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Formation of “hair” inclusions in rapidly grown potassium dihydrogen phosphate crystals
.........
ELSEVIER
CRYSTAL QROWTH
Journal of Crystal Growth 166 (1996) 228 233
Formation of "hair" inclusions in rapidly grown potassium dihydrogen phosphate crystals I.L. Smolsky ~'*, N.P. Zaitseva h, E.B. Rudneva ~, S.V. Bogatyreva b ~LInstitute qf Crystallography, Russian Academy of Sciences, Moscow, Russian Federation b Moscow State University, Moscow, Russian Federation
Abstract A special kind of liquid inclusions named " h a i r s " are described in the present work, These inclusions were observed in the crystals grown from a point seed at rates of 10-30 mm per day in the [001] direction. It was shown that formation of " h a i r " inclusions cannot be described by known mechanisms. Their occurrence is not connected with the dislocation structure but probably induced by the morphological conditions on growing surface at high growth velocities.
1. Introduction
KDP group crystals are widely used in laser technology. Large crystals of high optical quality are required for use in powerful laser systems. The formation of liquid inclusions during the crystal growth process is an important problem in the production of large optical elements. Recent studies [1] have shown that locations of such inclusions coincide with the areas of high depolarisation losses that restrict their use in high power laser systems. Liquid inclusions in crystals grown from solutions have been observed repeatedly [2-8]. In most cases their formation occurs at a high growth velocity concerned with inhomogeneous distribution of structural particles near the growing surface. The reasons for these processes are not clear. Only a few mechanisms for the formation of inclusions have been discussed.
' Corresponding author.
The formation of hollow cores of dislocations with a Burgers vector b of more than 10 A has been discussed more thoroughly. Frank predicted their existence in 1951 [9]. Such holes were detected in SiC [10,11] and KDP [12] crystals at the tops of the growth hillocks formed by individual dislocations or their bunches. More frequently, inclusions formed under certain hydrodynamic conditions were observed. Usually this type of inclusions, named "veils", has a zonal structure [2-4,13]. If the crystal grows in the [001] and [00]] directions at the same time and the flow of the solution is along the Z-axis, veils are formed on the rear crystal faces because of the solution steams, which deplete the growing surface of structural particles [2,3]. Moreover, it has been pointed out [4] that the beginning of the formation of veils coincides with the moment when the dislocations are displaced from the face centre to the edges in the area of higher supersaturation. In a number of works [5-7] oriented chains of liquid inclusions were observed. Their orientations
00-.-0.48/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PII S0022-t)248(96)0008()- 2
I.L. Smolsky et al. /Journal of Cr3.'stal Growth 166 (1996) 228-233
usually coincide with crystallographic directions with low indices - [001], [011], [010]. Their formation and concentration had been connected with fluctuations of temperature [7,12] and supersaturation [7] (the more supersaturation, the higher the concentration of inclusions). In Ref. [7] it was suggested that this kind of inclusion could be formed because of the capture of solution by the angles of the growth steps. Many kinds of oriented liquid inclusions of various shapes and orientations were observed in KDP crystals grown from gels and water solutions [5]. The sizes of these inclusions ranged from 5 to 250 /~m. Unfortunately, the growth conditions were not described. A special type of oriented inclusion is described in the present work. These " h a i r " inclusions can be observed in KDP crystals grown by a high velocity technique [14] or in large crystals grown under traditional regimes.
2. Experimental procedure The crystals were grown from "point" seeds under constant supersaturation o-= 10% [14]. Supersaturation was supported by decreasing the temperature during the growth process. Growth velocity in the [001] direction was about 15 ram/day. The seeds
229
were mounted at the centre of a platform reversibly rotated. During crystal growth, rotations were 20 s clockwise, 3 s - stop, 20 s - anticlockwise. The final crystals had dimensions up to 10 c m × 10 cm × 15 cm. Plates 2 mm thick were cut from the crystals. Their surfaces were polished for studies of liquid inclusions by means of optical microscopy and X-ray topography. The methods of Lang [15] and doublecrystal X-ray topography have been used for the studies. X-ray topographs were exposed in Mo K c~ irradiation on the R-2 nuclear photoplates with an emulsion of 50 /.~m thickness.
