefers a longer glide vector a [ 1 0 0 ] , avoiding in this way to generate a fault. Since a[ 100]o is a lattice vector such a dislocation is perfect. Glide now proceed along the [ 100 ]o "furrows" of the wavy layer of tilted CuO6 octahedra. An interpretation of the dislocations as the bordering partials of a shear plane seems improbable because of the strongly crystallographic orientation of the shear planes observed in the same specimens, on the one hand, and the rather random orientation of the dislocations in the (010)o plane in fig. 7(a) on the other hand [ 11 ]. 5.2. Defects in the modulated structure
As already mentioned, the modulated structure only occurs in a rather small volume fraction of the crystals. The shear plane separation is relatively constant; the smallest and most frequency observed one being ~ 1.33 nm as can be judged from figs. 19 and 20. However deviations from strict periodicity occur and apparently isolated shear planes occur occasionally as well (figs. 12 and 13). In view of the fact that according to our model the shear planes accommodate an oxygen deficiency the specimen must be slightly inhomogeneous and overall slightly oxygen deficient. The almost strict periodicity of the shear planes over large areas (fig. 20) can be understood by assuming that there is a repulsive interaction between parallel shear planes, the interaction being presumably mainly of an elastic nature with possibly a Coulomb contribution due to local charge imbalance along the interface Sometimes "hair-pin" shaped arrangements are observed, as for instance in fig. 19. Such arrangements were thought to play a role in the propagation of shear planes [ 13]. In fig. 19 the resolution, although not excellent, due to the relative thickness of the sample in that area, it is nevertheless sufficient to suggest a concrete model. The geometrical con-
592
G. Van Tendeloo, S. Amelinckx / Long-pertod shear structure in
La2CuO
4 6
Fig. 19. "Hairpin" shaped configuration of shear planes. In this rather thick part of the foil the lanthanum columns are imaged as bright dots. This image is analyzed in detail in the text and represented schematically in figs. 21 and 22.
figuration is represented schematically in fig. 21. It should first be noted that the geometry o f the rows of bright dots in the thick part o f fig. 20 suggests that these are the images o f l a n t h a n u m columns. The staggered arrangement o f the double rows o f these bright dots is consistent with the geometry o f the L a O - L a O layers in the structure a n d not with that o f the copper columns. At the tip o f the "hairp i n " three rows o f bright dots are presented in the correct arrangement to represent a three-layer lamellae o f LaO, i.e, one s u p p l e m e n t a r y layer o f LaO terminating on both ends at a shear plane. The atomic a r r a n g e m e n t o f the left end o f the tip is represented schematically in fig. 22 ( a ) . The offset p e r p e n d i c u l a r to the layer planes between the perovskite blocks I and II on both sides o f the shear plane is taken up by the s u p p l e m e n t a r y LaO layer, which simultane-
ously introduces a dislocation due to the insertion of one additional LaO layer. The upward curvature o f the lattice planes along the tip o f the " h a i r - p i n " is consistent with the presence of such a dislocation at both t e r m i n a t i o n s o f the s u p p l e m e n t a r y LaO layer. The right h a n d t e r m i n a t i o n o f the tip is blunted by the presence o f a small facet o f shear plane in the twin orientation. As a result the a t o m i c configuration of the tip at the right end is the m i r r o r image o f that at the left end (fig. 2 2 ( b ) ) . In fact the level difference between the perovskite layers in the right half o f fig. 22 is taken up (i.e., the gap is filled) in two steps. The first one is the f o r m a t i o n o f the twin as shown in fig. 2 2 ( b ) ; this results in the presence o f an extra layer o f thickness 2×~2bo, t e r m i n a t i n g at the intersection line o f the twinned shear planes A and B, i.e., a dislocation line, with this edge c o m p o n e n t (~b) o f
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LazCuO~_,~
593
Fig. 20. Large area of shear structure at somewhat lower magnification viewed along the [ 101 ]o zone.
j l /
Fig. 21. Schematic representation of the observed microstructure in fig. 20; the deformation of the (010)o layer planes is indicated schematically: D~, D2 and D3 represent dislocations.
