- Email: [email protected]
Ex situ investigation of surface topography of as-grown potassium dihydrogen phosphate crystals by atomic force microscopy
ELSEWIER
Journal of Crystal Growth 169 (1996) 548-556
Ex situ investigation of surface topography of as-grown potassium dihydrogen phosphate crystals by atomic force microscopy Mariusz J. Krasiiiski a3*, Ranieri Rolandi b a Institute b Department
of Phwics,
Technical
of Physics, INFM,
University,
University
ul. Wrjlczai2ska 219. P-93 005 L6d2, Polund
of Genoa. via Dodecaneso
33, 1-13 146 Genoa. Ita!\
Received 4 May 1996
Abstract Surface topographies
of the (100) and {lOl} faces of as-grown
potassium
dihydrogen
phosphate
(KDP) crystals were
observed ex situ by atomic force microscopy (AFM). Growth hillocks, step bunching, growth spirals, 2D nucleus and hollow cores were detected. AFM images provided qualitative features and quantitative data on crystals grown under different conditions, concerning
which are in quite good agreement the use of the AFM is also included.
with theoretical
1. Introduction Scanning force microscopy is a relatively new and very promising technique for imaging and measuring surface features even of sub-nanometric dimensions [ 11. As shown by recent literature, its use in crystal growth research quickly increases, mainly owing to SFM capability to reveal elementary growth steps directly, without either covering by metal or preparing the samples otherwise [l-7]. Furthermore, SFM can operate in air as well as in a liquid environment and can be used for in situ inspection of the growth process [8-121. The rather long time needed for collecting a single image (up to 100 s) is the major drawback for in situ observation of fast growing
description.
A discussion
of the experimental
problems
crystals as KDP crystals. Elsewhere we deal with this problem [ 131. Another disadvantage of SFM is the relatively small scan area available (up to 125 pm by 12.5 pm) not allowing one to see larger growth features simultaneously. The most intriguing advantage of SFM is the potential possibility to observe atomic processes during growth [ 14,151. In this paper we present results of ex situ investigations of the surface morphology of as-grown KDP crystals, since these crystals were studied by various methods but, as far as we know, not yet thoroughly examined by SFM [4, I I, 131.
2. Experimental
details
2. I. Samples * Corresponding author. [email protected].
Fax:
0022-0248/96/$15.00 Copyright PII SOO22-0248(96)00414-S
+48
42 31 36 39; E-mail:
The seed crystals of KDP were grown in a big vessel at room temperature from a highly supersatu-
0 1996 Elsevier Science B.V. All rights reserved
M.J.
Krasiriski.
R. Rolandi
/ Journal
rated solution. The best seeds were mounted in a liquid jacket crystallizer with an inner volume of 1000 ml and were grown either for some days or when only faces had to be regenerated, a few hours. The starting material was KDP pure reagent (99% purity, Aldrich). The solution was slowly stirred by a magnetic stir bar on the bottom of the crystallization vessel. The crystals were placed eccentrically with respect to the stirrer axis. Crystallization was performed at different temperatures varying in the range 36-40°C. Stabilization of the temperature in the crystallizer was not worse than 0.05 K. Some observations on the seed crystals grown at high supersaturation have also been made. For SFM investigation, the crystals were quickly removed from the crystallizer and dried with a paper tissue, for preserving the crystal surface, and subsequently fixed by double adhesive tape in the SFM sample holder. 2.2. AFM equipment
of Cnstal
Growth
(19961
549
548-556
moval from the growth vessel. We have tested several methods described in the literature to minimize this shut-off effect. The commonly used procedure of washing with n-hexane very often results in blurred pictures and does not definitively stop the growth process. After many tests we conclude that the simplest method of drying crystals with paper tissue immediately after a quick extraction from the crystallizer produces the best results. The comparison of the ex situ images with those obtained from in situ experiments, which we describe in Ref. [ 131, confirms this conclusion. Once the crystal is dried, its SFM image remains stable for some time. In the case of KDP crystals, changes of the step pattern have not been observed for many days. This fact is not quite generalized, for example, the aspect of two day old sodium chlorate crystals was usually different from that of the freshly removed crystals. We must point out that the z-scale of our J scanner was calibrated by using the 180 nm dip
All measurements were carried out under ambient conditions by using a Nanoscope III atomic force microscope (Digital Instrument Inc., CA, USA) equipped either with a type J (120 by 120 pm scan area) or a type A (1 by 1 pm) scanner. Cantilevers with spring constants of 0.12 and 0.06 N/m (Digital Instrument Inc.) were used. Images were usually collected with scan frequencies of between 2 and 8 Hz and in both height and deflection modes, but the quantitative data of the step and profile heights were obtained only from height mode images. 2.3. Experimental
lh9
200
400
600
horizontal distance
800
1000
I nm
problems
For the correct evaluation of the data obtained in ex situ experiments, the preservation of the surfaces after the crystal removal from the growth solution is very important [16]. The problem is well known, but still remains unsolved satisfactory. During the removal from the crystallizer the monocrystal is exposed to a sudden change of supersaturation conditions that affects the step pattern firstly in the spiral centre, where the curvature plays a decisive role. Such an effect, observed by us, will be described in the second part of the paper. Thus, to correlate the step pattern with growth conditions, the step pattern should be frozen immediately after the crystal re-
0
200
400
600
horizontal distance
800
1000
I nm
Fig. 1. Measurement of steps height on a prismatic face from AFh4 data. (Top) original Am? section. (Bottom) after rotation in order to place terraces horizontally. The between the horizontal dotted lines on the lower graph is the unit cell dimension in the [ 1001direction.
