Is there any direct experiment to show the quantization of lattice vibrations?
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$\begingroup$ Does a measurement of the low-temperature heat capacity of a crystalline solid not count as direct experimental evidence? $\endgroup$– Mark MitchisonCommented Sep 20, 2013 at 16:23
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Lattice vibration excitations, i.e. phonons, are typically at energies of $\sim 25 meV$ which corresponds to room temperature. Therefore, neutron scattering with thermal neutrons is done. Thermal neutrons are neutrons from a nuclear power plant which are moderated to room temperature by sending them through a big tank of water, so they also have energies on the oder of $25meV$. Also, the de Broglie wavelength of neutrons is about 1 angstrom=$10^{-10}m$, so that neutrons are capable of resolving interaction motion.
In particular, 3-axis neutron spectroscopy is the experiment of choice to find the phonon dispersion relation. The dispersion relations obtained in experiments are in good agreement with those from quantum mechanical calculations, so there is strong experimental evidence to support the theory of phonons. I'm not sure if you had that in mind when you said 'direct'.
answered Sep 18, 2013 at 12:25