Electron density, diamond lattice

An extended material of valence electron spatial correlations (VEC) had been analyzed (Schubert, 1964), when it became apparent that one correlation of valence electrons alone is not sufficient for the explanation of crystal structures of metallic phases. The outer core electrons had to be taken into consideration. This may best be seen from the crystal structure of indium (Fig. 4) The lattice matrix of In may be given in diagonal form ai = (4.59 4.59 4.95) A. The explicit lattice constants are needed for verification that the proposed VEC is acceptable. The VEC is aj = aAi(l, —1,0 1,1,0 0,0,3/2) and may be decomposed into the equations at = a j + a2 a2 = - aj + a2 a3 = 3 a3/2, which may be verified by means of Fig. 4. If a correlation lattice is inserted into a crystal structure, this does not mean that there are positions of increased electron density in the cell, it only gives the commensurability which is favorable energetically. It is easily verified that the number of valence electron places per cell is = 12 and is equal to the number of valence electrons in the cell given above = 12. The A1 type of the VEC had been inferred from the diamond struc-... 

Figure 53. Variation of electron density in the diamond lattice...

Figure 2 Molecular orbital energies arising from a linear combination of atomic p orbitals plotted against the relative number of electronic states with each energy. Data are for 64 carbon atoms arranged in a diamond lattice with periodic boundaries in each direction. Energies (in eV) are calculated from the tight binding Hamiltonian of Xu et al. (Ref. 33). 1 0 he experimental lattice constant for diamond, a is the lattice constant used in the calculations, and is the second moment of the density of states.

The intensity of the structure centered around 1200 cm increases, whereas the intensity of the 1332 cm diamond line decreases. From the theoretical phonon density of states showing a maximum around 1200 cm, matching this line position, it has been concluded that the 1200-cm band is related to disorder within the diamond lattice [26]. However, other possibilities such as boron-related electronic transitions or defect-activated scattering by accoustic and optical phonons away form the zone center have also been mentioned. 

Refined X-ray methods have also been applied to other types of crystal [7—9). In some metals, for example, the inter-ionic electron minimum density corresponds to some few electrons spread over the lattice (2 for Mg, 3 for A1 for example). And in covalent crystals like diamond there are non-spherical interatomic concentrations corresponding to the chemists covalent bonds, although such effects are small even for germanium (7). 

Contrary to bulk diamond, the spin density is increased by sample purification because the treatment, for example, with concentrated oxidizing mineral acids, removes the graphitic layer from the surface of the nanoparticles (Section 5.3.4). In this way new, unsaturated bonding sites are generated. A part of the spin density, however, is localized in the crystal lattice for nanodiamond as well, and again nitrogen centers and other defects give rise to the unpaired electrons. 

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