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Growth and transformation of polytypes in MX2 compounds
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Journal of Crystal Growth 53 (1981) 574—578 North-Holland Publishing Company
GROWTH AND TRANSFORMATION OF POLYTYPES IN MX2 COMPOUNDS V.K. AGRAWAL * Instituto dePesquisas Espacias, INPE, Conseiho Nacional de Desenvolvimento CientIfico e Tecnológico, CNPq, 12200 S~oJosé dos Campos, S.F., Brasil Received 12 January 1981
On the basis of a review of experimental studies made on single crystals of Pb12, Cd12 and CdBr2, it has been shown that the high polytypes in a substance are formed as a matter of chance in the initial stages of the growth of crystals. They are in a metastable state and, therefore, transform generally into a basic type during growth or on annealing. As regards to formation of a basic type, the ionicity of the compound has been found to have a direct influence in determining which of the closely related structures will be formed. On the basis of polytypic structures of Cd12 and Pb12 reported so far, it has been found that the second and third neighbour anion—anion layer interactions dominate the interlayer interactions during growth and transformation of polytypes. A criterion for occurrence of Zhdanov number 3 in Zhdanov symbols of crystal structure is that it can occur only at places where the sum of all numbers preceding it is an odd number. This rule would help in the determination of structures of high polytypes of Cd12 and Pbl2.
1. Introduction The phenomenon of polytypism exhibited by a large number of substances has attracted solid state physicists due to the fact that different polytypic modifications of a substance possess different semiconducting, dielectric, optical and photovoltaic prop• erties which,in other words, are more or less sensitive to the structure type. The degree of polytypism exhibited by such substances, even by isostructural ones, is widely different, e.g., in Cd12 a large number whereas in CdBr2 only a few polytypes have been reported [1]. However, there is a common feature among all of them in that each substance, when grown under certain conditions, has a particular type, known as common or basic type, which occurs much more frequently than all other types. Different common types have been found to occur at different temperatures [2,3]. *
On leave of absence from Motilal Nehru College (University of Delhi), New Delhi 110021, India.
The predominance of one type over the others, although they have similar lattice energies, and the occurrence of long-period polytypes, although the presentisknowledge interactions in crystal lattice confined of to atomic short-range forces, have been puzzling features of the phenomenon. An attempt has been made to explain these features in the present paper on the basis of a review of the experimental studies made on single crystals of Pb12, Cd12 and CdBr2 and their mixed crystals by the author and his coworkers [4—13]. The compounds were chosen because they are isostructural but exhibit a different degree of polytypism and also different common types, viz. 2 H, 4 H, and 6 R, respectively [1]. 2. Experimental results The crystals of Pb12, Cd12 and CdBr2 grown by various methods have been studied using X-ray and electron diffraction, optical microscopy and transmission and scanning electron microscopy. The experimental results are summarized below.
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V.K. Agrawal / Growth and transformation of polytypes in MX
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The as-grown crystals of Cd12 and CdBr2 grown by vapour phase under stabilized growth conditions exhibited only the structure types 4 H and 6 R, respectively [11,14], whereas those grown from aqueous solutions under ordinary room temperature conditions showed a large number of ordered longperiod polytypes in Cd12 [4,15,16] and highly disordered structures in C dBr2 [4,9,17], particularly in the initial stages of their nucleation [5]. However, rhombohedral structures have generally been observed in the later parts of their growth [7]. The crystals of Cd12 grown by vapour phase under deliberately fluctuating, but controlled, temperature consisted of a mixture of types 4 H and 12 R [18]. The mixed crystals of Cd!2 and CdBr2 grown by vapour phase under stabilized growth conditions also exhibited a mixture of 4 H and 12 R [12]. Cd12 crystals grown from aqueous solutions under ordinary room temperature conditions during winter, when the ternperature in the laboratory varied from about 5 to 25°Cexhibited comparatively more of type 2 H and the higher polytypes based on it than those grown during summer, when the temperature variation was from about 25 to 40°C,although the common type at both times was 4 H. By a heat-treatment study of solution-grown Cd!2 crystals, it has been shown that the 12 R structure comes next to the basic type from the stability point of view [19]. In Pb!2 crystals grown by the gel method, the percentage of common type 2 H has been found to be decreasing on increasing the temperature of the gel [20] and 12 R had been reported to be the stable modification and the common type at the high ternperature of 260°C [3]. Impurity introduced into Pb!2 crystals caused an increase of incidence of polytypism [21]. Recent studies of as-grown Cd12 crystals of varying thickness grown by a vapour phase technique have shown that in the initial stage of their growth the structure is polycrystalline but on further growth a considerable reorientation and coalescence takes place forming a disordered layer structure. As the deposition proceeds further, the final product is 4 H [13]. Successive cleavage studies of solution grown Cd!2 crystals along the basal plane had also revealed that the polytypic transformation during growth is always accompanied by a greatly disordered structure [22].
