CRYSTAL GROWTH & DESIGN
Surface Topography of Dyed Potassium Dihydrogen Phosphate (KDP) Crystals
2007 VOL. 7, NO. 2 420-424
Yusuke Asakuma,* Eisuke Ukita, Kouji Maeda, Keisuke Fukui, Kenji Iimura, Michitaka Suzuki, and Mitsuaki Hirota Department of Mechanical and System Engineering, UniVersity of Hyogo, Shosha 2167, Himeji 671-2201, Japan ReceiVed April 8, 2006; ReVised Manuscript ReceiVed May 18, 2006
ABSTRACT: This paper describes the surface topography characteristics of the (100) and (101) faces of potassium dihydrogen phosphate (KDP) crystals by using atomic force microscopy (AFM) for nanoscale observation. Fractal dimensions of the surface pattern were measured, including step height and terrace distance of KDP crystals under different supersaturation levels and dye concentrations, and the relationship between dye concentration and surface structure was examined. 1. Introduction The crystallization process is extensively used as a method of separation and purification. Establishing a suitable growth technique is necessary for obtaining a functional crystal, and crystal properties such as morphology, growth rate, and purity are very important for the growth process of a single crystal. The single-crystal growth of metallic cation impurities has been studied.1-3 The crystal growth mechanism in the presence of impurities might be explained by the pinning effect.4-8 However, some inorganic crystals contain several types of organic dyes, and those inclusions cannot be explained by the impurity adsorption mechanism.9,10 Many types of metal ions, such as Fe3+ and Cr3+, are used as impurities, and their presence has been cited as causing the behaviors of pilling and spiral steps.11 On the other hand, organic dyes may behave as habit modifiers for some inorganic crystals. Coloring hourglass crystals have been investigated,12-15 and the crystal structure of coloring crystals has been widely studied.16-19 In particular, a report was presented on the coloring conditions of potassium dihydrogen phosphate (KDP) by two dyes (amaranth and sunset yellow FCF) as a function of dye concentration and supersaturation of KDP in an aqueous solution.9 In addition, the growth rate, morphology, and dye distribution of KDP crystals have also been systematically reported.10 Observations of steps on the crystal surface have mainly been made by optical microscopy. Although step patterns in the macroscopic region can be investigated by this technique, it is impossible to detect the step height and pattern at the microscopic level due to the microscope’s detection limit.20-22 Recently, the development of atomic force microscopy (AFM) has proved to be very useful for investigating the growth process at the molecular level from a solution.11,23-28 However, the effects of a dye on various crystal habits such as growth rate and step pattern have not been extensively published. Although some researchers have observed macro steps and bunches of micro steps by AFM, this cannot provide a perfect estimation of micro steps due to the wider region (around 50 × 50 µm2).29,30 Here, not only step height but also step patterns were considered by using the fractal dimension from a narrow AFM image, and we attempted to evaluate the formation of micro step patterns on (100) and (101) faces of single crystals quantitatively. Therefore, the purposes of this research are to quantitatively validate the bunching mechanism from fractal dimension data and to confirm other researchers’ results.11,24 This research was * To whom correspondence should be addressed. Phone: +81 792-674847. Fax: +81 792-67-4847. E-mail:
[email protected].
Table 1. Experimental Conditions supersaturation σ [mol of KDP/kg of H2O] dye concentration s [× 106 mol/ g of KDP]
0.046 0
1
0.092
0.138
2
4
performed to analyze the surface morphology of KDP single crystals grown on a seed from an aqueous solution by using AFM images. 2. Experimental Procedures All crystal growth experiments were carried out in a 1.6-L crystallizer by the method of temperature reduction. Distilled water was used as a solvent. First, seed crystals were obtained from a supersaturated solution, and a seed crystal measuring about 3 mm in diameter was chosen. After the specific supersaturated solution was heated to above 70 °C, the crystallizer was cooled and maintained at 40 °C with an external water bath. A single KDP crystal developed on each seed from the aqueous solution.11,23,24 Crystallization was performed at different supersaturation levels and impurity concentrations. After the desired period of growth (5 h), the crystal was quickly withdrawn from the solution, and the aqueous solution was rinsed by cyclohexane to remove water from the crystal surface. Table 1 shows the experimental conditions. Here, dye (sunset yellow FCF: C16H10N2O7S2Na2) is used as the impurity. The total amount of KDP, M1 mol in the solution, was determined via the level of supersaturation with
σ ≡ ((M1 - M0)/MW)
(1)
where M0 mol is the solubility of KDP at 40 °C and MW is the quantity of distilled water (kg).22 Using AFM (atomic forced microscope, Seiko Instruments, Inc.) to microscopically observe the growth face on the KDP crystal surface, both a shape image and an error signal image were obtained. The shape image shows the height contours on the crystal surface, while the error image comes from derivative values of the contour image representing micro step curves as stripped patterns. These image data were measured at various positions on the (100) and (101) faces of the crystal. Additionally, the analysis tool computed the step height at the nanoscale and the terrace width at the microscale from the shape image. Furthermore, the crystal growth rate was measured under each condition as a macro profile from the size of the seed and crystal after the growth.
