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Effects of ultrasonic waves on crystal growth
Journal of Crystal Growth 62 (1983) 458—464 North-Holland Publishing Company
458
EFFECTS OF ULTRASONIC WAVES ON CRYSTAL GROWTH Yoshiharu MURATA. Kaoru WADA and Masakuni MATSUOKA Department of Uhemical Engineering, Tokyo University of Agriculture antI Technology. Koganei, ToAyo 184, Japan Received 25 November 1982~ manuscript received in final form 22 February 1983
Effects of ultrasonic waves on the growth of ADP crystals were investigated by applying them perpendicularly to the (010) face. The observed growth rates were significantly reduced by the ultrasonic waves with lower frequencies and higher energy densities, contrary to the increase in volume diffusion rates in the bulk solution. This behavior was considered to be due to the decrease in the concentration of the completely dehydrated growth units on the surface of the growing crystals.
1. Introduction The application of ultrasonic waves to crystals growing from solutions is expected to affect the surface integration process as well as the volume diffusion process in the bulk solution. One of the present authors [1] has found that the rate of mass transfer in the dissolution of benzoic acid was significantly increased by the application of ultrasonic waves. But there seem to he no discussions on the effects of the waves on the surface integration process. The present study describes the effects of ultrasonic waves on crystal growth rates by applying them perpendicularly to the (010) face of a fixed single ADP (ammonium dihydrogen phosphate) crystal growing in an aqueous solution.
a transducer box (5). The transducer was set in a box filled with deaired silicone oil which was cooled by a liquid coolant to absorb heat generated by the ultrasonic waves. The details of the transducer box are given in fig. 2. The diameter of the transducer was 60 mm and the ultrasonic waves were generated by a wide band oscillator (16). The frequency covered a range from 200 and 1820 kHz. Because of attenuation of the ultrasonic waves in the solution, the sound energy density gradually decreased with distance, and so the crystal was placed at a distance of 30 mm from the _____
Ii] 10 to~1 17
2. Experimental apparatus and procedure The schematic diagram of the experimental apparatus used in this study is shown in fig. 1. A completely closed cylindrical crystallizer (2), 180 mm in diameter and 100 mm in height, was in!mersed in a constant temperature bath (1). A single ADP crystal (4). grown to 2—3 mm, was mounted on a crystal holder (3) which was adjustable so that the (010) face of the crystal could be oriented perpendicular or parallel to the surface of
6 12
1
14
tol5
to14
4~
to 5~
2
7
~
to~~
8
Fig. I. Schematic diagram of experimental apparatus: (I) constant temperature bath. (2) crystallizer. (3) crystal holder. (4) crystal. (5) transducer box, (6) microscope. (7) camera, (8) thermomodule, (9) thermosensor, (10) thermometer, (11) tern.
perature controlling system. (12) agitator. (13) heater. (14) thermosensor, (15) temperature controller. (16) ultrasonic oscillator. (17) balloon.
0022-0248/83/0000—0000/$03.00 © 1983 North-Holland
LI
Y. Murata et a!.
7—tefton fIIm,/
/
Effects of ultrasonic waves on crystal growth
1.—transducer ,,.—silicone oil
/ ________
~
I
________
il~~
I
Fig. 2. Schematic diagram of ultrasonic transducer box,
transducer, where it had been confirmed previously that the attenuation was practically negligible [1].The sound energy density at the position of the crystal was determined by a method of Nomoto [2]. The growth of the crystal was continuously observed through a microscope (6) and was photographed at a fixed time interval by a camera (7). The linear growth rate of the crystal was obtained by analyzing the successive photographs. Thewere temperatures the crsytallizer and systhe bath regulated byof means of controlling tems (11) and (15) with a thermomodule (8) and a heater (13) respectively. This thermomodule was able to act as a heater or a cooler depending on the direction of the feeding direct current. The temperature of the crystallizer was thus controlled to an accuracy of ±0.05°C. A turbine of impeller diameter of 60 mm with six flat blades was used as agitator for the crystallizer. All the experiments were carried out at an agitation speed of 480 rpm, which was experimentally determined from the condition that the growth rate did not increase with further increase in the agitation, i.e. the volume diffusion resistance was negligible. It is known that when ultrasonic waves are applied, some undesirable phenomena occur such as (1) bubble formation at the crystal surface owing to cavitation and (2) an increase in the solution temperature due to the absorption of the ultrasonic waves. To prevent these phenomena the following pre-treatments were adopted: (I) To prevent the bubble formation, the solutions were completely deaired and the crystallizer was filled up with the solution. The volume expansion or shrinkage of the solution owing to temperature changes was absorbed by a small balloon attached at the top of the crystallizer (17).
