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When thinking about how the lattice constant of silicon can be given up to eight decimal places without a remark for the temperature I realized that, it seems

most insulators and semiconductors seem to expand less than metals when exposed to heat.

Is there an intuitive connection between the band structure and the thermal expansion?

Hagadol
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  • I like the question. My spontaneous intuition is "The metal scaffold has less room for becoming chaotic when vibrational energy goes up. The band structure should be more symmetric/boring". But I may be totally off. – Nikolaj-K Dec 15 '13 at 19:49

2 Answers2

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Intuitive or not, a link between band structure and thermal expansion coefficient is hard to find. The reason is that the band structure is an equilibrium property of the un-distorted crystalline lattice and is directly connected to equilibrium positions, while thermal expansion coefficient is directly connected to anarmonic effects in the potential energy surface, i.e. to terms beyond quadratic approximation aroud the equilibrium structure. Said in a different way, expansion coefficient depends on band structure changes in correspondence of large collective displacements.

Even the metallic character of the bonds does not imply necessarily a larger thermal expansion coefficient. An example is Invar, a 36% nickel and 64% iron metallic alloy, which has a very low thermal expansion coefficient.

GiorgioP-DoomsdayClockIsAt-90
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I would say that your statement "most insulators and semiconductors seem to expand less than metals when exposed to heat" is simply false. Consider that rubber, plastics, and other organic insulators have huge thermal expansion coefficients compared to many metals. Ice, an insulator, has a 5x larger thermal expansion coefficient than platinum, a metal. Glass and titanium have roughly the same coefficient.

I think your observation is mostly limited to Silicon carbide, diamond, etc. where the lattice is just incredibly strong.

It is also worth mentioning that you can measure the average lattice spacing of any material at a finite temperature to many, many decimal places. All temperature does is broaden those positions, but you can still measure the center of the broadened peak to very high precision.

KF Gauss
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  • This might be putting words in OPs mouth but maybe they did specifically have in mind more classic crystal structures. Most of your counter examples are polymers bonded by dispersion or hydrogen bonds, or in the case of glass are amorphous which might (I know very little about glass) have a large impact on thermal properties. What about other giant covalent structures (SiO2, GaAs etc) or ionic structures (NaCl)? Maybe the key feature is just the gross bonding structure. – jacob1729 Mar 31 '19 at 15:30
  • @jacob1729 Bonding has everything to do with it, but the band structure and being a metal/insulator not so much. I think delving into the bonding of the structure is essentially a different question, albeit an important one. – KF Gauss Mar 31 '19 at 19:32