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The growth of potassium chloride crystals in the presence of lead
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Journal of Crystal Growth 13114 (1972) 454-457 © North.Holland Publishing Co.
THE GROWTIt OF POTASSIUM CHLORIDE CRYSTALS IN THE PRESENCt OF LEAD" G. PILKINGTON and W. J. D U N N I N G
Department of Physical Chemistr.v, The University, Bristol, England Potassium chloride seeds (cleave¢i from pure, melt grown crystals) were grown from aqueous solutiont .ith supersaturation ratios in the range 1.005 to 1.050 and with concentrations of lead chloride ~ 6 × 10 M. While the seeds were growing the {100} cleavage faces were studied by using reflection microscopy an two beam interference microscopy. On the initially flat cleavage Paces many growth ilills developed dur!ng the early stages of growth. Th, hills were approximately conical and their surfaces were inclined at angles ~ 3° to the close-packed {100} p; ~nes. The most steeply inclined hills grew most rapid!y, both parallel and perpendicular to the crystal surface and soon overran their neighbours. Crystal growth occurred solely through the continuing development of these hills. Profiles of growth hills were determined at time intervals and it was found that the development o1"the profiles could be described in terms of the kinematic theory of crystal growth. Furthermore, on the otherwise smooth surfaces of the hills, kinematic shock waves of sub-microscopic steps were observed. In many instances, the shock waves had the forms of spirals centered on the apices of the hills. These observations are consistent with the thesis that the hills originate at the points of emergence in the surface of groups of dis. locations with large Burgers vectors.
i. Introduction
Crystals of KC! grown from pure aqueous solutions are either polycrystalline or develop as hoppers and ultimately contain inclusions of solution; in fact, it may be impossible to grow single crystals from pure solutiont), in contrast to this large single crystals free from macroscopic defects can be grown with ease from solution containing small amounts of additives; one of the most effective additives for this purpose is the cation of leadS). In this investigation the surface feature of KCI crystals were studied during growth from solutions with various supersaturations and various PbCI2 concentrations. Different types of growth features were observed, each type occurring within a well defined domain of solution conditions. This paper reports the features observed in one of these domains, the domain within which large single crystals can be produced. 2. Experimental
Crystal seeds with {100} faces were cleaved with a razor blade from large melt grown crystals. The seeds were placed in a cell through whicl3 solution was continuously circulated from a stock flask; .'he concentrations of KCI and PbCI2 and the tempeiatt:re of the solution could be held coustant or changed indepen-
dently in a controlled manner when desired. The crystals were studied, while growing, by means of relk¢. tion microscopy and a standard metallurgical microscope; the optical arrange,,ent was similar to that used by previous workers3). A second, and similar, growth apparatus was also used. For the latter apparatus the crystals could be studied by means of a microscope fitted with an interference objective (a description of which has been given by TerrelP), but the properties of the solution could not be varied during growth. 3. Results 3. ! • DEVELOPMENT OF GROWTH HILLS
First a description is given of the growth re: ure~ observed when a solution with the following prop .ties was passed over cleaved crystal seeds; supersatut sion ratio (actual concentration, expressed in g KCI/g ~ xter divided by saturation concentration) i.005 to I 050. lead concentration ~ 6 x 10-s M, and temper: turc 25 °C to 45 °C. A variation of the solution prop ties within these limits changed only the speed with x ,ich the growth features developed. The features observed by optical microscopy on ese freshly cleaved surfaces were low angled grain be, 1daries, scratches made by the cleaving blaae, an~ the cleavage steps. At the initiation of growth the clea age
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;a) (b~ Fl~,. I. Crystal surface after (a) 24 rain, (b) 33 rain growth, x 100. steps, initially steep cliffs, advanced slowly, concomitantly becoming less steeply inclined to the cleavage plane. After a short time growth hills appeared; they formed at scratches, at points along the cleavage steps anti at points :where no features could previously be set~n on the surface. The hills were so densely packed or some parts of the surface that they overlapped bef e : they had grown to a size at which they could be c! ,fly distinguished (density > 10s/cruz). Elsewhere, a ~s ofabout 300 ~tm)2 contained only one or two hills o :ach of them (density ~ 103/cruz). As growth proc, ted, the steeper growth hills and the higher cleavage s ~ overran neighbouring features. ~e initial stages in the development of these growth t~ ~res could be studied in greater detail by the use of t beam interference microscopy. The fringe patterns ined by this method represent contour maps of the c~ loping surface. The hills which formed on any a cleavage face had slopes varying over a wide r; :,e, see figs. la, lb. he surfaces of the growth hills are vicinal faces incl,cd at small angles to the close-packed 100 plane.