of KDP section distance equal to
550
M.J. Krasiriski,
R. Rolandi / Journal
5 urn
of Ctytal
Growth
I69
f I9961548-556
steps. This effect, commonly known as tip etching, is smaller in solution but in the case of ex situ measurements in air can play a significant role. To avoid such etching the force between the tip and the surface should be minimized and cantilevers with a smaller spring constant should be used. To avoid tip-etching artifacts, it is important to check that the surface does not change in subsequent scannings. In some experiments we observed that the image quality depends on the scanning direction. The most impressive example is presented in Fig. 2. Scanning in one direction, a contaminated surface. with objects similar to 2D nucleus, appeared. Changing the scanning direction the image immediately became very clear with a normal step pattern.
3. Results and discussion
3. I. Step morphologv
1 nrn Fig. 2. The influence of scan angle on the quality of AFM pictures. Pictures present the same part of the (100) face of the KDP crystal but the scan direction in the case of (a) differs from (b) by about 20” Supersaturation 3.5%.
grooves of an interferometric grid. This value is very large compared to the height of monoatomic steps and one must relay on the scanner behaviour, which is not necessarily linear on an extended scale. The step height values obtained by the SFM are then less precise than X-ray crystallographic data. Furthermore, to avoid significant errors, the proper measurement of the step height requires the transformation of the raw sections as those shown in Fig. la. We chose to rotate the sections in order to put terraces horizontally (Fig. lb) instead to use the plane fit algorithm of Nanoscope III software. We did this off-line, after image acquisition by a numerical transforms. During the scanning the AFM tip can remove some part of the crystal, changing the shape of the
Macrosteps, i.e. steps much higher than unit cell dimension, and monosteps whose height is comparable to unit cell dimension were detected. There exists a general relation between growth conditions and step quality. For crystals grown at low supersaturation (< 2%) the lines of steps were complicated. Macrosteps were irregular and monoatomic steps were hardly detectable. The macrosteps pattern was very similar to that observed for tapered crystals. In case of crystals grown at higher supersaturation the step pattern was much more regular. Steps were
Fig. 3. The area of parallel steps abuts on the region of more complicated steps on the (100) face. Supersaturation 1.57~~ scan size 100 pm.
more periodic. forming clear terraces. Step edges were straighter with fewer vacancies. Monoatomic steps were easily detectable. Though the tendency described above is quite clear we must state that also in the case of crystals grown at low supersaturations, areas with nice, straight and parallel steps were detected. Fig. 3 shows the place on the surface where the area with nice parallel macrosteps abuts on the other with chaotic steps. The height of the elementary steps measured at the (I OO}face on most of pictures was about 0.74 nm (Fig. lb). This value is equal to the height of the KDP unit cell within the experimental error. In very few images, especially near the centre of the growth hillock, half-unit-cell steps were detected, but for steps far from the spiral centre. in practice, only unit-cell-high steps were observed. Half-unit-cell steps are expected on the { IOO} face of KDP crystals. Such steps were detected in some images but we observed that there exists a tendency for grouping
such steps to form one-unit-cell steps. Such a tendency has been observed by us also on the { IOO} face of sodium chlorate crystals, where almost all the detected half-unit-cell steps formed very close spaced pairs. On the { 101) face, 0.5 nm high steps were observed in agreement with the expectation and observation of other researchers [4]. The shape of steps on the (101) face was different from those of the steps on the { 100) face. The regular steps observed on the prismatic face often constitute sequences of almost parallel and even perfectly parallel lines. Steps on pyramidal faces were always less regular and lumpier.
Usually the crystal surfaces were covered by the macrosteps being the result of a process called step bunching. Fig. 4 presents a typical pattern of this type. The heights of such steps were different in
Fig. 3. Examples of step pattern on the (100) face (a). (c). and the (101) face (b). Cd). Supersaturations were: (a) 4.?%, Cd) 6%.
