- Email: [email protected]
Observation of two-dimensional nucleation on the {0 1 0} face of potassium hydrogen phthalate (KAP) crystals using ex situ atomic force microscopy
Journal of Crystal Growth 187 (1998) 111—118
Observation of two-dimensional nucleation on the M0 1 0N face of potassium hydrogen phthalate (KAP) crystals using ex situ atomic force microscopy G.R. Ester, P.J. Halfpenny* School of Materials Science, University of Bath, Bath BA2 7AY, UK Received 5 August 1997; accepted 3 November 1997
Abstract The surface topology of microcrystals of potassium hydrogen phthalate (KAP) grown at a relative supersaturation of approximately 26% has been investigated using ex situ atomic force microscopy (AFM). Two distinctly different plate-like habits were observed. The thicker of the two habits resulted from growth by a spiral mechanism on the M0 1 0N faces while a thinner, less common, plate-like morphology occurred due to growth by two-dimensional nucleation on this face. The nuclei, being both asymmetric and partially polygonised, are essentially identical in shape to that of the spirals observed on the thicker crystals. They range in size from about 1200 to 400 nm with the smallest of the nuclei being substantially larger than the estimated radius of the critical two-dimensional nucleus at this supersaturation. This is attributed to continued growth of the nuclei, during separation from the growth solution. The nuclei are distributed non uniformly across the surface of the crystals, being greatest in number at the edges and corners of the M0 1 0N face. This distribution reflects the expected variation in surface supersaturation across the crystal face. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.16.Ch; 81.10.D Keywords: Crystal growth; AFM; Nucleation
1. Introduction Studies of the growth of crystals by two-dimensional nucleation are comparatively rare. Most crystals contain dislocations and, provided one or
* Corresponding author. Fax: #44 1225 826098; e-mail: [email protected].
more of these have a screw component normal to the crystal face, the spiral mechanism [1] typically dominates. Even when crystals, by chance or design, are initially dislocation-free, growth accidents or mechanical deformation frequently result in the generation of dislocations with a consequent shift to spiral growth. Of the studies in which two-dimensional nucleation has been implicated, investigations of vapour growth of whiskers and platelets
0022-0248/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 0 2 4 8 ( 9 7 ) 0 0 8 4 4 - 0
112
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
dominate. Price [2] studied the thickening of cadmium platelets above a critical supersaturation for growth by two-dimensional nucleation. Transmission electron microscopy (TEM) was used to confirm zero dislocation density for many of the platelets [3]. Samuelson [4] observed the transition from whisker to nonwhisker growth of ZnS which was again ascribed to the onset of twodimensional nucleation. The thickening of Al O 2 3 whiskers beyond a critical supersaturation [5] similarly provided indirect evidence of the operation of two-dimensional nucleation. The use of electron microscopy in conjunction with surface decoration enabled the observation of the growth interface and two-dimensional nuclei on, for example, KCl [6,7] and NaCl [8] amongst others. Examples of twodimensional nucleation in the case of growth from solution, have also been reported, including, for example, electrochemical crystallisation of silver [9,10], growth of C H from solution [11], 36 74 growth of ammonium dihydrogen phosphate (ADP) from aqueous solution together with X-ray topographic confirmation of dislocation density [12] and, most recently, growth of protein crystals studied using atomic force microscopy (AFM) [13,14]. It is widely acknowledged that discrimination between potential growth mechanisms on the basis of kinetic data alone is fraught with difficulty. Direct observation of the growth interface is essential for an unambiguous identification of the mechanism. For solution growth, although there have been numerous reports of surface spirals, the direct observation of two-dimensional nucleation has, thus far, been confined to AFM studies of proteins, where the large step heights and small kinetic coefficients simplify the observations somewhat. The present study, in contrast, deals with the growth of a low molecular weight material, potassium hydrogen phthalate (KAP). Here, the comparatively small step heights and typically high step velocities render the observation of steps, particularly those associated with two-dimensional nuclei, far more problematic. The crystal structure of KAP has been determined by Okaya [15]. However, an exchange of the axes as performed by Jetten [16] will be used here. This gives the orthorhombic space group Pca2 with 1
lattice parameters a"0.9609 nm, b"1.3857 nm and c"0.6466 nm. KAP crystallises as M0 1 0N platelets bounded by, in descending order of importance: M1 1 0N, M1 1 1N, M1 2 1N, M2 1 0N, M1 2 0N and M1 0 2N [17]. A number of crystal growth studies have utilised KAP as a model compound for investigation of step kinetics and other fundamental aspects of growth behaviour from aqueous solution. These studies have used differential interference contrast microscopy (DICM) predominantly and include investigation of surface microtopography [18—21]; quantitative examination of the effects of impurities on step kinetics [22—24] and investigation of secondary nucleation and the formation of growth spirals due to impact on the surface of KAP during growth [25—27]. More recently, preliminary studies of the surface microtopography of KAP crystals have been carried out using atomic force microscopy [28]. X-ray diffraction topography has been used by a number of investigators, yielding information on the nature, density and distribution of growth-induced defects [29—32] and a detailed characterisation of dominant growth-induced dislocations [32].