459
(2) To prevent the temperature rise, the bath ternperature t was set to be lower than the crystallizer temperature T by the amount determined experimentally by a trial and error method. Before the application of ultrasonic waves, crystal growth rates were measured, then the irradiation was started and at the same time the thermomodule was reset to act as a heat sink by reversing the direction of the feeding current. The optimum value of the current was also determined experimentally by a trial and error method. In this way the heat generated by the ultrasonic waves was absorbed and the crystallizer temperature was kept constant at T. In practice, even by this method the rise of the solution temperature could not completely be avoided for an initial short period. Experimentally the maximum temperature rise was found to be lower than 0.2°C when the energy density3.ofand the ultrasonic lower to than 100 5 to 10 mm waves werewas required return erg/cm to the temperature T. When the crystallizer became thermally constant and the steady state of the crystal growth was provided, the measurement of the growth rate under the application of the ultrasonic waves was started. Although the saturation temperature of the solutions was chosen as 33.0°C. the concentration changed in the course of the vacuum deairing because of evaporation of water, so that the actual saturation temperature of each solution after the deairing was determined by a method similar to that used in a previous study [3].
3. Experimental results 3.1. Bubbling and exothermic phenomena owing to irradiation 3.1.1. Bubble formation at crystal surfaces
The application of ultrasonic waves to undeaired solutions causes bubble formation at the surface of the crystals as well as in the solution. Fig. 3a shows the bubbles lying in rows at the nodes of the ultrasonic waves, when they are irradiated parallel to the (010) face. Fig. 3h shows the random formation of the bubbles during irradiation perpendicular to the (010) face. The
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Y. Murata et al.
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Effects of ultrasonic waves on crystal growth
adhesion of the bubbles to the surface caused local
1.0
holes as shown in fig. 3c. Damage to the inside of the crystal occurs when ultrasonic waves with
08
higher energy density are applied, which appears as dark clouds in fig.growth 3d. On cessation of further andthesosurface, resultedtiny in bubbles of I to 2 ~tm were observed to exist at steps, by the use of a device previously reported [4]. They also caused grooves or cavities as the steps advanced as seen in fig. 3e. To prevent the formation of bubbles, each solu-
________
I I
—
.
~
oi.
—
0.2
—
~ satur ation temp I
0 3.1.2. Exothermic phenomena at crystal surfaces When ultrasonic waves were applied to a solution supercooled as low as 0.05°C, the crystal would dissolve locally or show some change in its
60 80 100 3) E (erg/~~
The effects of ultrasonic waves on the crystal
growth rate in terms of the ratio R/R*. where R* and R denote the linear growth rates with and without the application of ultrasonic waves respectively. were correlated experimentally with the
________
E~
0
°
3330°C
—
0.05°C
a
________
42
90
G
1200kHz
—
_______
•
132
-J
0.1
-
0
•&
•~
~—•~
~—~-----c%~
—0.1
0
10
20
30
40
e
120
3.2. Effects of ultrasonic waves on crystal growth rates
—
frequency
40
ble when the energy density is lower than 132 erg/cm3.
0.4
-
20
Fig. 5. Effect of ultrasonic energy on crystal growth.
step patterns if the absorption of the waves caused generation of heat at the crystal surface, since the actual supersaturation temperature of the solution is estimated to be 0.00 to 0.10°C because of the accuracy of the temperature control. Actually, however, the steps did not show any change, and the growth increments of the (010) face were negligible, independent of the energy densities of the applied ultrasonic waves, as shown in fig. 4. Therefore the effects of the exothermic phenomena on the growth rate can be concluded to be negligi-
0.2
33.oo~
supersaturation temp. 2.00°C 0
saturation temp. supersaturation temp.
800 11820
..~..
at20Torr.
