By André Julg (auth.)
Traditionally, while one offers with crystals, the 1st estate to be awarded is the periodicity of the lattice, and all tools of analysis are in accordance with this attribute, that's thought of crucial. actually, crystals range from the molecules of finite dimension which are studied in chemistry, in basic terms of their super huge variety of debris. moreover, the life of faces, which restrict the unfold of crystals in house, inevitably breaks the periodicity of the approach. For those purposes it truly is typical to use to crystals the recommendations and techniques which were largely demonstrated within the learn of molecules. Pauling first emphasised this aspect 1 and used it to give an explanation for the digital constitution of crystals, regarded as limitless and ideal. the purpose of this paintings is to teach, with assistance from a number of examples, the probabilities provided by way of quantum chemistry for tackling the issues of crystal digital constitution, of crystallographic preparations in addition to their macroscopic form, and of distortion results because of the presence of faces. the world relating to the life of strength bands (allowed or forbidden), hole, electrical, magnetic or optical homes should not touched upon.
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Additional resources for Crystals as Giant Molecules
The seven oxygen atoms form an octahedron with an additional oxygen atom above one of the octahedron faces. ~: SP3d3 hybridizations are possible. perhaps! orbitals also intervene. These hybridizations are unstable. At high temperatures zro 2 has the rutile structure, and La 20 3 and Nd 20 3 crystallize with the ~-M203 structure. b) Compounds of A B formula where B is a complex structure . . . . . . . n . . . . . . . . • . . . . . . . . . . . . •• ). The atoms situated on the periphery of ~ structure carry the atomic orbitals pointing in sufficiently open directions to be able to form localized molecular orbitals with orbitals of the metal atoms.
Discussion of the Results The theoretical results obtained for some crystals (Table 6) and the results obtained from the empirical formula (34) (Tables 8-10), permits a sufficiently extensive discussion. 9 in CaF 2 , MgF 2 , ZnO, ZnS. Two factors seem to play a role in the displacement of electron charge in localized orbitals ~ .. 13: (1) the difference in I~J electronegativity, ~x, between the atoms, and (2) their polarizability. The greater the difference in electronegativity, the greater is the displacement of the charge toward the more electronegative atom.
The integrals a = (~ +~ )/2 are deduced from atomic spectroscopy 32 (see Appendix A). Since the lattice of alkaline metals is homothetical (bcc arrangement), the bond orders are the same. The cohesive energy is proportional to the S integral. Table 2 indicates the obtained results. The decrease of the cohesive energy explains the decrease of the melting point. 8 22 64 The transition elements are particularly interesting. To a first approximation, we can admit that the ~-orbitals give a doubly used molecular orbital system.
Crystals as Giant Molecules by André Julg (auth.)