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Magnetic field effects on fractal morphology in electrochemical deposition
ELSEVIER
Physica B 211 (1995) 319-322
Magnetic field effects on fractal morphology in electrochemical deposition I. Mogi, M. Kamiko, S. Okubo Institute for Materials Research, Tohoku University, Sendai 980-77. Japan
Abstract Fractal pattern formations in electroless- and electro-depositions were investigated in magnetic fields of up fo 8 T as an experimental approach to the diffusion limited aggregation perturbed by particle drifts or convection.
1. Introduction Fractal pattern formation has been of scientific interest for the last decade. It is well-known that the diffusion limited aggregation (DLA) model proposed by Witten and Sander [1] produces a fractal aggregation pattern and is applicable to many real physical systems. Aggregation processes in nature, however, are not simply diffusionlimited, and hence the DLA simulation has been studied taking account of particle drifts or convection [2,3]. Electrochemical depositions are non-equilibrium and irreversible phenomena, being experimental examples of the DLA. Typical DLA-like patterns were observed in two-dimensional growth (metal-leaves) of zinc electrodeposits [4] and electroless deposits of copper [5] and silver [6]. In the electrodeposition of the Zn metal-leaf, there have been found several patterns (DLA-like, dendritic, dense-branching and stringy) depending on an applied voltage and the Zn 2 + concentration [7,8]. Similar patterns have been also found in other non-equilibrium systems [9], e.g. crystal growth, viscous fingers and bacterial colonies [10]. Much attention has been focused on fascinating subjects what factors are essential to the pattern formations or whether the pattern formations in different systems can be described by a common * Corresponding author.
underlying principle or not. Understandir~g of these problems remains incomplete. A magnetic field acts on migration of ions ~nd induces cyclotron motion or convection in an electrplytic solution owing to the Lorentz force. This is well-known as the magnetohydrodynamic (MHD) effect. In previous papers [6,11,12], we demonstrated that the M H D effect drastically changed the growth patterns of the metal-leaves grown by electroless- and electro-depositions, some of which were quite similar to those in viscous.I]fingers and bacterial colonies. In this paper we summange the magnetic field effect on the pattern !formation of the metal-leaves and consider the mechatfism of the pattern formations.
2. Experimental Schemes of the metal-leaf growth by the ele~roless- and electro-depositions are shown in Fig. 1. Silver metal-leaves were grown by sandwiching a piece of c~pper metal (3 x 3 x 0.02 mm 3) and a 0.075 M (M = mol/1) AgNO3 aqueous solution between two glass plates wit~ a distance of 60 lam. Lead metal-leaves were also grown by using the same cell with a piece of zinc metal and a 9.025 M Pb (CH3COO)2. Both electroless metal-leaves were grown for 2 h. The zinc metal-leaves were electrodepogited up to
0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 1 0 5 5 - 2
320
L Mogi et aL /Physica B 211 (1995) 319-322
t
Cathode (Carbon)
H AgNO3 aq. - - - ~
|
,~r,,Glassplate , ~ , ~u
Space~
~
~lm~"
MHD Convection
Electroless deposition
ZnSO4 aq. / ~ i ~
A?z°n~e"
Cathode
Electrodeposition
Fig. 1. Schematics of experimental setup of electroless- and electro-depositions in magnetic fields.
5.2 C in a 0.05 M ZnSO4 aqueous solution between two glass plates with a distance of 0.5 mm. An carbon rod ( ~ 2 mm) was used as a cathode and a zinc metal ring ( ~ 50 mm) as an anode. An applied voltages between the electrodes were 2 and 7.5 V, at which DLA-like and dendritic patterns grew, respectively. The magnetic field .was generated up to 8 T by a largebore ( ~ 220 mm) superconducting magnet in the High Field Laboratory of Tohoku University. The glass-plate cell was placed horizontally at the center of the magnet and the magnetic field was applied perpendicularly to the glass plates. Temperature within the magnet was controlled at 25 ___0.1°C by a water-circulating system. Image data of photographs of the metal-leaves were transferred to a personal computer by an image scanner, and a fractal dimension Dr was estimated by the boxcounting method: The pattern was covered by a square lattice of a size r and the number of squares including a part of the metal-leaf (N(r)) was counted. If the pattern is self-similar, the fractal dimension was estimated from the relation of N (r) oc r - °r.