(b) 6%.(c) 3%,and
552
M.J. Krasiriski. R. Rolandi / Journal of Ctytal Growth 169 ( 19961548-556
different crystals grown under the same growth conditions and in different places of the same crystal. Generally, these heights varied from two to 100 layers. Even in the one set of bunched steps, the heights of different steps were different though similar. Owing to the finite size of the tip, the AFM image is the convolution of the tip function and surface function [ 171. Therefore, surface profiles can be more or less altered according to the features of the profile itself. This effect made elementary steps hardly revealed in very steep profiles caused by bunched macrosteps, while, in less steep profiles, elementary steps were clearly visible. In most cases it was not possible to see the origin of the step bunching which, according to Cabrera and Vermileya, should be the foreign particles deposited on the surface. The particles were perhaps too small to be visible for the scanning sizes used (about 1-4 pm). However, cusps formed when steps are trying to squeeze through the fences of impurities were clearly observed. In these cases the image is in very good agreement with the theoretical prediction [ 181. The distances between the pinning points were between 70 and 200 nm. The calculated radius of the 2D nucleus under these conditions was less than 30 nm The terraces between macrosteps usually were occupied by a few, from one to five, monosteps. Areas as large as 10 pm2 covered exclusively by monosteps could be observed very often (Fig. 4~). The step spacing was usually not uniform and often 100 nm wide terraces were found near 600 nm wide terraces. The hydrodynamic conditions in our crystallizer were not defined very precisely, therefore it is very hard to find a correlation between steps spacing and supersaturation. As we know from interferometric data, supersaturation can vary significantly from place to place. According to Refs. [19,20], the local hydrodynamic conditions significantly affect the step pattern. However, we found that most of the spacings lay between 100 and 300 nm in agreement with the findings of Rashkovich and Chemov [19,20] who, in situ, studied the evolution of the growth hillocks on KDP prismatic faces by a Michelson interferometer. Since the interferometric set-up does not allow single steps to be revealed, they calculated the average slope of the growth hillocks. Assuming that only the unit cell steps exist their data can be
translated into step spacings. For supersaturation from 2% to 6% these spacings lie between 370 and 125 nm, respectively. Taking into account the supersaturation values used in our experiments, mostly between 2% and 4%, the spacings observed by AFM are in quite good agreement with the data obtained by Rashkovich and Chemov. In some pictures we observed quite big particles that look to be the stoppers for moving steps. It is clear that the existence of these particles immobilized on the surface effected in appearance of big bunched step. This type of step bunching with participation of big particles has perhaps taken place during residual growth after removing crystal from solution. AFM allows us to go down to atomic scale resolution. In fact we observed very nice pictures of the atomic structure on { 100] and ( 10 1) faces. To reveal the growth units on the step edges is particularly important for a complete description of the growth process. Despite the promising achievements of other researchers [9], we have a lot of problems to simultaneously see the atomic structure and step pattern though separately both phenomena were observed with no problem. Fig. 5 presents one rare image where the step edge and the atomic structure are visible. To avoid tip-etching effects such images required a very careful adjustment of the force acting on the crystal surface during scanning. It was not
Fig. 5. Very high magnification of the step edge on the prismatic face. The pattern in the picture is not the noise. it is an atomic picture of the crystal surface what was confirmed at higher magnification. Scan size 45 nm.
M.J. Krasihski, R. Rolandi/ Journal of Crytul Growth 169 (19961 548-556
553
possible to detect any errors in atomic structure what is common to AFM data [ 14,151 in contrary to STM results for other crystals. 3.3. Growth spirals
E
1000
c ;
-I-I
/
I
800 -j
According to the theory and experimental evidence, the steps on the {loo} face of KDP are generated mainly by screw dislocations and growth spirals should be detected. We have recorded numerous images showing the growth hillocks as a whole and the top part of them. Fig. 6a shows one of these spirals. This one is in fact the pair of co-operating spirals rotating in the same direction. The property of the spiral is different in the centre than far from it. Plotting the position of the consecutive step edges versus the number of edges, i.e. the number of revolutions a straight line not intersecting the origin of co-ordinates is obtained (Fig. 6b). This is probably caused by the shut-off effect mentioned earlier. According to Cabrera and Levine [21] the distance A between steps in the spiral is 19ya A=-----nakT’
0
,
,
,
(
,
(
,
I
01234567 b
edgenumber
Fig. 6. (a) Double spiral on the prismatic face and (b) the plot of the edge position versus the number of edges for the spiral presented above. Supersaturation 4.2%.
Fig. 7. The growth hillock on the (100) face seen at different Supersaturation 3.5%.
(1)
where y is the edge free energy of a growth unit in a step, a is the distance between growth units, u is supersaturation, k is the Boltzmann constant, T is crystallization temperature and IZ is the number of cooperating spirals. Using the slope of the curve in Fig. 6b, which represents the average steps spacing, we are obtaining a value of supersaturation of about 4.3%, which corresponds very well with 4.2% of real bulk supersaturation. In other experiments the value
magnifications:
(a) Far from centre; (b) Top: (c) Near dislocation
outcrops.
554
M. J. Krasiiiski. R. Rolandi / Journal of Crywtul Growth 169 ( 19961 548-556
calculated from AFM images was from 0 to 20% less than bulk supersaturation. It is known that the near surface supersaturation is always more or less lower than the bulk one depending on hydrodynamic conditions. The obtained values are then reasonable and in accordance with interferometric data [22-241. This can be regarded both as a proof of reasonableness of Eq. (I) and a proof that the step pattern (excluding the part near the centre of the spiral) detected in this case really reflects the growth process in solution and not the shut-off effect. Fig. 7 shows an interesting example of a growth hillock. Under low magnifications it seems to be a typical hillock originated from screw dislocation. Looking more precisely on the top of the hillock one can see that its origin, however, is a group of dislocations spread over an area of 100 nm by 100 nm. The height of the steps existing near the top of the growth hillock was a half unit cell. This picture may be an example of the real advantage of AFM (in sense of resolution) over the common observation techniques.