2. Experimental procedure Solutions for crystal growth were prepared using distilled water and Analar grade KAP (BDH) recrystallised once from distilled water. Small crystals, up to 100 lm in largest dimension, were precipitated onto glass slides from rapidly cooled droplets of solution. The saturation temperature of the growth solution was 35°C. Growth was carried out at an undercooling of approximately 10°C, corresponding to a relative supersaturation of approximately 26%. The solubility data of Solc et al. [33] were used for the preparation of KAP solutions and in the calculation of supersaturation. Nucleation and growth times were usually in the region of 3 min. The volume of the solution droplets used for growth was approximately 0.03 cm3 which, at an undercooling of 10°C, contained approximately 1 mg of excess solute. During a typical growth run less than 0.02 mg of KAP crystallised. This mass was estimated from the total volume of the crystallites formed. This corresponds to a change in the
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
supersaturation of less than 2% of its original value. The imposed supersaturation was thus effectively constant throughout a growth run. The growth solution was rapidly removed from the crystals by means of a jet of compressed air as reported previously [28]. The majority of the crystals nucleated on the M0 1 0N faces and adhered strongly to the glass slide even after removal of the growth solution. The samples were thus transferred on the glass slide directly to the AFM. AFM images were recorded using a Topometrix TMX 2010 scanning probe microscope with a Topometrix Discoverer AFM stage. Two types of piezoelectric scanner were employed: (a) a tripod scanner having 75 lm lateral scan range and 10.2 lm z-range or (b) for higher resolution small area images an 8 lm tube scanner with a 2.7 lm z-range. Silicon nitride ‘v’-shaped cantilevers with 200 lm arms and a square pyramidal tip with a nominal force constant of &0.03 N m~1 were used throughout. The AFM images shown below were all recorded using variable force mode. The only image processing performed was contrast adjustment. No image smoothing or noise removal was carried out.
3. Results The morphology of the small KAP crystals grown at high supersaturation was, in most cases, the same as that observed for larger crystals and that reported by other workers [17] at much lower supersaturations. The crystals were M0 1 0N platelets with a length to thickness ratio usually of around 10 : 1. Typical lateral dimensions of the crystals ranged from 20 to 100 lm. A significant proportion of the crystals, despite being of comparable lateral dimensions, were a factor of 10—15 times thinner than the majority of crystallites. Fig. 1 shows an AFM image illustrating the nature of the surface of a typical thick platelet crystal. The centre of a spiral is clearly visible. This is highly anisotropic with step spacing on one side of the spiral being about a factor of ten greater than on the other side. The spiral is also partially polygonised with steps lying approximately parallel to S1 0 1T directions, although the more widely spaced steps exhibit significant
113
Fig. 1. AFM image of the surface of a KAP crystal exhibiting a thick platelet morphology. Image area 9.6]9.6 lm2.
curvature. From constant force (topographic) image data, the steps were all found to be approximately 1.4 nm in height, i.e. of single unit cell height. The most important point in the present context, however, is the fact that the M0 1 0N surface is completely covered with steps emanating from such spirals. Fig. 2 shows an AFM image of the near-edge region of one of the thinner KAP crystals. The thick diagonal white line across the image is one edge of the crystal. A second edge is also visible. From topography mode images the crystal was found to be 230 nm in thickness. The nature of this surface is dramatically different from that shown in Fig. 2. It is essentially flat across most of the M0 1 0N face, except for a number of small islands of single unit cell height. The step patterns which covered the entire surface of the thicker crystals are not present in this sample. All the islands exhibit the same shape and orientation and are closely similar in both respects to the individual turns of the spiral shown in Fig. 2. The islands range from approximately 400 to 1200 nm in maximum dimension. Their number density varies markedly across the surface of the sample, being greatest at the edges and corners of the crystal face. Fig. 3 shows the variation in
114
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
Fig. 2. AFM image of the surface of a thin KAP platelet crystal. Image area 18]18 lm2.
the number of islands (a) from the crystal edge formed by the intersection of the (0 1 0) and (1 1 1) faces towards the crystal centre and (b) from one corner to the next along the same edge of the crystal.
4. Discussion AFM examination of these KAP microcystals grown at high supersaturation shows that the two distinct crystal morphologies observed are associated with two different growth mechanisms. The thicker platelets, with surfaces similar to that shown in Fig. 1 clearly grow by a dislocation spiral mechanism. However, the surface topology of the thin platelets, namely a molecularly flat face with isolated nuclei, is that expected for growth by twodimensional nucleation. For two-dimensional nucleation to dominate the growth of a crystal face, the corresponding growth sector must be free both of screw dislocations and of mixed dislocations having a screw component perpendicular to the crystal face. X-ray topographic studies of dislocations in relatively large (up to 1 cm) spontaneously nucleated crystals of
Fig. 3. The variation in number density of nuclei as a function of position on the crystal surface (a) from the crystal edge formed by the intersection of the (0 1 0) and (1 1 1) faces towards the crystal centre and (b) from one corner to the next along the same edge of the crystal.
KAP [32] have revealed that such crystals typically exhibit very low dislocation densities, particularly in the M0 1 0N growth sectors. Furthermore, the majority of dislocations were found to originate from inclusions which occurred in the latter stages of growth. The defect structure and characterisation of growth-induced dislocations in KAP crystals is discussed in detail elsewhere [32]. Given these observations and the absence of detectable inclusions in the majority of microcrystals grown in this study, it seems reasonable to suggest that occasionally some of these small crystals will have zero
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
dislocation density in the M0 1 0N growth sector. Under such circumstances, two-dimensional nucleation would be the only possibility for growth of the M0 1 0N faces and then only at high supersaturation. It is useful to compare the dimensions of the observed nuclei with the predicted critical radius of the two-dimensional nucleus. Cabrera and Levine obtained the following expression for the step spacing (y ) of a growth spiral [34]: 0 19ua y "19o " , (1) 0 # k¹p where o is the critical radius of the two-dimen# sional nucleus, u is the specific molecular volume, a is the step edge free energy, k is the Boltzmann constant, ¹ is temperature and p is the supersaturation. The separation of the more widely spaced set of steps in Fig. 1 is approximately 370 nm. Assuming expression (1) holds in the present case, one obtains a critical radius of about 20 nm. It was found that crystals growing by a spiral mechanism and those exhibiting two-dimensional nucleation occurred within a distance of approximately 100 lm of each other on a glass slide. It seems reasonable, therefore, to assume that the prevailing conditions, particularly supersaturation, for adjacent crystals nucleated on the same glass slide are very similar, if not identical. On this basis, the critical radius on an adjacent crystal growing by two-dimensional nucleation would also be close to 20 nm. It should be noted that, for two reasons, this value is an overestimate. First, it is based only on the larger step spacing of the anisotropic spiral. Secondly, due to probable overlap of the diffusion fields of the steps at high supersaturation, significant deviation from the behaviour predicted by Eq. (1) may occur. The estimate is, however, a useful guide. Although the value of y /o calculated by 0 # Carbrera and Levine [34] relates to an isotropic spiral, the work of Budevski and co-workers [35] indicates that this value is approximately independent of the spiral shape. Their calculations for three-, four- and six-cornered polygonised spirals all gave values of y /o close to 19. 0 # The nuclei visible in Fig. 2 vary in size from approximately 400 to 1200 nm. One would, however, expect this range to extend to dimensions comparable with the radius of the critical two-
