Structured electrodeposition in magnetic gradient fields | SpringerLink

Eur. Phys. J. Special Topics 220, 287–302 (2013) © EDP Sciences, Springer-Verlag 2013 DOI: 10.1140/epjst/e2013-01814-3

THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS

Review

Structured electrodeposition in magnetic gradient fields Margitta Uhlemann1,a , Kristina Tschulik1,3 , Annett Gebert1 , Gerd Mutschke2,4 , Jochen Fr¨ ohlich2 , Andreas Bund5 , Xuegeng Yang2 , and Kerstin Eckert2 1 2 3 4 5

IFW Dresden, PO Box 270016, 01171 Dresden, Germany Inst. Fluid Dynamics, Technische Universit¨ at Dresden, 01062 Dresden, Germany Dept. of Chemistry, Oxford University, Oxford OX1 3QZ, UK Inst. Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, 01314 Dresden, Germany Inst. Electrochem. Electroplating, Ilmenau University of Technology, 98693 Ilmenau, Germany Received 17 December 2012 / Received in final form 5 February 2013 Published online 26 March 2013 Abstract. Electrodeposition in superimposed magnetic gradient fields is a new and promising method of structuring metal deposits while avoiding masking techniques. The magnetic properties of the ions involved, their concentrations, the electrochemical deposition parameters, and the amplitude of the applied magnetic gradient field determine the structure generated. This structure can be thicker in regions of high magnetic field gradients. It can also be free-standing or inversely structured. The complex mechanism of structured electrodeposition of metallic layers in superimposed magnetic gradient fields was studied by different experimental methods, by analytical methods and by numerical simulation and will be discussed comprehensively.

1 Introduction Electrochemical deposition is a well-established technique for surface finishing, which includes functional coatings for corrosion protection, wear resistance, or decoration. Rapid development in microelectronics, sensor technology and micromechanical systems tends towards miniaturization and deposition of functional three-dimensional structures with high aspect ratios. Thereby, electrodeposition is the most cost-efficient method for production of high-quality deposits and also the method of choice for numerous industrial applications. Industrial routes towards micro- and nano-structured layers usually proceed via masking and templating techniques. Magnetic fields and their gradients are demonstrably a helpful tool for transport and mixing of conductive liquids in metallurgy, chemistry or bio-medicine, mostly by utilizing the magnetohydrodynamic effect. First investigations on the influence of magnetic fields on metal deposition were conducted at the end of the 19th century and the beginning of the 20th century [1,2]. Due to the low magnitude of the magnetic fields available at that time, the a

