SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION

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SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION

J. van Landuyt

To cite this version:

J. van Landuyt. SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION.

Journal de Physique Colloques, 1974, 35 (C7), pp.C7-53-C7-63. �10.1051/jphyscol:1974704�. �jpa-

00215860�

JOURNAL DE PHYSIQUE Colloque C7, suppliment au no 12, Tome 35, DCcembre 1974, page C7-53

SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION

J. VAN LANDUYT

Rijksuniversitair Centrum Antwerpen, Middelheimlaan, 1, B-2020 Antwerpen, Belgium

RBsumB. - Le cisaillement cristallographique apparait &tre un mecanisme, contr81e par les dbfauts, de formation des oxydes de series homologues telles que T ~ O Z - ~ , WO,-% partir de leurs phases stcechiometriques respectives Ti02 et WO3.

A p r b l'introduction des relations entre la non-stachiometrie et les structures de cisaillement et la description des edifices structuraux, un certain nombre de modeles physiques sur la formation et la transformation de ces structures, et la propagation des defauts nkcessaires sont discutks.

Les moddes suivants seront successivement consideres.

l o Mise en ordre et cisaillement.

2 O

Propagation de dislocations partielles.

3 O Migration cooperative.

4 O

Propagation de couples de plans cristallographiques en forme d'tpingle a cheveu.

Ces differents mod&les sont analysts et confrontts aux connaissances rkcemment acquises par l'amelioration des techniques d'observation en microscopie Clectronique B haute rCsolution.

La plupart des observations ont 6tC faites sur le systeme TinOzn-l. Des rksultats recents obtenus par microscopie a tr&s haute resolution sur WO3 sont Bgalement discutes.

Abstract. - Crysfallographic shear appears to be a defect-controlled type of process for the formation of the oxides in the homologous series such as TiO2-,, W03-% out of their respective stoichiometric phases Ti02 and WO3.

After an introductory chapter on the relation between non-stoichiometry and shear structures, giving a geometrical description of these particular structural edifices, various physical models will be discussed for the formation and transformation of these structures and the propagation of the defects involved. SuccessiveIy the following models will be taken into consideration :

l o An ordering-and-shear model.

2 O

A partial dislocation propagation model.

3 O

A cooperative migration model.

4 O A model based on the propagation of hairpin shaped couples of crystallographic planes.

These various propositions will be analysed and confronted with the vast amount of knowledge that has recently been acquired from the advent of the improved high resolution electron micros- copy observation techniques.

The analysis will be mainly illustrated from observations in transmission electron microscopy of the TinO2n-1-system. Some very recent ultra high resolution observations in WOs-% will be

discussed as well.

1. Introduction.

A contribution on shear struc- tures and crystallographic shear propagation might a t first reflection be considered t o be out of the scope of a conference o n splitting of dislocations. However i t is the purpose t o illustrate that the formation and pro- pagation of crystallographic shear planes which are two-dimensional defects such as stacking faults or antiphase boundaries d o belong in a sense t o the type of extended defects that make u p the subject of this conference.

In recent years, and primarely due t o the improve- ment of resolution i n electron microscopy techniques there has been a lot of studies performed on non-stoi- chiometric oxides derived from W 0 3 [I, 21, Nb,O, [3],

and TiO, [4, 5, 61 and mixed oxides [7]. These studies, apart from investigating the particular microstructure of the various members of these homologous series of oxides, have also contributed a lot t o the fundamen- tal question as t o why and how the crystallographic shear structures form and how they propagate,. how the phase transitions between the phases occur, etc.

I t is the purpose of this paper to give a review of the recent findings and t o discuss the various models proposed for these processes i n the light of the obser- vations nearly down t o the atomic scale.

2. Non-stoichiometry and shear structures. - I t has for a long time been thought that the only oxides

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974704

C7-54 J. VAN LANDUYT

which a metal could originate were directly related to the valency states of the ions in solution.

Titanium e. g. which is known as Ti4+, Ti3+ and Ti2+ was only expected to form 3 oxides : TiO,, Ti,O, and TiO. Any deviation from the valency ratio was then indicated by a fractional index such as for Ti : TiO, -, where x could have values up till 0.3.

