By Kurt Sköld and David L. Price (Eds.)
Sköld e.K., rate D.L. (eds.) Neutron scattering (AP, 1986-1987)(ISBN 0124759653)
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Extra resources for Neutron Scattering
When Q becomes so large that IQ U I z 1, the phonon expansion is no longer meaningful, and a more useful limiting case is the “impulse approximation” where the target atom recoils as an effectively free particle. 5 in connection with the energy moments of the scattering function. 30 DAVID L. 6. Anharmonic Effects At higher temperatures, and even at low temperatures for quantum solids, the atomic displacements can be such a large fraction of the interatomic distances that the harmonic approximation on which the previous sections are based is not valid (for reviews of anharmonic effects in crystals see Ref.
3). For systems with no long-range order, like glasses and other amorphous solids, all the elastic scattering is diffuse and one must in principle know all the time-averaged atomic positions in order to calculate S,,(Q). 4. One-Phonon Scattering We return to Eq. 48) and consider the second term in the expansion. This gives . x ( Q ui(0)Q ut,(t))eiQ'(''-') e -ifit/' d t. Once again we can use the normal mode expansion of Eq. 43) and the quantum theory of harmonic oscillators to get 1. 61a) and These functions predict peaks in the scattering function whenever E corresponds to hwj, where w j is a normal mode frequency of the system.
For conventional spectrometers the condition is that D2 cm2/s. , back-scattering spectrometers with resolution below 1 peV, the condition is that D L. Diffusion rates in these ranges are observed in fast-ion conductors and in certain metal hydrides. Diffusion in the solid-state in general proceeds by discontinuous steps between available quasi-equilibrium sites in the lattice. While residing at a given site, the particle undergoes thermal vibration, and occasionally the particle accumulates sufficient energy to make the transition to a nearby site.