Present state of polytypism in cadmium iodide crystals

Review Article phys. stat. sol. (a) 38, 11 (1976)

Subject alassification: 1.1 and 1.2; 10.2; 22.3; 22.4.1; 22.5; 22.6.3; 22.8

Department of Phyaics, Balzaraa Hindu University, Varanasil)

Present State of Polytypism in Cadminm Iodide Crystals

BY R. PEAS AD^)

Contents

1. Introduction

1.1 Polymorphism and polytypism 1.2 Earlier studies of cadmium iodide polytypes 1.3 Layer structure of CdI, 1.4 Geometry of dislocations in CdLI, crystals

2. Different theories of polytypism as applicable to cadmium iodide polytypes

2.1 Screw dislocation theory 2.2 Jagohinski’s theory

3. Nature of glides and existence of specific Z h d a n m s m b o l s

3.1 Feeble occurrence of polytypism based on 2H basic structure

4. X-Ray diffraction studies of cadmium iodide polytypes

4.1 Known polytypes and their growth 4.2 Existence of ordered and disordered structures 4.3 Different modes of phase transformations

5. Eleetron microscope studies for dislocations

5.1 Diffraction geometry 5.2 Low dislocation density regions : dislocation sources 5.3 Dissociated ribbons 5.4 High dislocation density regions 5.5 Moire pattern 5.6 Annealing effects

l ) Varanasi-5, India. *) Present address: Geological Survey of India, Geochronology and Isotope Geology

Division, 29, J. N. Road, Calcutta-16, India.

12 R. PEASAD

6. Decoration studies for the observation of dhloeation configuration

7. Calculation of stachdng fault energy : correlation between stacking fault energy and atomic structure of cadmium iodide polytgpes

8. Streakhg, arcing, and Splitting disorders of x-ray d i m t i o n spots in cud- mium iodide

8.1 Streaking 8.2 Arcing 8.3 splitting -

0. A brief idea of polytypism in other polytpfpic substunces

9.1 Silicon carbide 9.2 Zinc sulphide 9.3 Lead iodide 9.4 Minerals

10. A brief comparison of the results obtained on cadmium iodide with those of other polytypic substances

11. Conelusion

References

1. Introduction

I d Polpolphis in and polyttlpism

During the last decades the phenomenon of polytypism has been the subject of numerous investigations. The studies of polytypism are important for two reasons. First, the growth of polytypes is a special problem'in the field of kinematics of crystal growth, the understanding of growth mechanism, besides being of great interest in itself, is expected to throw light on the nature of long-range interatomic forces in crystals. Second, the complete understanding of the growth process and phase transformations will eventually lead to the controlled growth of polytypes; this is of immense importance from an applied point of view as different polytypes of the same substance are known to have physical properties (e.g. dielectric properties) differing on a known scale.

Polytypism is a special one-dimemional polymorphism. Polytypism is exhibited by certain close-packed and layer structures, viz. Sic, ZnS, (Xi&, Pbh, etc. The unit cell dimensions of different polytypes of the same substance are the same in two directions lying in a plane parallel to the stacked layers, and differ only in a direction perpendicular to the stacked layers. The phenomenon is limited to structures in which the first coordination of some atoms can be satisfied in more than one way, usually equivalent to cubic versus hexagonal close packings.

1.2 Earlier studies of cadmium iodide polytypes

Spiral markings upon cadmium iodide crystals went unnoticed for a long time. Prior to this discovery, Bunn [l, 21 reported the occurrence of roughly

Present State of Polytypism in Cadmium Iodide Crystals 13

concentric circular, at times hexagonal, markings on the (0001) basal faces of CdI, as evidence for layer growth in crystals. As these showed a marked tendency towards spiral formation, Forty [3, 41 undertook a careful study of this compound. During his studies of crystal growth, while crystallising the crystals from aqueous solution, he observed conclusively the existence of a wide range of growth pattarns upon numerous crystals. Employing interferometric methods, Forty [5 to 71 measured the step heights of growth spirals and found that they could be expressed as integer multiples of the thickness of a minimal sandwich. From the occurrence of a large number of step heights corresponding in magnitudes to the c-dimension of the possible polytypes ranging from 168. to 96H, Forty was led to infer the existence of polytypism in cadmium iodide.

Later, Mitchell [8 to 101 discovered more than thirty different polytypes of cadmium iodide and thus Forty’s prediction was upheld. Much earlier to Mitchell’s work Bozorth [ll] discovered the 2H polytype, which was later confirmed by Pinsker 1121, Mitchell, Trigunayat [13], Srivastava (141, Prasad [15], and Tiwari [16].

The polytype + which is now considered to be the most stable polytype of cadmium iodide was confirmed by several workers. Mitchell worked out the detailed atomic structures of small-period polytypes 6Ha, 8H, 12Ha, 12Hb, 12H,, and 14H. Except the polytypes 12Ha and 12Hb, rest of the polytypes were based on the basic 4II structure. In addition to this, i.e. the above modi- fications whose structures were determined, Mitchell also identified the types 16H, 18H, 20H, 24H,, 24H,, 24H,, 24Hd, 24R, 26H,, 26Hb, 28Ha, 32Ha, 40H,, MH,, 40&, 44H, 50H, 56H, 62H, and 64H. Mitchell suggested that different polytypes can be grouped under different structural series. He described the intensity distribution of series (22),11 and postulated that other series such as (22),, 1111, (22),, 2123, (22)n 33, all approaching to 4H should exist.

Mitchell [ 10,171 expressed the strong belief that Frank’s dislocation theory of polytypism was valid for the creation of polytypes in cadmium iodide, because many of the step heights reported by Forty could be correlated with the values of unit cell sizes of the polytypes discovered by him. Besides, he was also able to explain the existence of stmctural series. But the main drawback in his work was that the correlation was discovered between two different batches of the crystds, viz. the batch of crystals used by Forty for interferometric work and his own employed for X-ray diffraction work. Later, Trigunayat and Verma [18] conducted interferometric end X-ray diffraction studies upon the same crystals. Surprisingly, they found that a correlation between step height and X-ray unit cell height does not exist. This created same doubt about the applicability of screw dislocation theory in the caae of cadmium iodide polytypes. Srivastava and Verma [19, 203 went a step further by performing three investigations, namely the evaluation of the c-dimension of the unit cell, estimation of spiral step height, and determination of detailed atomic structure of the same crystal. Srivastava and Verma [19,20] worked out the detailed atomic structure of 22H,, 26H,, 26Hd, 28H, polytypes and showed that the growth features of these polytypes cannot be explained on the basis of screw dislocation theory. Chadha and Trigunayat [21] carried out similar observations on rhombohedra1 polytypes like 30R and 42R and reached at the same result. These authors pointed out that the formation of cadmium iodide polytypes may be explained on the basis of the layer transposition mechanism of Jagodzinski. However, no direct’ evidence for the existence of stacking faults

14 R. -AD

in cadmium iodide was available. Prasad and Srivastava [22,23] carried out detailed electron microscope studies of cadmium iodide and found that dissociation of dislocations into partials and widely dissociated ribbons was a common feature. Prasad and Srivastava [24, 15, 251 worked out the detailed atomic structure of 22H, 32H, 38H: 60R, and 72R polytypes and explained the formation of these polytypes on the basis of creation of ordered stacking faults in the basic 4H structure. Prasad and Srivastava [26] also calculated the stacking fault energy of cadmium iodide polytypes and showed that the structure with least stacking fault energy in general was favoured over other possible structures. Jain and Trigunayat [27] tried to determine the degree of disorder by analysing the intensity distribution on the c-axis oscillation photographs of several cadmium iodide polytypes. The disorder observed by them may, however, be not a true representative of one-dimensional disorder. The disorder may in fact arise from other reasons such as shape effect. Agrawal and Trigunayat [28,29] showed that the “arcing” of X-ray diffraction spots on the Laue photographs and oscillation photographs may arise due to formation of manifold tilt boundaries during crystal growth. According to these authors, the tilt boundaries consist of either partial or unit dislocations. Also Agrawal [30] pointed out that there exist a correlation between arcing and polytypism in cadmium iodide. The work of Agrawal and Trigunayat [28 to 301 suffers from the drawback that they did not present any evidence in favour of the existence of manifold rather peculiar tilt boundaries. Prasad and Sri- vastava [31] went a step further and carried out detailed electron microscope and decoration studies of cadmium iodide crystals with a view to observe the manifold tilt boundaries. They, however, found that tilt boundaries did not a t all exist in cadmium iodide crystals and the idea put forward by Agrawal and Trigunayat to explain arcing and other different shapes of X-ray diffraction spots was only an illusion. Tiwari et al. [32] later explained arcing on the basis of paracrystalline disorder and streaking of X-ray diffraction spots from platelet- shaped polytypic crystals arises due to the shape effect of the crystal [33]. La1 and Trigunayat [34], Tiwari and Srivastava [35, 361, and Rai and Sri- vastava [37,56] have recently studied the phase transformations in cadmium iodide. These authors have suggested different modes of phase transformations in cadmium iodide crysta,ls.

