VOLUME 75, NUMBER 16 PH YS ICAL REVIEW LETTERS 16 OCTOBER 1995 Kinetic Anisotropy and Dendritic Growth in Electrochemical Deposition D. Barkey, F. Oberholtzer, and Q. Wu Department of Chemical Engineering, University of New Hampshire, Durham, New Hampshire 03824 (Received 9 June 1995) It is shown that kinetic anisotropy stabilizes dendritic growth in electrochemical deposition of copper, and that in its absence the growth tips are unstable to splitting. The degree of anisotropy in the interfacial dynamics, which may be controlled through the chemistry of the electrolyte solution, was determined by the measurement of open-circuit potentials of single-crystal electrodes under nonequilibrium conditions. The experiments provide direct evidence that microscopic interfacial anisotropy in depositional growth stabilizes the dendritic morphology. PACS numbers: 68.70.+w, 05. 70.Ln, 81.10. Dn, 81.15. Pq A central problem in the study of pattern formation is the origin of selection rules that lead to reproducible structures in nonequilibrium growth [1, 2]. Much theoret- ical work has been directed to the question of whether interfacial anisotropy is a necessary condition for the for- mation of stable dendrites [3 — 11]. Experiments in fluid displacement have been put forward to provide physical evidence [12 — 14], but no depositional growth system has previously been reported in which interfacial kinetic pa- rameters can be controlled. Here we present results for a driven-growth system, based on electrochemical deposi- tion of copper by reduction of cupric ion in aqueous so- lution, in which the interfacial dynamics can be measured and varied to test the predictions of the theoretical mod- els. We show that kinetic anisotropy in the microscopic dynamics of the interface stabilizes the dendritic morphol- ogy, and that in our experiments in its absence the growth tips are unstable to splitting. A dendrite is a needle crystal characterized by its tip radius and growth velocity. Viewed in a moving refer- ence frame, it maintains a constant shape. The shape and growth velocity of a dendrite must allow a self-consistent and stable solution of the transport equation subject to ac- tivation and capillary boundary conditions [1]. Based on the boundary-layer model, Ben-Jacob et al. proposed that anisotropy is required to stabilize the tip against splitting [3 — 5]. The same conclusion was reached with the geo- metric model [6] and solutions to the full diffusion prob- lem [7 — 11]. Experiments with Iluid displacement in the anisotropic Hele-Shaw cell, where the anisotropy is intro- duced by milling channels in one plate of the cell, pro- vided additional support [12]. Buka and Palffy-Muhoray obtained a consistent result with liquid crystals in a Hele- Shaw cell, where the Iluid viscosity is anisotropic [13]. While the models have been formulated for solidification from the melt, both the models and the experiments with fluid displacement have been cited as evidence of the role of anisotropy in crystallization generally. The interpretation of results from Hele-Shaw cells was challenged by Couder et al. , who showed that stable parabolic fingers could be generated by the placement of a bubble on the tip [14]. They argued that it is the introduction of a length scale, the bubble diameter, that selects a stable tip. In addition, numerical simulation by Pines, Zlatkowski, and Chait [11] of the full dynamic problem without the steady state assumption showed selection of a stable tip without anisotropy. Resolution of the issue requires a physical system in which deposition of a single material can be performed with and without interfacial anisotropy. Several stud- ies have addressed the role of equilibrium interfacial anisotropy in dendritic solidification and precipitation by comparing the shape and growth velocity with the predic- tions of theoretical models [15 — 19]. Pairs of materials with contrasting surface-tension anisotropies, pivalic acid/ succinonitrile [15,18], and pivalic acid/ammonium chlo- ride [19] have also been examined. In part because of the restricted range of parameters, no strong conclusions can be made regarding a particular theoretical model, al- though there is evidence that the dendrite shape is inde- pendent of the magnitude of anisotropy for small values [15,19]. However, these studies do not apply directly here because none of the materials produce tip splitting, and the anisotropy is fixed for a given material. Electrochemical deposition was introduced to the field of pattern formation as a means of producing a wide range of morphologies including tip splitting and dendritic branches as well as diffusion limited aggregates [20 — 23]. It was soon recognized that interfacial anisotropy could lead to a transition from tip splitting to dendritic growth as deposition parameters were varied [23]. In these in- vestigations, however, the use of high-resistivity solutions forced the application of high field strengths, which mask the interfacial polarization. In electrochemical deposition from well-supported electrolyte solutions, where Ohmic dissipation is greatly reduced, the interface presents a sub- stantial portion of the impedance, making the interfacial dynamics experimentally accessible. To examine the role of interfacial dynamics and anisotropy in electrochemical deposition, we performed potential measurements on the metal-solution interface of copper single-crystal electrodes in supported solu- tions. Electrodes with orientations of (100), (110), and (111) were studied in a conventional three-electrode 2980 0031-9007/95/75(16)/2980(4)$06. 00 1995 The American Physical Society