These vicinal surfaces consist of trains of submicroscopic steps separated by flat lands of (100) surface. During growth the steps advance, the lateral movement of each contributing a small increment of growth perpendieular to the (100) face. The steps are generated by growth sources at the apices of the hills; the flux o f steps generated at any given time is called the activity of the sourceS). The growth sources originating many of the hills became inactive after a short period of growth; these hills subsequently continued to increase in diameter and developed flat tops. For the early stages of growth it was very common for the activities of growth sources to change unpredictably and abruptly, both increases and decreases being observed. This caused successive rings of the surface of the growth hills to have different slopes. As growth proceeded the activities changed less often and the number of hills diminished as the steep ones overran their neighbours. After about 50 lain of bulk growth perpendicular to the surface the hills present were steep and their density was about l/ram-'. During the following 2 mm of bulk growth, which is the most
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456
G. P I L K I N G T O N A N D W. J, D U N N I N G
that has been studied, the density o f the growth hills on the surface remained approximately constant. Occasionally, a new growth hill developed on the side o f an existing one: presumably because o f an increase, in activity o f a previously dominated growth source; alternatively, a growth hill became less steep and was overrun ~ , a neighbour. .)
3 . 2 . THE PROFILES OF GROWTH HILLS
As noted above, a vicinal surface consists of a train of steps on a close-packed surface, Frank 6) examined the ~ t y in which such a vicinal surface would develop if the rate of advance of the steps across the closepacked face depended only on local step spacing. He found that the development of the face is described mathematically by a kinematic wave equation. Further, if the step velocity increases with decreasing spacing, smoothly curved concave regions o f the vicinal face are unstable ~Jth respect to the formation of discontinuities in surface orientation [see fig. 3, the profile in (d) changes to the profile in (e)]. For the mathematical description of the development o f the face these discontinuities are analogous to shock waves. By making measurements on the fringe patterns of the type shown in fig. l, one can construct profiles of the growth hills. Further, by determining profiles at a series of times one can monitor the step kinetics. Sucl" an analysis for the KCI crystals indicated that the step velocity increased with decreasing spacing, the profiles consisting of smoothly curved convex regions and shock wave discontinuities in concave regions in agreement with the prediction of Frank6). 3.3. KINEMATIC SHOCK WAVES The shock waves have been studied extensively using reflection microscopy; the visibility of the waves becomes less for smaller angles of discontinuity and they cannot be resolved for angles less than about -~°. Shock waves were seen on growth hills a short time after growth had started. On average, clearly visible ones were observed on 20 o/,~of the hills at any particular instant, but this percentage varied from crystal to crystal. The systems of shock waves car, de divided into three classes. A system of class (a) consists of a shock wave in the form of a single closed loop on a growth hill: alternatively there may be two or more closed loops in xhich case they have different degrees of
(b) Fig. 2, (a) Spiral shock wave, (b) transforming into double. start spiral. ×165.
visibility and the spacings between successive loops are different. A system of class (b) consists of a series of closed loops which are equally spaced, while one of class (c) consists of a shock wave in the form of a spiral. In general, systems of class (a) were observed on hills with small slopes, while systems of the other two classes were seen on steep hills. The shock waves were difficult to resolve when they were close to the sm~mits of the hills, becoming most clearly visible at a dislance o f 10-60 I~m from it. In some instances the forn~ of a shock wave system of type (b) or (c) remained una! ,red for about an hour, but usually continual chang~ 0ccurred. For example, sometimes each newly fo ned turn of a spiral was of a lower resolution then it r 3redecessor leading to the apparent disappearance c the system; at other times a spiral shock wave split rot0 two or more, usually fainter, shock waves at its ce tre, see figs 2a and 2b, with the subsequent developmc : 0f a multi-start spiral. Changes also occurred which led to the appeal ice o f fresh shock wave systems. However, in general, ~, eer and fainter systems of shock waves were seen as gr, .th proceeded on the cleavage face and after about ! m of bulk growth there were very few clearly visible syst, ~s.
