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By Gould R.F. (ed.)

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Extra info for Addition and Condensation Polymerization Processes

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In 1996, after five homologous series, Pr7 O12 , Pr9 O16 , Tb11 O20 , Pr40 O72 , and Pr24 O44 , were determined by refined neutron diffraction data, the fluorite-type module theory and principles integrated all of the known phases in the Ce, Pr, and Tb oxides into a single series, Rn O2n−2m , where m follows directly from the equal probability that any of the eight oxygen sites in the fluorite-type module could be vacant. , 1996; Kang and Eyring, 1997a, 1997b). Based on the fluorite-type module theory the thermodynamic properties, hysteresis, and reactions between the homologous series can be elucidated and the structures of homologous series experimentally discovered may be modeled.

In the binary lanthanide higher oxides each cation has same valence flexibility when the distance between cation–cation and cation–oxygen is modified. This special capability of mixed valences of the Ce, Pr, and Tb cations provide the electron hopping processes required to balance the electric charge due to an oxygen omission (vacancy). The neutralization of the electric charges can be achieved by the electron hopping. Based on these fundamental rules the eight oxygen atoms of a fluorite unit cell should have an a priori equal possibility to be vacant.

Thus the site on the surface would have a higher activity for reaction. C. Kang FIGURE 30 The activity of the Tb atoms on the surface of {111} facets of TbOx . The four arrows indicate the nano-twin crystal. The atoms at the right upper corner are very active during the electron beam radiation. Its temperature is about 600 °C. The left surface of this nano-twin is the {111} surface which has a low energy, and atoms at this surface are not active. , 2005a, 2005b). The electrons in the narrow f band are favorable to become itinerant electrons when the distance between the two cations of a tetrahedron is increased due to the presence of an oxygen vacancy, while the distance between the shifted cations and the neighboring oxygen anions, which move toward the vacancy resulting in a regular tetrahedron, is decreased forming a p–f hybridized band.

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Addition and Condensation Polymerization Processes by Gould R.F. (ed.)

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