Orientational defects mobility

This information allows us to make tentative estimates of the concentration of orientational defects in pure ice, using an equation like (7.1), and of their mobility. It is clear from the energies involved that they should be much more numerous in pure ice than are the ion states. The energy barrier to proton motion is comparable in height to that for ion states but twice as wide, so that it is possible, and indeed turns out to be the case, that the anomalously high mobility of ionic states does not extend to orientational defects. Experimental information, derived from studies of the electrical properties of ice, is summarized for convenience in table 7.3. 

A real ice crystal at a finite temperature is, however, not perfect but contains an equilibrium concentration of point defects, as discussed in chapter 7. The most important of these in pure ice, from our present point of view, are the d- and L-orientational defects, since the product of their concentration and mobility is about 100 times greater than the same product for ion states, so that they provide the dominant relaxation mechanism. 

The fact that the dielectric relaxation of ice is accurately described by a simple Debye curve implies that only a single mechanism is involved. Bjerrum (1951) discussed the possible reorientation mechanisms in ice—either ion-state motion or orientational defect motion—and concluded that the latter was the relevant process. As we shall see later, his conclusion is correct for pure ice, where the greater concentration of L- and D-defects more than makes up for their lower mobility, compared with ion... 

The Einstein relation between diffusion coefficient and mobility is assumed to apply for the motion of orientational defects but may not apply for the quantum tunnelling motion of ion states. (It should be noted in passing that some workers define with a sign opposite to that used here.)... 

For concentrations of anunonia or hydrogen fluoride less than about 10 cm the contribution made to by orientational defects is constant and has a sign determined primarily by the mobility ratio which is not well known from other... 

In this formalism the mobility is determined partly by the value of AW (which occurs as AW ) and partly by the scattering of ion-state waves by lattice vibrations in the form of phonons. Because the ion-state band is so narrow and the difference between proton vibrational levels is so large compared with typical phonon energies, it is not possible for (k) to be scattered to a new state (k ) by emission or absorption of a single phonon. Instead, so that energy and momentum can be conserved, scattering must occur by the simultaneous emission and absorption of a pair of phonons of nearly equal energy. The analysis is therefore rather complicated but, if we assume that orientational defects are present in sufficient concentration that polarization effects do not block ion paths, the... 

Fig. 3.3. Illustration of the main proton transfer mechanisms (a) defect mechanism in a densely packed structure (b) loosely packed structure with a high concentration of mobile species (c) quasi-liquid state with a proton jump contribution In (a) the conductivity is favoured by intrinsic (interstitial rabbits) or extrinsic (impurity elephant) point defects. An orientation defect (hippopotamus in the wrong orientation) can also favour disorder of rabbits (Oj for Zr02 CaO, H for KHSO4) (b) the tree sublattice is a perfectly stable loosely packed structure and a high rabbit disorder can exist without affecting the host lattice (e.g. NH4 in p-AljOj) (c) only the mobile species sublattice is considered here these entities are moving with different speeds in different directions and some are hopping such may be the image of a quasi liquid or surface liquid (V205.nH20, HUP).

Just as with liquid crystals, electric fields could be used to study defect mobility. For such a study one would want to begin with a well-defined and simple system. For example, two sections with uniformly aligned lamellae could be annealed together with an orthogonal lamellar orientation, thus forming a wall defect. Movement of the wall defect in response to an electric field would reveal the mobility of the wall, because the alignment force can be calculated and the velocity measured. 

Ion entry into a growing oxide occurs at the metal-oxide interface for cations and at the oxide-gas interface for anions. Davies et al. [ 11 ] have shown that one or both species can be mobile in an oxide undergoing anodization. The choice of mobile ion is related to the structure of the oxide, whether it is crystalline or noncrystalline, as discussed below. In the case of cation movement, the properties of the metal affect the rate of oxide growth. Such characteristics as crystal orientation, defects, and impurities are important. In the case of anion movement, gas pressure and the presence of moisture are most significant. 

The iacrease of defect mobility along the chains in oriented Durham polyacetylene and the dispersion of the resonant-Raman spectra demonstrate that the stretching process has increased the lengths of defect-free polyene chains in the material. In contrast, unstretched films show properties consistent with chains that are frequently interrupted by defects. These defects are likely to be chain twists or bends which may be readily removed by the stretch alignment process, and are thus conformational rather than chemical in origin. 

At elevated temperatures, where the electron lifetime was much shorter than the pulse lengths of a few nanoseconds used, a second mobile species could be observed as a slowly decaying after-pulse conductivity component for large pulses. This was attributed to proton conduction with a proton mobility of 6.4 x 10 cm /Vs in H,0 ice and a somewhat lower value in D2O ice. ° In the case of the proton, the mobility was found to have an apreciable negative activation energy of 0.22 eV. The motion and trapping of protons was tentatively explained in terms of an equilibrium between free protons and a proton complexed with an orientational L-defect. °... 

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