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3. Discussion On the basis of experimental results, it is established that if a polytypic substance is grown under well stabilized growth conditions, its single crystals exhibit only one particular type of structure. Addition of impurities in the charge, fluctuating temperature and supersaturation, i.e. unstabiized growth conditions and their influence on stoichiometry, rate of crystallization, and creation and movement of dislocations are responsible for the formation of various polytypes. High polytypes, which generally occur in the initial stage of the growth of crystals, grown either by vapour phase or from aqueous solutions, are in the metastable state which, during subsequent growth or on annealing, transform into another polytype, generally into a basic type. Since the growth conditions are fluctuating in the initial stage of nucleation of crystals, a high polytype is obviously formed accidentally. However, once it is formed it does not change in situ if the growth conditions existing at the time of its nucleation remain highly stabilized, which, of course, is difficult to achieve for long duration, particularly in solution growth. Otherwise, it would transform into another ordered polytype via disordered arrangement of layers since, ordered structures are energetically more favourable than disordered ones. That is why, the same high polytype does not occur even on both the basal faces of a platy crystal; a high polytype with a particular layer sequence is rarely repeated; they generally form in the initial stages of growth of crystals; a polytypic transformation during growth is always accompanied by much disorder. Such disordered crystals have a tendency to transform into a basic type during growth or on annealing. Therefore, the controlled growth of a desired high polytype does not seem to be possible. On comparing the commonly observed structures of Pb12 2 H (A7B)(A7B), Cd12 4 H (A’yB)(CaB), or (A’yB)(A~3C),and CdBr2 6 R (A’yB)(Cj3A)(BaC), where A, B and C represent the positions of halogen ions and the greek letters metal ions, it is seen that the second sandwich in each of them, keeping the first one the same, has a different orientation with respect to each other. There are only four possible orientations, viz. AB, AC, CB and CA (the positions of the metal ions, represented by greek letters, are —
—
—
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automatically determined by the I-layer stacking mode), which the second sandwich can have if the first one is in AB orientation, giving rise to 3 different structures — 2 H, 4 H, 4 H and 6 R, respectively, From the point of view of interlayer interactions, there is a considerable difference between these struc-
tures. In 2 H, all the anion—anion ‘second neighbours are in the same orientation, in 4 H only the alternates are, whereas, in 6 R all are in different orientations,
2 compounds
either in A or B orientation since no two successive layers can be in the same orientation in these structures. However, 13 would prevent the 4th layer from
adopting the A orientation because it violates the condition (ii) described above; therefore, it could take only the B position resulting in the formation of 4 H(ABCB). Since the tendency of the structure to continue during further growth is that of 2 H, the
next sandwich would be in CB orientation, resulting
Thus, it is apparent that the strength of interlayer interactions in these compounds is in decreasing
in the formation of a faulted 2 H structure. However, as an ordered structure is energetically more favour-
order. The same conclusion was earlier drawn by the author [23] from considerations of their geometrical structure and then correlating it with the frequency of occurrence of stacking faults in their crystals. Recently, by estimation of interactions in Cd12 by light scattering techniques, it has been shown that the
able than a disordered faulted one, a regular 4 H structure may continue to be formed. Depending upon interlayer interactions, it may further transform into another type; obviously, its probability of transformation in Pb!2 would be less than that in Cd12 because of stronger interlayer interactions in the
nearest neighbour interlayer interaction dominates
former. That explains the high incidence of poly-
the interlayer interaction [24]. Apparently, the mcidence of polytypism in a compound as a result of transformation of. its common type into other polytypes would depend on these interactions, Recently, the author [25] has reported that the basic hexagonal types of Cd!2 and Pb!2 are transformed more frequently into those rhombohedral structures for which (i) the hexagonality is almost the same as that of their parents, (ii) the top and bottom anion layers of two successive sandwiches, respectively, are not in the same orientation and (iii) the stacking fault energy is minimum. On the basis of these conditions he has explained the formation of frequently observed rhombohedral polytypes, viz. 12 R1(l3)3, 18 R1(2l21)3, 18 R2(13l1)3 and 24 R1(22l2)3 and the non-occurrence in Cd!2 and Pb12 of other probable types, viz. 6 R(°°)and 12 R2(31)3. On the basis of these conditions, the polytypic transformation appears to depend mainly on anion—anion second and third neighbour interactions (referred to as ~2 and ~ respectively, in the following) as explained below. Cation—cation layer interaction does not seem to play an independent role because cation layers may take any orientation irrespective of its predecessors through synchro-shear motion [26]. First consider the transformation in Pb12 of which the common type is 2 H(ABAB...). A stacking fault occurring at third layer of the sequence would transform it from A to C and then the 4th layer can be
typism in Cd!2 compared to that in Pb!2 when grown under ordinary room temperature conditions. On further growth of 4 H(AB)(CB), the third sandwich can be in two equally probable orientation, viz. (AB) or (CA), if only ~ and ~ are taken into account, because second and third sandwiches in both cases form a 4 H structure {(CB)(AB)} or {(CB)(CA)} and, similarly, the fourth sandwich can adopt either of the orientations (CB) or (AC) in the former case, or (CB) or (BA) in the latter. So, either 4 H would continue to grow or would transform into one of the following three sequences: (i) (AB)(CB)(CA)(BA) 12 R1(13)3 (ii) (AB)(CB)(AB)(AC) 8 H(2123) (iii) (AB)(CB)(CA)(CB) 8H(2l23). ... ... ...