-
200 400
0.6 “~~[,lf(kHz) —
,_.,
tion was carefully deaired by boiling under vacuum
0.3
46 1
50
60
70
(mm)
Fig. 4. Effect of exothermic phenomena by ultrasonic waves at the interface between surface and solution on crystal growth.
/
Y. Murata et al.
462
Eftects of ultrasonic waves on crystal growth
0.4
1.0 0.8 -
0.6 0./.
0.3
satuIntemp348O’C~~~ frequency 400kHz sound energy density
3
°~-..
saturation temp. 30.00’C supersaturation temp. 2.00°C
-
frequency
0.2
42 erg /cm
E
.
CrCl3 •
100 ppm
1600 kHz
0.1
Ia
0.2
i:r:
0 I
0
I
0.5 1.0 1.5 2.0 supersaturation temperature (‘C)
0
~
2.5
—0.1 0
Fig. 6. Effect of supercooling on crystal growth under the conditions off= 400 kHz and E= 42 erg/cm3.
20
40 E
60
80
100
(erg/cm3)
Fig. 7. Effect of ultrasonic energy on crystal growth Er pure and impure solutions.
sound energy density E and the frequency f. The relation between the ratio and E under the condi-
tions of constant supersaturation temperature of 2.00°C and the frequencies of 200, 400, 800 and
that the growth rate decreases rapidly when the supersaturation temperatures become larger. in addition, the possibility of recovering the
1820 kHz, as shown in fig. 5, indicates that this ratio, and hence the growth rate, decreases with increasing energy densities of the ultrasonic waves and that this effect is larger as the frequency becomes lower. The effects of supersaturation ternperature at 400 kHz are shown in fig. 6, indicating
6
0kHz
______
~
2
I
frequency
0 —
growth activity of a (010) face which had been “poisoned” by the addition of chromium trichloride, known as an active growth inhibitor [5], was examined. From the experimental results at 1600 kHz. as shown in fig. 7, the recovery of the growth
200 400
-
—~--
—
±!g©~®® -‘
1
8-
a
—
6-
411’!
z
2
102
-
00
0
sound energy dens
0
—
8’
220 erg/cm3
6-
4. I
10
2
ii I
4682
I
10
III 2
4683
NRe
I
10
2
I
I
468a
I
——
10
Fig. 8. Correlation between N~ 1,and N~0. (a) After Steinherger and Treyhal [7]: (h) after Garner and Hoffman [8].
Y. Murata et a!
/
Effects of ultrasonic waves on crystal growth
activity was found to be impossible when ultrasonic waves having energy density lower than 85 erg/cm3 were applied, 3.3. Effects of ultrasonic waves on volume diffusion
One of the authors [1] has correlated the effects of ultrasonic waves on the volume diffusion rate in terms of the Sherwood number N 55 as a function of the Reynolds number NRC, frequency f and sound energy density E, as shown in fig. 8, and has obtained the following relations, 1/3. IVShc~f,
NSHcrE
These were found from experiments on the dis-
solution in water of benzoic acid disk pellets. As seen from the figure, the application of the ultrasonic waves caused the Sherwood number to increase particularly in the laminar flow region. For example, the value of Nsh was increased by a factor of about 20 at 200 kHz and at the NRC of 1000 in comparison with the values without irradiation. This is remarkable for the waves with lower
463
increases as the degree of supersaturation increases, the territorial area of each growth unit is reduced,
resulting in diminution of the life time and in an increase in the number of less dehydrated growth units. Of the following two possible effects: (1) the promotion of leaving of the growth units by the irradiation pressure and (2) the dehydration of the growth units by the adsorption of the ultrasonic waves, the effect (2) cannot be predominant according to the results shown in fig. 6, even if the dehydration actually occurs by the absorption of theHence ultrasonic waves (I) [6].is discussed here in detail. the effect .
.
The following relation between the sound intensity I, the amplitude of acoustic radiation pressure ip
and the amplitude of displacement ~ is known: 2
I=~p)
2
/pC=~pC(2irffl.
(10)
where p denotes the solution density and C the
sound velocity. In addition. the sound intensity and the sound energy density can be related by the equation
frequencies. I=ExC.