These materials have for a longtime been described as defective with respect to the stoichiometric compo- sition (S. C.) i. e. they were considered as solid solu- tions of Schottky and Frenkel defects or vacancies and interstitials.

This model (Schottky-Wagner) was acceptable for small deviations from S. C. (- but its validity became questionable for larger deviations.

There were for instance indications of structural nature that the transition from one S. C. to another was not a continuous one. To explain this behaviour it became necessary to conceive models where ordering of the point defects, as well short range as long range order, plays an important role.

The formation of shear structures is one and a rather spectacular way to do so which has recently gained lots of attention as well from physicists as from chemists.

@ Anion sites to be elhhded

(a)

3. Shear structures. - Some 20 years ago Ma- gneli [8] had detected by X-ray analysis of the systems W0,-WO, and Moo2-MOO, the existence of a large number of phases of the type (W, Mo),O,,-, i. e.

a homologous series of oxides with only slightly differ- ing compositions. Later other series of this type have been identified e. g. W,O,,-, by the group of Wads- ley [9] and Ti,O ,,,-, (with n = 5 ... 9) by the group of Andersson [lo]. These phases were called Magneli phases.

Another extensive series is derived from niobium pentoxide by substitution of part of the NbSf by Ti4+, Nb4+ and W6+ or part of the 02- by F-.

I t was observed that the structure of all these phases were always closely related with that of the stoichio- metric compound (WO,, TiO, and Nb,O, respecti- vely).

Phenomenologically this relation can be described as originating from a shear- and -collapse process which has been called crystallographic shear (abbreviated as CS), whereas the structures derived in this way are called : shear structures.

A definition of this model can be formulated : Crystallographic and periodic occurrence of changes

Shear ah[llol

FIG. 1. -Phenomenological model for creating a shear plane in a ReOytype structure (paper and scissor-model). a) Perfect ReOs-structure of corner sharing octahedra ; the cut along (310) is indicated ; b) The shear is performed along b ; c) If b is parallel with the shear plane a conservative antiphase boundary results ;

d ) (100)-shear plane.

SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION C7-55

in coordination or after Wadsley : the periodic occurrence of defects caused by the compression of a simple structure along well determined planes where the coordination polyhedra are joined in a different way than in the stoichiometric (simple) structure.

This definition becomes immediately evident by taking a closer look at the structures in question, in particular e. g. the W0,-series.

The W0,-structure can be described as a slightly deformed Re0,-structure which itself consists of an infinite tridimensional arrangement ofoctahedra [MO6], joined together by corner sharing (M stands for a metallic element) as illustrated in figure 1. If now the crystal is cut along a lattice plane (a typical shear plane for these structures is ( 130 )), and one crystal part is displaced as shown in figure lb, an arrangement is obtained where the octahedra along this plane are now joined by edges instead of the corners. It is clear that this mechanism changes the composition since along the plane because of the change in coordination one now has an excess of W with respect to the 1 : 3 ratio in the matrix. Such a plane is called a shearplane, or a CS-plane and if these shear planes occur periodi- cally one obtains a shear structure. WO, becomes W,,O,,-, where n is determined by the spacing and the orientation of the shear planes.

From this paper- and -scissor model it is furthermore clear it is essential that the vector describing the displa-

octahedral complexes and the arrangement of these along a ( 120 }-C. S. plane in W0,-,.

It is clear that this phenomenological description can also be used to describe other than unidimensional shear structures. There are several examples of two dimensional structures such as (W0,35V0,65)205, a mixed (W-V)-pentoxide whose structure was deter- mined by Israelsson and Kihlborg [12] to be as shown in figure 3.