3. Estimation Method of AFM Image To estimate the step pattern of a KDP single crystal, the fractal dimension, D, was employed as defined by the following equations:31
N(r)rD ) C
(2)
log N(r) ) -D log r + log C
(3)
10.1021/cg0602055 CCC: $37.00 © 2007 American Chemical Society Published on Web 01/09/2007
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Crystal Growth & Design, Vol. 7, No. 2, 2007 421
Figure 1. Derivation of fractal dimension (a) error image (binary mode) (b) multiple-pixel images.
Figure 2. Overview of KDP crystal.
the macro step from the step-height data (cross-sectional view) of the AFM image. It is easy to identify the macro step and micro step because the height of the macro step integrates multiple micro steps.11 This fractal dimension represents an index of complexity. For concrete numerical values in this dimension, the value shows 1 in the case of a simple step pattern such as a straight line. On the other hand, if a complex step curves over the entire image, the value approaches 2. The value of the fractal dimension ranges from 1.0 to 1.2 in the case of a contour line as in an AFM image. Even if the step line consists of a straight line at lower resolution (1/r ) 2 or 4), it becomes smooth at higher resolution (1/r ) 256 or 512). In this case, the fractal dimension can be considered valid. The step slope does not indicate the terrace width distribution so precisely because the slope provides information on the average terrace width only. Consequently, the standard deviation of the terrace width, which is necessary to determine the disorder behavior, was introduced. 4. Results
Figure 3. Growth rate vs dye concentration.
where r is the inverse of the image pixel number, that is, the length from 0 to 1, and N(r) is defined as the number of pixels, including the step curve, in each image. For example, the value of N(r) vs r can be obtained from the curve of the error signal image as shown in Figure 1. First, the error image is converted into the binary mode image (a). Next, the number of pixels N(r) is counted against the multiple-pixel images in (b), each of which has a pixel number (1/r). The fractal dimension is calculated from eq 3 by the mean-square method. This fractal dimension is a profile of the micro step because the analytical region is 1 × 1 µm2. The binary-mode image was produced after neglecting
4.1. Step Height and Terrace Width. Figure 2a shows a typical KDP crystal with non-colored (100) and colored (101) faces as illustrated in (b). This image shows that the dye molecule is distributed into the (101) sector selectively. The relationship between dye concentration, s, and growth rate is shown in Figure 3 in the case of σ ) 0.138 mol of KDP/kg of H2O10. The growth rate of the (100) face was higher than that of the (101) face when the dye was not present in the mother liquid (s ) 0). In contrast, the difference in the growth rate between the (100) and (101) faces decreased as the dye concentration increased. This figure means that dye molecules on the (101) face and the (100) face suppressed the growth of KDP and that the dye is adsorbed on both faces and distributed into the (101) face selectively. The step height was measured for each experimental condition using the cross-sectional view, Figure 4b, from information on
Figure 4. Measurement of step height. (a) Shape image; (b) cross-sectional view from point a to point b.