of such an effect. Some holes are spread near the top of the growth hillock. These hollow cores are not placed in the centre of the growth spiral but on the steps. The splitting of the step by hollow core can be observed. The diameter of the holes shown in Fig. 9 is less than 40 nm, which is a reasonable value for hollow cores. In Fig. 9b the section through the hollow core is presented. In fact the shape of the core section produced by AFM is strongly influenced by the tip shape and we can only be sure that the depth of the core is greater than 4-5 nm. In order to study more precisely the core characteristic we increased the force of the tip on the surface. The tip was removing material layer by layer allowing us to see the inner part of the hollow core at increasing
3.4. 20 nucleation Though in the majority of experiments we have observed the hillocks or set of nearly parallel steps originated perhaps from edges, we have also detected some examples of 2D nuclei. These were observed on crystals grown at high supersaturation (> 10%). In Fig. 8a the island placed on the terrace between two steps is visible. The radius of the island is about 200 nm. It is much greater than the radius of critical nucleus at this supersaturation. In Fig. 8b the huge island without any signs of dislocation outcrop is visible. Despite the right part of the picture, the large width of the terraces (500 nm and more> supports the assumption concerning 2D nucleation. On the right part of the picture perhaps the step-bunching process took place causing the decrease of step distances. Due to the shut-off effect described earlier, the hypothesis that nucleation took place after the crystal removal from solution can not be excluded.
Fig. 8. Two-dimensional
The last features observed on the KDP surface were hollow cores [25]. Fig. 9 presents an example
islands on the prismatic face of the
crystal grown at high supersaturation ( > 10%). Step edges were enhanced by the software.
tween theoretical description and real step pattern on the crystal surface. In some cases the quantitative agreement is also pretty good. The possibility of examination of very small structures by AFM is with no doubt much better than in the case of the other method. For example AFM allowed us to precisely measure the height of the steps. Despite this, AFM can not be regarded as a self-sufficient method for the study of the crystal growth process. The significant problems during in situ measurements, and the very small areas available for study, require the use of other methods together with AFM. It would be very reasonable to join the sophisticated interferometric methods [26.27]. which are delivering very good real-time data, with investigation (on the same crystal) by AFM. Because the AFM is examining 5 only a small part on the surface. the growth conditions near the crystal surface should be determined 4 very precisely. The crucial question in the case of ex E situ measurements is how representative is the surI3 face of the crystal thrown out from solution. Onuma E et al. [28] showed that the crystal exposed for some .EJ 2 time to air needs time to start growing again after i! placing in solution. This indicates that crystals should 1 be rather examined in situ. and ex situ data must be ..____....,,..........................,................................... treated very carefully. The in situ study by AFM in I I I I the case of KDP is very difficult [4,13] but maybe 0 200 800 400 600 some progress will be made after improving the b AFM ability [29.30]. horizontal distance I nm Fig. Y. (a) Hollow cores on the prismatic face of the KDP crystal and (b) a section through one of the hollow cores. Supersaturation 3%.
depth. The position of the holes remained the same during this process. This procedure showed that, within the experimental errors, the hollow cores were perpendicular to the face. Only in the case of two holes have we observed the disappearance of the hole after removing a few layers of material detecting the core bottom. In other cases the image during the process remained stable suggesting that the depth of the other cores were greater than 20 layers which were removed.
Acknowledgements We are grateful to Professor F. Bedarida for his encouragement and helpful discussions. Support to this work by MURST (40% and 60% funds) and INFM is gratefully acknowledged. M.J.K. thanks the Italian Ministry of Foreign Affairs for financial support during work at University of Genoa and Polish Committee for Scientific Research for mobility grant.
References 4. General considerations
and conclusions
The AFM studies of the crystal surface (not only in this case) proved the qualitative agreement be-
[l] S. Magonov, Appt. Spectrosc. Rev. 2X (1993) I. [2] W. Littke. M. Haber and H.J. Guntherodt.
I22 (I 992)80.
J. Crystal Growth
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M.J. KrasiAski. R. Rolandi/Journal
[3] M.A. George, M. Azulay, H.N. Jayatirtha, Y. Biao, A. Burger, W.E. Collins and E. Silberman, J. Crystal Growth 137 (1994) 299. [4] J.J. De Yoreo, T.A. Land and B. Dair, Phys. Rev. Lett. 73 (1994) 838. [5] S. Kipp, S. Kammer, R. Lackmann, J. Rolfs, U. Tanneberger and W. Beckmann, Cryst. Res. Technol. 29 (1994) 1005. [6] K. Onuma, A. Ito, T. Teteishi and T. Kameyama, I. Crystal Growth 148 (1995) 201. [7] A.J. Derksen, W.J.P. Van Enckewort and M.S. Couto, J. Phys. D: Appl. Phys. 27 (1994) 2580. [8] S.D. Durbin and W.E. Carlson, J. Crystal Growth 122 (1992) 71. [9] P.E. Hilner, S. Manne, A.J. Gratz and P.K. Hansma, Disc. Faraday Sot. 95 (1993) 191. [lo] B. Muller-Zulow, S. Kipp, R. Lackmann and M.A. Schneeweiss, Surf. Sci. 311 (1994) 153. [ 1 I] T.A. Land, J.D. Lee and J.J. De Yoreo. in: the 1 Ith Int. Conf. on Crystal Growth, 1995, Abstracts p. 119. [12] T.A. Land, A.J. Malkin. Yu.G. Kuznetsov, A. McPherson and J.J. De Yoreo, J. Crystal Growth 166 (1996) 893. [13] M.J. Krasinski and R. Rolandi, Cryst. Res. Technoi. 31 (1996) 179. [I41 R.T. Williams and R.M. Wilson and H. Liu, Nucl. Instrum. Methods B 65 (1992) 473. [15] A.L. Shluger, R.M. Wilson and R.T. Wilson, Phys. Rev. B 49 (1994) 4915.
