I. GENERAL DISLOCATION THEORY, STRUCTUREAND PROPERTIESRelation Between the Fine Structure of Dislocations and theCrystal StructureBY S. AMELINCKXS.C.K.-C.E.N., Mol (Belgium)Received 13th July, 1964The detailed structure of dislocations reflects the crystal structure especially if the Burgers vectorbecomes large, which is likely to be the case in relatively complicated crystals. The dissociationof dislocations into ribbons of stacking faults is most easily observed in layer structures because theglide planes are then parallel to the plane of observation in electron microscopy. For a number oflayer structures striking combinations of stacking fault ribbons and dislocations, which can readilybe interpreted on the basis of the crystal structure, have been observed.Ribbons consisting of two,four and six partials are discussed in relation with the structures of tin disulphide, talc and thechromium halides respectively. The observation of ribbons allows to deduce values for the stackingfault energy.Originally a dislocation line was thought of as a linear discontinuity withoutmuch structure. This simple picture is a reasonably good description as long asone ignores the details of the crystal structure. However, dislocations in realcrystals present usually a fine structure which has a close connection with the crystalstructure.The first successful attempt to relate the dislocation structure to the crystalstructure is due to Heidenreich and Shockley.1 These authors pointed out thatglide dislocations with a Burgers vector a/2 [ l i O ] in (111) planes of face-centredcubic metals should under certain circumstances be extended, i.e., should consistof two partial dislocations with Burgers vectors a/6 [2ii] and a/6 flTI].Betweenthe two partials the normal stacking sequence is perturbed: these is a stackingfault. In face-centred cubic metals this fault is equivalent to one lamella in thehexagonal arrangement. The simplest glide dislocation in one of the simpleststructures thus turns out to have already a fine structure : two partial dislocationsand the associated ribbon of stacking fault. The whole assembly is called anextended dislocation or a ribbon. The concept has been very fruitful since it allowedone to explain qualitatively and even quantitatively the differences in behaviourwith respect to plastic deformation of different face-centred cubic crystals.Theelectron microscope has brought striking direct confirmation of the existence ofextended dislocations. Moreover, as a result of the electron microscopic observ-ations in a large number of substances, it became clear that more complicatedarrangements of partials and stacking faults occur. In most cases, an obviousand direct relation between the dislocation fine structure and the crystal structureis found. It is the purpose of this paper to discuss this relationship on the basis ofthe electron microscopic evidence.8 FINE STRUCTURE OF DISLOCATIONSGEOMETRY OF GLIDE PLANESThe movement of dislocations usually takes place on those planes for which thebinding between successive layers is weakest.These planes are usually the closest-packed planes. In a number of crystals the geometry of the glide planes can beapproximated by a close-packed planar arrangement of rigid spheres (fig. 1,a). Ifthis is the case the relative glide movement of two such planes from one position tothe next crystallographically equivalent one takes place in two steps as shown infig. 1. This can immediately be " felt " if one tries to slide the two rigid layers ofspheres one with respect to the other. The two steps result because the spheres inone layer tend to follow, during their movement, the valleys in the other layer ofspheres. This picture is the basis of the Shockley partial scheme, each glide stepcorresponding to one partial.In a number of crystal structures the glide planeshave this structure. A number of such structures are tabulated in table 1. Themost probable position of the glide plane is indicated by means of an arrow.TABLE 1structure stacking symbolcadmium iodidecadmium chloridemolybdenum sulphide aBatbubta/3atbab. . .chromium chloridediamondwurtzite aatbbtaatbp . . .aylbtcPlatbalc . . .aa t bB t CY t aa t bB t CYA complication immediately arises if these layers are "defective ". Let usconsider for example the arrangement of fig. 1,b which occurs in silicate layer struc-tures. The presence of regularly arranged " vacancies " increases the repeat distanceO r O 0A A 80 0 0 0(4" O O O O (6)0 0 0 00 0 00 0 .0 .0 0(c) . "AX2. 0xt0 . 0 0 A0 0 .FW. 1 . 