Calculated quantities

Estimated uncertainties in the calculated quantities required an analysis of both measurement uncertainty and method uncertainty. The uncertainty in quantities such as the specimen conductivity are based upon standard propagation of errors techniques [42,43]. However, the estimate of uncertainty in the total charge passed Q_T requires an additional analysis of the method uncertainty. Equation 3 represents not only a means of calculating Q_T, it is also a discrete approximation of the continuous function of current that varies with time. As a numerical method, trapezoid integration has inherent uncertainty that is a function of both the time interval and the curvature of the function being integrated [44].

Since the curvature in the function of current versus time differs from specimen to specimen, a general approach was needed for the analysis of the method uncertainty. In this experiment, the current through the specimen was measured every minute. From these measurements one can perform a propagation of errors calculation based upon Eqn. 3 to yield a measurement uncertainty for a time interval of one minute. Also, one could extract every other datum, as if the current was measured every two minutes, and perform the same uncertainty calculation. A comparison of these two results would indicate the effect of changing from a time interval of one minute to two minutes. Fortunately, the number 360 (the number of minutes in 6 hours) has many possible multiplicative factors. For Sample C-2, the extraction of every n-th datum was repeated for a number of n values, the measurement uncertainty calculated, and the results plotted in Fig. 11, with the error bars representing 2$\sigma$. Based upon these results, for measurement intervals less than 10 minutes, there appears to be no significant method uncertainty contribution to the overall uncertainty.

Figure 11: Demonstration of the difference between measurement uncertainty and method uncertainty using data for Specimen C-2.