Fig.1: data acquisition using a Doppler motion at the monochromator.
The backscattering monochromator is moved with a velocity vD parallel to the reciprocal lattice vector τ . Thus the energy of the reflected neutrons is modified via a longitudinal Doppler effect: (in first order and for vD << vi; the neutrons "see" a different lattice constants in case of a moving lattice). One registers the scattered neutrons as a function of the Doppler velocity vD. The maximum achievable Doppler speed vD determines the maximum energy transfer that can be reached. The Doppler velocity is varied periodically (sinusoidal function in v(t) diagram of Fig.1) and for identical analyser- and monochromator-crystals (same temperature and orientation) the corresponding energy transfer is centred around E=0. If we count a neutron at time tD then we have to know which speed v(tM) the monochromator had earlier at time tM = tD.-TMD (TMD = neutron flight time from the monochromator to the detector) when the neutron was at the monochromator. Neutrons are then accumulated into the corresponding equidistant velocity channels v(tM) (Fig.1; rhs for detector and lhs for monitor). The neutron flight times between the monochromator and the detector or monitor, TMD and TMM, are assumed to be constant, because kf is fixed and we neglect the variation of the monochromator position and the small change of neutron speed (valid for IN10, IN16 and BSS; HFBS and RSSM have 3 times larger monochromator amplitudes and higher speed, thus T is no longer a constant). Data are acquired with constant time bins of typically several 10 Ás and thus, for a non-linear Doppler velocity, a constant rate signal (e.g. background) shows up as the inverted function of the periodic Doppler motion (see monitor spectrum in the left vertical graph of Fig.5a). The monitor spectrum indicates how much time is spent measuring each velocity channel, g(tC), multiplied by the distribution function g(v0), the number of neutrons available in the primary beam around velocity v0. The Doppler velocity profile is often sinusoid-like, but in order to get a more equal measuring time distribution over the spectrum one might try to build Doppler drives which approach a triangular velocity profile. As for the sample scattering, elastically scattered neutrons will show up as a peak in the middle of the spectrum, the width of which corresponds to the instrumental resolution R(ω). The right hand side of Fig.1 shows that a Lorentzian-like scattering law will be distorted due to the non-linear Doppler motion and thus each spectrum has to be divided by the monitor spectrum (assuming a low background). An offset of the measured energy transfer range from zero can be achieved by choosing Doppler-monochromator-crystals with different d-spacing (e.g. Si1-xGex ), orientation or temperature from that of the analyser system (typically Si(111)).
October 20, 2005