4 ~ ) Close-packed layer of spheres-a glide path is indicated; (b) ring pattern of spheresof the type occurring in silicate layer structures ; (c) closepacked layer with two different kinds ofatoms ; (d) graphite ring pattern.in the plane and as a result the number of elementary glide steps may become largerthan two. In the particular case shown, the nearest crystallographically equivalentposition is reached after four steps. Longer glide paths may be considered; oneconsisting of eight steps is indicated in fig. 1,bS. AMELINCKX 9The same type of complication may arise because all atoms in the close-packedlayer are not of the same chemical nature (fig. 1,c) or because layers adjacent to theclose-packed layers, between which glide takes place, are defective.As a resultof this, the atoms which make up the close-packed layers are no longer equivalent ;the repeat distance increases and hence the number of glide steps increases as well.An example of this is met, e.g., in the chromium chloride structure (fig. 2). Thechromium ions form a hexagonal ring pattern in the octahedral interstices betweentwo close-packed chlorine layers. As a result two kinds of chlorine ions are tobe considered. The shortest repeat distances are now of the type X1X2 and follow-ing the valleys this distance can be covered in four unit steps as shown in fig. 2.0, 9, chlorine; 0, chromiumFIG. 2.-Sandwich layer of the chromium chloride and chromium bromide structure.The unitcell is outlined by means of a double line.One therefore expects the dislocations to be split into four partials, each partialperforming one slip step. The details of this process are discussed below.The idealized titanium oxide structure offers another example. The structureconsists of a hexagonally-packed arrangement of oxygen atoms containing titaniumions in octahedral interstices. The filling of the interstices by titanium ions is asfollows. In one plane filled and empty rows of octahedral interstices alternate.In successive layers the filled rows alternate as well. This idealized structure isshown in fig. 3 4 b. It is now evident that the repeat distance depends on the direc-tion of the Burgers vector. For the [Ool] Rurgers vector it remains the same as forthe oxygen lattice, but in the directions [ l O i ] and [ O i l ] it has doubled.In the lattercase, dissociation into partials takes place.Filling some of the interstices between the layers which glide one with respectto the other may also result in an increased repeat distance. Let us consider, forexample, the structure of aluminium oxide whereby 3 of the octahedral intersticesin one layer are filled according to the ring pattern of fig. 4. It is clear that theshortest identity vectors have become of the type X1X2. They can be decomposedin four unit steps [2].We shall now apply these principles to a number of structures and comparethe predictions with the observations10 FINE STRUCTURE OF DISLOCATIONSCLOSE-PACKED STRUCTURESNO DISSOCIATIONWe shall first consider structures where glide takes place between close-packedplanes and where as a result the geometrical conditions for dissociation in Shockleypartials are satisfied.Even in such cases it is possible that undissociated dislocationsare observed ; this is due to the fact that the stacking fault energy may be too large.ab CFIG. 3.-Idealized titanium oxide structure projected on the (100) plane of rutile.FIG. 4.-Aluminium oxide structure projected on the basal plane.Examples of crystals where this occurs are aluminium,3 antimonium telluride andbismuth telluride.4In other close-packed structures the glide plane may be different from the close-packed plane. This is, e.g., the case in crystals with the sodium chloride structure,such as magnesium oxide and nickel oxide.In these crystals the (1 10) plane func-tions as a glide plane. If a dislocation with a a/2 [110] Burgers vector and a (1iO)glide plane should dissociate the atom configuration in the faulted region wouldbe such as to bring ions with the same sign in contact. This leads to an excessivelylarge stacking fault energy of Coufomb origin and hence to undissociated dislocationsS. AMELINCKX 11A similar reasoning applies to the calcium fluoride structure ; as a result dislocationsare found to be undissociated in substances like uranium dioxide and calciumfluoride.5~ 6DISSOCIATION INTO TWO PARTIALSLOW STACKING FAULT ENERGY ALLoys.-The Simplest example Of dissociationinto two partials is found in the low stacking fault energy alloys.7 Such alloys areformed if to a face-centred cubic metal an impurity is added which, when presentin sufficient concentration, would give rise to a hexagonal phase.Adding aluminiumto copper or tin to silver decreases, for instance, the stacking fault energy. In suchalloys the dislocations are visibly extended (fig. 5). From contrast experiments itwas possible to establish that these faults are of the intrinsic type.8CADMIUM IODIDE smucmm.