IX - 4
THE G R O W T H OF POTASSIUM C H L O R I D E CRYSTALS IN THE PRESENCE OF LEAD
457
the spiral shock wave would extend all the way to the dislocation group at its centre; also, it would slowly disappear6). However, the shock waves were found to that within a distance of about 10 I~m from the summit a different relationship between step spacing and velocity existed and profiles similar to that shown in figs. 3c and 3d could be formed. The smoothly concave regions in these profiles would become unstable as their distance (c) from the summit exceeded 10 ~m and they would gradually transform into shock waves which would become 0 iT fully developed at a distance of about 50 I~m from the (d) summit. As they continued to advance down the growth hill the shock waves would slowly fade away6). As growth proceeded the dislocations would extend into the freshly deposited crystal, a process which would be accompanied by changes in the spatial arrangement of the dislocations within the group. This in turn would change the relative orientations of the spiral steps; consequently the form of the shock wave system Fig. 3. could be changed while the activity of the dislocation 4. Discussion group and hence the average slope of the hill remained The spiral forms of the shock waves of type (c) sug- unaltered. More drastic rearrangement of the dislocations dugest that the growth sources were groups of screw dislocations emerging in the surfaces, and the behaviour ring growth could result in a group splitting into two or more parts which could become so distantly spaced described above suggest the following model. Consider the growth hill originated by a group of as to operate as independent growth sources, generally n elementary dislocations of like sign grouped suffi- with reduced activities. Similar processes may exist ciently closely together for all of them to act in coopera- whereby dislocation groups unite producing a source tion as a growth source, The step pattern originated by of higher activity. Rearrangements of this type would the ~ource consists o f n similar concentric spirals. These account for the changes in the activities of growth step could be equally spaced in orientation about the sources which were most common in the early stages t ait; then ~he height of the surface of the hill at any of growth. slf/i~ distance from the summit and relative to a plane References [ier ndicular to the axis of the hill would vary with ori~ ation in the way shown in fig. 3a (for n = 10). I) R. F. Strickland-Constable, Cr.vstallizatitm (Academic Press, 1968) p. 267. Silv ~rly the height of the surface in any fixed orienta- 2) London, P. H. Egli and S. Zerfoss, Discussions Faraday Soc, 5 ( 19491 61 : tio, ,'ould vary with distance from the summit in the P. H. Egli and L. R. Johnson, in: The Art and Science o f Growing Crystals, Ed. J. J. Gilman (Wiley, London, 1963) p. Wa: flown in fig. 3b. Alternatively the spirals could be 194. but .ed about one orientation, figs. 3c and 3d. 3) N. Albon and W. J. Dunning, Acta. Cryst. 12 (1959) 219: S ,pose that the steps advance from the summit of A. E. Morgan and W. J. Dunning, J. Crystal Growth 7 (1970) 179. ,...tile It in such a manner as to form a surface profile 4) A. C. Terrell, The Microscope and Crystal Front 14 (1964) sire r to that in fig. 3d; then the kinetics of step 174. n'lo~ aent are such that a kinematic shock wave would 5) W. K. Burton, N. Cabrera and F. C. Frank, Plail.Trans. Roy. Soc. London A 243 (1951) 299. be , eeloped, fig. 3e, and this would have a spiral 6) F. C. Frank, in: Gr~,wth and Perfection of Crystals Eds. R. H. Shal • If step movement close to the summit were Doremus, B. W. Roberts and D. Turnbull (Wiley, New Yock, desc; ~t~edby the same kinetics as movement far from it 1958) p. 411. ,
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IX - 4
Journal of Crystal Growth 13114 (1972) 454-457 © North.Holland Publishing Co.
