Chemical Education Today
Commentary
In Defense of the Metallic Bond John J. Gilman Materials Science and Engineering, University of California at Los Angeles, Los Angeles, CA 90095;
[email protected] The Issue A few years ago, J. K. Burdett suggested that the term “metallic bond” be dropped from the chemist’s lexicon (1). This was seconded in an adjacent paper by L. C. Allen (2). More recently, Burdett made the same suggestion in two of his books (3). The gist of his argument is that metals are simply extended molecules and can be described in terms of molecular orbitals without a need for a “metallic bond”. This has some merit, but is rather parochial. Since a strong majority (~3/4) of the chemical elements are metals, why not recognize the metallic bond as the general case with ionic and covalent bonds as special cases? In the covalent special case the bonding orbitals and electron pairs happen to be matched, but typically they are not. Ductility—Quintessence of a Metal From the viewpoint of metallurgy, an unfortunate trend of the past several decades seems to have contributed to Burdett’s position. It started 50 years ago with the invention of the transistor. This focused massive attention by physicists on the role of metals as electrical conductors in electronic devices. As a result, the definition of a metal became shifted from its traditional emphasis on mechanical properties (which developed during the ages of native metals, bronzes, cast irons, steels, and light alloys) to an emphasis on electrical properties. But the uniqueness of metals comes from their ductility (or malleability), not from their electrical conductivity. That is why the preponderance of their consumption has been associated with their structural properties. It is misleading to call conductive polymers “organic metals”, “synthetic metals”, and similar objectionable terms. Another unfortunate trend comes from oversimplification of the theory of metals. This has resulted, in part, from the popularity of the density functional theory. It is not directly the fault of the theory, but comes from some of its applications. Probability amplitudes (from which electron densities are derived) are replaced in this theory by the electron densities themselves. However, density is a scalar quantity, so of itself, it does not contain the tensorial information that is so important in the behavior of solid metals. Phase information also tends to get lost. From high-precision calculations of electron densities, gradients can be obtained that yield the tensorial properties, but these calculations are lengthy and hence often not done. Many computations have also tended to obfuscate understanding of cohesion by applying pair potentials to the theory of metals. Pair potentials are assumed, of course, in simple molecular orbital theory. They are valid for diatomic molecules, but little else. Which is why chemists dealing with larger molecules often turn to VSEPR theory. For solids (metals), elasticity theory yields tensorial information. 1330
Most real metals are polycrystalline aggregates, and even for the most simple crystals (cubic ones), three elastic coefficients are the minimum needed to specify the response of a specimen to strains. One coefficient (the bulk modulus) is needed for changes of volume, and two coefficients for shear strains. If a crystal is described in terms of pair potentials, then a specific relationship between the two shear coefficients must exist. It is called the Cauchy condition after the renowned French mathematician who deduced it. Its validity was proven experimentally by Voigt in about 1887. It is not satisfied by most metals. Only a few per cent of the metallic elements satisfy it. Just as there is no such thing as a “purely covalent” molecule or a “purely ionic” crystal, there are no “purely metallic” metals. All three categories represent limiting cases. All of them mix to form hybrids. All are needed in the chemical lexicon. Chemists have traditionally dealt with gases and liquids far more than with solids, but metal gases and liquids are studied much less than metallic solids. All solids are more complex than gases or liquids, and solid metals are particularly complex. The complexity does not arise in spite of the metallic bond, but because of it. Because it is not localized to the regions between atoms and there are sometimes a large number of wavelengths associated with it, the metallic bond leads to various collective effects. Among them are ferromagnetism, antiferromagnetism, charge density waves, plasmons, and the behavior of dislocations. Some of these are not deeply understood. Metallic Bonds in Technology The distinction between metallic bonds and covalent bonds has had nontrivial effects in technology. For example, it destroyed one great corporation, and would have destroyed another except for a taxpayer rescue. Rolls Royce, Ltd. was persuaded to use a graphite composite (covalent bonds) to make the compressor blades in a new aircraft gas-turbine design, instead of titanium (metallic bonds). When the designs and tooling were complete and it was time to begin deliveries to airframe makers such as Lockheed Aircraft, it was discovered that the graphite blades were too brittle to pass the “bird test” in which the carcass of a bird is thrown into the engine intake. This crude, but crucial, test stripped out the compressor blades. A major redesign was required, resulting in lengthy delivery delays. Consequently, Rolls Royce became bankrupt, and never fully recovered. A principal customer, Lockheed, was left without the engines it needed for its delivery schedule— so it also went bankrupt, but was bailed out by the U.S. government. All because the occupied molecular orbitals in graphite are qualitatively different from those in titanium! A more subtle case has been much in the public eye lately, namely, the sinking of the Titanic. What would have been
Journal of Chemical Education • Vol. 76 No. 10 October 1999 • JChemEd.chem.wisc.edu
Chemical Education Today