-The A X 2 cadmium iodide structure offers a par-ticularly simple example of glide between close-packed planes. This structurecan be described by the stacking symbol aybaybayb . . . The italic lettersrepresent the anions or X-ions, while the greek letters represent the cations or A-ions.The close-packed planes of cations are sandwiched between two close-packed layers of anions. They occupy the octahedral interstices. The bindingbetween two successive X-layers is probably weaker than between an A- and an X-layer. This results in easy cleavage and glide between the two close-packed X-layers. As a consequence partials with Burgers vectors of the type Ao, Bo or aA,aB are to be expected.* They have indeed been found in cadmium iodide and tindisulphide.9 The ribbons are particularly wide in tin disulphide, of which an exampleis shown in fig. 5. Glide on the X-X glide plane produces a stacking fault of thetype ayb ayb cpa cpa . . . which can be considered as one lamella in the cadmiumchloride structure for which the stacking symbol is ayb cpa bac .. . The sand-wiches XAX remain unsheared in this process. Similar ribbons are observed inthe closely related cadmium chloride structure as, for instance, in nickel bromideby Price.10 In this case the stacking fault is one lamella of the cadmium iodidestructure.MOLYBDENUM smPmE.-Dislocations in this substance have been studied bya number of investigators.11-13 At least two different kinds of dislocations havebeen found : undissociated dislocations and widely dissociated dislocation ribbons(fig. 7). The structure of molybdenum sulphide can be represented by the stackingsymbol apa bab afla bab . . . The italic letters refer to sulphur ions and the greekletters to molybdenum ions.The binding between two sandwiches limited bysulphur layers is mainly of the van der Waals type and hence considerably weakerthan the covalent bonds between molybdenum and sulphur. It is therefore reason-able to expect that s-S glide, i.e., glide between two sulphur layers will be easierthan MoS-glide. A priori it might even seem unlikely that glide on MoS-glide planeswould take place at all. However, as we shall see, the observations are consistentwith the two types of glide planes. The structure of molybdenum sulphide is shownschematically in fig. 8 ; the complete Burgers vectors are of the type AB as referredto fig. 8. For both assumptions concerning the location of the slip plane in thestructure, glide takes place between close-packed layers and on a purely geometricalbasis dissociation into partials is possible in either case.Whether a visible dis-sociation occurs or not will depend on the value of the stacking fault energy. Inthe same specimens one finds an almost equal fraction of very wide ribbons on the* Use is made of a modified Thompson notation for denoting Burgers vectors, see, e.g., ref. (25)12 FINE STRUCTURE OF DISLOCATIONSone hand and of undissociated dislocations on the other hand. The Burgers vectorsof these different types of dislocations were determined using the extinction criteriumg.b. = 0. In this way one finds that the undissociated dislocations or the singledislocations have Burgers vectors of the type AB of the partials in the ribbons haveBurgers vectors of the type Aa+oB.The simplest way to account for these twoFIG. 8.4tructure of molybdenum sulphide as projected on the c-plane. 2 I ’’ \ I ‘ /’_--_--i a ) tbl (C)FIQ. 9.--(a) View in space of the molybdenum sulphide structure emphasizing the bond directions ;(b) projection on the c-plane of the normal environment of the molybdenum ions ; (c) projectionon the c-plane of the distorted environment of the molybdenum ion resulting from Mo-S glide.FIG. 10.-Analysis in terms of Burgers vectors of fig. 7. Use is made of an adapted Thompsonnotation.types of dislocations or stacking faults is to assume that MoS-glide as well as SS-glide takes place. On SS-glide the environment of the molybdenum ions will notchange, i.e., the normal orientation of the covalent bonds along the diagonals ofthe triangular prism will be conserved (fig.9a). On the other hand, MoS-glideover a vector like Aa would give rise to a stacking sequence a/3ababaybcpc . . .whereby the environment of the molybdenum is wrong in one layer ; this environ-ment is shown in fig. 9 c ; and it is clear that the MoS bonds are now orienteS. AMELINCKX 13differently. It is therefore reasonable to assume that the high-energy stacking faultis associated with glide on an MoS type glide plane whereas the low-energy stackingfault is associated with SS-glide. The interaction between a perfect dislocation anddislocation ribbons is visible in fig. 7. The analysis in terms of Burgers vectorsof this photograph is shown in fig. 10. It is now clear that for one family of partialsthe Burgers vectors at the crossing perfect dislocations are mutually perpendicularexplaining the small degree of interaction whilst for the other family they are atan angle of 30" giving rise to strong interaction.This analysis confirms indirectlythe model given above.SUPER-LATTICES IN CLOSE-PACKED STRUCTURES : ORDERED ALLOYSConsider for simplicity the dislocations in the ordered AuCu3 superlattice.The passage of a dislocation with Burgers vector a/2-[110] restores the geometricalorder but leaves a so-called anti-phase boundary as represented schematically on atwo-dimensional model in fig. 11. A certain energy per unit area is associated witho e o e o e o e o e oe o e o o o e o e o e0 . 