Triple axis scattering

Scattering on the Triple-Axis-Diffractometer [1,2] at the HASYLAB high-energy beamline BW5 is performed in the horizontal plane using an Eulerian cradle as sample stage and a germanium solid-state detector. The beam is monochromatized by a singlecrystal monochromator (e.g. Si 111, FWHM 5.8 ), focused by various slit systems (Huber, Riso) and iron collimators and monitorized by a scintillation counter. The instrument is controlled by a p-VAX computer via CAMAC. 

In the double-crystal mode, tilts and dilations can only be distinguished by use of more than one reflection and then reconstructing the strain field. A direct method for producing tilt or dilation maps involves the use of an analyser crystal after the specimen. In the true triple-axis geometry (Figrue 10.17), the analyser selects the scattered intensity from a small voltrme of reciprocal space. It is easy to see... 

In order to determine the dynamics of atoms we have to carry out an inelastic neutron scattering measurement. With a reactor source this can be done with a triple-axis spectrometer, which has an analyzer crystal. Tripleaxis refers to the three axes for the monochromator, sample, and analyzer, all moving independently and controlled by a computer. With a pulsed source we use a mechanical chopper, which is a rotating cylinder with a hole perpendicular to the rotating axis that allows neutrons with a chosen range of velocity to go through. The neutrons scattered by the sample are detected... 

Figure 1. Schematic of a triple-axis inelastic neutron spectrometer. The thermal-ized beam from the reactor is monochromated by Bragg reflection from crystal M. Neutrons that scatter from the sample S are energy analyzed by Bragg reflection from crystal A and enter detector D.

Inelastic neutron scattering, on the other hand, usually employs a monochromatic neutron beam and records the intensity of the scattered neutron beam as a function of neutron kinetic energy. Such inelastic collision spectra are monitored as a function of the applied field and the (usually low) temperature. The observed peaks then represent the energy differences of thermally populated and excited unpopulated multiplet states. Inelastic neutron scattering experiments can be conducted using triple-axis, backscattering, or time-of-flight spectrometers. 

Shirane, G., Shapiro, G., and Tranquada, J.M., Neutron Scattering with a Triple-Axis Spectrometer. Cambridge University Press, Cambridge, 2002. 

Inelastic coherent scattering measurements using single crystals may focus on selected modes. For triple-axis spectroscopy, the work of Shirane et al. sets the standard by which most other smdies can be gauged (Figures 7 and 8). For additional examples, see the monograph by Shirane, Shapiro and Transquada. Measured phonon densities of... 

The conventional polarized beam experiment is useful only for systems with polarization dependent cross sections. More information can often be gained if the polarization of the scattered neutrons is measured relative to the incident polarization (polarization analysis). This may be done in a triple-axis mode with a polarization sensitive analyzing crystal (Fig. 11). The technique was introduced experimentally by Moon et al. (59). In their apparatus the magnetic field at the sample may be rotated about a horizontal axis. With the sample field vertical the neutron polarization remains vertical, but with the sample field horizontal the neutron polarization at the sample becomes horizontal (a reverse rotation occurs after the sample so that the polarization at the analyzing crystal is again vertical). Thus P can be either parallel or perpendicular to the scattering vector n. 

Measurements of dispersion curves provide information about the interatomic forces in solids. In fact, a dispersion curve is a function of the vibration frequency V on the wavelength X. The methods of neutron spectroscopy based on the phenomenon of diffraction of heat neutrons by crystals enables one to graph the dispersion curves of solids. The most accurate measurements of these curves are obtained by the inelastic neutron scattering using triple axis spectrometers. 

Fig. tt.5-2tta,b BaTiOs. Triple-axis neutron spectrometer scans at constant frequency across the sheet of diffuse scattering at 150 °C. The path of the scans is shown in the inset, (a) shows the elastic scan (v = 0), where the high background level is due to nuclear incoherent scattering, (b) Ineleastic scan (v = 0.97 x 10 Hz)... 

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