(2)
4. Discussion
From eqs. (I) and (2) the following equations are derived:
Assuming that the above result, that the volume diffusion rate is enhanced by the ultrasonic waves in the unsaturated solution, holds even in the
~
supersaturated solutions, and that the surface integration process is not affected by the ultrasonic waves, one can expect that the crystal growth rate will increase when ultrasonic waves are applied. Contrary to this prediction, however, figs. 5 and 6 show a reduction in the growth rates. Therefore it must be concluded that the ultrasonic waves influence the surface integration process. On a surface of a crystal growing from a supersaturated solution, growth units exist and they migrate to kinks or steps to be integrated. If we assume that the growth units are dehydrated only when they are migrating on the surface, the degree of dehydration of the growth units is dependent on the average life time of the growth units on the surface and on the supersaturation. Because the number of the growth units adhering to the surface
~1
=
T~E~~/2E
V
2~rf
‘
(3)
4) -
For aqueous ADP solutions with the saturation temperature of 33.0°C, it is known that p = 1.12 g/cm3 and C = 1650 m/s, so that the numerical relations between E and i~lpcan be calculated and are summarized in table Ia. It can he seen that a crystal surface placed at a position of energy density of 100 erg/cm3 is being exposed to the pressure ~p of 2.47 bar, which seems enough to excite the motion of the adhering growth units and to pull them apart from the surface. Since the affinity of atoms of less dehydrated growth units is weaker than that of highly dehydrated ones, the former is more influenced by the pressure than the latter. Consequently newly adhering growth units are easily activated by the ultrasonic waves, hence a
Y. Murata et a!.
464
/
Effects of ultrasonic waves on crystal growth
Table I Numerical re]ations between sound energy density E and amplitude of acoustic radion pressure ~p, and between frequency f and amplitude of displacement ~ at E 100 erg/cm3 (a) Numerical relations between E and .~p
_____________________________________________ 3) E (erg/cm 42 50 80 100
~Xp(bar) 1.58 1.75 2.20 2.47
(h) Numerical relations betweenf and ~ f(l/s) 200 400 800 1820
~(A) 1064 532 266 177
decrease in the fraction of highly dehydrated growth units results. This mechanism explains the experimental results shown in fig. 6 that the growth rates decrease as the supersaturation temperature increases. The amplitude of displacement ~ calculated from eq. (4) for various frequencies at the sound energy density of 100 erg/cm3 are shown in table lb. Since the value of ~ is 1064 A at 200 kHz, the growth units on, or in the vicinity of, the surface suffer from the periodic displacement of 1064 A at
magnitude of the displacement and the step height
of the ADP crystals growing from pure solutions are of the same order of magnitude~the latter has
been reported to lie in the range of (1.0—1.5)>< 103A and to increase to (6—9)>< l0~A when CrCl added [3]. 3 was 5. Conclusions The effects on the growth rate of applying
ultrasonic waves perpendicularly to the (010) face of ADP crystals growing from completely deaired aqueous solutions were investigated. It was found
that the ultrasonic waves decreased the growth rates particularly when the waves with lower frequencies and larger sound energy densities were applied. This decrease was inferred to be due to the decrease in the concentration of completely dehydrated growth units adhering to the crystal surface.
References [I] Y. Muraia and H. Ishizaka. in: Preprinis 33rd Ann. Meeting of the Soc. Chem. Engrs. Japan. Kyoto. 1968. p. 15.
121 0. [31Y.
Nomoto and S. Okui. J. Phys. Soc. Japan 3 (1948) 471. Murata and S. Sone. Kagaku Kogaku Ronhunshu 8 (1982) 430
the maximum. As seen from fig. 5 and table lb.
[4) Y. Murata, S. Sone and K. Wada. J. Crystal Growth 58
the growth rate decreases as the displacement increases. But further discussion is not possible in
[5] R.J. Davey and J.W. Mullin, J. Crystal Growth 26 (1974)
(1982) 243.
this study to make clear why and how the displacement of the ultrasonic waves affects the
[6] 0. Nomoto. J. Phys. Soc. Japan II (1956) 827: 12 (1957)
surface process.
[7] R.L. Steinherger and RE. Treyhal. AIChF. J. 6 (1960) 227.
Nevertheless it is noteworthy to add that the
300. [8] FF1. Garner and J.M. Hoffman. AIChE J. 7 (1961) 148.