3. Results
Fig. 2 shows various patterns of the metal-leaves grown by electroless- and electro-deposition in magnetic
fields. The magnetic field considerably changes the growth pattern, and the pattern change depends on the metal-leaf. A typical DLA pattern of the Ag metal-leaf becomes denser with increasing magnetic field, and being dense branching morphology (DBM) with a beautiful circular periphery at 8 T. The fractal dimension of the metal-leaf is 1.62 at 0 T, which is in good agreement with the DLA simulation F1], and 1.69 at 8 T. On the other hand, the pattern change is more drastic in electrodeposition. As the magnetic field increases, a DLAlike pattern of the Zn metal-leaf changes into spiral (0.5 T), dense (2 T) and at last compact (8 T) patterns. The fractal dimension is 1.40 + 0.2 for the DLA-like and spiral patterns and approaches 2 with increasing magnetic field. The growth pattern of the Pb metal-leaf changes from the symmetric dendrite at 0 T into asymmetric dendrites in the magnetic fields, which have side branches developing on one side of main branches. Its fractal dimension increases from 1.59 at 0 T to 1.66 at 8 T, reflecting the denser pattern in magnetic field. On the other hand, the pattern change of the electrodeposited Zn dendrite is diverse; a spiral asymmetric dendrite (0.1 T), DBM-like (0.2 T) and compact (8 T) patterns. Despite the diversity of the pattern, the fractal dimension is a nearly constant value of 1.77 _ 0.02 below 0.5 T.
321
1. Mogi et al./Physica B 211 (1995) 319-322
IElectroless deposition I
0T DLA (Dt=1.62)
2T
0T
IT
Dendrite(Df-- 1 . 5 9 )
4T
8T DBM (Df=1.69)
4T
8T
Asymmetric dendrite
(Dr= 1.66)
IElectr~teposition I Zn ~
~
~
~
(2V) 0T
0.5T
DLA-like
Spiral
(Dr=1.40)
(Dr=1.40)
2T
Dense
8T
Compact
Zn (7.5V) 0T
0.IT
0,2T
8T
Dendrite Asymmetric dendrite DBM-like Compact (Df=l.77)
(Df=l.75)
(Df=l.78)
Fig. 2. Magnetic field dependence of the metal-leaf patterns in electroless- and electro-depositions.
4. Discussion The electroless depositions are redox (reduction oxidation) reactions of Cu + 2Ag + ~ C u 2+ + 2Ag~,, Zn + Pb 2 + ~ Z n 2 + + Pb,L, and they are caused by the difference in redox potentials between two kinds of metals. The electrodeposition is simple reduction of Zn 2 + on the cathode. If the electron
transfer process is sufficiently faster than the ion diffusion process, the metal-leaf growth in both depositions is controlled by the diffusion of ions, and being the DLA pattern. It has open-ramified structure in Which some short branches cease to grow owing to the screening effect of adjacent longer branches. The dendritic growth of the metal-leaf indicates that the aggregation is controlled by not only the ion diffusion but also the surface kinetic process, in which the growth unitsi of metals diffuse on the growing interface and are crystallized at kinks or steps.
322
I. Mogi et al./Physica B 211 (1995) 319-322
When the magnetic fields are applied to the metal-leaf cell as depicted in Fig. 1, the diffusive motion of cations are affected by the Lorentz force which induces cyclotron motions. Its radius at 8 T was estimated to be ~ 4 ~tm for Ag ÷, which is very small compared with the metalleaf sizes (1-3 cm). How does such a microscopic effect influence the macroscopic morphology in the electroless deposition? The cyclotron motion reduces a contact probability of ions with the growing interface of the aggregate, and making the aggregation process not simply diffusion-limited but both diffusion- and reactioncontrolled [13]. The reaction-controlled process reduces the screening effect, and hence the aggregation pattern could become the DBM. In the electrodeposition, the magnetic field brings about the counterclockwise M H D convection around the cathode as well as the cyclotron motion of ions. Nagatani and Sagu6s [3] carried out the computer simulation of the DLA with rotating flow around the seed and demonstrated that the rotating flow leads to spiral branches oriented toward the upstream. The spiral pattern of the Zn metal-leaf at 0.5 T is obviously caused by the M H D convection, and the spiral direction, however, is toward the downstream, which is opposite to that of the computer simulation. A possible reason for this difference is that an effective sticking probability is less than unity in the electrodeposition in the magnetic field because of the low contact probability of the cyclotron motion of ions. When anisotropy is present in crystal growth, the magnetic field effect gets diverse. In the electroless deposition of the Pb metal-leaf, the dendrite becomes asymmetric in the magnetic fields and the dendritic structure remains even at 8 T, indicating that the cyclotron motion of ions does not disturb the surface kinetic process. On the other hand, in the Zn electrodeposition the dendrite no longer grows in the fields higher than 0.2 T, indicating that the M H D convection disturbs the surface diffusion and prevents the growth units from sticking at kinks or steps. The Zn metal-leaf at 0.1 T has considerably interesting structure of the spiral asymmetric dendrite, in which the main branches elongate toward the downstream and the side branches develop on the upstream side of the main branches. This structure results from the
competition of the low sticking probability and high arrival probability. The M H D convection gets stronger with increasing magnetic field and thins the diffusion layer around the aggregate [14]. The Zn metal-leaves, consequently, become compact at both 2 and 7.5 V in 8 T.