ofCtyta1
Growth 169 (1996) 548-556
1161 B. van der Hoek, J.P. van der Eerden and P. Bennema, J. Crystal Growth 56 (1982) 108. [17] D. Keller, Surf. Sci. 253 (1991) 353. [ 181 W.J.P. van Enckevort, in: Science and Technology of Crystal Growth, Eds. J.P. van der Eerden and O.S.L. Bruinsma (Kluwer, Dordrecht, 1995) p. 355. [19] A.A. Chernov and L.N. Rashkovich, J. Crystal Growth 84 (1987) 389. [20] A.A. Chernov, Contemp. Phys. 30 (1989) 251. [21] N. Cabrera and M.M. Levine, Philos. Mag. 1 (1956) 450. [22] M.J. Krasinski, in: Industrial Crystallization 93, Ed. Z.H. Rojkowski, Warsaw, 1993, p. 4-077. [23] F. Bedarida, J. Crystal Growth 79 (1986) 43. 1241 K. Onuma, K. Tsukamoto and I. Sunagawa, J. Crystal Growth 98 (1989) 377. [25] B. van der Hoek, J.P. van der Eerden and P. Bennema, J. Crystal Growth 56 (1982) 62 I. [26] K. Onuma, T. Kameyama and K. Tsukamoto. J. Crystal Growth 137 (1994) 610. [27] P.G. Vekilov. L.A. Monaco and F. Rosenberger, J. Crystal Growth 148 (1995) 289 [28] K. Onuma, K. Tsukamoto and I. Sunagawa, Microgravity Sci. Technol. 2 (1992) 62. [29] S. Kipp, R. Ldckmann and M.A. Schneeweiss, J. Crystal Growth 141 (1994) 291. [30] S. Kipp. R. Lackmann and M.A. Schneeweiss, Ultramicroscopy 57 (1995) 333.
Journal of Crystal Growth 169 (1996) 548-556
Ex situ investigation of surface topography of as-grown potassium dihydrogen phosphate crystals by atomic force microscopy Mariusz J. Krasiiiski a3*, Ranieri Rolandi b a Institute b Department
of Phwics,
Technical
of Physics, INFM,
University,
University
ul. Wrjlczai2ska 219. P-93 005 L6d2, Polund
of Genoa. via Dodecaneso
33, 1-13 146 Genoa. Ita!\
Received 4 May 1996
Abstract Surface topographies
of the (100) and {lOl} faces of as-grown
potassium
dihydrogen
phosphate
(KDP) crystals were
observed ex situ by atomic force microscopy (AFM). Growth hillocks, step bunching, growth spirals, 2D nucleus and hollow cores were detected. AFM images provided qualitative features and quantitative data on crystals grown under different conditions, concerning
which are in quite good agreement the use of the AFM is also included.
with theoretical
1. Introduction Scanning force microscopy is a relatively new and very promising technique for imaging and measuring surface features even of sub-nanometric dimensions [ 11. As shown by recent literature, its use in crystal growth research quickly increases, mainly owing to SFM capability to reveal elementary growth steps directly, without either covering by metal or preparing the samples otherwise [l-7]. Furthermore, SFM can operate in air as well as in a liquid environment and can be used for in situ inspection of the growth process [8-121. The rather long time needed for collecting a single image (up to 100 s) is the major drawback for in situ observation of fast growing
description.
A discussion
of the experimental
problems
crystals as KDP crystals. Elsewhere we deal with this problem [ 131. Another disadvantage of SFM is the relatively small scan area available (up to 125 pm by 12.5 pm) not allowing one to see larger growth features simultaneously. The most intriguing advantage of SFM is the potential possibility to observe atomic processes during growth [ 14,151. In this paper we present results of ex situ investigations of the surface morphology of as-grown KDP crystals, since these crystals were studied by various methods but, as far as we know, not yet thoroughly examined by SFM [4, I I, 131.
2. Experimental
details
2. I. Samples * Corresponding author. [email protected].
Fax:
0022-0248/96/$15.00 Copyright PII SOO22-0248(96)00414-S
+48
42 31 36 39; E-mail:
The seed crystals of KDP were grown in a big vessel at room temperature from a highly supersatu-
0 1996 Elsevier Science B.V. All rights reserved
M.J.
Krasiriski.
