Editing Metallic bonding (section)

==History==
{{Unreferenced section|date=October 2009}}

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 (vector)|magnitude]], ''not'' the direction of the momentum vector '''[[wave 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 zone]]s 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 diagram]]s were developed. Despite all this progress, the nature of [[Intermetallic|intermetallic compounds]] and [[Alloy|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 [[Law of multiple proportions#Law 3: Law of Multiple Proportions|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 [[William Hume-Rothery|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 [[Electron cyclotron resonance|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 [[semiconductor]]s. 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.

As powerful as the band structure model proved to be in describing metallic bonding, it remains a one-electron approximation of a many-body problem: the energy states of an individual electron are described as if all the other electrons form a homogeneous background. Researchers such as Mott and Hubbard realized that the one-electron treatment was perhaps appropriate for strongly delocalized [[azimuthal quantum number|'''s'''- and '''p'''-electrons]]; but for '''d'''-electrons, and even more for '''f'''-electrons, the interaction with nearby individual electrons (and atomic displacements) may become stronger than the delocalized interaction that leads to broad bands. This gave a better explanation for the transition from localized [[unpaired electron]]s to itinerant ones partaking in metallic bonding.