J. Phys. Chem. 1993, 97, 10774-10782
10774
Morphology and Growth Kinetics of Large Sodium Chlorate Crystals Grown in the Presence and Absence of Sodium Dithionate Impurity R. Ristic,’ J. N. Sherwood,* and K. WojciechowskF Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow GI IXL,U.K. Received: May 6, I 993e
A study has been made of the influence of variations in cooling rate (supersaturation) and impurity content of the changes in morphology (habit and surface features) of sodium chlorate crystals grown from aqueous solution. The habit was found to vary from pure cubic at high cooling rates to cuboid with relatively small (1 10) and ( i l I), (Til), (1 Ti), and (1 11) faces at low cooling rates. Optical examination of the as grown surfaces of the resulting crystals revealed the presence of growth hillocks and surface features characteristicof dislocationassociated growth mechanisms. This speculation was supported by the distribution of dislocations in the various growth sectors, identified by Lang topography. These observations were supplemented by growth rate studies which confirmed that the morphological changes resulted from changes in supersaturation during growth. Controlled addition of sodium dithionate to the solution during growth had no influence on the growth mechanism of the natural habit faces, as evidenced by the surface features, but led to the rapid development of new tetrahedral ( l i l ) , (1 IT), (11 l), and (Til) faces. It is shown that these faces play the major role in the habit modification as a consequence of the structural similarity of the dithionate ion to the chlorate ions which compose these faces. The ready substitution of the so3moiety for the C103-ion obstructs the normal development of the face in the manner of a “tailor-made” habit modifier.
The habit of a crystal is determined by the relative growth rates of the various faces bounding the crystal. It is dependent on several internal and external factors. Internal factors are those which are associated with the crystal itself, such as crystal structure, dislocations, and other defects. External factors are those imposed on the crystal by the crystallization conditions. These conditionsare defined either by externalgrowth parameters, such as temperature, supersaturation, and hydrodynamics, or by the introduction of impurity into the solution. Sodium chlorate (NaClO3) is comparatively easy to crystallize, and its habit is known to be easily modified. It crystallizes in the cubic structure (space group P213) and normally exhibits a morphology dominated by { 100) faces with occasionally formed (1 lo), (1201, and some { 111) facets. The relative simplicity of its structure and behavior makes it a useful material for fundamental studies of habit modification caused by both internal and external factors. The first studies of habit modification of sodium chlorate were carried out by Burin,' who concluded that in well-stirred highly supersaturated solutionsof pure material at constant temperature the morphology of the growing crystal is determined by the crystallographic structure and is cubic. Later, Kern2 proposed that the habit of NaC103 is purely cubic only at low supersaturations and that tetrahedral faces tend to appear at higher supersaturations. Hemade no mention, however, about theeffect of growth rates on morphology. Kern’s proposals were subsequently supported by Aoki’s3 analysis of the morphology of NaClO3 crystals using the method of “linkage of coordination polyhedra” developed by him. Kern’s proposals were later contradicted, however, by Simon: whose observationsappear to support Bunn. He found that at very high supersaturations the cube is the only growth form and that additional faces appear with decreasing supersaturation. He proposed that the appearance of additional { 1lo), { 1201,and (1 1 1) faces is not due to theeffect of supersaturation alone but is strongly Current address: Instituteof Physics, P.O. Box 57,Belgrade, Yugoslavia.
r Current address: Institute of Physics, Technical University of Lcdz, Wolczanska 219, 93-005Lodz,Poland. 0
Abstract published in Advance ACS Abstrocts, September IS, 1993.