-

cement must have a component perpendicular the _FIG. 3. -Structure of (W0.65V0.35)205 after Israelsson and

plane, otherwhise no compression or change in compo- Kihlborg [12].

sition does occur ; this is clear from figure l c where an antiphase boundary is formed (in fact shear planes

could be called ^: non-conservative antiphase bounds- Figure 4 clearly illustrates how this Structure could

ries). be derived from the Re0,-stacking of corner sharing

A paiticularly interesting proof for the occurrence octahedra by performing the C. S. procedure in two and the appearance of crystallographic shear planes stages along two sets of planes as indicated on the is shown in figure 2 due to Iijima [ll]. Using very high figure.

resolution technique in transmission electron micro- scopy he was able to reveal the individual [MO6]-

tc

FIG. 2. - Ultra high resolution electron micrograph of a CS- plane in WOs-, (Iijima [Ill). A projection of the structure model is juxtaposed in the same orientation for comparison.

FIG. 4. - Successive stages of two-dimensional CS-process.

If this process is repeated periodically, a structure is formed consisting of (4 x 4)-blocks of octahedraat two levels. The octahedra share the edges along { 110 }-planes. Between the levels there is only corner sharing of the octahedra.

This mixed oxide is a member of the group of oxides

derived from the Nb,O,-H structure which itself

C7-56 J. VAN LANDUYT

consists of (3 x 4)-blocks joined by edge sharing as structure, the relation being one of the shear structure mentioned earlier. These mixed oxides are formed by type as we defined in the previous paragraph.

partial substitution of the cations by elements with The rutile structure can be considered as being

other valencies. composed of chains of [TiO,]-octahedra (Fig. 7),

An example of the image of this structure obtained by TEM is shown in figure 5 here the 14 x 14 A blocks are visible [13]. Figure 6 shows a more recent observa- tion on the same material illustrating clearly the amount of detail that can nowadays be deduced from high resolution images.

FIG. 5. -Electron micrograph resolving the (110)-planes of (w0.65V0.35)205.

FIG. 7.

Rutile structure model illustrating the chains of edge-sharing octahedra. The chains are interlinked - - bv corner-

sharing.

linked by edge sharing. The chains themselves are interlinked by corner sharing. It is thus clear that in a similar way as for the Re0,-type structures changes in composition can be accommodated by changes in coordination. Because of the more complicated arrangement of the octahedra in chains a simple repre-

FIG. 6. - Ultra high resolution micrograph of the same material as in figure 4 illustrating the advances recently obtained in reso-

lution techniques.

(a)

A part from the shear structures derived from the Re0,-structure there are also a whole series of phases derived from the rutile Ti0,-structure of the type Tino,,-, which we will now describe in some detail

since our observations mainly concern this homolo- _(b) cma ^{: .}

^{; :}

^{: : : ; , . ,}

^.

^.

^{( c )}

gous series. b i [ F ! ! [ i , , j j j

j

/ j

j

-

JT+w+?;

_N.

4. Shear structures derived from TiO,. - A number ^-0. -0-

&. . . .. .. . . .

.-

- -.

-.--

of oxides in the Tino,,-, homologous series had

already some time ago been studied by X-ray analysis ..n..0-.~.0.. ^a a

and the structures of the members with varying from _{FIG. 8. -} Rutile structure. a) One unit cell of the tetragonal 4 to 10 determined [lo]. It appears that these strut- structure. 6 ) (a-c) and (ab)-projections of the idealized structure.

tures are quite closely related to the parent rutile ^c) The undeformed structure in the same projections.

SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION C7-57

sentation as for WO, is not possible ; we shall therefore make use of the structure description whereby the lattice of anions is considered as a close packed framework with the cations in interstitial (octahedral) sites [4].

Figure 8 illustrates this model in two projections in a slightly idealized drawing. In the (a-c) projection which shows two layers of the close packed oxygen framework it is seen how the cations occupy octahedral sites along rows (or chains) in the c-direction, filled rows of octahedra alternate with empty ones in the a-direction. The non-idealized structure has been juxtaposed for comparison in the same projections.

The same type of phenomenological description for crystallographic shear defects can now easily be visualized on the (a, c)-projection. This is illustrated in figures 9 and 10 for three types of possible sbear planes : (121), (132) and (011). It is clear that the (011)-plane is actually no shear plane for the displa- cement vector as indicated, but gives rise to a conven- tional antiphase boundary. Periodic occurrence of these CS-planes gives rise to the shear structures of the homologous series. One member, Ti,Og, is represented in figure 11. The regularly spaced (121)-CS-planes are marked by thick lines. A unit cell of the matrix is also indicated.

a b c

FIG. 9. - Successive stages in the creation of a (121)-CS-plane in rutile.