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interest was only marginal. Fahidy [3] resurrected the idea and established the field of magnetoelectrochemistry based on systematic experimental and theoretical studies of various steps in electrochemical processes. Especially the influence of homogeneous magnetic fields on mass transport in electrochemical processes was studied in detail. Due to the action of the Lorentz force, which generates convection in the electrolyte, mass transport may increase significantly. This main effect in electrochemistry was called the magnetohydrodynamic (MHD) effect and is well-established. In contrast, moderate magnetic field effects on charge transfer kinetics were proven neither for deposition, nor for dissolution processes. Experimentally detected changes in charge transfer might be attributed to indirectly altered mass transport [4]. The classical MHD effect was studied by Aogaki et al. [5, 6] for Cu deposition in a rectangular channel with parallel electrodes and perpendicular applied magnetic fields. He found a semi-empirical dependence of the current density on the amplitude of the magnetic field. The finding was proven for different electrochemical systems and experimental setups by several research groups [7–9]. Recent studies in cells with vertical wall electrodes exposed to different homogeneous and inhomogeneous magnetic fields have led to a more detailed understanding of the convection pattern being created and of the transient effects during the onset of electrolysis [10–14]. Besides the macroscopic MHD effect, the Aogaki group introduced the micro-MHD effect that acts on the micro-scale and generates micro-scaled vortices which propagate into the bulk electrolyte, if the magnetic field is applied parallel to the electric field and perpendicular to the electrode [15]. MHD effects at micro electrodes were investigated by White et al. [16,17]. As already stated, magnetic fields superimposed on electrochemical processes can induce convection in the electrolyte, which increases mass transport indicated by a rise in the limiting current density. In deposition processes, the applied magnetic field may have an impact on the morphology or on the structure of the deposits, as shown by numerous studies. Mostly, smoother deposit surfaces were observed for metals, e.g. Cu, Ni, Co, Fe and alloys of these [18–22]. The electrodeposition of non-noble metals usually leads to defect-afflicted surfaces, as the deposition is accompanied by the reduction of protons which leads to adhesion of hydrogen bubbles, an increase in the pH value, and subsequent spontaneous hydroxide formation. The MHD effect can minimize the increase in the pH value when proton reduction occurs under mass transport control. In addition, it may remove the hydrogen bubbles from the surface by locally induced convection [23–26]. In contrast to the large number of studies devoted to the influence of homogeneous magnetic fields on electrochemical reactions and deposition processes, only few investigations have dealt with the action of inhomogeneous magnetic fields on electrochemical processes. High magnetic gradient fields can either be generated by superconducting magnets, the use of which is typically limited to fundamental studies. A simpler way to generate high gradient fields can be obtained by placing ferromagnetic electrodes in homogeneous magnetic fields or by employing permanent magnets. Besides the known action of the Lorentz force, another magnetic force, the magnetic field gradient force, plays an important role in inhomogeneous magnetic fields. The magnetic field gradient force, discussed in detail in the theoretical part of this review, may exceed the Lorentz force by orders of magnitude, especially when inhomogeneous magnetic fields are applied perpendicular to the electrode. This force is directly proportional to the magnetic properties, i.e. the magnetic susceptibility of the involved species. Ragsdale et al. and Grant et al. observed an increase or decrease in the limiting current density for the reduction of paramagnetic nitrobenzene, dependent on the magnetizability of the electrode (Fe or Pt) and the orientation of the electrode to the applied magnetic field [27, 28]. The reduction of paramagnetic O2 molecules was investigated in superconducting magnets with a flux density of

Electromagnetic Flow Control in Metallurgy, Crystal Growth and Electrochemistry 289

up to 7 T [29], in stray fields of permanent magnets with dB 2 /dz ≤ 15.7 T2 /m [30] and in the stray field of a hard magnetic alloy deposited in a nanoscaled aluminatemplate matrix (105 − 107 T2 /m) [31]. An increase in the limiting current density was observed for all systems, reaching more than 500% for the last design. For all diamagnetic systems investigated so far, no effect was detected. Electrochemical deposition experiments in inhomogeneous magnetic fields are very rare. First Fahidy et al. performed Cu deposition experiments in a solenoidal magnetic field with dB/dy ≤ 10−1 T/m. They obtained deposition rates 10 times higher than in homogeneous magnetic fields of the same magnitude [32]. Electrochemical displacement reactions of the systems Zn + 2 Ag+ → Zn2+ + 2 Ag,

Cu + 2 Ag+ → Cu2+ + 2 Ag

(1)

were studied in thin rectangular cells inserted in a superconducting magnet. The shape of the grown Ag dendrites depended strongly on the magnetic properties of the displaced ions (Cu2+ is paramagnetic, whereas Zn2+ and Ag+ are diamagnetic) and on the position inside the vertical bore magnet, i.e. the magnitude of the field gradient. Also, a strong impact on the natural convection was noticed [33]. Recently, it has been proven that employing high magnetic gradient fields during electrodeposition enables structuring of deposits or well-controlled dissolution of metals. Remarkable electrochemical deposition experiments were performed by Gorobets et al. [34]. They deposited Ni by using a steel mesh placed behind a working electrode and superimposed a homogeneous magnetic field of 0.5 T. The steel mesh was magnetized; the magnetic flux lines were concentrated at the nodes of the mesh, generating high gradients above the nodes. The Ni deposits were thickest above the position of the nodes. Dunne et al. [35–37] obtained structured deposits of Cu and Zn by using arrays of NdFeB magnets as sources for locally high magnetic field gradients. Cu deposited from paramagnetic ions showed the highest layer thickness in areas with the highest magnetic field. The structure was reversed for Zn, deposited from diamagnetic Zn2+ ions, or Cu with addition of strongly paramagnetic Dy3+ or Gd3+ ions, which are electrochemically inert. The authors discussed the deposition rate and the structure in terms of magnetic pressure on the diffusion layer dependent on the strength of the magnetic field. This review aims to demonstrate the possibilities and advantages of producing structured deposits of metals and alloys by electrodeposition in applied high magnetic field gradients. First the theoretical background is highlighted and discussed under the aspect of the main results obtained. The second focus is the fundamental understanding of the mechanisms behind and the contribution of the magnetically induced forces in interaction with other driving forces involved in the deposition process.

