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Figures

  figure268
Figure 1: Densely branched growth in quasi-2D electrochemical deposition. (a) Radial geometry. Zinc deposited from 0.05M tex2html_wrap_inline803 at 10V, with tex2html_wrap_inline547 mm and R=4.2 cm. (b) Flat geometry. Copper deposited from 0.1M tex2html_wrap_inline809 at 5V with R=4 mm.

  figure277
Figure 2: Dimensionless growth rate tex2html_wrap_inline555 of the tex2html_wrap_inline557 th harmonic in the three-dimensional radial geometry. Conductivity anisotropy tex2html_wrap_inline559 = 0.01, tex2html_wrap_inline823 , and tex2html_wrap_inline709 . Lines are plotted for tex2html_wrap_inline827 . As the branches become increasingly resistive, the critical mode number below which all modes are stable increases. The dependence on R is very weak provided tex2html_wrap_inline569 .

  figure288
Figure 3: Plot of the critical perturbation harmonic tex2html_wrap_inline571 as a function of the amount of dissipation tex2html_wrap_inline573 and degree of anisotropy tex2html_wrap_inline559 in the three-dimensional radial geometry model, with tex2html_wrap_inline823 , and tex2html_wrap_inline709 . Dissipation and anisotropy both help stabilize the DBM.

  figure294
Figure 4: Plot of the critical perturbation harmonic tex2html_wrap_inline571 as a function of the size of the pattern, tex2html_wrap_inline583 , in the three-dimensional radial geometry model, with tex2html_wrap_inline585 and tex2html_wrap_inline709 . Lines are plotted for tex2html_wrap_inline589 , tex2html_wrap_inline591 , tex2html_wrap_inline593 , and tex2html_wrap_inline595 . Predictions for the size-dependent crossover to stable growth in the anisotropic limit given by Eq. (18), tex2html_wrap_inline597 , 8, 10.5, and 13 for the four tex2html_wrap_inline573 values respectively, agree well with the jump in tex2html_wrap_inline571 for the full solution.



David G. Grier
Mon May 20 13:07:47 CDT 1996