.O.O*

oO. *

.om

0 O * O . o e

0 0 0 * o 0 0 * 0 .

* * . *

. .

FIG. 10. - CS-plane in (132)-orientation and antiphase boun- dary in (011)-plane.

RG. 11. - Structure model for one member of the TinOzn-1 series : Tis09 as created by periodic (121)-CS-planes.

5. Observations. - In this chapter we present some experimental facts about the appearance and beha- viour of shear structures and CS-planes as observed in transmission electron microscopy and mainly in rutile. The non-stoichiometric rutile crystals have been prepared by in situ recrystallization of oxide films detached from oxidized titanium sheet by dissolution of the latter [4]. The films are initially non-stoichio- metric and can be intentionally further oxidized by beam heating to observe subsequent phases of the homologous series until nearly stoichiometric rutile with only isolated CS-planes is left as shown in figure 12. The fringe patterns correspond to CS-planes inclined with respect to the electron beam imaged just like stacking faults. They can be characterized by an a-value, a = 2 ng.R where g is the diffraction vector and R the displacement vector ; a is equal to n in this case 1141. A drastic rearrangement after a heating puls is shown in figure 13 where to the right the CS-planes are grouped in regular sequence giving ride to a block of shear structure.

Three particular members of the series are shown in figure 14 where the CS-planes are seen on edge as fine lines 151. The planes are of the { 132 )-type and the phases are respectively Ti,,O,,, Ti,,O,, and Ti,,O,,.

A typical diffraction pattern of an area containing matrix material as well is shown in figure 15. From the shift of the superlattice spots with respect to the

5

C7-58 J. VAN LANDUYT

FIG. 15. - Typical diffraction pattern of a (132)-shear structure.

FIG. 12. - Electron micrograph of nearly stoichiometric rutile. matrix spots the displacement vector could be derived

I I

The zip-zag shapped fringe patterns are inclined isolated CS- _planes. being < 155 > which is close to < ^{01 1} >

expected from the structural model [15].

An unexpected experimental fact was the plane that was deduced from crystallographic diffraction analysis such as illustrated in figure 16. The plane of these isolated defects was determined as { 275 ). However

FIG. _13. - Rearrangement configuration of a group of CS- planes. Before and after a heating puls in the microscope.

FIG. 14. - Lattice images of three members of Ti,O~~-~-series.

They correspond resp. with TiloOlg, Tit 5 0 2 9 and Tiz805s- compositions.

FIG. 16. - CS-pIanes in nearly stoichiometric rutile oriented

for the determination of the plane of the defects : (275).

SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION (27-59

detailed analysis also by others (Bursill and Hyde [6]) revealed that shear plane intergrowths do occur in rutile and any plane such as :

is a possible shear plane ; the orientation of the plane is related to the amount of non-stoichiometry to be accommodated. Various possible intergrowth planes are drawn in figure 17.

SHEAR PLANE INTERGROWTHS Rutile

FIG. 17. - Schematic illustration of various intergrowth orien- tations for the CS-planes in Ti02 in the same projection as

figure 8b.

Two particularly interesting heating sequences of isolated configurations of CS-planes are illustrated in figures 18 and 19. They prove that these interfaces can perform two distinct types of motion. Figure 18 shows the elimination of a closed rectangular loop of fault. It is clear that certain segments of the loop must move perpendicular to themselves. This movement must be the result of cooperative jumps of titanium ions from one interstice in one row to an interstice

in the next row along a whole plane. Figure 19 shows the progressive elimination of interfaces by a longitu- dinal change in extent ; this movement implies a combi- nation of climb (non-conservative) and glide (conser- vative) motions. Between successive photographs the crystal was heat pulsed. The same type of cooperative diffusion has been postulated independently by Wadsley and Andersson [9] in the models that will be discussed hereafter.

