Precession geometry

The main book dealing with the precession method is that of Buerger (1964). The precession method is used to record an undistorted representation of a single plane of RLPs and their associated intensities. In order to achieve this the crystal is carefully set so that the plane of the RLPs is perpendicular to the X-ray beam. The normal to this plane, the zone axis, is then precessed about the X-ray beam axis. A layer-line screen with a transparent annulus allows RLPs of the plane of interest to pass through to the film. The screen intercepts all other diffracted rays. The motion of the crystal, screen and film are coupled together to maintain the coplanarity of the film, the screen and the zone. 

Before the zero-layer photograph is taken a niobium filter (for Mo Ka) or a nickel filter (for Cu Ka) is introduced into the X-ray beam path and a screen is placed between the crystal and the film at a distance from the crystal of 

Angular correction, e, in degrees and minutes of arc A r.l.u. Distance displacement (mm) for three crystal to film distances  

The distance between spots A is related to the reciprocal cell parameter a by the formula 

In the upper-layer precession photograph the film is advanced towards the crystal by a distance D and the screen is placed at a distance 

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Figure 4.24 (a)Geometry of precession photography. Reflections from a single... 

Fig. 3.5 Illustration of the precession of the magnetization vector in the xy-plane. The angle through which the vector has precessed is given by o>at. On the right-hand diagram we see the geometry for working out the x and y components of the vector.

Fig. 4.9. Classical geometries associated with the three polarisations

The most common two-dimensional technique employs a precession camera, but any technique giving two-dimensional undistorted images of the reciprocal lattice is suitable as well. From these undistorted images, the geometry of the diffraction pattern can be analyzed by simple visual inspection. In the case of a precession camera study, the crystal must be mounted so as to have the (001) plane perpendicular to the goniometer rotation axis. In fact, the stacking of layers in micas is along c and the periodicity in reciprocal... 

The spontaneous muon spin precession frequency below 7n was observed by Hofinaim et al. (1978) in polycrystalline material and more recently by Ekstrom et al. (1996, 1997) in a sin e-crystal specimen. The amplitude of the precession signal is larger in the c geometry, meaning that the local field lies predominantly in the basal plane as well. Typical data for the temperature dependence of the precession frequency are shown in fig. 33. The stopping site of the muon is not known, but calculations of the dipolar fields... 

Fig. 36. ZF pSR data on single-wystalline Er in the magnetically ordered states. The measurements were done in the perpendicular geometry. Left Temperature dependence of the spin precession ftequencies. After Schreier et al. (2000a). Right Temperature dependence of the two spontaneous precession ftequencies (bottom) and their damping rates (top) in the FM state. Solid and open symbols distinguish the two signals. After Hartmarm et al.

Gubbens et al. (1995b) concentrated on the behavior of relaxation rates both above and below 7n in the c geometry. These experiments were carried out at the ISIS pulsed facility, which precludes the observation of spontaneous spin precession patterns above the... 

Fig. 82. Left Temperature dependence of spontaneous muon spin precession frequency and of relaxation rate of the associated non-oscillating signal in magnetically ordered PrCojSij. Right Field dependence of the paramagnetic relaxation rate near the Neel temperature (top) and fit to a critical law (bottom) for ZF and LF measurements as indicated. The measuring geometry is always c. After Gubbens et al. (1997a, 1998).

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