2 Theory Electrochemical processes taking place under the influence of magnetic fields experience magnetic volume forces which act on the electrolyte. As a result, convection can be forced, which then influences mass transfer. Two different magnetic forces are to be mentioned here. The Lorentz force is described as the cross product of the electric current density j and the magnetic induction B fL = j × B.

(2)

Due to the small electrical conductivities of aqueous electrolytes (σ ∼ 10 S/m) and assuming small convection velocities (|u| 1 m/s), both induced electric currents and induced magnetic fields can safely be neglected, and the force density is only determined by the external quantities.

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Table 1. Selected values of the magnetic susceptibility χ, its molar value χmol and the susceptibility of an aqueous 1 M solution χsol at T = 295 K (from [43]). H2 O Bi3+ Ti3+ , Cu2+ V3+ , Ni2+ Cr3+ , Co2+ Fe2+ 2+ Mn , Fe3+ Dy3+

χ −9.1 · 10−6

χmol [m3 /mol]

χsol (1 mol/l)

−5.0 · 10−10 1.57 · 10−8 4.19 · 10−8 7.86 · 10−8 1.26 · 10−7 1.83 · 10−7 5.5 · 10−7

−9.6 · 10−6 6.7 · 10−6 3.29 · 10−5 6.96 · 10−5 1.17 · 10−4 1.74 · 10−4 5.41 · 10−4

If ions or molecules of the electrolyte possess a magnetic moment, a magnetic field causes a torque, which despite the thermal motion, somewhat aligns the magnetic dipoles and thus magnetizes the fluid. This magnetization M = χsol H is proportional to the magnetic susceptibility χsol of the electrolyte and the magnetic field strength H. Importantly, in an inhomogeneous magnetic field, there is a force acting on the magnetic dipoles [38]. Thus, in a magnetized fluid, there is a volume force density acting on the electrolyte which can be derived from the divergence of the magnetic stress tensor (for details we refer to [39–42]). It reads fm = μ0 χH∇H = μ0 χsol ∇

H2 2

(3)

and will be called the magnetic gradient force in the following. Here, μ0 denotes the magnetic permeability of vacuum. The magnetic susceptibility of the electrolyte may vary in space and comprises the contributions from all magnetic species. χmol ci . (4) χsol = χH2 O + i i

Here, χH2 O , χmol and ci denote the susceptibility of water and the molar susceptii bility and the concentration of species i, respectively. Paramagnetic and diamagnetic behavior corresponds to positive and negative values of the susceptibility, respectively. The diamagnetic contribution of the water molecules to the susceptibility of the solution can be considered homogeneous in space for electrolytes with bulk species concentrations (c0i < 10 M). For selected species, values of the susceptibility are given in Table 1. As the magnetic susceptibility of an aqueous solution is usually χsol 1, the magnetic field and also its gradient can be assumed to be given by the external field only. Furthermore, as it can be seen from the expression on the right side of Eq. (3), if the concentration of each species remains constant, the magnetic gradient force is a potential force [44]. Apart from these two magnetic forces mentioned above, the electrochemical reaction taking place at the electrodes causes the electrolyte density to change, which often gives rise to natural convection. The buoyancy force, assuming small density changes (Boussinesq approximation), reads βi (ci − c0i ). (5) f G = ρ0 g i

