Effects of the Crystal Lattice

If we now consider the effect of the crystal lattice, by introducing Madelung constant M and multiplying by Avogadro s number Nq (i.e., the number of atoms per weight formula unit), we get... 

Fig. 1 General scheme of the origin of the 3d ion energy levels with different interactions considered. From the left to the right (a) the LS terms (Coulomb interaction between the 3d electrons) (b) crystal field splitting of the LS terms (c) SO splitting of the crystal field energy levels (d) Ham quenching of the SO splitting (effect of the crystal lattice vibrations)...

THE EFFECTS OF THE CRYSTAL LATTICE ON THE ELECTRONIC DISTRIBUTION OF THE NITRITE ION IN THE FERROELECTRIC PHASE OF NaNOj... 

Lattice factor Function describing the effects of the crystal lattice structure on scattered x-ray... 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

For the spinel, Hercyanite, cissume that the cation changes in valence state. Then, draw a diagram illustrating the probable ion diffusion processes, give the diffusion conditions and the diffusion reactions, including the effect of induced crystal lattice defects. 

The electronic properties of solids can be described by various theories which complement each other. For example band theory is suited for the analysis of the effect of a crystal lattice on the energy of the electrons. When the isolated atoms, which are characterized by filled or vacant orbitals, are assembled into a lattice containing ca. 5 x 1022 atoms cm 3, new molecular orbitals form (Bard, 1980). These orbitals are so closely spaced that they form essentially continuous bands the filled bonding orbitals form the valence band (vb) and the vacant antibonding orbitals form the conduction band (cb) (Fig. 10.5). These bands are separated by a forbidden region or band gap of energy Eg (eV). 

Nevertheless, fluoride does lead to a reduction in the solubility of hydroxyapatite in aqueous solution, even in the absence of trace levels of fluoride in solution, and hence can be seen to have an effect in the solid state as well [57], Apatites are complex and diverse materials which have the general formula Caio(P04)eX2 (X = F, Cl, OH) and they represent a crystallographic system, in which there can be considerable replacement of species. Thus, with little or no change in the dimensions of the crystal lattice, there can be exchanges of OH for F, Ca + for Sr +, and PO4 for CO and all of these are known to occur in biological systems. Natural hydroxyapatite, for example, is often partially carbonate substituted [58]. 

Several theories to explain this effect were proposed. One of them attributes the effect to the formation of an electronic hot gas, the temperature of which would be much higher than that of the crystal lattice... 

Crystal surfaces. Crystal surfaces may be viewed as vast defects inasmuch as the lattice forces are incompletely balanced. The effects of this imbalance are partially offset by distortion of the crystal lattice near the surface, but crystal surfaces still show a strong tendency to adsorb other... 

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