Acknowledgements The authors wish to thank the members of the High Field Laboratory and Cryogenic Center of Tohoku University for operating the superconducting magnet. This work was supported in part by Advanced Technology Institute and Grant-in-Aid for Scientific Research on Priority Areas (No. 236) from the Ministry of Education, Science and Culture.
References [1] T.A. Witten and L.M. Sander, Phys. Rev. Lett. 47 (1981) 1400. [2] P. Meakin, Phys. Rev. B 28 (1983) 5221. [3] N. Nagatani and F. Sagu~s, J. Phys. Soc. Japan 59 (1990) 3447. [4] M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo and Y. Sawada, Phys. Rev. Lett. 53 (1984) 286. I-5] A.S. Paranjpe, S. Bhakay-Tamhane and M.B. Vasan, Phys. Lett. A 140 (1989) 193. [6] I. Mogi, S. Okubo and Y. Nakagawa, J. Phys. Soc. Japan 60 (1991) 3200. 1-7] Y. Sawada, A. Dougherty and J.P. Gollub, Phys. Rev. Lett. 56 (1986) 1260. I-8] D. Grier, E. Ben-Jacob, R. Clarke and L.M. Sander, Phys. Rev. Lett. 56 (1986) 1264. [9] T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1989). 1-10] H. Fujiwara and M. Matsushita, J. Phys. Soc. Japan 60 (1991) 88. [11] I. Mogi, S. Okubo and Y. Nakagawa, J. Crystal Growth 128 (1993) 258. [12] I. Mogi, M. Kamiko, S. Okubo and G. Kido, unpublished. [13] I. Mogi, S. Okubo and G. Kido, Fractals 1 (1993) 475. [14] R. Aogaki, F. Fueki and T. Mukaibo, Denki Kagaku 43 (1975) 504, 509.
Physica B 211 (1995) 319-322
Magnetic field effects on fractal morphology in electrochemical deposition I. Mogi, M. Kamiko, S. Okubo Institute for Materials Research, Tohoku University, Sendai 980-77. Japan
Abstract Fractal pattern formations in electroless- and electro-depositions were investigated in magnetic fields of up fo 8 T as an experimental approach to the diffusion limited aggregation perturbed by particle drifts or convection.
1. Introduction Fractal pattern formation has been of scientific interest for the last decade. It is well-known that the diffusion limited aggregation (DLA) model proposed by Witten and Sander [1] produces a fractal aggregation pattern and is applicable to many real physical systems. Aggregation processes in nature, however, are not simply diffusionlimited, and hence the DLA simulation has been studied taking account of particle drifts or convection [2,3]. Electrochemical depositions are non-equilibrium and irreversible phenomena, being experimental examples of the DLA. Typical DLA-like patterns were observed in two-dimensional growth (metal-leaves) of zinc electrodeposits [4] and electroless deposits of copper [5] and silver [6]. In the electrodeposition of the Zn metal-leaf, there have been found several patterns (DLA-like, dendritic, dense-branching and stringy) depending on an applied voltage and the Zn 2 + concentration [7,8]. Similar patterns have been also found in other non-equilibrium systems [9], e.g. crystal growth, viscous fingers and bacterial colonies [10]. Much attention has been focused on fascinating subjects what factors are essential to the pattern formations or whether the pattern formations in different systems can be described by a common * Corresponding author.
underlying principle or not. Understandir~g of these problems remains incomplete. A magnetic field acts on migration of ions ~nd induces cyclotron motion or convection in an electrplytic solution owing to the Lorentz force. This is well-known as the magnetohydrodynamic (MHD) effect. In previous papers [6,11,12], we demonstrated that the M H D effect drastically changed the growth patterns of the metal-leaves grown by electroless- and electro-depositions, some of which were quite similar to those in viscous.I]fingers and bacterial colonies. In this paper we summange the magnetic field effect on the pattern !formation of the metal-leaves and consider the mechatfism of the pattern formations.