1.3 Layer structure 01 Cd12

Cadmium iodide is an ionic compound in which iodine ions are much larger (approximately double) than the cadmium ions, the ionic radii being

rm = 0.97 A , rI = 2.16 A . The structure consists of a close packing of iodine ions with Cd-ions lying in the interstices. The ratio of radii rCJrI = 0.45 permits the Cd-ions to occupy the octahedral voids, the composition then requiring a 6:3 coordination of Cd- and I-ions. However, there are only half as many Cd-atoms as I-atoms in the structure, and therefore only one half of the total octahedral voids can be occupied. The Cd-ions form close-packed layers, occupying alternate layers of octahedral voids between I-ions as shown in Fig. 1. Thus the Cd- and I-layers arenot stacked alternately; there isone Cd-layer after every two I-layers. The structure, therefore, consists of extended molecular sheets piled over each other. Each molecular sheet consists of a layer of Cd-ions sandwiched between


Fig. 1 Fig. 2 Fig. 1. Layer structure of cadmium iodide. The two “minimal sandwiches” are linked by weak van der Wads bonds. Large circles represent I-ions and the smaller ones Cd-ions [41]

Fig. 2. Structure of a minimal sandwich of CdT, in projection on (0001). The small circles represent Cd-ions in the plane of the paper and the larger circles the I-ions above and below;

Cd-ions lie in octahedral voids between close-packed I-layers [41]

two close-packed layers of I-ions, and has been called by Forty a “minimal sandwich”. The structure of a minimal sandwich is shown in Fig. 2 in projection on (0001) and was first determined by Bozorth. The bonding within the sandwich is purely ionic in character. The sandwiches themselves are held together by very weak van der Waals typeforces. Thisprovidesit with a perfect cleavage. The different polytypes consist of different manners of close pecking (A, B, and C) of iodine ions, the position of cadmium ions being then automatically determined. The coordination polyhedra in all these are the octahedra with a Cd-ion in the centre and I-ions a t the corners. The arrangement of the coordination octahedra for the simplest structures ABABABAB ... is shown in Fig. 3, the corresponding hexagonal unit cell is shown in Fig. 4.

The coordination Octahedra in the structure are almost regular, three of the 1-1 distances being 4.21 A and the other three 4.24 A. Moreover, these distances are nearly equal to the sums of ionic radii of I , indicating that the I-ions are almost in contact with each other. The observed cd-I distance is, however, only 2.99 A while the sum of ionic radii is 3.13 A. This decrease in Cd-I distance

n

Fig. 3 Fig. 4 Fig. 3. Packing of the coordination in CdI , type AyB AyB AyB ... The I-ions lie a t the cor-

ners and the Cd-ions in the centre of octahedra [41]

Fig. 4. Hexagonal unit cell of the two-layered CdI, polytype. Open circles represent I-ions and black circles the Cd-ions [41]

16 R. PRASAD

has been attributed to polarization effects. The hexagonal unit cell dimensions of the two-layered ABABAB ... structure have been reported as a = b = 4.24 A, c = 6.84 A, space group P3ml.

1.4 Geometry of dislocutions in CdIs crystals The dislocation geometry in the CdI, structure can be derived based on the

description given by Amelinckx [38]. The usual dislocation configuration in this structure is confined to basal planes. Fig. 5 shows the Burgers vector for baaal dislocations PR, PQ,QR, and their negatives, these refer to the Burgers vector of unit dislocations. The type PR unit dislocation has lPRl = a, a being the basal lattice translation of the unit cell. In the light of the description given by Amelinckx [38], a perfect unit dislocation of the type PR may dissociate according to the scheme PR = Pa + aR and this dissociation produces a region of stacking faults in the otherwise perfect crystal. A. dissociation of the type PR = aP + Ra is also equally probable. In the cadmium iodide type structure the glide plane is the (0001) plane. There are, however, two types of glide planes - one 111 glide plane where the glide occurs between iodine and iodine layers and other is Cd/I glide plane where the glide occurs between a cadmium layer and a iodine layer. In the following, the different glide planes will be separately considered.

+ 3 +

--t -%

--+

+ + 3

+ + +

(i) 1/1 glide: AyB Ay 4 BAyB AyB . . . (1) AyBAy BCPACPA ... (2)

In the above, equation (1) is the ideal 2 H structure and the vertically downward arrow represents the position of glide planes. The passage of a partial changes the structure sequence shown in equation (2) and this results in stacking faults. The glide vectors are of the type Po + aR. - + +

(ii) Cd/I glide: AyB Ay J. BAyB AyB ... (3) AyB Ay C BaC BarC ... (4)

In this, the vertically downward arrow represents the position of the Cd/I type glide plane. The S t N C t W 0 sequence shown in equation (3) is changed to the structure shown in (4) as a result of Cd/I type glide. The above process would bring one layer of Cd atoms into tetrahedral interstices, the positions for Cd atoms are octahedral positions. Therefore, this type of glide will be much less probable.

(iii) Another type of Cd/I glide: AyB A$ yB AyB AyB ... (5 ) AyB APA CPA CPA ... (6)

Fig. 6 . Burgera vector for basal unit and partial dislocations. Dissociation of unit dislocations takes place accord-

+ + - + ing to the reaction of the type PR = Pa + OR P

Present State of Polytypkm in Cadmium Iodide Crystals 17

Here the Burgers vector of the fault will be of the type (Po + aR). Theabove sequence in equation (6) contains a sequence APA, this type of mndwich is found in the MoS, structure for which the sequence is APA APA APA APA ...

+ +

2. Different Theories of Polytypism as Applicable to Cadmiurn Iodide Polytypes

As such there are many theories of polytypism [39,40,42,81 to 841. There is no single theory which can explain the polytypic growth in all the polytypic substances. A detailed description of different theories of polytypism is given in Verma and Krishna's book [41]. We will, however, give here a short description of the screw dislocation theory and disorder theory of Jagodzinski which have been discussed by various workers with regard to the growth of cadmium iodide polytypes.

2.1 Screw dislocutiun theory

Frank [42], on seeing the photographs of Verma [43] and Forty [3], suggested that the polytypism might be brought about by spiral growth of crystals with screw dislocations of different Burgers vectors. According to him, the crystals may initially grow in thin plates of uniform thickness by a surface nucleation mechanism in accordance with the theory of perfect crystal growth, as the supersaturation is then high. The platelet will then become self-stressed through the non-uniform distribution of impurities, ultimately up to its theoretical yield strength when it will buckle. The buckle will be relieved by a slip in the crystal platelet, exposing one or more steps terminated upon its surface. The end upon which the step is pivoted will be a dislocation centre. These steps will wind up theinselves into growth spirals by the well-known Frank mechanism. The crystal subsequently growing will necessarily have the structure corresponding to the step, because the once created identity will be maintained in future growth by the very nature of the dislocation mechanism. The step heights of various magnitudes will give rise to different polytypes. Frank explained the formation of different polytypes belonging to the (22),11 series by the screw dislocation mechanism in MI,. Mitchell gave the idea of coopera- tion of several dislocations to explain the formation of different polytypes in cadmium iodide having structures other than the (22),11 series.

2.2 JagoMnsWe theory

Jagodzinski [47 to 501 has raised serious doubts about the validity of the screw dislocation mechanism in the growth of polytypic crystals. His points of objection against the screw dislocation mechanism are the following:

1. The energy required for the creation of an edge dislocation with a Burgers vector (+a + + b ) or (+u + + b) or an integer multiple of these would be much less than the energy required for the creation of a screw dislocation, with a huge Burgers vector, as postulated by Frank.

2. The high energy required for the creation of a screw dislocation can come from the lattice only when the crystal has grown to a considerable volume, by which time it would have already settled down to a certain structure. Screw dislocations can, therefore, cause growth only in the later stages, thereby determining only the surface structure. 2 physics (a) 38/1

18 R. PRASAD

3. If the growth takes place by screw dislocations soon after the formation bf the nucleus, the (0001) face on which growth spirals appear will obtain the maximum velocity of growth- making the crystal elongated along the c-axis. But in practice, the crystals are platelets parallel to (0001). 4. One-dimensional disorder is generally encountered from polytypic crystals

which is strongly against the screw dislocation theory. Jagodzinski gave’ an alternative mechanism for the growth of polytypic

crystals. He argued that the polytypes are grown through accidental stacking faults in the basic structure and the ordering is provided through the vibration entropy of the structure. Based on this idea, he performed very tedious theoretical calculations and calculated the fault order degree and published the results in a number of papers [44 to 501. A detailed account of his calculations is given in Verma and Krishna’s book [41]. According to Jagodzinski’s theory the generally expected structural form of a polytypic crystal is disordered. However, if the vibration entropy of the structure is sufficient to provide order to the created accidental faults, the resulting structure will be ordered. Among the disordered structure the degree of disorder will depend upon the extent to which the vibration entropy is able to reduce the order.

In 1960 Frank’s screw dislocation theory was shown to be incapable of explaining the formation of polytypes. Trigunayat and Verma [18], Srivastava [14], Trigunayat and coworkers [21, 28, 29, 341, Prasad and Srivastava [23, 241 supported Jagodzinski’s theory and discarded the screw dislocation theory. Until now, it is not very well established which of the two theories is really able to explain the growth characteristics of cadmium iodide polytypes. It is SO because of the fact that there are already so many experimental evidences which are against the screw dislocation theory and there are no straight forward ways to calculate theoretically the vibration entropy of the structures.