115
dimensional nucleus. Yet the smallest of the observed nuclei is more than an order of magnitude larger than even the overestimated value of o dis# cussed above. It should be noted that, on other samples, surface features less than 20 nm across have been routinely observed, thereby indicating that if two-dimensional nuclei of the estimated critical dimensions were present they would be detectable. Since separation of a crystal from its growth solution cannot be instantaneous, it follows that the cessation of growth does not occur instantly. It clearly depends upon the techniques used for separation and for observation of the surface as to whether such changes are detectable. Given that, under favourable conditions AFM is capable of molecular resolution, it is probably the most sensitive of all the available techniques in this respect. The fact that all the nuclei observed are substantially larger than the critical radius indicates that growth continued during separation from the solution. Furthermore, this growth proceeded at a lower supersaturation than that prior to separation otherwise new two-dimensional nuclei, much closer in size to the critical radius, would have formed and would be visible in the AFM images. Comparing the smallest observed nuclei with the expected critical radius, it would appear that the faster steps have moved through a distance of approximately 350 nm during separation of these crystals from their growth solutions. This figure allows for the approximately 10 : 1 ratio of the velocities of the fast and slow step orientations. If the actual supersaturation during removal were known, it would be possible to estimate the time interval over which the solution removal occurred. Although this supersaturation is not well defined, it is still possible to establish the order of magnitude of this time interval. From the step velocity measurements of Hottenhuis and Lucasius [23], the kinetic coefficient b of the fast moving S1 0 1T steps can be estimated at approximately 50 lm s~1. The step velocity v, supersaturation p, and the kinetic coefficient b are related thus: v"bp.
(2)
On this basis, the velocity of the fast S1 0 1T oriented steps on the M0 1 0N face of KAP is approximately 13 lm s~1 at a supersaturation of 26%. At
116
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
this velocity, the 2D nuclei would have grown from critical dimensions to the smallest size observed ex situ in a period of approximately 30 ms. This represents the shortest time interval in which the solution removal could have occurred. It is more difficult to set an upper limit on this time interval. However, the shape of the nuclei provides some insight. It has been observed that the spiral shape becomes progressively more polygonised with decreasing supersaturation [36]. A noticeable onset of this change occurs at around 10% relative supersaturation with steps becoming considerably straighter. It is reasonable to assume that islands which are substantially greater than the critical two-dimensional nucleus, would exhibit shape changes similar in nature to those of spiral turns of the same size. In the present case, however, the nuclei or islands exhibit essentially the same shape as that observed for turns of the spirals on crystals grown at the same high supersaturation. This implies that although the supersaturation decreases during solution removal, preventing new nuclei close to critical dimensions being present, this decrease is not large enough to produce the shape change observed for turns of spirals on KAP at lower supersaturation. Thus, it appears that the supersaturation during removal remains above approximately 10% and so the time interval for solution removal by a jet of compressed air is of the order of a few tens of milliseconds. From the large step velocities at the high supersaturations employed here, it follows that ex situ observation of two-dimensional nuclei in the case of small molecule materials such as KAP requires extremely rapid separation of crystal and solution to ensure a cessation of growth which is as abrupt as possible. A separation slower than that discussed here but similar in terms of the prevailing supersaturation, would result in more extensive growth and coalescence of the nuclei to leave a completely flat crystal face. In addition to samples exhibiting two-dimensional nuclei, some thin, almost perfectly flat crystals were observed in the course of this study. The crystals discussed here were grown under a bulk supersaturation of approximately 26%. It is well known, however, that the surface supersaturation is the true driving force for crystal growth. Under most growth conditions, the bulk super-
saturation will exceed that at the crystal surface because of a diffusion boundary layer. A relatively small number of studies have addressed the measurement of surface supersaturation together with its relation to bulk supersaturation and growth kinetics. These have included the use of Mach—Zehnder interferometry [37,38] and holography [39,40]. Two important points arise from these studies, particularly from Ref. [37]. First, there is a considerable difference between surface and bulk supersaturation which increases with decreasing solution velocity across the surface. Secondly, the surface supersaturation exhibits substantial variations across a crystal face, being larger at the edges than at the centre. The effects of such variations upon the activity of growth hillocks have been observed using Michelson interferometry in the case of barium nitrate [41]. In the present study, we clearly observe enhanced two-dimensional nucleation at the edges and particularly at the corners of the crystals. This is to be expected and is a direct consequence of the higher surface supersaturation in these areas of the crystal faces. There are several other factors which could yield substantially different surface topology from that shown in Fig. 1. Although none of these can account for all features of this surface, it is useful to consider these factors for the sake of completeness. (i) Poor surface protection during removal of solution might be put forward as an explanation for the absence of steps on a crystal surface. In the present case, however, the thin flat crystals are observed to be surrounded by crystals exhibiting clearly defined steps and spirals all within a few hundred microns or less of each other. (ii) A pair of dislocations of opposite sign can generate closed loops of steps. Such a source, however, produces concentric loops rather than the single loops visible in Fig. 2. (iii) It has been suggested that edge dislocations [42,43] and stacking faults [44] can act as sites for preferential two-dimensional nucleation. Such sites would again yield not single but concentric loops, although of rather less regular spacing than a dislocation pair. The distribution of nuclei across the surface is a further indication that the latter two explanations can be discounted. It is well established that growth-induced dislocations adopt orientations nearly normal to the face of the growth
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
sector in which they occur. Consequently, the density of dislocations emerging on a crystal face tends to be greatest at the centre, not the edge, of that face. X-ray topographic examination of defect densities and distributions [32] has confirmed this general observation for the specific case of KAP crystals.