THE GROWTIt OF POTASSIUM CHLORIDE CRYSTALS IN THE PRESENCt OF LEAD" G. PILKINGTON and W. J. D U N N I N G
Department of Physical Chemistr.v, The University, Bristol, England Potassium chloride seeds (cleave¢i from pure, melt grown crystals) were grown from aqueous solutiont .ith supersaturation ratios in the range 1.005 to 1.050 and with concentrations of lead chloride ~ 6 × 10 M. While the seeds were growing the {100} cleavage faces were studied by using reflection microscopy an two beam interference microscopy. On the initially flat cleavage Paces many growth ilills developed dur!ng the early stages of growth. Th, hills were approximately conical and their surfaces were inclined at angles ~ 3° to the close-packed {100} p; ~nes. The most steeply inclined hills grew most rapid!y, both parallel and perpendicular to the crystal surface and soon overran their neighbours. Crystal growth occurred solely through the continuing development of these hills. Profiles of growth hills were determined at time intervals and it was found that the development o1"the profiles could be described in terms of the kinematic theory of crystal growth. Furthermore, on the otherwise smooth surfaces of the hills, kinematic shock waves of sub-microscopic steps were observed. In many instances, the shock waves had the forms of spirals centered on the apices of the hills. These observations are consistent with the thesis that the hills originate at the points of emergence in the surface of groups of dis. locations with large Burgers vectors.
i. Introduction
Crystals of KC! grown from pure aqueous solutions are either polycrystalline or develop as hoppers and ultimately contain inclusions of solution; in fact, it may be impossible to grow single crystals from pure solutiont), in contrast to this large single crystals free from macroscopic defects can be grown with ease from solution containing small amounts of additives; one of the most effective additives for this purpose is the cation of leadS). In this investigation the surface feature of KCI crystals were studied during growth from solutions with various supersaturations and various PbCI2 concentrations. Different types of growth features were observed, each type occurring within a well defined domain of solution conditions. This paper reports the features observed in one of these domains, the domain within which large single crystals can be produced. 2. Experimental
Crystal seeds with {100} faces were cleaved with a razor blade from large melt grown crystals. The seeds were placed in a cell through whicl3 solution was continuously circulated from a stock flask; .'he concentrations of KCI and PbCI2 and the tempeiatt:re of the solution could be held coustant or changed indepen-
dently in a controlled manner when desired. The crystals were studied, while growing, by means of relk¢. tion microscopy and a standard metallurgical microscope; the optical arrange,,ent was similar to that used by previous workers3). A second, and similar, growth apparatus was also used. For the latter apparatus the crystals could be studied by means of a microscope fitted with an interference objective (a description of which has been given by TerrelP), but the properties of the solution could not be varied during growth. 3. Results 3. ! • DEVELOPMENT OF GROWTH HILLS
First a description is given of the growth re: ure~ observed when a solution with the following prop .ties was passed over cleaved crystal seeds; supersatut sion ratio (actual concentration, expressed in g KCI/g ~ xter divided by saturation concentration) i.005 to I 050. lead concentration ~ 6 x 10-s M, and temper: turc 25 °C to 45 °C. A variation of the solution prop ties within these limits changed only the speed with x ,ich the growth features developed. The features observed by optical microscopy on ese freshly cleaved surfaces were low angled grain be, 1daries, scratches made by the cleaving blaae, an~ the cleavage steps. At the initiation of growth the clea age
IX - 4
;a) (b~ Fl~,. I. Crystal surface after (a) 24 rain, (b) 33 rain growth, x 100. steps, initially steep cliffs, advanced slowly, concomitantly becoming less steeply inclined to the cleavage plane. After a short time growth hills appeared; they formed at scratches, at points along the cleavage steps anti at points :where no features could previously be set~n on the surface. The hills were so densely packed or some parts of the surface that they overlapped bef e : they had grown to a size at which they could be c! ,fly distinguished (density > 10s/cruz). Elsewhere, a ~s ofabout 300 ~tm)2 contained only one or two hills o :ach of them (density ~ 103/cruz). As growth proc, ted, the steeper growth hills and the higher cleavage s ~ overran neighbouring features. ~e initial stages in the development of these growth t~ ~res could be studied in greater detail by the use of t beam interference microscopy. The fringe patterns ined by this method represent contour maps of the c~ loping surface. The hills which formed on any a cleavage face had slopes varying over a wide r; :,e, see figs. la, lb. he surfaces of the growth hills are vicinal faces incl,cd at small angles to the close-packed 100 plane.
