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Dislocation characterization in crystals of potash alum grown by seeded solution growth under conditions of low supersaturation
Journal of Crystal Growth 121 (1992) 709—716 North-Holland
~
CRYSTAL GROWTH
Dislocation characterization in crystals of potash alum grown by seeded solution growth under conditions of low supersaturation H.L. Bhat
~,
R.I. Ristié
2
J.N. Sherwood and T. Shripathi ~
Department of Pure and Applied Chemistry, Unitersity of Strathclyde, Glasgow GI 1XL, Scotland, UK Received 26 February 1992
An analysis has been carried out of the genesis and character of growth dislocations present in all growth sectors of single crystals of potash alum. The crystals, grown from seeded solutions by the temperature lowering method under conditions of low supersaturation, presented the well-developed forms: (111) dominant, (100) and {110). Growth dislocations formed predominately during refacetting of the edges and corners of the seed, rounded during preparation and insertion into the supersaturated solution. From here they become refracted into the {111) sectors which proved to be the most defective. Smaller numbers of dislocations form at the (111), (100) and {110} seed interfaces and propagate in these sectors.In crystals of inferior quality, a number of inclusions were found predominantly in the fast growing (100) sectors which become the source of additional dislocations. Dislocations present in the original seed did not propagate across the interface into the developing crystal. Dislocations of all characters were observed. The principal Burgers vectors were found to be (100), <110) and (111).
1. Introduction Due to the relatively large metastable zonewidth of its saturated solutions, its symmetrical prismatic habit and relative ease of growth, potash alum has been used as a model system in the detailed examination of the crystal growth process under a wide range of conditions. One generally studied problem has been that of growth rate dispersion. The first systematic study of the growth kinetics of potash alum led Bennema et al. [1] to propose that growth of the (111) faces occurred by a compound mechanism in which dislocation controlled growth and polynuclear two-dimensional nucleation occurred simultaneously. This
2
Permanent address: Department of Physics, Indian Institute of Science, Bangalore-560012, India. Permanent address: Institute of Physics, P.O. Box 57 11000 Belgrade, Yugoslavia. Permanent address: Inter University Consortium, University Campus, Indore (MP) 452001, India.
0022-0248/92/$05.00 © 1992
—
was followed by the observations of Mullin and Garside [2] on growth rate dispersion in which some crystals were shown to yield a zero growth rate for long periods of time. This intriguing phenomenon was later shown by them to occur also in attrition fragments [31and was linked to the problem of growth rate variations which follow secondary nucleation in industrial crystallizers [4]. At a later time Human [5] and, separately, Van Enckewort [61 using larger crystals, showed that the dispersion occurred principally on the (100) and (110) faces with the (111) faces propagating at a constant rate. The general explanation of this phenomenon was that the dispersion reflects varying concentrations of dislocation step sources at the surfaces of the crystals; fracture yielding particles containing different numbers of dislocations either from the original non-uniform distribution of growth dislocations in the crystal or as result of plastic .
.
deformation accompanying the deformation and fracture process. Studies on the distribution of dislocations in potash alum crystals by Gits-Leon
Elsevier Science Publishers B.V. All rights reserved
710
H.L. Bhat et a!.
/ Dislocation
characterization in crystals of potash alum
et al. [7] showed that large numbers of dislocations could be developed in the (100) sectors. They produced evidence to show that the noted variation of growth rate could well be dislocation controlled. Both Human [5]and Van Enckewort [6] later separately questioned whether or not a dislocation associated mechanism was necessary to account for the dispersion, but produced no evidence to support their speculation. More recently evidence has been presented by Ristié, Sherwood and Shripathi to demonstrate that growth rate dispersion still occurs in the (100) sectors, despite the presence of continuously propagating dislocation sources [81. In an attempt to define the basic cause of growth rate dispersion in this and in other materials, we have made a detailed study of the influence of dislocations and the fracture process on the growth of crystals of this material. In the present paper we report on the initial characteri zation of the dislocation structure of potash alum which is fundamental to the understanding of the later kinetic studies. The characterization was carried out mainly using the invisibility criteria of X-ray topographic images [91.In a few cases, growth dislocation line direction analysis has also been used [10]. .
.
Fig. 1. A typical potash alum crystal grown under low supersaturation.
3. Results 3.1. Genesis of dislocations
2. Experimental procedure Single crystals of potash alum (potassium aluminium sulphate dodecahydrate) of 100 cm3 were grown by the controlled slow cooling of a seeded saturated solution [11]. The cooling rate was adjusted to maintain a low supersaturation during all stages of growth (0.3—0.6 K day i) in order to minimize the number of defects generated in the crystal. The resulting crystals were optically highly perfect (fig. 1). Oriented sections of the crystals for X-ray topographic analysis were cut from the grown crystals using a solvent soaked string saw. The sections were polished to 1 mm thickness, using a water-soaked tissue paper before recording the topographs. All topographs were recorded on Agfa structurix D4 film using Mo Ka radiation.