[2] [3] [4] [5] [6] [7] [8] [9] [10]
5. Conclusions
[11]
Microcrystals of potassium hydrogen phthalate, grown at high supersaturation to dimensions of less than 100 lm, have been found to exhibit two distinctly different crystal morphologies. Ex situ atomic force microscopy of the crystal surfaces clearly demonstrates that the thicker platelet morphology observed is associated with growth by a spiral mechanism and the other, thinner morphology is due to growth by two-dimensional nucleation. The nuclei present on the surface of the thinner crystals lie within a relatively narrow size range from approximately 400 to 1200 nm, the smallest of which are substantially larger than the estimated radius of the critical two-dimensional nucleus. This observation is attributed to the fact that cessation of growth during solution removal is not instantaneous. The observed nonuniform distribution of nuclei reflects the variation in surface supersaturation, being greatest at the edges and corners of the crystals.
[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
Acknowledgements
[27]
The authors gratefully acknowledge financial support of this work by EPSRC. Support for a studentship (GRE) was provided by the School of Materials Science, University of Bath and CLRC Daresbury Laboratory. Assistance from the Centre for Electron Optical Studies, University of Bath is also acknowledged.
[28]
References [1] W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. Roy. Soc. London 243 (1959) 299.
[29] [30] [31] [32] [33] [34] [35] [36] [37]
117
P.B. Price, Phil. Mag. 5 (1960) 473. P.B. Price, J. Appl. Phys. 32 (1961) 1747. H. Samuelson, J. Appl. Phys. 32 (1961) 309. R.C. DeVries, G.W. Sears, J. Chem. Phys. 31 (1959) 1256. H.J. Meyer, B.J. Stein, J. Crystal Growth 49 (1980) 707. H.J. Meyer, B.J. Stein, J. Crystal Growth 60 (1982) 123. K.W. Keller, J. Crystal Growth 76 (1986) 469. R.A. Kaishev, E. Budevsky, Contemp. Phys. 8 (1967) 489. E. Budevsky, V. Bostanov, G. Staikov, Annual. Rev. Mater. Sci. 10 (1980) 85. B. Simon, A. Grassi, R. Boistelle, J. Crystal Growth 26 (1974) 77. A.A. Chernov, Contemp. Phys. 30 (1989) 251. A.J. Malkin, T.A. Land, Yu.G. Kuznetsov, A. McPherson, J.J. DeYoreo, Phys. Rev. Lett. 75 (1995) 2778. A.J. Malkin, Yu.G. Kuznetsov, W. Glantz, A. McPherson, J. Phys. Chem. 100 (1996) 11736. Y. Okaya, Acta Crystallogr. 19 (1965) 879. L.A.M.J. Jetten, Thesis, University of Nijmegen, 1983. M.H.J. Hottenhuis, J.G.E. Gardeniers, L.A.M.J. Jetten, P. Bennema, J. Crystal Growth 92 (1988) 171. W.J.P. van Enckevort, L.A.M.J. Jetten, J. Crystal Growth 60 (1982) 275. W.J.P. van Enckevort, Progr. Crystal Growth Charact. 9 (1984) 1. L.A.M.J. Jetten, B. van der Hoek, W.J.P. van Enckevort, J. Crystal Growth 62 (1983) 603. M.H.J. Hottenhuis, C.B. Lucasius, J. Crystal Growth 94 (1989) 708. M.H.J. Hottenhuis, C.B. Lucasius, J. Crystal Growth 78 (1986) 379. M.H.J. Hottenhuis, C.B. Lucasius, J. Crystal Growth 91 (1988) 623. M.H.J. Hottenhuis, A. Oudenampsen, J. Crystal Growth 92 (1988) 513. M.P.W. Derks, A.E.D.M. van der Heijden, M. Elwenspoek, J. Crystal Growth 94 (1989) 527. A.E.D.M. van der Heijden, M. Elwenspoek, J.P. van der Eerden, J. Crystal Growth 98 (1989) 398. A.E.D.M. van der Heijden, M. Elwenspoek, J. Crystal Growth 99 (1990) 1087. G.R. Ester, R. Price, P.J. Halfpenny, J. Crystal Growth 182 (1997) 95. Zhao Qing-Lan, Acta Phys. Sinica 37 (1988) 1345. Zhao Qing-Lan, Huang Yi-Sen, Acta Physica Sinica 38 (1989) 1134. Zhao Qing-Lan, Huang Yi-Sen, J. Synthetic Crystals 19 (1990) 249. G.R. Ester, P.J. Halfpenny, in preparation. Z. Solc, J. Kvapil, J. Vlcek, Kristall Tech. 8 (1973) 59. N. Cabrera, M.M. Levine, Philos. Mag. 1 (1956) 450. E. Budevski, G. Staikov, V. Bostanov, J. Crystal Growth 29 (1975) 316. R. Price, G.R. Ester, P.J. Halfpenny, in preparation. K. Onuma, K. Tsukamoto, I. Sunagawa, J. Crystal Growth 98 (1989) 377.
118
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
[38] J.C. van Dam, F.H. Mischgofsky, J. Crystal Growth 84 (1987) 539. [39] F. Bedarida, J. Crystal Growth 79 (1986) 43. [40] F. Bedarida, L. Zefiro, P. Boccacci, D. Aquilano, M. Rubbo, G. Vaccari, G. Mantovani, G. Sgualdino, J. Crystal Growth 89 (1988) 395.
[41] K. Maiwa, K. Tsukamoto, I. Sunagawa, J. Crystal Growth 102 (1990) 43. [42] K.W. Keller, J. Crystal Growth 78 (1986) 509. [43] E. Bauser, H. Strunk, J. Crystal Growth 51 (1981) 362. [44] N. Ming, K. Tsukamoto, I. Sunagawa, A. Chernov, J. Crystal Growth 91 (1988) 11.
