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Effects of impurity upon the habit changes in NaBrO3 crystals grown from aqueous solution
Journal of Crystal Growth 212 (2000) 507}511
E!ects of impurity upon the habit changes in NaBrO crystals grown from aqueous solution Tetsuo Inoue*, Kazumi Nishioka Faculty of Engineering, The University of Tokushima, 2-1 Minamijosanjima, Tokushima 770-8506, Japan Received 1 September 1999; accepted 10 January 2000 Communicated by G.B. Stringfellow
Abstract The e!ects of impurity (acetic acid, 1.15 mol%) upon the habit changes of NaBrO crystals have been investigated. The crystals were grown from aqueous solution under the following conditions: (i) supersaturations: ln(C/Ce)"0}0.24, (Ce: equilibrium mole fraction), (ii) growth temperatures: 20}643C. The results of habit changes were shown in a plot of growth temperature against supersaturation (such a plot is called a morphodrome). It was found that the impurity e!ects on the habit changes were more important in the low supersaturation range than in the high supersaturation range. 2000 Elsevier Science B.V. All rights reserved. Keywords: Crystal habit; NaBrO ; Impurity e!ect; Crystal growth from aqueous solution
1. Introduction In our previous paper [1], we reported the habit changes of NaBrO crystals grown from a non doped solution. NaBrO crystals belong to the crystal class 23 and space group P2 3 (Z"4). However, the gross morphologies of the crystals grown in the experiment have taken on three distinct forms: +1 0 0, (cubic habit), +1 1 1, (tetrahedral habit) and the combination of +1 0 0, and +1 1 1, as most prominent faces, which all belong to one of the crystal classes mentioned above. The following experiments were carried out in this work. (1) The range of supersaturation (p"ln(C/Ce), Ce; equilibrium mole fraction) examined was
* Corresponding author.
spread from p"0}0.1 (previous paper [1]) to p"0}0.24 in the growth from pure solution. (2) The e!ects of impurity of acetic acid (1.15 mol%) upon the habit changes were investigated.
2. Experimental method The mother solutions were prepared by dissolving the NaBrO (reagent, 99.5%) in the distilled water doped with acetic acid (1.15 mol%). The process of crystal growth was observed in situ under an optical microscope. The apparatus was the same as in our previous paper [1]. A heating stage was set on the microscope stage. A PID controller was used to set the temperature of the sample contained on a microscope slide. The heating stage was used to determine the equilibrium coexistence
0022-0248/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 2 3 5 - 9
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T. Inoue, K. Nishioka / Journal of Crystal Growth 212 (2000) 507}511
temperature of a seed crystal and an aqueous solution. Once the equilibrium temperature was determined, the temperature could then be rapidly lowered resulting in a supersaturation of the sample solution and growth of the seed crystal. As the seed grew, the growth process was photographed and recorded on a video tape in some cases. The habit changes were examined by varying the growth temperatures and/or supersaturations. The range of supersaturations (p"ln(C/Ce)) and growth temperatures examined were 0}0.24 and 15}643C, respectively. The solubility curves of NaBrO in the doped solvents were obtained by an evaporation method [2] (Fig. 1). The processes of preparing a sample and isolating a single seed crystal were somewhat elaborate. For experimental details, refer to our previous paper [1]. After the equilibrium temperature was determined for a sample growth of the seed was observed. The seed was partially re-dissolved until it was nearly spherical. Next, the temperature returned to the equilibrium temperature. After waiting for an hour, the temperature of the sample was reduced by *¹ and the growth of the crystal was photographed periodically for the following several hours. From the *¹ data and solubility curves (Fig. 1), the supersaturation of the solution in each
Fig. 1. Temperature dependence of solubility of NaBrO in water doped with acetic acid of 1.15 mol%.