3. Nature of Glides and Existence of Specific Zhdanov Symbols

In all the structural analytical works on cadmium iodide polytypes a limitation is put on the existence of Zhdanov symbols, that is that only three Zhadnov symbols namely 1, 2, and 3 are present in the zigzag sequence of cadmium iodide polytypes. There seems to be no explanation of this limitation. Very recently Prasad and Srivastava [all explained that the occurrence of Zhdanov numbers limited to only 1, 2, and 3 is a natural outcome of the fact that the cadmium iodide polytypes are formed through the creation of ordered stacking faults in the basic 4H or (AyB) (CaB) structure in which A, B, and C represent the positions of iodine layers. and a, p, y the positions of cadmium layers. The creation of stacking faults bounded by partials is equivalent to a slip of one close-packed layer over the other, the slip vector being of the type a/3(1120). The slip amounts to a change in orientation of the close-packed layers, i.e. A + B, B --+ C, C + A or A -+ C, B -+ A, C -+ B and a likewise change for cadmium layers. As we have already said previously there are two possible glides in cadmium iodide, one is I/I glide and the other Cd/I glide. The occurrence of stacking faults through 111 glide is more feasible (as the sandwiches are held together by weak van der Waals type forces) as compared to Cd/I glide (as the forces within the sandwich are ionic). As a representative case, we consider the effect of stacking faults through 1/1 glide in two sandwiches of basic 4H


structure ABI CBABCB

ACBCAC (A) 4.14.1.1 4

ABACBCAC (7) The above is an example of single stacking fault and represents the clockwise change. The sequence (7) corresponds to the Zhdanov sequence 13211 or 3212 and corresponds to the 8H structure. We thus see that the created sequence has the Zhdanov symbols limited to 1, 2, and 3 only. Now let us see the effect of double and triple faults. Double fault

ABI CBABCB

ACI BCAC

ABCB

(A) .1 J 4JJ.1 (V) not possible

( V ) 4.14.6 (A) not possible

Triple fault ABACABCB

ABACABAC (9) In the above V represents an anticlockwise shift, A + C, B + A, and C +B.

The sequence (8) corresponds to the Zhdanov sequence 1232 which again represents the 8H structure. The sequence (9), however, represents the basic 48: structure corresponding to the sequence (22). While considering the above sequences, the 111 glide was taken to occur after the first sandwich; the 111 glide can also take place after two and three sandwiches, leading to other possible sequences. The schemes are described below.

(i) Single fault ABCBl ABCB

CABA (V) 4J.JJ. (A) not possible

ABCBCABA

ABCBABl CB

AC (A) $4 (8) not possible

ABCBABAC :

20 R. PEASAD

Double fault (ii)

ABCBCACB (12) The sequence shown in (10) is unstable as two adjacent layers are in the same AA orientation. The sequence (11) corresponds to 3212. The sequence (12) created through double fault corresponds to 2123. Here again we see that three 8H structures, viz. 3212,1232, and 2123 all contain the Zhdanov numbers limited to only 1, 2, and 3. Creation of so many structures of the same periodicity also confirms the well established experimental fact that in cadmium iodide each of the polytypes has several structural variants. Now we will examine the effect of Cd/I glide to create the stacking faults and ultimately to the creation of polytypes.

AyB CaB AylB CaB J- $4 4 Cd/I glide

ClAPC -+ @YB) (Caw (AYC) (APC) (13) $44 I/Iglide

BYlA -+ (AYB) (CaB) (AYC) (BY4 (14) 4 Cd/I glide C

(AYB) (CaBI (AYC) (BYC) . (16) The sequence (13) is created through Cd/I glide done and is equivalent to Zhdanov symbols 23111 or 3311 but the sequence is energetically unfavourable since in the third sandwich (AyC) cadmium layer y and iodine layer C are in the same orientation. Similarly, creation of sequence (14) through one Cd/I and one 111 glide is also not possible. The sequence shown in (15) obtained through two Cd/I and one 111 glides is equivalent to 242 or 44. This sequence is also energetically unfavourable. The sandwiches (AyC) and (ByC) have adjacent layers y and iodine layer C which are in the same orientation.

In this way we see that the creation of polytypes is most feasible through 111 glide and the polytypes so created contain Zhdanov symbols limited to only 1, 2, and 3 in their zigzag sequence. On the other hand, Cd/I glide is far less probable as it always leads to structures which are energetically improbable. A detailed account of this has been given by Prasad and Srivastava [61].

3.1 Feeble occurrence of polytypism based on 2 R bask s t m t u r e

Apart from the polytypes based on 4H, there are few polytypes which are based on 2H or AyB AyB AyB .-- basic structure of cadmium iodide. It is really strange why there is only a rare occurrence of polytypes based on the 2H basic structure. Prasad [52] has applied the idea of glide schemes in the case of 2H basic structure dso and analysed the results based on the schemes of stacking faults. He has shown that in the case of 2H basic structure apart from


the Cd/I glide, I/I glide is also unable to produce polytypes to some extent. This is so because of the fact that when 111 glide operates in a limited number of 2H basic units it produces structures which are energetically improbable. The formation of polytypes from 2H basic structure requires a high density of stacking faults through 111 glide. The creation of a high demity of ordered stacking faults from the basic phase seems to be rarely encountered as compared to the creation of a low density of ordered stacking faults. Had the low density of orderedstackingfaults (stackingfaultsin two or three unitsor so) beableto produce new structures, the basic phase 2H would also have been as active, in principle, as that of basic 4H phase in producing polytypic structures. It should be pointed out here that the polytypic structures resulting from the 4H basic phase and envolving high density of stacking faults are also rare. Since the high density of ordered stacking faults is rarely encountered, the polytypes based on 2H basic phase are also rare.

4. X-Ray Diffraction Studies of Cadmium Iodide Polytypes While there were strong favours and disfavours for the applicability of the

screw dislocation mechanism, the alternative mechanism to screw dislocation mechanism was the layer transposition mechanism of Jagodzinski. According to Jagodzinski’s disorder theory, the ordered structures are special cases of disordered structures. If the vibration entropy is sufficient to produce order, we get the ordered structures. According to him ordered and disordered structures existing together are expected, while the existence of the same is not explicable in the framework of the screw dislocation theory. Naturally the subject required an extensive X-ray study. Different workers therefore studied extensively cadmium iodide crystals by X-rays. During X-ray investigations many well ordered polytypes were encountered and many ordered and disordered structures existing together in the same crystal piece were also found. In the following the results are summarised.

4.1 Known polytypes and their gTowth

More than a hundred polytypes of cadmium iodide have been discovered so far but the structures of all have not been solved. So far as the growth of cadmium iodide polytypes is concerned, serious doubts have been expressed by many workers about the applicability of the screw dislocation theory but on the other hand, there are no straightforward ways to calculate the vibration entropy of the structures. Therefore, the growth of cadniium iodide polytypes may be understood on the basis of the occurrence of ordered stacking faults in the basic 4R structure. The dispute as to how the order is achieved by the created stacking faults is still not well resolved. However, the ordered stacking faults may be deformation type stacking faults (slip of layers) or intrinsic stacking faults (growth faults). If the hexagonality of the structure is the same as that of the basic 4H structure, the polytypic structure would have been grown through the occurrence of deformation type stacking faults in the basic 4 B structure. I f the hexagonality of the polytypic structure is less than the hexagon- di ty of the basic 4H structure, the polytypic structures would have been grown either through the occurrence of intrinsic stacking faults alone in the basic 4H structure or through a combination of deformation and intrinsic stacking faults [53]. However, there are certain polytypic structural series about which it can be ascertained that they grow only through the occurrence of intrinsic

22 R. %SAD

stacking faults. The polytypes of these series contain a certain number of basic structure units and then (11) units a t the end of the structure. These well-known series are (22)Jl, (22)Jll l .

4 6 Existence 01 ordered and disordered structures

Disordered and ordered structures existing together is a very common feature in cadmium iodide polytypic structures. This indicates that the probabllity of the applicability of the screw dislocation theory is far less as compared to the disorder theory of Jagodzinski. The ordered and disordered structures in cadmium iodide exist simultaneously in two different ways. One is that the same face of the crystal or the crystal as ti whole exhibits the disordered and ordered structures existing together. When an a-axis oscillation photograph of such crystals is taken by X-ray diffraction, it shows sharp spots and a superimposed streak. The sharp spots correspond to the ordered structure and the superimposed streak corresponds to a disordered structure existing together with the ordered structure. Many of such crystals were found by Trigunayat [13] and Srivastava [14]. Fig. 6 shows an X-ray oscillation photograph from a cadmium iodide crystal of this category. The other type of ordered and disordered structures existing together in the same crystal piece is in the form of that one face of the crystal exhibits completely ordered structure and the other face of the same crystal exhibits disordered structure. Fig. 7 is an example of this category of disorder.

The existence of these structures has given a drawback to the applicability of the screw dislocation theory in the case of cadmium iodide polytypes. Screw dislocation theory having lost its ground, disorder theory seems to be an alternative mechanism. It, therefore, requires a detailed theoretical work to unfold the real cause of growth mechanism of polytypic structures. Recently Jain and Trigunayat [27] have tried to find out experimentally thc degree of disorder of CdT, polytypes but their work suffers from the drawback that the c-axis oscillation photographs furnished by them may not be true represen- tatives of the real lattice disorder. At this moment, therefore, it will be safe to say that the cadmium iodide polytypes are formed through creation and ordering of stacking faults in the basic 411 structure and sometimes in the basic 2H structure. The real cause of ordering is still not well understood and requires some more studies.