Under the low supersaturation conditions used in this study, growth dislocations were observed to form predominately at the seed interface. No dislocations were observed to develop from the seed into the newly forming crystal. The new dislocations formed mainly in regions where the seed corners and edges had become rounded due to dissolution during preparation. The principal result of this damage was to reveal rough non-habit surfaces. The recapping of these and the consequent mismatch at the corners and edges is apparently taken up by the formation of dislocations. This process is well-exemplified by the topograph shown in fig. 2. Relatively few dislocations spring from the (111) habit faces (A and B) and even the cut (110) face (C), despite some abrasion of the (111) faces. In contrast, the rounded corners are the sites of generation of
H.L. Bhat ci a!.
/ Dislocation characterization
in crystals of potash alum
711
rate than the {111} surfaces (see, for example, the rapidly diminishing area of the (110) sector in fig. 2). Consequently, these clouds of growth dislocations readily cross the contracting growth sector boundaries (G~and G2) into the adjacent (111) ~
sectors making them the most defective Limitation of supersaturation to minimal val ues during the early stages of refacetting leads to a more clean healing of the interface and hence the generation of fewer dislocations (fig 3) in the new crystal In this way low concentrations of non interacting dislocations could be produced so
‘
r
that the line directions could be defined 3 2 Analysis of dislocation types
10mm,
~
At room temperature the crystal structure of potash alum is cubic, space group Pa3 with a
~
=
Fig. 2. X-ray topograph of a section of a potash alum crystal grown over a seed having natural (100) (N), abraded (111} (A, B) and cut {1 10) (C) faces. The dark line are areas surrounding the seed define the strain developed at the refacetting interface. g = 2~ftThe dark lines G1 and G2 are {110):{111) growth sector boundaries.
clouds of dislocations which form the dominant defect structure of the sample. The {100} and (110) surfaces grow initially at a much more rapid
1.2158 nm and four molecules per unit cell. The grown crystals (fig. 1) show a dominantly octahe.
dral habit with predominant (111) faces and minor (100) and (110) faces. The most likely Burgers vectors of dislocations are (100), (110) and (111). Using these values and the reported elastic constants of potash alum [12], we have defined theoretically the growth directions of dislocations [10], to be compared with some of the experimentally observed directions. These calculations are sum-
Table 1 Calculated line directions and line energies with (100), (110) and (Iii) Burgers vectors in the various growth sectors of potash alum Type
Growth sector
Burgers vector
Character
0(1, n) ~ (deg)
Energy (eV/nm)
1A lB 1C ID 2A 2B 2C 2D 2E 3A 3B 3C 3D 3F
(100) (100) (100) (100) (111) (111) (111) (111) (111) (110) (110) (110) (110) (110)
[010] [100] [101] [011) [110] [111] [010] [111] [101] [110] [0011 [100] [110]
Edge Screw Mixed Edge Edge Screw Mixed Mixed Mixed Screw Edge Mixed Edge Mixed
0.0 0.0 17.0 0.0 0.0 0.0 10.0 19.0 10.0 0.0 0.0 6.3 0.0 18.0
142.6 124.9 244.8 285.2 297.3 276.5 130.8 358.1 231.8 221.8 144.2 128.7 300.9 272.4
Liii]
~ 0(1, n) is the angle between the growth dislocation line direction I and growth normal n.
712
H.L. Bhat et a!.
/ Dislocation characterization in
N
—
_________________________________
g,220
10mm Fig. 3. X-ray topograph of a {iIO) section of a pota~shalum crystal showing very low dislocation density. g = 220.
marized in table 1, in which the various potential dislocation systems are enumerated by sector. This numeration is used in the text to indicate the potential character of the dislocations observed. In order to characterize the dislocations in typical crystals, two types of sections were examined: a (110) section to reveal the distribution of dislocations in the (100) and (111) type sectors and a (100) section to show dislocations in the (110) and (010) type sectors. 3.2.1. {iio} Section Topographs of a typical section taken using different diffraction vectors are shown in figs. 4a—4d. Fig. 4e summarizes schematically the vanous features. Particularly notable are the strongly contrasted growth sector boundaries between the various sectors. The variable trajectory of these shows well the considerable variations which occur in growth rate of the (100) faces. That the variations occur in this face and not in the {111} face has been defined by growth rate measurements [13]. In the original topographs, similar smaller serrations are noticeable on the (110): (111) boundaries. These variations and their shape are consistent with previous observation of a dispersive growth rate of the (100) and (110) faces, compared with a constant growth rate of the (111) faces [5,61.The considerable variation in
crystals of potash alum
trajectories of all growth sector boundaries throughout the section results in continuous changes in the line directions of the dislocations as they cross these boundaries. Care must therefore be taken in defining the dislocation directions. Consequently analysis is made only of those dislocations which propagate linearly from the seed interface to the bounding facet. (100) Sectors. In these sectors there can be seen only three dislocations. They follow a linear trajectory from the seed normal to the growing interface. They are in contrast in figs. 4a, 4c and 4d, but out of contrast in fig. 4b. This and their line direction defines them as of pure edge character and hence of Burgers vectors of (010) or .