0022-3654/93/2097- 10774$04.00/0
dependent on the direction of the solution flow. These two factors are potentially interrelated. This variation of opinion is not so contradictoryas first appears. It reflects two different aspects of the problem: the prediction of macromorphology on the basis of crystallographic structure (the equilibrium morphology) and the definition of the growth morphology,which is dependent mostly on various kinetic growth factors. Confusion between these two concepts can lead to misleading conclusions. The effect of additives on the habit of NaC103 crystals has been studied systematically by B~ckley.~ He investigated the effect of Rod2- and related ions on the habit of NaC103 crystals and found that a change in the morphology from cuboid to tetrahedral form occurs at different levels of impurity content for each additive. The growth mechanism of sodium chlorate crystals from pure solution has been investigatedover a wide range of supersaturation. Bennema6made very precise measurements of growth rate as a function of supersaturation at very low supersaturation ( (110) > (111). This inference is in agreement with the experimentally observed morphological importance of the growth habit of NaCIO3 crystals obtained from pure solution (Tables I and 11). On this basis and from the crystallographic structure of NaClOs, it is expected that the (100) faces should exhibit the free development of growth layers by two-dimensional nucleation or spiral growth mechanisms, the (110)faces should show striations parallel to the ( 100) directions,and the (111)faces should present a rough appearance without any structure. The observation of thesurfacefeaturesof the(100)isinaccord with theseexpectations (Figure la). However, both the (110) and (1 11) faces also show
10776 The Journal of Physical Chemistry, Vol. 97, No. 41.1993
Ristic et al.
a
,=
,
Figure 2. X-ray topograph of a (1 10) slice of a sodium chlorate crystal grown at a cooling rate of 0.03 K/day; reflection 002; Mo Ka radiation.
-7-.A
,
Figure 1. Surface features of the natural habit faces of sodium chlorate crystals grown from pure solution: (a) the (100) face showing growth hillocks A and B on it, (b) the (1 10) face with growth layers initiated at the edge of the crystal situated on the bottom of photograph, and (c) the ( 1 1 1) face showing the movement of growth layers from the source situated at C.
layered growth features (Figure l b and IC). The crystal edges and growth hillocks appeared to act as sources of growth layers. The layers were especially thick on the faces grown at higher cooling rates. This suggests that these faces are also of F type. This apparent disagreement with expectation must be either a consequence of the difficulties involved in making accurate predictions of the PBCs for ionic crystals or an indication that the influence of other factors should be taken into account. All the crystals investigatedby X-ray topography show bundles of line defects running almost perpendicularly to the growth surface as seen in Figures 2 and 3. The dislocations mostly originate at the central portion of the bounding surface between the seed and newly grown portion. Three different types of line defects were distinguished: curved, straight, and polygonized (see Figures 2 and 3). The crystals grown at lower cooling rates and hence supersaturations contain higher dislocation densities with all typesof linedefects, whereas thosegrown at higher cooling rates were more perfect with straight dislocation lines. Detailed X-ray topographic investigations of dislocations in self-seeded sodium chlorate crystals carried out by Hooper et al.12showed that all crystals contain growth dislocations of edge, mixed, and screw character. Examination of the topographs in Figure 3a and 3b, based on the extinction contrast criteria (pb = 0, screw; g b X 1 = 0, edgelo),confirms that the same types of dislocations are also present in the seeded crystals. g is the diffraction vector of the incident X-radiation, and b and 1are the Burgers and line vectors of the dislocations, respectively. The
2mm
Figure 3. X-ray topographs of a { 100)slice of a sodium chlorate crystal grown at cooling rate of 1.05 K/day: reflections (a) 002 and (b) 020; Mo Ka radiation.
presence of such a high density of dislocation sourcesimplies that all habit faces of sodium chlorate (Tables I and 11) most probably grow by a dislocation mechanism. The high dislocation densities, formed at low cooling rates in both (110) and ( 111)growth sectors, suggest that these faces will grow' by -a cooperating spiral growth mechanism since the
Morphology and Growth Kinetics of Crystals
Figure 4. The function R = n u ) for growth on the (100)faces observed for 10 different crystals. Each of these crystals was refaceted and grown at the same supersaturation.