trial was calculated. In our previous paper [1] which deals with growth from a pure solution, the range of supersaturations (p) examined was 0}0.1. In this work, further experiments on the habit changes were made in a range of higher supersaturations (p'0.1) in the growth from a pure solution. 3. Result Fig. 2 presents the photographs of the three growth shapes of the NaBrO crystals obtained in this experiment. The miller indices of the crystal faces were determined by measuring the interfacial angles by a two-circle re#ecting goniometer. The crystals shown in Figs. 2(a)}(c) were surrounded by the +1 0 0,, +1 1 1) and their combination (+1 0 0,#+1 1 1,), respectively. These three growth shapes were formed depending on the growth temperatures and supersaturations. The combination shape of +1 0 0, and +1 1 1, was called &polyhedron' in our previous paper [1]. Figs. 3 and 4 show the results of the growth morphology of NaBrO crys tals which were grown in the pure solution and the solutions doped with 1.15 mol% acetic acid, respectively. The data in lower supersaturation range (p"0}0.1) shown in Fig. 3, were already reported in our previous paper [1], but the data in higher supersaturation range (p'0.1) were newly obtained in this work. The following results were found from these data. (1) The domain of +1 0 0, (cubic habit) is located at the higher temperature region as compared to +1 1 1, (tetrahedral habit) for a wide range of supersaturations for both pure and doped solutions. (2) It was found from Fig. 3 that the transition temperature from +1 1 1, (tetrahedral habit to +1 0 0, (cubic habit) began to decrease at the high supersaturation (p.0.12). This was not found in our previous work [1]. (3) The transition temperature for the change from +1 1 1, (tetrahedral habit) to +1 0 0, (cubic habit) was higher in the impurity doped case than for the pure case in the low supersaturation range. This will be ascribed to the impurity e!ects.
T. Inoue, K. Nishioka / Journal of Crystal Growth 212 (2000) 507}511
509
Fig. 3. Morphodrome of NaBrO grown from nominally pure solution.
Fig. 4. Morphodrome of NaBrO in the presence of acetic acid of 1.15 mol%.
Fig. 2. Typical examples of three growth shapes of NaBrO crystals grown from the solutions doped with acetic acid (1.15 mol%). (a) +1 0 0, (cubic habit), after growth of 17 min. (a) indicates +1 0 0,. Growth temperature is 333C. ln(C/Ce)"0.14. (b) +1 1 1, (tetrahedral habit), after growth of 24 min. (b) indicates +1 1 1,. Growth temperature is 303C. ln(C/Ce)"0.09. (c) +1 0 0, and +1 1 1, (intermediate habit), after growth of 8 h. (a) and (b) indicate +1 0 0, and +1 1 1,, respectively. Growth temperature is 503C. ln(C/Ce)"0.01.
(4) As shown in Fig. 4, the transition temperature from +1 1 1, (tetrahedral habit) to +1 0 0, (cubic habit) in the doped solution abruptly decreased with an increase of supersaturation. Moreover the boundary line, which shows the dependence of the transition temperature on the supersaturation, was slightly shifted to the left by impurity doping in the high supersaturation region.
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T. Inoue, K. Nishioka / Journal of Crystal Growth 212 (2000) 507}511
(5) The domain of intermediate shape began in the low temperature and low supersaturation "eld and then broadened with increasing temperature (Figs. 3 and 4).
4. Discussion The crystal habit is determined by the growth rates of the various faces of the crystal. A fast growing face will quickly disappear and so a slow growing face will be dominant on the crystal form. If the normal growth rate R is higher than R a +1 0 0, crystal (cubic habit) will grow. Whereas if the R is higher than R , a +1 1 1, crystal (tetrahedral habit) will grow. Intermediate crystals will grow when the di!erence between the R and R was small. A standard explanation of the impurity e!ects on the growth rates of crystal faces is as follows: (i) Cabrera and Vermilyea [3] presented a model in which the advancing steps are pinned by immobile impurities adsorbed on the surface and become curved and slow down. According to the theory, the blocking of the steps occurs below a critical supersaturation p due to impurity absorption. Above p the steps &squeeze' themselves through these pinning points and the step velocity v, is given by
g[p(p!p )] , p'p , (1) 0, p6p , where p is a supersaturation and g is a normalization constant. (ii) Kubota and Mullin [4] presented a mathematical model describing crystal growth rates from aqueous solution as a function of impurity concentration, supersaturation and growth temperature. According to the model, the relative face growth rate G/G in the presence of impurity is expressed by the following equation: v"
G/G "1!ah , where
(2)
a"ca/(k¹p¸),
(3)
where G is the face growth rate in the presence of impurity, G the face growth rate in pure solution,
