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Neutron scattering experiments are sometimes used to study atomic diffusion in solid materials. My intuition is that the typical speeds of the atoms diffusing in the material--say, the diffusion constant (in cm^2/s) divided by the atomic spacing (in angstroms)--must be comparable to the speed of the incident neutrons for any information about diffusion to be gained. Much faster neutrons should see only a snapshot of the target atoms frozen in time, while much slower neutrons should see only average densities of the target atoms.

Is this reasoning correct? (Can anyone point me to a good introduction?)

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The diffusion is determined from the broadening of the usual elastic scattering peaks. This is known as quasielastic scattering. There is no requirement for the neutron speed to be related to the diffusion speed.

Have a look at this book for an introduction to the subject.

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