dislocation outcrop separation in the dislocation bundles is less than 19pc/2 (pc is the radius of the two-dimensional critical nucleus).13~14This situation results in faster growth rates than would be expected for growth at relatively low dislocation densities and in the absence of dislocation bundles. For these reasons, it is reasonable to accept that the { 110) and (111) faces will grow increasingly faster than the (100) faces at higher cooling rates (and hence supersaturation) and therefore will vanish quickly from the natural habit of NaClO3 observed at lower cooling rates. Our results (Tables I and 11) suggest that the upper limit of their persistence is when growth is developed at approximately 0.04 K/day. Growth Kinetic Studies. It is of interest to consider the role of crystal growth kinetics and mechanism in the habit modification process. Figure 4 gives the growth rate R of the {loo}faces as a function of the supersaturation u in a standard kinetic growth cell.11 Ten different (001) slices were used to obtain this dependence. It should be noted that in all experiments the refaceting of each slice prior to the measurement of the growth rate took place at the same supersaturation at which it would continue to grow. Also, the only form present during growth was (001). Under these circumstances, a nonlinear R = f l u ) dependence is obtained. Within the error, this approximates to the pattern expected of the BCF theory,I3parabolic at low supersaturations ( u I 2%) and linear above this. On this basis, growth should occur by the development of (noncooperating) single spirals in the parabolic region and growth by cooperating spirals in the linear region. In order to test this speculation, the grown crystals were subjected to transmission X-ray topography. Figure 5 confirms that at u < 2% the crystals contain well-separated individual dislocations and that dislocation bundles are absent. At u > 2%, the dislocation density is much higher, and dislocation bundles form. These observations are consistent with the conclusion that the growth takes place by a dislocation-controlled mechanism. The dislocations observed in the whole range of supersaturations are linear and normal to the growth interface. They are therefore of pure edge or screw character.I2 We would also note that the (100) sector, facing the solution flow, grows faster than the opposite (TOO) sector. This difference,whichalsocauses a change of crystal habit, may be explained by differences in hydrodynamic
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10777 environment combined with variations in interface kinetics.l5-I7 The flow rate of the saturated solution was always adjusted to a level at which the growth of the particular face under examination was not diffusion limited. In contrast to the above results, slight modifications to the growth mechanism result when additional forms are present in the growing crystal. Figure 6 shows the growth rate of the {loo} and {110)faces of a large (0.7 X 0.7 X 0.7 cm3) NaC103 crystal measured simultaneouslyas a function of supersaturation. Under these circumstances, the growth rates of both the { 100)and (1 10) faces show a linear dependence on supersaturation over an equivalent range. The reason becomes obvious when the underlying structure is considered. Multifaceted crystals have a fairly high dislocation density (see Figure 2). This develops principally from the large number of small inclusions trapped in the (100) and { 110) sectors during refaceting at the relatively high refaceting supersaturation (a = 2.5%) necessary to generate the different form (Figure 7). Attempts to reinitiate growth at lower supersaturations resulted in the lossof the additional form. Theseparationdistance between the outcrops of the dislocation bundles which develop is usually less than 19pC/2. The growth therefore most likely takes place by a cooperating spiral mechanismI3J4 at all supersaturations studied, which would lead to the linear R versus u dependence observed (Figure 6). The principal interesting feature of this analysis is that the (110) faces always grow faster than the { 100) faces in the range of supersaturations investigated. This arises because the density of inclusions, and therefore dislocationsformed, during refaceting in the {l10) sector is much larger than that in the (100) sector. Thus, under constant growth conditions (temperature, supersaturation, and flow rate) the total activityof dominant dislocation groups in the { 110)sector will be much stronger than that for the { 100)sector. Since the growth rate is directly proportional to the activity of the source of growth steps, the { 110) faces will grow faster then the {loo}faces. The variation of the ratio Rllw)/Rlllo) with supersaturation is shown in Figure 8. Up to a supersaturation of about 0.5%, the ratio Rllm)/R{I10) decreases rapidly. Following this, it decreases more slowly to 0.5, indicating that the {l10)faces grow twice as fast as the { 100) faces. The critical value of supersaturation, at which the (1 10) faces start to recede from the natural NaC103 morphology, can be estimated from the data in Figure 8 by using simple geometrical considerations. From Figure 9, the displacements of the (100) and { 110)faces after the time At are Alllw) and Al~llo),respectively. The area of the (100) face remains constant if
Al,lwl = Af~loo~*COS (Y which then divided by At gives
or Rl~ml/R,llo) = cos(45') = 0.71 The critical supersaturation corresponding to this ratio is ucr = 0.17% (see Figure 8). Above this value, the (110) faces will disappear in the course of growth. In contrast, below this supersaturation, the (1 10) face will persist with time as a habit face of NaClO3 crystal. This analysis explains conclusively why the { 110)faces become morphologically important at low cooling rates and hence low supersaturations (Table I). The simultaneous measurement of the growth rate of the (111) faces with the (100) and (110) faces was not experimentally possible. However, taking intoaccount the fact that thedislocation density is always the highest in this sector,'* it is reasonable to expect that there will be a greater number of active sources of
Ristic et al.