.
(110) type. Since the dislocation with the shortest Burgers vector is energetically more favourable (table 1), we designate them as type 1A dislocations of Burgers vector (010). (110) Sectors. In this crystal and in other crystals grown under similar conditions, no dislocations were found in the (110) sectors. However, as we shall see later, crystals grown at higher cooling rates (>0.5 K/day), and hence higher refaceting and growth rates, were needed to develop dislocations in this sector. (111) Sectors. As noted above, these sectors are the most prominent and usually the most defective. Due to the large dimensions of the seed relative to the final crystal, dislocations origmate from different regions at the seed interface. Thus many propagate into the experimental slice from sources outside the section. As we see in fig. 4e, a large number of dislocations present in the (111) sectors are of such type. The dislocation line segments appearing in the external regions beyond the dashed lines have probably emanated from such sources, and their orientation is not well defined. Further, since many dislocations in these sectors interact with each other, their trajectories tend to become nonlinear. All these factors render the line direction analysis complicated and therefore the Burgers vector assignments were made predominantly for isolated dislocations with well-defined origins.
H.L. Bhat ci al.
/ Dislocation characterization
in crystals of potash alum
713
~.Oa4~
(a)
,~J
(c)
a 10mm
.~•
(b}
g 220
.
V.
(d)
~
~ 0
9
0
‘I,
_;~$4s
\\
<
~
~
(e) Fig. 4. X-ray topographs of a (hO) slice of potash alum with different g vectors: (a) g = 220; (b) g (e) schematic diagram of(c); Mo Ka radiation.
=
004; (c) g
=
33~(d) g
333;
714
H.L. Bhat ci a!.
/ Dislocation characterization in crystals of potash alum
Dislocations marked as of types 2A and 2B (fig. 4 and table 1) propagate from the seed normal to the growing interface, and hence are of dominantly screw or edge character. Regrettably, due to the orientation of these dislocations relative to the crystal lattice, there are no suitable orthogonal X-ray reflections with which to define them by extinction contrast. Nevertheless, some (2A) are absent when the diffraction vectors lie
almost parallel to the line direction (figs. 4c and 4d), which indicates that they are edge type with the most likely Burgers vector (110). The dislocations which are still in contrast and lie normal to the growing face (marked 2B in fig. 4e) must then be of screw type with Burgers vector (111). The remaining dislocations which propagate continously in this sector are all of strongly mixed character. Of these, dislocations marked 2C (fig.
g,004
~,040
____
b~
1A
-
(a)
.
g,022
(c)
.
b
B
~-
10mm
~1A
g,022
3A
10mm
(d)
•
10mm
Fig. 5. X-ray topographs of (hOO) slice of a poorer quality crystal exhibiting heavily dislocated {hOO) growth sectors: (a) g g = 040; (c) g = 02~(d) g = 022. Note that the growth sector boundaries are not visible in these reflections.
=
004; (b)
I-IL. Bhat ci a!.
/ Dislocation
characterization in crystals of potash alum
4e) make an angle of 17° with the growth normal. Dislocation line analysis calculations [10] indicate that the most likely Burgers vector that fits with this trajectory is (010). Further, it is interesting to note that dislocations marked D, though present in the (111) sectors, run almost parallel to (110), making a very large angle with the growth normal. These dislocations are almost out of contrast in the 004 reflection, suggesting that the Burgers vector must lie in the plane perpendicular to the (001) direction. That they are not of pure screw type is evident from the fact that they are weakly contrasted in the orthogonal reflection 220. Therefore they must be mixed dislocations. However, theoretical calculations based on the minimum energy do not predict such high angles for the most likely Burgers vectors considered here, 3.2.2. {iOO} Section Figs. 5a—5d show the topographs of a (1001 section of a crystal grown at a rate of > 0.5 K/day taken using several diffraction vectors, This crystal section contains a number of inclusions particularly in the (1001 growth sector. The central part of these topographs around the seed is strongly contrasted because of the clouds of dislocations developed at the interface and which become almost immediately refracted into the (111) sectors above and below the section. Bundies of dislocations originate from the various inclusions present along the (100) growth directions. It should be noted that most of the dislocations present in this sector run normal to the growing faces and hence must be of pure character. The dislocations marked 1A in figs. Sa and Sb are out of contrast in the reflections 004 and 040. This defines them to be of edge type possibly with Burgers vector (010) as defined above. However, from figs. 5a and 5b we can also see that some dislocations (1B) still remain in contrast in the above reflections. Hence these bundies contain both screw and edge dislocations, Also to be noted are a few dislocations (1C) in this sector which are inclined to the growth normal. By dislocation line analysis their orientation with respect to the growth direction defines them to be of Burgers vector (010).