Observation of two-dimensional nucleation on the M0 1 0N face of potassium hydrogen phthalate (KAP) crystals using ex situ atomic force microscopy G.R. Ester, P.J. Halfpenny* School of Materials Science, University of Bath, Bath BA2 7AY, UK Received 5 August 1997; accepted 3 November 1997
Abstract The surface topology of microcrystals of potassium hydrogen phthalate (KAP) grown at a relative supersaturation of approximately 26% has been investigated using ex situ atomic force microscopy (AFM). Two distinctly different plate-like habits were observed. The thicker of the two habits resulted from growth by a spiral mechanism on the M0 1 0N faces while a thinner, less common, plate-like morphology occurred due to growth by two-dimensional nucleation on this face. The nuclei, being both asymmetric and partially polygonised, are essentially identical in shape to that of the spirals observed on the thicker crystals. They range in size from about 1200 to 400 nm with the smallest of the nuclei being substantially larger than the estimated radius of the critical two-dimensional nucleus at this supersaturation. This is attributed to continued growth of the nuclei, during separation from the growth solution. The nuclei are distributed non uniformly across the surface of the crystals, being greatest in number at the edges and corners of the M0 1 0N face. This distribution reflects the expected variation in surface supersaturation across the crystal face. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.16.Ch; 81.10.D Keywords: Crystal growth; AFM; Nucleation
1. Introduction Studies of the growth of crystals by two-dimensional nucleation are comparatively rare. Most crystals contain dislocations and, provided one or
* Corresponding author. Fax: #44 1225 826098; e-mail: [email protected].
more of these have a screw component normal to the crystal face, the spiral mechanism [1] typically dominates. Even when crystals, by chance or design, are initially dislocation-free, growth accidents or mechanical deformation frequently result in the generation of dislocations with a consequent shift to spiral growth. Of the studies in which two-dimensional nucleation has been implicated, investigations of vapour growth of whiskers and platelets
0022-0248/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 0 2 4 8 ( 9 7 ) 0 0 8 4 4 - 0
112
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
dominate. Price [2] studied the thickening of cadmium platelets above a critical supersaturation for growth by two-dimensional nucleation. Transmission electron microscopy (TEM) was used to confirm zero dislocation density for many of the platelets [3]. Samuelson [4] observed the transition from whisker to nonwhisker growth of ZnS which was again ascribed to the onset of twodimensional nucleation. The thickening of Al O 2 3 whiskers beyond a critical supersaturation [5] similarly provided indirect evidence of the operation of two-dimensional nucleation. The use of electron microscopy in conjunction with surface decoration enabled the observation of the growth interface and two-dimensional nuclei on, for example, KCl [6,7] and NaCl [8] amongst others. Examples of twodimensional nucleation in the case of growth from solution, have also been reported, including, for example, electrochemical crystallisation of silver [9,10], growth of C H from solution [11], 36 74 growth of ammonium dihydrogen phosphate (ADP) from aqueous solution together with X-ray topographic confirmation of dislocation density [12] and, most recently, growth of protein crystals studied using atomic force microscopy (AFM) [13,14]. It is widely acknowledged that discrimination between potential growth mechanisms on the basis of kinetic data alone is fraught with difficulty. Direct observation of the growth interface is essential for an unambiguous identification of the mechanism. For solution growth, although there have been numerous reports of surface spirals, the direct observation of two-dimensional nucleation has, thus far, been confined to AFM studies of proteins, where the large step heights and small kinetic coefficients simplify the observations somewhat. The present study, in contrast, deals with the growth of a low molecular weight material, potassium hydrogen phthalate (KAP). Here, the comparatively small step heights and typically high step velocities render the observation of steps, particularly those associated with two-dimensional nuclei, far more problematic. The crystal structure of KAP has been determined by Okaya [15]. However, an exchange of the axes as performed by Jetten [16] will be used here. This gives the orthorhombic space group Pca2 with 1
lattice parameters a"0.9609 nm, b"1.3857 nm and c"0.6466 nm. KAP crystallises as M0 1 0N platelets bounded by, in descending order of importance: M1 1 0N, M1 1 1N, M1 2 1N, M2 1 0N, M1 2 0N and M1 0 2N [17]. A number of crystal growth studies have utilised KAP as a model compound for investigation of step kinetics and other fundamental aspects of growth behaviour from aqueous solution. These studies have used differential interference contrast microscopy (DICM) predominantly and include investigation of surface microtopography [18—21]; quantitative examination of the effects of impurities on step kinetics [22—24] and investigation of secondary nucleation and the formation of growth spirals due to impact on the surface of KAP during growth [25—27]. More recently, preliminary studies of the surface microtopography of KAP crystals have been carried out using atomic force microscopy [28]. X-ray diffraction topography has been used by a number of investigators, yielding information on the nature, density and distribution of growth-induced defects [29—32] and a detailed characterisation of dominant growth-induced dislocations [32].
2. Experimental procedure Solutions for crystal growth were prepared using distilled water and Analar grade KAP (BDH) recrystallised once from distilled water. Small crystals, up to 100 lm in largest dimension, were precipitated onto glass slides from rapidly cooled droplets of solution. The saturation temperature of the growth solution was 35°C. Growth was carried out at an undercooling of approximately 10°C, corresponding to a relative supersaturation of approximately 26%. The solubility data of Solc et al. [33] were used for the preparation of KAP solutions and in the calculation of supersaturation. Nucleation and growth times were usually in the region of 3 min. The volume of the solution droplets used for growth was approximately 0.03 cm3 which, at an undercooling of 10°C, contained approximately 1 mg of excess solute. During a typical growth run less than 0.02 mg of KAP crystallised. This mass was estimated from the total volume of the crystallites formed. This corresponds to a change in the
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
supersaturation of less than 2% of its original value. The imposed supersaturation was thus effectively constant throughout a growth run. The growth solution was rapidly removed from the crystals by means of a jet of compressed air as reported previously [28]. The majority of the crystals nucleated on the M0 1 0N faces and adhered strongly to the glass slide even after removal of the growth solution. The samples were thus transferred on the glass slide directly to the AFM. AFM images were recorded using a Topometrix TMX 2010 scanning probe microscope with a Topometrix Discoverer AFM stage. Two types of piezoelectric scanner were employed: (a) a tripod scanner having 75 lm lateral scan range and 10.2 lm z-range or (b) for higher resolution small area images an 8 lm tube scanner with a 2.7 lm z-range. Silicon nitride ‘v’-shaped cantilevers with 200 lm arms and a square pyramidal tip with a nominal force constant of &0.03 N m~1 were used throughout. The AFM images shown below were all recorded using variable force mode. The only image processing performed was contrast adjustment. No image smoothing or noise removal was carried out.
