Metallic bonding

Metallic bonding is a type of chemical bonding that arises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of delocalized electrons) and positively charged metal ions. It may be described as the sharing of free electrons among a structure of positively charged ions (cations). Metallic bonding accounts for many physical properties of metals, such as strength, ductility, thermal and electrical resistivity and conductivity, opacity, and lustre.

Metallic bonding is not the only type of chemical bonding a metal can exhibit, even as a pure substance. For example, elemental gallium consists of covalently-bound pairs of atoms in both liquid and solid-state—these pairs form a crystal structure with metallic bonding between them. Another example of a metal–metal covalent bond is the mercurous ion (Hg²⁺
₂).

As chemistry developed into a science, it became clear that metals formed the majority of the periodic table of the elements, and great progress was made in the description of the salts that can be formed in reactions with acids. With the advent of electrochemistry, it became clear that metals generally go into solution as positively charged ions, and the oxidation reactions of the metals became well understood in their electrochemical series. A picture emerged of metals as positive ions held together by an ocean of negative electrons.

With the advent of quantum mechanics, this picture was given a more formal interpretation in the form of the free electron model and its further extension, the nearly free electron model. In both models, the electrons are seen as a gas traveling through the structure of the solid with an energy that is essentially isotropic, in that it depends on the square of the magnitude, not the direction of the momentum vector k. In three-dimensional k-space, the set of points of the highest filled levels (the Fermi surface) should therefore be a sphere. In the nearly-free model, box-like Brillouin zones are added to k-space by the periodic potential experienced from the (ionic) structure, thus mildly breaking the isotropy.

The advent of X-ray diffraction and thermal analysis made it possible to study the structure of crystalline solids, including metals and their alloys; and phase diagrams were developed. Despite all this progress, the nature of intermetallic compounds and alloys largely remained a mystery and their study was often merely empirical. Chemists generally steered away from anything that did not seem to follow Dalton's laws of multiple proportions; and the problem was considered the domain of a different science, metallurgy.

The nearly-free electron model was eagerly taken up by some researchers in metallurgy, notably Hume-Rothery, in an attempt to explain why intermetallic alloys with certain compositions would form and others would not. Initially Hume-Rothery's attempts were quite successful. His idea was to add electrons to inflate the spherical Fermi-balloon inside the series of Brillouin-boxes and determine when a certain box would be full. This predicted a fairly large number of alloy compositions that were later observed. As soon as cyclotron resonance became available and the shape of the balloon could be determined, it was found that the balloon was not spherical as the Hume-Rothery believed, except perhaps in the case of caesium. This revealed how a model can sometimes give a whole series of correct predictions, yet still be wrong in its basic assumptions.

The nearly-free electron debacle compelled researchers to modify the assumpition that ions flowed in a sea of free electrons. A number of quantum mechanical models were developed, such as band structure calculations based on molecular orbitals, and the density functional theory. These models either depart from the atomic orbitals of neutral atoms that share their electrons, or (in the case of density functional theory) departs from the total electron density. The free-electron picture has, nevertheless, remained a dominant one in introductory courses on metallurgy.

The electronic band structure model became a major focus for the study of metals and even more of semiconductors. Together with the electronic states, the vibrational states were also shown to form bands. Rudolf Peierls showed that, in the case of a one-dimensional row of metallic atoms—say, hydrogen—an inevitable instability would break such a chain into individual molecules. This sparked an interest in the general question: when is collective metallic bonding stable, and when will a localized bonding take its place? Much research went into the study of clustering of metal atoms.