715
As can be seen from the topograph, despite the poorer quality of the crystal, the (110) growth sectors are again practically devoid of dislocations. Those dislocations (3A) which appear in the upper (1101 sector in fig. 5a run normal to the growing interface. They are out of contrast in fig. Sd and must be of screw type with the Burgers vector (110) (table 1). In the topograph they appear to terminate before reaching the edge of the crystal, giving the impression that they are inclined to the slice plane. We note, however, that the section tapers at the edge, as can be seen by the appearance of Pendellösung fringes near to the edge (fig. Sc). Hence the termination is apparent rather than real. A few dislocations originating from the inclusions and running initially in the (100) growth sectors become refracted into the (110) sectors. As in the (110) section, this sample also has a number of dislocations, the line directions of which seem to change their course and appear nonlinear. In figs. 5a—5d, at least two such dislocation bundles are prominent (b). The reason for this behaviour can be inferred from a careful examination of the topographs themselves. In fig. Sb one can discern weakly contrasted (0011 :(110) growth sector boundaries. A comparison of fig. Sb with fig. 5a clearly indicates that these two bundles of dislocations are trapped in the growth sector boundaries for considerable lengths, after which they become refracted into the adjacent (1101 sectors. Their trajectories therefore follow that of the growth sector boundaries. Similar explanations, however, cannot be given for the nonlinear dislocations found in the (110) section.
4. Conclusions The following conclusions can be made regarding the nature of the defect structure in the various sectors of crystals grown under low supersaturation conditions: (1) Due to dispersion of growth rates in the (100) and (110) growth sectors, all growth sector boundaries follow highly irregular trajectories. (2) The (100) growth sectors of this crystal contam mostly dislocations of pure edge character
716
H.L. Bhat et a!.
/ Dislocation
characterization in crystals of potash alum
and Burgers vectors (010). They form predominantly at inclusions where these occur. Few form at the seed interface. (3) The, (110) growth sectors are often dislocation free. Even in the crystals of generally poorer quality they remain more highly perfect than other sectors. Dislocations of predominantly screw character can form under the conditions used. (4) The (111) sectors in potash alum are the most defective containing dislocations of all characters. A high crystal symmetry, coupled with the presence of irregular growth sector boundaries which intersect all sections and cause dislocation refraction, makes the analysis of the dislocations in this sector rather complicated. The dominant Burgers vectors are (111), (110) and occasionally (100). (5) Trapping of dislocations in the growth sector boundaries is one of the reasons for the occurrence of nonlinear dislocations in this crystal.
Acknowledgements This work was initiated under the auspices of an ICI Joint Research Scheme, the financial support of which is gratefully acknowledged. We also acknowledge the financial support of SERC through the Specially Promoted Programme in Particulate Technology. H.L.B. and J.N.S. thank
the British Council for their support through the HE Link Programme.
References [1] P. Bennema, R. Kern and B. Simon, Phys. Status Solidi i9 (1967) 211. [2] J.W. Mullin and J. Garside, Trans. Inst. Chem. Engrs. 45 (1967) 285. [3] J. Garside, in: Industrial Crystallization, Eds. E.J. de Jong and S.J. Jan~ié,North Holland, Amsterdam, 1979, p 143. [4] C.M. Van ‘t Land B.C. Wienk, in: Industrial Crystallizalion, Eds. E.J. de Jong and S.J. Jan~i~ (North-Holland, Amsterdam, 1979) p. 143. [5] H.J. Human, Doctoral Thesis, Catholic University, Nijmegen (1981). [6] sity, W.J.P. van Enckevort, Nijmegen (1982). Doctoral Thesis, Catholic Univer[7] S. Gits-Leon, F. Lefaucheux, M.C. Robert, J. Crystal Growth 44 (h978) 345. [8] RI. Risti~,J.N. Sherwood and T. Shripathi, J. Crystal Growth 102 (1990) 245. [9] A.R. Lang, in: Modern Diffraction and Imaging Techniques, Eds. S. Amelinckx et al. (North-Holland, Amsterdam, 1970) p. 407. [10] H. Klapper, Phys. Status Solidi (a) 14 (1972) 99. [ii] R.M. looper, B.J. McArdle, R.S. Narang and J.N. Sherwood, in: Crystal Growth, Ed. B.R. Pamplin (Pergamon, Oxford, 1980) p. 395. [12] S. Haussiihl, Z. Krist. 116 (1961) 371. [13] RI. Ristié, J.N. Sherwood and T. Shripathi, to be published.
