Ice crystals containing impurities

Although the treatment given in the previous section was for pure ice, there is nothing in the derivation of the results (9-3o)-(9.35) restricting them to this case except for the carrier concentrations tif, which are related to the partial conductivities cr by (9.31). Those results may therefore be applied to ice crystals containing known amounts of particular impurities simply by making the necessary adjustments to the concentrations n. Any impurities which leave the concentrations of ion states and valence defects unaltered will have negligible effect on the electrical properties. 

From (9.32), which shows that is determined by the least effective conductivity mechanism, it is evident that this static conductivity may be quite critically dependent upon the presence of proton-donor or proton-acceptor impurities and, in this sense, the behaviour of ice is quite analogous to that of electronic semiconductors like germanium or silicon. Mole fractions of impurity which are significant are of the order of io . The high-frequency conductivity and relaxation time t are, from (9.30) and (9.35), rather less sensitive to impurity content than is Tg but are still directly affected at higher doping levels. The static dielectric constant depends on purity in a rather complex way, as we shall discuss presently. 

Steinemann (1957) has measured the electrical properties of ice doped with hydrogen fluoride and finds that at—io°C the static conductivity cTg is proportional to the square root of hydrogen fluoride concentration 

Jaccard (1959) has measured the conductivity of a heavily hydrogen-fluoride-doped crystal (mhf = i 7 x cm s) over a wide temperature range and finds an activation energy of 

as discussed before, the effective activation energy for proton transport is zero, we conclude that this is the energy for liberation of a positive ion state from a substitutional hydrogen fluoride molecule in ice. 

---

We have already discussed the high-pressure measurements of Chan et al. (1965) which show that the static conductivity dielectric relaxation time t is controlled by orientational defects. Equations (9.32) and (9.35) therefore lead us to the conclusion that, for pure ice, (T 4. ctjjl. This is borne out by the work on ice crystals containing impurities which we shall discuss in the next section, and indeed that work led to this conclusion several years before the high-pressure results were available. 

---