458
EFFECTS OF ULTRASONIC WAVES ON CRYSTAL GROWTH Yoshiharu MURATA. Kaoru WADA and Masakuni MATSUOKA Department of Uhemical Engineering, Tokyo University of Agriculture antI Technology. Koganei, ToAyo 184, Japan Received 25 November 1982~ manuscript received in final form 22 February 1983
Effects of ultrasonic waves on the growth of ADP crystals were investigated by applying them perpendicularly to the (010) face. The observed growth rates were significantly reduced by the ultrasonic waves with lower frequencies and higher energy densities, contrary to the increase in volume diffusion rates in the bulk solution. This behavior was considered to be due to the decrease in the concentration of the completely dehydrated growth units on the surface of the growing crystals.
1. Introduction The application of ultrasonic waves to crystals growing from solutions is expected to affect the surface integration process as well as the volume diffusion process in the bulk solution. One of the present authors [1] has found that the rate of mass transfer in the dissolution of benzoic acid was significantly increased by the application of ultrasonic waves. But there seem to he no discussions on the effects of the waves on the surface integration process. The present study describes the effects of ultrasonic waves on crystal growth rates by applying them perpendicularly to the (010) face of a fixed single ADP (ammonium dihydrogen phosphate) crystal growing in an aqueous solution.
a transducer box (5). The transducer was set in a box filled with deaired silicone oil which was cooled by a liquid coolant to absorb heat generated by the ultrasonic waves. The details of the transducer box are given in fig. 2. The diameter of the transducer was 60 mm and the ultrasonic waves were generated by a wide band oscillator (16). The frequency covered a range from 200 and 1820 kHz. Because of attenuation of the ultrasonic waves in the solution, the sound energy density gradually decreased with distance, and so the crystal was placed at a distance of 30 mm from the _____
Ii] 10 to~1 17
2. Experimental apparatus and procedure The schematic diagram of the experimental apparatus used in this study is shown in fig. 1. A completely closed cylindrical crystallizer (2), 180 mm in diameter and 100 mm in height, was in!mersed in a constant temperature bath (1). A single ADP crystal (4). grown to 2—3 mm, was mounted on a crystal holder (3) which was adjustable so that the (010) face of the crystal could be oriented perpendicular or parallel to the surface of
6 12
1
14
tol5
to14
4~
to 5~
2
7
~
to~~
8
Fig. I. Schematic diagram of experimental apparatus: (I) constant temperature bath. (2) crystallizer. (3) crystal holder. (4) crystal. (5) transducer box, (6) microscope. (7) camera, (8) thermomodule, (9) thermosensor, (10) thermometer, (11) tern.
perature controlling system. (12) agitator. (13) heater. (14) thermosensor, (15) temperature controller. (16) ultrasonic oscillator. (17) balloon.
0022-0248/83/0000—0000/$03.00 © 1983 North-Holland
LI
Y. Murata et a!.
7—tefton fIIm,/
/
Effects of ultrasonic waves on crystal growth
1.—transducer ,,.—silicone oil
/ ________
~
I
________
il~~
I
Fig. 2. Schematic diagram of ultrasonic transducer box,
transducer, where it had been confirmed previously that the attenuation was practically negligible [1].The sound energy density at the position of the crystal was determined by a method of Nomoto [2]. The growth of the crystal was continuously observed through a microscope (6) and was photographed at a fixed time interval by a camera (7). The linear growth rate of the crystal was obtained by analyzing the successive photographs. Thewere temperatures the crsytallizer and systhe bath regulated byof means of controlling tems (11) and (15) with a thermomodule (8) and a heater (13) respectively. This thermomodule was able to act as a heater or a cooler depending on the direction of the feeding direct current. The temperature of the crystallizer was thus controlled to an accuracy of ±0.05°C. A turbine of impeller diameter of 60 mm with six flat blades was used as agitator for the crystallizer. All the experiments were carried out at an agitation speed of 480 rpm, which was experimentally determined from the condition that the growth rate did not increase with further increase in the agitation, i.e. the volume diffusion resistance was negligible. It is known that when ultrasonic waves are applied, some undesirable phenomena occur such as (1) bubble formation at the crystal surface owing to cavitation and (2) an increase in the solution temperature due to the absorption of the ultrasonic waves. To prevent these phenomena the following pre-treatments were adopted: (I) To prevent the bubble formation, the solutions were completely deaired and the crystallizer was filled up with the solution. The volume expansion or shrinkage of the solution owing to temperature changes was absorbed by a small balloon attached at the top of the crystallizer (17).