a the e!ectiveness factor of an impurity, h the fractional surface coverage of the crystal surface by impurities, c the edge free energy, at the surface area occupied by one crystallizing molecule, k the Boltzmann constant, ¹ the growth temperature, and ¸ the separation of active sites available for impurity adsorption. The following results were derived from this model: if h , c and ¸ were constant for these growth conditions, the relative growth rate G/G would increase (approach one) with increas ing of the product of ¹ by p (the product is called K hereafter), since a decreases as K is increased (Eq. (2)). Here it should be noted that the impurity e!ect becomes small as the relative growth rate G/G approaches one. (iii) Derksen et al. [5] measured the bunching, blocking and velocity of the [1 0 0] steps on the (0 0 1) face of potassium bichromate (K Cr O ) as a function of supersaturation and discussed in terms of the model for step propagation in#uenced by time-dependent impurity adsorption. In this model, the concentration of adsorbed impurities is not constant, but is a time-dependent function. If the time interval until the next step passes is short, this second step will encounter only a few adsorbed impurities in front of it and these will hardly hinder the step. They measured [1 0 0] step velocity, on the (0 0 1) face of K Cr O , as a function of the relative supersaturation. The experimental points were "tted with Eq. (1) derived by Cabrera and Vermiliyea [3]. For low step velocities, the "ts with Eq. (1) were fairly good. At higher supersaturations the "tting curves give step velocities far too low in comparison with experimental data. This shows that the e!ects of impurity adsorption on the step velocities become smaller in the higher supersaturations. It should be noted that time-dependent impurity adsorption is not taken into account in Eq. (1). As described in result (2), the doping of the impurity enlarged the +1 1 1, domain to the high-temperature region in the low supersaturation region. This shows that the normal growth rate R was re duced by a selective adsorption of the impurity on the +1 1 1, faces, and that a higher temperature was needed to remove the impurity e!ect. This was explained as follows. The product K must be large in order to reduce the impurity e!ect as shown in Eq. (3). Therefore, a higher temperature was needed
T. Inoue, K. Nishioka / Journal of Crystal Growth 212 (2000) 507}511
to have large K at lower supersaturation. As shown in Fig. 4, the transition temperature in the doped case was abruptly decreased as the supersaturation was increased. This will be qualitatively explained by the model of Kubota et al., although the timedependent impurity adsorption is not taken into account in the model. However it could not be explained by the model why the boundary line, which shows the dependence of the transition temperature on the supersaturation, was slightly shifted to the left by the impurity doping in the high supersaturation region (Fig. 3). Here it should be noted that the model by Kubota et al. is based on the growth model of step spreading on the surface such as the spiral growth and time dependent impurity adsorption is not taken into account in the model. In the future, studies on the e!ects of time dependent impurity adsorption upon the step velocities will be needed for understanding our experimental results in the high supersaturation range. The intermediate shape is formed in the case where the di!erence between R and R was small. The crystals of intermediate shape were formed in the "eld of low supersaturations and high temperatures as shown in Figs. 3 and 4. This suggests that the di!erence in growth rates among the faces tend to decrease with increasing temperatures and decreasing supersaturations, although the rea-
511
son for this is not clear at present. Several intermediate-shaped crystals were formed at random in the wide range of supersaturations. It is because the face growth rates are also governed by kinetic factors (surface and bulk di!usion, activity of dislocations, etc.) as well as &supersaturations and temperatures'.
Acknowledgements This study was supported in part by a Grantin-Aid for Scienti"c Research (C) from the Ministry of Education, Science, Sports and Culture of Japan.
References [1] E.R.C. Holcomb, T. Inoue, K. Nishioka, J. Crystal Growth 158 (1996) 336. [2] H. Chihara (Ed.), Experimental method in Physics and Chemistry, Kagaku Dohjin Co, Tokyo, 1979, p. 119 (Chapter 18) (in Japanese). [3] N. Cabrera, D.A. Vermiliyea, in: R.H. Doremus et al., (Eds.), Growth and Perfection of Crystals, Wiley, New York, 1958, p. 393. [4] N. Kubota, J.W. Mullin, J. Crystal Growth 152 (1995) 203. [5] A.J. Derksen, W.J.P. van Enckevort, M.S. Couto, J. Phys. D Appl. 27 (1994) 2580.
