Application to In-Situ Studies of Electrochemical Processes
Anodic oxides in which ionic current density depends exponentially on field form films of uniform thickness that are ideal for study by ellipsometry. In-situ studies of such systems are carried out at current densities which ensure that an ellipsometer can track the electrochemical processes. (The instrument used here has a response time of 0.1 second and a resolution of 0.001 degrees.) The results plotted below are from the vanadium oxidation experiment in the logarithmic transients section. The information obtained there complements what we learn from ellipsometry, and helps us construct models of the electrochemical processes.
The experiment is performed on a vanadium electrode immersed in an organic electrolyte with a low water concentration (vanadium oxide dissolves in water), and consists of five steps. In the first, a constant anodic current is applied to the electrode to grow an oxide film at a uniform rate until a specified potential is reached. In the second, the current is reduced by a factor of two and made cathodic to convert the film to a reduced phase. In the third, the original current is reapplied to oxidize the film. The current remains constant through the fourth and fifth steps, the fourth converting the film back to the original oxide, and the fifth recovering the thickness lost during step three. The results obtained in the experiment are shown below on a composite plot of potential versus time (left and lower scales) and analyzer versus polarizer (right and upper scales).
In step one, vanadium and (to a lesser extent) oxygen move through the film under the influence of a high field and cause uniform film growth (once the film is established on the surface). In step two, hydrogen moves through the reduced phase under the influence of a high field (an unusual property of the vanadium system), and electrons move through the underlying oxide in the opposite direction. The reduced phase is less soluble in the electrolyte. In step three, hydrogen (and some oxygen) move through the reoxidized phase under the influence of a high field and electrons move to the substrate through the underlying reduced phase. Vanadium does not enter the film in this step, so the oxygen that enters the film combines with hydrogen. Step four begins when the interface in step three reaches the substrate, vanadium begins to enter the film, and an interface sweeps outward as the film dehydrates. In step five the film returns to its thickness at the end of step one, replacing what was lost in step three.
The final curve in the figure (in pink and only on the P-A plot) shows what happens if the current applied in step three is insufficient counter dissolution of the oxide. As the reduced phase is planed away the optical data acquired enable its refractive index to be determined directly. The index of the oxide can also be determined directly, but experiments at different initial thicknesses are needed to determine the index of the hydrated oxide. Step three ends with a loop that terminates at a well-defined cusp. The loop fits an interface-sweeping model, and a set of the cusps can be analyzed to determine the index of the hydrated oxide.
Once refractive index values are determined for the component layers, it is relatively easy to fit the conversion processes to the illustrated interface-sweeping models. The only exception occurs at the end of step two and the beginning of step three, and here again the final pink curve is useful. The optical data in step two trace out a smooth curve, but the curve deviates progressively from the model as the field in the reduced phase collapses. This is due to a secondary process that begins at this point and, as the pink curve shows, reverses at the beginning of step three.
The next applet shows the detailed optical analysis on an expanded scale. The growth curves for the anodic oxide and the reduced film are calculated using the index values determined in the simplex algorithm programs. Index values for the hydrated oxide are determined in the same way as for the anodic oxide, but require data from experiments performed over a range of film thicknesses. The field-dependence of the index of the anodic oxide must be taken into account to fit the Step 2 conversion, and this also requires measurements over a range of film thicknesses. The calculations themselves are done using a general anisotropic/absorbing multilayer routine originally written in QuickBasic by Donald De Smet.
First, theoretical film-growth curves are shown sequentially for the three phases. Next, theoretical conversion curves are shown for Steps 2, 3, and 4. These curves begin on one growth curve and end on a second. The shape of each curve depends on whether the conversion proceeds by an interface sweeping in from the electrolyte or out from the substrate. For steps 2 and 3 the curves are drawn for the interface sweeping inward. For step 4 the curve is drawn for the interface sweeping outward. Once the six theoretical curves are in place, the experimental data are superimposed on top.