an incident became a tragedy, not because of bad naval architecture or bad seamanship, but because of bad steel. The steel from which the hull of the ship was constructed was dirty and therefore brittle. It contained too many microscopic inclusions (covalently bonded), pushing the ductile–brittle transition temperature of the steel above the temperature of the North Sea’s water. As a result the glasslike Titanic literally cracked into pieces. One simple clue that there is something special (i.e., different) about ideal metallic bonds compared with ideal covalent bonds is provided by crystal structures. The most simple metals are the alkali elements: Li, Na, K, Rb, and Cs. Their crystal structures are mostly body-centered cubic. Also, at very high pressures, many metals, in addition to the several transition metals that normally have this structure, become bcc. (4 ). From the viewpoint of the packing of spheres, the most dense structure is face-centered cubic (or ideal hexagonal close-packed). However, from the viewpoint of the packing of point nuclei, Frank (5) has pointed out that the bcc pattern is the most dense. Another way of saying this is: at constant volume, the bond lengths are shorter for the bcc structure than for the fcc structure. The difference is about 3%. This maximizes the electrostatic interaction between the small volumes of the positive ions and the large volumes of the valence electrons in the alkali metals. For the valence electrons of the alkalis to maximize the volumes they occupy, they must be delocalized. This accounts for their high electronic conductivities as well as their high ductilities. In order for a solid to have high ductility, one of the conditions is that dislocations in it must be highly mobile. In pure metals this is the case, but not in conductive polymers. High mobility means that the energy of the atomic core of a dislocation (where the atoms shear over one another) is nearly independent of the exact position of the center of the core. That is, there is no localized bonding of the atoms that face each other across the plane of shear. In still other words, the local region of shear behaves as a liquid of very low viscosity such as that of an electron liquid (10{3–10{4 poise). Direct measurements confirm this, indirectly confirming the delocalized bonding. Electronic conduction that is induced by photoirradiation can be high in brittle nonmetals. In some cases this may be accompanied by photoinduced softening (photoplasticity), but the slightly plastic nonmetal does not become ductile. Conduction is proportional to the product of chargecarrier concentration and carrier mobility. Although the concentration can be raised in nonmetals, the mobility does not reach the levels found in metals because the bonding is not delocalized. This justifies saying that covalent bonding is a limited case of metallic bonding, not the other way around. Covalent bonding concentrates the electronic charge between pairs of atoms through the use of bonding orbitals (in contrast to antibonding orbitals). This leads to tetrahedral, octahedral, and trigonal prismatic crystal structures, but rarely, if ever, to body-centered cubic structures.
Thus the covalent and metallic cases are two different ways of maximizing the electrostatic interaction between the positive nuclei and the valence electrons. Like most opposites they merge into one another under certain conditions, but this does not mean that the “pure” cases are not reasonably distinct. Concluding Remarks What seems most desirable is for chemists to stop identifying electronic conduction with the essence of a metal. It is only one of the important characteristics. The location of the plasmon frequency relative to the visible part of the optical spectrum is another (it determines the luster). The most important of all is the ductility (malleability). What solid substance, other than gold, can start opaque and be beaten with a hammer until it becomes so thin that it is translucent? What solids other than metals have fracture toughness in excess of 103 J m{2 ? The delocalized character of metallic bonding manifests itself in a variety of properties, including alloying, compound formation, conduction, magnetism, shear and bulk stiffnesses, and plasticity. The shear stiffnesses are particularly pertinent to the differences between covalent and metallic bonding. For the ideal covalent case, diamond, the average of its two shearstiffness moduli is 5.4 Mbar and its bulk modulus is 4.4 Mbar. For an ideal metal, say aluminum, the corresponding values are 0.29 Mbar and 0.79 Mbar. Thus diamond is stiffer in shear than in volume compression, whereas the opposite is true for aluminum. The modulus ratio for diamond is 1.22 and for aluminum it is 0.37. Having the bond charge localized between the atoms in diamond stiffens the angles between its nearest-neighbor directions (a la VSEPR theory), whereas the angles between the nearest-neighbor directions in aluminum can be changed easily because the valence electrons are delocalized. The relative plastic responses are even more extreme. Pure aluminum is liquidlike compared with pure diamond. Dislocation mobility differs between them by a factor of 1012 or more, at room temperature. This is because the valence charge density in aluminum is uniform, whereas there are large gradients in the charge density in diamond. All that I have stated above is implied in the works of Pauling (6 ), albeit in different words. Thus, I see no reason for chemists to abandon the term “metallic bond” any more than physicists should speak only of Fermions rather than electrons and positrons. Literature Cited 1. Anderson, W. P.; Burdett, J. K.; Czech, P. T. J. Am. Chem. Soc. 1994, 116, 8808. 2. Allen, L. C.; Capitan, J. F. J. Am. Chem. Soc. 1994, 116, 8810. 3. Burdett, J. K. Chemical Bonds—A Dialog; Wiley: New York, 1997; Chapter 9, pp 81 ff. Burdett, J. K. Chemical Bonding in Solids; Oxford University Press: New York, 1995. 4. Ruoff, A. L.; Xia, H.; Luo, H.; Vohra, Y. K. Rev. Sci. Instrum. 1990, 61, 3830. 5. Frank, F. C. Philos. Mag. Lett. 1992, 66, 81. 6. Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1960.
JChemEd.chem.wisc.edu • Vol. 76 No. 10 October 1999 • Journal of Chemical Education
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