2. Experimental Schemes of the metal-leaf growth by the ele~roless- and electro-depositions are shown in Fig. 1. Silver metal-leaves were grown by sandwiching a piece of c~pper metal (3 x 3 x 0.02 mm 3) and a 0.075 M (M = mol/1) AgNO3 aqueous solution between two glass plates wit~ a distance of 60 lam. Lead metal-leaves were also grown by using the same cell with a piece of zinc metal and a 9.025 M Pb (CH3COO)2. Both electroless metal-leaves were grown for 2 h. The zinc metal-leaves were electrodepogited up to
0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 1 0 5 5 - 2
320
L Mogi et aL /Physica B 211 (1995) 319-322
t
Cathode (Carbon)
H AgNO3 aq. - - - ~
|
,~r,,Glassplate , ~ , ~u
Space~
~
~lm~"
MHD Convection
Electroless deposition
ZnSO4 aq. / ~ i ~
A?z°n~e"
Cathode
Electrodeposition
Fig. 1. Schematics of experimental setup of electroless- and electro-depositions in magnetic fields.
5.2 C in a 0.05 M ZnSO4 aqueous solution between two glass plates with a distance of 0.5 mm. An carbon rod ( ~ 2 mm) was used as a cathode and a zinc metal ring ( ~ 50 mm) as an anode. An applied voltages between the electrodes were 2 and 7.5 V, at which DLA-like and dendritic patterns grew, respectively. The magnetic field .was generated up to 8 T by a largebore ( ~ 220 mm) superconducting magnet in the High Field Laboratory of Tohoku University. The glass-plate cell was placed horizontally at the center of the magnet and the magnetic field was applied perpendicularly to the glass plates. Temperature within the magnet was controlled at 25 ___0.1°C by a water-circulating system. Image data of photographs of the metal-leaves were transferred to a personal computer by an image scanner, and a fractal dimension Dr was estimated by the boxcounting method: The pattern was covered by a square lattice of a size r and the number of squares including a part of the metal-leaf (N(r)) was counted. If the pattern is self-similar, the fractal dimension was estimated from the relation of N (r) oc r - °r.
3. Results
Fig. 2 shows various patterns of the metal-leaves grown by electroless- and electro-deposition in magnetic
fields. The magnetic field considerably changes the growth pattern, and the pattern change depends on the metal-leaf. A typical DLA pattern of the Ag metal-leaf becomes denser with increasing magnetic field, and being dense branching morphology (DBM) with a beautiful circular periphery at 8 T. The fractal dimension of the metal-leaf is 1.62 at 0 T, which is in good agreement with the DLA simulation F1], and 1.69 at 8 T. On the other hand, the pattern change is more drastic in electrodeposition. As the magnetic field increases, a DLAlike pattern of the Zn metal-leaf changes into spiral (0.5 T), dense (2 T) and at last compact (8 T) patterns. The fractal dimension is 1.40 + 0.2 for the DLA-like and spiral patterns and approaches 2 with increasing magnetic field. The growth pattern of the Pb metal-leaf changes from the symmetric dendrite at 0 T into asymmetric dendrites in the magnetic fields, which have side branches developing on one side of main branches. Its fractal dimension increases from 1.59 at 0 T to 1.66 at 8 T, reflecting the denser pattern in magnetic field. On the other hand, the pattern change of the electrodeposited Zn dendrite is diverse; a spiral asymmetric dendrite (0.1 T), DBM-like (0.2 T) and compact (8 T) patterns. Despite the diversity of the pattern, the fractal dimension is a nearly constant value of 1.77 _ 0.02 below 0.5 T.
321
1. Mogi et al./Physica B 211 (1995) 319-322
IElectroless deposition I
0T DLA (Dt=1.62)
2T
0T
IT
Dendrite(Df-- 1 . 5 9 )
4T
8T DBM (Df=1.69)
4T
8T
Asymmetric dendrite
(Dr= 1.66)
IElectr~teposition I Zn ~
~
~
~
(2V) 0T
0.5T
DLA-like
Spiral
(Dr=1.40)
(Dr=1.40)
2T
Dense
8T
Compact
Zn (7.5V) 0T
0.IT
0,2T
8T
Dendrite Asymmetric dendrite DBM-like Compact (Df=l.77)
(Df=l.75)
(Df=l.78)
Fig. 2. Magnetic field dependence of the metal-leaf patterns in electroless- and electro-depositions.