Fig. 6. X-ray 15" a-axis oscillation photo- Fig. 7. X-ray 15" a-axis oscillation photograph of a cadmium iodide crystal exhib- graph of a cadmium iodide crystal exhibiting ordered and disordered structures iting a disordered structure. The other

existing together face of this crystal has a completely ordered structure

Present State of Polgtypism in Cadmium Iodide Crystals 23

4.3 Different modes of plume transfwrmuttons

Phase transformation studies in cadmium iodide were first initiated by La1 and Trigunayat [34]. Later on Tiwari and Srivastava [35, 361 made a detailed study of phase transformations in cadmium iodide and suggested the probable mechanism for different modes of phase transformations. The most common mode of phase transformation reported by Tiwari and Srivastava [36] was that the polytypes were converted to the 4H basic structure with superimposed disorder. In some cases a polytype is converted to another polytype with the =me periodicity but with a different arrangement of layer sequence. Based on electron microscope evidence for the change of stacking fault sequences, Tiwari and Srivastava explained the different modes of phase transformations in the following manner:

When cadmium iodide polytypes are annealed under vacuum, the most probable effect of annealing is to disturb and/or change the ordered distribution of stacking faults in three ways: (i) the order may be completely destroyed and a disordered structure results; (ii) an ordered distribution may produce another ordered distribution ; (iii) a change involving both of these processes. If the starting structure is partially disordered, then the same mechanisms of phase transformation as described by (i), (ii), and (iii) will also hold good for the ordered part of the structure. For the disordered part, however, a different transformation mode is expected. For the disordered part, the degree of disorder may increase or decrease depending upon whether the stacking fanlts are more randomly distributed or get some order by the annealing treatment. If all the randomly distributed stacking faults get complete order on annealing, a completely ordered structure will be the product of the phase transformation.

Another very curious result has been given by Tiwari and Srivastava based on the scheme of stacking faults, and that is that a hexagonal or rhombohedra1 polytype can be converted to another hexagonal or rhombohedral polytype with the same periodicity but with a different arrangement of layer sequence. These authors [54] have shown that by deformation stacking faults (layer trans- positions) a nH, or nR, polytype will be changed to nH, or nR, polytype, nH, or nR, polytype. etc. or it will be transformed to the basic 4H structure. Later on, they [55] worked out the detailed atomic structure of 84R, polytype as [(22), 2111211, and studied the phase transformation of this polytype. The 84% polytype was converted to 84R, polytype with the structure [(22), 1212111, on heating. The layerwise scheme put forward by Tiwari and Srivastava for the conversion of 84R, polytype to 84R, polytype was as follows:

(ABCB), ABICBCBCA

ACACl AB

BC

(ABCB), ABACACBC

.l&J..l.l&

4.1

Apart from this, some studies have also been done by Rai and Srivastava [66] regarding the phase transformation of CdI, polytypes. Their results are almost similar to those of Tiwari and Srivastava. However, they have obtained a new transformation where a 42R polytype is converted to 12H polytype on heating

24 R. Pusan

which on further heating is converted to 4H. This result has put one fact on sound footings and that is that both hexagonal and rhombohedra1 polytypes can be created from the 4H basic structure by the creation and ordering of stacking faults in it.

Tiwari and Srivastava and Rai and Srivastava have also +awn the conclusion that the stacking fault energy of the transformed structure is always less than the parent starting structure and, therefore, the most common modeA of phase transformation is towards basic 4H structure. That means the phase transformation is governed by stacking fault energy. The polytype formation is also governed by stacking fault energy. Since the phase transformation is a regrowth process where the stacking faults are rearranged, the stacking fault result appears to be of value.

6. Electron Microscope Studies for Dislocations

It was believed that the polytypes of cadmium iodide were formed due to creation and ordering of stacking faults in the basic structures. Creation of stacking faults means that the stacking fault energy of cadmium iodide should be very small and which in turn means that the unit dislocation can be easily dissociated into partial dislocations. Much work has been done on other crystals with layer structure [67] but observations of dislocations were not available in cadmium iodide. This is probably due to the fact that cadmium iodide crystals when exposed to normal electron beam in electron microscope decompose quickly. This behaviour of cadmium iodide is in contrast to several other crystals having layer structures. Prasad and Srivastava, therefore, felt the most important necessity to somehow study cadmium iodide crystals under electron microscope and to observe whether stacking faults really exist in cadmium iodide crystals.

The observations of dislocations in cadmium iodide are of importance from another point of view, too. Agrawal and Trigunayat [28, 291, while explaining the “arcing” and “splitting” of X-ray diffraction spots in CdI, crystalspostulated the existence of manifold tilt boundaries, but no evidence was presented. So Prasad and Srivastava made a detailed electron microscope study of cadmium iodide crystals and obtained several useful results. In order to avoid the decomposition of crystals, small condenser apertures (20 or 50 pm) were employed and full excitation of condenser lenses was used. The observations were made at 60 kV and sometimes at 80 kV. In order to improve thermal contact of crystals, several variations, such as using a small mesh grid, sandwiching the crystal between two grids, mounting the crystals with a silver paint, etc. were used. It was noticed that those regions of the crystals which were either near to or surrounded by grid bars and thus had a better thermal contact with the grid, could be studied easily under moderate electron beam illumination without any damage. It should be pointed out here that except the studies carried out by Prasad and Srivastava, no other electron microscope studies are available in literature till now on this compound. In the following, we describe in brief the diffraction geometry and important results obtained by Prasad and Srivastava.

5.1 Dijjraction geometry

The crystals of cadmium iodide studied under electron microscope were in the form of basal oriented platelets. Therefore, the diffraction pattern always corresponds to the (00.1) oriented reciprocal lattice net. The spots in the net

Present State of Polytypism ixi Chdmium Iodide Crystals 25

Fig. 8 Fig. 9 Fig. 8. Usual diffraction pattern of a CdI, crystal observed in the electron microscope

Fig.9. Diffraction pattern of CdI, crystal observed under two-beam conditions in the electron microscope. The two bright spots correspond to the direct beam and a 11.0 type reflection. The presence of joint 10.0 type spots arranged on LL hexagonal grid near the direct

beam can be noticed

are arranged on hexagonal grids [68,59]. Fig. 8 shows a representative electron diffraction pattern of a CdI, crystal. The diffraction spots arranged on the hexagonal grid nearest to the origin are of 10.0 type and those arranged on the next hexagonal grid are of 11.0 type. For an interpretation of dislocations, a two-beam condition is necessary. This was obtained by tilting the crystal flake in such a way that in the observed diffraction pattern besides the direct beam only one difffraction spot was strong. Fig. 9 shows a two-beam- excitation condition, the operating diffraction vector being 911.0. The contrast observed at dislocations depends on the factor g - b. It is found in the case of the cadmium iodide structure that the term g b is an integer like zero or &l for six 11.0 type diffraction vectors (9). For these diffraction vectors, therefore, the partials behave like perfect dislocations, the partials with parallel Burgers vectors form ribbons. In 11.0 type reflections, since 9. b is an integer, no stacking fault contrast appears. For a 10.0 type diffraction vector the term g - b is always non-integer and thus stacking fault contrast appears. Also, in 10.0 type reflections the partials are always invisible for g . b = +1/3 and visible for g - b = 1213. Under certain conditions the partials are invisible even for g - b = &2/3 [57, 581.

We now proceed to describe the electron microscope investigations of dislocation configurations.

5.2 Low dislocation density regions : dislocation sources

Low dislocation density regions were often observed in vapour grown crystals 1401 and appear to be produced by the operation of a dislocation source. Fig. 10 shows a typical didocation configuration of this type. In this figure ABCD k a dislocation source and the dislocations LM, NP, etc. have 6een produced by the source operation. Prasad and Srivastava [31] have described in detail how

26 R. PRASAD

b

Fig. 10. Low dislocation density region observed in the transmission electron microscope showing dislocations produced by e multiple mechanism. The dislocations are in the form of half loops c

& c Fig. 11. Successive stages of the formation of dislocations shown in

Fig. 10

these dislocations are produced by the operation of a dislocation source. Ac- cording to them the configuration did not seem to correspond to a simple Frank- Read source, because the configurations expected by the operation of a simple Frank-Read source pinned at one or two points are in the form of spirals or complete loops. But as is evident from Fig. 10, the didocations are in the form of half loops and not complete loops. The discussion advanced by Prasad and Srivastava [31] for the formation of these half loops is explicable with the help of Fig. 11. Initially, the dislocation configuration is as shown in Fig. l l a . The dislocation has its portions AB and CD on two parallel basal planes which are along the slip plane of the crystal. The portion BC lies on the (101 1) pyram- idal plane and thus cannot glide. The dislocation is thus pinned at B and C as far as basal glide is concerned, the ends A and D of the dislocation emerge at the surfaces along the edges of the basal planes and are, therefore, free to move along the edge of the slip plane. The dislocation segment CD is shown to bow out successively in Fig. l l b and c, in the end the bowed portion meets the edge leaving a nearly semi-circular loop and the bowed portion CD which can repeat the process again and thus numerous half loops can be produced.