0 e o e o e 0 .00 e o o 0 0 e 0 e 0 .o e o e o e o e o e o e 0e o e o e o e o e o o o eFIG. 11 .-Two-dimensional model for a strip of anti-phase boundary limited by two dislocationsin an ordered alloy.such an anti-phase boundary. A second perfect dislocation in the same glide planeand following the first one restores both geometrical and chemical order. Fromthese considerations it will be evident that the two perfect dislocations are coupledby means of a strip of anti-phase boundary. Depending on the specific energy ofthis boundary closely or more widely coupled perfect dislocations will result. Sincemoreover each perfect dislocation may split into Shockley partials, ribbons of fourcomponents tend to form. A model for such a ribbon is shown in fig. 12.If thestacking fault energy is large and the anti-phase boundary energy small one willonly observe coupled perfect dislocations. The distance between these perfectdislocations depends on the anti-phase boundary energy in the same way as thedistance between partials depends on the stacking fault energy. The anti-phaseboundary energy itself will depend on the ordering parameter ; in completely dis-ordered alloys there will be no coupling since the ordering parameter is zero; thedistance would be minimum in the completely ordered alloy. An example of so-called super-dislocations in the ordered alloy Ni3Mn is shown in fig. 13.14 Couplingof dislocations due to ordering also takes place in the suboxide of niobium whichresults from the ordering of interstitial oxygen in niobium metal 146 (fig.14). Thesuperlattice unit cell of this suboxide as referred to the body-centred niobiumstructure is outlined in fig. 15. For two of the [ l l l ] directions of the niobiumlattice the repeat distance is not doubled in the suboxide lattice. In the two other[ill] directions, this is the case. This remark explains the co-existence of singledislocations and super-dislocations visible in fig. 1414 FINE STRUCTURE OF DISLOCATIONSDISSOCIATION I N MORE THAN TWO PARTIALS: CHROMIUM CHLORIDEAND CHROMIUM BROMIDEThe structure of chromium chloride can be described as a cubic close-packingof chlorine ions with the chromium ions in octahedral interstices. The chromiumions are arranged in layers and build a ring pattern similar to that in graphite leaving6 of the sites unoccupied.The chromium layers alternate with two chlorine layersfollowing the scheme, aylb cpla balc, where the greek letters represent chromiumand the italic letters chlorine. The index indicates the 3 of the sites which are leftempty. The structure can be referred to a hexagonal unit cell which is shown inprojection on the c-plane in fig. 2. The unit cell is indicated by the double line;Stacking faultAnti -Phase boundaryFIG. 12.-Model for a ribbon of four dislocations in an ordered alloy of the type AuCu3. Stackingfaults and anti-phase boundary are indicated by a different cross-hatching.it is three such sandwiches high. Since all observed dislocation patterns are situatedin the foil plane, which is the c-plane, it is justified to conclude that the c-plane isthe main glide plane.It is almost obvious then to locate the glide plane betweentwo chlorine layers since the binding is weakest there. Ball model considerationsshow that the possible glide movements have perfect Burgers vectors of the typeXlX2 and its five equivalent vectors.From the projection of fig. 2 these vectors can dissociate into four partial vectorsof the Shockley type according to the scheme,- -X& = a+&+;+>.A crystallographically equivalent position can also be reached after 6 steps in thedirection XI X3 and in the crystallographically equivalent ones. This large vectorcan be decomposed into 6 partial vectors according to the schemS. AMELINCKX 15Whereas in the first case the glide path has to “ go around ” one atom, the glide pathhas zig-zag shape in the second case.The observations show a majority of six-foldribbons which seems to suggest that most glide is according to the second scheme.This can be understood on the basis that the zig-zag path is a better approximationto a straight line than the “ around the corner” path. All simple glide paths areindicated in fig. 2. The conclusion from the previous paragraph can be formulatedin dislocation language by saying that perfect dislocations in chromium chlorideform either multi-ribbons of four partials separated by three stacking faults or ofsix partials linked together by five stacking faults. Both types of multi-ribbonsFIG. 