4. Discussion The electroless depositions are redox (reduction oxidation) reactions of Cu + 2Ag + ~ C u 2+ + 2Ag~,, Zn + Pb 2 + ~ Z n 2 + + Pb,L, and they are caused by the difference in redox potentials between two kinds of metals. The electrodeposition is simple reduction of Zn 2 + on the cathode. If the electron
transfer process is sufficiently faster than the ion diffusion process, the metal-leaf growth in both depositions is controlled by the diffusion of ions, and being the DLA pattern. It has open-ramified structure in Which some short branches cease to grow owing to the screening effect of adjacent longer branches. The dendritic growth of the metal-leaf indicates that the aggregation is controlled by not only the ion diffusion but also the surface kinetic process, in which the growth unitsi of metals diffuse on the growing interface and are crystallized at kinks or steps.
322
I. Mogi et al./Physica B 211 (1995) 319-322
When the magnetic fields are applied to the metal-leaf cell as depicted in Fig. 1, the diffusive motion of cations are affected by the Lorentz force which induces cyclotron motions. Its radius at 8 T was estimated to be ~ 4 ~tm for Ag ÷, which is very small compared with the metalleaf sizes (1-3 cm). How does such a microscopic effect influence the macroscopic morphology in the electroless deposition? The cyclotron motion reduces a contact probability of ions with the growing interface of the aggregate, and making the aggregation process not simply diffusion-limited but both diffusion- and reactioncontrolled [13]. The reaction-controlled process reduces the screening effect, and hence the aggregation pattern could become the DBM. In the electrodeposition, the magnetic field brings about the counterclockwise M H D convection around the cathode as well as the cyclotron motion of ions. Nagatani and Sagu6s [3] carried out the computer simulation of the DLA with rotating flow around the seed and demonstrated that the rotating flow leads to spiral branches oriented toward the upstream. The spiral pattern of the Zn metal-leaf at 0.5 T is obviously caused by the M H D convection, and the spiral direction, however, is toward the downstream, which is opposite to that of the computer simulation. A possible reason for this difference is that an effective sticking probability is less than unity in the electrodeposition in the magnetic field because of the low contact probability of the cyclotron motion of ions. When anisotropy is present in crystal growth, the magnetic field effect gets diverse. In the electroless deposition of the Pb metal-leaf, the dendrite becomes asymmetric in the magnetic fields and the dendritic structure remains even at 8 T, indicating that the cyclotron motion of ions does not disturb the surface kinetic process. On the other hand, in the Zn electrodeposition the dendrite no longer grows in the fields higher than 0.2 T, indicating that the M H D convection disturbs the surface diffusion and prevents the growth units from sticking at kinks or steps. The Zn metal-leaf at 0.1 T has considerably interesting structure of the spiral asymmetric dendrite, in which the main branches elongate toward the downstream and the side branches develop on the upstream side of the main branches. This structure results from the
competition of the low sticking probability and high arrival probability. The M H D convection gets stronger with increasing magnetic field and thins the diffusion layer around the aggregate [14]. The Zn metal-leaves, consequently, become compact at both 2 and 7.5 V in 8 T.
Acknowledgements The authors wish to thank the members of the High Field Laboratory and Cryogenic Center of Tohoku University for operating the superconducting magnet. This work was supported in part by Advanced Technology Institute and Grant-in-Aid for Scientific Research on Priority Areas (No. 236) from the Ministry of Education, Science and Culture.
References [1] T.A. Witten and L.M. Sander, Phys. Rev. Lett. 47 (1981) 1400. [2] P. Meakin, Phys. Rev. B 28 (1983) 5221. [3] N. Nagatani and F. Sagu~s, J. Phys. Soc. Japan 59 (1990) 3447. [4] M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo and Y. Sawada, Phys. Rev. Lett. 53 (1984) 286. I-5] A.S. Paranjpe, S. Bhakay-Tamhane and M.B. Vasan, Phys. Lett. A 140 (1989) 193. [6] I. Mogi, S. Okubo and Y. Nakagawa, J. Phys. Soc. Japan 60 (1991) 3200. 1-7] Y. Sawada, A. Dougherty and J.P. Gollub, Phys. Rev. Lett. 56 (1986) 1260. I-8] D. Grier, E. Ben-Jacob, R. Clarke and L.M. Sander, Phys. Rev. Lett. 56 (1986) 1264. [9] T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1989). 1-10] H. Fujiwara and M. Matsushita, J. Phys. Soc. Japan 60 (1991) 88. [11] I. Mogi, S. Okubo and Y. Nakagawa, J. Crystal Growth 128 (1993) 258. [12] I. Mogi, M. Kamiko, S. Okubo and G. Kido, unpublished. [13] I. Mogi, S. Okubo and G. Kido, Fractals 1 (1993) 475. [14] R. Aogaki, F. Fueki and T. Mukaibo, Denki Kagaku 43 (1975) 504, 509.