10778 The Journal of Physical Chemistry, Vol. 97, No. 41,1993
-
--
2mm
(1) 9,200
1
'.
b
2mm -
2mm
*
C
Figure 5. X-ray topographs of 001 slices of the crystals, the kinetics of which are presented in Figure 4 (a) 1.54%. (b) 2.05%, and (c) 2.27%. Reflections: ( 1 ) 200 and (2) 020. Mo Kar radiation.
steps in this sector than in the other two sectors. A reasoning similar to that applied for the (1 10) faces suggests that, under equivalent growth conditions, the (1 11) faces would be the first to disappear from the morphology of NaClO3 crystal as the supersaturation is increased. This accords.with observation. Growth Habit in the Presence of Impurity, The crystal habit showed marked changes with increasing sodium dithionate impurity concentration (Table 111). The most significant effect was the development of the four alternate (1 11) faces to those which resulted from supersaturation changes in the growth of the
pure crystals. We shall refer to these faces, which are marked by hatching in Figure 1lb, as the (111)faces. In summary, the normal cuboid habit of the seed changed from a (100) cuboid truncated by four small (iii)faces at 70 ppm to a (iii) tetrahedron with small (100) faces at 140 ppm and to a (TIT) tetrahedron without (100) faces for 210 ppm. Above this concentration, at a constant supersaturation only, the growth of the (iii)faces became considerably slower and tended to stop. These faces were rounded and rough. On continued increase of the supersaturation, renucleation occurred at the maximum point
The Journal of Physical Chemistry, Vol. 97, No. 41,1993 10119
Morphology and Growth Kinetics of Crystals
I
t+at
RxlO%d
\ \
\
10.0
0
8.0-
'
t
0;
I I
I I
6.0.
I
4.0.
I
2.0-
n
0
.. . 1
1
1
d
d
0
v
Figme 6. Growth rate of the (100)and (1 10)faces of sodium chlorate measured simultaneously on the same crystal as a function of supersaturation.
I
I
8
Figure9. Schematic representation of the displacement of the (100)and ( 1 10) faces as a function of time.
TABLE IIk Percentage of Area of Different Faces of NaClO3 in Relation to Impurity Content in Solutions
70 70 140 210
Figure 7. The inclusions in the (1 10)and (100)growth sectors captured during the refaceting process. The large density of inclusions in the refaceting region of the (1 10)sector servesas a source of the high density of dislocations which form in this sector.
0.85
-0.80
za=
-
0.75
8
d=0.70
0.65 0.60 0.55 0.50 Figure 8. Variation of the ratio Rl~oo)/R{l~ol as a function of supersaturation.