E!ects of impurity upon the habit changes in NaBrO crystals grown from aqueous solution Tetsuo Inoue*, Kazumi Nishioka Faculty of Engineering, The University of Tokushima, 2-1 Minamijosanjima, Tokushima 770-8506, Japan Received 1 September 1999; accepted 10 January 2000 Communicated by G.B. Stringfellow
Abstract The e!ects of impurity (acetic acid, 1.15 mol%) upon the habit changes of NaBrO crystals have been investigated. The crystals were grown from aqueous solution under the following conditions: (i) supersaturations: ln(C/Ce)"0}0.24, (Ce: equilibrium mole fraction), (ii) growth temperatures: 20}643C. The results of habit changes were shown in a plot of growth temperature against supersaturation (such a plot is called a morphodrome). It was found that the impurity e!ects on the habit changes were more important in the low supersaturation range than in the high supersaturation range. 2000 Elsevier Science B.V. All rights reserved. Keywords: Crystal habit; NaBrO ; Impurity e!ect; Crystal growth from aqueous solution
1. Introduction In our previous paper [1], we reported the habit changes of NaBrO crystals grown from a non doped solution. NaBrO crystals belong to the crystal class 23 and space group P2 3 (Z"4). However, the gross morphologies of the crystals grown in the experiment have taken on three distinct forms: +1 0 0, (cubic habit), +1 1 1, (tetrahedral habit) and the combination of +1 0 0, and +1 1 1, as most prominent faces, which all belong to one of the crystal classes mentioned above. The following experiments were carried out in this work. (1) The range of supersaturation (p"ln(C/Ce), Ce; equilibrium mole fraction) examined was
* Corresponding author.
spread from p"0}0.1 (previous paper [1]) to p"0}0.24 in the growth from pure solution. (2) The e!ects of impurity of acetic acid (1.15 mol%) upon the habit changes were investigated.
2. Experimental method The mother solutions were prepared by dissolving the NaBrO (reagent, 99.5%) in the distilled water doped with acetic acid (1.15 mol%). The process of crystal growth was observed in situ under an optical microscope. The apparatus was the same as in our previous paper [1]. A heating stage was set on the microscope stage. A PID controller was used to set the temperature of the sample contained on a microscope slide. The heating stage was used to determine the equilibrium coexistence
0022-0248/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 2 3 5 - 9
508
T. Inoue, K. Nishioka / Journal of Crystal Growth 212 (2000) 507}511
temperature of a seed crystal and an aqueous solution. Once the equilibrium temperature was determined, the temperature could then be rapidly lowered resulting in a supersaturation of the sample solution and growth of the seed crystal. As the seed grew, the growth process was photographed and recorded on a video tape in some cases. The habit changes were examined by varying the growth temperatures and/or supersaturations. The range of supersaturations (p"ln(C/Ce)) and growth temperatures examined were 0}0.24 and 15}643C, respectively. The solubility curves of NaBrO in the doped solvents were obtained by an evaporation method [2] (Fig. 1). The processes of preparing a sample and isolating a single seed crystal were somewhat elaborate. For experimental details, refer to our previous paper [1]. After the equilibrium temperature was determined for a sample growth of the seed was observed. The seed was partially re-dissolved until it was nearly spherical. Next, the temperature returned to the equilibrium temperature. After waiting for an hour, the temperature of the sample was reduced by *¹ and the growth of the crystal was photographed periodically for the following several hours. From the *¹ data and solubility curves (Fig. 1), the supersaturation of the solution in each
Fig. 1. Temperature dependence of solubility of NaBrO in water doped with acetic acid of 1.15 mol%.