~
CRYSTAL GROWTH
Dislocation characterization in crystals of potash alum grown by seeded solution growth under conditions of low supersaturation H.L. Bhat
~,
R.I. Ristié
2
J.N. Sherwood and T. Shripathi ~
Department of Pure and Applied Chemistry, Unitersity of Strathclyde, Glasgow GI 1XL, Scotland, UK Received 26 February 1992
An analysis has been carried out of the genesis and character of growth dislocations present in all growth sectors of single crystals of potash alum. The crystals, grown from seeded solutions by the temperature lowering method under conditions of low supersaturation, presented the well-developed forms: (111) dominant, (100) and {110). Growth dislocations formed predominately during refacetting of the edges and corners of the seed, rounded during preparation and insertion into the supersaturated solution. From here they become refracted into the {111) sectors which proved to be the most defective. Smaller numbers of dislocations form at the (111), (100) and {110} seed interfaces and propagate in these sectors.In crystals of inferior quality, a number of inclusions were found predominantly in the fast growing (100) sectors which become the source of additional dislocations. Dislocations present in the original seed did not propagate across the interface into the developing crystal. Dislocations of all characters were observed. The principal Burgers vectors were found to be (100), <110) and (111).
1. Introduction Due to the relatively large metastable zonewidth of its saturated solutions, its symmetrical prismatic habit and relative ease of growth, potash alum has been used as a model system in the detailed examination of the crystal growth process under a wide range of conditions. One generally studied problem has been that of growth rate dispersion. The first systematic study of the growth kinetics of potash alum led Bennema et al. [1] to propose that growth of the (111) faces occurred by a compound mechanism in which dislocation controlled growth and polynuclear two-dimensional nucleation occurred simultaneously. This
2
Permanent address: Department of Physics, Indian Institute of Science, Bangalore-560012, India. Permanent address: Institute of Physics, P.O. Box 57 11000 Belgrade, Yugoslavia. Permanent address: Inter University Consortium, University Campus, Indore (MP) 452001, India.
0022-0248/92/$05.00 © 1992
—
was followed by the observations of Mullin and Garside [2] on growth rate dispersion in which some crystals were shown to yield a zero growth rate for long periods of time. This intriguing phenomenon was later shown by them to occur also in attrition fragments [31and was linked to the problem of growth rate variations which follow secondary nucleation in industrial crystallizers [4]. At a later time Human [5] and, separately, Van Enckewort [61 using larger crystals, showed that the dispersion occurred principally on the (100) and (110) faces with the (111) faces propagating at a constant rate. The general explanation of this phenomenon was that the dispersion reflects varying concentrations of dislocation step sources at the surfaces of the crystals; fracture yielding particles containing different numbers of dislocations either from the original non-uniform distribution of growth dislocations in the crystal or as result of plastic .
.
deformation accompanying the deformation and fracture process. Studies on the distribution of dislocations in potash alum crystals by Gits-Leon
Elsevier Science Publishers B.V. All rights reserved
710
H.L. Bhat et a!.
/ Dislocation
characterization in crystals of potash alum
et al. [7] showed that large numbers of dislocations could be developed in the (100) sectors. They produced evidence to show that the noted variation of growth rate could well be dislocation controlled. Both Human [5]and Van Enckewort [6] later separately questioned whether or not a dislocation associated mechanism was necessary to account for the dispersion, but produced no evidence to support their speculation. More recently evidence has been presented by Ristié, Sherwood and Shripathi to demonstrate that growth rate dispersion still occurs in the (100) sectors, despite the presence of continuously propagating dislocation sources [81. In an attempt to define the basic cause of growth rate dispersion in this and in other materials, we have made a detailed study of the influence of dislocations and the fracture process on the growth of crystals of this material. In the present paper we report on the initial characteri zation of the dislocation structure of potash alum which is fundamental to the understanding of the later kinetic studies. The characterization was carried out mainly using the invisibility criteria of X-ray topographic images [91.In a few cases, growth dislocation line direction analysis has also been used [10]. .
.
Fig. 1. A typical potash alum crystal grown under low supersaturation.