3. Observations and discussion The hair inclusions are visible to the naked eye under side lighting (Fig. 1). They appear as fine fibres a few centimetres long, variously deflected from the Z-axis. They can be located at both dipyramidal and prismatic growth sectors. It is well known that dislocations mainly spread in KDP crystals in definite directions according to the orientations of minimum elastic energy [16]. In outline the observed liquid inclusions are much the same as the dislocations in their distribution in the crystal. It was found on closer examination that most
Fig. I. A general view of "hair" inclusion arrangementin the rapidly grown KDP crystal.
I.L. Smolsky et al. / Journal of Crystal Growth 166 (1996) 228-233
230
of the hairs are long chains of dozens or hundreds of liquid inclusions. Many forms of chains were observed by the use of the optical microscope: straight (Fig. 2b); slightly bent (Fig. 2e); polygonal lines (Figs. 2a, 2c and 2d).
It was difficult to observe the whole chains because of their inclination to the specimen plane. Little inclusions are from 3 to 30 /xm in size and variously extended along the chain. Various kinds of chains are presented in Fig. 2.
~[loo1
Fig. 2. The chains of inclusions in the rapidly grown KDP crystal. X-cut: (a-e) optical photographs; (f) the double-crystal X-ray topograph of the same place as on the photograph (e), g [404].
LL. Smolsky et al. / Journal of C~stal Growth 166 (1996) 228-233
The angle between the chains and the Z-axis changes from 20 ° to 90 ° . The size of the inclusions is much more than that in the case of hole formation [12] and the chains do not all coincide with dislocations. Evidently the coincidence of some orientations is accidental. It means that the formation mechanism of these liquid inclusions is different from that described in Refs. [9-12]. To establish the mutual arrangement of inclusions and other defects, X-ray topographs were made. It is evident from their analysis that the chains are not dislocation contributors. Moreover, their locations do not coincide with those of the dislocation lines (Fig. 2f). The capture of liquid inclusions along some directions has been described [6-8] arising from the formation of an unstable configuration of the step edge when the elementary steps join into a macrostep. Because the feed for the crystallisation front is not equal for various parts of the front, inclusions are formed. In particular, this takes place under high supersaturation. Two models for the formation of liquid inclusions are discussed. The first is that, initially, better feeding for the top part of a macrostep forms the hanging edge that afterwards closes to the step and the inclusion emerges. In the second, the capture is caused by the rectangular edges of the macrostep. In both cases inclusions are located in the growing face, whereas hairs form angles with it. Moreover, these angles do not coincide with the optimum orientations of dislocations and growth
231
steps. There is probably another mechanism of inclusion formation. One possible mechanism can be suggested as follows. Generally the rear faces of vicinal hillocks in relation to the flow direction represent favourable conditions to macrostep formation [17]. The character of the macrostep arrangement is changing from the top of the hillock to its bottom. The microphotograph (Fig. 3) shows a hillock on the dipyramidal face of a rapidly grown KDP crystal (the top is outside the field of view on the left). The shape and period of macrosteps are changing from the top of the hillock to its bottom. As a result liquid inclusions emerge at the surface. A more detailed view of the mechanism of inclusion formation may be deduced from close examination of the macrostep shape of vicinal hillocks on the prism face (Fig. 4). The X-ray topographs of this hillock are shown in Figs. 4a and 4b. It may be deduced from the shapes of macrosteps at the slopes of hillock O (Fig. 4c) that the growth steps change their orientations sharply at the hillock edge AOC, while a relatively smooth change of step orientation occurs at the other hillock diagonal BOD. As pointed out in Ref. [18], the motion of the hillock steps can be realised by the tangential propagation of two kinds of kinks (negative and positive) along the edges of steps. There is a difference in the kink integration energy a n d / o r a difference in the activation energy needed to enter a kink site. It leads not only to the difference in the kink density. A topo-
Fig. 3. An optical photograph of the vicinal surface on the [101] face covered by macrosteps. The process of inclusion formation is clearly seen.