Here, g, ρ0 , βi and c0i denote the vector of gravitational acceleration, the density of the bulk electrolyte, the volume expansion coefficient and the bulk concentration of species i, respectively. To describe the ratio of these three forces mentioned,


dimensionless numbers were introduced in [44] where it was shown that for magnetic elements (e.g. NdFeB magnets, magnetized iron rods) of small diameter d < 1 mm, the magnetic gradient force clearly dominates over the Lorentz force in magnitude. Under the assumption of small density changes, only the rotational part of the magnetic gradient force is able to force convection of the electrolyte [44]. The curl of Eq. (3) reads μ0 mol χi ∇ci × (∇H 2 ). (6) ∇ × fm = 2 i Thus, convection can only be driven in regions where gradients of both the magnetic species and the magnetic field do exist. As only the cross product of both gradients contributes, this term vanishes on the symmetry axis of the magnet. If several species are carrying magnetic moments, concentration changes of inert magnetic ions become relevant for the magnetic gradient force. This is especially important if strongly paramagnetic cations are present in the electrolyte [45, 46] which is discussed in more detail below.

3 Methods A short summary of the electrochemical and characterization methods, the measurement of fluid flow generated in the electrolyte, and the concentration distribution in front of the electrodes is given. In addition, the numerical simulation is described briefly. For more details, we refer to the references mentioned below. 3.1 Electrochemical methods Electrochemical deposition experiments were performed in a three electrode setup arranged in a cylindrical Teflon® cell coupled to a potentiostat described in detail in [47]. The anodic and cathodic compartments of the cell were separated by a Nafion® membrane. As working electrodes (WE), glass disks covered with 200 nm of Au and with a diameter of 13 mm and a thickness of 70 μm or 150 μm were used. To generate magnetic field gradients (∇B), iron wires or platelets of desired number and shape embedded in PVC or epoxy resin were placed directly behind the WE. Homogeneous magnetic fields up to 0.5 T were applied perpendicular to the WE to adjust a welldefined ∇B at the surface of the WE. The distribution of the magnetic flux density and its gradient at the working electrode for the different ∇B-templates were simulated using the commercial finite element solver Amperes 6.0. Electrochemical standard techniques, including electrochemical quartz crystal microbalance measurements (EQCM), were applied to study the electrochemical and deposition behavior. The deposition of Cu, Co, Fe and their alloys was carried out from simple sulfate-based electrolytes of different concentration without the addition of complexing agents, levelers, or brighteners at a pH value of 3. The deposition of Bi was performed from nitrate-based electrolytes. 3.2 Characterization The impact of magnetic fields on topography, morphology and structure of the deposits was characterized by several standard characterization methods, including optical profilometry and microscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD), and cross-sectional

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analysis by focused ion beam (FIB) coupled with SEM. Energy dispersive X-ray spectroscopy (EDX) coupled with SEM or TEM, as well as Auger electron spectroscopy, were used to determine the chemical composition of the deposits.

3.3 Measurement of fluid flow Astigmatism particle tracking velocimetry (APTV) measurements were performed in a modified electrochemical cell to study three-dimensional fluid flows generated during the electrochemical deposition of Cu and Bi with and without superimposed magnetic fields in situ. Spherical particles were added to the electrolyte, and the movement of the particles was observed and analyzed. Details about this newly developed in situ method, the optical setup, the cell design and the analysis are described in [48–50].

3.4 Measurement of concentration field The concentration measurement based on interferometric methods to study the MHD effects on mass transport dates back to the early work of O’Brien [51]. We used a self-designed Mach-Zehnder interferometer to map the real-time, two-dimensional concentration distribution. The technique is based on the linear change in the refractive index as concentration of the solution changes. The data acquisition and analysis processes were described in detail in [52].

3.5 Numerical simulations Numerical simulations of metal deposition in inhomogeneous magnetic fields caused by small cylindrical NdFeB magnets positioned near the cathode were performed by finite element methods [53, 54]. Various electrolytes in cubic and cylindrical cells with different electrode arrangements were considered. In more detail, steady simulations of Cu deposition at vertical electrodes were performed in the limiting current regime [44] based on the theoretical model of [55, 56] extended by buoyancy forces. In addition, transient simulations of metal deposition from electrolytes with two magnetic metal species were performed with horizontal electrodes [46]. Here, a Butler-Volmer boundary condition of the electrically active species is implemented, and the temporal behavior of convection, species concentration, and metal layer thickness in the vicinity of the magnet can be studied.