The observations of a mixture of 4 H and 12 R in almost all the vapour grown crystals of CdI2_~Brx [12]; the vapour grown Cd!2 crystals grown under fluctuating, but controlled, temperature [18]; its frequent occurrence in solution grown Cd!2 crystals [7]; and at high temperature in Pb!2 crystals [3] imply that only cI~2and ~I~3dominate the interlayer interactions during their growth. The transformation of polytypes below 16 H into 4 H after one heating run, whereas that of 12 R occurs only after a large number of heating runs at 270°C [19] substantiate this conclusion. Regarding occurrence of 8 11(2123), either it would obtain by a dislocation a memory to continue to grow as 8 H or a faulted 4 H would be formed;
V,K, Agrawal / Growth and transformation of polytypes in MX
2 compounds
both types have been observed experimentally in solution grown Cd!2 and gel grown Pb12 crystals [1,27]. Conversely, in CdBr2 the common structure is 6 R(AB)(CA)(BC) having the top and bottom anion layers of all successive sandwiches, respectively, in the same orientation. A stacking fault occurring at any place in the sequence will disturb this regularity and also changes its hexagonality, except that for a twinned 6 R(AC)(BA)(CB). Probably, these factors prevent the transformation of 6 R into other structures and allow the frequent occurrence of twinned 6 R [14,17]. CdBr2 crystals grown by mixing HBr/ Br2 in undersaturated aqueous solutions at ordinary room temperature conditions have exhibited some percentage (‘-‘l 1%) of 4 H, while majority of them are 6 R/twinned 6 R and/or disordered types [4,9,17], whereas the others grown at a constant temperature of ‘-‘40°Chave shown some ordered polytypes too. Recently, the author and his coworkers [28] have reported the structure of a new CdBr2 polytype 12 R as (l3)3’mixed with 4 H and 6 R, and have also found others like 12 H and 36 R (unpublished). It has been shown that 12 R is formed as a result of transformation of 4 H, as in Cd!2, and not of 6 R. Low supersaturation of the solution and presence of HBr/Br2 in it appear to be responsible for small incidence of polytypism and higher degree of disorder in solution grown CdBr2 crystals. The transformation of Cd!2 and Pb12 polytypes on heating has been explained so far in terms of the creation and movement of isolated and extended dislocations, their boundaries and other obstacles like impurities, etc. [1]. Recently, the reversible transformations in some crystals of Pb!2 at high temperature, viz. 2H to 30 R at 130°Cand 2 H to 12 R at 260°C, have been reported by Minagawa [27]. On the basis of interlayer interactions, the type 2 H should be transformed into 12 R via 4 H and it is indeed substantiated experimentally in that the latter has been found to exist in some crystals even at the high temperature of 260°Cand also occurs in coalescence with 12 R in some of the vapour grown crystals [27]. Besides, Zallen and Slade [29] observed by Raman scattering the conversion into the 4 H type of Pb12 crystals upon heating at ‘~145°C. However, it was surprising to note from the ABC-sequence of 30 R (111313)3 that it could not be formed directly
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from any 1011 structure since the first and tenth layers in the sequence of 30 R were found to be in the same orientation; the nH-3nR mechanism of formation of rhombohedral polytypes [20] probably fails in this case. On looking at the Zhdanov symbols of 30 R (111313)3, they seem to be very close to those of 12 R (131313), so it could only be conjectured that at high temperature 30 R is transformed into 12 R or vice versa. The conditions described above for polytypic transformation imply that not only the Zhdanov number 4 should be absent in the transformed structures of Cd12 and Pb12, but also the number 3 should occur only at the positions where the sum of the numbers occurring before it is an odd number, e.g., the structures like (13)3, (111313)3 and (1232) are possible but not those illustrated by (3 1)3, (2321), or (113131)3. All, but two, of the reported structures of nearly 120 polytypes of Cd12 and Pb!2 so far [1,27, 30—32] have been found to observe this rule. Of the two exceptions, one 6 H(33) was reported only once in Cd!2 in 1941 [33] and the other 32 H[(22)532l123] appeared to be wrongly reported since the intensities calculated by the author for this structure did not agree with the reported observed intensities [34]. It, therefore, shows that not only the transformed structures follow the above mentioned conditions, the high polytypes formed during growth, too, observe them. This criterion of Zhdanov number would make the determination of atomic structures of high polytypes easier since it would reduce considerably the number of theoretically possible structures of a polytype: for example, on the basis of this criterion, 12 R can have only one structure (13)3, 18 R two (1311)3 and (2121)3, 24 R four (2213)3, (212111)3, (211121)3 and (131111)3, 6 H one (2211), 8 H three (221111), (121121) and (1232), and so on. As regards to the formation of a basic type in a substance, a correlation has been found to exist between the cubicity (i3) of the structure and the ionicity of the compound. The former is defined as the ratio of the number of anion layers in fcc orientation to the total number of them in the unit cell. The basic types for Pb12, Cd!2 and CdBr2 are found to be in an increasing order of 13, viz. j3 = 0 for 2 H, 1/2 for 4 H, unity for 6 R. The ionicity of these compounds has also been reported to be in the same order —
—
—
—
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VK. Agrawal / Growth and transformation of polytypes in MX
[35,36]. The series can also be extended to CdC12 which is more ionic than CdBr2 and exhibits only the 6 R structure without any disorder. Thus the ionicity of the compound appears to have a direct influence in determining which of these closely related structures, i.e. the basic type, should be formed. On the basis of this correlation, it is easy to understand the occurrence of different basic typed in a substance due to change in growth temperature, supersaturation, or composition. Various structures had been found in Mg—In, Mg—In—Cd and Au—Cd alloys separately by varying the relative composition of their elements, and the composition dependence of hexagonality (ci), where ci = 1 —13, of the observed structures in terms of the electron-to-atom ratio had been reported in these alloys [37,38].
