By Richard C. Alkire, Dieter M. Kolb
This can be a necessary booklet for researchers in electrochemistry; it covers components of either primary and functional value, with stories of top of the range. the cloth is especially good awarded and the alternative of subject matters displays a balanced editorial coverage that's welcomed.
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This can be a necessary booklet for researchers in electrochemistry; it covers components of either primary and sensible value, with stories of top of the range. the cloth is especially good awarded and the alternative of issues displays a balanced editorial coverage that's welcomed.
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Extra resources for Advances in Electrochemical Sciences and Engineering, Vol. 8
This widening yields a resistance increase which inﬂuences hR . However, compared with the true grain boundary resistance, this e¤ect becomes negligible for large rgb -values. Similar considerations are valid with respect to the grain boundary capacitance. Again, a correction factor hC takes account of displacement currents across neighboring grain boundaries and C 2 ¼ hC egb Agb wgb ð44Þ results. The ﬁnite element calculations revealed that hC and 1=hR are almost identical as long as uniform grain boundary properties are assumed and hC A 2:5 is a reasonable estimate for a polycrystal with cubic-shaped grains.
The low-voltage data obtained across one grain boundary can be expected to be considerably inﬂuenced by neighboring grain boundaries. For high voltages, however, the situation changes considerably: once the resistance of the investigated grain boundary breaks down at the critical voltage, the current mainly ﬂows across this boundary provided no surrounding grain boundary resistances break down as well. Consequently, the measured breakdown voltage reﬂects the true breakdown voltage of the grain boundary under investigation (if electrode and bulk contributions are negligible).
Only the outer equipotential lines di¤er signiﬁcantly from those in a single crystal, indicating that the resistance is mainly determined by the bulk conductivity close to the microelectrode. Therefore the spreading resistance formula Eq. (34) is a rather good approximation in order to quantify the resistance measured on a grain. According to Fig. 19b, the deviation from Rspr is always less than about 15% if the grain size ðLg Þ is ﬁve times larger than the contact diameter ðd me Þ. Even for d me ¼ 0:4 Lg an estimate of the bulk conductivity is possible with an error of at most 25%.
Advances in Electrochemical Sciences and Engineering, Vol. 8 by Richard C. Alkire, Dieter M. Kolb