Proton lattices

Equation 13 can be solved numerically for Tc as a function of the proton-lattice coupling. The parameters are chosen so as to fit the experimental value of Tc for KDP. For C = 21 732 K/A and g2ygAyf close to those used for perovskite oxides, Tc Ikdp = 115 K. In Fig. 3 Tc is shown as a function of C with all other parameters fixed. Including the deuteration effects (Table 2), Ter = C Idkdp/C Ikdp 1 2. With this estimate TcIdkdp = 168 K. C itself depends only weakly on /, g2y g4 but a strong dependence on/ is observed, which is the coupling between the PO4 shells and the K" " ions. This, on the other hand, should not be dependent on deuteration. 

Fig. 4.5 Weathering reactions at the surface of a feldspar (after Raiswell et al. 1980). (a) Broken bonds become protonated by H+ dissociated from carbonic acid and ionic-bonded Ca2+ is released to solution, (b) Protonated lattice, (c) Further severing of ionic bonds causes complete protonation of the edge tetrahedron, (d) Edge tetrahedron is completely removed to solution as HiSith.

Fig. 23.3. Inelastic neutron scattering spectra of y-MnOj powder. The spectrum of the sample is recorded at 4 K and the spectrum of the same sample heated previously at 450 "C has been subtracted. Bonds are assigned to localized protons (OH .HjO) whereas the diffuse and broad continuum above 100cm seems related to a proton gap (proton lattice gap) (with courtesy ). The INS spectrum of Ho.ssMnOj prepared by chemical reduction of y-MnOj shows three peaks near 1120, 2200 and 3100 cm which are assigned to the 0 - 1, 0 - 2 and 0 — 3 transitions of an isotropic oscillator, respectively. This triplet may correspond to a non-specific bonded proton at the centre of the octahedral cavity .

Figure Bl.13.2. Spin-lattice and spin-spm relaxation rates (R and/ 2> respectively) for a carbon-13 spin directly bonded to a proton as a fiinction of correlation time at the magnetic fields of 7 and 14 T.

Figure 5.8. Paramagnetic ion-induced spin-lattice relaxation rates (rp) of the protons of 5.1c and 5.1 f in CTAB solution and of CTAB in the presence of 5.1c or 5.1 f, normalised to rpfor the surfactant -CH-j. The solutions contained 50 mM of CTAB, 8 mM of 5.1c or 5.1f and 0 or 0.4 mM of [Cu (EDTA) f ...

In all cases, water and carbonic acid, the latter of which is the source of protons, are the main reactants. The net result of the reaction is the release of cations (Ca " ), Mg ", K", Na" ) and the production of alkalinity via HCO. When ferrous iron is present in the lattice, as in biotite, oxygen consumption may become an important factor affecting the weathering mechanism and the rate of dissolution. 

The spatial localization of H atoms in H2 and HD crystals found from analysis of the hyperfine structure of the EPR spectrum, is caused by the interaction of the uncoupled electron with the matrix protons [Miyazaki 1991 Miyazaki et al. 1991]. The mean distance between an H atom and protons of the nearest molecules was inferred from the ratio of line intensities for the allowed (without change in the nuclear spin projections. Am = 0) and forbidden (Am = 1) transitions. It equals 3.6-4.0 A and 2.3 A for the H2 and HD crystals respectively. It follows from comparison of these distances with the parameters of the hep lattice of H2 that the H atoms in the H2 crystal replace the molecules in the lattice nodes, while in the HD crystal they occupy the octahedral positions. 

If the amount of the sample is sufficient, then the carbon skeleton is best traced out from the two-dimensional INADEQUATE experiment. If the absolute configuration of particular C atoms is needed, the empirical applications of diastereotopism and chiral shift reagents are useful (Section 2.4). Anisotropic and ring current effects supply information about conformation and aromaticity (Section 2.5), and pH effects can indicate the site of protonation (problem 24). Temperature-dependent NMR spectra and C spin-lattice relaxation times (Section 2.6) provide insight into molecular dynamics (problems 13 and 14). 

That is, the H-bonded network provides a natural route for rapid transport. This phenomenon of proton jumping thus occurs with little actual movement of the water molecules themselves. Ice has an electrical conductivity close to that of water because such proton jumps also readily occur even when the water molecules are fixed in a crystal lattice. Such conduction of protons via H-bonded networks has been offered as an explanation for a number of rapid proton transfers of biological significance. 

There is a lively controversy concerning the interpretation of these and other properties, and cogent arguments have been advanced both for the presence of hydride ions H" and for the presence of protons H+ in the d-block and f-block hydride phases.These difficulties emphasize again the problems attending any classification based on presumed bond type, and a phenomenological approach which describes the observed properties is a sounder initial basis for discussion. Thus the predominantly ionic nature of a phase cannot safely be inferred either from crystal structure or from calculated lattice energies since many metallic alloys adopt the NaCl-type or CsCl-type structures (e.g. LaBi, )S-brass) and enthalpy calculations are notoriously insensitive to bond type. 

The diagrams also indicate why neutral c/oio-boranes BnHn4.2 are unknown since the 2 anionic charges are effectively located in the low-lying inwardly directed orbital which has no overlap with protons outside the cluster (e.g. above the edges or faces of the Bg oct edron). Replacement of the 6 Ht by 6 further builds up the basic three-dimensional network of hexaborides MB6 (p. 150) just as replacement of the 4 H in CH4 begins to build up the diamond lattice. 

Different solid-state NMR techniques CPMAS NMR, the second moment of the signal, the spin-lattice relaxation time in the rotating frame T p) were combined to reach the conclusion that in the case of por-phine H2P the double-proton transfer is followed by a 90° rotation within the crystal (see Scheme 2). 

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