The precession electron diffraction (PED) technique is a relatively new method and was proposed by Vincent and Midgley in 1994 . The PED method is similar to the well-known X-ray (Buerger) precession technique . However, it performs a precession movement of the primary electron beam around the microscope’s optical axis instead of that of a single crystal around a fixed primary X-ray beam direction. The PED technique has recently been developed rapidly mainly due to the availability of commercial and convenient setups. These setups can be implanted on most modern transmission electron microscopes (TEMs). The PED patterns look very similar to the SAED (conventional selected-area electron diffraction) patterns and micro-/nano- beam electron diffraction patterns. The main advantage of PED is to remove strong dynamical effects from the diffraction patterns and to provide more kinematical data, e.g. remove extra spots induced by dynamical effects.
PED technique is close to hollow-cone diffraction technique but normally uses a parallel or nearly parallel incident electron beam. In PED technique, the electron beam is deflected twice. The electron beam first scans angularly around the optical axis on a pivot point, which is intersection point between the TEM optical axis and the specimen. The scan coils are normally deflection coils underneath the condenser lenses as shown in Figure 3906a. The diffraction pattern, located in the back focal plane of the objective lens, moves following the movement of the incident electron beam along the circumference of a circle. The movement diameter of diffraction pattern depends on the precession angle α. The primary electron beam and the diffracted beams are descanned (after they have left the specimen) in the same way that stationary diffraction patterns  are obtained in conventional TEMs. The beam deflection by the descan coils is exactly a compensation of the scan operation, meaning both scan and descan are simultaneously performed in order to stop the movement of diffraction pattern and to produce a stationary spot pattern on the screen or detector.
The intensity of the diffraction spots is an integral over excitation error s. Different from hollow-cone diffraction technique, because PED works at the pivot point on the TEM sample, this technique can be used to perform local diffraction analysis at high spatial resolution, e.g. on nano-particles.
Figure 3906a. Schematic illustration of PED setup in TEM systems. Here, only the two beam condition is shown but the real diffraction image is a pattern consisting of many diffraction spots. The scan and descan coils are shown in the two blue dotted boxes. The three red solid circles indicate the pivot point on the TEM specimen.
The two insets indicate the function of the corresponding portions of the PED setup.
Figure 3906b presents patterns taken from a 40-nm thick silicon (Si) crystal close to the  orientation, showing the effects of scan coils and descan coils. In Figures 3906b (a) and (b), the fine arcs and circles are formed with pure scan or pure descan, respectively. Figure 3906b (c) shows a diffraction pattern with both proper scan and descan on, resulting in a stationary diffraction pattern.
Figure 3906b. (a) With scan on but with descan off, (b) With descan on but with scan off, and (c) Stationary spot diffraction pattern formed with both scan and descan on at a precession angle of 1.7°. Adapted from 
For symmetry determination with both XRD and electron diffraction crystallography, we are looking for symmetry-related reflections. Then, the difference between the two techniques is mainly on systematically forbidden reflections:
i) In XRD profiles, the forbidden reflections typically have absolutely zero intensity.
ii) In SAED patterns, such forbidden reflections always have some degree of intensity due to double diffraction from multiple scattering.
Therefore, in SAED analysis, to minimize the multiple scattering, we need to use extremely thin specimens. Fortunately, the PED gives an opportunity to provide closer kinematical conditions than SAED. However, in most cases, the forbidden reflections in PED patterns will not be fully absent since the patterns are produced as a sum of many misaligned electron diffraction patterns and screw axes can only be completely absent if the zone axis of the crystal is perfectly aligned.
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