The species which arise when sodium atoms are absorbed by a zeolite (Na-Y) have been studied using ab-initio molecular dynamics methods. Calculations pertinent to a wide range of doping levels have been performed, and the factors which determine the preferred arrangements of the added electrons and ions were identified. At low levels of up to one added sodium atom per sodalite unit, the added electron is transferred to the interior of the sodalite cage to form highly ionized molecular species (predominantly Nq3+ at the zeolite Stoichiometry studied) leaving the added ion coordinated to a nearby oxide site in the supercage. The interactions between Nq3+ species were studied and are discussed with reference to magnetic resonance and susceptibility data. At higher doping levels, the added electrons form ionized molecular clusters in the supercage rather than the small metal particles whose presence had been postulated. The character of these clusters is determined by electronic structure effects, analogous to those which influence the structure of gas-phase clusters, and by their desire to remain coordinated to oxide ions at the windows between supercages. Parallels between the behavior of metal atoms absorbed by zeolites and by liquid ammonia, crown ethers, and other solvents are examined.
Contrary to popular belief, a linearized approximation of the Zoeppritz equations may be used to estimate the reflection coefficient for angles of incidence up to and beyond the critical angle. These supercritical reflection coefficients are complex, implying a phase variation with offset in addition to amplitude variation with offset (AVO). This linearized approximation is then used as the basis for an AVO waveform inversion. By incorporating this new approximation, wider offset and angle data may be incorporated in the AVO inversion, helping to stabilize the problem and leading to more accurate estimates of reflectivity, including density reflectivity.
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