4 Results and discussion 4.1 Deposition of copper and bismuth First investigations were performed in vertical, parallel electrodes with a ∇B-template containing three Fe wires [47]. The structure of the Cu layer deposited from an electrolyte containing 0.01 M CuSO4 reflects the distribution of the magnetic field gradient generated by the ∇B-template, as shown in Fig. 1. The thickness distribution of the deposit can be directly correlated with the magnetic flux density distribution at the WE. The optical image in Fig. 1c demonstrates an upward-directed and slightly distorted deposit shape. From the electrochemical parameters and the applied field, the value of the two magnetic forces, fL and fm can be roughly estimated. They are


Fig. 1. Optical image of a ∇B-template containing three Fe wires (a), the calculated distribution of the magnetic flux density at the working electrode for this template magnetized by an external field of 500 mT (b) and the resulting structured Cu deposit (c), line profile across one spot (d).

16000

4

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14000

12000

10000

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Fig. 2. Left: normal component of the concentration gradient ∂c/∂n [mol/m4 ] at the cathode obtained from a numerical simulation in the limiting current regime. CuSO4 concentration c0 = 2.8 mM. Right: ∂c/∂n along the horizontal line through the center of the electrode. The diameter of the magnet is sketched in gray (from [57]). 3

both on the order of 102 N/m . The driving force for natural convection, the gravitational force f G , is also on this order of magnitude. Therefore, the observed drop-like shape of the deposit might be caused by a complex convective phenomenon due to the overlap of natural convection and the convection generated by the two magnetically induced forces. Numerical simulations performed at slightly different material parameters (see Fig. 2) reproduce the deposition pattern observed experimentally [44, 57]. Additionally, by switching off the magnetic gradient force artificially, in the simulations it was shown that the drop-like deposition pattern disappears. This supports the assumption that the structuring effect is dominated by the magnetic gradient force, whereas the influence of the Lorentz force at small magnet diameters can be neglected. The magnetic gradient force causes local convection which brings fresh electrolyte from the bulk of the cell towards the electrode region behind which the magnet is located. For further details we refer to [44]. In order to minimize the influence of natural convection on the deposition, the following experiments were carried out at horizontally aligned, downward-facing WEs. From the previously discussed experiments, the contributions and the relative dominance of fL and fm to the structuring mechanism was not clearly obvious. Therefore, deposition of Cu and Bi layers was performed, since the ions of these elements are different in their magnetic properties. Cu2+ ions are paramagnetic, while Bi3+ ions

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Fig. 3. Left: current density-time transients for electrolytes with different Cu2+ ion concentration. Center: optical images of the deposited structures. Right: corresponding surface profiles.

are diamagnetic. As shown before, structured Cu deposits were formed in applied magnetic gradient fields (Fig. 1c), whereas homogeneous Bi films were obtained [58]. According to the physical meaning of fm (Eq. (3)), the force depends on the properties of the involved species. Hence, due to the very low absolute susceptibility of Bi3+ ions, the action of fm is negligible. As fL is similar for both Cu and Bi systems, it cannot cause the structuring observed for Cu. Thus, it can be concluded that a sufficient contribution from fm is mandatory. The Cu deposits at regions of high ∇B are not only thicker, but also show strongly increased grain size and surface roughness. This was attributed to a locally increased deposition rate caused by the mentioned convective effects. The influence of the concentration of paramagnetic Cu2+ ions in the electrolyte used for Cu deposition in a magnetic gradient field was studied under the first assumption, that with increasing paramagnetic susceptibility of the electrolyte, the structure might be more distinct. As shown in Fig. 3, the opposite behavior was observed for a ∇B-template of 21 Fe wires with a diameter of 1 mm embedded in epoxy resin. With increasing concentration of Cu2+ ions, the deposit structure formed after passing the same charge was less pronounced, with respect to topography and morphology. The surface profile, Fig. 3(b), is more structured for the lowest concentration with a minimum in the center of the wire placed behind the WE. This is consistent with the ∇Bdistribution at the surface of the WE [59]. These results reveal that the structuring is related to the concentration change of paramagnetic ions, rather than to the total magnetic susceptibility of the electrolyte. The whole electrolyte is diamagnetic for the lowest Cu2+ ion concentration. With increasing concentration of Cu2+ ions in the electrolyte, the deposition is not purely mass-transfer-controlled anymore, but charge transfer contributes as well. Hence, no limiting current density is observed in the i(t) transient, and therefore the concentration gradient of Cu2+ ions is not fully developed. Consequently, the driving force for the deposit structuring is reduced. The experimental results are in perfect agreement with theoretical studies of Mutschke et al. [44]. They emphasize that only the rotational part of the magnetic field gradient force (∇× fm ) (Eq. (6)) can induce electrolyte convection. Thus, only the molar magnetic susceptibilities of ions, which form concentration gradients during deposition, contribute to this driving force. The diamagnetic contribution of solvent molecules is negligible [44]. To understand the deposition mechanism and the postulated electrode-normal local convection induced by the field gradient force [44], in situ velocity measurements were performed during potentiostatic Cu electrodeposition. For the first time, astigmatism particle tracking velocimetry (APTV) was employed to enable