Re erences [1] G.C. Trigunayat and A.R. Verma, in: Crystallography and Crystal Chemistry of Materials with Layered Structures, Ed. F. Levy (Reidel, Dordrecht, 1976) p. 269. [2] W.F. Knippenberg, Philips Res. Rept. 18 (1963) 161. [3] T. Minagawa, Acta Cryst. A31 (1975) 823. [4] V.K. Agrawal, Ph.D. Thesis, University of Delhi, India (1970). [5] V.K. Agrawal, ActaCryst. A26 (1970) 567. 161 V.K. Agrawal, Crystal Lattice Defects 8 (1978) 7. [7] V.K. Agrawal, Phys. Status Solicli 57 (1980) 143. [8] V.K. Agrawal and G.C. Trigunayat, Ada Cryst. A25 (1969) 401. [9] V.K. Agrawal and G.C. Trigunayat, Acta Cryst. A26 (1970) 426. [10] V.K. Agrawal, G.K. Chadha and G.C. Trigunayat, Acta Cryst. A26 (1970) 140. [11] S.D. Sharma, K. Mehrotra and V.K, Agrawal, J. Electrochem. Soc. 124 (1977) 945. [12] S.D. Sharma; K. Mehrotra and V.K. Agrawal, J. Electrochem. Soc. 126 (1979) 325.
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[131S.D.
Sharma, G.L. Sharma and V.K. Agrawal, J. Crystal Growth 49 (1980) 580. [14] K. Mehrotra, J. Crystal Growth 44 (1978) 45, [15] V.K. Agrawal, G.K. Chadha and G.C. Trigunayat, Ada Cryst. B26 (1970) 1911.
1161 R.S. Mitchell, [17] R.S. Mitchell,
Z. Krist. 108 (1956) 296. Z. Krist. 117 (1962) 309. [18] S.D. Sharma, G.L. Sharma and V.K. Agrawal, to be published. [191 G. Lal and G.C. Trigunayat, J. Solid State Chem. 9 (1974) 132 [20] J.l. Hanoka and V. Vand, I. Appl, Phys. 39 (1968) 5286. [21] M. Chand and G.C. Trigunayat, J. Crystal Growth 39 (1977) 299. [22] Gyaneshwar and G.C. Trigunayat, J. Solid State Chem. 15 (1975) 127 [23] V.K. Agrawal, Phys. Letters 34A (1971) 82. [24]S. Nakashima, H. Katahama, M, Daimon and A. Mitsuishi, Solid State Commun. 31(1979) 913. [25] V.K. Agrawal, Mater. Res. Bull. 14 (1979) 907. [26] S. Amelinckx, The Direct Observation of Dislocations, Suppl. 6 of Solid State Physics, Eds. F. Seitz and D. Turnbull (Academic Press, New York, 1964). [271T. Minagawa, J. Appl. Cryst. 12 (1979) 57. [28] S.D. Sharma, G.L. Sharma and V.K. Agrawal, Acta Cryst. B36 (1980) 26. [29] R. Zallen and M.L. Slade, Solid State Commun. 17 (1975) 1561. [30] P.C. Jam and G.C. Trigunayat, Acta Cryst. B34 (1978) 2677. [31] P.C. Jam and G.C. Trigunayat, Z. Krist. 142 (1975) 121. [32] P.C. Jam, M.A. Wahab and G.C. Trigunayat, Acta Cryst. B34 (1978) 2685. 133] Z.G. Pinsker, Acta Physicochim. URSS 14 (1941) 503. 1341 R, Prasad and O.N. Srivastava, Z. Krist. 131 (1970) 376. [35] R.C, Evans, An Introduction to Crystal Chemistry Cambridge Univ. Press, UK, 1966). [36] M.R. Tubbs, Phys. Status Solidi 49(1972)11. [37] M. Kogachi and K. Katada, J. Phys. Chem. Solids 36 (1975) 501. [38] M. Hirabayashi, K. Hiraga and N. mo, J. Phys. Soc. Japan 27 (1969) 80.
