Running coordination number

Fig. C. The pair correlation function gHu and the running coordination number hh.

G. Pair Correlation Function and Running Coordination Number... 

The number of j particles around a particle i is given as a function of the distance r of the j particles from the particle i and is defined as the running coordination number y(r) ... 

The Time Dependence of the Running Coordination Numbers within the First and Second Coordination Spheres0... 

That is, the average number of oxygen atoms within a spherical shell of radius for a metal ion chosen to be at the origin. If Vg is chosen as Td, this value of the running coordination number is usually referred to as the coordination number, which we write in a generalization of the Cotton-Wilkinson notation as /imo- Thus far, the temporal stability of the aquaion has not been mentioned even for labile aquaions such as K+ or Cl , nuo can always be defined in the preceding sense. Whether the concept of an aquaion is useful in the Cotton-Wilkinson description is a different matter. 

Figure 6. Running coordination numbers rtNa-o (r) and nci-o (r) for bulk ice and rigid ice lattice with constrained oxygens.

Figure 48. Solute-solvent radial distribution functions and running coordination numbers. The radial distribution (the solid line using the left scale) and the running coordination number (the dashed line using the right scale) are plotted versus distance in angstroms for the distribution of water oxygens around apolar atoms (o) Asp-48 Cs (b) Ser-72 O3 (c) Asn-46 C 3 and ((i) Gly-71 C .

Fig. 2.53 The function goo ( ) for three different temperatures, as indicated next to each curve, computed by the method of molecular dynamics. The monotonically increasing curves give the running coordination number CN- [Redrawn with changes from Stillinger and Rahman (1971,1972).]...

All of the features of the radial distribution function were simulated by the model particles. There is a sharp first peak at R = R/a = 0.975, corresponding to = 2.75 A (with a = 2.82 A). The second peak occurs at jR = 1.69, corresponding to = 4.76 A, which is a little above the experimental value of about R = 4.6 A. Also, the average coordination number, computed up to the first minimum (following the first maximum), is 5.5, which is somewhat higher than the experimental value of about 4.4. Figure 6.32 also shows the running coordination number, i.e., the function... 

An example of the two Gaussian fit is shown in Fig. 4.8. The running coordination numbers were calculated based up to an r value where G r) became positive. These values are shown in brackets... 

In this section we have a closer look at ways to determine the limit of the first coordination shell and thereby also the preferred coordination number that in the energy-scaled version of the bond valence approach becomes an additional empirical parameter required to determine the expected equilibrium bond distance Coordination numbers Nc(M-0) for the oxides of 158 types of cations M were redetermined from 8829 reference cation enviromnents. To this end all cation oxygen distances up to 5-8 A were calculated for the reference structures and therefrom the running coordination number Arcn calculated as a function of the bond distance Rm < which should yield a plateau in-between coordination shells and correspondingly a minimum in a plot of the differentiated term JA/rcn(M-0)/ dRm vs. Rm - a synopsis of both plots was then used to identify the preferred coordination number Nq for cations (cf. the example M = in Fig. 11). 

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