LL. Smolskv et al. / Journal qf Crysml Growth 166 (1996) 228-233
232
a)
Z
•
g-02.0
"-4
---,- (ij 020
b)
B/
d-~ ~
d-,', d÷~
c)
"y
Fig. 4. A central part of the vicinal hillock on the prism face of KDP crystal: (a,b) projection X-ray topographs with opposite diffraction vector g: (c) a sketch of a position of edges and a form of macrosteps on the surface of the vicinal hillock.
graphic contrast of the sections of the edge images AO and OC, as well as BO and OD, indicates the difference in the lattice parameters at the opposite sides of these edges, i.e. in the vicinal sectors. It follows from the image contrast that the lattice parameters are slightly larger in the vicinal sectors AOB and COD than in the vicinal sectors BOC and AOD. This difference is related to the different stoichiometry, or impurity, entering as a result of the structural distinction between the positive kinks and negative ones. It is seen also that the macrostep successions are less stable in the AOD and BOC vicinal sectors than in the AOB and COD sectors. This may be related to a deficiency of some structural units in the solution and the formation of slowly moving large macrokinks, especially during rapid growth. These macrokinks can not be annihilated by kinks of the opposite sign due to structural differences so the sites where macrokinks are generated are favoured for the formation of inclusions. An additional reason for inclusion formation is the well-known Gibbs-Thomson statement that the higher the curvature of growth step, the higher the supersaturation necessary to cause step movement. The segments of steps having macrokinks are the places in which the step curvature is maximal and therefore it moves more slowly. As the result, the
empty channels ("hairs") can be formed especially near the places of the macrokink breaking. In our case, the crystals were grown under reverse stirring. The changes of the flow direction do not appreciably influence the formation of liquid inclusions. The displacement of the growing pyramidal face during the period of unidirectional flow is about 7 - 8 p~m, whereas the size of the inclusions is from 3 to 30 /~m. This means that the conditions required for the formation of hairs are stable enough to allow the formation of extended channels or chains of inclusions. Usually a few growth hillocks exist on the growing face at the same time, so it is possible that inclusion generation happens in the area of the sectorial boundary, that is, the place where the steps from various hillocks come together. The formation of liquid inclusions depends on the purity of the solution because of the impurity dependence of the step velocity and macrostep formation. The higher the impurity concentration the higher the activity of these processes. 4. Conclusion A special type of liquid inclusions ("hair" inclusions) is described in this paper. At least two mecha-
LL. Smolsky et al. / Journal of Crystal Growth 166 (1996) 228-233
nisms exist for the generation of inclusions or their chains inclined at large angles to the growing crystal surface. The first is the formation of hollows at the cores of dislocations with a large Burgers vector [10-12]. The second leads to the formation of hair inclusions because of morphological instability during crystal growth at high velocities. The details of the second mechanism are still not clear.
Acknowledgements The research described in this publication was made possible in part by Grant # MKD000 from the International Science Foundation. The authors are grateful to Dr. A.E. Voloshin for help in X-ray topography studies. References [1] J.J. De Yoreo, N.P. Zaitseva, Z.U. Rek, T.A. Land and B.W. Woods, Appl. Phys. Lett., to be published. [2] R. Janssen-van Rosmalen and P. Bennema, J. Crystal Growth 42 (1977) 224.
233
[3] R. Janssen-van Rosmalen, Thesis, Technical University Delft, 1977. [4] W.J.P. van Enckevort, R. Janssen-van Rosmalen, H. Klapper and W.H. Van der Linden, J. Crystal Growth 60 (1982) 67. [5] M.S. Joshy and A.V. Antony, Kristall Tech. B 14 (1979) 527. [6] R. Brooks, A.T. Horton and J.L. Torgesen, J. Crystal Growth 2 (1968) 279. [7] M.S. Joshi and B.K. Paul, J. Crystal Growth 22 (1974) 321. [8] R. Rodriguez, M. Aguil6 and J. Tejada, J. Crystal Growth 47 (1979) 518. [9] F.C. Frank, Acta Cryst. 4 (1951) 497. [10] I. Sunagawa and P. Bennema, J. Crystal Growth 46 (1979) 451. [11] 1. Sunagawa and P. Bennema, J. Crystal Growth 53 (1981) 490. [12] W.J.P. van Enckevort, R. Janssen-van Rosmalen and W.H. Van der Linden, J. Crystal Growth 49 (1980) 502. [13] R. Janssen-van Rosmalen, W.H. Van der Linden, E. Dobbinga and D. Visser, Kristall Tech. B 13 (1978) 17. [14] L.N. Rashkovich, Vestnik AN SSSR 9 (1984) 15. [15] A.R. Lang, Acta Cryst. 12 (1959) 249. [16] H. Klapper, Yu.M. Fishman and V.G. Lutsau, Phys. Status Solidi (a) 21 (1974) 115. [17] A.A. Chernov, Yu.G. Kuznetstov, I.L. Smolsky and V.N. Rozhansky, Krystallografia 31 (1986) 1193. [18] J.W. Noor and B. Dam, J. Crystal Growth 76 (1986) 243.