These vicinal surfaces consist of trains of submicroscopic steps separated by flat lands of (100) surface. During growth the steps advance, the lateral movement of each contributing a small increment of growth perpendieular to the (100) face. The steps are generated by growth sources at the apices of the hills; the flux o f steps generated at any given time is called the activity of the sourceS). The growth sources originating many of the hills became inactive after a short period of growth; these hills subsequently continued to increase in diameter and developed flat tops. For the early stages of growth it was very common for the activities of growth sources to change unpredictably and abruptly, both increases and decreases being observed. This caused successive rings of the surface of the growth hills to have different slopes. As growth proceeded the activities changed less often and the number of hills diminished as the steep ones overran their neighbours. After about 50 lain of bulk growth perpendicular to the surface the hills present were steep and their density was about l/ram-'. During the following 2 mm of bulk growth, which is the most
IX - 4
456
G. P I L K I N G T O N A N D W. J, D U N N I N G
that has been studied, the density o f the growth hills on the surface remained approximately constant. Occasionally, a new growth hill developed on the side o f an existing one: presumably because o f an increase, in activity o f a previously dominated growth source; alternatively, a growth hill became less steep and was overrun ~ , a neighbour. .)
3 . 2 . THE PROFILES OF GROWTH HILLS
As noted above, a vicinal surface consists of a train of steps on a close-packed surface, Frank 6) examined the ~ t y in which such a vicinal surface would develop if the rate of advance of the steps across the closepacked face depended only on local step spacing. He found that the development of the face is described mathematically by a kinematic wave equation. Further, if the step velocity increases with decreasing spacing, smoothly curved concave regions o f the vicinal face are unstable ~Jth respect to the formation of discontinuities in surface orientation [see fig. 3, the profile in (d) changes to the profile in (e)]. For the mathematical description of the development o f the face these discontinuities are analogous to shock waves. By making measurements on the fringe patterns of the type shown in fig. l, one can construct profiles of the growth hills. Further, by determining profiles at a series of times one can monitor the step kinetics. Sucl" an analysis for the KCI crystals indicated that the step velocity increased with decreasing spacing, the profiles consisting of smoothly curved convex regions and shock wave discontinuities in concave regions in agreement with the prediction of Frank6). 3.3. KINEMATIC SHOCK WAVES The shock waves have been studied extensively using reflection microscopy; the visibility of the waves becomes less for smaller angles of discontinuity and they cannot be resolved for angles less than about -~°. Shock waves were seen on growth hills a short time after growth had started. On average, clearly visible ones were observed on 20 o/,~of the hills at any particular instant, but this percentage varied from crystal to crystal. The systems of shock waves car, de divided into three classes. A system of class (a) consists of a shock wave in the form of a single closed loop on a growth hill: alternatively there may be two or more closed loops in xhich case they have different degrees of
(b) Fig. 2, (a) Spiral shock wave, (b) transforming into double. start spiral. ×165.
visibility and the spacings between successive loops are different. A system of class (b) consists of a series of closed loops which are equally spaced, while one of class (c) consists of a shock wave in the form of a spiral. In general, systems of class (a) were observed on hills with small slopes, while systems of the other two classes were seen on steep hills. The shock waves were difficult to resolve when they were close to the sm~mits of the hills, becoming most clearly visible at a dislance o f 10-60 I~m from it. In some instances the forn~ of a shock wave system of type (b) or (c) remained una! ,red for about an hour, but usually continual chang~ 0ccurred. For example, sometimes each newly fo ned turn of a spiral was of a lower resolution then it r 3redecessor leading to the apparent disappearance c the system; at other times a spiral shock wave split rot0 two or more, usually fainter, shock waves at its ce tre, see figs 2a and 2b, with the subsequent developmc : 0f a multi-start spiral. Changes also occurred which led to the appeal ice o f fresh shock wave systems. However, in general, ~, eer and fainter systems of shock waves were seen as gr, .th proceeded on the cleavage face and after about ! m of bulk growth there were very few clearly visible syst, ~s.