3. Results The morphology of the small KAP crystals grown at high supersaturation was, in most cases, the same as that observed for larger crystals and that reported by other workers [17] at much lower supersaturations. The crystals were M0 1 0N platelets with a length to thickness ratio usually of around 10 : 1. Typical lateral dimensions of the crystals ranged from 20 to 100 lm. A significant proportion of the crystals, despite being of comparable lateral dimensions, were a factor of 10—15 times thinner than the majority of crystallites. Fig. 1 shows an AFM image illustrating the nature of the surface of a typical thick platelet crystal. The centre of a spiral is clearly visible. This is highly anisotropic with step spacing on one side of the spiral being about a factor of ten greater than on the other side. The spiral is also partially polygonised with steps lying approximately parallel to S1 0 1T directions, although the more widely spaced steps exhibit significant
113
Fig. 1. AFM image of the surface of a KAP crystal exhibiting a thick platelet morphology. Image area 9.6]9.6 lm2.
curvature. From constant force (topographic) image data, the steps were all found to be approximately 1.4 nm in height, i.e. of single unit cell height. The most important point in the present context, however, is the fact that the M0 1 0N surface is completely covered with steps emanating from such spirals. Fig. 2 shows an AFM image of the near-edge region of one of the thinner KAP crystals. The thick diagonal white line across the image is one edge of the crystal. A second edge is also visible. From topography mode images the crystal was found to be 230 nm in thickness. The nature of this surface is dramatically different from that shown in Fig. 2. It is essentially flat across most of the M0 1 0N face, except for a number of small islands of single unit cell height. The step patterns which covered the entire surface of the thicker crystals are not present in this sample. All the islands exhibit the same shape and orientation and are closely similar in both respects to the individual turns of the spiral shown in Fig. 2. The islands range from approximately 400 to 1200 nm in maximum dimension. Their number density varies markedly across the surface of the sample, being greatest at the edges and corners of the crystal face. Fig. 3 shows the variation in
114
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
Fig. 2. AFM image of the surface of a thin KAP platelet crystal. Image area 18]18 lm2.
the number of islands (a) from the crystal edge formed by the intersection of the (0 1 0) and (1 1 1) faces towards the crystal centre and (b) from one corner to the next along the same edge of the crystal.
4. Discussion AFM examination of these KAP microcystals grown at high supersaturation shows that the two distinct crystal morphologies observed are associated with two different growth mechanisms. The thicker platelets, with surfaces similar to that shown in Fig. 1 clearly grow by a dislocation spiral mechanism. However, the surface topology of the thin platelets, namely a molecularly flat face with isolated nuclei, is that expected for growth by twodimensional nucleation. For two-dimensional nucleation to dominate the growth of a crystal face, the corresponding growth sector must be free both of screw dislocations and of mixed dislocations having a screw component perpendicular to the crystal face. X-ray topographic studies of dislocations in relatively large (up to 1 cm) spontaneously nucleated crystals of
Fig. 3. The variation in number density of nuclei as a function of position on the crystal surface (a) from the crystal edge formed by the intersection of the (0 1 0) and (1 1 1) faces towards the crystal centre and (b) from one corner to the next along the same edge of the crystal.
KAP [32] have revealed that such crystals typically exhibit very low dislocation densities, particularly in the M0 1 0N growth sectors. Furthermore, the majority of dislocations were found to originate from inclusions which occurred in the latter stages of growth. The defect structure and characterisation of growth-induced dislocations in KAP crystals is discussed in detail elsewhere [32]. Given these observations and the absence of detectable inclusions in the majority of microcrystals grown in this study, it seems reasonable to suggest that occasionally some of these small crystals will have zero
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
dislocation density in the M0 1 0N growth sector. Under such circumstances, two-dimensional nucleation would be the only possibility for growth of the M0 1 0N faces and then only at high supersaturation. It is useful to compare the dimensions of the observed nuclei with the predicted critical radius of the two-dimensional nucleus. Cabrera and Levine obtained the following expression for the step spacing (y ) of a growth spiral [34]: 0 19ua y "19o " , (1) 0 # k¹p where o is the critical radius of the two-dimen# sional nucleus, u is the specific molecular volume, a is the step edge free energy, k is the Boltzmann constant, ¹ is temperature and p is the supersaturation. The separation of the more widely spaced set of steps in Fig. 1 is approximately 370 nm. Assuming expression (1) holds in the present case, one obtains a critical radius of about 20 nm. It was found that crystals growing by a spiral mechanism and those exhibiting two-dimensional nucleation occurred within a distance of approximately 100 lm of each other on a glass slide. It seems reasonable, therefore, to assume that the prevailing conditions, particularly supersaturation, for adjacent crystals nucleated on the same glass slide are very similar, if not identical. On this basis, the critical radius on an adjacent crystal growing by two-dimensional nucleation would also be close to 20 nm. It should be noted that, for two reasons, this value is an overestimate. First, it is based only on the larger step spacing of the anisotropic spiral. Secondly, due to probable overlap of the diffusion fields of the steps at high supersaturation, significant deviation from the behaviour predicted by Eq. (1) may occur. The estimate is, however, a useful guide. Although the value of y /o calculated by 0 # Carbrera and Levine [34] relates to an isotropic spiral, the work of Budevski and co-workers [35] indicates that this value is approximately independent of the spiral shape. Their calculations for three-, four- and six-cornered polygonised spirals all gave values of y /o close to 19. 0 # The nuclei visible in Fig. 2 vary in size from approximately 400 to 1200 nm. One would, however, expect this range to extend to dimensions comparable with the radius of the critical two-
115