3. Results 3.1. Genesis of dislocations
2. Experimental procedure Single crystals of potash alum (potassium aluminium sulphate dodecahydrate) of 100 cm3 were grown by the controlled slow cooling of a seeded saturated solution [11]. The cooling rate was adjusted to maintain a low supersaturation during all stages of growth (0.3—0.6 K day i) in order to minimize the number of defects generated in the crystal. The resulting crystals were optically highly perfect (fig. 1). Oriented sections of the crystals for X-ray topographic analysis were cut from the grown crystals using a solvent soaked string saw. The sections were polished to 1 mm thickness, using a water-soaked tissue paper before recording the topographs. All topographs were recorded on Agfa structurix D4 film using Mo Ka radiation.
Under the low supersaturation conditions used in this study, growth dislocations were observed to form predominately at the seed interface. No dislocations were observed to develop from the seed into the newly forming crystal. The new dislocations formed mainly in regions where the seed corners and edges had become rounded due to dissolution during preparation. The principal result of this damage was to reveal rough non-habit surfaces. The recapping of these and the consequent mismatch at the corners and edges is apparently taken up by the formation of dislocations. This process is well-exemplified by the topograph shown in fig. 2. Relatively few dislocations spring from the (111) habit faces (A and B) and even the cut (110) face (C), despite some abrasion of the (111) faces. In contrast, the rounded corners are the sites of generation of
H.L. Bhat ci a!.
/ Dislocation characterization
in crystals of potash alum
711
rate than the {111} surfaces (see, for example, the rapidly diminishing area of the (110) sector in fig. 2). Consequently, these clouds of growth dislocations readily cross the contracting growth sector boundaries (G~and G2) into the adjacent (111) ~
sectors making them the most defective Limitation of supersaturation to minimal val ues during the early stages of refacetting leads to a more clean healing of the interface and hence the generation of fewer dislocations (fig 3) in the new crystal In this way low concentrations of non interacting dislocations could be produced so
‘
r
that the line directions could be defined 3 2 Analysis of dislocation types
10mm,
~
At room temperature the crystal structure of potash alum is cubic, space group Pa3 with a
~
=
Fig. 2. X-ray topograph of a section of a potash alum crystal grown over a seed having natural (100) (N), abraded (111} (A, B) and cut {1 10) (C) faces. The dark line are areas surrounding the seed define the strain developed at the refacetting interface. g = 2~ftThe dark lines G1 and G2 are {110):{111) growth sector boundaries.
clouds of dislocations which form the dominant defect structure of the sample. The {100} and (110) surfaces grow initially at a much more rapid
1.2158 nm and four molecules per unit cell. The grown crystals (fig. 1) show a dominantly octahe.
dral habit with predominant (111) faces and minor (100) and (110) faces. The most likely Burgers vectors of dislocations are (100), (110) and (111). Using these values and the reported elastic constants of potash alum [12], we have defined theoretically the growth directions of dislocations [10], to be compared with some of the experimentally observed directions. These calculations are sum-
Table 1 Calculated line directions and line energies with (100), (110) and (Iii) Burgers vectors in the various growth sectors of potash alum Type
Growth sector
Burgers vector
Character
0(1, n) ~ (deg)
Energy (eV/nm)
1A lB 1C ID 2A 2B 2C 2D 2E 3A 3B 3C 3D 3F
(100) (100) (100) (100) (111) (111) (111) (111) (111) (110) (110) (110) (110) (110)
[010] [100] [101] [011) [110] [111] [010] [111] [101] [110] [0011 [100] [110]
Edge Screw Mixed Edge Edge Screw Mixed Mixed Mixed Screw Edge Mixed Edge Mixed
0.0 0.0 17.0 0.0 0.0 0.0 10.0 19.0 10.0 0.0 0.0 6.3 0.0 18.0
142.6 124.9 244.8 285.2 297.3 276.5 130.8 358.1 231.8 221.8 144.2 128.7 300.9 272.4
Liii]
~ 0(1, n) is the angle between the growth dislocation line direction I and growth normal n.
712
H.L. Bhat et a!.