459
(2) To prevent the temperature rise, the bath ternperature t was set to be lower than the crystallizer temperature T by the amount determined experimentally by a trial and error method. Before the application of ultrasonic waves, crystal growth rates were measured, then the irradiation was started and at the same time the thermomodule was reset to act as a heat sink by reversing the direction of the feeding current. The optimum value of the current was also determined experimentally by a trial and error method. In this way the heat generated by the ultrasonic waves was absorbed and the crystallizer temperature was kept constant at T. In practice, even by this method the rise of the solution temperature could not completely be avoided for an initial short period. Experimentally the maximum temperature rise was found to be lower than 0.2°C when the energy density3.ofand the ultrasonic lower to than 100 5 to 10 mm waves werewas required return erg/cm to the temperature T. When the crystallizer became thermally constant and the steady state of the crystal growth was provided, the measurement of the growth rate under the application of the ultrasonic waves was started. Although the saturation temperature of the solutions was chosen as 33.0°C. the concentration changed in the course of the vacuum deairing because of evaporation of water, so that the actual saturation temperature of each solution after the deairing was determined by a method similar to that used in a previous study [3].
3. Experimental results 3.1. Bubbling and exothermic phenomena owing to irradiation 3.1.1. Bubble formation at crystal surfaces
The application of ultrasonic waves to undeaired solutions causes bubble formation at the surface of the crystals as well as in the solution. Fig. 3a shows the bubbles lying in rows at the nodes of the ultrasonic waves, when they are irradiated parallel to the (010) face. Fig. 3h shows the random formation of the bubbles during irradiation perpendicular to the (010) face. The
IL
46(1
Y. tiuraja ci a!
J:/,iS
I’ of uliraso,iii nai’i’~ on ri ‘ia!
~‘,
a i/i
r
4
b
4 p
Fig. 3. l’hiit grapli~of so ri aces sho’a I ng uI! ra s~ ‘n u eli eu!
Y. Murata et al.
/
Effects of ultrasonic waves on crystal growth
adhesion of the bubbles to the surface caused local
1.0
holes as shown in fig. 3c. Damage to the inside of the crystal occurs when ultrasonic waves with
08
higher energy density are applied, which appears as dark clouds in fig.growth 3d. On cessation of further andthesosurface, resultedtiny in bubbles of I to 2 ~tm were observed to exist at steps, by the use of a device previously reported [4]. They also caused grooves or cavities as the steps advanced as seen in fig. 3e. To prevent the formation of bubbles, each solu-
________
I I
—
.
~
oi.
—
0.2
—
~ satur ation temp I
0 3.1.2. Exothermic phenomena at crystal surfaces When ultrasonic waves were applied to a solution supercooled as low as 0.05°C, the crystal would dissolve locally or show some change in its
60 80 100 3) E (erg/~~
The effects of ultrasonic waves on the crystal
growth rate in terms of the ratio R/R*. where R* and R denote the linear growth rates with and without the application of ultrasonic waves respectively. were correlated experimentally with the
________
E~
0
°
3330°C
—
0.05°C
a
________
42
90
G
1200kHz
—
_______
•
132
-J
0.1
-
0
•&
•~
~—•~
~—~-----c%~
—0.1
0
10
20
30
40
e
120
3.2. Effects of ultrasonic waves on crystal growth rates
—
frequency
40
ble when the energy density is lower than 132 erg/cm3.
0.4
-
20
Fig. 5. Effect of ultrasonic energy on crystal growth.
step patterns if the absorption of the waves caused generation of heat at the crystal surface, since the actual supersaturation temperature of the solution is estimated to be 0.00 to 0.10°C because of the accuracy of the temperature control. Actually, however, the steps did not show any change, and the growth increments of the (010) face were negligible, independent of the energy densities of the applied ultrasonic waves, as shown in fig. 4. Therefore the effects of the exothermic phenomena on the growth rate can be concluded to be negligi-
0.2
33.oo~
supersaturation temp. 2.00°C 0
saturation temp. supersaturation temp.
800 11820
..~..
at20Torr.
