Nearest-neighbor bond lengths

The EXAFS, which occurs at higher energies above the edge, is due to the interference between the outgoing and the backscattered photoelectron waves (10-14). EXAFS provides information about the local structure of the x-ray absorbing atom. Typically, nearest neighbor bond lengths and coordination numbers can be determined to 0.02 A (1%) and one atom in four (25%) (4 ). The accuracy of these determinations is somewhat worse for outer-shell atoms, for disordered systems, or for systems with asymmetric distributions of atoms within a shell (15,16). 

Figure 19. Nearest-neighbor bond length distribution functions for the time-averaged 3584-particle WCA liquid at p = 0.83. The figure shows the contributions from ordered regions (dotted line), disordered regions (dashed line), and the overall distribution (solid line).

Nearest neighbor covalency effects in transition metal systems are normally described by the two Racah parameters B and C. Qualitatively, reductions in B and C are predicted to occur with pressure due to enhancements in covalency expected from increased metal-ligand orbital overlap as the nearest neighbor bond length decreases. In order to assess the effect of pressure on B and C, the effect of pressure on Dq needs to be known or transitions whose energies are independent or approximately independent of Dq need to be considered. The effect of pressure on Dq will be considered below and can be determined experimentally. If suitable spectroscopic data in absorption and/or emission is available, it is therefore possible to determine the effect of pressure on B and C. 

Ma et al. [147,162,163] argued that pressure-induced covalency effects can be understood in terms of the radial expansion of the valence electron wavefunc-tions as the nearest neighbor bond length decreases with pressure. They considered an isotropic compression model based on the scaHng of the Slater integrals... 

Equation (13) indicates that an understanding of the variation of crystal field strength with pressure requires knowledge of the variation of Dq with the nearest neighbor bond length R and the variation of R with R Much of the theoretical work has been directed at these two quantities. 

Fig. 4. Variation of the Slater covalency parameter F2 of Eu + and Sm + as a function of average nearest neighbor bond length R. The data points represent values in different host lattices. Solid arrows show the variation of F2 with pressure...

A crystal-chemical equation has been derived for the hardness of minerals. The Mohs hardness of p-BN has been calculated to be 11.6 (while the experimental datum is 11.5) for details, see [24]. Theoretical approaches for examining the bulk moduli of zinc blende type solids include an ab initio method requiring only the atomic number of the constituent atoms and an empirical approach based on the nearest-neighbor bond lengths. Both methods give comparable results. The bulk modulus for p-BN has thus been calculated to be Bq = 367 GPa (experimental modulus Bo = 465 GPa) [41]. 

Two theoretical approaches to examine the bulk moduli of hard solids (including p-BN) have been described, i.e., an ab initio method requiring only the atomic numbers of the bonding partners, and an empirical approach using the nearest-neighbor bond lengths [13]. 

The nearest-neighbor bond lengths along the c-direction (expressed as h) and off c-axis (expressed as foi) can be calculated as... 

Table 4.2 Calculated nearest-neighbor bond lengths, the defect energy levels (E,) relative to the valence band maximum for negatively charged substitutional impurities, and the energy (AE) required to form the positively charged AX center from the substitutional acceptors.

The main difficulty, therefore, lies in the construction of a suitable and cheap bias potential. Fichthorn et al. [44] developed a so-called bond-boost method, in which the boost potential is derived from the concept of bond breaking events in a solid. Thus, the boost potential in this approach is a function of all nearest-neighbor bond lengths associated with the atoms of interest. Using this technique, these authors studied the diffusion of Cu adatoms, dimers and vacancies on a Cu(OOl) surface [44]. In these simulations, average boost factors in the range lO -lO were obtained in the temperature range 230-600 K. 

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