ELSEVIER
CRYSTAL QROWTH
Journal of Crystal Growth 166 (1996) 228 233
Formation of "hair" inclusions in rapidly grown potassium dihydrogen phosphate crystals I.L. Smolsky ~'*, N.P. Zaitseva h, E.B. Rudneva ~, S.V. Bogatyreva b ~LInstitute qf Crystallography, Russian Academy of Sciences, Moscow, Russian Federation b Moscow State University, Moscow, Russian Federation
Abstract A special kind of liquid inclusions named " h a i r s " are described in the present work, These inclusions were observed in the crystals grown from a point seed at rates of 10-30 mm per day in the [001] direction. It was shown that formation of " h a i r " inclusions cannot be described by known mechanisms. Their occurrence is not connected with the dislocation structure but probably induced by the morphological conditions on growing surface at high growth velocities.
1. Introduction
KDP group crystals are widely used in laser technology. Large crystals of high optical quality are required for use in powerful laser systems. The formation of liquid inclusions during the crystal growth process is an important problem in the production of large optical elements. Recent studies [1] have shown that locations of such inclusions coincide with the areas of high depolarisation losses that restrict their use in high power laser systems. Liquid inclusions in crystals grown from solutions have been observed repeatedly [2-8]. In most cases their formation occurs at a high growth velocity concerned with inhomogeneous distribution of structural particles near the growing surface. The reasons for these processes are not clear. Only a few mechanisms for the formation of inclusions have been discussed.
' Corresponding author.
The formation of hollow cores of dislocations with a Burgers vector b of more than 10 A has been discussed more thoroughly. Frank predicted their existence in 1951 [9]. Such holes were detected in SiC [10,11] and KDP [12] crystals at the tops of the growth hillocks formed by individual dislocations or their bunches. More frequently, inclusions formed under certain hydrodynamic conditions were observed. Usually this type of inclusions, named "veils", has a zonal structure [2-4,13]. If the crystal grows in the [001] and [00]] directions at the same time and the flow of the solution is along the Z-axis, veils are formed on the rear crystal faces because of the solution steams, which deplete the growing surface of structural particles [2,3]. Moreover, it has been pointed out [4] that the beginning of the formation of veils coincides with the moment when the dislocations are displaced from the face centre to the edges in the area of higher supersaturation. In a number of works [5-7] oriented chains of liquid inclusions were observed. Their orientations
00-.-0.48/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PII S0022-t)248(96)0008()- 2
I.L. Smolsky et al. /Journal of Cr3.'stal Growth 166 (1996) 228-233
usually coincide with crystallographic directions with low indices - [001], [011], [010]. Their formation and concentration had been connected with fluctuations of temperature [7,12] and supersaturation [7] (the more supersaturation, the higher the concentration of inclusions). In Ref. [7] it was suggested that this kind of inclusion could be formed because of the capture of solution by the angles of the growth steps. Many kinds of oriented liquid inclusions of various shapes and orientations were observed in KDP crystals grown from gels and water solutions [5]. The sizes of these inclusions ranged from 5 to 250 /~m. Unfortunately, the growth conditions were not described. A special type of oriented inclusion is described in the present work. These " h a i r " inclusions can be observed in KDP crystals grown by a high velocity technique [14] or in large crystals grown under traditional regimes.
2. Experimental procedure The crystals were grown from "point" seeds under constant supersaturation o-= 10% [14]. Supersaturation was supported by decreasing the temperature during the growth process. Growth velocity in the [001] direction was about 15 ram/day. The seeds
229
were mounted at the centre of a platform reversibly rotated. During crystal growth, rotations were 20 s clockwise, 3 s - stop, 20 s - anticlockwise. The final crystals had dimensions up to 10 c m × 10 cm × 15 cm. Plates 2 mm thick were cut from the crystals. Their surfaces were polished for studies of liquid inclusions by means of optical microscopy and X-ray topography. The methods of Lang [15] and doublecrystal X-ray topography have been used for the studies. X-ray topographs were exposed in Mo K c~ irradiation on the R-2 nuclear photoplates with an emulsion of 50 /.~m thickness.
