Editing Electron diffraction (section)

=== Low-energy electron diffraction (LEED) ===
{{main|Low-energy electron diffraction}}{{anchor|Low-energy electron diffraction}}
{{anchor|Figure 20}}{{anchor|Figure 21}}{{Multiple image
| total_width       = 250
| align             = right
| direction         = vertical
| image1            = Ewald construction for electron diffraction on a two-dimensional lattice, side view.svg
| caption1          = Figure 20:  Ewald sphere construction for LEED, with the shape function streaks indicated, <math>k_i</math> the incident beam and <math>k_f</math> one of the diffracted beams.
| image2            = Si100Reconstructed.png
| caption2          = Figure 21: LEED pattern of a Si(100) reconstructed surface. The underlying lattice is a square lattice, while the surface reconstruction has a 2x1 periodicity. Also seen is the electron gun that generates the primary electron beam; it covers up parts of the screen.
| alt1              = Connection between the wavevectors for low energy electrons and reciprocal space.
| alt2              = Experimental LEED pattern from a reconstructed silicon surface.
}}

Low-energy electron diffraction (LEED) is a technique for the determination of the surface structure of [[single crystal|single-crystalline]] materials by bombardment with a [[collimated beam]] of low-energy electrons (30–200 eV).<ref name="Oura">{{cite book |author1=K. Oura |author2=V. G. Lifshifts |author3=A. A. Saranin |author4=A. V. Zotov |author5=M. Katayama |title=Surface Science |url=https://archive.org/details/surfacesciencein00oura_931 |url-access=limited |publisher=Springer-Verlag, Berlin Heidelberg New York |date=2003 |pages=[https://archive.org/details/surfacesciencein00oura_931/page/n10 1]–45|isbn=9783540005452 }}</ref> In this case the Ewald sphere leads to approximately back-reflection, as illustrated in [[#Figure 20|Figure 20]], and diffracted electrons as spots on a fluorescent screen as shown in [[#Figure 21|Figure 21]]; see the main page for more information and references.<ref name="VanHove" /><ref name="LEEDB">{{Cite book |last1=Moritz |first1=Wolfgang |url=https://www.worldcat.org/oclc/1293917727 |title=Surface structure determination by LEED and X-rays |last2=Van Hove |first2=Michel |date=2022 |isbn=978-1-108-28457-8 |location=Cambridge, United Kingdom |pages=Chpt 3–5 |oclc=1293917727}}</ref> It has been used to solve a very large number of relatively simple surface structures of metals and semiconductors, plus cases with simple chemisorbants. For more complex cases transmission electron diffraction<ref name=":15" /><ref>{{Cite journal |last1=Gilmore |first1=C.J. |last2=Marks |first2=L.D. |last3=Grozea |first3=D. |last4=Collazo |first4=C. |last5=Landree |first5=E. |last6=Twesten |first6=R.D. |date=1997 |title=Direct solutions of the Si(111) 7 × 7 structure |url=https://linkinghub.elsevier.com/retrieve/pii/S0039602897000629 |journal=Surface Science |language=en |volume=381 |issue=2–3 |pages=77–91 |doi=10.1016/S0039-6028(97)00062-9|bibcode=1997SurSc.381...77G |url-access=subscription }}</ref> or surface x-ray diffraction<ref>{{Cite journal |last=Robinson |first=I. K. |date=1983 |title=Direct Determination of the Au(110) Reconstructed Surface by X-Ray Diffraction |url=https://link.aps.org/doi/10.1103/PhysRevLett.50.1145 |journal=Physical Review Letters |language=en |volume=50 |issue=15 |pages=1145–1148 |doi=10.1103/PhysRevLett.50.1145 |bibcode=1983PhRvL..50.1145R |issn=0031-9007|url-access=subscription }}</ref> have been used, often combined with [[scanning tunnelling microscopy|scanning tunneling microscopy]] and [[density functional theory]] calculations.<ref>{{Cite journal |last1=Enterkin |first1=James A. |last2=Subramanian |first2=Arun K. |last3=Russell |first3=Bruce C. |last4=Castell |first4=Martin R. |last5=Poeppelmeier |first5=Kenneth R. |last6=Marks |first6=Laurence D. |date=2010 |title=A homologous series of structures on the surface of SrTiO3(110) |url=https://www.nature.com/articles/nmat2636 |journal=Nature Materials |language=en |volume=9 |issue=3 |pages=245–248 |doi=10.1038/nmat2636 |pmid=20154691 |bibcode=2010NatMa...9..245E |issn=1476-4660}}</ref>

LEED may be used in one of two ways:<ref name="VanHove" /><ref name="LEEDB" />
# Qualitatively, where the diffraction pattern is recorded and analysis of the spot positions gives information on the symmetry of the surface structure. In the presence of an [[adsorbate]] the qualitative analysis may reveal information about the size and rotational alignment of the adsorbate unit cell with respect to the substrate unit cell.<ref name="VanHove" />
# Quantitatively, where the intensities of diffracted beams are recorded as a function of incident electron beam energy to generate the so-called I–V curves. By comparison with theoretical curves, these may provide accurate information on atomic positions on the surface.<ref name="LEEDB" />