15.-Unit cell of niobium suboxide referred to the parent body-centred structure of niobium.have in fact been observed ; six-fold ribbons are shown in fig.16. The modelsfor these multi-ribbons are represented in fig. 17. Whereas in the six-fold ribbonsonly partials with two different Burgers vectors occur, three different Burgers vectorsoccur in the four-fold ribbons. The models for these different ribbons have beenconfirmed by contrast experiments. It has further been shown 15 that the relativespacing of the partials is directly related to the relative energies of the differentstacking faults present in the ribbons. It turns out that a wrong stacking of thechlorine ions as well as a wrong stacking of the chromium ions contributes to thestacking fault energy.The stacking fault with the highest energy results whenthe stacking of the chlorine ions is wrong and when moreover the two layers ofchromium ions come one vertically above the other. For a detailed analysis werefer to ref. 15.The structure of chromium bromide is closely related to that of chromiumchloride. The bromine ions are hexagonally close-packed with the chromium ionsin octahedral interstices. The structure consists again of the same sandwiches asin the chromium chloride structure, only differently stacked. In this case againthe high-energy stacking fault results when in successive layers the chromium ionscome all one on top of the other. Again six- and four-fold ribbons are observed,however, the succession of stacking faults of different energies is different, givingrise to ribbons of a different aspect (fig.16,b)16 FINE STRUCTURE OF DISLOCATIONSCOVALENT STRUCTURESDIAMOND STRUCTUREThe diamond structure can be represented by the symbol aab j3cy aabpcy . . .Glide is presumably easier between the planes a and a (21 and j3, or c and y) becausethis implies breaking the smallest number of bonds. However, dissociation intopartials has to take place between two close-packed layers, i.e., between a and b, pand c, or y and a. The stacking fault resulting from glide on the (1 11) plane wouldthen have the structure ctabpcy bbc yaa bpc yaa . . ., i.e., it would consist of onelamella of the wurtzite structure. An undissociated dislocation is shown in fig.18,a. A dissociated dislocation containing an intrinsic fault is represented in fig.18,b.Dissociation with formation of a ribbon containing an extrinsic fault leadsto the structure shown in fig. 18,c.FIG. 17.-Models for multi-ribbons in the FIG. 18.Dislocations in the diamond structure :chromium halides. (a) undissociated dislocations ; (b) dislocationribbons containing an intrinsic fault; (c) dis-location ribbons containing an extrinsic fault.In silicon crystals twisted about a [1 1 11 axis at 1200°C and then slowly cooled,hexagonal networks lying in the (111) plane perpendicular to the twisting axis wereobserved.16 In these networks all nodes are dissociated. One family of nodescontains an intrinsic fault the other an extrinsic fault. A schematic view of thegeometry as well as the lettering pattern are shown in fig.19, while fig. 20 representsan observed region. A cut along the lines XY and UV of fig. 19 is given in fig. 18.This cross-section shows the structure of the intrinsic and extrinsic faults respectively.The conclusion from these observations is that in silicon and also in germanium,intrinsic as extrinsic stacking faults have small energy.16, 17 Observation on stackingfault triangles in silicon are in accord with this conclusion.1FIG. 5.-Extended nodes in a copper 4 % aluminium alloy (by courtesy of A. Art).[See page 11.FIG. 6.-Wide dislocation ribbons in tin disulphide. Note the presence of a triple ribbon.[See page 11.[To face page 1 6 FIG. 7.-Dislocation ribbons and undissociated dislocations in molybdenum sulphide.The analysisin terms of Burgers vectors is given in fig. 10.[See page 11FIG. 13.-Super-dislocations in the ordered alloy Ni3Mn (by courtesy of Marcinkowski).[See page 13.FIG. 14.--Single and super-dislocations in ordered niobium suboxide (by courtesy of J. Van Landuyt).[See page 13FIG. 16.--Multi-ribbons in chromium chloride (a) and chromium bromide (b).[Seepage 15FIG. 20.-Network of extended nodes in silicon crystal deformed by twisting about the [ l l l ] axis[See page 16.perpendicular to the foil plane. The inset shows extended nodes in germanium.PIG. 23.