Defects Bjerrum

FIGURE 2.2 (a) Two-dimensional proton-disordered ice lattice (Bjerrum defect illustrated... 

Bjermm defects act as catalysts to promote dipole turns, with one fault for every 106 molecules, corresponding to a turn rate of 10-12 s-1 at an orientation fault site. Devlin and coworkers (Wooldridge et al 1987) suggested that Bjerrum defects are essential to the growth of hydrates from the vapor phase. 

Davidson and Ripmeester (1984) discuss the mobility of water molecules in the host lattices, on the basis of NMR and dielectric experiments. Water mobility comes from molecular reorientation and diffusion, with the former being substantially faster than the water mobility in ice. Dielectric relaxation data suggest that Bjerrum defects in the hydrate lattice, caused by guest dipoles, may enhance water diffusion rates. 

Gruen and Marcelja considered that the electric and polarization fields are not proportional in the vicinity of a surface and that while the electric field has the ion concentrations as its source, the source of the polarization field is provided by the Bjerrum defects. The coupled equations for the electric and polarization fields were derived through a variational method. Attard et al.14 contested the Gruen—Marcelja model because, to obtain an exponential decay of the repulsion, the nonlocal dielectric function was assumed to have a simple monotonic dependence upon the wavelength (eq 33 in ref 13). This was found to be inconsistent with the exact expression for multipolar models.14 In addition, the characteristic decay length for polarization (denoted in eq 18, ref 13) is inversely proportional to the square of the (unknown) concentration of Bjerrum defects in ice. While at large concentrations of Bjerrum defects the disordered ice becomes similar to water and the traditional Poisson—... 

Boltzmann equation is recovered, a low concentration of Bjerrum defects provided a much too large polarization decay length (ref 13 indicated as an example the value ... 

The dismption of hydrogen bonding constitutes an appealing possible explanation of the hydration force. Attard and Batchelor presented a two-dimensional lattice model, and concluded that both the preexponential factor and the decay length of the hydration force are determined by only one unknown parameter, the concentration w of Bjerrum defects in the vicinity of the surface... 

FIRST-PRINCIPLES STUDY OF BJERRUM DEFECTS IN ICE IH AN ANALYSIS OF FORMATION AND MIGRATION PROPERTIES... 

Figure 1 a) Formation of a D-L Bjerrum defect pair, b) Corresponding relaxed DFT structure. 

Even though from the conceptual point of view the role of Bjerrum defects is well established", their molecular structure and energetics, remains a subject of debate. Recent atomistic studies based on empirical water potentials have provided important qualitative insight into the structure and dynamics of Bjerrum defects, although they have not yet attempted to make direct contact with experimental conductivity data. Furthermore, the few ab initio studies " involve clusters that are too small to reliably capture the properties of a defect embedded in bulk crystal. 

In this contribution, we present a first-principles study of the structure and energetics of Bjerrum defects in ice h using a large supercell subject to periodic boundary conditions. The results are interpreted in the context of experimental electrical conductivity data for doped ice Ih, using the framework of Jaccard s defect-based microscopic electrical theory of ice ... 

In both pure as well as doped ice, the electrical conductivity due to Bjerrum defects is essentially controlled by L defects. According to Jaccard s electrical theory of ice it takes the form... 

The dielectric relaxation process of ice can be understood in terms of proton behavior namely, the concentration and movement of Bjerrum defects (L- and D-defect) and ionic defects (HaO and OH ), which are thermally created in the ice lattice. We know that ice samples highly doped with HE or HCl show a dielectric dispersion with a short relaxation time r and low activation energy of The decreases in the relaxation time and... 

Polar deep ice. Polar deep ice is made of snow under a compressing process. The dielectric properties of polar ice core samples have been reported as having small values of relaxation time rand activation energy.The observation of small rvalues for the core ice samples suggests that Bjerrum defects are more numerous in polar ice than in ordinary ice. The impurity concentration of polar ice is not sufficiently high to decrease the rvalue the HCl concentration is about 2x10 mol/1 for Byrd core ice. Since we know that polar deep ice has structures of clathrate gas hydrate, imperfection in the structures and the existence of gas molecules in the ice lattice seem to affect the dielectric properties.It is well known that the dielectric properties of ice samples derived from polar deep ice that has melted and refrozen are similar to those of ordinary ice. ... 

Dielectric properties differ between ice samples grown from the vapor phase and the liquid phase the relaxation time and activation energy of ice grown from the vapor phase have lower values than of liquid growth ice. This difference suggests that vapor-phase growth introduces a crystal imperfection (such as vacancies and inclusion of gas) with increasing Bjerrum defects. 

The structure of this paper is as follows in section 2 we briefly describe the formation mechanism of the Bjerrum defects used in this study and their possible ideal diffusion pathways, and in section 3 we introduce jump rates and diffusion coefficients in solids. In... 

Finally the diffusion coefficient for the Bjerrum defects is found as ... 

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