of curvature to yield a new tetrahedral growth oriented at 60° to the original face. Figure 10 shows some typical examples of the results obtained. From the above results, it is obvious that sodium dithionate has a very strong effect on the growth morphology of sodium chlorate crystals. A concentration of only one S 2 0 6 2 - ion to every
86.5 91.4 37.8 5.1
-
-
13.5 8.6 62.6 94.9
SO00 C103ions is sufficient to change the cuboid habit to simple tetrahedral habit. It is of interest to consider this change from a structural viewpoint and to confront its implications with our experimental results. X-ray crystal structure studies18 show that sodium chlorate has four anions and four cations per unit cell (Figure 1la). Each of the C103- ions is arranged in the structure such that the three oxygen atoms (separation 2.38 A) lie in one of four of the (111) planes (Figure 11b). These are bound to a chlorine atom placed on the trigonal axis which passes normally through the O3triangle and situated 0.48 A from this. The sodium ion lies below the chlorine at a distance of 6.12 A. Thus we have the situation that opposite (111)-type faces will present either sodium ionsor chlorate oxygens to the growth solution and will be of different polarities. One of these faces is then susceptible to the influence of supersaturation changes to allow the development of morphological changes, the other to the addition of dithionate impurity. From a structural viewpoint, the large separation of the sodium ion from the chlorate ion means that the latter can act as a dip01e.I~ This leads to the conclusion that the (111) planes with sodium ions facing outward are not crystallographically stable. Consequently, they will present atomically rough surfaces which in pure solutions under all conditions will grow much faster than the other faces and hence "grow out". This would then account for the fact that they arenever observedin sodiumchloratecrystals grown from pure solution. We therefore identify these planes with the (iii)planes. Comparing parts a and b of Figure 11, we see that these should be ( i i i ) , ( i l l ) , ( l i l ) , and (111). This speculation is confirmed by the modifying influence of the dithionate ion on the crystal habit. The dithionate ion comprises two SO3 tetrahedra of closely similar size to the C103ion linked through the sulfur atoms. Wyckoff18cites the average distance between the oxygen atoms of the dithionate ion as 2.44 compared with 2.38 A for the chlorate ion. Thus, the dithionate ion can act as a "tailor-made" habit modifier and can occupy a C103- site on the sodium-rich surface. The protruding SO3 will inhibit growth, so these surfaces will appear on growth from impure solutions and eventually dominate. Cessation of growth will follow the poisoning of all growth centers by the impurity. It is noted from Figure 1ICthat the twos03 tetrahedra
10780 The Journal of Physical Chemistry* Vol. 97, No. 41,1993
Ristic et al.
2 ---
Ti-
b
a
-
C
b I
Figure 10. Examples of sodium chlorate crystals showing the change of habit caused by S Z O ~ions: ~ - (a) cuboid habit obtained from solution without impurity; (b) tetrahedral habit of a crystal grown from solution containing 210 ppm of S2062-; and (c) a new tetrahedral growth,oriented at 60° to the original face, on a crystal grown from solution containing 600 ppm of S Z O ~ ~ Cooling -. rates (a) 0.64 K/day, (b) 0.09 K/day, and (c) 0.72 K/day.
of the dithionate ion are disposed at 60° to each other. It is tempting to speculatethat this arrangement guides therenucleated crystal into this orientation (Figure 1Oc) and defines an epitaxial relationship between habit modifier and subsequent growth. Figures 12 and 13 show ex-situ surface features on the (loo), (1 lo), (1 111, and (iii) faces. All these faces, apart from the (iii), are natural habit faces of NaClO3 crystals grown from pure solution and then subjected to regrowth from the dithionatedoped solution. The (iii) face is that along which the crystal was cut in order to observe the growth behavior of this type of face. The surface features on the {loo),( 1lo), and ( 111) faces show conclusively that layered growth still takes place on these faces even when they grow from impurity-doped solution. We conclude that no change of growth mechanism occurs on addition of the impurity. On the other hand, the growth rate of the (Ti!) face is considerably slower than that of the other faces. The growth features of this face show a rough structure (Figure 13a). Examination of this surface at higher magnification revealed the
I
Na
0 CI 113
C Figme 11. (a) Arrangement of Na+ and C103- ions in the structure of sodium chlorate. (b) The natural habit of a NaClO3 q t a l showing the arrangement of Clef ion on the (1 11) face. The (1 11) facts (dashed lines) are those defining the tetrahedral habit in the presence of the impurity. (c) The structure of positive (1) and negative (2) sublayers parallel to the (1 11) planes of the NaClOs crystal. The arrow (3) shows the preferable facets of adsorption of S20a2- anions on the (iii)crystal faces.
