Theoretical models for interpreting the dielectric behaviour of HF-doped ice
To understand the recent dielectric measurements made on HF-doped ice single crystals requires a full knowledge of the concentration of electrical defects present in ice and their subsequent interactions. Previous interpretations of the behaviour of HF-doped ice have concentrated upon specific features in isolation, whereas this paper presents analyses of a data set of 139 temperature and impurity combinations from 17 HF-doped ice single crystals. The interpretation of the behaviour of these crystals is in terms of several possible theoretical models. All models are based upon the common assumptions that HF molecules enter the ice lattice substitutionally and that excess Bjerrum and ionic defects can be formed at the HF sites. They also use the theory of electrical conduction in ice by Jaccard (1959) and the defect equilibria analysis in ice by Kroger (1974).
All models yield values for the concentration, mobility, energy of formation and charges for the different types of electrical defect considered to be generated.
From the model which assumes that only three fluorine centres exist, the approximate derived values of the mobility and charge for the L-defect and positive ionic defect are as follows: μ L = 5 × 10-8 m2 V-1 s-1 at 273 K, eDL = 0.44e; μ + = 2.7 × 10-8 m2 V-1 s-1 at 273 K, e ± 0.73 e .
Finally, using the derived defect conductivities and the Jaccard theory of electrical conduction, the relaxation tune of HF-doped ice has been successfully predicted over a wide range of temperature and fluoride concentration.