Atomic size considerations

A systematic approach to the crystal chemistry of borides is possible on the simple basis of atom size considerations, as well as the tendency of B to form covalent skeletons. 

In addition to electronegativity and atomic size considerations, the other important factor governing the structure of carbides is the nature of the bond between the carbon atom and the other element forming the compound. One should note that bonding, electronegativity, and atom size are all interrelated. 

From Tsai s pioneering discoveries [25,27], we know that atomic size, electronegativity, and valence electron counts play substantial roles in the formation of QCs. These criteria are expressed by the Hume-Rothery rules [30,31]. However, three additional highlights are also important in the consideration of possible candidate systems, at least from the viewpoint of chemists. 

These three structures are the predominant structures of metals, the exceptions being found mainly in such heavy metals as plutonium. Table 6.1 shows the structure in a sequence of the Periodic Groups, and gives a value of the distance of closest approach of two atoms in the metal. This latter may be viewed as representing the atomic size if the atoms are treated as hard spheres. Alternatively it may be treated as an inter-nuclear distance which is determined by the electronic structure of the metal atoms. In the free-electron model of metals, the structure is described as an ordered array of metallic ions immersed in a continuum of free or unbound electrons. A comparison of the ionic radius with the inter-nuclear distance shows that some metals, such as the alkali metals are empty i.e. the ions are small compared with the hard sphere model, while some such as copper are full with the ionic radius being close to the inter-nuclear distance in the metal. A consideration of ionic radii will be made later in the ionic structures of oxides. 

The rather complex structure of the compound NaZn13 was studied by Ketelaar (1937) and by Zintl and Haucke (1938). Every Na atoms is surrounded by 24 Zn atoms at the same distance. The lattice parameters of several MeZn13 compounds pertaining to this structural type are, in a first approximation, independent of the size of the alkali (or alkaline earth) metal atom. Similar consideration may be made for the MeCd13 compounds. Zintl, therefore, considered the fundamental component of this crystal structure to be a framework of Zn (or Cd) atoms with the alkali (or alkaline earth) metal atoms occupying the holes of the framework. However notice (Nevitt 1967) that in compounds MeX13 radius ratios (rMe/rx) deviating by more than about 15% from the mean value 1.54 are unfavourable for the occurrence of the structure. 

An attempt has also been made to derive the binding energy of atoms in clusters from a measurement of the critical energy deficit of cluster ions. For n+ cluster ions of m atom size, from consideration of Born-Haber energy cycle, the critical ion energy deficit can be easily shown to be given by100... 

It is well known that the elements in framework of zeolite molecular sieves greatly influence the properties and behaviors of these materials [1-3], The introduction of heteroatoms into the framework has become one of most active fields in study of zeolites. The investigations were mostly focused on the methods to introduce heteroatoms into the framework (for examples, hydrothermal synthesis and post-synthesis), the mechanisms for incorporations, the effect of heteroatoms on the acid-base properties and the catalytic features of modified samples [1-10]. Relatively less attention was paid to the effect of treatment process on the porous properties of samples although the incorporation of heteroatoms, especially by the so-called post-synthesis, frequently changes the distribution of pore size. Recently, we incorporated Al, Ga and B atoms into zeolites (3 by the post-synthesis in an alkaline medium named alumination, galliation and boronation, respectively. It was found that different trivalent elements inserted into the [3 framework at quite different level. The heteroatoms with unsuitable atom size and poor stability in framework were less introduced, leading to that a considerable amount of framework silicon were dissolved under the action of base and the mesopores in zeolite crystal were developed. As a typical case, the boronation of zeolites (3 and the accompanied formation of mesopores are reported in the present paper. 

Usually the radius of curvature p at the sharp notch of the crack is determined by the atomic sizes and is very small. It is immediately evident that the stress concentration at the sharp notches of the microcracks can become extremely large due to the above stress intensity factor, and the fracture should start propagating from there. Although this analysis indicates clearly where the instabilities should occur, it is not sufficient to tell us when the instability does occur and the fracture propagation starts. This requires a detailed energy balance consideration. 

Steric aspects The fluorine atom is considerably smaller than the rest of the halogen atoms. Seen from the steric point of view it resembles more hydrogen than chlorine (Table 15.17). Effectively fluoro-derivatives differ from the other halogenated derivatives because fluorine forms with carbon particularly stable bonds and, in contrast to other halogens, is only rarely ionized or displaced. Because it is both chemically inert and of small size organic fluorine is often compared to hydrogen. 

From one vibration to another there can be considerable variation and, generally, the displacement of electron rich atoms will influence the spectral intensities more than electron poor atoms. Thus, since polarisability increases with atomic size, Raman spectra involving the heavier atoms are easier to observe, as demonstrated by the weakness of hydrogen s vibrational features in metal hydridocarbonyls ( 11.2.6). It also follows that the optically strong features of a spectmm may mask weaker vibrations of interest, a common problem in intercalate and catalytic systems. 

---