IX - 4
THE G R O W T H OF POTASSIUM C H L O R I D E CRYSTALS IN THE PRESENCE OF LEAD
457
the spiral shock wave would extend all the way to the dislocation group at its centre; also, it would slowly disappear6). However, the shock waves were found to that within a distance of about 10 I~m from the summit a different relationship between step spacing and velocity existed and profiles similar to that shown in figs. 3c and 3d could be formed. The smoothly concave regions in these profiles would become unstable as their distance (c) from the summit exceeded 10 ~m and they would gradually transform into shock waves which would become 0 iT fully developed at a distance of about 50 I~m from the (d) summit. As they continued to advance down the growth hill the shock waves would slowly fade away6). As growth proceeded the dislocations would extend into the freshly deposited crystal, a process which would be accompanied by changes in the spatial arrangement of the dislocations within the group. This in turn would change the relative orientations of the spiral steps; consequently the form of the shock wave system Fig. 3. could be changed while the activity of the dislocation 4. Discussion group and hence the average slope of the hill remained The spiral forms of the shock waves of type (c) sug- unaltered. More drastic rearrangement of the dislocations dugest that the growth sources were groups of screw dislocations emerging in the surfaces, and the behaviour ring growth could result in a group splitting into two or more parts which could become so distantly spaced described above suggest the following model. Consider the growth hill originated by a group of as to operate as independent growth sources, generally n elementary dislocations of like sign grouped suffi- with reduced activities. Similar processes may exist ciently closely together for all of them to act in coopera- whereby dislocation groups unite producing a source tion as a growth source, The step pattern originated by of higher activity. Rearrangements of this type would the ~ource consists o f n similar concentric spirals. These account for the changes in the activities of growth step could be equally spaced in orientation about the sources which were most common in the early stages t ait; then ~he height of the surface of the hill at any of growth. slf/i~ distance from the summit and relative to a plane References [ier ndicular to the axis of the hill would vary with ori~ ation in the way shown in fig. 3a (for n = 10). I) R. F. Strickland-Constable, Cr.vstallizatitm (Academic Press, 1968) p. 267. Silv ~rly the height of the surface in any fixed orienta- 2) London, P. H. Egli and S. Zerfoss, Discussions Faraday Soc, 5 ( 19491 61 : tio, ,'ould vary with distance from the summit in the P. H. Egli and L. R. Johnson, in: The Art and Science o f Growing Crystals, Ed. J. J. Gilman (Wiley, London, 1963) p. Wa: flown in fig. 3b. Alternatively the spirals could be 194. but .ed about one orientation, figs. 3c and 3d. 3) N. Albon and W. J. Dunning, Acta. Cryst. 12 (1959) 219: S ,pose that the steps advance from the summit of A. E. Morgan and W. J. Dunning, J. Crystal Growth 7 (1970) 179. ,...tile It in such a manner as to form a surface profile 4) A. C. Terrell, The Microscope and Crystal Front 14 (1964) sire r to that in fig. 3d; then the kinetics of step 174. n'lo~ aent are such that a kinematic shock wave would 5) W. K. Burton, N. Cabrera and F. C. Frank, Plail.Trans. Roy. Soc. London A 243 (1951) 299. be , eeloped, fig. 3e, and this would have a spiral 6) F. C. Frank, in: Gr~,wth and Perfection of Crystals Eds. R. H. Shal • If step movement close to the summit were Doremus, B. W. Roberts and D. Turnbull (Wiley, New Yock, desc; ~t~edby the same kinetics as movement far from it 1958) p. 411. ,
.... ,
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IX - 4