Orientational defect, hydrogen bonds

Figure 5. Time-averaged structure of a protonic defect in perovskite-type oxides (cubic case), showing the eight orientations of the centrai hydroxide ion stabiiized by a hydrogen-bond interaction with the eight next-nearest oxygen neighbors. ...

Each listed type of randomization (orientional, hydrogen-bonding network, nuclear spin statistics, isotopes, impurities, defects, and others that could be cited) makes independent contributions to S0 0. Hence, it seems safe to conclude that no macroscopic sample of real substance that ever appeared on Earth satisfies S0 = 0, i.e., that every real substance represents an imperfect exception to the third law as commonly stated. 

The Hamiltonian (480) of orientational oscillations of ionic groups in the hydrogen-bonded chain can be related to the model of easy-axis ferromagnetic in transversal external field 2Trot. The Hamiltonian (480) resembles the Hamiltonian (451) in outward appearance, and this means that we can reduce the problem to the previous one. However, we are interested in the explicit form of parameters Or<)l and UIot. For this purpose we should start from the appropriate classical Hamiltonian that describes the motion of an oriental defect in the hydrogen bonded chain [325] ... 

A particularly important question involves the understanding of the role of crystal defects in the peculiar electrical behaviour of ice 4. Upon the application of an electric field, the solid becomes polarized by the thermally activated reorientation of the molecular dipoles. Niels Bjerrum postulated the existence of orientational defects, which represent local disruptions of the hydrogen-bond network of ice 4, to explain the microscopic origin of this phenomenon. 

Figure 9-5. A fragment of a centrosymmetric crystal structure with the molecules (represented as arrows parallel to their molecular dipoles) NH+—N hydrogen-bonded into antiparallel chains along [y] (the anions are neglected for clarity). The ideal crystal structure with antiparallel molecules in neighbouring chains is marked in green (full arrowheads). Due to defects in the fourth and seventh chains, in which 5 and 6 molecules have reversed orientation, respectively, two polar nanoregions are formed. The red and blue colours and open arrowheads mark these nanoregions, the polarisation of which is indicated with large grey arrows...

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