However the behaviour as observed for inclined boundaries in figure 19 could also be due to the withdrawal of two closely spaced CS-planes pinched off at the top of the hairpin kind as visible in figure 20.

6. Models for the generation and propagation of crystallographic shear planes. - It is clear that the paper- and- scissor model described in paragraph 3 is not realistic : it is only a good phenomenological description for shear structures and their crystallo- graphic relation with the parent oxide.

In recent years a number of mechanisms has been proposed for the generation of shear planes. All such mechanisms describe how a stoichiometric crystal of the type MO, or MO, can be transformed into a non- stoichiometric one by the regular introduction of shear planes generating in this way compounds of homolo-

gous oxide series.

The details of the proposed mechanisms are different however ; we shall briefly point out the main characte- ristics of the mechanisms which have been put forward sofar. We shall then present some observations which seem to suggest that none of these mechanisms is entirely satisfactory and discuss their particular appli- cability.

6 . 1 ORDERING AND SHEAR MODEL. - According to this model due to Gado [16] the crystal looses oxy- gen and on doing so anion vacancies are produced which migrate into the crystal and subsequently order

FIG. 18. - Dynamical sequence of a closed loop of CS-planes heated in the electron microscope. In d ) the loop has

disappeared completely. This sequence clearly implies lateral movement of the boundaries.

C7-60 J. VAN LANDUYT

FIG. 19. - Heating sequence illustrating longitudinal shrinkage of CS-planes.

FIG. 20: - Typical area with closely spaced CS-planes where clearly some hairpin shaped arrangements are observed.

into walls across which the crystal subsequently shears, annihilating in this way the vacancies and generating a shear plane. The model does not give any details about the mechanism by which shear planes can move. The Gado model is pictured in figure 21 for the case of Re03.

Characteristics. - a) Ordering spots should be present in the diffraction pattern before the shear structure is formed.

b) Shear planes are always very regularly spaced.

c ) No isolated shear planes occur.

Remarks. - This very hypothetical model does not agree with the hitherto reported observations. Only very recently some evidence is reported for the pre- shear ordening of point defects in WO, [ll].

qriioJ,

@ m e t a l at m = 0 , cnlon ot z = t 2

0 onion at I = O anion vacancy r ^bR

FIG. 21. - Ordering and shear model (Gado) in ReOs-type structure.

6 . 2 THE DISLOCATION MODEL. - In this model proposed by Anderson and Hyde [17] the anion vacancies form disc-shaped aggregates which collapse and generate in this way vacancy loops limited by partial dislocations. The dislocations now act as vacancy sinks and attract further vacancies which make the dislocation loops grow by climb extending in this way the shear plane. The mechanism is represented schematically in figure 22.

Characteristics. - a) Initial stages should show faulted loops or shear planes limited by dislocations.

b) Shear planes grow longitudinally.

c ) No lateral displacement takes place.

SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION C7-61

~ b i o l ,

0 anlor; at 2.0 9 onion vacancy 2

I---+

? ' b

@ metal ot z = O , anlon ot z=l/;,

1%

FIG. 22. - Dislocation model (Anderson and Hyde).

Remarks. - Dislocation limited shear planes are only occasionally observed and mostly in materials approaching the stoichiometric composition from larger deviations.

Lateral displacement is necessary for the subsequent ordering of the shear planes into the shear structure:

6.3 THE COOPERATIVE MIGRATION MODEL. - Anders- son and Wadsley [9] assumed cation planes to move

cooperatively into the crystal. The cations jump hereby into adjacent empty interstices in the way shown in figure 23. Oxygen is released at the surface each time a cation plane moves into the crystal.

Characteristics. - a) Isolated shear planes are easily accounted for.

b) The crystallography is expected to be determined by the surface.

c) No longitudinal growth of shear planes takes place.

Remarks. - As pointed out by Bursill and Hyde [I81 the occurrence of single shear planes requires the cooperative movement of a very large number of ions. The model does not account for longitudinal growth of the CS-planes. This model implies cation interstitial mobility.

