Distorted ion model

As discussed above, whereas for open structures the zero-pressure structures are calculated more accurately with the distorted ion model than with the spherical ion model, for close-packed systems the zero-pressure structures are calculated just as well with the spherical ion model. In the same way, the distorted ion model leads to improvements in the compression at high pressures for open structures but not for close-packed structures. Although the agreement with experiment is reasonable for calculated changes in volume with pressure, the calculated structures are generally less compressible than observed experimentally (i.e.,the bulk moduli are too high). 

The calculated enthalpies for silica in the quartz and stishovite phases are shown in Figure 3 as a funetion ofpressure. The stishovite structure beeomes more stable than the quartz strueture at 3.5 GPa with the distorted ion model, and at 21 GPa with the spherical ion model. In comparison, the experimental zero temperature transition pressure for the quartz to stishovite phase transition is estimated to be 5.5 GPa from thermodynamic data [53], and the transition pressure for the similar cristobalite to stishovite phase transition is caleulated to be 6 GPa by periodie Hartree-Fock methods [54]. The non-spherical distortions improve the modeling of this phase transition by stabilizing stishovite with respeet to quartz the greater stabilization ofstishovite occurs because the distortions strengthen three bonds per anion in stishovite, and only two bonds per anion in quartz (the bonds are significantly covalent in both structures, as shown above in the plots of the electron density distributions). 

EXAFS studies of the Jahn-Teller distorted ions Cr(H20)g and Cu(HjO)g are worth of mentioning. This situation is particularly interesting because it not only involves one short (strong) and one long (weak) bond within the same complex but it also shows the limitations of EXAFS. It has been reported that the presence of the weak bond is not apparent in the Fourier transform of %(k) k due to the Nj/r dependence and the large cr term, and more detailed modeling is needed for the extraction of the EXAFS parameters In fact, both 4-ligand (equatorial) and... 

Further Kramer has measured the peak area ratio in the ESCA spectrum of the 2-norbomyl cation (from the figure published by Olah) and found it is not 2 5 (as required by the nonclassical ion model) but 4.5 1 or 6 1, depending on the method of measurement. Olah, however, points out that in the ESCA spectrum the main thing is not the ratio of peak areas which is often distorted due to admixtures coming from the vacuum systems and so can somewhat vary from experiment to experiment, but that of the AEb value. Finally, Kramer assumes the reported spectrum to belong to a neutral compound or a mixture of substances rather than to a stable ion. But according to Olah, the NMR spectra of the solutions under study before and after the recording of the ESCA spectrum are perfectly identical and coincide with that of the 2-norbornyl cation. 

Figure 3. Enthalpy of silica in quartz and stishovite structures as a function of pressure Key squares quartz, circles stishovite open symbols distorted ion electron gas model closed symbols spherical ion electron gas model.

Figure 4. CaClj a, b lattice parameters as a function of pressure. When a = b, the CaCl2 structure reduces to stishovite. Square distorted ion election gas model circles TTAM model.

Figure 5. Enthalpies of phases in Magnesium Silicate system as a function of pressure, relative to the binary oxides (stishovite and periclase). (a) distorted ion electron gas model (b) spherical ion electron gas model.

A realistic model must account not only for the classical electrostatic interaction Ugi, but also for three interactions accounting for the quantum nature of electrons. The exchange-repulsion, or van der Waals repulsion U gp is a consequence of the Pauli principle, while the dispersion (van der Waals attraction) arises from correlated fluctuations of the electrons. Last, the induction term reflects the distortion of the electron density in response to electric fields, including incipient charge transfer associated with bond formation. In molten salts, all these interactions can be taken into account in molecular dynamics (MD) simulations in the framework of the polarizable ion model [1],... 

In our model of an ionic lattice, we have thought of the ions as being spherical in shape. This is not always the case. In some cases, the positive charge on the cation in an ionic lattice may attract the electrons in the anion towards it. This results in a distortion of the electron cloud of the anion and the anion is no longer spherical (Figure 19.7). We call this distortion ion polarisation. The ability of a cation to attract electrons and distort an anion is called the polarising power of the cation. 

Various other interactions have been considered as the driving force for spin-state transitions such as the Jahn-Teller coupling between the d electrons and a local distortion [73], the coupling between the metal ion and an intramolecular distortion [74, 75, 76] or the coupling between the d electrons and the lattice strain [77, 78]. At present, based on the available experimental evidence, the contribution of these interactions cannot be definitely assessed. Moreover, all these models are mathematically rather ambitious and do not show the intuitively simple structure inherent in the effect of a variation of molecular volume considered here. Their discussion has to be deferred to a more specialized study. 

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