Schematic drawing of ideal homogeneous and inhomogeneous corrosion of a calcium layer with a gas volume on one side: For both, optical and electrical calcium corrosion test, ideal homogenous corrosion is assumed as model for the interpretation of the measurement data so far.
Schematic drawing of the experimental setup. The calcium sample was placed in a gas cell purged with nitrogen, maintaining a very low partial pressure of water vapor due to leakage. The corrosion of the calcium layer was observed by three methods simultaneously: The transmission through the sample (optical test) was determined with a CCD-camera and the resistance (electrical test) via electrodes in 4-wire-sensing mode. The topography was measured in situ via AFM (topography test).
First experiment: Corrosion of a 60 nm calcium layer in the gas cell was observed with the AFM in contact mode. (a) and (b) depict the calcium layer after 3.5 and 4.5 h, respectively. Growing plateaus and a smooth base plane can be distinguished. (c) The height difference between both scans. The histogram of the height differences is shown at the bottom. Peak (3) belongs to the new plateau area grown between both scans (bright fringes), peak (2) to the slightly elevated base plane; its shoulder (1) to the almost unchanged, former plateaus.
The corrosion of the 60 nm calcium layer was observed with three different methods in parallel. The optical data were evaluated using a linear dependency and Lambert-Beer law from integral transmission values, respectively. The initial drop in topography curve results from the formation of corrosion nuclei at the surface. WVTRs are denoted. The estimated amount of calcium left and the estimated lag time strongly depend on the method used.
1st and 4th AFM-scan of the same area of the 60 nm calcium layer during corrosion, showing the evolution of surface features during the time interval noted on the left. (a) Formation of corrosion nuclei. (b) Isolated islands grew, touched each other, and covered the whole surface short after. Three nuclei are marked in both scans as guide to the eye.
Optical transmission through a 1000 nm thick calcium film. While the residual calcium height seems to decrease everywhere with time, one can easily see strong lateral inhomogeneities (a)–(c). Note that the lamp was driven at full intensity to see as much as possible through the remaining thicker calcium areas. The areas of corroded calcium are therefore in the saturation regime of the CCD-camera.
Photo of a 60 nm glass-glass encapsulated calcium film. The cross-section is depicted in the inset. Inhomogeneous corrosion is visible with the bare eye. Density of corrosion sites differs over the same sample.
Illustration of calcium corrosion including inhomogeneous corrosion and a small component of homogeneous corrosion.
Simulation: Electrical calcium test applied to geometries of ideal inhomogeneous corrosion. The exemplary cases a = b and a = 2b are depicted with their corresponding elementary cells in (a) and (b), respectively. (c) The simulated results are compared with the homogeneous case. (d) The corresponding WVTRs are shown – derived from the slopes in (c) for the case of a constant reaction rate.
Calculation: Lambert-Beer law and linear approach applied to optical images of a calcium layer corroding only inhomogeneously. While the linear approach gives the correct curve, the Lambert-Beer approach underestimates the amount of calcium left the more the higher the initial calcium height h0 is.
WVTRs and lag times from the same sample by different methods. Minimum and maximum values are obtained by different choices of the fit-range. A height of 60 nm was assumed to calculate the WVTRs. ±4% for Lambert-Beer results from the errors of the absorption coefficient and the initial height.
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