/ Dislocation characterization in
N
—
_________________________________
g,220
10mm Fig. 3. X-ray topograph of a {iIO) section of a pota~shalum crystal showing very low dislocation density. g = 220.
marized in table 1, in which the various potential dislocation systems are enumerated by sector. This numeration is used in the text to indicate the potential character of the dislocations observed. In order to characterize the dislocations in typical crystals, two types of sections were examined: a (110) section to reveal the distribution of dislocations in the (100) and (111) type sectors and a (100) section to show dislocations in the (110) and (010) type sectors. 3.2.1. {iio} Section Topographs of a typical section taken using different diffraction vectors are shown in figs. 4a—4d. Fig. 4e summarizes schematically the vanous features. Particularly notable are the strongly contrasted growth sector boundaries between the various sectors. The variable trajectory of these shows well the considerable variations which occur in growth rate of the (100) faces. That the variations occur in this face and not in the {111} face has been defined by growth rate measurements [13]. In the original topographs, similar smaller serrations are noticeable on the (110): (111) boundaries. These variations and their shape are consistent with previous observation of a dispersive growth rate of the (100) and (110) faces, compared with a constant growth rate of the (111) faces [5,61.The considerable variation in
crystals of potash alum
trajectories of all growth sector boundaries throughout the section results in continuous changes in the line directions of the dislocations as they cross these boundaries. Care must therefore be taken in defining the dislocation directions. Consequently analysis is made only of those dislocations which propagate linearly from the seed interface to the bounding facet. (100) Sectors. In these sectors there can be seen only three dislocations. They follow a linear trajectory from the seed normal to the growing interface. They are in contrast in figs. 4a, 4c and 4d, but out of contrast in fig. 4b. This and their line direction defines them as of pure edge character and hence of Burgers vectors of (010) or .
.
(110) type. Since the dislocation with the shortest Burgers vector is energetically more favourable (table 1), we designate them as type 1A dislocations of Burgers vector (010). (110) Sectors. In this crystal and in other crystals grown under similar conditions, no dislocations were found in the (110) sectors. However, as we shall see later, crystals grown at higher cooling rates (>0.5 K/day), and hence higher refaceting and growth rates, were needed to develop dislocations in this sector. (111) Sectors. As noted above, these sectors are the most prominent and usually the most defective. Due to the large dimensions of the seed relative to the final crystal, dislocations origmate from different regions at the seed interface. Thus many propagate into the experimental slice from sources outside the section. As we see in fig. 4e, a large number of dislocations present in the (111) sectors are of such type. The dislocation line segments appearing in the external regions beyond the dashed lines have probably emanated from such sources, and their orientation is not well defined. Further, since many dislocations in these sectors interact with each other, their trajectories tend to become nonlinear. All these factors render the line direction analysis complicated and therefore the Burgers vector assignments were made predominantly for isolated dislocations with well-defined origins.
H.L. Bhat ci al.
/ Dislocation characterization
in crystals of potash alum
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H.L. Bhat ci a!.
/ Dislocation characterization in crystals of potash alum
Dislocations marked as of types 2A and 2B (fig. 4 and table 1) propagate from the seed normal to the growing interface, and hence are of dominantly screw or edge character. Regrettably, due to the orientation of these dislocations relative to the crystal lattice, there are no suitable orthogonal X-ray reflections with which to define them by extinction contrast. Nevertheless, some (2A) are absent when the diffraction vectors lie
almost parallel to the line direction (figs. 4c and 4d), which indicates that they are edge type with the most likely Burgers vector (110). The dislocations which are still in contrast and lie normal to the growing face (marked 2B in fig. 4e) must then be of screw type with Burgers vector (111). The remaining dislocations which propagate continously in this sector are all of strongly mixed character. Of these, dislocations marked 2C (fig.
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I-IL. Bhat ci a!.
/ Dislocation
characterization in crystals of potash alum
4e) make an angle of 17° with the growth normal. Dislocation line analysis calculations [10] indicate that the most likely Burgers vector that fits with this trajectory is (010). Further, it is interesting to note that dislocations marked D, though present in the (111) sectors, run almost parallel to (110), making a very large angle with the growth normal. These dislocations are almost out of contrast in the 004 reflection, suggesting that the Burgers vector must lie in the plane perpendicular to the (001) direction. That they are not of pure screw type is evident from the fact that they are weakly contrasted in the orthogonal reflection 220. Therefore they must be mixed dislocations. However, theoretical calculations based on the minimum energy do not predict such high angles for the most likely Burgers vectors considered here, 3.2.2. {iOO} Section Figs. 5a—5d show the topographs of a (1001 section of a crystal grown at a rate of > 0.5 K/day taken using several diffraction vectors, This crystal section contains a number of inclusions particularly in the (1001 growth sector. The central part of these topographs around the seed is strongly contrasted because of the clouds of dislocations developed at the interface and which become almost immediately refracted into the (111) sectors above and below the section. Bundies of dislocations originate from the various inclusions present along the (100) growth directions. It should be noted that most of the dislocations present in this sector run normal to the growing faces and hence must be of pure character. The dislocations marked 1A in figs. Sa and Sb are out of contrast in the reflections 004 and 040. This defines them to be of edge type possibly with Burgers vector (010) as defined above. However, from figs. 5a and 5b we can also see that some dislocations (1B) still remain in contrast in the above reflections. Hence these bundies contain both screw and edge dislocations, Also to be noted are a few dislocations (1C) in this sector which are inclined to the growth normal. By dislocation line analysis their orientation with respect to the growth direction defines them to be of Burgers vector (010).