the Burgers vector, is present along this line. The configuration around the line where the interface B intersects with the tip facet is now the mirror image of that present around the left end of the tip facet
and which is represented in fig. 22(a). Calling the Burgers vectors of the dislocations D~, D2 and D3 respectively b~, b2 and b 3 the following relations have to be satisfied for topological reasons: R~.e=bl.e; R2"e=b2.e and 2Rl-e=b3.e. Without the twin facet present the dislocations at the right end of the "hairpin" tip would have to have a Burgers vector b: + ha, which is presumably too large to be stable. The total energy can be lowered by the dissociation into two dislocations D2 and D 3. This dissociation is accompanied by the formation of a segment of shear planes D2D3 in twin orientation and by the shortening of the extra layer LaO between D~ and D2, as well as by reorientation of the right shear plane (fig. 21 ). The configuration at D 3 is elastically equivalent to a dislocation but there is no supplementary half plane. It is assumed that in the symmetrical position D 3 (fig. 22(b) ) there is no offset across the shear plane, the shared edge of the octahedra projects horizontally there.
594
G. Van Tendeloo, S. Amelinckx / Long-period shear structure in LaeCu04_,~ (B) ,
i i
~
",\
i
/Uo {al
®
kf o kf ~ "0" ~
/ @
i
/ Da
shear plane
u o
o
y,,, U ; " U it
/('
(b)
'(A)
Fig. 22. (a) Atomic arrangement around the dislocation D~ in fig. 21. (b) Atomic arrangement around the dislocation D 3 in fig. 2 I. The shear plane along ( 110)o changes abruptly its orientation into the "twin" orientation ( 1 T 0)o.
6. Conclusions
mechanism for shear structures, have been observed
[14]. Even though the material was prepared taking all precautions in order to achieve exact stoichiometry the material was found to be slightly oxygen deficient. As well isolated crystallographic shear planes, as one-dimensional periodic shear structures were observed. The oxygen deficiency is inhomogeneously distributed throughout the material as judged from the distribution of shear planes. The hairpin-shaped configuration of shear planes which was considered to be a characteristic feature of one of the proposed propagation mechanisms for shear planes [ 13 ], was observed and studied in detail with atomic resolution. Also single ending shear planes which play a role in an alternative formation
Acknowledgements This work has been performed in the framework of the Institute for Materials Science (IMS) of the University of Antwerp under an IUAP-contract with the Ministry of Science Policy. We are grateful to L. Pintschovius (Karlsruhe) and W. Weber (Dortmund, Karlsruhe) for providing the single crystal of LaCuO4. The authors also acknowledge stimulating discussions with J. Van Landuyt (RUCA), F. Weill (Bordeaux) and L. Pintschovius (Karlsruhe).
G. Van Tendeloo, S. Amelinckx /Long-period shear structure in La2CuO~_6
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[8] C. Chaillout, S.W. Cheong, Z. Fisk, M.S. Lehmann, M. Marezio, B. Monosin and J.E. Schirber, Physica C 158 (1989) 183. [9] P.E. Zolliker, D.E. Cox, J.B. Parise, E.M. McCarron III and W.E. Farneth (preprint) [ 10] A.H. Davies and R.J.D. Tilley, Nature 326 (1987) 859. [ l l ] Prahibha L. Gai and E.M. McCarron III, Science 247 (1990) 553. [ 12 ] D. Van Dyck, J. Danckaert, W. Coene, E. Selderslaghs, D. Broddin, J. Van Landuyt and S. Amelinckx, in: Computer Simulations of Electron Microscope Diffraction and Images, eds. W. Krakow and O'Keefe (The Minerals, Metals and Materials Society, 1989) p. 107. [ 13 ] J. Van Landuyt and S. Amelinckx, J. Solid State Chem. 6 (1973) 222. [ 14 ] B.G. Hyde and L.H. Bursill, in: The Chemistry of Extended Defects in Non-Metallic Solids (North Holland, Amsterdam, 1970) p. 347.