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Understanding electrical conductivity.

Late in the 1800’s chemists had postulated atoms were bound to each other by either ionic or covalent bonds. No one could explain how three-quarters of the Periodic Table had this abnormally high value of electrical conductivity. Therefore we needed to come up with another form of bonding to account for these observations. The answer was metallic bonding. Why is it called metallic bonding? My guess is that because it is seen in metals.
The need for a “metallicbonding” theory was brought on by the observation of electrical conductivity. The first model that attempted to account for the high observed value of electrical conductivity was put forth in 1900 by a German physicist, Paul Drude.
Paul Drude's early attempt was to model metals as a gas of free electrons moving about ion cores, where the ion core, in fact, is a mix of the nucleus plus all the inner shell electrons. This explained the observations but did not predict nor quantify anything. So, it was quickly recognized that this view of metals didn't take us very far. So, we had to wait for the next installment, which took place about 30 years later as part of the quantum revolution.
The first one is by Felix Bloch, and this came out in 1928. Interestingly this was his Ph.D. thesis. What he did for his thesis, under the supervision of Heisenberg at Leipzig, was interesting and cutting edge for the time. Bohr talked about atomic hydrogen because condensed matter inherently contains many more complexities. However, Bloch saw through this and proposed his Ph.D. thesis: quantum theory of solids.
Simply stated, let's take quantum theory and apply it to solids. So he put forth a quantum theory of solids as his Ph.D. thesis. And, here's what he did – without the complex equations and derivations, it's quite simple;
First, he recognized that atoms in a metal are arranged in periodic positions. There is an order to them. It's not just thrown together in some random jumble. So, atoms in a solid are set in regular patterns (these have come to be known as crystals). So, he took that as one foundation.
Second, he thought electrons free to move around would be subject to a potential. Remember, Drude thought that the valence electrons are free to move around. And, he says, well, if these valence electrons are free to move around, what would they be subjected to? They would be subjected to a potential.
This is how the energy levels in even a single hydrogen atom were derived. We've got the positive charge of the core; we've got the negative charge of the electron. So, now I've got an electron, and it sees the net positive charge of the atomic core. But, in a solid, it sees an array. It sees periodic variation in potential. So, that's the second thing he notes: periodic potential acts on the valence electrons. Next, he invoked wave mechanics. Remember, Schrödinger's equation was only enunciated a couple years earlier, in 1926.
So here's a Ph.D. student who hears about the Schrödinger equation as applied to a gaseous atom, and expands it. He applies it to condensed/solid matter. He solves the Schrödinger equation with these constraints. And, what does he get? He gets a set of solutions, actually more like a family of solutions. These give rise to a set of wavelengths of the electron that could move quickly through the crystal, they could propagate. In other words, by invoking the wavelength properties of the electron, he can rationalize how these valence electrons can move through barriers that classical physics would impose. And so, pretty soon, out falls electronic conductivity theory.
So we now had several atomic bond theories to account for atoms staying together. Atoms or ions in minerals are glued together by electrical bonds that are ionic, covalent, or metallic. The types and intensities of these bonds in a mineral determine its physical and chemical properties, including hardness and conductivity.
Ionic bonded materials usually have moderate hardness and fairly high melting points. They are generally soluble and are poor conductors of electricity because their constituent ions are fairly stable and neither lose nor gain electrons easily.
Covalent bonds are the strongest of the chemical bonds. Covalently bonded materials generally have very high melting points and are generally insoluble. They typically do not conduct electricity as solids or even when they are put into solution. Like this beautiful piece of granite.
Minerals like gold and silver have properties that cannot be explained in terms of ionic or covalent bonds. For example, the malleability and electrical conductivity of either metal cannot be readily explained by the localized sharing or complete transfer of electrons. Instead, the bonding electrons in metals like gold and silver are imagined as highly delocalized and free to move from one atom to the next. Thus the electrons form a “fluid glue” that keeps the positively charged metal ions from flying apart. Metals are generally ductile and malleable. They are conductive and not very hard. They are highly symmetric because metallic bonds are non-directional. Metals exhibit high conductivity which slowly decreases with temperatures (due to carrier scattering by vibrating atomic cores – but that is a different topic). The non-directional nature of the metallic bond leads to the ductility or extreme plasticity of metals.