5.3 Dissociated ribbons The most important observation in connection with the growth of cadmium

iodide polytypes obtained by Prasad ansd Srivastava was the profuse occurrence of dissociation of dislocations and the accompanying stacking fault&. The two- fold and three-fold ribbons were abundantly observed in cadmium iodide crystals. Fig. 12a shows a dislocation network, seen under bright field at two- beam conditions with a &fraction vector corresponding to a 11.0 type reflection from a solution grown and cleaved cadmium iodide crystal. Notice that several dislocations are dissociated, these are visible as two-fold ribbons. Fig. 12b shows another example of dissociated dislocations in a solution grown and cleaved crystal. Here the dislocations are in the form of multifold ribbons. Crossing over of ribbons is also visibile in this figure. C and E represent the places where the dislocations cross over. Fig. 13 shows another example of dissociated dislocations taken at two-beam conditions with a 11.0 operating reflection from a cadmium iodide crystal grown from the vapour phase. Some two-fold ribbons can be seen at TI and T3. Three-fold ribbons at places marked T, and T4 can also


Fig. 13. Transmission electron micrograph showing two-fold and three-fold ribbons from a vapour grown crystal of cadmium

iodide

Fig. 12. Transmission electron micrographs showing a) dissociated dislocations in a thin basal oriented platelet of cadmium iodide from solution grown and cleaved crystals, b) multiple ribbons in solution grown and rleaved crystals. Crossing over

of ribbons is visible a t C and E

be seen. Three-fold ribbons are formed by the fusion of two-fold ribbons. Two- fold ribbon a t T, on a casual look seem to suggest the presence of a four-fold ribbon, however, close observation reveals that two separate two-fold ribbons exist. For the ribbon T, a shade contrast between pairs of partials is visible. This is due to the presence of comparatively strong 10.0 type reflection besides the 11.0 type operating reflection. Due to this additional reflection a double

Fig. 14. The same crystal region (ABC serves as the reference region) imaged with two different operating reflections. The operating reflection is a) 11.0 type and b) 10.0 type. The directions of the operating reflections are shown by arrows. It can be seen that the partials around the regions marked by small arrows have almost disappeared in b), a weak

stacking fault contrast (shade contrast) can also be seen in b)

28 R. h m

Fig. 15. Partial dislocation ribbons in cadmium iodide crystal in 11.0 operating reflection. Crossing over of ribbons on parallel planes can be observed, some of the regions where crosaing over has taken place are marked by arrows

dislocation image appears at QQ’. Fig. 14a and b represent another example ,of dislocation ribbons from the same crystal region from vapour grown crystal. Fig. 14a was taken in 11.0 type operating reflection and Fig. 14b in 10.0 type operating reflection. It is evident from these figures that some of the partids which were visible in Fig. 14a had disappeared in Fig. 14b. In vapour grown crystals, usually the dislocation density was small as the crystals were directly transferred onto the grid of the electron microscope and presumably all the dislocations observed were grown-in dislocations. In the case of solution grown and cleaved crystals, some dislocations were also introduced during the cleaving process, but the deductions regarding the dissociation of dislocations and stacking fault energy will not depend upon the method of crystal growth and thinning process. The above examples show that the stacking fault energy of cadmium iodide is very small, which has an important bearing on the growth of polytypic crystals.

The dislocation ribbons situated on nearby plames may interact and cross each other, this results in a change in the initial dislocation configuration. The geometry of the configuration resulting from crossing over depends mainly on the type of Burgers vector of the original ribbons. Interactions and the crossing over of ribbons were very often observed by Prasad [la] in cadmium iodide crystals. Rg. 15 represents an example of above type.

5.4 High dislocatfon densftg regions

In most of the cases where solution grown crystals [39] thinned by cleaving were studied under the electron microscope, regions with high dislocation density were observed, because besides the grown-in dislocations many dislocations were introduced during the cleaving process. These together with the grown-in dislocations produced complicated dislocation patterns of high dislocation density. Fig. 16 represents a high dislocation density region. It can be seen that this dislocation pattern is of “bird-nest” type and is reminescent of the patterns observed in deformed metals and alloys.

5.5 Moir6 pattema

Another noticeable feature observed under electron microscope by Prasad and Srivastava [15] waa the formation of a Moird pattern. A typical example of Moir6 pattern obtained from a solution grown and cleaved crystal is shown

Present State of Polytypism in-Cadmium Iodide Crystals 29

Fig.

dislc high

16. Electron miorograph showing a dislocation density region. The

ication pattern resembles those of deformed metals and alloys

in Fig. 17. The Moirk fringes are produced due to overlapping crystals and in the case of cadmium iodide,.as the crystals grow in flat platelets, the basal planes of the two overlapping crystals would be parallel (interplanar spacing for two crystals would be the same) and the Moire pattern would arise due to a rotation between the two crystals. The pattern formed would therefore be a rotational Moirk pattern. The said rotations leading to the displacements between crystal blocks are important in relation to the disorder observed on the diffraction patterns by Agrawal and Trigunayat 128, 291.

5.6 Annealing eflects

5.6.1 shuffling of partial dislocations

When single crystal regions containing partial dislocations were heated gently by slightly increasing the beam current, a change in dialocation configuration was noticed. Fig. 18a and b show clearly that after heating, the partials in the region W have disappeared, while the partial around CD remains unaltered, also a new ribbon near PP' has nucleated. This observation suggests that the shuffling of partials and the accompanying stacking faults, under controlled heat treatment, is possible in cadmium iodide crystals. This result indicates that stacking fault sequences can be changed by heating, this in turn means that the cadmium iodide polytypes can undergo phase transformations. The polytypic phase transformation analysis with reference to above figurea has already been described by Prasad [60].

30 R. PRASAD

Fig. 18. Change in the configuration of partial dislocations. a) and b) represent the same crystal region before and after heating (the marks a t the boundary and the dislocation around CD serve as reference points). Notice the change in the dislocation configuration of partials in the region MM'DC, many partials have disappeared. Nucleation of a fresh ribbon

around PP' can also be noticed

5.6.2 Formation of dislocation loops

When the single crystal regions which were devoid of dislocations were heated by a moderate electron beam, by suddenly increasing the beam current in the electron microscope, two different features were found to develop. These were : (i) the formation of dislocation loops and (ii) eventual decomposition of the crystal. Fig. 19 which represents hexagonal prismatic dislocation loops was obtained after a bombardment for a short duration (3 to 4 s) of a single crystal region devoid of dislocations. Prasad and Srivastava [31] have reported that diffraction patterns revealed that these hexagonal loops were not tiny crystals. The formation of loops appears to be an aggregation of point defects in the form of molecular vacancies produced by the bombardment of thin single crystal regions devoid of dislocations by negative ions. The production of point defects seems to be similar to that of gold single crystals 1611, lead iodide crystals [62, 631, and cadmium crystals [64]. On repeated or prolonged bombardment of single crystal regions the crystal decomposed. Fig. 20 represents the decomposed region obtained after prolonged bombardment of a single crystal region.

Prasad and Srivastava in spite of their very detailed electron microscope study of cadmium iodide single crystals could not find the presence of the

Present State of Polytypism in (ladmium Iodide Crystals 31

Fig. 20. Electron micrograph of a decomposed region obtained ader

prolonged electron bombardment

manifold rather peculiar tilt boundaries proposed by Agrawal and Trigunayat [28, 291 in order to explain arcing and splitting of X-ray diffraction spots from MI, crystals.

6 . Decoration Studies for the Observation of Dislocation Configuration

The macroscopic tilt boundaries proposed by Agrawal and Trigunayat can also be observed by decoration techniques. Prasad and Srivastava [31] attempted to use decoration techniques also to observe macroscopic tilt boundaries in cadmium iodide crystals. They decorated the cadmium iodide crystals by cadmium metal aa noble metals like gold or silver react with the iodine in the crystal and so disturb the stoichiometry of the cadmium iodide crystals. After decorating the cadmium iodide crystals, an optical microscope was used to observe the configuration of dislocations. In the following we describe the results obtained by Prasad and Srivastava by the decoration technique in cadmium iodide crystals:

1. Prasad and Srivastava observed the existence of linear dislocation arrays in cadmium iodide crystals. Fig. 21 shows a typical example of dislocation arrays observed in decorated crystals of cadmium iodide. There are two arrays visible in the picture observed and are marked as AB and CD. The tilt boundaries conjectured by Agrawal and Trigunayat [28, 291 are perpendicular to the basal plane and since in the observations carried out by Prasad and Srivastava, the crystals

Fig. 21. Two oppositely placed linear dislocation arrays AB and CD revealed by decoration with cadmium particles in cadmium

iodide crystals

Fig. 22. Twist boundary (hexagonal grid of dislocations) revealed by deooration. 80, BO, and CO represent the branches of the

hexagonal mesh

Fig. 23. Helical dislocation observed by deooration. ABCDE represents Q single

,helioal dislocation

were ;viewed along the directions perpendicular to the basal plane, the tilt boundaries would not be revealed. The crystals were, therefore, tilted slightly so that the tilt boundaries may become visible if they exist a t all. But Pramd and Srivastava [31] have reported that they carried the above described experiment on more than 100 crystals of cadmium iodide and even then the tilt boundaries were not revealed. An array of dislocations lying in the same slip plane observed by Prasad and Srivastava can be produced if the dislocations which are created from some source are held up by some obstacle.

2. Another observation revealed by the decoration technique was the presence of a dislocation network representative of EL twist boundary. Fig. 22 shows an example of this type of boundary. The twist boundary is produced due to slight rotation of two close-packed planes (cadmium iodide sandwiches) against each other about a direction normal to their close-packed planes.

