Atomic size relative sizes

The space filling model developed by Corey, Pauling, and Koltun is also known as the CPK model, or scale model [197], It shows the relative volume (size) of different elements or of different parts of a molecule (Figure 2-123d). The model is based on spheres that represent the "electron cloud . These atomic spheres can be determined from the van der Waals radii (see Section 2.10.1), which indicate the most stable distance between two atoms (non-bonded nuclei). Since the spheres are all drawn to the same scale, the relative size of the overlapping electron clouds of the atoms becomes evident. The connectivities between atoms, the bonds, are not visualized because they are located beneath the atom spheres and are not visible in a non-transparent display (see Section 2.10). In contrast to other models, the CPK model makes it possible to visualize a first impression of the extent of a molecule. 

As with the molecular connectivity indices, higher-order shape indices have also been defined. The kappa indices themselves do not include any information about the identity of the atoms. This is the role of the kappa-alpha indices. Tlie alpha value for each atom is a measure of its size relative to some standard (chosen to be the sp -hybridised carbon) ... 

The medium-size rings (7 to 12 ring atoms) are relatively free of angle strain and can easily take a variety of spatial arrangements. They are not large enough to avoid all nonbonded interactions between atoms. 

Van der Waals interactions 0.4-4.0 0.2 Strength depends on the relative size of the atoms or molecules and the distance between them. The size factor determines the area of contact between two molecules The greater the area, the stronger the interaction. 

In metals, the distance between the individual atoms in the lattice is of the order of 0-4 nm and only atoms of very small size are able to penetrate interstitially. This takes place, for instance, in the diffusion of hydrogen into iron, and of carbon into austenite, etc. This type of interstitial diffusion is usually rapid, since the inward movement of the solute atoms is relatively unhampered. 

The electron configuration or orbital diagram of an atom of an element can be deduced from its position in the periodic table. Beyond that, position in the table can be used to predict (Section 6.8) the relative sizes of atoms and ions (atomic radius, ionic radius) and the relative tendencies of atoms to give up or acquire electrons (ionization energy, electronegativity). 

In each set, the atomic volumes increase going from halogen to inert gas to alkali metal, as shown graphically in Figure 6-9c. Figure 6-10 shows models constructed on the same scale to show the relative sizes of atoms indicated by the atomic volumes and by the packing of the ions in the ionic solids. 

If the ionization energy E is regarded as a measure of the distance between the electron and the nuclear charge, what do the ionization energies of Be and Ba indicate about the relative sizes of the two atoms ... 

FIGURE Bj4 Think of a fly at the center of this stadium that is the relative size of the nucleus of an atom if the atom were magnified to the size of the stadium. 

Figure 1.48 illustrates the trends in ionic radii, and Fig. 1.49 shows the relative sizes of some ions and their parent atoms. All cations are smaller than their parent... 

FIGURE 1.49 The relative sizes of some cations and anions compared with their parent atoms. Note that cations (pink) are smaller than their parent atoms (gray), whereas anions (green) are larger. 

FIGURE 3.33 A typical d molecular orbital energy-level diagram for a heteronuclear diatomic molecule AB the relative contributions of the atomic orbitals to the molecular orbitals are represented by the relative sizes of the spheres and the horizontal position of the boxes. In this case, A is the more electronegative of the two elements. 

It is to be expected that the relative values of the univalent crystal radius would be of significance with respect to physical properties involving atomic sizes. That this is true for the viscosity of the rare gases is seen from the radii evaluated by Herzfeld (Ref. 12, p. 436) from viscosity data He, 0.04 (0.93) Ne, 1.18 (1.12) Ar, 1.49 (1.54) Kr, 1.62 (1.69) Xe, 1.77 (1.90). (The values in parentheses are the univalent crystal radii.)... 

It should not be thought that the structure of every intermetallic compound can be treated so simply the discussion of such struetural features as the transfer of electrons between atoms, the occurrence of strained bonds, the significance of relative atomic sizes, and the electron-atom ratio (Hume-Rothery ratio) must, however, be postponed to later papers. 

Bearing in mind that the relative sizes of the ions permit isomorphous replacement of OH by F but not by Cl, we write with considerable confidence the formula (Si, Al, Fe, P)18O20(OH, F)laCl, which agrees well with analyses 1, 2, and 3. Inasmuch as aluminium (as well as phosphorus) may replace silicon with coordination number 4, it is evident that there are at least five silicon atoms in the unit, corresponding to the chemical formula... 

Neon and xenon are gases at room temperature, but both become liquids if the temperature is low enough. Draw a molecular picture showing the relative sizes and polarizabilities of atoms of neon and xenon, and use the picture to determine which substance has the lower boiling point. 

The zinc blende type is unknown for truly ionic compounds because there exists no pair of ions having the appropriate radius ratio. However, it is well known for compounds with considerable covalent bonding even when the zinc blende type is not to be expected according to the relative sizes of the atoms in the sense of the above-mentioned considerations. Examples are CuCl, Agl, ZnS, SiC, and GaAs. We focus in more detail on this structure type in Chapter 12. 

The tendency to form solid solutions depends mainly on two factors, namely the chemical relationship between the elements and the relative size of their atoms. 

Although these projections of organic molecules on surfaces deemphasize the stereochemistry of the adsorbed species, they are easy to draw and properly reveal the relative sizes and locations of surface atoms and organic species. When greater stereochemistry is desired, three-dimensional drawings may be made as shown in Scheme 1.3. 

The relative size of atomic orbitals, which is found to increase as their energy level rises, is defined by the principal quantum number, n, their shape and spatial orientation (with respect to the nucleus and each other) by the subsidiary quantum numbers, Z and m, respectively. Electrons in orbitals also have a further designation in terms of the spin quantum number, which can have the values +j or — j. One limitation that theory imposes on such orbitals is that each may accommodate not more than two electrons, these electrons being distinguished from each other by having opposed (paired) spins, t This follows from the Pauli exclusion principle, which states that no two electrons in any atom may have exactly the same set of quantum numbers. 

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