Editing Electron diffraction (section)

==== Selected area electron diffraction ====

The simplest diffraction technique in TEM is selected area electron diffraction (SAED) where the incident beam is wide and close to parallel.<ref name="HirschEtAl" />{{Rp|location=Chpt 5-6}} An aperture is used to select a particular region of interest from which the diffraction is collected. These apertures are part of a thin foil of a heavy metal such as [[tungsten]]<ref name="Pella" /> which has a number of small holes in it. This way diffraction information can be limited to, for instance, individual crystallites. Unfortunately the method is limited by the spherical aberration of the objective lens,<ref name="HirschEtAl" />{{Rp|location=Chpt 5-6}} so is only accurate for large grains with tens of thousands of atoms or more; for smaller regions a focused probe is needed.<ref name="HirschEtAl" />{{Rp|location=Chpt 5-6}}

If a parallel beam is used to acquire a diffraction pattern from a [[single-crystal]], the result is similar to a two-dimensional projection of the crystal reciprocal lattice. From this one can determine interplanar distances and angles and in some cases crystal symmetry, particularly when the electron beam is down a major zone axis, see for instance the database by Jean-Paul Morniroli.<ref name="Atlas">{{Cite book |last=Morniroli |first=Jean-Paul |url=https://www.electron-diffraction.fr/software_059.htm |title=The atlas of electron diffraction zone axis patterns |year=2015 |location=Webpage and hardcopy}}</ref> However, projector lens aberrations such as [[Barrel Distortion|barrel distortion]] as well as dynamical diffraction effects (e.g.<ref>{{Cite journal |last1=Honjo |first1=Goro |last2=Mihama |first2=Kazuhiro |date=1954 |title=Fine Structure due to Refraction Effect in Electron Diffraction Pattern of Powder Sample Part II. Multiple Structures due to Double Refraction given by Randomly Oriented Smoke Particles of Magnesium and Cadmium Oxide |url=http://dx.doi.org/10.1143/jpsj.9.184 |journal=Journal of the Physical Society of Japan |volume=9 |issue=2 |pages=184–198 |doi=10.1143/jpsj.9.184 |issn=0031-9015|url-access=subscription }}</ref>) cannot be ignored. For instance, certain diffraction spots which are not present in x-ray diffraction can appear,<ref name="Atlas" /> for instance those due to [[Jon Gjønnes|Gjønnes]]-Moodie extinction conditions.<ref name="Gjønnes 65–67"/> {{anchor|Figure 11}}[[File:Crystal orientation and diffraction.gif|thumb|300px|Figure 11: Diffraction pattern of [[magnesium]] simulated using CrysTBox for various crystal orientations. Note how the diffraction pattern (white/black) changes with the crystal orientation (yellow).|alt=A pair of image showing how diffraction patterns change with the orientation of the crystal.]]

If the sample is tilted relative to the electron beam, different sets of crystallographic planes contribute to the pattern yielding different types of diffraction patterns, approximately different projections of the reciprocal lattice, see [[#Figure 11|Figure 11]].<ref name="Atlas" /> This can be used to determine the crystal orientation, which in turn can be used to set the orientation needed for a particular experiment. Furthermore, a series of diffraction patterns varying in tilt can be acquired and processed using a [[diffraction tomography]] approach. There are ways to combine this with [[direct methods (crystallography)|direct methods]] algorithms using electrons<ref name="Sufficient" /><ref name="White" /> and other methods such as charge flipping,<ref name="Lukas1">{{Cite journal |last=Palatinus |first=Lukáš |date=2013 |title=The charge-flipping algorithm in crystallography |url=https://scripts.iucr.org/cgi-bin/paper?S2052519212051366 |journal=Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials |volume=69 |issue=1 |pages=1–16 |doi=10.1107/S2052519212051366 |pmid=23364455 |bibcode=2013AcCrB..69....1P |issn=2052-5192|doi-access=free }}</ref> or automated diffraction tomography<ref>{{Cite journal |last1=Kolb |first1=U. |last2=Gorelik |first2=T. |last3=Kübel |first3=C. |last4=Otten |first4=M.T. |last5=Hubert |first5=D. |date=2007 |title=Towards automated diffraction tomography: Part I—Data acquisition |url=http://dx.doi.org/10.1016/j.ultramic.2006.10.007 |journal=Ultramicroscopy |volume=107 |issue=6–7 |pages=507–513 |doi=10.1016/j.ultramic.2006.10.007 |pmid=17234347 |issn=0304-3991|url-access=subscription }}</ref><ref>{{Cite journal |last1=Mugnaioli |first1=E. |last2=Gorelik |first2=T. |last3=Kolb |first3=U. |date=2009 |title="Ab initio" structure solution from electron diffraction data obtained by a combination of automated diffraction tomography and precession technique |url=http://dx.doi.org/10.1016/j.ultramic.2009.01.011 |journal=Ultramicroscopy |volume=109 |issue=6 |pages=758–765 |doi=10.1016/j.ultramic.2009.01.011 |pmid=19269095 |issn=0304-3991|url-access=subscription }}</ref> to solve crystal structures.