Coordination number distributions

After the thermalization run, configuration sampling begins to obtain RDCF and coordination number distribution. Figure 11 shows one single system configuration, mean RDCF, coordination number distribution and configuration structure factor S(q) with an example. 

Figure 10-6. (a) Ion-oxygen radial distribution functions obtained from a QMCF MD simulation of Pd(II) (solid line) and Pt(II) (dashed line) in aqueous solution. Coordination number distribution within the first shell for (b) Pd(II) and (c) Pt(II) and associated exchange plots for (d) Pd(II) and (e) Pt(II)... 

Figure 10-7. (a) Snapshot of a QMCF MD simulation of Hg2+ in aqueous solution, (b) Hg(I)-oxygen solid line) and Hg(I)-hydrogen dashed line) radial distribution functions, (c, d) Coordination number distribution within the first shell for both Hg(I) atoms and associated exchange plots (e, f)... 

As a starting structure we used a crystobalite-like structure as this crystalline form is more stable at the high temperature of the flame synthesis. As is well known, the particle surface is covered by hydroxyl groups which terminate all broken bonds on a particle body. To present the particle structure as a whole the interatomic distance distribution function as a sum of sets of Gauss functions with a small broadening parameter of 0.05 A was used. To present the particle chemical behavior as a whole the coordination number distribution for all atom types has been used. 

In Fig. 1 the space structure, the interatomic distance and coordination number distribution function for the most regular diamond-like silicon dioxide structure is presented. This cluster was constructed as 3x3x3 extended crystobalite cells and it containings 708 atoms. This cluster has been used as a reference for highly regular structures. 

Fig. 1. The space structure, the interatomic distance and coordination number distribution function for the most regular diamond-like silicon dioxide structure.

No obvious separation of molecules into network vs interstitial types suggests itself. This fact is consistent with the single-peak character of the hydrogen-bond coordination number distributions exhibited in Fig. 19. It also seems to diminish the validity of the interstitial models that have been proposed to explain liquid water. 

The structure of LiTa02F2, as reported by Vlasse et al. [218], is similar to a ReC>3 type structure and consists of triple layers of octahedrons linked together through their vertexes. The layers are perpendicular to the c axis, and each layer is shifted, relative to the layer below, by half a cell in the direction (110). Lithium atoms are situated in the centers of the tetragonal pyramids (coordination number = 5). The other lithium atoms are statistically distributed along with tantalum atoms (coordination number = 6) at a ratio of 1 3. The sequence of the metal atoms in alternating layers is (Ta-Li) - Ta - (Ta-Li). Positions of oxygen and fluorine atoms were not determined. The main interatomic distances are (in A) Ta-(0, F) - 1.845-2.114 Li-(0, F) - 2.087-2.048 (O, F)-(0,F) - 2.717-2.844. 

The structure leads to a general formula for the micas namely, KXMY.1Oio(OH,r )2, with 2 < < 3, in which X represents cations of coordination number 6 (Al+3, Mg+, Fe++, Fe+3, Mn++, Mn+3, Ti+ Li+, etc.) and Y cations of coordination number 4 (Si+4, A1+3, etc.). The subscript n can have any value between 2 (hydrargillite layer) and 3 (complete octahedral layer). K+ can be partially replaced by Na+ and possibly to some extent by Ca++. This formula represents satisfactorily the.numerous recently published mica analyses almost without exception.6 The distribution of the various ions X and Y must be such as to give general agreement with the electrostatic valence rule. 

The X-ray absorption fine structure (XAFS) methods (EXAFS and X-ray absorption near-edge structure (XANES)) are suitable techniques for determination of the local structure of metal complexes. Of these methods, the former provides structural information relating to the radial distribution of atom pairs in systems studied the number of neighboring atoms (coordination number) around a central atom in the first, second, and sometimes third coordination spheres the... 

The distribution of the observed higher borides among the five structural types (MB2, MB4, MBg, MB]2 and Mg ) presented in Table 1, which shows correlations with the metallic radius r. values of which are in order of decreasing magnitude (r, corresponds to coordination number 12). In order to discuss the existence of the actinide borides, the table also shows the unit cell volume V of the borides MB4, MBg and MB,2. 

Rumpf (R4) has derived an explicit relationship for the tensile strength as a function of porosity, coordination number, particle size, and bonding forces between the individual particles. The model is based on the following assumptions (1) particles are monosize spheres (2) fracture occurs through the particle-particle bonds only and their number in the cross section under stress is high (3) bonds are statistically distributed across the cross section and over all directions in space (4) particles are statistically distributed in the ensemble and hence in the cross section and (5) bond strength between the individual particles is normally distributed and a mean value can be used to represent each one. Rumpf s basic equation for the tensile strength is... 

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