Directional character

It is sometimes convenient to combine aos to form hybrid orbitals that have well defined directional character and to then form mos by combining these hybrid orbitals. This recombination of aos to form hybrids is never necessary and never provides any information that could be achieved in its absence. However, forming hybrids often allows one to focus on those interactions among directed orbitals on neighboring atoms that are most important. 

A classic feature of erosion-corrosion is the directional character of the metal loss. The metal loss will be oriented along the direction of fluid flow or according to turbulence patterns. However, other corrosion modes may produce directionality in metal loss and could be confused... 

This type of argument leads us to picture a metal as an array of positive ions located at the crystal lattice sites, immersed in a sea of mobile electrons. The idea of a more or less uniform electron sea emphasizes an important difference between metallic bonding and ordinary covalent bonding. In molecular covalent bonds the electrons are localized in a way that fixes the positions of the atoms quite rigidly. We say that the bonds have directional character— the electrons tend to remain concentrated in certain regions of space. In contrast, the valence electrons in a metal are spread almost uniformly throughout the crystal, so the metallic bond does not exert the directional influence of the ordinary covalent bond. 

The nonlocalized or mobile electrons account for the many unique features of metals. Since metallic bonds do not have strong directional character, it is not surprising that many metals can be easily deformed without shattering their crystal structure. Under the influence of a stress, one... 

We have already learned that metals may be deformed easily and we have explained this in terms of the absence of directional character in metallic bonding. In view of this principle, it is not surprising that two-element or three-element metallic crystals exist. In some of these, regular arrangements of two or more types of atoms are found. The composition then is expressed in simple integer ratios, so these are called metallic compounds. In other cases, a fraction of the atoms of the major constituent have been replaced by atoms of one or more other elements. Such a substance is called a solid solution. These metals containing two or more types of atoms are called alloys. 

Ions stack together in the regular crystalline structure corresponding to lowest energy. The structure adopted depends on the radius ratio of cation and anion. Covalent character in an ionic bond itnposes a directional character on the bonding. 

Figure 4. Association of 812(8,2)12 polyhedra in 8 5 showing (a) the directed character of intericosahedral bonds, as well as the existence of large voids in the boron framework, (b) the filling of voids by additional 8 and Y atoms (partial projection onto the ac plane according to ref. 9).

Note that both force and area are vectors, whereas pressure is a scalar. Hence the directional character of the force is determined by the orientation of the surface on which the pressure acts. That is, the component of force acting in a given direction on a surface is the integral of the pressure over the projected component area of the surface, where the surface vector (normal to the surface component) is parallel to the direction of the force [recall that pressure is a negative isotropic stress and the outward normal to the (fluid) system boundary represents a positive area]. Also, from Newton s third law ( action equals reaction ), the force exerted on the fluid system boundary is of opposite sign to the force exerted by the system on the solid boundary. 

Note that the vector (directional) character of the convected momentum terms (i.e., mV) is that of the velocity, because m is a scalar (i.e., tit = pV A is a scalar product). 

Given the intensity of discussion of both creation and intelligent design, both of which propose an outside influence on evolution which has no simple scientific explanation, we must make our position clear. As far as we can see the directional character of evolution of our ecosystem, illustrated by the cone on the cover of this book, requires only one act for which we can see no explanation. We know of no cause of the Big Bang and the limitations it imposed on the cosmos observed in the laws of Nature. It is these laws alone which we use in our analysis. The laws contain possibilities both of systematic development which is the centre of our discussion and of random events. The first we relate, in the evolution of life, to chemotypes and the second to the appearance of species within chemotypes, see the cover of this book. At no time in this chapter, or in any other chapter do we invoke any other kind of activity. 

Note that the three wave functions arising from the p py, and pz orbitals are identical except for the directional character as indicated by the subscripts. Therefore, they must represent a triply degenerate set (the t2g set, which will be apparent later). 

Finally, an important if tentative conclusion emerges concerning the symmetry of distribution functions, which could be relevant to the general theory of polarization and to current ideas about liquid structure. Theoretical analysis in terms of radially symmetric models does not necessarily tell us about the structure of a system, because the short-range forces, by their very nature, have a directional character which is not lost in any averaging process. Is it this averaged directional force which is responsible for structure in liquids and solutions ... 

The properties of a substance depend in part upon the type of bonds, between the atoms of the substance and in part upon the atomic arrangement and the distribution of the bonds. The atomic arrangement is itself determined to a great extent by the nature of the bonds the directed character of covalent bonds (as in the tetrahedral carbon atom) plays an especially important part in determining the configura-... 

The size and shape of molecules are as much a part of molecular structure as is the order in which the component atoms are bonded. Contrary to the impression you may get from structural formulas, complex molecules are not flat and formless, but have well-defined spatial arrangements that are determined by the lengths and directional character of their chemical bonds. It is not easy to visualize the possible arrangements of the bonds in space and it is very helpful to have some kind of mechanical model that reflects the molecular geometry, including at least an approximation to the relative lengths of the bonds. Ball-and-stick models such as the ones used by Patemo (Section 1-ID) fill this purpose admirably. 

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