F.H pair

Tunnelling recombination of primary F, H pairs can result either in closely spaced v+,i pairs (the so-called a, I centres) which annihilate immediately due to Coulomb interaction and a consequently large instability radius. However some i ions occur in crowdion configurations, and leave vacancy moving away up to 4-5 ao even at 4 K [31]. The distinctive feature of tunnelling recombination is its temperature independence, which makes it one of the major low-temperature secondary processes in insulating solids with defects. 

This interaction arises from the overlap of the deformation fields around both defects. For weakly anisotropic cubic crystals and isotropic point defects, the long-range (dipole-dipole) contribution obeys equation (3.1.4) with a(, ip) oc [04] (i.e., the cubic harmonic with l = 4). In other words, the elastic interaction is anisotropic. If defects are also anisotropic, which is the case for an H centre (XJ molecule), in alkali halides or crowdions in metals, there is little hope of getting an analytical expression for a [35]. The calculation of U (r) for F, H pairs in a KBr crystal has demonstrated [36] that their attraction energy has a maximum along an (001) axis with (110) orientation of the H centre reaching for 1 nn the value -0.043 eV. However, in other directions their elastic interaction was found to be repulsive. 

To illustrate the general theory developed above, let us briefly consider here as an example the recombination of the geminate F, H pairs in alkali halide crystals. Steady-state experiments on irradiated alkali halides show that during the linear heating of a sample T = T() + fit (j3 is a heating rate, To is initial temperature), several recombination (annealing) stages are observed e.g., in KBr separated by several K [8, 80], This process was simulated theoretically by Kotomin et al. [77, 81]. 

In the case of F, H centres in alkali halides their maximum attraction and repulsion correspond to the configurations 1 and 2 in Fig. 4.8(b). Even for the nearest F, H pair in KBr, the attraction energy is rather small ss 0.04 eV. 

Fig. 3.7. Schematic representation of relaxed excited states in an alkali halide. a ground slate h-. self-trapped cxciton consisting of a centre and an electon c F.H pair centre. The electron is represented by its orbit (drawn line) marked by the letter e, the CIJ pseudomolecule (i.e. the trapped hole) by CI-CI. See also text...

The model originating from this work invokes, as a first step, the relaxation of a free exciton in the neighbourhood of a lattice distortion induced by Eu. This leads to an e-F Vk centre (where e stands for electron, and Vk for the Vk hole center consisting of a BrJ molecule on two Br sites). Subsequently an off-center self-trapped exciton is formed, viz. a nearest-neighbor F-H pair (where F is the well-known F center, in which an electron is trapped at an anion vacancy, and H is the H center, which can be regarded as an X J molecule occupying an X anion site the anion concerned here is Br see also Sect. 3.3.1). This pair is assumed to be stabilized by the presence of a substitutional 0 ion which is much smaller than Ba. The photostimulable center is then a F,u -F-H complex. 

To illustrate the relationship between the microscopic structure and experimentally accessible information, we compute pseudo-experimental solvation-force curves F h)/R [see Eq. (22)] as they would be determined in SEA experiments from computer-simulation data for T z [see Eqs. (93), (94), (97)]. Numerical values indicated by an asterisk are given in the customary dimensionless (i.e., reduced) units (see [33,75,78] for definitions in various model systems). Results are correlated with the microscopic structure of a thin film confined between plane parallel substrates separated by a distance = h. Here the focus is specifically on a simple fluid in which the interaction between a pair of film molecules is governed by the Lennard-Jones (12,6) potential [33,58,59,77,79-84]. A confined simple fluid serves as a suitable model for approximately spherical OMCTS molecules confined... 

The simplest explanation for the hydrogen bond is based upon the polar nature of F—H, O—H, and N—H bonds. In a molecule such as H20, the electron pair in the O—H bond is displaced toward the oxygen nucleus and away from the hydrogen nucleus. This partial ionic character of the O—H bond lends to the hydrogen atom some positive character, permitting electrons from another atom to approach closely to the proton even though the proton is already bonded. A second, weaker link is formed. 

Since the electronegativities of the elements follow the order, F > O > N, the charge separation for the bonds in these three molecules should follow the order, F-H > O-H > N-H. The same order also should be followed when each of these hydrogen atoms forms hydrogen bonding with a lone pair of electrons on a neighboring molecule. 

Expressions for Sq(H) for / < 2 and a subvolume of parallelepipedal shape are given in Table 7.1. Though the shape factor for the dipole moment is imaginary, combination of the Friedel pairs F(H) and F(H) in the summation... 

The VSEPR treatment is best approached by considering the ion as made up from three ions F + H+ + F. The central proton possesses no electrons until the ligand fluoride ions supply two each. The two pairs of electrons repel each other to give the observed linear configuration of the three atoms. The two pairs of electrons would occupy the Is and 2s orbitals of the hydrogen atom and, what with a considerable amount of interelectronic repulsion, would not lead to stability. 

Recently, the same series of six polyimides was studied by positron annihilation spectroscopy to determine die fractional free volume directly. In all three H/F analogue pairs, the increased free volume of the fluorinated polymer accounted for around 50% of the observed decrease in refractive index and dielectric constant. This result confims an astonishingly large free volume contribution predicted by our earlier estimates.Future work will investigate the generality of this result to other polymer systems. 

They have calculated the continuous diffusion equation (3.2.30) with U(r) = -a/r3 for several kinds of nn F, H centres in the crystalline lattice. Figure 3.9 demonstrates well that both defect initial separation and an elastic interaction are of primary importance for geminate pair recombination kinetics. The 3nn defects are only expected to have noticeable survival probability. Its magnitude agrees well with equation (3.2.60). 

In many cases of interest tunnelling recombination of defects is accompanied by their elastic or Coulomb interaction, which is actual, e.g., for F, H and Vk, A0 pairs of the Frenkel defects in alkali halides, respectively. In these cases the equation defining the steady-state recombination profile is... 

Crick, F. H. C., Codon-anticodon pairing The wobble hypothesis. J. Mol. Biol. 19 548-555, 1966. A classic paper. 

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