Coordination number defined

The symbols suggested by Jensen, based on Niggli s proposals, describe the local coordination by means of coordination number ratios. For instance, a formula AEm/n will indicate a binary compound where m is the coordination number (defined as the nearest-neighbour number (NNN)) of atoms E around A and n is the similarly defined coordination number of A around E. 

NaCl, is the most common of the binary structures, with over one-half of the 400 compounds so far investigated having this structure. In this structure, the coordination number (defined as the number of nearest neighbors) for both cations and anions is 6. In the CsCl structure (Fig. 3.1 ), the coordination number for both ions is 8. ZnS exists in two polymorphs, namely, the zinc blende and the wurtzite structures shown in Fig. 3.1r and d, respectively. In these structures the coordination number is 4 that is, all ions are tetrahedrally coordinated. 

Va(r, t) is the instantaneous volume (see Figure 8.1), mANJ rj) is the instantaneous integrated coordination number defined as [39]... 

Thus the coordination number, defined as the number of bonds issuing from the atom under consideration, is not very useful to describe the structure of a molecule. 

Fig. 5.9. The conditional average binding energy as a function of the coordination number [defined in Eq. (5.37)] for a system of spherical particles with parameters a = 1.0, ejkT — 0.5. The density is indicated next to each curve.

The most important differences between the two curves in Fig. 6.8 are the following (1) The first coordination number, defined by... 

The coordination number, defined as the number of spheres in contact with any neighboring spheres, is used to characterize the voidage of packing. Table 2 lists the coordination numbers from 3 to 12 and its associated voidage. The coordination numbers of 4, 6, 8, 10, and 12 correspond to arrangements that are regular as shown in Table 1. 

There are two independent coordinates that define the plane of a loop. If the loop is phase inverting, one of these coordinates must be phase inverting, the other, phase preserving. Out of the infinite number of possible candidates, a convenient choice are reaction coordinates (Section I). Any one of the three reaction coordinates connecting two of the anchors can be used for the... 

The ratio to z depends only on (gag-, zjx, = 2/3 tga.g, and the ratio of x, /Xq has a constant value equal to 0.578. To clarify the trajectory equation of inclined jets for the cases of air supply through different types of nozzles and grills, a series of experiments were conducted. The trajectory coordinates were defined as the points where the mean values of the temperatures and velocities reached their maximum in the vertical cross-sections of the jet. It is important to mention that, in such experiments, one meets with a number of problems, such as deformation of temperature and velocity profiles and fluctuation of the air jet trajectory, which reduce the accuracy in the results. The mean value of the coefficient E obtained from experimental data (Fig. 7.25) is 0.47 0.06. Thus the trajectory of the nonisothermal jet supplied through different types of outlets can be calculated from... 

The term secondary valency has been superseded by the term coordination number . This may be defined as the number of donor atoms associated with the central metal atom or ion. For many years a distinction was made between coordination number in this sense and in... 

Coordination numbers higher than 6 are rare and in some cases are known to involve chelating N03 ions which not only have a small bite but, may also be coordinated asymmetrically so that the coordination number is not well defined. 

The coordination chemistry of the large, electropositive Ln ions is complicated, especially in solution, by ill-defined stereochemistries and uncertain coordination numbers. This is well illustrated by the aquo ions themselves.These are known for all the lanthanides, providing the solutions are moderately acidic to prevent hydrolysis, with hydration numbers probably about 8 or 9 but with reported values depending on the methods used to measure them. It is likely that the primary hydration number decreases as the cationic radius falls across the series. However, confusion arises because the polarization of the H2O molecules attached directly to the cation facilitates hydrogen bonding to other H2O molecules. As this tendency will be the greater, the smaller the cation, it is quite reasonable that the secondary hydration number increases across the series. 

Once the electronic Schrodinger equation has been solved for a large number of nuclear geometries (and possibly also for several electronic states), the PES is known. This can then be used for solving the nuclear part of the Schrodinger equation. If there are N nuclei, there are 3N coordinates that define the geometry. Of these coordinates, three describe the overall translation of the molecule, and three describe the overall rotation of the molecule with respect to three axes. Eor a linear molecule, only two coordinates are necessary for describing the rotation. This leaves 3N-6(5) coordinates to describe the internal movement of the nuclei, the vibrations, often chosen to be... 

S Tantalum and niobium are present in the crystal structure in the form of complex ions. The lowest coordination number, 6, corresponds to the formation of slightly distorted octahedrons. The linking and packaging of the octahedrons depends on the X Me ratio, where X is the total number of oxygen and fluorine atoms, and Me is the total number of tantalum or niobium ions as well as other metals that can replace tantalum or niobium in the octahedral polyhedron. The crystal structure type can be defined based on the X Me ratio, as follows ... 

In an ionic solid, the coordination number means the number of ions of opposite charge immediately surrounding a specific ion. In the rock-salt structure, the coordination numbers of the cations and the anions are both 6, and the structure overall is described as having (6,6)-coordination. In this notation, the first number is the cation coordination number and the second is that of the anion. The rock-salt structure is found for a number of other minerals having ions of the same charge number, including KBr, Rbl, MgO, CaO, and AgCl. It is common whenever the cations and anions have very different radii, in which case the smaller cations can fit into the octahedral holes in a face-centered cubic array of anions. The radius ratio, p (rho), which is defined as... 

The Number of Polyhedra with a Common Corner. The Electrostatic Valence Principle.—The number of polyhedra with a common corner can be determined by the use of an extended conception of electrostatic valence. Let ze be the electric charge of a cation and v its coordination number. Then the strength of the electrostatic valence bond going to each comer of the polyhedron of anions about it is defined as... 

The Fe(l1l) surface is composed of four-fold coordinated atoms and exposed second layer atoms that are seven-fold coordinated while the Fe(l10) and Fe(lOO) planes have only six-fold and four-fold coordinated atoms respectively. Here we have defined the coordination number as the number of nearest neighbor atoms. Dumesic s proposal that the seven-fold coordinated atom is an important component of the catalytically active site is not contradicted by our results ( ). It is also worth noting that the relative roughness or openess of the each plane follows the same progression as their catalytic activities. Table II also shows that the activity of each of the two less active surfaces was markedly enhanced by sputtering with Ar. It is possible that sputtering has exposed seven-fold coordinate atoms at the surface or that it is the roughness of the surface that is responsible for the structure senstivity of the reaction rate. 

The structure of a-C H films may be thus pictured as sp--carbon atoms in condensed aromatic clusters, dispersed in an sp- -rich matrix, which confers to the network its characteristic rigidity. This situation can also be regarded as a random covalent network in which the sp" clusters of a defined size take part in the structure as an individual composed atom with its corresponding coordination number [17]. Such kinds of models have been successfully used to describe the dependence of a-C H film mechanical properties on composition, hybridization, and sp" clustering [23]. 

In a stable ionic structure the valence (ionic charge) of each anion with changed sign is exactly or nearly equal to the sum of the electrostatic bond strengths to it from adjacent cations. The electrostatic bond strength is defined as the ratio of the charge on a cation to its coordination number. 

CaMo508 provides a link to calcium channels in biological systems. This mixed oxide contains Mo/O columns, of which groups of four define channels in which the Ca2+ cations reside. There is no clearly defined coordination number for these cations Ca-0 distances range from 2.39 A upwards, there being ten oxygens at fairly regularly spaced distances up to 3.04 A from the Ca2+ (117). 

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