Fig. 4. Left: isosurfaces of the jet-like 3D fluid flow in the high ∇B setup. The large arrows are included for a better visualization of the observed fluid motion. Right: distribution of the Cu2+ concentration near the WE at high (indicated by the sketched Fe wire position) and low magnetic field gradients during deposition (I-III) and dissolution (IV-VI).

three-dimensional measurements in a large part of the cell volume. A complex threedimensional fluid flow was observed in a simple electrode setup described in more detail in [48–50,60, 61] and shown in Fig. 4(a). Besides the electrode-normal velocity attributed to fm , a rotational velocity component is induced by fL . Moreover, to determine the influence of the observed convection on the local concentration of Cu2+ , in situ concentration measurements during cyclovoltammetric studies were performed by Mach-Zehnder interferometry. Figure 4(b) shows the concentration distribution at different stages of polarization. The images I to III represent the deposition, IV to VI show the dissolution at different potentials. During deposition the diffusion layer formed in regions of high field gradient is enhanced compared to regions with low field gradient. When the potential is shifted in the anodic direction, the Cu layer begins to dissolve. The concentration of Cu2+ ions is higher in regions of higher field gradient. Most interesting is the observation that, even 30 s after the measurement was finished, an increased concentration of Cu2+ was visible near the WE in the region of high magnetic field gradients [61].

4.2 Deposition of magnetic structures and magnetic alloys Besides deposition of Cu structures, magnetic structures of Co, Fe and their alloys are of special interest for applications. It was found that the structuring effect was more pronounced for magnetic metals and alloys, since the magnetic susceptibilities of Co2+ and Fe2+ ions are more than one order of magnitude higher than the susceptibility of Cu2+ ions. Additionally, the saturation magnetization is highest for CoFe alloys, which means that the growing structure is also magnetized and contributes to the magnitude of the magnetic gradient field. Both metals are less noble than Cu, and the deposition process is accompanied by hydrogen evolution. It was demonstrated that homogeneous magnetic fields superimposed during deposition may improve the quality of the deposit, as formed hydrogen bubbles can be removed easily [23–26]. Moreover, the deposited mass was found to increase with applied external magnetic field and to correlate with the saturation magnetization and the magnetic susceptibilities of the ions involved, as shown in Fig. 5.

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Fig. 5. Enhancement of deposited mass obtained by EQCM measurements for Co, Fe, and CoFe alloys (a), Fe deposited for t = 6.5 min (b) and Co deposited for t = 25 min (c). Bs = saturation magnetization

Fig. 6. Magnetic field gradient simulation and optical images of free-standing Cu structures obtained with the 21 Fe wire template (diameter 1 mm) after 1, 10 or 20 cycles and the corresponding height profiles; μm-scaled Cu structure using 50 μm Fe foils and EDX line profile, Co structure (21 Fe wires) and CoFe structure obtained with magnetized Fe platelets (2 mm).