R. Rolandi
/ Journal
rated solution. The best seeds were mounted in a liquid jacket crystallizer with an inner volume of 1000 ml and were grown either for some days or when only faces had to be regenerated, a few hours. The starting material was KDP pure reagent (99% purity, Aldrich). The solution was slowly stirred by a magnetic stir bar on the bottom of the crystallization vessel. The crystals were placed eccentrically with respect to the stirrer axis. Crystallization was performed at different temperatures varying in the range 36-40°C. Stabilization of the temperature in the crystallizer was not worse than 0.05 K. Some observations on the seed crystals grown at high supersaturation have also been made. For SFM investigation, the crystals were quickly removed from the crystallizer and dried with a paper tissue, for preserving the crystal surface, and subsequently fixed by double adhesive tape in the SFM sample holder. 2.2. AFM equipment
of Cnstal
Growth
(19961
549
548-556
moval from the growth vessel. We have tested several methods described in the literature to minimize this shut-off effect. The commonly used procedure of washing with n-hexane very often results in blurred pictures and does not definitively stop the growth process. After many tests we conclude that the simplest method of drying crystals with paper tissue immediately after a quick extraction from the crystallizer produces the best results. The comparison of the ex situ images with those obtained from in situ experiments, which we describe in Ref. [ 131, confirms this conclusion. Once the crystal is dried, its SFM image remains stable for some time. In the case of KDP crystals, changes of the step pattern have not been observed for many days. This fact is not quite generalized, for example, the aspect of two day old sodium chlorate crystals was usually different from that of the freshly removed crystals. We must point out that the z-scale of our J scanner was calibrated by using the 180 nm dip
All measurements were carried out under ambient conditions by using a Nanoscope III atomic force microscope (Digital Instrument Inc., CA, USA) equipped either with a type J (120 by 120 pm scan area) or a type A (1 by 1 pm) scanner. Cantilevers with spring constants of 0.12 and 0.06 N/m (Digital Instrument Inc.) were used. Images were usually collected with scan frequencies of between 2 and 8 Hz and in both height and deflection modes, but the quantitative data of the step and profile heights were obtained only from height mode images. 2.3. Experimental
lh9
200
400
600
horizontal distance
800
1000
I nm
problems
For the correct evaluation of the data obtained in ex situ experiments, the preservation of the surfaces after the crystal removal from the growth solution is very important [16]. The problem is well known, but still remains unsolved satisfactory. During the removal from the crystallizer the monocrystal is exposed to a sudden change of supersaturation conditions that affects the step pattern firstly in the spiral centre, where the curvature plays a decisive role. Such an effect, observed by us, will be described in the second part of the paper. Thus, to correlate the step pattern with growth conditions, the step pattern should be frozen immediately after the crystal re-
0
200
400
600
horizontal distance
800
1000
I nm
Fig. 1. Measurement of steps height on a prismatic face from AFh4 data. (Top) original Am? section. (Bottom) after rotation in order to place terraces horizontally. The between the horizontal dotted lines on the lower graph is the unit cell dimension in the [ 1001direction.
of KDP section distance equal to
550
M.J. Krasiriski,
R. Rolandi / Journal
5 urn
of Ctytal
Growth
I69
f I9961548-556
steps. This effect, commonly known as tip etching, is smaller in solution but in the case of ex situ measurements in air can play a significant role. To avoid such etching the force between the tip and the surface should be minimized and cantilevers with a smaller spring constant should be used. To avoid tip-etching artifacts, it is important to check that the surface does not change in subsequent scannings. In some experiments we observed that the image quality depends on the scanning direction. The most impressive example is presented in Fig. 2. Scanning in one direction, a contaminated surface. with objects similar to 2D nucleus, appeared. Changing the scanning direction the image immediately became very clear with a normal step pattern.
3. Results and discussion
3. I. Step morphologv
1 nrn Fig. 2. The influence of scan angle on the quality of AFM pictures. Pictures present the same part of the (100) face of the KDP crystal but the scan direction in the case of (a) differs from (b) by about 20” Supersaturation 3.5%.
grooves of an interferometric grid. This value is very large compared to the height of monoatomic steps and one must relay on the scanner behaviour, which is not necessarily linear on an extended scale. The step height values obtained by the SFM are then less precise than X-ray crystallographic data. Furthermore, to avoid significant errors, the proper measurement of the step height requires the transformation of the raw sections as those shown in Fig. la. We chose to rotate the sections in order to put terraces horizontally (Fig. lb) instead to use the plane fit algorithm of Nanoscope III software. We did this off-line, after image acquisition by a numerical transforms. During the scanning the AFM tip can remove some part of the crystal, changing the shape of the
Macrosteps, i.e. steps much higher than unit cell dimension, and monosteps whose height is comparable to unit cell dimension were detected. There exists a general relation between growth conditions and step quality. For crystals grown at low supersaturation (< 2%) the lines of steps were complicated. Macrosteps were irregular and monoatomic steps were hardly detectable. The macrosteps pattern was very similar to that observed for tapered crystals. In case of crystals grown at higher supersaturation the step pattern was much more regular. Steps were
Fig. 3. The area of parallel steps abuts on the region of more complicated steps on the (100) face. Supersaturation 1.57~~ scan size 100 pm.
more periodic. forming clear terraces. Step edges were straighter with fewer vacancies. Monoatomic steps were easily detectable. Though the tendency described above is quite clear we must state that also in the case of crystals grown at low supersaturations, areas with nice, straight and parallel steps were detected. Fig. 3 shows the place on the surface where the area with nice parallel macrosteps abuts on the other with chaotic steps. The height of the elementary steps measured at the (I OO}face on most of pictures was about 0.74 nm (Fig. lb). This value is equal to the height of the KDP unit cell within the experimental error. In very few images, especially near the centre of the growth hillock, half-unit-cell steps were detected, but for steps far from the spiral centre. in practice, only unit-cell-high steps were observed. Half-unit-cell steps are expected on the { IOO} face of KDP crystals. Such steps were detected in some images but we observed that there exists a tendency for grouping
such steps to form one-unit-cell steps. Such a tendency has been observed by us also on the { IOO} face of sodium chlorate crystals, where almost all the detected half-unit-cell steps formed very close spaced pairs. On the { 101) face, 0.5 nm high steps were observed in agreement with the expectation and observation of other researchers [4]. The shape of steps on the (101) face was different from those of the steps on the { 100) face. The regular steps observed on the prismatic face often constitute sequences of almost parallel and even perfectly parallel lines. Steps on pyramidal faces were always less regular and lumpier.