-Extended node in aluminium nitride seen under three different contrast conditions.[See page 18FIG. 25.-Ribbons in indium selenide seen under different contrast conditions (by courtesy ofMarinkovic).[Seepage 19.FIG.28. Dislocation configurations in graphite seen under two different contrast conditions.Note the presence of a triple ribbon, which is completely out of contrast in (b).[Seepage 20FIG. 33.-Multi-ribbon in talc seen under different contrast conditions showing that alternatingpartials of the quartet have the same Burgers vectors as in the model of fig. 32.[See page 23FIG. 37..-Change in width of ribbons in tealite on crossing an anti-phase boundary AB of the[See page 24.type shown in fig. 36 (by courtesy of V. Marinkovic)S. AMELINCKX 17THE WURTZITE STRUCTUREAluminium nitride, for instance, crystallizes in the wurtzite structure whichcan be described in terms of the close-packing of spheres by means of the symbolsequence aab paa bp.Here a or p denotes nitrogen, and Q or b aluminium. Fig.214 is a schematic view of the structure as seen along the c-direction while the cross-section is shown in fig. 21,b. Since all observed dislocation patterns are situatedFIG. 19.-Geometry of network of extended nodes in silicon. Cross-sections across the two typesof ribbons are shown in fig. 18,b and c.a-P-a-d-b-FIG. 21.-The wurtzite structure : (a) projection on the c-plane ; (b) side view along the directionAU showing the two types of glide planes I and LI.in the c-plane this plane must be the main glide plane.19 Like in the diamond struc-ture there are two possible locations for the glide planes ; either between a and p,or a and b, or between b and p (or a and a) ; these will be called type I and type I1glide planes respectively.They are indicated in fig. 21,b. The perfect 60" dis-location in type I1 glide planes can be represented as in fig. 2 2 4 In this dislocationmodel the number of AlN bonds to be broken on motion is smaller than that for thetype I glide plane. However, it is not clear how such a dislocation could dis-sociate into partials. However, this becomes possible if the glide plane is of type I18 FINE STRUCTURE OF DISLOCATIONSThe extended 60" dislocation in type I glide planes would then appear as representedin fig. 22,b or c. The glide vectors of the partials are indicated as Aa and aB withrespect to fig. 21. The fault within the dislocation ribbon would have the stackingb/3aabpcyaacyaa which is equivalent to one lamella of the sphalerite structure,which can be symbolized as aorb/Icyaab/3cy, as shown in fig.22. The observationsprove that dissociation takes place; fig. 23 shows an extended node in the sub-limation-grown platelet of aluminium nitride.8FIG. 22.-Dislocations in the wurtzite structure : (a) undissociated dislocations ; (b) and (c) twopossible ways of dissociating into patials for the dislocations (a). The arrows indicate the atommovements.Sublimed crystals of zinc sulphide were studied by Blank et aZ.20 The crystalswere in the wurtzite (high-temperature form) when grown ; on cooling the stackingfault energy becomes effectively negative and all dislocations which are present inthe basal plane split into infinitely wide stacking fault ribbons transforming in thisway one lamella of wurtzite into the sphalerite structure. This could be deducedfrom the diffraction pattern which shows streaking in the c-direction due to faultson the c-planes.Moreover, it shows the spots due to the sphalerite modification.21In view of the polar nature of crystals of the sphalerite and of the wurtzite type,dislocations of opposite sign can also be distinguished from a chemical point ofview. In AlN, for instance, one can distinguish " Al" dislocations and " N "dislocations; by this we mean that for an edge dislocation the supplementary halfplane would end in the one case on a row of Al-ions-in the other case, on a rowof N-ions.It would be of interest to compare the width of " aluminium ribbons "with the width of " nitrogen ribbons ". Contrast experiments distinguish the twokinds of ribbons ; it is sufficient to determine the sign of the dislocations.STRUCTURES RELATED TO THE WURTZITE STRUCTUREThe structure of the sulphides and selenides of gallium and indium is closelyrelated to that of wurtzite ; 22 it consists of four-layered lamellae which can be de-scribed by a symbol like aPPa. A schematic view of such a four-layer lamella isshown in fig. 21. In gallium sulphide and in indium selenide, e.g., the stackingsymbol is a p fi a b a a b a p /3 a. The binding within the four layer lamellae is oS . AMELINCKX 19the covalent type and hence very strong. However, the binding between four layerlamellae is of the van der Waals' type.Glide will therefore preferentially take placebetween two close-packed sulphur or selenium layers and again dissociation intoShockley partials becomes possible. An example of dislocation ribbons observedin indium selenide is visible in fig. 25.23 The photograph shows two different con-trasts of the same area allowing a Burgers vector determination. The resultingvectors are indicated on the photograph.FIG. 24.