3. Yet another observation was the existence of helical dislocations, Fig. 23 shows a helical dislocation configuration. The general mechanism for the formation of helical dislocations has been discussed by Amelinckx et al. [66] and Thomos and Whelan [66]. The zigzag helical dislocations were similar to those observed by Forty [62, 631 in lead iodide and were probably produced by vacancy precipitation on a group of predominantly screw dislocations.

The decoration observations of Prasad and Srivastava coupled with their electron microscope observations confirmed that the peculiar tilt boundaries conjectured by Agrswal and Trigunayat [28,29] do not exist a t all in cadmium iodide crystals and, therefore, the cause of arcing, streaking, etc. disorders needed reconsideration.

7. Calculation of Stacking Fault Energy: Correlation between Stacking Fault Energy and Atomic Structure of Cadmium Iodide Polytypes

As said earlier, it is believed that the polytypes of cadmium iodide are formed through the occurrence of stacking faults in some basic structures such as 4EI (2H) and their consequent ordering. There can be a number of ways in which some specific number of layers can be arranged to form a structure having that


specific number of layers. However, a structure sequence having the minimum stacking fault energy will be favoured over the other possible structures. The structure having a stacking fault energy very near to the minimum stacking fault energy may also crystallise. This means that more than one structure may also exist having the same number of structural layers but with different arrangement of the atomic structure sequence. All these structures will have stacking fault energies very near to one another and all approaching approximately the minimum stacking fault energy. This is in agreement with the experimental observations in the case of cadmium iodide polytypes. In the light of the above discussion, i t is apparent that the calculation of stacking fault energy is of great value. Prasad and Srivaatava [26] calculated the stticking fault energies of cadmium iodide polytypes following Hirth and Lothe's [ 671 procedure for close-packed structures and a definite correlation between stacking fault energy and atomic structure of polytypes was found to exist, i.e. mostly the atomic structures of cadmium iodide polytypes correspond to minimum or sometimes very near to minimum stacking fault energy. Prasad andSrivastava [26] calculated the stacking fault energy in terms of the distortion energy yn per pair. Later on Tiwari and Srivastava [55] went a step further and converted the distortion energy y,, in terms of bond length 9. Table 1 shows the stacking fault energies in terms of y,, for various possible structures of the 60R polytype. The correct atomic structure sequence for this polytype is [(22), 12231, or (ABCB),ABACABAC ---. Table 2 shows the stacking fault energies in terms of the distortion energy yn of all the polytypes of cadmium iodide having a known atomic structure sequence.

The minimum stacking fault energy criterion has two-fold advantages. The first is that it lends credit to the fact that the polytypes of cadmium iodide are formed through the occurrence of ordered stacking faults in the basic structure and the second is that i t drastically reduces the time of calculation of the atomic structure factor of the polytypes, in particular of those having very large unit cell height. Therefore, the method of calculating the minimum stacking fault energy is much simpler. So for calculating the correct atomic structure factor, one needs to calculate the stacking fault energy of all the possible structures. To arrive at the correct atomic structure, one then needs to pick up the structure with minimum stacking fault energy and a few more structures

Table 1 Stacking fault energies for the possible structures of 6OR polytype of cadmium iodide. The polytype is based on 4H or (22) or (ABCBABCB ...) structure. [(22), 12231, belongs to the

correct atomic structure

No. 1 possible structure i stacking fault energies, E,t

[(22), 12231, or (ABCB), ABACABAC ... [(22), 22131, or (ABCB), ABCBABAC ... [(22), 23121, or (ABCB), ABCBACAC ... [(22), 2121111, or (ABCB), ABCBCACA ... [(22), 31311, or (ABCB), ABCACABC ... [(22), 13131, or (ABCB)S ABACBCBA ... [(22), 3111111, or (ABCB), ABCACACA ...

Stacking fault energies have been shown only for one third of the structure. 3 physic8 (a) %/I

34 R. PRASAD

Tab le 2 Stacking fault energies of the polytypes of cadmium iodide with known atomic structure ~

No.

1 ~

2

3

4 5

6

7

8

9

10

polytypes belonging to (22),11 series, cf: 6H, 10H, 14H, 18H, 22H, 26H ... (22),1111 series, hf. 8H,, 12H,, 28H, ... 12H,

12R 12Hb

32H

60R and 72R

30R and 42R

B4R1

MRa

structure

(22),11, n = 1, 2, 3,4, ... or (ABCB), AB

(22),1111 or (ABCB), ABAB. 12 = 1.2, 3, ... (22)2123 or (ABCB)ABCBCACB (13), or ABAC ... 21211212 or ABCBCACACBCB (22),321123 or (ABCB), ABCAC BCBCACB [(22),122313 with n = 3 and 4, respectively, or (ABCB),,ABACABAC ... with m = 3 and 4, respectively [(22),121213 or (ABCB),ABACAC ... with m = 1 and 2 respectively [( 22),211121], or (ABCB),ABCBCBCA .. . [(22),121211], or (ABCB),ABACACBC ...

stacking fault energy, Est

For rhombohedra1 polytypes the stacking fault energies have been shown only for one third of the structure.

having stacking fault energies very near to the minimum and calculate the structure factor of only these few structures. In this way, one can arrive at the correct atomic structure saving a lot of time.

8. Streaking, Arcing, and Splitting Disorders of X-Ray Diffraction Spots in Cadmium Iodide

8.1 Streaking The existence of disorder forms one of the basic postulates of Jagodzinski’s

mechanism. The disorder envisaged by Jagodzinslu manifests itself in the form of streaking of X-ray diffraction spots on 10.1 and other similar rows. In this type of streaking, the spots are extended in directions parallel to the c*-axis and run into each other parallel to this axis.

Besides this type of streaking, the c-axis oscillation photographs from cadmium iodide crystals exhibit a curious type of streaking disorder. In this curious disorder, the 10.1 and other similar rows consist of two parts, one part


(above or below the zero layer) consists of unusually sharp spots, while the other part (below or above the zero layer) consists of streaked spots. Fig. 24 shows a c-axis oscillation photograph from a platelet-shaped cadmium iodide crystal. It is clear from this photograph that the c-axis oscillation photographs from platelet-shaped cadmium iodide crystals exhibit the above described curious type of streaking. It is because of this anomalous streaking that c-axis oscillation photographs from cadmium iodide crystals do not exhibit sharp discrete spots and are therefore unsuitable for the identification of polytypes or for structure determination. The curious type of streaking behaviour was earlier noticed by Trigunayat [13, 681 and Srivastava [14] but the cause of this remained unexplained. Later on Prasad and Srivastava [33] on seeing the photographs of Trigunayat [ 131, Srivastava [ 141, and Jain and Trigunayat [27] repeated the experiments in general from platelet-shaped and big polytypic crystals of cadmium iodide, lead iodide, silicon carbide, etc. and they found that the c-axis oscillation photographs from platelet-shaped polytypic crystals in general exhibit the above described curious type of streaking. These authors showed that the curious streaking and arcing of X-ray diffraction spots in c-axis oscillation photographs from platelet-shaped polytypic crystals was due to size and shape effects of crystals [33] and did not represent any real lattice disorder envisaged by Jagodzinski. Based on their explanation for the curious type of streaking, caution is necessary in analysing the c-axis oscillation photographs for the evaluation of stacking disorder. Thus, the previous deductions by Jain and Trigunayat [27] for the fault order degree need reconsideration.

8.2 Arcing

Besides the shape effect induced streaking disorder, the X-ray diffraction spots from cadmium iodide crystals often exhibit another type of disorder known as “arcing”. Here, the spots are extended in directions which are in- clined to the c*-axis, usually the direction of extension is nearly perpendicular to c*. Arcing also was observed long ago in cadmium iodide crystals [13, 141, it was only recently when Agrawal and Trigunayat [28, 291 tried to explain the origin of arcing in cadmium iodide crystals. As pointed out previously, the explanation advanced by them was mainly based on the speculation for the existence of tilt boundaries. Later on Prasad and Srivastava [22, 23, 311 made thorough electron microscope and decoration studies on cadmium iodide single crystals and reached a t the conclusion that the peculiar tilt boundaries suggested by Agrawal and Trigunayat did not a t all exist in cadmium iodide crystals. The most usual observed dislocation configuration was the dissociation of dislocations into partial ribbons lying in the basal plane and the diffraction pattern from these did not show any arcing. These results of Prasad and Srivastava 3’

36 R. PRASAD

Table 3

Polytypes of S i c with known atomic structure

NO.