3. Observations and discussion The hair inclusions are visible to the naked eye under side lighting (Fig. 1). They appear as fine fibres a few centimetres long, variously deflected from the Z-axis. They can be located at both dipyramidal and prismatic growth sectors. It is well known that dislocations mainly spread in KDP crystals in definite directions according to the orientations of minimum elastic energy [16]. In outline the observed liquid inclusions are much the same as the dislocations in their distribution in the crystal. It was found on closer examination that most
Fig. I. A general view of "hair" inclusion arrangementin the rapidly grown KDP crystal.
I.L. Smolsky et al. / Journal of Crystal Growth 166 (1996) 228-233
230
of the hairs are long chains of dozens or hundreds of liquid inclusions. Many forms of chains were observed by the use of the optical microscope: straight (Fig. 2b); slightly bent (Fig. 2e); polygonal lines (Figs. 2a, 2c and 2d).
It was difficult to observe the whole chains because of their inclination to the specimen plane. Little inclusions are from 3 to 30 /xm in size and variously extended along the chain. Various kinds of chains are presented in Fig. 2.
~[loo1
Fig. 2. The chains of inclusions in the rapidly grown KDP crystal. X-cut: (a-e) optical photographs; (f) the double-crystal X-ray topograph of the same place as on the photograph (e), g [404].
LL. Smolsky et al. / Journal of C~stal Growth 166 (1996) 228-233
The angle between the chains and the Z-axis changes from 20 ° to 90 ° . The size of the inclusions is much more than that in the case of hole formation [12] and the chains do not all coincide with dislocations. Evidently the coincidence of some orientations is accidental. It means that the formation mechanism of these liquid inclusions is different from that described in Refs. [9-12]. To establish the mutual arrangement of inclusions and other defects, X-ray topographs were made. It is evident from their analysis that the chains are not dislocation contributors. Moreover, their locations do not coincide with those of the dislocation lines (Fig. 2f). The capture of liquid inclusions along some directions has been described [6-8] arising from the formation of an unstable configuration of the step edge when the elementary steps join into a macrostep. Because the feed for the crystallisation front is not equal for various parts of the front, inclusions are formed. In particular, this takes place under high supersaturation. Two models for the formation of liquid inclusions are discussed. The first is that, initially, better feeding for the top part of a macrostep forms the hanging edge that afterwards closes to the step and the inclusion emerges. In the second, the capture is caused by the rectangular edges of the macrostep. In both cases inclusions are located in the growing face, whereas hairs form angles with it. Moreover, these angles do not coincide with the optimum orientations of dislocations and growth
231
steps. There is probably another mechanism of inclusion formation. One possible mechanism can be suggested as follows. Generally the rear faces of vicinal hillocks in relation to the flow direction represent favourable conditions to macrostep formation [17]. The character of the macrostep arrangement is changing from the top of the hillock to its bottom. The microphotograph (Fig. 3) shows a hillock on the dipyramidal face of a rapidly grown KDP crystal (the top is outside the field of view on the left). The shape and period of macrosteps are changing from the top of the hillock to its bottom. As a result liquid inclusions emerge at the surface. A more detailed view of the mechanism of inclusion formation may be deduced from close examination of the macrostep shape of vicinal hillocks on the prism face (Fig. 4). The X-ray topographs of this hillock are shown in Figs. 4a and 4b. It may be deduced from the shapes of macrosteps at the slopes of hillock O (Fig. 4c) that the growth steps change their orientations sharply at the hillock edge AOC, while a relatively smooth change of step orientation occurs at the other hillock diagonal BOD. As pointed out in Ref. [18], the motion of the hillock steps can be realised by the tangential propagation of two kinds of kinks (negative and positive) along the edges of steps. There is a difference in the kink integration energy a n d / o r a difference in the activation energy needed to enter a kink site. It leads not only to the difference in the kink density. A topo-
Fig. 3. An optical photograph of the vicinal surface on the [101] face covered by macrosteps. The process of inclusion formation is clearly seen.
LL. Smolskv et al. / Journal qf Crysml Growth 166 (1996) 228-233
232
a)
Z
•
g-02.0
"-4
---,- (ij 020
b)
B/
d-~ ~
d-,', d÷~
c)
"y
Fig. 4. A central part of the vicinal hillock on the prism face of KDP crystal: (a,b) projection X-ray topographs with opposite diffraction vector g: (c) a sketch of a position of edges and a form of macrosteps on the surface of the vicinal hillock.