Journal of Crystal Growth 53 (1981) 574—578 North-Holland Publishing Company
GROWTH AND TRANSFORMATION OF POLYTYPES IN MX2 COMPOUNDS V.K. AGRAWAL * Instituto dePesquisas Espacias, INPE, Conseiho Nacional de Desenvolvimento CientIfico e Tecnológico, CNPq, 12200 S~oJosé dos Campos, S.F., Brasil Received 12 January 1981
On the basis of a review of experimental studies made on single crystals of Pb12, Cd12 and CdBr2, it has been shown that the high polytypes in a substance are formed as a matter of chance in the initial stages of the growth of crystals. They are in a metastable state and, therefore, transform generally into a basic type during growth or on annealing. As regards to formation of a basic type, the ionicity of the compound has been found to have a direct influence in determining which of the closely related structures will be formed. On the basis of polytypic structures of Cd12 and Pb12 reported so far, it has been found that the second and third neighbour anion—anion layer interactions dominate the interlayer interactions during growth and transformation of polytypes. A criterion for occurrence of Zhdanov number 3 in Zhdanov symbols of crystal structure is that it can occur only at places where the sum of all numbers preceding it is an odd number. This rule would help in the determination of structures of high polytypes of Cd12 and Pbl2.
1. Introduction The phenomenon of polytypism exhibited by a large number of substances has attracted solid state physicists due to the fact that different polytypic modifications of a substance possess different semiconducting, dielectric, optical and photovoltaic prop• erties which,in other words, are more or less sensitive to the structure type. The degree of polytypism exhibited by such substances, even by isostructural ones, is widely different, e.g., in Cd12 a large number whereas in CdBr2 only a few polytypes have been reported [1]. However, there is a common feature among all of them in that each substance, when grown under certain conditions, has a particular type, known as common or basic type, which occurs much more frequently than all other types. Different common types have been found to occur at different temperatures [2,3]. *
On leave of absence from Motilal Nehru College (University of Delhi), New Delhi 110021, India.
The predominance of one type over the others, although they have similar lattice energies, and the occurrence of long-period polytypes, although the presentisknowledge interactions in crystal lattice confined of to atomic short-range forces, have been puzzling features of the phenomenon. An attempt has been made to explain these features in the present paper on the basis of a review of the experimental studies made on single crystals of Pb12, Cd12 and CdBr2 and their mixed crystals by the author and his coworkers [4—13]. The compounds were chosen because they are isostructural but exhibit a different degree of polytypism and also different common types, viz. 2 H, 4 H, and 6 R, respectively [1]. 2. Experimental results The crystals of Pb12, Cd12 and CdBr2 grown by various methods have been studied using X-ray and electron diffraction, optical microscopy and transmission and scanning electron microscopy. The experimental results are summarized below.
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V.K. Agrawal / Growth and transformation of polytypes in MX
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The as-grown crystals of Cd12 and CdBr2 grown by vapour phase under stabilized growth conditions exhibited only the structure types 4 H and 6 R, respectively [11,14], whereas those grown from aqueous solutions under ordinary room temperature conditions showed a large number of ordered longperiod polytypes in Cd12 [4,15,16] and highly disordered structures in C dBr2 [4,9,17], particularly in the initial stages of their nucleation [5]. However, rhombohedral structures have generally been observed in the later parts of their growth [7]. The crystals of Cd12 grown by vapour phase under deliberately fluctuating, but controlled, temperature consisted of a mixture of types 4 H and 12 R [18]. The mixed crystals of Cd!2 and CdBr2 grown by vapour phase under stabilized growth conditions also exhibited a mixture of 4 H and 12 R [12]. Cd12 crystals grown from aqueous solutions under ordinary room temperature conditions during winter, when the ternperature in the laboratory varied from about 5 to 25°Cexhibited comparatively more of type 2 H and the higher polytypes based on it than those grown during summer, when the temperature variation was from about 25 to 40°C,although the common type at both times was 4 H. By a heat-treatment study of solution-grown Cd!2 crystals, it has been shown that the 12 R structure comes next to the basic type from the stability point of view [19]. In Pb!2 crystals grown by the gel method, the percentage of common type 2 H has been found to be decreasing on increasing the temperature of the gel [20] and 12 R had been reported to be the stable modification and the common type at the high ternperature of 260°C [3]. Impurity introduced into Pb!2 crystals caused an increase of incidence of polytypism [21]. Recent studies of as-grown Cd12 crystals of varying thickness grown by a vapour phase technique have shown that in the initial stage of their growth the structure is polycrystalline but on further growth a considerable reorientation and coalescence takes place forming a disordered layer structure. As the deposition proceeds further, the final product is 4 H [13]. Successive cleavage studies of solution grown Cd!2 crystals along the basal plane had also revealed that the polytypic transformation during growth is always accompanied by a greatly disordered structure [22].
