Simple Atomic Structure

To understand the structures of organic molecules and how these molecules react, we need a mental picture of the bonds that hold the atoms together. Several different models or pictures are used to describe the chemical bond. Which picture we use depends on what we are trying to accomplish. In this chapter we will learn about the simplest picture, which describes a covalent bond as a shared pair of electrons and uses Lewis structures to represent molecules. Although this model is not complex, it will be adequate for most of our uses. (In Chapter 3 we will look at a more complex model for bonding.) Most of what is covered in this chapter should be a review. 

In the simplest model, bonding can be considered to result from the special stability associated with a filled outer shell of electrons. The noble gases, such as helium, neon, and argon, which already have a filled outer shell of electrons, have little tendency to form bonds. Atoms of the other elements, however, seek to somehow attain a filled outer shell of electrons. The two ways in which they accomplish this goal result in two types of bonding ionic and covalent. 

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Boron compounds with nonmetals, i.e., boron hydrides, carbides, nitrides, oxides, silicides, and arsenides, show simple atomic structures. For example, boron nitride (BN) can be found in layered hexagonal, rhombohedral, and turbostratic or denser cubic and wurtzite-like structures, as well as in the form of nanotubes and fullerenes. Boron compounds with metalloids also differ from borides by electronic properties being semiconductors or wide-gap insulators. 

The simple atomic structures found in the noble gases generally have similar physical properties to simple molecular gases. 

Liquid metals, because of their simple atomic structure, suffer no radiation damage. 

Knowing the lattice is usually not sufficient to reconstruct the crystal structure. A knowledge of the vectors (a, b, c) does not specify the positions of the atoms within the unit cell. The positions of the atoms withm the unit cell is given by a set of vectors i., = 1, 2, 3... u where n is the number of atoms in the unit cell. The set of vectors, x., is called the basis. For simple elemental structures, the unit cell may contain only one atom. The lattice sites in this case can be chosen to correspond to the atomic sites, and no basis exists. 

This structure is called close packed because the number of atoms per unit volume is quite large compared with other simple crystal structures. 

The atomic structure of a surface is usually not a simple tennination of the bulk structure. A classification exists based on the relation of surface to bulk stnicture. A bulk truncated surface has a structure identical to that of the bulk. A relaxed surface has the synnnetry of the bulk stnicture but different interatomic spacings. With respect to the first and second layers, lateral relaxation refers to shifts in layer registry and vertical relaxation refers to shifts in layer spacings. A reconstructed surface has a synnnetry different from that of the bulk synnnetry. The methods of stnictural analysis will be delineated below. 

Descriptors have to be found representing the structural features which are related to the target property. This is the most important step in QSPR, and the development of powerful descriptors is of central interest in this field. Descriptors can range from simple atom- or functional group counts to quantum chemical descriptors. They can be derived on the basis of the connectivity (topological or... 

We begin by looking at the smallest scale of controllable structural feature - the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). 

It is possible to write a simple Lewis structure for foe S042- ion, involving only single bonds, which follows foe octet rule. However, Linus Pauling and others have suggested an alternative structure, involving double bonds, in which foe sulfur atom is surrounded by six electron pairs. 

This chapter builds an understanding of atomic structure in four steps. First, we review the experiments that led to our current nuclear model of the atom and see how spectroscopy reveals information about the arrangement of electrons around the nucleus. Then we describe the experiments that led to the replacement of classical mechanics by quantum mechanics, introduce some of its central features, and illustrate them by considering a very simple system. Next, we apply those ideas to the simplest atom of all, the hydrogen atom. Finally, we extend these concepts to the atoms of all the elements of the periodic table and see the origin of the periodicity of the elements. 

Although the comer atoms must move apart to convert a simple cube into a body-centered cube, the extra atom in the center of the stracture makes the body-centered cubic lattice more compact than the simple cubic structure. All the alkali metals, as well as iron and the transition metals from Groups 5 and 6, form ciystals with body-centered cubic structures. 

