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I have tried a google search and checked my condensed matter books but I can't find out what pulsed neutron diffraction is and how it differs from inelastic neutron scattering.

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The most fundamental thing is that "diffraction" generally denotes an elastic process in this context. The "pulsed" part likely refers to the structure of the beam--a bunch of neutrons in short time, and then a long delay before the next bunch which allows better discrimination of what detected event is related to what beam bucket--always a problem with neutrons which have complicated behaviors on long time scales compared to charged particles.

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