International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B. ch. 4.1, p. 405
Section 4.1.5.2. Measurement with neutrons
aChemical Crystallography Laboratory, University of Oxford, 9 Parks Road, Oxford OX1 3PD, England |
The inelastic scattering of neutrons by phonons gives rise to changes of energy which are readily measured and converted to frequencies using equation (4.1.4.1
). The corresponding wavevector q is derived from the momentum conservation relation (4.1.4.4
). Nearly all phonon dispersion relations determined to date have been obtained in this way. Well over 200 materials have been examined, including half the chemical elements, a large number of alloys and diatomic compounds, and rather fewer molecular crystals (Dolling, 1974
; Bilz & Kress, 1979
). Phonon dispersion curves have been determined in crystals with up to ten atoms in the primitive cell, for example, tetracyanoethylene (Chaplot et al., 1983
).
The principal instrument for determining phonon dispersion relations with neutrons is the triple-axis spectrometer, first designed and built by Brockhouse (Brockhouse & Stewart, 1958). The modern instrument is unchanged apart from running continuously under computer control. A beam of thermal neutrons falls on a single-crystal monochromator, which Bragg reflects a single wavelength on to the sample in a known orientation. The magnitude of the scattered wavevector, and hence the change of energy on scattering by the sample, is found by measuring the Bragg angle at which the neutrons are reflected by the crystal analyser. The direction of k is defined by a collimator between the sample and analyser.
In the `constant Q' mode of operating the triple-axis spectrometer, the phonon wavevector is kept fixed while the energy transfer is varied. This allows the frequency spectrum to be determined for all phonons sharing the same q; the spectrum will contain up to 3n frequencies, corresponding to the 3n branches of the dispersion relations.
In an inelastic neutron scattering experiment, where the TDS intensity is of the order of one-thousandth of the Bragg intensity, it is necessary to use a large sample with a volume of 1 cm3, or more. The sample should have a high cross section for coherent scattering as compared with the cross sections for incoherent scattering and for true absorption. Crystals containing hydrogen should be deuterated.
Dolling (1974) has given a comprehensive review of the measurement of phonon dispersion relations by neutron spectroscopy.
References



