Effect of clustering on the space-charge relaxation phenomena in fluorite-type solid solutionsSr1−xDyxF2+xandSr1−xErxF2+x

In this paper we present the results of ionic thermocurrent (ITC) and dielectric loss experiments on two systems of solid solutions: ${\mathrm{Sr}}_{1-x}{\mathrm{Dy}}_x{\mathrm{F}}_{2+x}$ and ${\mathrm{Sr}}_{1-x}{\mathrm{Er}}_x{\mathrm{F}}_{2+x}$. The materials investigated have the fluorite structure, and the value of $x$ has been varied in the range $0\le x\le 0.4$. In contrast with results published in earlier papers on solid solutions ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{F}}_{2+x}$, we find, for the above-mentioned materials, that clustering plays an important role. It appears that clustering becomes more and more important with decreasing ionic radius of the trivalent lanthanide. We have observed that for Yb-, Er-, and Dy-doped crystals the concentration of next-nearest-neighbor (NNN) dipoles decreases for $R{\mathrm{F}}_3$ concentrations higher than 0.4, 0.6, and 1.0 mol%, respectively. The ITC peak associated with space-charge relaxation shows a complicated behavior as a function of the $R{\mathrm{F}}_3$ concentration ($R=\mathrm{Dy}\mathrm{or}\mathrm{Er}$). For low concentrations the space-charge relaxation peak shifts to lower temperatures with increasing concentration until a minimum value for the temperature is reached. For ${\mathrm{Sr}}_{1-x}{\mathrm{Er}}_x{\mathrm{F}}_{2+x}$ and ${\mathrm{Sr}}_{1-x}{\mathrm{Dy}}_x{\mathrm{F}}_{2+x}$ the concentrations for which this minimum occurs are 0.6 and 1.0 mol%, respectively; i.e., the same concentrations as those mentioned above, where the NNN dipole concentration has its maximum value. The position of the high-temperature (HT) band turns out to be related to the concentration of dipoles in the low-concentration range. In heavily doped materials the position of the HT band probably depends upon the number of clusters present. It will be concluded that clustering is very complex and that it is not possible to draw unambiguous conclusions from our experimental results concerning the defect structure of heavily doped materials. In spite of this we have presented a few possible descriptions which may be applicable.