715
As can be seen from the topograph, despite the poorer quality of the crystal, the (110) growth sectors are again practically devoid of dislocations. Those dislocations (3A) which appear in the upper (1101 sector in fig. 5a run normal to the growing interface. They are out of contrast in fig. Sd and must be of screw type with the Burgers vector (110) (table 1). In the topograph they appear to terminate before reaching the edge of the crystal, giving the impression that they are inclined to the slice plane. We note, however, that the section tapers at the edge, as can be seen by the appearance of Pendellösung fringes near to the edge (fig. Sc). Hence the termination is apparent rather than real. A few dislocations originating from the inclusions and running initially in the (100) growth sectors become refracted into the (110) sectors. As in the (110) section, this sample also has a number of dislocations, the line directions of which seem to change their course and appear nonlinear. In figs. 5a—5d, at least two such dislocation bundles are prominent (b). The reason for this behaviour can be inferred from a careful examination of the topographs themselves. In fig. Sb one can discern weakly contrasted (0011 :(110) growth sector boundaries. A comparison of fig. Sb with fig. 5a clearly indicates that these two bundles of dislocations are trapped in the growth sector boundaries for considerable lengths, after which they become refracted into the adjacent (1101 sectors. Their trajectories therefore follow that of the growth sector boundaries. Similar explanations, however, cannot be given for the nonlinear dislocations found in the (110) section.
4. Conclusions The following conclusions can be made regarding the nature of the defect structure in the various sectors of crystals grown under low supersaturation conditions: (1) Due to dispersion of growth rates in the (100) and (110) growth sectors, all growth sector boundaries follow highly irregular trajectories. (2) The (100) growth sectors of this crystal contam mostly dislocations of pure edge character
716
H.L. Bhat et a!.
/ Dislocation
characterization in crystals of potash alum
and Burgers vectors (010). They form predominantly at inclusions where these occur. Few form at the seed interface. (3) The, (110) growth sectors are often dislocation free. Even in the crystals of generally poorer quality they remain more highly perfect than other sectors. Dislocations of predominantly screw character can form under the conditions used. (4) The (111) sectors in potash alum are the most defective containing dislocations of all characters. A high crystal symmetry, coupled with the presence of irregular growth sector boundaries which intersect all sections and cause dislocation refraction, makes the analysis of the dislocations in this sector rather complicated. The dominant Burgers vectors are (111), (110) and occasionally (100). (5) Trapping of dislocations in the growth sector boundaries is one of the reasons for the occurrence of nonlinear dislocations in this crystal.
Acknowledgements This work was initiated under the auspices of an ICI Joint Research Scheme, the financial support of which is gratefully acknowledged. We also acknowledge the financial support of SERC through the Specially Promoted Programme in Particulate Technology. H.L.B. and J.N.S. thank
the British Council for their support through the HE Link Programme.
References [1] P. Bennema, R. Kern and B. Simon, Phys. Status Solidi i9 (1967) 211. [2] J.W. Mullin and J. Garside, Trans. Inst. Chem. Engrs. 45 (1967) 285. [3] J. Garside, in: Industrial Crystallization, Eds. E.J. de Jong and S.J. Jan~ié,North Holland, Amsterdam, 1979, p 143. [4] C.M. Van ‘t Land B.C. Wienk, in: Industrial Crystallizalion, Eds. E.J. de Jong and S.J. Jan~i~ (North-Holland, Amsterdam, 1979) p. 143. [5] H.J. Human, Doctoral Thesis, Catholic University, Nijmegen (1981). [6] sity, W.J.P. van Enckevort, Nijmegen (1982). Doctoral Thesis, Catholic Univer[7] S. Gits-Leon, F. Lefaucheux, M.C. Robert, J. Crystal Growth 44 (h978) 345. [8] RI. Risti~,J.N. Sherwood and T. Shripathi, J. Crystal Growth 102 (1990) 245. [9] A.R. Lang, in: Modern Diffraction and Imaging Techniques, Eds. S. Amelinckx et al. (North-Holland, Amsterdam, 1970) p. 407. [10] H. Klapper, Phys. Status Solidi (a) 14 (1972) 99. [ii] R.M. looper, B.J. McArdle, R.S. Narang and J.N. Sherwood, in: Crystal Growth, Ed. B.R. Pamplin (Pergamon, Oxford, 1980) p. 395. [12] S. Haussiihl, Z. Krist. 116 (1961) 371. [13] RI. Ristié, J.N. Sherwood and T. Shripathi, to be published.