Usually the crystal surfaces were covered by the macrosteps being the result of a process called step bunching. Fig. 4 presents a typical pattern of this type. The heights of such steps were different in
Fig. 3. Examples of step pattern on the (100) face (a). (c). and the (101) face (b). Cd). Supersaturations were: (a) 4.?%, Cd) 6%.
(b) 6%.(c) 3%,and
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different crystals grown under the same growth conditions and in different places of the same crystal. Generally, these heights varied from two to 100 layers. Even in the one set of bunched steps, the heights of different steps were different though similar. Owing to the finite size of the tip, the AFM image is the convolution of the tip function and surface function [ 171. Therefore, surface profiles can be more or less altered according to the features of the profile itself. This effect made elementary steps hardly revealed in very steep profiles caused by bunched macrosteps, while, in less steep profiles, elementary steps were clearly visible. In most cases it was not possible to see the origin of the step bunching which, according to Cabrera and Vermileya, should be the foreign particles deposited on the surface. The particles were perhaps too small to be visible for the scanning sizes used (about 1-4 pm). However, cusps formed when steps are trying to squeeze through the fences of impurities were clearly observed. In these cases the image is in very good agreement with the theoretical prediction [ 181. The distances between the pinning points were between 70 and 200 nm. The calculated radius of the 2D nucleus under these conditions was less than 30 nm The terraces between macrosteps usually were occupied by a few, from one to five, monosteps. Areas as large as 10 pm2 covered exclusively by monosteps could be observed very often (Fig. 4~). The step spacing was usually not uniform and often 100 nm wide terraces were found near 600 nm wide terraces. The hydrodynamic conditions in our crystallizer were not defined very precisely, therefore it is very hard to find a correlation between steps spacing and supersaturation. As we know from interferometric data, supersaturation can vary significantly from place to place. According to Refs. [19,20], the local hydrodynamic conditions significantly affect the step pattern. However, we found that most of the spacings lay between 100 and 300 nm in agreement with the findings of Rashkovich and Chemov [19,20] who, in situ, studied the evolution of the growth hillocks on KDP prismatic faces by a Michelson interferometer. Since the interferometric set-up does not allow single steps to be revealed, they calculated the average slope of the growth hillocks. Assuming that only the unit cell steps exist their data can be
translated into step spacings. For supersaturation from 2% to 6% these spacings lie between 370 and 125 nm, respectively. Taking into account the supersaturation values used in our experiments, mostly between 2% and 4%, the spacings observed by AFM are in quite good agreement with the data obtained by Rashkovich and Chemov. In some pictures we observed quite big particles that look to be the stoppers for moving steps. It is clear that the existence of these particles immobilized on the surface effected in appearance of big bunched step. This type of step bunching with participation of big particles has perhaps taken place during residual growth after removing crystal from solution. AFM allows us to go down to atomic scale resolution. In fact we observed very nice pictures of the atomic structure on { 100] and ( 10 1) faces. To reveal the growth units on the step edges is particularly important for a complete description of the growth process. Despite the promising achievements of other researchers [9], we have a lot of problems to simultaneously see the atomic structure and step pattern though separately both phenomena were observed with no problem. Fig. 5 presents one rare image where the step edge and the atomic structure are visible. To avoid tip-etching effects such images required a very careful adjustment of the force acting on the crystal surface during scanning. It was not
Fig. 5. Very high magnification of the step edge on the prismatic face. The pattern in the picture is not the noise. it is an atomic picture of the crystal surface what was confirmed at higher magnification. Scan size 45 nm.
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possible to detect any errors in atomic structure what is common to AFM data [ 14,151 in contrary to STM results for other crystals. 3.3. Growth spirals
E
1000
c ;
-I-I
/
I
800 -j
According to the theory and experimental evidence, the steps on the {loo} face of KDP are generated mainly by screw dislocations and growth spirals should be detected. We have recorded numerous images showing the growth hillocks as a whole and the top part of them. Fig. 6a shows one of these spirals. This one is in fact the pair of co-operating spirals rotating in the same direction. The property of the spiral is different in the centre than far from it. Plotting the position of the consecutive step edges versus the number of edges, i.e. the number of revolutions a straight line not intersecting the origin of co-ordinates is obtained (Fig. 6b). This is probably caused by the shut-off effect mentioned earlier. According to Cabrera and Levine [21] the distance A between steps in the spiral is 19ya A=-----nakT’
0
,
,
,
(
,
(
,
I
01234567 b
edgenumber
Fig. 6. (a) Double spiral on the prismatic face and (b) the plot of the edge position versus the number of edges for the spiral presented above. Supersaturation 4.2%.
