Recently I’ve been reading more about anharmonic properties of crystals, for instance metals. There are phenomena, such as thermal expansion, or electrical conductivity (resistivity), that appear to primarily be related to imperfections in the crystal structure, or to non-harmonic behaviour of the material. A material with a purely harmonic response should have no resistance, and should have no dimensional change when heated or cooled. Instead of thinking of the flow of electrons through a material, one might think of a wave function for the distributed gas of electrons.
This is somewhat prompted by a reading of Blakemore’s book on solid state, mentioned in my post about a year ago (April 20th, 2014) on the topic of transparent metals. I had occasion to return to Blakemore’s book again because of a new investigation. And he is as stimulating as ever!
So here’s the basic idea: Instead of thinking about the flow of electrons (as particles), think about propagation of a wave. That leads one to thinking about optics, and indexes of refraction, and the possibility of focusing etc. For instance, it is standard to talk about the speed with which electrons flow through a metal, and compare different models in terms of the wildly different speeds they predict. Do the three noble metals — copper, silver and gold — have the same speeds of electron flow? Otherwise said, would they have the same index of refraction? Can we make a copper-silver-gold alloy that can act as a lens or a waveguide?
Conversely, one can think of traditional wave models, and consider them in terms of particle flow models, eg the resistance (or conductivity) of glass.
Just some late-night idle musing. Maybe something will intrigue you.
Best wishes,
Ken Roberts
14-Mar-2015
Logic, Astronomy, Science, and Ideas Too 