422 Crystal Growth & Design, Vol. 7, No. 2, 2007
Asakuma et al. Table 3. Terrace Width Distributions of (101) Face dye concentrations s [× 106 mol/ g of KDP] 0 1 2 4 average width
Figure 5. Relationship between step height and supersaturation. Table 2. Terrace Width Distributions of (100) Face dye concentrations s [× 106 mol/ g of KDP] 0 1 2 4 average width
supersaturation σ [mol of KDP/kg of H2O] 0.046 0.092 0.138 83.8 40.7 48.2 71.2 60.9
78.4 55.1 76.2 78.2 72.0
112.1 77.2 94.2 95.1 94.7
standard deviation 39.3 27.5 39.6 50.5
the contour shape image in Figure 4a. Figure 5 shows the averaged step height on the (100) and (101) faces under different supersaturation conditions and dye concentrations. The averaged step heights of the (100) and (101) faces were approximately 0.3-0.4 nm and 0.5-0.6 nm, respectively, while the ratio of the (101) step height to the (100) step height was about 1.4, which corresponded to the morphology of pure KDP. This was because the growth unit of the KDP crystal is essentially different in the (100) and (101) directions.32 The operating conditions such as the dye concentration, s, and supersaturation, σ, did not influence the individual step heights. The step-height values on the (100) face mostly agree with the values in reference.11 The terrace width was measured for each experimental condition by the same method as that for step height in Figure 4. Here, a perpendicular line was chosen against the step to measure the terrace width. When a hillock was found in the AFM image, a line to measure the terrace width was drawn from the hillock. Table 2 presents the values of average terrace width from each image. Because there was little influence of the standard deviation on supersaturation, each value was
supersaturation σ [mol of KDP/kg of H2O] 0.046 0.092 0.138 38.32 44.72 54.24 77.4 53.67
77.8 88.24 76.08 57.8 74.98
57.8 136.0 154.5 67.6 104.0
standard deviation 18.0 44.8 41.6 43.6
averaged against the supersaturation. The standard deviation of the terrace width distribution of the (101) face changed with dye concentration, s. These values mean that the distribution of the terrace width becomes monodisperse in the case of the (101) face and s ) 0 (without dye); on the other hand, the distribution of the (101) face becomes polydisperse due to the existence of the dye molecule on the surface. Figure 6 shows the effect of the bunching mechanism on the terrace width caused by the dye molecule in an illustration and a cross-sectional AFM image. The following Schwoebel Effect33 could explain the behavior of the small standard deviation in the case without dye (s ) 0). Even if the terraces were disordered, the values of terrace width became close to each other. For example, the step growth rate in front of the wider terrace became faster and the wider terrace tended to narrow due to the higher possibility of the KDP molecules being captured at wider terraces. Accordingly, the terrace width distribution became stable, as shown in Figure 6a. On the other hand, if the dye molecule blocked step propagation, there was a longer time interval during which the terrace in front of the blocked step was exposed in the solution as shown in Figure 6b. Consequently, the terrace width distribution became disordered, as evidenced from the large standard deviation data, because the step propagation speed became increasingly slower due to impurities. 4.2. Effect of the Dye Concentration and Supersaturation on the Step Pattern. Figure 7 shows the fractal dimension, which indicates the complexity of the step pattern, versus the dye concentration, s, and the supersaturation, σ. The fractal dimension of the (101) face was larger than that of the (100) face, because the dye was absorbed and distributed into the (101) face selectively. Additionally, the fractal dimension of the (101) face became large as the dye concentration increased. These behaviors mean that the step pattern becomes disordered due to the dye molecule. However, it was difficult to observe the effect of supersaturation on the fractal dimension accurately. In the same way as with the terrace width distribution of Figure 6, this disordered mechanism, in which the step pattern became
Figure 6. Step-bunching mechanism from a cross-sectional view (a) without impurity and (b) with impurity.
Surface Topography of Dyed KDP Crystals
Crystal Growth & Design, Vol. 7, No. 2, 2007 423
and the shape image of Figure 8b. Accordingly, impurities increased the step pattern’s complexity. The same behavior has been observed in the case of K2SO4 crystal with organic dye as an impurity.29 5. Conclusions Surface morphology captured in AFM images was studied for single KDP crystals grown from an aqueous solution containing dye. Specifically, this paper investigated the effects of the impurity concentration in a solution on values of crystal steps, such as the terrace width distribution, the step height, and the step pattern. The results indicated that step height was not influenced by supersaturation or dye concentration; the values for these were about 0.3-0.4 nm for the (100) face and about 0.5-0.6 nm for the (101) face. Furthermore, the distribution of the terrace width became monodisperse in the case of the (101) face and s ) 0 (without dye). On the other hand, the distribution of the (101) face became polydisperse due to the presence of dye molecules. The step pattern was not significantly influenced by the supersaturation. The pattern of the (101) face became more complex due to the dye additive. Some characteristics such as terrace width, width distribution, and the complexity of the step pattern could be explained by the fractal dimension and the standard deviation from AFM images. References Figure 7. Relationship between fractal dimension and supersaturation (a) (100) face and (b) (101) face.
Figure 8. Step-disordered mechanism from shape image (a) without impurity and (b) with impurity.
more complex, was considered from the step bunching, as shown in Figure 8. Figure 8a shows that step propagation speed was constant without the dye in the solution because the step was not interrupted by anything. On the other hand, if the dye molecule was adsorbed on the terrace, the step speed was suppressed by the dye molecule, as shown in the illustrations
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