23.5 Metallic Bonding

In our discussion of metallurgy we have confined ourselves to discussing the methods employed for obtaining metals in pure form. Metallurgy is also concerned with understanding the properties of metals and with developing useful new materials. As with any branch of science and engineering, our ability to make advances is coupled to our understanding of the fundamental properties of the systems with which we work. At several places in the text we have referred to the differences between metals and nonmetals with regard to both physical and chemical behavior. Let's now consider the distinctive properties of metals and then relate these properties to a model for metallic bonding.

Physical Properties of Metals

You have probably held a length of copper wire or an iron bolt at some time. Perhaps you have even seen the surface of a freshly cut piece of sodium metal. These substances, although distinct from one another, share certain similarities that enable us to classify them as metallic. A fresh metal surface has a characteristic luster. In addition, metals that we can handle with bare hands have a characteristic cold feeling related to their high heat conductivity. Metals also have high electrical conductivities; electrical current flows easily through them. Current flow occurs without any displacement of atoms within the metal structure and is due to the flow of electrons within the metal. The heat conductivity of a metal usually parallels its electrical conductivity. For example, silver and copper, which possess the highest electrical conductivities, also possess the highest heat conductivities. This observation suggests that the two types of conductivity have the same origin in metals, which we will soon discuss.

Most metals are malleable, which means that they can be hammered into thin sheets, and ductile, which means that they can be drawn into wires (Figure 23.12). These properties indicate that the atoms are capable of slipping with respect to one another. Ionic solids or crystals of most covalent compounds do not exhibit such behavior. These types of solids are typically brittle and fracture easily. Consider, for example, the difference between dropping an ice cube and a block of aluminum metal onto a concrete floor.

Most metals form solid structures in which the atoms are arranged as close-packed spheres. For example, copper possesses a cubic close-packed structure in which each copper atom is in contact with 12 other copper atoms. The number of valence-shell electrons available for bond formation is insufficient for a copper atom to form an electron-pair bond to each of its neighbors. If each atom is to share its bonding electrons with all its neighbors, these electrons must be able to move from one bonding region to another.

Electron-Sea Model for Metallic Bonding

One very simple model that accounts for some of the most important characteristics of metals is the electron-sea model. In this model the metal is pictured as an array of metal cations in a "sea" of valence electrons, as illustrated in Figure 23.13. The electrons are confined to the metal by electrostatic attractions to the cations, and they are uniformly distributed throughout the structure. However, the electrons are mobile, and no individual electron is confined to any particular metal ion. When a metal wire is connected to the terminals of a battery, electrons flow through the metal toward the positive terminal and into the metal from the battery at the negative terminal. The high heat conductivity of metals is also accounted for by the mobility of the electrons, which permits ready transfer of kinetic energy throughout the solid. The ability of metals to deform (their malleability and ductility) can be explained by the fact that metal atoms form bonds to many neighbors. Changes in the positions of the atoms brought about in reshaping the metal are partly accommodated by a redistribution of electrons.

Figure 23.13 Schematic illustration of the electron-sea model of the electronic structure of metals. Each sphere is a positively charged metal ion.

The electron-sea model, however, does not adequately explain all properties. For example, according to the model, the strength of bonding between metal atoms should increase as the number of valence electrons increases, resulting in a corresponding increase in melting points. However, the group 6B metals (Cr, Mo, W), which are in the center of the transition metals, have the highest melting points in their respective periods. The melting points on either side of the center are lower (Table 23.2), which implies that the strength of metallic bonding first increases with increasing number of electrons and then decreases. Similar trends are seen in other physical properties of the metals, such as the heat of fusion, hardness, and boiling point.

In order to explain some of the physical properties of metals, we need a more refined model than the electron-sea model to describe metallic bonding. We obtain a better model by applying the concepts of molecular-orbital theory to metals.

Molecular-Orbital Model for Metals

In considering the structures of molecules such as benzene, we saw that in some cases electrons are delocalized, or distributed, over several atoms. It is useful to think of the bonding in metals in a similar way. The valence atomic orbitals on one metal atom overlap with those on several nearest neighbors, which in turn overlap with atomic orbitals on still other atoms.

We saw in Section 9.7 that the overlap of atomic orbitals leads to the formation of molecular orbitals. The number of molecular orbitals is equal to the number of atomic orbitals that overlap. In a metal the number of atomic orbitals that interact or overlap is very large. Thus, the number of molecular orbitals is also very large. Figure 23.14 shows schematically what happens as increasing numbers of metal atoms come together to form molecular orbitals. As overlap of atomic orbitals occurs, bonding and antibonding molecular-orbital combinations are formed. The energies of these molecular orbitals lie at closely spaced intervals in the energy range between the highest- and lowest-energy orbitals. Consequently, interaction of all the valence atomic orbitals of each metal atom with the orbitals of adjacent metal atoms gives rise to a huge number of molecular orbitals that extend over the entire metal structure. The energy separations between these metal orbitals are so tiny that for all practical purposes we may think of the orbitals as forming a continuous band of allowed energy states, referred to as an energy band, as shown in Figure 23.14.

Figure 23.14 Schematic illustration of how the number of molecular orbitals increases and their energy spacing decreases as the number of interacting atoms increases. In metals these interactions form a nearly continuous band of molecular orbitals that are delocalized throughout the metal lattice. The number of electrons available does not completely fill these orbitals.

The electrons available for metallic bonding do not completely fill the available molecular orbitals; we can think of the energy band as a partially filled container for electrons. The incomplete filling of the energy band gives rise to characteristic metallic properties. The electrons in orbitals near the top of the occupied levels require very little energy input to be "promoted" to still higher energy orbitals, which are unoccupied. Under the influence of any source of excitation, such as an applied electrical potential or an input of thermal energy, electrons move into previously vacant levels and are thus freed to move through the lattice, giving rise to electrical and thermal conductivity.

Trends in properties of transition metals, such as the melting point (Table 23.2), can be readily explained by the molecular-orbital model. Recall the molecular-orbital description of second-period diatomic molecules. Half of the molecular orbitals were bonding, and half were antibonding. As we proceed across the period, the bond order generally increases until N2, at which point it begins to decrease. This trend occurs because N2 possesses the right number of electrons to completely fill the bonding molecular orbitals while leaving the higher-energy antibonding molecular orbitals empty.

The energy states that lead to the band for transition metals can likewise be divided roughly into two types: lower-energy states that result from metal-metal bonding interactions, and those at higher energy that result from metal-metal antibonding interactions. The group 6B metals (Cr, Mo, W) possess the correct number of electrons to fill the portion of the energy band that results from metal-metal bonding interactions and to leave the metal-metal antibonding orbitals empty. Metals with a smaller number of electrons than the group 6B metals have fewer metal-metal bonding orbitals occupied. Metals with a greater number of electrons than the group 6B metals have more metal-metal antibonding orbitals occupied. In each case the metal-metal bonding should be weaker than that of the group 6B metals, consistent with the trends in melting point and other properties. Of course, factors other than the number of electrons (such as atomic radius, nuclear charge, and the particular packing structure of the metal) also play a role in determining the properties of metals.

This molecular-orbital model of metallic bonding (or band theory, as it is also called) is not so different in some respects from the electron-sea model. In both models the electrons are free to move about in the solid. However, the molecular-orbital model is more quantitative than the simple electron-sea model; many properties of metals can be accounted for by quantum mechanical calculations using molecular-orbital theory.