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Since the Russian work as early as 1950s [1], electron crystallography has been continuously developed as an effective technique for solving the difficult crystal structures, which could not be solved by X-ray methods. Electron diffraction is usually complementary to powder X-ray diffraction. Comparing with X-ray crystallography, the major difficulties in TEM are smaller tilt range with goniometer stages and smaller physical dimension of specimens placed in the objective lens polepiece gap. However, electron-crystallographic methods still have their advantages:

       i) The method of powder X-ray diffraction works best for micrometer-sized crystals and becomes less useful for crystals in the nanometer range [5] because the kinematic X-ray diffraction from perfect crystal lattices shows essentially delta functions for the line profiles of the individual reflections. However, the situation for smaller crystals becomes rather complex and the Bragg peaks may shift simultaneously as well as get asymmetrically or even anisotropically broadened [6], especially the powder X-ray diffraction for nanocrystals become less and less characteristic because more and more Bragg peaks overlap due to the peak broadening [7] and the intensity diminishes until they become difficult to distinguish from the background. Furthermore, higher spatial resolution is needed because the surface and near surface regions of nanocrystals are highly distorted or relaxed with respect to the bulk crystal structure. For instance, the grains of many crystalline materials, e.g. high T_c superconductors, are too small in size and are too imperfect in periodicity for an X-ray single crystal analysis to be performed, but are applicable for electron-microscopic (EM) observations;
       ii) The atomic scattering factors for electrons are very different from those for X-rays and it is easier for electron diffraction to observe light atoms in the presence of much heavier atoms;
       iii)  X-rays are much less sensitive than electrons to changes in the electrostatic potential. The stronger interaction of the incident electrons with matter allows us to obtain the information about subtle crystallographic details that are usually undetectable in X-ray diffraction technique;
       iv) The EM is the only technique that can provide a microscope image as well as a diffraction pattern at atomic resolution.
       v) X-ray diffraction statistically gives us a good idea of the average sample, electron diffraction in TEM allows us to obtain local structure information.
       vi) In contrast to X-ray diffraction, the Ewald sphere is very flat for electron diffraction in TEM.
       vii) Powder x-ray diffraction provides the lattice-plane spacings and the corresponding intensities, but does not give the interplanar angles.
       viii) A sample that appears crystalline to a local probe such as nano-beam electron diffraction may appear amorphous to powder X-ray diffraction because both techniques have very different spatial resolutions.

For instance, the structures of several unknown compounds including ceramic oxides [2], a new Ti–Se compound [3] and an Al_mFe precipitate in an aluminum alloy [4] have been solved with electron diffraction techniques. More information on the advantages of electron diffraction techniques can also be found in this book.

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) XRD obeys Friedel's Law because it can be approximately described by kinematical scattering. This limits the number of the space groups of crystals that can be determined by XRD to fifty. For electron diffraction, multiple (dynamical) scattering of the incident electrons in the TEM specimen occurs so that the Friedel's law is broken down, and thus the crystals with all the 230 space groups can be identified. Especially, unlike XRD, CBED patterns are very sensitive to the presence or absence of a center of symmetry.
        ii) In XRD profiles, the forbidden reflections typically have absolutely zero intensity.
        iii) 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, precession electron diffraction (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.

Note that for electron diffraction, if the specimen has thickness gradient, the thicker part shows intensities in the forbidden reflections, indicating multiple diffractions while the thinner part shows zero intensity in the same type of reflections.

It is important to summarize that XRD can determine crystal structures with high precision, while CBED is highly sensitive to the presence or absence of symmetry operations through strong dynamic effects. Therefore, combining the two techniques enabled us to determine unambiguously the true structure of crystals.

Table 3497 summarizes the key comparison between X-ray and electron diffractions.

[1] B. Vainshtein, Structure Analysis by Electron Diffraction, Pergamon Press, London, 1964.
[2] W. Sinkler, E. Bengu, L.D. Marks, Acta Crystallogr. A 54 (1998) 591.
[3] T.E. Weirich, X.D. Zou, R. Ramlau, A. Simon, G.L. Cascarano, C. Giacovazzo, S. Hovmoller, Acta Crystallogr. A 56 (2000) 29.
[4] J. GjØnnes, V. Hansen, B.S. Berg, P. Runde, Y.F. Cheng, K. Gj^nnes, D.L. Dorset, C.J. Gilmore, Acta Crystallogr. A 54 (1998) 306.
[5] J. A. López Pérez, M. A. López Quintela, J. Mira, J. Rivas, and S. W. Charles. Advances in the preparation of magnetic nanoparticles by the microemulsion method. Journal of Physical Chemistry B, 101(41):8045 - 8047, 1997.
[6] Ungár, T.: Microstructure of nanocrystalline materials studied by powder diffraction. Z. Kristallogr. Suppl. 23 (2006) 313–318.
[7] Pinna, N.: X-Ray diffraction from nanocrystals. Progr. Colloid. Polym. Sci. 130 (2005) 29–32.
[8] Junliang Sun and Xiaodong Zou, Structure determination of zeolites and ordered mesoporous materials by electron crystallography, Dalton Transactions, 39, 8355-8362, (2010).
[9] U. Kolb, T. Gorelik, C. K¨ ubel, M. T. Otten and D. Hubert, Ultramicroscopy, 2007, 107, 507.
[10] D. L. Zhang, P. Oleynikov, S. Hovm¨ oller and X.D. Zou, Z. Kristallogr., 2010, 225, 94.