trial was calculated. In our previous paper [1] which deals with growth from a pure solution, the range of supersaturations (p) examined was 0}0.1. In this work, further experiments on the habit changes were made in a range of higher supersaturations (p'0.1) in the growth from a pure solution. 3. Result Fig. 2 presents the photographs of the three growth shapes of the NaBrO crystals obtained in this experiment. The miller indices of the crystal faces were determined by measuring the interfacial angles by a two-circle re#ecting goniometer. The crystals shown in Figs. 2(a)}(c) were surrounded by the +1 0 0,, +1 1 1) and their combination (+1 0 0,#+1 1 1,), respectively. These three growth shapes were formed depending on the growth temperatures and supersaturations. The combination shape of +1 0 0, and +1 1 1, was called &polyhedron' in our previous paper [1]. Figs. 3 and 4 show the results of the growth morphology of NaBrO crys tals which were grown in the pure solution and the solutions doped with 1.15 mol% acetic acid, respectively. The data in lower supersaturation range (p"0}0.1) shown in Fig. 3, were already reported in our previous paper [1], but the data in higher supersaturation range (p'0.1) were newly obtained in this work. The following results were found from these data. (1) The domain of +1 0 0, (cubic habit) is located at the higher temperature region as compared to +1 1 1, (tetrahedral habit) for a wide range of supersaturations for both pure and doped solutions. (2) It was found from Fig. 3 that the transition temperature from +1 1 1, (tetrahedral habit to +1 0 0, (cubic habit) began to decrease at the high supersaturation (p.0.12). This was not found in our previous work [1]. (3) The transition temperature for the change from +1 1 1, (tetrahedral habit) to +1 0 0, (cubic habit) was higher in the impurity doped case than for the pure case in the low supersaturation range. This will be ascribed to the impurity e!ects.
T. Inoue, K. Nishioka / Journal of Crystal Growth 212 (2000) 507}511
509
Fig. 3. Morphodrome of NaBrO grown from nominally pure solution.
Fig. 4. Morphodrome of NaBrO in the presence of acetic acid of 1.15 mol%.
Fig. 2. Typical examples of three growth shapes of NaBrO crystals grown from the solutions doped with acetic acid (1.15 mol%). (a) +1 0 0, (cubic habit), after growth of 17 min. (a) indicates +1 0 0,. Growth temperature is 333C. ln(C/Ce)"0.14. (b) +1 1 1, (tetrahedral habit), after growth of 24 min. (b) indicates +1 1 1,. Growth temperature is 303C. ln(C/Ce)"0.09. (c) +1 0 0, and +1 1 1, (intermediate habit), after growth of 8 h. (a) and (b) indicate +1 0 0, and +1 1 1,, respectively. Growth temperature is 503C. ln(C/Ce)"0.01.
(4) As shown in Fig. 4, the transition temperature from +1 1 1, (tetrahedral habit) to +1 0 0, (cubic habit) in the doped solution abruptly decreased with an increase of supersaturation. Moreover the boundary line, which shows the dependence of the transition temperature on the supersaturation, was slightly shifted to the left by impurity doping in the high supersaturation region.
510
T. Inoue, K. Nishioka / Journal of Crystal Growth 212 (2000) 507}511
(5) The domain of intermediate shape began in the low temperature and low supersaturation "eld and then broadened with increasing temperature (Figs. 3 and 4).
4. Discussion The crystal habit is determined by the growth rates of the various faces of the crystal. A fast growing face will quickly disappear and so a slow growing face will be dominant on the crystal form. If the normal growth rate R is higher than R a +1 0 0, crystal (cubic habit) will grow. Whereas if the R is higher than R , a +1 1 1, crystal (tetrahedral habit) will grow. Intermediate crystals will grow when the di!erence between the R and R was small. A standard explanation of the impurity e!ects on the growth rates of crystal faces is as follows: (i) Cabrera and Vermilyea [3] presented a model in which the advancing steps are pinned by immobile impurities adsorbed on the surface and become curved and slow down. According to the theory, the blocking of the steps occurs below a critical supersaturation p due to impurity absorption. Above p the steps &squeeze' themselves through these pinning points and the step velocity v, is given by
g[p(p!p )] , p'p , (1) 0, p6p , where p is a supersaturation and g is a normalization constant. (ii) Kubota and Mullin [4] presented a mathematical model describing crystal growth rates from aqueous solution as a function of impurity concentration, supersaturation and growth temperature. According to the model, the relative face growth rate G/G in the presence of impurity is expressed by the following equation: v"
G/G "1!ah , where
(2)
a"ca/(k¹p¸),
(3)
where G is the face growth rate in the presence of impurity, G the face growth rate in pure solution,