presence of block-like structures composed of tiny, flat hillocks suggesting that the growth was taking place by two-dimensional nucleation (Figure 13b). This observation leads to the following conclusions: (i)Thefaces(ill),(lil),(lli),and(iii)become stable at impurity levels of sodium dithionate approximately greater than 70 ppm; (ii) these faces have the lowest growth rate
Morphology and Growth Kinetics of Crystals
'1
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10781
a
pr
" : C
nrr
Figure 13. The(TTT)surfaceofasodiumchloratecrystalgrownatcooling rate of 0.09 K/day from solution containing 210 ppm of S20a2- ions: (a) general appearanceshowingthe "rough" structure of the surface and (b) magnified part of the surface shown in (a) revealing tiny flat hillocks.
Figure 12. Surface microphotographsshowing the layered structure of the habit faces of sodium chlorate grown at a cooling rate of 0.09 K/day from solution containing 210 ppm of S2062- ions: (a) the {loo)face, (b) the { 1 10) face, and (c) the { 1 1 1 ) face.
and therefore determine the morphology of NaC103 crystals; and (iii) at this point, we feel it is not appropriate to state conclusively what the growth mechanism of these faces is, although there is some experimental evidence to suggest that the growth takes place by two-dimensional nucleation at impurity levels greater than 70 ppm and by normal growth if the impurity level is less then 70 ppm. The appearance of these four faces, crystallographically unstable for growth from the pure solution, and the retardation of their growth rate due to the presence of the dithionate ions can be explained as follows. First, the nonexistence of the (ill), (111). (lli), and (111) faces in the puresolution strongly suggeststhat these faces behave as rough Sor K faces. In terms of the periodic bond chain theory, this means they behave like an F-face above the roughening transition temperature. Since a step at T > 0 Kcan be considered to to be rough, it can be concluded that an S face which is purely made up of steps behaves like a rough face. Second, NaCIO3 has no center of symmetry, and as a consequence the atomic configuration of parallel faces is not identical. The above faces which form upon addition of impurity have Na+ ions facing the surface, unlike the parallel faces which have C103- ions and are F-type faces. The former, as rough faces, will grow much faster in pure solution than the other faces by so-called normal growth. Therefore, they grow out and do not contribute to the natural habit of the NaClO3 crystal. However, in the presence of sodium dithionate, it is quite obvious that these faces will serve as the places where incorporation of S Z O ~ions ~ - is the strongest. This
means that the number of unsaturated bonds on these faces will decrease considerably. In turn, this causes a decrease in the surface free energy. As a consequenceof this they become stable, and retardation of their growth rates due to the strong adsorption layers becomes dominating in the habit modification. Once adsorbed, the S2062-ions perturb the regular deposition of further substrate layers. Consequently, the growth rates of the (iii) faces are decreased with respect to the other unaffected surfaces, resulting in the change of the crystal morphology (Figure lob). That the S Z O ~ions ~ - are eventually included into the bulk of the crystal via overgrowth was confirmed by chemical analysis.