6.4 THE HAIRPIN PROPAGATION MODEL. - Van Lan- duyt and Amelinckx [I91 have proposed an alternative model based on observations of non-stoichiometric rutile, where hairpin shaped arrangements of CS-planes were observed. For comparison reasons the model is represented for Re0,-type structures in figures 24.

It is assumed that the non-stoiclziometry results from loss of oxygen at internal or external surfaces, and the simultaneous inward migration of cation interstitials.

Nucleation of loops of shear planes occurs at the surface where e. g. a narrow strip of anions is lost releasing oxygen and simultaneously a strip of cations moves inwards from the surface. The active area in this

0 o n ~ o n at z = 0 @ m e t a l at 2 = 0 ,

¹ anlon to gas anion at z=1/2

r"

FIG. 23. - Cooperative migration model (Wadsley and Andersson) figures 21, 22 and 23 after Bursill and Hyde [18].

C7-62 J. VAN LANDUYT

cation at z = o , anion at z = 1

2 o anion at z - o 0 cation interst.

FIG. 24. - Hairpin model illustrated in the ReO3-structure for easy comparison with models I, 11 and III (J. van Landuyt and

S. Amelinckx).

model is clearly the tip of the hairpin where as well cooperative jumps as interstitial migration occurs.

Propagation of this tip creates a couple of CS-planes in its wake.

Characteristics. - a) 'Hairpin shaped CS-plane arrangements should be observed.

b) Isolated cS-planes'can occur since lateral motion is easily accounted for by longitudinal propagation of steps as shown in figure 25.

FIG. 25. - Schematic illustration of a mechanism for lateral growth by longitudinal propagation of ledges.

Remarks. - Until1 now the hairpin shaped arran- gements have only been observed in Ti0,-, and in some periodic antiphase boundary structures.

7. Discussien. - The ordering and shear model 1 lacks at this moment satisfactory experimental evi- dence. The pre-shear ordering phase should yield supplementary diffraction spots which have not been observed as yet.

The dislocation model I1 gives an excellent means for longitudinal growth of CS-planes by dislocation climb. However, the nucleation stage of closed loops of CS-planes has not been observed as yet. Models I11 + IV are somewhat related and one could say that the mechanism for sideways motion of the CS-planes in model IV is in fact the cooperative migration of model 111. That the side ways movement is real can be observed from the rearrangement confi- guration shown in figure 26 and of course from the earlier discussed sequence in figure 18.

FIG. 26. - a) Quasi-regular configuration of a limited number of shear planes where the defects are still coupled two by two.

b) Rearranged configuration of a limited number of shear planes.

The side faces of the hairpins in model IV are

formed by particularly stable interfaces. The orienta-

tion of these faces determines which homologous

series is being formed, whereas the concentration of

shear planes or their spacing determines which member

of the series is being generated (i. e. value of n). This

can be deduced from figure 27 where model IV was

represented for the rutile structure in the close-packing

arrangement. (121)-CS-planes introduce more changes

in coordination than (132) and certainly than (011)-

SHEAR STRUCTURES AND CRYSTALLOGRAPHIC SHEAR PROPAGATION C7-63

(011) o anion cation

@ cation interst.

FIG. 27.

Hairpin model illustrated for three favorable shear plane orientations in rutile.

planes that only become conservative antiphase boun- daries with some coordination errors at the tip of the couple.

Model IV is furthermore in accord with the results of a review paper by Hurlen [20] who concludes that the non-stoichiometry in rutile results from titanium interstitials. In a recent critical review Kofstad [21]

also concludes that at high temperatures and low pressures interstitial titanium ions are the predomi- nating defect in oxygen deficient rutile. The mechanism explains in one model the formation of shear planes, their lateral displacement and longitudinal growth

necessary for the formation of the shear structures in TiO,. It is furthermore in agreement with all the hitherto reported observations.

The formation of the two-dimensional shear struc- tures is easily accounted for.

It has also a striking resemblance with the mecha- nisms proposed recently for the formation and pro- pagation of the dissociated antiphase boundary arran- gements in periodic APB-structures such as in the X-phase 1221, Ni,Mo [23], and [24]. Also in the Cu,Au-system often hairpin shaped couples of anti- phase boundaries are observed [25].

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