4.3 Pulsed electrodeposition Aiming at improved structuring, especially to obtain free-standing three-dimensional structures, the pulse reverse plating (PRP) method was employed in superimposed magnetic field gradients [50, 62]. During the deposition step of the PRP cycle, a thicker deposit developed in regions of high magnetic field gradients. During the subsequent dissolution step, the layer dissolved until no deposit remained in regions of low magnetic field gradients. Due to the dissolution step, the concentration of metal ions was slightly increased at the electrode surface. Therefore, in the following deposition cycle deposit growth was enhanced in regions of high magnetic field gradients. Repeating the cycles showed that the deposit height is correlated with the number of cycles, as illustrated in Fig. 6. The shape of the growing structure reflected the field gradient distribution at the working electrode. Free-standing structures were obtained for Cu, Co, Fe, and CoFe alloys and for various magnetic field gradient templates containing Fe wires or platelets. Additionally, it was demonstrated that μm-scaled magnetic building blocks yield μm-scaled free-standing structures.


Fig. 7. (a) Limiting-current, charge and mass enhancement during Bi deposition in electrolytes containing Mn2+ ions depending on the external magnetic field and optical images with and without magnetic field, respectively. (b) Change of concentration of the Mn2+ ions.

4.4 Influence of inert paramagnetic ions At first glance, the structuring of metal deposits seems to be limited to electrochemically active paramagnetic ions. This may be concluded from the underlying theory, which is based on the magnetic field gradient, the concentration gradient in front of the electrode, the resulting magnetic field gradient force, and the locally generated convection. Reverse Bi structures were obtained when depositing diamagnetic Bi3+ ions from electrolytes where electrochemically inert paramagnetic Mn2+ ions were added [49,63], as shown in Fig. 7. Maxima of deposit thickness correlate with regions of lowest field gradients at the working electrode. This is opposite to Cu, Fe or Co structures deposited from electrochemically active paramagnetic ions shown previously. It is assumed that the magnetic field gradient force generates a convection directed away from the electrode, pushing Bi3+ ions containing electrolyte to regions of low gradient fields and resulting in enhanced deposition in these regions. This correlates with the observation that, with increased magnetic field gradients, the limiting current density as well as the deposited mass increase. The postulated convection was verified by APTV measurements [49]. An enrichment of Mn2+ ions was also observed in regions of high magnetic field gradients, even without applied potential, by interferometric measurements. The builtup of a concentration gradient of Mn2+ ions in these areas yields a change in the concentration of Bi3+ ions because of charge conservation during deposition of Bi. Therefore, the reverse structuring can be explained by the action of the field gradient force. In fact, it can be shown analytically that the addition of strongly paramagnetic Mn2+ ions in the case of Cu deposition changes the sign of the curl of the magnetic gradient force [46, 57]. Thus, the direction of convection is inverted, which consequently leads to reduced deposition rates in the vicinity of the magnet, instead of enhanced deposition as in case of simple Cu electrolytes. Figure 8 shows numerical simulations of these two deposition scenarios taking place in a cylindrical cell. Behind the cathode on top, a cylindrical NdFeB magnet (radius 0.5 mm) is placed in the electrode center. Shown on top are the copper ion concentration and the electrolyte convection 10 s after switching on the current. At the bottom, the temporal evolution of the thickness of the deposited Cu layer is shown. This figure gives support to the explanation mentioned beforehand. For further details we refer to [46]. 4.5 Spontaneous enrichment of manganese ions Mach-Zehnder interferometry was used to quantitatively map the concentration distribution of the solution in situ, so that the mass transport could be studied in an

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Fig. 8. Top: concentration of Cu2+ and normalized velocity of the electrolyte shown in a (r, z)-region of the cell below the magnet (radial extent sketched on top) 10 s after starting the electrolysis. Left – Cu (umax = 0.03 mm/s), right – Cu-Mn (umax = 0.05 mm/s). Bottom: corresponding evolution of the thickness of the deposited Cu layer (from [46]). 1200 s

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Fig. 9. (a) Enrichment of Mn2+ in a magnetic gradient field 1200 s after the magnet was applied on top of the cell. (b) and (c) show the concentration contour plot and the velocity vector plot associated with the downward flow after the magnet was removed. The concentration change in (a) and (b) are in mM (from [69]).

applied magnetic field during Cu deposition [64–68]. As can be seen from the above section, a reversed structure was obtained for Bi deposition in an inhomogeneous magnetic field when paramagnetic, but electrochemically inert Mn2+ ions were added to the electrolyte. We carried out a simple concentration measurement to understand the effect. A permanent NdFeB magnet was applied above the cubic cell (side length 10 mm), which contained solutions of different MnSO4 concentrations.