Fig. 7. The growth hillock on the (100) face seen at different Supersaturation 3.5%.
(1)
where y is the edge free energy of a growth unit in a step, a is the distance between growth units, u is supersaturation, k is the Boltzmann constant, T is crystallization temperature and IZ is the number of cooperating spirals. Using the slope of the curve in Fig. 6b, which represents the average steps spacing, we are obtaining a value of supersaturation of about 4.3%, which corresponds very well with 4.2% of real bulk supersaturation. In other experiments the value
magnifications:
(a) Far from centre; (b) Top: (c) Near dislocation
outcrops.
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calculated from AFM images was from 0 to 20% less than bulk supersaturation. It is known that the near surface supersaturation is always more or less lower than the bulk one depending on hydrodynamic conditions. The obtained values are then reasonable and in accordance with interferometric data [22-241. This can be regarded both as a proof of reasonableness of Eq. (I) and a proof that the step pattern (excluding the part near the centre of the spiral) detected in this case really reflects the growth process in solution and not the shut-off effect. Fig. 7 shows an interesting example of a growth hillock. Under low magnifications it seems to be a typical hillock originated from screw dislocation. Looking more precisely on the top of the hillock one can see that its origin, however, is a group of dislocations spread over an area of 100 nm by 100 nm. The height of the steps existing near the top of the growth hillock was a half unit cell. This picture may be an example of the real advantage of AFM (in sense of resolution) over the common observation techniques.
of such an effect. Some holes are spread near the top of the growth hillock. These hollow cores are not placed in the centre of the growth spiral but on the steps. The splitting of the step by hollow core can be observed. The diameter of the holes shown in Fig. 9 is less than 40 nm, which is a reasonable value for hollow cores. In Fig. 9b the section through the hollow core is presented. In fact the shape of the core section produced by AFM is strongly influenced by the tip shape and we can only be sure that the depth of the core is greater than 4-5 nm. In order to study more precisely the core characteristic we increased the force of the tip on the surface. The tip was removing material layer by layer allowing us to see the inner part of the hollow core at increasing
3.4. 20 nucleation Though in the majority of experiments we have observed the hillocks or set of nearly parallel steps originated perhaps from edges, we have also detected some examples of 2D nuclei. These were observed on crystals grown at high supersaturation (> 10%). In Fig. 8a the island placed on the terrace between two steps is visible. The radius of the island is about 200 nm. It is much greater than the radius of critical nucleus at this supersaturation. In Fig. 8b the huge island without any signs of dislocation outcrop is visible. Despite the right part of the picture, the large width of the terraces (500 nm and more> supports the assumption concerning 2D nucleation. On the right part of the picture perhaps the step-bunching process took place causing the decrease of step distances. Due to the shut-off effect described earlier, the hypothesis that nucleation took place after the crystal removal from solution can not be excluded.
Fig. 8. Two-dimensional
The last features observed on the KDP surface were hollow cores [25]. Fig. 9 presents an example
islands on the prismatic face of the
crystal grown at high supersaturation ( > 10%). Step edges were enhanced by the software.
tween theoretical description and real step pattern on the crystal surface. In some cases the quantitative agreement is also pretty good. The possibility of examination of very small structures by AFM is with no doubt much better than in the case of the other method. For example AFM allowed us to precisely measure the height of the steps. Despite this, AFM can not be regarded as a self-sufficient method for the study of the crystal growth process. The significant problems during in situ measurements, and the very small areas available for study, require the use of other methods together with AFM. It would be very reasonable to join the sophisticated interferometric methods [26.27]. which are delivering very good real-time data, with investigation (on the same crystal) by AFM. Because the AFM is examining 5 only a small part on the surface. the growth conditions near the crystal surface should be determined 4 very precisely. The crucial question in the case of ex E situ measurements is how representative is the surI3 face of the crystal thrown out from solution. Onuma E et al. [28] showed that the crystal exposed for some .EJ 2 time to air needs time to start growing again after i! placing in solution. This indicates that crystals should 1 be rather examined in situ. and ex situ data must be ..____....,,..........................,................................... treated very carefully. The in situ study by AFM in I I I I the case of KDP is very difficult [4,13] but maybe 0 200 800 400 600 some progress will be made after improving the b AFM ability [29.30]. horizontal distance I nm Fig. Y. (a) Hollow cores on the prismatic face of the KDP crystal and (b) a section through one of the hollow cores. Supersaturation 3%.
depth. The position of the holes remained the same during this process. This procedure showed that, within the experimental errors, the hollow cores were perpendicular to the face. Only in the case of two holes have we observed the disappearance of the hole after removing a few layers of material detecting the core bottom. In other cases the image during the process remained stable suggesting that the depth of the other cores were greater than 20 layers which were removed.
Acknowledgements We are grateful to Professor F. Bedarida for his encouragement and helpful discussions. Support to this work by MURST (40% and 60% funds) and INFM is gratefully acknowledged. M.J.K. thanks the Italian Ministry of Foreign Affairs for financial support during work at University of Genoa and Polish Committee for Scientific Research for mobility grant.
References 4. General considerations
and conclusions
The AFM studies of the crystal surface (not only in this case) proved the qualitative agreement be-
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