A comparison of fractal dimensions determined from atomic force microscopy and impedance spectroscopy of anodic oxides on Zr–2.5Nb

Changes in the topology of anodic oxides grown on a two-phase Zr–2.5Nb alloy have been observed with atomic force microscopy (AFM) as a function of oxide thickness. For thin films grown with relatively low anodization voltages, the oxide formed over the β-Zr phase of the alloy appeared rougher and protruded above that grown over the more abundant α phase. When the anodization voltage was ∼80 V, the average thickness of the anodic film reached ∼200–300 nm, and the oxide formed over the α phase changed abruptly to become as rough as that formed initially above the β regions. Area-scale fractal dimensions have been calculated from the AFM measurements for these oxides as a function of anodization voltage. These values agree remarkably well with ‘surface’ fractal dimensions inferred from analyses of electrochemical impedance spectra in which the oxide is treated as the dielectric in a fractal capacitor.