1 2 3 4 6 6 7 8 9

10 11

~

12

13 14 15

16 17 18

19 20 21

22

23 24 25 26 27

28 29 30 31 32

33

2H 3c 4H 6H 8H 9T 1 OH, lOH, 15R 16H

87R, 106R, 123R, 141R, and 393R 39R, 57R, and l l l R

33T 36H 39H

54H 69R, 81H

99R 174R l68R and 273R

51& 69Rp

19H and 267R

27H 27R 76R 90R 14H and 18H

20H 51R,

21R 189R

33R

120%

Zhdanov s y x layer sequence

ABAB ... ABCABC ... ABCB ABCACB ABCABACB ABCABCACB ABCACBCACB ABCABCBACB ABCBACABACBCACB (ABCACB), ABCB (ABCACB),ABCAC ..., where n = 2, 3, 4, 6, 6, 7, and 21, respectively

(ABCACB),ABCACBA ..., where n = 1, 2, and 5, respectively

(ABCACB),ABCACB ACBCAB ACBCAB ACB (ABCACB),ABCACB(CABACB),CABACB (ABCACB),ABCACB(CABACB),CAB ACABCB (ABCACB),ABCACBCABACBCABACB ABCABACBCABACBCACBCABAC . .. (ABCACB),ABCACBACB(CABACB), CABACB (ABCACB),ABCACBCAC ... (ABCACB),ABCABC(ACBABC),ACBA . .. (ABCBACABACBCACB)3ABCBACABCBA . .. for 168R and (ABCBACABACBCACB),ABC BACABACBCABAC ... for 273R (ABCBACABACBCACB)ABCB for 19H and (ABCBACABACBCACB),ABC BACABACBCAC ... for 267R (ABCBAC ...) ABCACBABCACB (ABCBABCBA ...) (ABCAC ...) ABCBACABAC ... (ABCBA ...) ABCBACABCBACABA ... (ABCB),ABCACB, where n = 2 and 3, respectively

(ABCB),ABCAB ACB (ABCB),ABCBA ... ABCAC(BCAC),BCABACABACABCBA ... ABCACBA ... (ABCACBACABCBACBCABACB)2 ABCACBACABCBACBCABCBA ... ABCACBABCAC ...

Present State of Polytypism in Cadmium Iodide Crystills 37

No. I polytype 1 Zhdanov notation

34 147R [(333%321,

35 24R, (53)a

Table 3 (continued)

layer sequence

(ABCACBABCAC .. .)ABCACB ABCACBCABA ... ABCABCBA ...

36

9. A Brief Idea of Polytypism in Other Polytypic Substances

It will be worthwhile to review briefly the existing state of polytypism in other polytypic substances.

9.1 Silicon cavbide

Various polytypes of silicon carbide consist of identical hexagonal networks of Si and C stacked alternately and differ simply by the variation in the mode of stacking of these layers. The basic structures of silicon carbide are 3C or ABCABC ..., 6H or (33) or ABCACBABCACB ... , 15R or 232323 or ABCBA -

84R [(Ws(3%13 , (ABCACB),ABCACBCABA ...

Present State of Polytypism in Cadmium Iodide Crystills 37

Table 3 (continued)

were in agreement with similar observations in other substances [57, 711. Agra- wal advanced an explanation that arcing and the occurrence of polytypism were intimately connected. Other polytypic substances such as Sic, ZnS, etc. do not exhibit any arcing, but a fairly large number of polytypes are found in these compounds [4l, 69 J and, therefore, the existence of some correlation between arcing and occurrence of polytypism also does not seem valid. Tiwari, Prasad and Srivastava tried to explain arcing in the light of disorder produced by other imperfections [go] and reached a t the conclusion that arcing cannot be explained on the basis of other types of lattice defects (such as stacking faults). The diffraction patterns exhibiting arcing in cadmium iodide crystals are very similar to the diffraction patterns observed from chain molecules [72], macro- lattices of synthetic fibres, the atomic lattice in ammonia catalyst [73, 741. The arcing in these is known to arise due to paracrystalline distortion. Tiwari et al. [32], therefore, suggested that the arcing in cadmium iodide may also arise due to paracrystalline distortion. Paracrystalline distortion may arise in two possible ways; it may arise due to water molecules trapped or absorbed during crystal growth and it may also arise due to the growth of incoherent nuclei on the flat crystal surface leading to small gaps between different domains of the crystal.

8.3 Splitting

Besides the curious type of streaking and arcing disorder a third variety of disorder exists where (i) X-ray diffraction spots are split into two or more closely spaced spots and (ii) a row of spots dissociates into two rows, one of which is shifted with respect to the other along directions other than that represented by the c*-axis. Tiwari and Srivastava [75] have pointed out that in the case of cadmium iodide polytypic crystals, the splitting of spots occurs due to step-like geometry of the polytypic crystal ; the step-like surface geometry of the crystal arises due to the occurrence of growth spirals on the crystal surface. The dissociation of a row of spots takes place due to shape induced absorption of the X-ray beam.

9. A Brief Idea of Polytypism in Other Polytypic Substances

It will be worthwhile to review briefly the existing state of polytypism in other polytypic substances.

9.1 Silicon cavbide

Various polytypes of silicon carbide consist of identical hexagonal networks of Si and C stacked alternately and differ simply by the variation in the mode of stacking of these layers. The basic structures of silicon carbide are 3C or ABCABC ..., 6H or (33) or ABCACBABCACB ... , 15R or 232323 or ABCBA -

38 R. PRASAD

CABACBCACB ... and 4H or (22) or ABCBABCB ... , etc., where A, B, and C represent Sic double layers. Of these, 6H, 15R, and 4H are the most abundant. Up to date more than 100 polytypes of Sic based on the above basic structures have been discovered and atomic structures of about 50 polytypes have been solved. A detailed description of Sic polytypes is given in the book of Vema and Krishna [41] and in the review article of Shaffer [85]. Table 3 describes various polytypes of Sic with known atomic structures. Most of the polytypes of Sic are grouped into different structural series. The most popular structural series based on 6H or (33) or ABCACB ... are [(33),3213 or (ABCACB),ABCAC ... , and [(33),3413 or (ABCACB),ABCACBA ... , where n = 1, 2, 3, ... , etc. The formation of these polytypes is governed by the introduction of stacking faults in the end of the basic structure unit. The popular structural series based on the 15R basic structure are [(23),2213 or [(ABCBA ...) ABCB] ... and [(23),33Is or [(ABCBA ...) ABCACB] ... , etc., where n can take any value but not a multiple of 3. The structural series based on the 4H basic structure are (22),33 or (ABCB),ABCACB and [(22),2313 or (ABCB),ABCBA ... , where n = 1, 2, 3, ... , etc. Apart from these structural series in Sic, there are many polytypes which have the stacking faults somewhere in the middle of the basic structure sequence.

The growth of different polytypes of Sic was initially explained in terms for Frank’s screw dislocation theory. According to this theory, the. long-period polytypes of Sic grow from some basic structures like 6H, 15R, and 4H by the creation of screw dislocations. The Burgers vector of this screw dislocation is a non-integer multiple of the height of the parent unit cell. Due to the partial nature of the screw dislocation a stacking fault is introduced a t the end of the basic structure units. Thus the screw dislocation theory was able to account of the formation of different structural series in Sic, where the stacking faults were introduced a t the end of basic structure units. Jagodzinski [44 to 461 raised doubts about the applicability of the screw dislocation theory based on energy considerations. Trigunayat and Verma [ 181 found that some long-period polytypes of cadmiumiodide did not have any correlation between the spiral step height and the X-ray unit cell height. This created more doubts about the applicability of the screw dislocation theory. Krishna and Verma [41] worked out the detailed atomic structure of long-period polytypes of Sic, viz. 57R, 111R, 36H, etc. and found that the screw dislocation theory was not able to explain the formation of these polytypes. The polytypic crystal 36H showed the presence of two different polytypes 36H, and 36Hb. The atomic structure of 36Hb showed faults both at the end and in the middle of (33) basic structure units which cannot be incorporated into the framework of the screw dislocation theory. Also the co-existence of the two 36-layered structures in the same crystal piece is not expected based on the screw dislocation theory. Later, Jagodzinski’s theory envolving vibration entropy induced ordering of stacking faults was thought to be an alternative mechanism which can successfully explain the growth of different polytypes of Sic. But the main difficulty with this theory is that until now, there are no straightforward ways to calculate the vibration entropy of the structures. Recently, Rai [84] has given the idea that a modified form of the screw dislocation theory may explain the growth of different polytypes of Sic. According to him, the initial platelet consists of pairs of f.c.c. microtwins. One of the microtwins of a pair is a clockwise microtwin ABCA ... and the other counterclockwise ACBA ... The axial screw dislocation in such a platelet will cause the formation of polytypes.


Dubey et al. [86] have very recently found out the 189R polytype which is based on 21R polytype and the 147R polytype which is based on 33R polytype and explained their formation on the basis of microtwin induced screw dislocations and pointed out that 21R and 33R may be the next basic structures of silicon carbide.

Whichever theory is capable of explaining the formation of polytypes in Sic, one thing is definite and that is that the formation of different polytypes is crucially dependent on the role of stacking faults in the basic structure. Based on this Prasad and Srivastava [37] calculated the theoretical stacking fault energy of different polytypes of Sic following the modified version of Hirth and Lothe [67]. They found that like cadmium iodide polytypes, the correct atomic structure of Sic polytypes also follow the minimum stacking fault energy criterion.

The phase transformation studies of Sic polytypes have been carried out by Knippenberg and co-workers [88 to 901. In the latest studies they reported the transformation of 2H whiskers to 6H, and 3C, 4H, 15R crystals to 6H in the temperature range of 1500 to 2830 "C. They observed that in the above transformations, a detachment of molecules from the interior of the structure, i.e. from the Sic lattice into the surface layer took place.

Phase transformations in low identity period polytypes of Sic have been studied in detail by Krishna et al. [79]. It has been found that the 2H or AB AB... modification transforms to the 3C structure at temperatures between 1400 and 1600 "C and directly to the 6H or ABCACB ... structure a t 2400 "C in argon atmosphere. They have concluded that the 2H modification is probably meta- stable at all temperatures while 3C is a stable low-temperature form. The transformations proceed through insertion and ordering of stacking faults. The real cause of ordering has not been pointed out and still needs investigation.

