Do the ideas of Bloch wavefunction and Bragg scattering of electrons which apply to crystals also apply to liquid Mercury ? Why is it that electrons in the liquid are not localised by the disordered positions of the mercury ions ?
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1$\begingroup$ Do you think that delocalization is due to the periodic structure? What about delocalization in a covalent molecule? $\endgroup$– nasuCommented Nov 14, 2020 at 5:29
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2 Answers
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Have a look on the applicability of Bloch's theorem
a Bloch-wave description applies more generally to any wave-like phenomenon in a periodic medium.
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Mercury is a liquid at room temperatures thus has no lattice structure to have a Bloch's wave function. It forms crystals when it freezes, so then it could apply, as with all lattices.
The same is true for Bragg scattering , it applies only in the crystal phase.
Why is it that electrons in the liquid are not localised by the disordered positions of the mercury ions ?
This is a question that you could ask for any liquid , water as an example, and the answer is the kinetic energy (due to temperature) of the molecules forming the liquid does not allow to bond into a solid structure, and form regular lattices, to have periodic space solutions for the behavior of electrons and ions.
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$\begingroup$ So is it correct that the metallic nature of conduction in mercury are not described in terms of Bloch electrons ? $\endgroup$ Commented Nov 15, 2020 at 6:19
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$\begingroup$ of liquid mercury, yes. A different model is need to account for the fluidity and lack of periodicity. $\endgroup$– anna vCommented Nov 15, 2020 at 7:30
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Disorder does not necessarily mean insulation and order does not imply conduction. For example, solid Si is a semiconductor and liquid Si a metal. Amorphous Si has no band gap and is a semiconductor.
The Hubbard model explains when electrons are localised, as in insulators and semiconductors, or delocalized, as in metals. Consider a lattice with one valence electron per site. The hopping matrix element t is the hamiltonian matrix element between two states with an electron displaced between nearest neighbors. The on-site repulsion U is the energy required for two electrons to be at the same site. If t dominates the electrons are delocalised, if U dominates they are localised.