graphic contrast of the sections of the edge images AO and OC, as well as BO and OD, indicates the difference in the lattice parameters at the opposite sides of these edges, i.e. in the vicinal sectors. It follows from the image contrast that the lattice parameters are slightly larger in the vicinal sectors AOB and COD than in the vicinal sectors BOC and AOD. This difference is related to the different stoichiometry, or impurity, entering as a result of the structural distinction between the positive kinks and negative ones. It is seen also that the macrostep successions are less stable in the AOD and BOC vicinal sectors than in the AOB and COD sectors. This may be related to a deficiency of some structural units in the solution and the formation of slowly moving large macrokinks, especially during rapid growth. These macrokinks can not be annihilated by kinks of the opposite sign due to structural differences so the sites where macrokinks are generated are favoured for the formation of inclusions. An additional reason for inclusion formation is the well-known Gibbs-Thomson statement that the higher the curvature of growth step, the higher the supersaturation necessary to cause step movement. The segments of steps having macrokinks are the places in which the step curvature is maximal and therefore it moves more slowly. As the result, the
empty channels ("hairs") can be formed especially near the places of the macrokink breaking. In our case, the crystals were grown under reverse stirring. The changes of the flow direction do not appreciably influence the formation of liquid inclusions. The displacement of the growing pyramidal face during the period of unidirectional flow is about 7 - 8 p~m, whereas the size of the inclusions is from 3 to 30 /~m. This means that the conditions required for the formation of hairs are stable enough to allow the formation of extended channels or chains of inclusions. Usually a few growth hillocks exist on the growing face at the same time, so it is possible that inclusion generation happens in the area of the sectorial boundary, that is, the place where the steps from various hillocks come together. The formation of liquid inclusions depends on the purity of the solution because of the impurity dependence of the step velocity and macrostep formation. The higher the impurity concentration the higher the activity of these processes. 4. Conclusion A special type of liquid inclusions ("hair" inclusions) is described in this paper. At least two mecha-
LL. Smolsky et al. / Journal of Crystal Growth 166 (1996) 228-233
nisms exist for the generation of inclusions or their chains inclined at large angles to the growing crystal surface. The first is the formation of hollows at the cores of dislocations with a large Burgers vector [10-12]. The second leads to the formation of hair inclusions because of morphological instability during crystal growth at high velocities. The details of the second mechanism are still not clear.
Acknowledgements The research described in this publication was made possible in part by Grant # MKD000 from the International Science Foundation. The authors are grateful to Dr. A.E. Voloshin for help in X-ray topography studies. References [1] J.J. De Yoreo, N.P. Zaitseva, Z.U. Rek, T.A. Land and B.W. Woods, Appl. Phys. Lett., to be published. [2] R. Janssen-van Rosmalen and P. Bennema, J. Crystal Growth 42 (1977) 224.
233
[3] R. Janssen-van Rosmalen, Thesis, Technical University Delft, 1977. [4] W.J.P. van Enckevort, R. Janssen-van Rosmalen, H. Klapper and W.H. Van der Linden, J. Crystal Growth 60 (1982) 67. [5] M.S. Joshy and A.V. Antony, Kristall Tech. B 14 (1979) 527. [6] R. Brooks, A.T. Horton and J.L. Torgesen, J. Crystal Growth 2 (1968) 279. [7] M.S. Joshi and B.K. Paul, J. Crystal Growth 22 (1974) 321. [8] R. Rodriguez, M. Aguil6 and J. Tejada, J. Crystal Growth 47 (1979) 518. [9] F.C. Frank, Acta Cryst. 4 (1951) 497. [10] I. Sunagawa and P. Bennema, J. Crystal Growth 46 (1979) 451. [11] 1. Sunagawa and P. Bennema, J. Crystal Growth 53 (1981) 490. [12] W.J.P. van Enckevort, R. Janssen-van Rosmalen and W.H. Van der Linden, J. Crystal Growth 49 (1980) 502. [13] R. Janssen-van Rosmalen, W.H. Van der Linden, E. Dobbinga and D. Visser, Kristall Tech. B 13 (1978) 17. [14] L.N. Rashkovich, Vestnik AN SSSR 9 (1984) 15. [15] A.R. Lang, Acta Cryst. 12 (1959) 249. [16] H. Klapper, Yu.M. Fishman and V.G. Lutsau, Phys. Status Solidi (a) 21 (1974) 115. [17] A.A. Chernov, Yu.G. Kuznetstov, I.L. Smolsky and V.N. Rozhansky, Krystallografia 31 (1986) 1193. [18] J.W. Noor and B. Dam, J. Crystal Growth 76 (1986) 243.