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3. Discussion On the basis of experimental results, it is established that if a polytypic substance is grown under well stabilized growth conditions, its single crystals exhibit only one particular type of structure. Addition of impurities in the charge, fluctuating temperature and supersaturation, i.e. unstabiized growth conditions and their influence on stoichiometry, rate of crystallization, and creation and movement of dislocations are responsible for the formation of various polytypes. High polytypes, which generally occur in the initial stage of the growth of crystals, grown either by vapour phase or from aqueous solutions, are in the metastable state which, during subsequent growth or on annealing, transform into another polytype, generally into a basic type. Since the growth conditions are fluctuating in the initial stage of nucleation of crystals, a high polytype is obviously formed accidentally. However, once it is formed it does not change in situ if the growth conditions existing at the time of its nucleation remain highly stabilized, which, of course, is difficult to achieve for long duration, particularly in solution growth. Otherwise, it would transform into another ordered polytype via disordered arrangement of layers since, ordered structures are energetically more favourable than disordered ones. That is why, the same high polytype does not occur even on both the basal faces of a platy crystal; a high polytype with a particular layer sequence is rarely repeated; they generally form in the initial stages of growth of crystals; a polytypic transformation during growth is always accompanied by much disorder. Such disordered crystals have a tendency to transform into a basic type during growth or on annealing. Therefore, the controlled growth of a desired high polytype does not seem to be possible. On comparing the commonly observed structures of Pb12 2 H (A7B)(A7B), Cd12 4 H (A’yB)(CaB), or (A’yB)(A~3C),and CdBr2 6 R (A’yB)(Cj3A)(BaC), where A, B and C represent the positions of halogen ions and the greek letters metal ions, it is seen that the second sandwich in each of them, keeping the first one the same, has a different orientation with respect to each other. There are only four possible orientations, viz. AB, AC, CB and CA (the positions of the metal ions, represented by greek letters, are —
—
—
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automatically determined by the I-layer stacking mode), which the second sandwich can have if the first one is in AB orientation, giving rise to 3 different structures — 2 H, 4 H, 4 H and 6 R, respectively, From the point of view of interlayer interactions, there is a considerable difference between these struc-
tures. In 2 H, all the anion—anion ‘second neighbours are in the same orientation, in 4 H only the alternates are, whereas, in 6 R all are in different orientations,
2 compounds
either in A or B orientation since no two successive layers can be in the same orientation in these structures. However, 13 would prevent the 4th layer from
adopting the A orientation because it violates the condition (ii) described above; therefore, it could take only the B position resulting in the formation of 4 H(ABCB). Since the tendency of the structure to continue during further growth is that of 2 H, the
next sandwich would be in CB orientation, resulting
Thus, it is apparent that the strength of interlayer interactions in these compounds is in decreasing
in the formation of a faulted 2 H structure. However, as an ordered structure is energetically more favour-
order. The same conclusion was earlier drawn by the author [23] from considerations of their geometrical structure and then correlating it with the frequency of occurrence of stacking faults in their crystals. Recently, by estimation of interactions in Cd12 by light scattering techniques, it has been shown that the
able than a disordered faulted one, a regular 4 H structure may continue to be formed. Depending upon interlayer interactions, it may further transform into another type; obviously, its probability of transformation in Pb!2 would be less than that in Cd12 because of stronger interlayer interactions in the
nearest neighbour interlayer interaction dominates
former. That explains the high incidence of poly-
the interlayer interaction [24]. Apparently, the mcidence of polytypism in a compound as a result of transformation of. its common type into other polytypes would depend on these interactions, Recently, the author [25] has reported that the basic hexagonal types of Cd!2 and Pb!2 are transformed more frequently into those rhombohedral structures for which (i) the hexagonality is almost the same as that of their parents, (ii) the top and bottom anion layers of two successive sandwiches, respectively, are not in the same orientation and (iii) the stacking fault energy is minimum. On the basis of these conditions he has explained the formation of frequently observed rhombohedral polytypes, viz. 12 R1(l3)3, 18 R1(2l21)3, 18 R2(13l1)3 and 24 R1(22l2)3 and the non-occurrence in Cd!2 and Pb12 of other probable types, viz. 6 R(°°)and 12 R2(31)3. On the basis of these conditions, the polytypic transformation appears to depend mainly on anion—anion second and third neighbour interactions (referred to as ~2 and ~ respectively, in the following) as explained below. Cation—cation layer interaction does not seem to play an independent role because cation layers may take any orientation irrespective of its predecessors through synchro-shear motion [26]. First consider the transformation in Pb12 of which the common type is 2 H(ABAB...). A stacking fault occurring at third layer of the sequence would transform it from A to C and then the 4th layer can be
typism in Cd!2 compared to that in Pb!2 when grown under ordinary room temperature conditions. On further growth of 4 H(AB)(CB), the third sandwich can be in two equally probable orientation, viz. (AB) or (CA), if only ~ and ~ are taken into account, because second and third sandwiches in both cases form a 4 H structure {(CB)(AB)} or {(CB)(CA)} and, similarly, the fourth sandwich can adopt either of the orientations (CB) or (AC) in the former case, or (CB) or (BA) in the latter. So, either 4 H would continue to grow or would transform into one of the following three sequences: (i) (AB)(CB)(CA)(BA) 12 R1(13)3 (ii) (AB)(CB)(AB)(AC) 8 H(2123) (iii) (AB)(CB)(CA)(CB) 8H(2l23). ... ... ...