a the e!ectiveness factor of an impurity, h the fractional surface coverage of the crystal surface by impurities, c the edge free energy, at the surface area occupied by one crystallizing molecule, k the Boltzmann constant, ¹ the growth temperature, and ¸ the separation of active sites available for impurity adsorption. The following results were derived from this model: if h , c and ¸ were constant for these growth conditions, the relative growth rate G/G would increase (approach one) with increas ing of the product of ¹ by p (the product is called K hereafter), since a decreases as K is increased (Eq. (2)). Here it should be noted that the impurity e!ect becomes small as the relative growth rate G/G approaches one. (iii) Derksen et al. [5] measured the bunching, blocking and velocity of the [1 0 0] steps on the (0 0 1) face of potassium bichromate (K Cr O ) as a function of supersaturation and discussed in terms of the model for step propagation in#uenced by time-dependent impurity adsorption. In this model, the concentration of adsorbed impurities is not constant, but is a time-dependent function. If the time interval until the next step passes is short, this second step will encounter only a few adsorbed impurities in front of it and these will hardly hinder the step. They measured [1 0 0] step velocity, on the (0 0 1) face of K Cr O , as a function of the relative supersaturation. The experimental points were "tted with Eq. (1) derived by Cabrera and Vermiliyea [3]. For low step velocities, the "ts with Eq. (1) were fairly good. At higher supersaturations the "tting curves give step velocities far too low in comparison with experimental data. This shows that the e!ects of impurity adsorption on the step velocities become smaller in the higher supersaturations. It should be noted that time-dependent impurity adsorption is not taken into account in Eq. (1). As described in result (2), the doping of the impurity enlarged the +1 1 1, domain to the high-temperature region in the low supersaturation region. This shows that the normal growth rate R was re duced by a selective adsorption of the impurity on the +1 1 1, faces, and that a higher temperature was needed to remove the impurity e!ect. This was explained as follows. The product K must be large in order to reduce the impurity e!ect as shown in Eq. (3). Therefore, a higher temperature was needed
T. Inoue, K. Nishioka / Journal of Crystal Growth 212 (2000) 507}511
to have large K at lower supersaturation. As shown in Fig. 4, the transition temperature in the doped case was abruptly decreased as the supersaturation was increased. This will be qualitatively explained by the model of Kubota et al., although the timedependent impurity adsorption is not taken into account in the model. However it could not be explained by the model why the boundary line, which shows the dependence of the transition temperature on the supersaturation, was slightly shifted to the left by the impurity doping in the high supersaturation region (Fig. 3). Here it should be noted that the model by Kubota et al. is based on the growth model of step spreading on the surface such as the spiral growth and time dependent impurity adsorption is not taken into account in the model. In the future, studies on the e!ects of time dependent impurity adsorption upon the step velocities will be needed for understanding our experimental results in the high supersaturation range. The intermediate shape is formed in the case where the di!erence between R and R was small. The crystals of intermediate shape were formed in the "eld of low supersaturations and high temperatures as shown in Figs. 3 and 4. This suggests that the di!erence in growth rates among the faces tend to decrease with increasing temperatures and decreasing supersaturations, although the rea-
511
son for this is not clear at present. Several intermediate-shaped crystals were formed at random in the wide range of supersaturations. It is because the face growth rates are also governed by kinetic factors (surface and bulk di!usion, activity of dislocations, etc.) as well as &supersaturations and temperatures'.
Acknowledgements This study was supported in part by a Grantin-Aid for Scienti"c Research (C) from the Ministry of Education, Science, Sports and Culture of Japan.
References [1] E.R.C. Holcomb, T. Inoue, K. Nishioka, J. Crystal Growth 158 (1996) 336. [2] H. Chihara (Ed.), Experimental method in Physics and Chemistry, Kagaku Dohjin Co, Tokyo, 1979, p. 119 (Chapter 18) (in Japanese). [3] N. Cabrera, D.A. Vermiliyea, in: R.H. Doremus et al., (Eds.), Growth and Perfection of Crystals, Wiley, New York, 1958, p. 393. [4] N. Kubota, J.W. Mullin, J. Crystal Growth 152 (1995) 203. [5] A.J. Derksen, W.J.P. van Enckevort, M.S. Couto, J. Phys. D Appl. 27 (1994) 2580.