dimensional nucleus. Yet the smallest of the observed nuclei is more than an order of magnitude larger than even the overestimated value of o dis# cussed above. It should be noted that, on other samples, surface features less than 20 nm across have been routinely observed, thereby indicating that if two-dimensional nuclei of the estimated critical dimensions were present they would be detectable. Since separation of a crystal from its growth solution cannot be instantaneous, it follows that the cessation of growth does not occur instantly. It clearly depends upon the techniques used for separation and for observation of the surface as to whether such changes are detectable. Given that, under favourable conditions AFM is capable of molecular resolution, it is probably the most sensitive of all the available techniques in this respect. The fact that all the nuclei observed are substantially larger than the critical radius indicates that growth continued during separation from the solution. Furthermore, this growth proceeded at a lower supersaturation than that prior to separation otherwise new two-dimensional nuclei, much closer in size to the critical radius, would have formed and would be visible in the AFM images. Comparing the smallest observed nuclei with the expected critical radius, it would appear that the faster steps have moved through a distance of approximately 350 nm during separation of these crystals from their growth solutions. This figure allows for the approximately 10 : 1 ratio of the velocities of the fast and slow step orientations. If the actual supersaturation during removal were known, it would be possible to estimate the time interval over which the solution removal occurred. Although this supersaturation is not well defined, it is still possible to establish the order of magnitude of this time interval. From the step velocity measurements of Hottenhuis and Lucasius [23], the kinetic coefficient b of the fast moving S1 0 1T steps can be estimated at approximately 50 lm s~1. The step velocity v, supersaturation p, and the kinetic coefficient b are related thus: v"bp.
(2)
On this basis, the velocity of the fast S1 0 1T oriented steps on the M0 1 0N face of KAP is approximately 13 lm s~1 at a supersaturation of 26%. At
116
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
this velocity, the 2D nuclei would have grown from critical dimensions to the smallest size observed ex situ in a period of approximately 30 ms. This represents the shortest time interval in which the solution removal could have occurred. It is more difficult to set an upper limit on this time interval. However, the shape of the nuclei provides some insight. It has been observed that the spiral shape becomes progressively more polygonised with decreasing supersaturation [36]. A noticeable onset of this change occurs at around 10% relative supersaturation with steps becoming considerably straighter. It is reasonable to assume that islands which are substantially greater than the critical two-dimensional nucleus, would exhibit shape changes similar in nature to those of spiral turns of the same size. In the present case, however, the nuclei or islands exhibit essentially the same shape as that observed for turns of the spirals on crystals grown at the same high supersaturation. This implies that although the supersaturation decreases during solution removal, preventing new nuclei close to critical dimensions being present, this decrease is not large enough to produce the shape change observed for turns of spirals on KAP at lower supersaturation. Thus, it appears that the supersaturation during removal remains above approximately 10% and so the time interval for solution removal by a jet of compressed air is of the order of a few tens of milliseconds. From the large step velocities at the high supersaturations employed here, it follows that ex situ observation of two-dimensional nuclei in the case of small molecule materials such as KAP requires extremely rapid separation of crystal and solution to ensure a cessation of growth which is as abrupt as possible. A separation slower than that discussed here but similar in terms of the prevailing supersaturation, would result in more extensive growth and coalescence of the nuclei to leave a completely flat crystal face. In addition to samples exhibiting two-dimensional nuclei, some thin, almost perfectly flat crystals were observed in the course of this study. The crystals discussed here were grown under a bulk supersaturation of approximately 26%. It is well known, however, that the surface supersaturation is the true driving force for crystal growth. Under most growth conditions, the bulk super-
saturation will exceed that at the crystal surface because of a diffusion boundary layer. A relatively small number of studies have addressed the measurement of surface supersaturation together with its relation to bulk supersaturation and growth kinetics. These have included the use of Mach—Zehnder interferometry [37,38] and holography [39,40]. Two important points arise from these studies, particularly from Ref. [37]. First, there is a considerable difference between surface and bulk supersaturation which increases with decreasing solution velocity across the surface. Secondly, the surface supersaturation exhibits substantial variations across a crystal face, being larger at the edges than at the centre. The effects of such variations upon the activity of growth hillocks have been observed using Michelson interferometry in the case of barium nitrate [41]. In the present study, we clearly observe enhanced two-dimensional nucleation at the edges and particularly at the corners of the crystals. This is to be expected and is a direct consequence of the higher surface supersaturation in these areas of the crystal faces. There are several other factors which could yield substantially different surface topology from that shown in Fig. 1. Although none of these can account for all features of this surface, it is useful to consider these factors for the sake of completeness. (i) Poor surface protection during removal of solution might be put forward as an explanation for the absence of steps on a crystal surface. In the present case, however, the thin flat crystals are observed to be surrounded by crystals exhibiting clearly defined steps and spirals all within a few hundred microns or less of each other. (ii) A pair of dislocations of opposite sign can generate closed loops of steps. Such a source, however, produces concentric loops rather than the single loops visible in Fig. 2. (iii) It has been suggested that edge dislocations [42,43] and stacking faults [44] can act as sites for preferential two-dimensional nucleation. Such sites would again yield not single but concentric loops, although of rather less regular spacing than a dislocation pair. The distribution of nuclei across the surface is a further indication that the latter two explanations can be discounted. It is well established that growth-induced dislocations adopt orientations nearly normal to the face of the growth
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
sector in which they occur. Consequently, the density of dislocations emerging on a crystal face tends to be greatest at the centre, not the edge, of that face. X-ray topographic examination of defect densities and distributions [32] has confirmed this general observation for the specific case of KAP crystals.
