Experimental bonded Ionic Radii

The difficulty of experimental determination of atomic radii comes from several reasons, mainly the blurring effect of thermal vibrations of atoms and the extreme complexity of theoretical interpretation of the experimental data [204]. Johnson [205, 206] noted that electron density of an atom in a metallic structure shows a 

At contacts of a cation (c) and an anion a), the outer electrons are affected by the nuclear charges resulting in the energies ZcVr and Z/ZVa, respectively. Because the former ratio is always larger than the latter, the electron cloud is shifted toward the cation. As a result, Z Vr decreases (as rc increases) and Z/Zfa increases (as decreases) this process will occur until the mutual influence of both ions is balanced. The equalization can be achieved in three ways [207]  

by changing the effective charges of ions until Zc = Za, at a constant bond length this gives Tc = ra, i.e. the bonded radii are equal to half the corresponding interatomic distances [208]  

by changing the bond length from the experimental value d to the sum of the covalent radii this allows to calculate the coefficients C = aoti in Eq. 1.23 for the ionic and covalent states and at Zc = Za makes possible to define the bond radii by the equation Cere = C d — Tc)  

by changing the interaction energies of ions Z /r, calculated from the linearly interpolated Z and C values and the corresponding radii, until Zc Zrc = Za Zfa. 

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The electron cloud around an atom makes the concept of atomic size somewhat imprecise. Even so, it is useful to refer to an atomic size or an atomic radius. Operationally, one can divide the experimentally determined distance between the centers of two chemically bonded atoms to arrive at the two atomic radii. If the bonding is covalent (see Chapter 9), the radius is called a covalent radius if the bonding is ionic, the radius is an ionic radius. The radius for a nonbonded situation may also be defined in terms of the distance of closest nonbonding approach and is called a van der Waals radius. These concepts of size are illustrated in Fig. 8-6. 

The following tables contain experimentally-determined commensurate structure parameters for alkali metal adsorption systems (only simple structures are listed). The temperatures quoted are the measurement temperature. The bond length quoted is the chemisorption bond length. Effective r (Eff r) is the chemisorption bond length minus the metalHc radius of the substrate atom. Excess r (Exc. r) is the Effective r minus the ionic radius of the alkali metal atom N is the coordination number of the alkali adatom. A coordination number denoted as indicates that due to surface reconstruction, an unambiguous assigmnent carmot be made. 

The calculation results of dissociation energy by the Eq. (4.7), given ion Table 4.2, demonstrated that Pc=flo- some molecules containing such elements as F, N and 0, the values of ion radius have been applied to register the bond ionic character for calculating Pg-parameter (in Table 4.2 marked with ). For such molecules as C, N, the calculations have been made by multiple bonds. In other cases the average values of bond energy have been applied. The calculated data do not contradict the experimental ones [2, 3]. 

A plot of the lattice constant a against the ionic radius is linear with positive deviations at the heaviest M (Tm, Yb, Lu). The occurrence of the structure is apparently determined by a combination of size effect and 4f electron bonding [20]. The influence of the interatomic distances (determined experimentally and calculated from ionic radii) on bond character and bond strength is discussed by [25], also see Lashkarev etal. [27] and Miller etal. [26]. 

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