9.2 Zinc sulphide

Strock and Brophy [91] found that ZnS crystals possess one-dimensional disorder, surface striations, bonded birefringence, and polytypism. ZnS which is iso-structural to Sic is known to display the maximum number of polytypes and so far more than 100 polytypes have been discovered. Table 4 describes the ZnS polytypes with known atomic structures. Mardix and Steinberger [81] have suggested that in zinc sulphide the polytype formation may be associated to periodic shear transformation. They found that the periodic slip manifested itself macroscopically in the form of tilting of some external facets of the crystal. The resulting tilt angle was found to be in accordance with the measured tilt angles. Secco d'Aragona et al. [80] have presented electron microscope evidence for the 2E (wurtzite) to 3C (sphalerite) phase transformation. Daniels [82] and Mardix et al. [83] studied the 2H + 3C transformation in ZnS and found that the phase transformations occurred through a periodic slip process governed by rotation and climb of partial dislocations around a screw dislocation parallel to [OO.l]. Rai et al. [92] undertook an electron microscope study of ZnS and found that in this substance the 3C --+ 2H phase transformation took place and that the polytype formation was the intermediate state of the 3C to 2H transformation. According to them, the phase transformations occur through micro- twinning. The random occurrence of microtwins causes one-dimensional disorder while the periodic occurrence of the same causes the formation of well ordered polytypes. Later,Rai [84] pointed out that the periodic occurrence of micro-

40 R. PRASAD

Table 4 Polytypes of zinc sulphide with known atomic structures

No.

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

-36

4H 6H 8H 9R

10H, 10H, 12R 14H 14H 15R 16H 18R 20H 20H 21R 24H 24H 24H 24H 24H 24H 24H 24H 24R 26H 28H 36R 48R 48R 48R 48R 60R 60R 60R 72R 72R

Zhdanov notation

(22) (33) (44) (21)s (55) (82) (31), (77)

(321, (88) (42)s

(311213 (7557)

(9564)

(5423)

(522362) (533423)

(16422)

(71052) (8943) (33242253) (33422433) (159) (531,

(9559)

(97)s (124)s (742313

(182),

(17423)

(6222)s

(433222),

(1 1432), (522353), (61152), (954613

layer sequence

ABCB ABCACB ABCABACB ABCBCACAB ABCABCBACB ABCABCABCB ABCA ... (ABC),A(BAC),B ABCABCBACBCACB ABCAC ...

ABCABA ... (ABC),BABCBAC(ABC),B (ABC),BACABCBACBCACB ABCACAC ... (ABC),ABACBACABCA(BAC)zB (ABC),ABACBABCB (ABC),(ACB),(CAB),ACB (ABC),AB(ACB),(ABC),B (ABC),(BAC),ABCACB ABCACBABCBACBCAC(BCA),CB ABCACBABCABACABACBABCACB

ABCABCBA ... (ABC),BACBCACB (ABC),(ACB)zCACB(ACB)3 (ABC),ACBCAC ... (ABCX(ACB),A ... (ABC),ACBA ... (ABC),ABACBABCBA ... ABCABACB(CABA), ... (ABC),AC ... (ABC),BACBCABA ... (ABC),BABCBACABCABAC . . . (ABC),(ACB),CABCAC ... (ABC),(ACB),CAB(CBA), ...

(ABC)3(BAC)2B

(ABC),(ACB),

twins in ZnS may be due to the presence of screw dislocations. Thus in ZnS, too, the subject matter of polytypism is still not well resolved.

9.3 Lead iodide

The compound lead iodide which is iso-structural to cadmium iodide has less tendency towards polytypism. Polytypes in this compound are found in the “gel” grown crystals. The occurrence of polytypism is enhanced by the addition of some impurities like silver or silver iodide. The formation of polytypes in lead iodide has been attributed to the occurrence of screw dislocations around a foreign nucleus. However, a detailed study of polytypism is not available, probably because of the difficulty in getting high-periodicity polytypesby the usual methods


of growth (viz. solution, vapour transport, etc.). The “gel” method of crystal growth is somewhat encouraging as i t usually produces high-periodicity polytypes. However, no detailed theory has been worked out as yet which may rea- sonably interpret the growth process of lead iodide polytypes.

Regarding the phase transformations, the only studies available in literature are those of Prasad and Srivastava [77, 781. In lead iodide, when basic phases like 2H, 4H, etc. are heated suitably under vacuum, they are converted to high- periodicity polytypes with some superimposed disorder [77]. The high periodicity polytypes, on the other hand, do not change their structure even after repeated annealing runs [78].

9.4 Minerals

Ungemach [93] has described the two minerals coquimbite and paracoquimbite, both with the formula Fe,O, . 3 SO, - 9 H,O, to be polytypic. The series of crystal forms of coquimbite are hexagonal while those of paracoquimbite are rhombohedral. Ungemach [94] has also shown that the minerals parasite and synchisite exist in three polytypic forms namely u (hexagonal), (rhombohedral), and y (hexagonal) all with the chemical formula (CeF),Ca(CO,),.

The hexagonal ferrite family of ferrimagnetic oxides possess mixed-layer polytypes of the form Ba,Me,Fe,O, [95 to 1001.

Three kaolin (china clay) minerals, kaolinite, nacrite, and dichrite are also polytypic. These are made up of complex layers of A1,0,. 2 SiO, - 2 H,O stacked over each other in different ways [loll.

Very recently Ayres [ 1021 studied samples of naturally occurring moIybdenite from 87 localities of Australia and Papua New Guinea. He found that 90% of them were hexagonal(2H) polytypes, the remainder being rhombohedral(3R) polytypes, and mixtures of the two. The 2H, polytypes occur in phernatites, quartz veins, and skarns and 3R polytypes and mixtures are more common in granites and porphyry copper deposites.

Potassium cobalticyanide K,Co(CN), is known to display three different polytypes [ 1031.

10. A Brief Comparison of the Results Obtained on Cadmium Iodide with Those of Other Polytypic Substances

It will be worthwhile to compare the existing situation of growth characteristics in cadmium iodide polytypes with those of the growth characteristics of the polytypes of other substances. I n the case of lead iodide which is iso- structural to cadmium iodide, the polytypes are believed to grow through the screw dislocations around a foreign nucleus (silver or silver iodide) [76].Regard- ing the phase transformations in lead iodide, the results obtained are entirely different to that of phase transformations in cadmium iodide. In lead iodide, as has been said earlier, the basic phases like 2H, 4H, etc., on heating are converted to high-periodicity polytypes with superimposed disorder and the high- periodicity polytypes do not change even after repeated annealing runs [78]. I n cadmium iodide the high-periodicity polytypes are converted to the basic 4H structure with some superimposed disorder, sometimes they are converted to polytypes with lower periodicity than the starting polytype and sometimes a polytype is converted to a polytype with the same periodicity, but with a different arrangement of the layer sequence. This basic difference in phase trans-

42 R. PRASAD

formations in cadmium iodide and lead iodide is probably due to the crucial role of impurities in lead iodide. The cadmium iodide polytypes have no effect of impurities. In the case of silicon carbide, too, the situation of growth characteristics is also presently hanging between the screw dislocation theory and the disorder theory of Jagodzinski. There are experimental evidences which sometimes favour the disorder theory and disfavour the acrew dislocation theory and vice versa. The phase transformations in low identity period polytypes of silicon carbide are believed to proceed through the insertion and ordering of stacking faults "791. The same is also true for cadmium iodide and lead iodide. The cause of ordering is still not well resolved. In the case of zincsulphide, thefrequency of occurrence of polytypism is very high. The polytypism in this compound is thought to be of martensitic type. However, recently Rai [84] coupled with the electron microscope observation of Rai et al. [92] has expressed that polytypism in zinc sulphide may be caused by the existence of microtwins, the ordering may be provided by screw dislocations. It is certain that the growth and phase transformations in cadmium iodide polytypes are entirely different to those in zinc sulphide polytypes.

11. Conclusion

Summarising, a review of all the works relating to growth and phase transformations of cadmium iodide polytypes has been given. Much experimental work has been done by different workers in relation to growth characteristics of cadmium iodide polytypes and their phase transformations. Still, there is no definite clue as to which theory can successfully explain the growth characteristics of cadmium iodide polytypes. The electron microscope studies carried out by Prasad and Srivastava have put one fact on strong footings and that is that the stacking faults are introduced in the basic structure during the growth of polytypes. However, much theoretical work in the field of polytypism is necessary like mechanical deformation problem or thermodynamical stability problem including heat content etc. Some theoretical models need to be devel- oped to calculate the vibration entropy of the polytypic crystals.

Aeknozaledgements

The author is thankful to Prof. S. Amelinckx, S.C.K./C.E.N., Mol, Belgium for his keen interest in the present work. He is highly indebted to Dr. 0. N. Srivastsva, Reader, Department of Physics, Banares Hindu University, Vara- nasi for his constant help in all the possible ways through this work. The author is also thankful to Prof. P. Krishna, Department of Physics, Banaras Hindu University, Varanasi for his goodwill and interest.

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(Received January 21, 1976)

Present state of polytypism in cadmium iodide crystals

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