Conclusions From this analysis we can make the following conclusions: (i) The morphology of pure sodium chlorate crystal grown at different cooling rates is cuboid modified by ( 1 10)and ( 1 11) faces in the range of cooling rates 0.007-0.03 K/day and pure (100) cuboid in the range 0.04-2 K/day. All natural faces of the NaC103 crystal have a layered growth structure in the observed range of cooling rates; i.e., they are F faces. The likely source of the growth layers is outcrops of screw/mixed dislocations. (ii) Kinetic data show that (100)faces can grow from pure solution by either noncooperating single spirals (parabolic R = flu) dependence) or by cooperating spirals (linear R = f l u ) dependence). The (110)faces show a linear R =flu) dependence over the full equivalent range of supersaturation. (iii) The critical supersaturation at which the (1 10)faces start todisappear from the natural habit of the sodium chloratecrystals grown from pure solution was estimated to be approximately 0.17%. (iv) The growth mechanism of the natural faces does not change at all theconcentrationvaluesofsodiumdithionateas an impurity. (v) The sodium chlorate crystals start changing their habit when approximately 70 ppm sodium dithionate is added to the
10782 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
growth solution. The new set of tetrahedral planes which appear at this level and develop progressively with increasing levels of impurity content consists of the ( i l l ) , ( l i l ) , ( l l i ) , and (171) faces. These are the habit faces of the tetrahedron formed at high levels of added sodium dithionate. (vi) The absence of the ( i l l ) , ( l i l ) , ( l l i ) , and (117) faces from the natural habit of NaC103 crystal grown from pure solution is likely to be a consequenceof their rough nature on the molecular scale and the very high surface free energy caused by many unsaturated bonds. An interesting surface phase transition takes place in the presence of Na2S206.2H20 whereby these faces pass from a region of rough structure (normal growth) to a region of layered (probably two-dimensional) growth. The onset of this transition is strongly dependent on the impurity level and supersaturation. Acknowledgment. This work was supported by an SERC award made under the auspices of the Specially Promoted Programme in Particulate Technology. K.W. thanks the University of Strathclyde for theawardof a Research Scholarship. Theauthors acknowledge helpful discussions with Dr. K.J. Roberts. References and
Notes
( 1) Bunn, C. Chemical Crystallography;Clarendon Press; Oxford, 196 1;
p 21.
Ristic et al. (2) (3) (4) (5) (6) (7)
Kern, R. Bull. Soc. Franc. Miner. Cris?. 1965, 78, 497. Aoki, Y. Mem. Fac. Sci., Kyushu Uniu.,Ser. D. Geol. 1979,24,75. Simon, B. J. Cryst. Growth 1983, 61, 167. Buckley, H. Manchester Memoirs 1938-39, 83, 31. Bennema. P. J . Cryst. Growrh. 1967, I , 287. Hosoya, S.; Kitamura, M. Mineral. J. (Japan) 1978. 9, 137, 147. Hosoya. S.; Kitamura, M.; Miyata, T. Mineral. J. (Japan) 1978. 9, 73. (8) Ohara, M.; Reid, R. C. Modelling of Crystal Growrh Rates from Solution; Prentice Hall: Englewood Cliffs, NJ, 1973. (9) Hooper, R. M.; McArdle, B. J.; Narang, R. S.; Sherwood, J. N. In Crysral Growrh, 2nd ed.;Pamplin, B. R., Ed.; Pergamon, 1980. (10) Lang, A. In Modern Dif/racrionandImaging Techniques;Amelincx, S., et al., Eds.; North Holland: Amsterdam, 1970; p 407. (11) Rubbo, M.; Sherwood, J. N. J. Cryst. Growrh 1983, 61, 210. (12) Hooper, R. M.; Roberts, K. J.; Sherwood, J. N. J. Marerial Sci. 1983, 18, 81. (13) Burton, W. K.; Cabrera, N.; Frank, F. C. Phil. Trans. Roy. SOC. (London) 1951,243, 299. (14) Bennema, P. In IndusrrialCrysrallisotion;Mullin, J. W., Ed.; Plenum Press, 1976; p 91. ( 1 5 ) Jansen-van Rosmalen, R.; Bennema, P. J . Crysr. Growth 1977.42, 224. (16) Gits-Leon, S.;Robert, M. C.; Zarka, A. Bull. Mineral. 1978, 101, 39. (17) van Enckevort, W. J. P.; Jansen-van Rosmalen, R.; Klapper, H.; van der Linden, W. J . Crys?. Growth 1982, 60, 67. (18) Wyckoff, R. W. G. The Strucrure of Crysrals; Chemical Catalog Company; John Wiley & Sons: New York, 1960; p 276. (19) Mason, W. P. Phys. Rev. 1946, 70, 529. (20) Martinez, S.; Garcia-Blanco, S.; Rivoir, L. Acta Crystallogr. 1956, 9, 145.