-
200 400
0.6 “~~[,lf(kHz) —
,_.,
tion was carefully deaired by boiling under vacuum
0.3
46 1
50
60
70
(mm)
Fig. 4. Effect of exothermic phenomena by ultrasonic waves at the interface between surface and solution on crystal growth.
/
Y. Murata et al.
462
Eftects of ultrasonic waves on crystal growth
0.4
1.0 0.8 -
0.6 0./.
0.3
satuIntemp348O’C~~~ frequency 400kHz sound energy density
3
°~-..
saturation temp. 30.00’C supersaturation temp. 2.00°C
-
frequency
0.2
42 erg /cm
E
.
CrCl3 •
100 ppm
1600 kHz
0.1
Ia
0.2
i:r:
0 I
0
I
0.5 1.0 1.5 2.0 supersaturation temperature (‘C)
0
~
2.5
—0.1 0
Fig. 6. Effect of supercooling on crystal growth under the conditions off= 400 kHz and E= 42 erg/cm3.
20
40 E
60
80
100
(erg/cm3)
Fig. 7. Effect of ultrasonic energy on crystal growth Er pure and impure solutions.
sound energy density E and the frequency f. The relation between the ratio and E under the condi-
tions of constant supersaturation temperature of 2.00°C and the frequencies of 200, 400, 800 and
that the growth rate decreases rapidly when the supersaturation temperatures become larger. in addition, the possibility of recovering the
1820 kHz, as shown in fig. 5, indicates that this ratio, and hence the growth rate, decreases with increasing energy densities of the ultrasonic waves and that this effect is larger as the frequency becomes lower. The effects of supersaturation ternperature at 400 kHz are shown in fig. 6, indicating
6
0kHz
______
~
2
I
frequency
0 —
growth activity of a (010) face which had been “poisoned” by the addition of chromium trichloride, known as an active growth inhibitor [5], was examined. From the experimental results at 1600 kHz. as shown in fig. 7, the recovery of the growth
200 400
-
—~--
—
±!g©~®® -‘
1
8-
a
—
6-
411’!
z
2
102
-
00
0
sound energy dens
0
—
8’
220 erg/cm3
6-
4. I
10
2
ii I
4682
I
10
III 2
4683
NRe
I
10
2
I
I
468a
I
——
10
Fig. 8. Correlation between N~ 1,and N~0. (a) After Steinherger and Treyhal [7]: (h) after Garner and Hoffman [8].
Y. Murata et a!
/
Effects of ultrasonic waves on crystal growth
activity was found to be impossible when ultrasonic waves having energy density lower than 85 erg/cm3 were applied, 3.3. Effects of ultrasonic waves on volume diffusion
One of the authors [1] has correlated the effects of ultrasonic waves on the volume diffusion rate in terms of the Sherwood number N 55 as a function of the Reynolds number NRC, frequency f and sound energy density E, as shown in fig. 8, and has obtained the following relations, 1/3. IVShc~f,
NSHcrE
These were found from experiments on the dis-
solution in water of benzoic acid disk pellets. As seen from the figure, the application of the ultrasonic waves caused the Sherwood number to increase particularly in the laminar flow region. For example, the value of Nsh was increased by a factor of about 20 at 200 kHz and at the NRC of 1000 in comparison with the values without irradiation. This is remarkable for the waves with lower
463
increases as the degree of supersaturation increases, the territorial area of each growth unit is reduced,
resulting in diminution of the life time and in an increase in the number of less dehydrated growth units. Of the following two possible effects: (1) the promotion of leaving of the growth units by the irradiation pressure and (2) the dehydration of the growth units by the adsorption of the ultrasonic waves, the effect (2) cannot be predominant according to the results shown in fig. 6, even if the dehydration actually occurs by the absorption of theHence ultrasonic waves (I) [6].is discussed here in detail. the effect .
.
The following relation between the sound intensity I, the amplitude of acoustic radiation pressure ip
and the amplitude of displacement ~ is known: 2
I=~p)
2
/pC=~pC(2irffl.
(10)
where p denotes the solution density and C the
sound velocity. In addition. the sound intensity and the sound energy density can be related by the equation
frequencies. I=ExC.