-Four-layered lamella occurring in the structures of InSe, Gas and GaSe.GLIDE BETWEEN CLOSE-PACKED LAYERS WITH OMISSIONSTWO PARTIALS; GRAPHITEThe structure of graphite is shown schematically in fig. 1,d and in fig. 26. Itconsists of a stacking of hexagonally linked layers of carbon atoms as shown inprojection in fig.26,a. The normal stacking can be described by the symbol a b a b a b . . ., i.e., half of the atoms come vertically above each other. X-ray evidence forthe occurrence of rhombohedra1 graphite with a stacking symbol a b c a b c (fig.26,b) is found occasionally in deformed samples. The c-plane is the glide andcleavage plane. In cleaved specimens all dislocation arrangements are thereforeparallel to the plane of observation. It is found that all basal dislocations aresplit into 0.1 p wide ribbons.24325 This can be interpreted in the following way.The vectors in the c-plane which connect one atom to the nearest crystallographicallyequivalent one are ABAC and BC (fig. 26) as well as their negatives; these are thepotential glide vectors. They can be decomposed into two partial vectors accordingto the reaction AB = Aa+aB; in other words, the perfect dislocations can splitinto two partial dislocations having Burgers vectors enclosing an angle of 120".The stacking fault between the two partials is then one lamella in the rhombohedralstacking as represented in fig.27. Geometrically, a second type of dissociationwould be possible, for instance, AC = Afl+flC as shown in fig. 26,c. The corres-ponding first partial would bring one layer on top of the second one. The energyassociated with such an A-over-A stacking is, however, considerably higher thanthat of the rhombohedral stacking fault. The second type of dissociation probablydoes not take place for that reason.Burgers vector determinations have confirmedthe picture outlined here. A model of an extended dislocation having the proposedBurgers vectors is represented in fig. 27. No CC-bonds are broken only deforma-tion of the hexagons is required to take up the strain.As can be judged fromfig. 28 the three partials go out of contrast simultaneously which shows that theyThree-fold ribbons are frequently observed in graphite20 FINE STRUCTURE OF DISLOCATIONShave the same Burgers vectors. The Burgers vectors are indicated in fig. 28. Thethree-fold ribbons result from the fusion of two single ribbons according to thereactions :(Aa+oB) +(oC+ An) = AoS Ao+ Aa.Hexagonat RhombOnedral.( d )( @ IFIG. 26.-Ctructure of graphite : (a) cross-sections for the hexagonal form ; (6) cross-section forthe rhombohedra1 form ; (c) projection on the c-plane showing the a, b and c positions ; (d) schemefor denoting Burgers vectors in the c-plane ; (e) scheme for denoting Burgers vectors perpendicularto the c-plane.a aIa ab bb bFIG.27.-Model for 60" dislocation in graphite. No C-C bonds are broken, only distorted.It is clear that the three Burgers vectors are the same. A detailed discussion ofthe geometry of three-fold ribbons is given in ref. (25). In boron nitride, which hasthe same structure as graphite except that two kinds of atoms alternate along aring, the dislocations appear to be undissociatedS. AMELINCKX 21MORE THAN TWO PARTIALS; TALCTalc is a complicated silicate layer structure; it can be considered as a stackingof multilayers in which the succession of single layers is 0-Si-(0-O€€)--Mg-(0-OH)-Si-0. A cross-section through such a rnultilayer is shown in fig.29.The (0-OH) layers are close-packed and magnesium is in the octahedral inter-stices. The silicon atoms are tetrahedrally surrounded by oxygen atoms. It isassumed that on glide these multilayers remain unsheared. The structure of the0SiOand OH:O;; A1 OH0FIG. 29.-Cross-section through a talc multi-layer.FIG. 30.-Structure of the oxygen layers limiting a talc multilayer. The monoclinic unit cell oftalc is outlined.limiting oxygen layers is represented in fig. 30. The bonding between successivemultilayers is due to van der Waals bonding and hence is weak; as a result, glideand cleavage take place between two such oxygen sheets.The stacking of the oxygensheets is not known unambiguously26 but a model which seems to explain theobserved features is shown in fig. 31.27 The shortest glide vector that will repro-duce the same configuration is along the a-direction in fig. 30. Using a ball modelit will be realized that glide proceeds in at least four steps which are indicated in fig.31. Taking into account the monoclinic symmetry glide in the b-direction takese i a t steps (fig. 30). In dislocation language it means that the dislocation wit22 FINE STRUCTURE OF DISLOCATIONSBurgers vector splits into four partial dislocations forming a ribbon of which amodel is shown in fig. 32. On the other hand, glide in the direction A A 2 wouldWI C )FIG.31.