[2] [3] [4] [5] [6] [7] [8] [9] [10]
5. Conclusions
[11]
Microcrystals of potassium hydrogen phthalate, grown at high supersaturation to dimensions of less than 100 lm, have been found to exhibit two distinctly different crystal morphologies. Ex situ atomic force microscopy of the crystal surfaces clearly demonstrates that the thicker platelet morphology observed is associated with growth by a spiral mechanism and the other, thinner morphology is due to growth by two-dimensional nucleation. The nuclei present on the surface of the thinner crystals lie within a relatively narrow size range from approximately 400 to 1200 nm, the smallest of which are substantially larger than the estimated radius of the critical two-dimensional nucleus. This observation is attributed to the fact that cessation of growth during solution removal is not instantaneous. The observed nonuniform distribution of nuclei reflects the variation in surface supersaturation, being greatest at the edges and corners of the crystals.
[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
Acknowledgements
[27]
The authors gratefully acknowledge financial support of this work by EPSRC. Support for a studentship (GRE) was provided by the School of Materials Science, University of Bath and CLRC Daresbury Laboratory. Assistance from the Centre for Electron Optical Studies, University of Bath is also acknowledged.
[28]
References [1] W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. Roy. Soc. London 243 (1959) 299.
[29] [30] [31] [32] [33] [34] [35] [36] [37]
117
P.B. Price, Phil. Mag. 5 (1960) 473. P.B. Price, J. Appl. Phys. 32 (1961) 1747. H. Samuelson, J. Appl. Phys. 32 (1961) 309. R.C. DeVries, G.W. Sears, J. Chem. Phys. 31 (1959) 1256. H.J. Meyer, B.J. Stein, J. Crystal Growth 49 (1980) 707. H.J. Meyer, B.J. Stein, J. Crystal Growth 60 (1982) 123. K.W. Keller, J. Crystal Growth 76 (1986) 469. R.A. Kaishev, E. Budevsky, Contemp. Phys. 8 (1967) 489. E. Budevsky, V. Bostanov, G. Staikov, Annual. Rev. Mater. Sci. 10 (1980) 85. B. Simon, A. Grassi, R. Boistelle, J. Crystal Growth 26 (1974) 77. A.A. Chernov, Contemp. Phys. 30 (1989) 251. A.J. Malkin, T.A. Land, Yu.G. Kuznetsov, A. McPherson, J.J. DeYoreo, Phys. Rev. Lett. 75 (1995) 2778. A.J. Malkin, Yu.G. Kuznetsov, W. Glantz, A. McPherson, J. Phys. Chem. 100 (1996) 11736. Y. Okaya, Acta Crystallogr. 19 (1965) 879. L.A.M.J. Jetten, Thesis, University of Nijmegen, 1983. M.H.J. Hottenhuis, J.G.E. Gardeniers, L.A.M.J. Jetten, P. Bennema, J. Crystal Growth 92 (1988) 171. W.J.P. van Enckevort, L.A.M.J. Jetten, J. Crystal Growth 60 (1982) 275. W.J.P. van Enckevort, Progr. Crystal Growth Charact. 9 (1984) 1. L.A.M.J. Jetten, B. van der Hoek, W.J.P. van Enckevort, J. Crystal Growth 62 (1983) 603. M.H.J. Hottenhuis, C.B. Lucasius, J. Crystal Growth 94 (1989) 708. M.H.J. Hottenhuis, C.B. Lucasius, J. Crystal Growth 78 (1986) 379. M.H.J. Hottenhuis, C.B. Lucasius, J. Crystal Growth 91 (1988) 623. M.H.J. Hottenhuis, A. Oudenampsen, J. Crystal Growth 92 (1988) 513. M.P.W. Derks, A.E.D.M. van der Heijden, M. Elwenspoek, J. Crystal Growth 94 (1989) 527. A.E.D.M. van der Heijden, M. Elwenspoek, J.P. van der Eerden, J. Crystal Growth 98 (1989) 398. A.E.D.M. van der Heijden, M. Elwenspoek, J. Crystal Growth 99 (1990) 1087. G.R. Ester, R. Price, P.J. Halfpenny, J. Crystal Growth 182 (1997) 95. Zhao Qing-Lan, Acta Phys. Sinica 37 (1988) 1345. Zhao Qing-Lan, Huang Yi-Sen, Acta Physica Sinica 38 (1989) 1134. Zhao Qing-Lan, Huang Yi-Sen, J. Synthetic Crystals 19 (1990) 249. G.R. Ester, P.J. Halfpenny, in preparation. Z. Solc, J. Kvapil, J. Vlcek, Kristall Tech. 8 (1973) 59. N. Cabrera, M.M. Levine, Philos. Mag. 1 (1956) 450. E. Budevski, G. Staikov, V. Bostanov, J. Crystal Growth 29 (1975) 316. R. Price, G.R. Ester, P.J. Halfpenny, in preparation. K. Onuma, K. Tsukamoto, I. Sunagawa, J. Crystal Growth 98 (1989) 377.
118
G.R. Ester, P.J. Halfpenny / Journal of Crystal Growth 187 (1998) 111—118
[38] J.C. van Dam, F.H. Mischgofsky, J. Crystal Growth 84 (1987) 539. [39] F. Bedarida, J. Crystal Growth 79 (1986) 43. [40] F. Bedarida, L. Zefiro, P. Boccacci, D. Aquilano, M. Rubbo, G. Vaccari, G. Mantovani, G. Sgualdino, J. Crystal Growth 89 (1988) 395.
[41] K. Maiwa, K. Tsukamoto, I. Sunagawa, J. Crystal Growth 102 (1990) 43. [42] K.W. Keller, J. Crystal Growth 78 (1986) 509. [43] E. Bauser, H. Strunk, J. Crystal Growth 51 (1981) 362. [44] N. Ming, K. Tsukamoto, I. Sunagawa, A. Chernov, J. Crystal Growth 91 (1988) 11.