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I don't understand how one would exactly determine a dispersion relation

of phonons experimentally.

There are two equations, one for momentum and one for energy conservation:

[tex]\vec{k} - \vec{k^{'}} = \vec{G} + \vec{K} [/tex]

[tex]\omega - \omega ^{'} = \omega(K) [/tex]

where [tex]\omega(K)[/tex] is the energy difference of the scattered neutrons,

[tex]\vec{k} [/tex], [tex] \vec{k^{'}} [/tex] are the wave vectors of the neutrons before and

after scattering, [tex]\vec{K} [/tex] is the created phonon and [tex]\vec{G} [/tex] a

reciprocal lattice vector.

The question is, how is the difference [tex]\vec{k} - \vec{k^{'}} [/tex] respectively [tex]\vec{K} [/tex] determined experimentally?

Of course I also have to know [tex]\vec{G} [/tex].

thanks

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# Experimental dispersion relation of phonons

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