(2)
4. Discussion
From eqs. (I) and (2) the following equations are derived:
Assuming that the above result, that the volume diffusion rate is enhanced by the ultrasonic waves in the unsaturated solution, holds even in the
~
supersaturated solutions, and that the surface integration process is not affected by the ultrasonic waves, one can expect that the crystal growth rate will increase when ultrasonic waves are applied. Contrary to this prediction, however, figs. 5 and 6 show a reduction in the growth rates. Therefore it must be concluded that the ultrasonic waves influence the surface integration process. On a surface of a crystal growing from a supersaturated solution, growth units exist and they migrate to kinks or steps to be integrated. If we assume that the growth units are dehydrated only when they are migrating on the surface, the degree of dehydration of the growth units is dependent on the average life time of the growth units on the surface and on the supersaturation. Because the number of the growth units adhering to the surface
~1
=
T~E~~/2E
V
2~rf
‘
(3)
4) -
For aqueous ADP solutions with the saturation temperature of 33.0°C, it is known that p = 1.12 g/cm3 and C = 1650 m/s, so that the numerical relations between E and i~lpcan be calculated and are summarized in table Ia. It can he seen that a crystal surface placed at a position of energy density of 100 erg/cm3 is being exposed to the pressure ~p of 2.47 bar, which seems enough to excite the motion of the adhering growth units and to pull them apart from the surface. Since the affinity of atoms of less dehydrated growth units is weaker than that of highly dehydrated ones, the former is more influenced by the pressure than the latter. Consequently newly adhering growth units are easily activated by the ultrasonic waves, hence a
Y. Murata et a!.
464
/
Effects of ultrasonic waves on crystal growth
Table I Numerical re]ations between sound energy density E and amplitude of acoustic radion pressure ~p, and between frequency f and amplitude of displacement ~ at E 100 erg/cm3 (a) Numerical relations between E and .~p
_____________________________________________ 3) E (erg/cm 42 50 80 100
~Xp(bar) 1.58 1.75 2.20 2.47
(h) Numerical relations betweenf and ~ f(l/s) 200 400 800 1820
~(A) 1064 532 266 177
decrease in the fraction of highly dehydrated growth units results. This mechanism explains the experimental results shown in fig. 6 that the growth rates decrease as the supersaturation temperature increases. The amplitude of displacement ~ calculated from eq. (4) for various frequencies at the sound energy density of 100 erg/cm3 are shown in table lb. Since the value of ~ is 1064 A at 200 kHz, the growth units on, or in the vicinity of, the surface suffer from the periodic displacement of 1064 A at
magnitude of the displacement and the step height
of the ADP crystals growing from pure solutions are of the same order of magnitude~the latter has
been reported to lie in the range of (1.0—1.5)>< 103A and to increase to (6—9)>< l0~A when CrCl added [3]. 3 was 5. Conclusions The effects on the growth rate of applying
ultrasonic waves perpendicularly to the (010) face of ADP crystals growing from completely deaired aqueous solutions were investigated. It was found
that the ultrasonic waves decreased the growth rates particularly when the waves with lower frequencies and larger sound energy densities were applied. This decrease was inferred to be due to the decrease in the concentration of completely dehydrated growth units adhering to the crystal surface.
References [I] Y. Muraia and H. Ishizaka. in: Preprinis 33rd Ann. Meeting of the Soc. Chem. Engrs. Japan. Kyoto. 1968. p. 15.
121 0. [31Y.
Nomoto and S. Okui. J. Phys. Soc. Japan 3 (1948) 471. Murata and S. Sone. Kagaku Kogaku Ronhunshu 8 (1982) 430
the maximum. As seen from fig. 5 and table lb.
[4) Y. Murata, S. Sone and K. Wada. J. Crystal Growth 58
the growth rate decreases as the displacement increases. But further discussion is not possible in
[5] R.J. Davey and J.W. Mullin, J. Crystal Growth 26 (1974)
(1982) 243.
this study to make clear why and how the displacement of the ultrasonic waves affects the
[6] 0. Nomoto. J. Phys. Soc. Japan II (1956) 827: 12 (1957)
surface process.
[7] R.L. Steinherger and RE. Treyhal. AIChF. J. 6 (1960) 227.
Nevertheless it is noteworthy to add that the
300. [8] FF1. Garner and J.M. Hoffman. AIChE J. 7 (1961) 148.