The observations of a mixture of 4 H and 12 R in almost all the vapour grown crystals of CdI2_~Brx [12]; the vapour grown Cd!2 crystals grown under fluctuating, but controlled, temperature [18]; its frequent occurrence in solution grown Cd!2 crystals [7]; and at high temperature in Pb!2 crystals [3] imply that only cI~2and ~I~3dominate the interlayer interactions during their growth. The transformation of polytypes below 16 H into 4 H after one heating run, whereas that of 12 R occurs only after a large number of heating runs at 270°C [19] substantiate this conclusion. Regarding occurrence of 8 11(2123), either it would obtain by a dislocation a memory to continue to grow as 8 H or a faulted 4 H would be formed;
V,K, Agrawal / Growth and transformation of polytypes in MX
2 compounds
both types have been observed experimentally in solution grown Cd!2 and gel grown Pb12 crystals [1,27]. Conversely, in CdBr2 the common structure is 6 R(AB)(CA)(BC) having the top and bottom anion layers of all successive sandwiches, respectively, in the same orientation. A stacking fault occurring at any place in the sequence will disturb this regularity and also changes its hexagonality, except that for a twinned 6 R(AC)(BA)(CB). Probably, these factors prevent the transformation of 6 R into other structures and allow the frequent occurrence of twinned 6 R [14,17]. CdBr2 crystals grown by mixing HBr/ Br2 in undersaturated aqueous solutions at ordinary room temperature conditions have exhibited some percentage (‘-‘l 1%) of 4 H, while majority of them are 6 R/twinned 6 R and/or disordered types [4,9,17], whereas the others grown at a constant temperature of ‘-‘40°Chave shown some ordered polytypes too. Recently, the author and his coworkers [28] have reported the structure of a new CdBr2 polytype 12 R as (l3)3’mixed with 4 H and 6 R, and have also found others like 12 H and 36 R (unpublished). It has been shown that 12 R is formed as a result of transformation of 4 H, as in Cd!2, and not of 6 R. Low supersaturation of the solution and presence of HBr/Br2 in it appear to be responsible for small incidence of polytypism and higher degree of disorder in solution grown CdBr2 crystals. The transformation of Cd!2 and Pb12 polytypes on heating has been explained so far in terms of the creation and movement of isolated and extended dislocations, their boundaries and other obstacles like impurities, etc. [1]. Recently, the reversible transformations in some crystals of Pb!2 at high temperature, viz. 2H to 30 R at 130°Cand 2 H to 12 R at 260°C, have been reported by Minagawa [27]. On the basis of interlayer interactions, the type 2 H should be transformed into 12 R via 4 H and it is indeed substantiated experimentally in that the latter has been found to exist in some crystals even at the high temperature of 260°Cand also occurs in coalescence with 12 R in some of the vapour grown crystals [27]. Besides, Zallen and Slade [29] observed by Raman scattering the conversion into the 4 H type of Pb12 crystals upon heating at ‘~145°C. However, it was surprising to note from the ABC-sequence of 30 R (111313)3 that it could not be formed directly
577
from any 1011 structure since the first and tenth layers in the sequence of 30 R were found to be in the same orientation; the nH-3nR mechanism of formation of rhombohedral polytypes [20] probably fails in this case. On looking at the Zhdanov symbols of 30 R (111313)3, they seem to be very close to those of 12 R (131313), so it could only be conjectured that at high temperature 30 R is transformed into 12 R or vice versa. The conditions described above for polytypic transformation imply that not only the Zhdanov number 4 should be absent in the transformed structures of Cd12 and Pb12, but also the number 3 should occur only at the positions where the sum of the numbers occurring before it is an odd number, e.g., the structures like (13)3, (111313)3 and (1232) are possible but not those illustrated by (3 1)3, (2321), or (113131)3. All, but two, of the reported structures of nearly 120 polytypes of Cd12 and Pb!2 so far [1,27, 30—32] have been found to observe this rule. Of the two exceptions, one 6 H(33) was reported only once in Cd!2 in 1941 [33] and the other 32 H[(22)532l123] appeared to be wrongly reported since the intensities calculated by the author for this structure did not agree with the reported observed intensities [34]. It, therefore, shows that not only the transformed structures follow the above mentioned conditions, the high polytypes formed during growth, too, observe them. This criterion of Zhdanov number would make the determination of atomic structures of high polytypes easier since it would reduce considerably the number of theoretically possible structures of a polytype: for example, on the basis of this criterion, 12 R can have only one structure (13)3, 18 R two (1311)3 and (2121)3, 24 R four (2213)3, (212111)3, (211121)3 and (131111)3, 6 H one (2211), 8 H three (221111), (121121) and (1232), and so on. As regards to the formation of a basic type in a substance, a correlation has been found to exist between the cubicity (i3) of the structure and the ionicity of the compound. The former is defined as the ratio of the number of anion layers in fcc orientation to the total number of them in the unit cell. The basic types for Pb12, Cd!2 and CdBr2 are found to be in an increasing order of 13, viz. j3 = 0 for 2 H, 1/2 for 4 H, unity for 6 R. The ionicity of these compounds has also been reported to be in the same order —
—
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VK. Agrawal / Growth and transformation of polytypes in MX
[35,36]. The series can also be extended to CdC12 which is more ionic than CdBr2 and exhibits only the 6 R structure without any disorder. Thus the ionicity of the compound appears to have a direct influence in determining which of these closely related structures, i.e. the basic type, should be formed. On the basis of this correlation, it is easy to understand the occurrence of different basic typed in a substance due to change in growth temperature, supersaturation, or composition. Various structures had been found in Mg—In, Mg—In—Cd and Au—Cd alloys separately by varying the relative composition of their elements, and the composition dependence of hexagonality (ci), where ci = 1 —13, of the observed structures in terms of the electron-to-atom ratio had been reported in these alloys [37,38].