The measurement was carried out for 20 minutes at room temperature. A local enrichment of the Mn2+ concentration was observed at the top of the cell, where the field gradient was highest. The concentration contour plots in Figs. 7 and 9 clearly reveal the enrichment. The shape of the concentration layer corresponds to the spatial distribution of the largest component of the magnetic field gradient force. This unexpected phenomenon was not restricted to MnSO4 solutions; a similar behavior was also found in solutions of MnCl2 or Gd(NO3 )3 . When the magnet was removed after 20 minutes of operation, the enriched concentration layer quickly dropped to the bottom, which proved the enrichment did exist. The relaxation of the layer also generated a downward flow in the middle of the cell which was visualized both by concentration measurements using Mach-Zehnder interferometry and by velocity measurements using particle image velocimetry [69], see Fig. 9.

5 Conclusion Electrodeposition is, in general, a very cost-efficient and non-invasive method of electrochemical deposit structuring. It is a matter of interest not only for fundamental researchers, but also for the electroplating industry. Extensive investigations in the last decades have proven that when homogeneous magnetic fields are superimposed during metal electrodeposition, the deposition rates increase and better deposit quality is achieved. Recently, it has been demonstrated that structured metal layers can be deposited from electrolytes containing paramagnetic ions when magnetic gradient fields are superimposed during the deposition. In summary, three different types of deposition experiments were undertaken: (i) for direct structuring it was found that maxima of deposit thickness coincide with maxima of the magnetic field gradient if the electrochemical active ions are paramagnetic (Cu2+ , Fe2+ , Co2+ ); (ii) reverse structures were obtained for electrochemically active diamagnetic (Bi3+ ) or weakly paramagnetic (Cu2+ ) ions by the addition of strong paramagnetic (Mn2+ ) ions which are electrochemically inert; (iii) more sophisticated free-standing structures were deposited by pulse-reverse plating. The structuring effect for the different types of deposits was attributed to a local convection of the electrolyte driven by the magnetic field gradient force. Because the concentration changes very close to the electrode surface, i.e. inside the diffusion layer, the rotational part of the magnetic gradient force is able to force convection of the electrolyte. It was shown by numerical simulation that an electrode-normal fluid flow advects ion-rich electrolyte to the concentration boundary and increases the deposition rate. The flow is directed away from the region of high magnetic gradient field in cases that result in inverse structuring. Furthermore, the role of the magnetic field gradient force in relation to the Lorentz force becomes more pronounced for decreasing characteristic length scales of the magnetic gradient field. The numerical simulation was verified by a new in situ method, in situ astigmatism particle tracking velocimetry. This method was applied during potentiostatic electrodeposition of Cu and Bi in different magnetic gradient fields. A complex three-dimensional fluid flow was observed. Thus, the electrode-normal convection driven by the magnetic field gradient force which was predicted theoretically was also proven experimentally. Additionally, the local concentration of paramagnetic Cu2+ ions during potentiodynamic deposition and dissolution in magnetic gradient fields was investigated by interferometry. It was observed that, in regions of high magnetic gradients, the diffusion layer grows more rapidly during the Cu deposition process and persists longer during the dissolution step. By the same method, it was shown for the first time that, even without applied potential, an enrichment of paramagnetic Mn2+ ions

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from a homogeneous solution takes place in regions of high magnetic field gradients, although their Brownian motion should lead to an immediate delocalization. In conclusion, the structured electrodeposition in applied magnetic field gradients proceeds by a complex mechanism based on the action of the magnetic field gradient force. It was demonstrated that locally induced convection is the key factor in structuring. This was proven by numerical simulation as well as by measurements of the local velocity distribution and the concentration distribution near the electrode. The question of what the minimum scale is for structures produced by this method, remains an open task for future research. We gratefully acknowledge financial support from Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Centre 609 “Electromagnetic Flow Control in Metallurgy, Crystal-Growth and Electrochemistry” (Projects C5, C6 and C11).

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