-Model for the stacking of the oxygen layers in the talc structure.( a ) < b )FIG. 32.-Model for dislocation ribbons in talc. The Burgers vectors forma zig-zag sequence : (a) edge ribbon ; (b) mew ribbon.produce eight-fold ribbons. The dissociation will be observable provided the energyof the stacking faults concerned is small enough. That this is the case can be judgeS. AMELINCKX 23from fig. 33. The zig-zag configuration of partial Burgers vectors has been con-firmed by contrast experiments (fig. 33).27GLIDE BETWEEN NON-CLOSE-PACKED PLANESWe shall only discuss tin sulphide and the closely related tealite (tin-lead sulphide).Tin sulphide crystallizes in the orthorhombic structure shown in fig.34; 28 thiscan be considered a deformed sodium chloride structure. It has a pronouncedlamellar character giving rise to perfect cleavage along the c-plane. The glideplane is also parallel to the c-plane according to Hoffmann.28 The probable loca-tion of the cleavage plane and also of the glide plane is indicated by arrows in fig. 34which represents the structure as viewed along the a-direction. The projectionon the c-plane of two layers of the tin sulphide structure, one on each side of theFIG. 34.-Structure of tin sulphide (SnS) and of tealite (SnPbSz). The arrows indicate the probablelocation of the glide plane.glide plane, is shown in fig. 35. From ball model considerations, possible glidevectors are ii and g. The glide vector ii could dissociate into the two partial vectorsiil and ii2 with gain in energy. Other dissociations are not obvious.The interestof these compounds from a dislocation point of view lies in the fact that the glideplane is not a close-packed plane and hence that the potential Burgers vectors arenot at angles of 120" as it is usually the case for close-packed planes, but form anangle of 90".The structure of tealite is the same as that of tin sulphide except that the tin sitescan be occupied as well by tin as by lead. Hoffmann 28 did not determine whetheror not tin and lead form an ordered arrangement. However, from the observationThe probable complete Burgers vectors are indicated in fig. 3524 FINE STRUCTURE OF DISLOCATIONSof anti-phase domains in tealite one can conclude that an ordered arrangementmust be present.In ref. (29) a detailed discussion is presented on the possible anti-phase boundary structures in this compound. From the diffraction pattern andfrom the characteristics of the fringe pattern associated with these anti-phaseboundaries one can conclude that the ordered structure must be as shown schem-atically in fig. 36 in which are considered tin and lead planes: in one type of c-plane the cations consist of tin ions whereas in the other type of c-plane they consistFIG. 35.-Projection on the c-plane of two planes of the tin sulphide structure one each side ofthe glide plane.Pb+Sn-I } 2y=0.236- S n v P b - ,1 i - 2 ~ ~ 0 . 2 6 4I - Sn Fb-- c IIPb -------I-------!% - i 2yIFIG. 36.-Cchematic view of anti-phase boundary in tealite.of lead ions.In a given type of c-plane only one kind of cation is present29 Fromfig. 36 it is now clear that the glide plane in one crystal part is situated between twotin layers whereas the corresponding glide plane in the other crystal part is situatedbetween two lead layers. As we shall see, the behaviour of ribbons on crossingan anti-phase boundary reflects the change in composition.The dislocations in tealite appear to be dissociated presumably according to thescheme shown in fig. 32, Z = 51 + 52. If such a ribbon crosses an anti-phase boundaryof the type discussed above (fig. 36) the chemical composition of the planes on bothsides of the glide plane, changes for the same dislocation ribbon from tin into leador vice versa ; it is therefore expected that also the stacking fault energy will change.This is what is observed in fig.37 where the ribbon changes its width on crossingthe anti-phase boundary AB. Since the foil has constant thickness the change inwidth can only be due to a change in stacking fault energy.All illustrations used in this paper are taken from papers by Dr. Delavignetteand the author, unless stated otherwise. I wish to thank Dr. Delavignette for hispermission to use them. I am also grateful to Dr. A. Art, V. 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