Re erences [1] G.C. Trigunayat and A.R. Verma, in: Crystallography and Crystal Chemistry of Materials with Layered Structures, Ed. F. Levy (Reidel, Dordrecht, 1976) p. 269. [2] W.F. Knippenberg, Philips Res. Rept. 18 (1963) 161. [3] T. Minagawa, Acta Cryst. A31 (1975) 823. [4] V.K. Agrawal, Ph.D. Thesis, University of Delhi, India (1970). [5] V.K. Agrawal, ActaCryst. A26 (1970) 567. 161 V.K. Agrawal, Crystal Lattice Defects 8 (1978) 7. [7] V.K. Agrawal, Phys. Status Solicli 57 (1980) 143. [8] V.K. Agrawal and G.C. Trigunayat, Ada Cryst. A25 (1969) 401. [9] V.K. Agrawal and G.C. Trigunayat, Acta Cryst. A26 (1970) 426. [10] V.K. Agrawal, G.K. Chadha and G.C. Trigunayat, Acta Cryst. A26 (1970) 140. [11] S.D. Sharma, K. Mehrotra and V.K, Agrawal, J. Electrochem. Soc. 124 (1977) 945. [12] S.D. Sharma; K. Mehrotra and V.K. Agrawal, J. Electrochem. Soc. 126 (1979) 325.
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[131S.D.
Sharma, G.L. Sharma and V.K. Agrawal, J. Crystal Growth 49 (1980) 580. [14] K. Mehrotra, J. Crystal Growth 44 (1978) 45, [15] V.K. Agrawal, G.K. Chadha and G.C. Trigunayat, Ada Cryst. B26 (1970) 1911.
1161 R.S. Mitchell, [17] R.S. Mitchell,
Z. Krist. 108 (1956) 296. Z. Krist. 117 (1962) 309. [18] S.D. Sharma, G.L. Sharma and V.K. Agrawal, to be published. [191 G. Lal and G.C. Trigunayat, J. Solid State Chem. 9 (1974) 132 [20] J.l. Hanoka and V. Vand, I. Appl, Phys. 39 (1968) 5286. [21] M. Chand and G.C. Trigunayat, J. Crystal Growth 39 (1977) 299. [22] Gyaneshwar and G.C. Trigunayat, J. Solid State Chem. 15 (1975) 127 [23] V.K. Agrawal, Phys. Letters 34A (1971) 82. [24]S. Nakashima, H. Katahama, M, Daimon and A. Mitsuishi, Solid State Commun. 31(1979) 913. [25] V.K. Agrawal, Mater. Res. Bull. 14 (1979) 907. [26] S. Amelinckx, The Direct Observation of Dislocations, Suppl. 6 of Solid State Physics, Eds. F. Seitz and D. Turnbull (Academic Press, New York, 1964). [271T. Minagawa, J. Appl. Cryst. 12 (1979) 57. [28] S.D. Sharma, G.L. Sharma and V.K. Agrawal, Acta Cryst. B36 (1980) 26. [29] R. Zallen and M.L. Slade, Solid State Commun. 17 (1975) 1561. [30] P.C. Jam and G.C. Trigunayat, Acta Cryst. B34 (1978) 2677. [31] P.C. Jam and G.C. Trigunayat, Z. Krist. 142 (1975) 121. [32] P.C. Jam, M.A. Wahab and G.C. Trigunayat, Acta Cryst. B34 (1978) 2685. 133] Z.G. Pinsker, Acta Physicochim. URSS 14 (1941) 503. 1341 R, Prasad and O.N. Srivastava, Z. Krist. 131 (1970) 376. [35] R.C, Evans, An Introduction to Crystal Chemistry Cambridge Univ. Press, UK, 1966). [36] M.R. Tubbs, Phys. Status Solidi 49(1972)11. [37] M. Kogachi and K. Katada, J. Phys. Chem. Solids 36 (1975) 501. [38] M. Hirabayashi, K. Hiraga and N. mo, J. Phys. Soc. Japan 27 (1969) 80.