There are at least four types of chemical bonding. Some crystals have open atomic structures, while others are close-packed. Also, many crystals are anisotropic. Therefore, although making hardness measurements is relatively simple, understanding the measured values is not simple at all. 

The principal intention of the present book is to connect mechanical hardness numbers with the physics of chemical bonds in simple, but definite (quantitative) ways. This has not been done very effectively in the past because the atomic processes involved had not been fully identified. In some cases, where the atomic structures are complex, this is still true, but the author believes that the simpler prototype cases are now understood. However, the mechanisms change from one type of chemical bonding to another. Therefore, metals, covalent crystals, ionic crystals, and molecular crystals must be considered separately. There is no universal chemical mechanism that determines mechanical hardness. 

Although we have described the structures of several molecules in terms of hybrid orbitals and VSEPR, not all structures are this simple. The structures of H20 (bond angle 104.4°) and NH3 (bond angles 107.1°) were described in terms of sp3 hybridization of orbitals on the central atom and comparatively small deviations from the ideal bond angle of 109° 28 caused by the effects of unshared pairs of electrons. If we consider the structures of H2S and PH3 in those terms, we have a problem. The reason is that the bond angle for H2S is 92.3°, and the bond angles in PH3 are 93.7°. Clearly, there is more than a minor deviation from the expected tetrahedral bond angle of 109° 28 caused by the effect of unshared pairs of electrons ... 

We can determine the amount of empty space in the simple cubic (a space-filling model is shown in Figure 7.15) structure by considering it to have an edge length l, which will be twice the radius of an atom. Therefore, the radius of the atom is 1/2, so the volume of one atom is (4/3)7r(l/2)3 = 0.52413, but the volume of the cube is P. From this we see that because the cube contains only one atom that occupies 52.4% of the volume of the cube, there is 47.6% empty space. Because of the low coordination number and the large amount of empty space, the simple cubic structure does not represent an efficient use of space and does not maximize the number of metal atoms bonded to each other. Consequently, the simple cubic structure is not a common one for metals. 

To illustrate this, take the situation in a very common and relatively simple metal structure, that of copper. A crystal of copper adopts the face-centered cubic (fee) structure (Fig. 2.8). In all crystals with this structure slip takes place on one of the equivalent 111 planes, in one of the compatible <110> directions. The shortest vector describing this runs from an atom at the comer of the unit cell to one at a face center (Fig. 3.10). A dislocation having Burgers vector equal to this displacement, i <110>, is thus a unit dislocation in the structure. 

For an fee lattice a particularly simple surface structure is obtained by cutting the lattice parallel to the sides of a cube that forms a unit cell (see Fig. 4.6a). The resulting surface plane is perpendicular to the vector (1,0,0) so this is called a (100) surface, and one speaks of Ag(100), Au(100), etc., surfaces, and (100) is called the Miller index. Obviously, (100), (010), (001) surfaces have the same structure, a simple square lattice (see Fig. 4.7a), whose lattice constant is a/ /2. Adsorption of particles often takes place at particular surface sites, and some of them are indicated in the figure The position on top of a lattice site is the atop position, fourfold hollow sites are in the center between the surface atoms, and bridge sites (or twofold hollow sites) are in the center of a line joining two neighboring surface atoms. 

The three cases discussed here are the simplest and most important surface structures. Other surface planes, such as (210) or (311), have a lower density of surface atoms and tend to be less stable. In a few cases, notably gold, even these simple surfaces are not stable but reconstruct, forming denser surface structures with a lower surface energy. Adsorption of a species usually lifts this reconstruction, i.e. the original simple surface structure is restored [2], We will discuss an example in Chapter 15. 

In the early part of the twentieth century, then, a simple model of atomic structure became accepted, now known as the Rutherford nuclear model of the atom, or, subsequently, the Bohr-Rutherford model. This supposed that most of the mass of the atom is concentrated in the nucleus, which consists of protons (positively charged particles) and neutrons (electrically neutral particles, of approximately the same mass). The number of protons in the nucleus is called the atomic number, which essentially defines the nature of... 

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