Metallic Bond - History

History

As chemistry developed into a science it became clear that metals formed the large 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 the 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 more formal interpretation in the form of the free electron model and its further extension, the nearly free electron model. In both of these models the electrons are seen as a gas traveling through the lattice 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 correction of the model, box-like Brillouin zones are added to k-space by the periodic potential experienced from the (ionic) lattice.

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 the construction of phase diagrams became accessible. Despite all this progress the nature of intermetallic compounds and alloys largely remained a mystery and their study was often 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 almost-free electron model was eagerly taken up by some researchers in this field, notably Hume-Rothery in an attempt to explain why certain intermetallic alloys with certain compositions would form and others would not. Initially his attempts were quite successful. Basically 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 indeed predicted a fairly large number of observed alloy compositions. Unfortunately, as soon as cyclotron resonance became available and the shape of the balloon could be determined, it was found that the assumption that the balloon was spherical did not hold at all, except perhaps in the case of caesium. This reduced many of the conclusions to examples of how a wrong model can sometimes give a whole series of correct predictions.

The free-electron debacle showed researchers that the model assuming that the ions were in a sea of free electrons needed modification, and so a number of quantum mechanical models such as band structure calculations based on molecular orbitals or the density functional theory were developed. In these models, one either departs 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 education.

The electronic band structure model became a major focus not only for the study of metals but even more so for the study of semiconductors. Together with the electronic states, the vibrational states were also shown to form bands. Peierls showed that, in the case of a one-dimensional row of metallic atoms, say hydrogen, an instability had to arise that would lead to the breakup of such a chain into individual molecules. This sparked an interest in the general question: When is collective metallic bonding stable and when will a more localized form of bonding take its place? Much research went into the study of clustering of metal atoms.

As powerful as the concept of the band structure proved to be in the description of metallic bonding, it does have a drawback. It remains a one-electron approximation to a multitudinous many-body problem. In other words, the energy states of each electron are described as if all the other electrons simply form a homogeneous background. Researchers like Mott and Hubbard realized that this was perhaps appropriate for strongly delocalized s- and p-electrons but for d-electrons, and even more for f-electrons the interaction with electrons (and atomic displacements) in the local environment may become stronger than the delocalization that leads to broad bands. Thus, the transition from localized unpaired electrons to itinerant ones partaking in metallic bonding became more comprehensible.