Nearest-neighbor distribution function

Fig. 6.17. The nearest neighbor distribution function for randomly dispersed sites (solid line). The associated pair distribution (dashed line) applies when there is a Coulomb attraction between oppositely charged states.

The luminescence efficiency is given by the fraction of electron-hole pairs which are created farther than R from the nearest defect (Street et al. 1978). The distribution of distances is the nearest neighbor distribution function, G R), for randomly dispersed defects, which is (Williams 1968)... 

A. Nearest-Neighbor Distribution Function and Pair Correlation Function... 

The situation is complicated by the fact that each experimental data set is only a limited and random representation of the true distribution. Therefore, from an experimental data set the true distribution can never be derived but only approximated. This approximation is referred to as the estimator. Particular obstacles in deriving estimators from experimental data sets are presented by edge effects (Diggle, 1983 Karlsson and Liljeborg, 1994). For an object set that is confined to a region W, the edge-corrected estimator d r) for the nearest-neighbor distribution function is calculated as ... 

For concentrated suspensions of hard spheres, the radial distribution function for the fluid phase is generated from the solution to the Percus-Yevick [37] equation using a Heaviside step function mviltiplied by a nearest neighbor geometric function for a disordered fluid. TTie result is a function for the compressibility derived by Carnahan and Starling [25] ... 

One of the main characteristics of the statistical properies of the spectra is the level spacing distribution (Eckhardt, 1988 Gutzwiller, 1990) function. In this work we calculate the nearest-neighbor levelspacing distribution (Eckhardt, 1988 Gutzwiller, 1990). 

A much more satisfactory random network model has been discussed by Alben and Boutron 82h They used a model, proposed by Polk 78> for Ge(as), scaled to fit the observed nearest neighbor 00 distance of H20(as), and with H atoms added to the OO bonds according to the Pauling ice rule that guarantees the presence of only H20 molecules 65>. In the Polk model the bond length is everywhere the same and the 000 angles are distributed with root mean square deviation of 7° about 109°. For the case of Ge(as), the observed and model radial distribution functions are in excellent agreement. 

The presence of local cation ordering in Mg2Ga and MgsGa - CO3 LDHs noted in Sect. 3.3.1 has been confirmed by means of both EXAFS and by calculation of the electron radial distribution function from the Fourier transform of the diffracted X-ray intensity. In each case the gallium was found to have six magnesium ions and no galhum ions as next-nearest neighbors [39]. 

This function is the integrally normalized probability for each water molecule being oriented such that it makes an angle B between its OH bond vectors and the vector from the water oxygen to the carbon atom. This function is calculated for those molecules within 4.9 A of the carbon atom (nearest neighbors), as this distance marks the first minimum in the pair distribution function for that atom. The curve in Figure 10 is typical for hydrophobic hydration (22). 

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