Editing Electron diffraction (section)

==== Bulk and surface superstructures ====
Many materials have relatively simple structures based upon small unit cell vectors <math>\mathbf a,\mathbf b,\mathbf c</math> (see also note{{efn|name=RecP}}). There are many others where the repeat is some larger multiple of the smaller unit cell (subcell) along one or more direction, for instance <math>N\mathbf a, M\mathbf b, \mathbf c</math>. which has larger dimensions in two directions. These [[Superstructure (condensed matter)|superstructures]]<ref name=Janner77 /><ref name="Bak">{{Cite journal |last=Bak |first=P |date=1982 |title=Commensurate phases, incommensurate phases and the devil's staircase |url=http://dx.doi.org/10.1088/0034-4885/45/6/001 |journal=Reports on Progress in Physics |volume=45 |issue=6 |pages=587–629 |doi=10.1088/0034-4885/45/6/001 |issn=0034-4885|url-access=subscription }}</ref><ref name=Jannsen2006/> can arise from many reasons:
# Larger unit cells due to electronic ordering which leads to small displacements of the atoms in the subcell. One example is [[antiferroelectricity]] ordering.<ref>{{Cite journal |last1=Randall |first1=Clive A. |last2=Fan |first2=Zhongming |last3=Reaney |first3=Ian |last4=Chen |first4=Long-Qing |last5=Trolier-McKinstry |first5=Susan |date=2021 |title=Antiferroelectrics: History, fundamentals, crystal chemistry, crystal structures, size effects, and applications |url=https://ceramics.onlinelibrary.wiley.com/doi/10.1111/jace.17834 |journal=Journal of the American Ceramic Society |language=en |volume=104 |issue=8 |pages=3775–3810 |doi=10.1111/jace.17834 |s2cid=233534909 |issn=0002-7820}}</ref>
# Chemical ordering, that is different atom types at different locations of the subcell.<ref>{{Cite journal |last1=Heine |first1=V |last2=Samson |first2=J H |date=1983 |title=Magnetic, chemical and structural ordering in transition metals |url=https://iopscience.iop.org/article/10.1088/0305-4608/13/10/025 |journal=Journal of Physics F: Metal Physics |volume=13 |issue=10 |pages=2155–2168 |doi=10.1088/0305-4608/13/10/025 |bibcode=1983JPhF...13.2155H |issn=0305-4608|url-access=subscription }}</ref>
# Magnetic order of the spins. These may be in opposite directions on some atoms, leading to what is called [[antiferromagnetism]].<ref>{{Cite web |date=2019-09-13 |title=6.8: Ferro-, Ferri- and Antiferromagnetism |url=https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Book%3A_Introduction_to_Inorganic_Chemistry_(Wikibook)/06%3A_Metals_and_Alloys-_Structure_Bonding_Electronic_and_Magnetic_Properties/6.08%3A_Ferro-_Ferri-_and_Antiferromagnetism |access-date=2023-09-26 |website=Chemistry LibreTexts |language=en}}</ref>

{{anchor|Figure 14}}[[File:Transmission electron diffraction pattern of Si (111) 7x7.png|thumb|Figure 14: Electron diffraction from a thin silicon (111) sample with a 7x7 reconstructed surface|left|alt=An electron diffraction pattern from a silicon surface with a reconstructed surface]]
In addition to those which occur in the bulk, superstructures can also occur at surfaces. When half the material is (nominally) removed to create a surface, some of the atoms will be under coordinated. To reduce their energy they can rearrange. Sometimes these rearrangements are relatively small; sometimes they are quite large.<ref>{{Cite journal |last1=Andersen |first1=Tassie K. |last2=Fong |first2=Dillon D. |last3=Marks |first3=Laurence D. |date=2018 |title=Pauling's rules for oxide surfaces |journal=Surface Science Reports |language=en |volume=73 |issue=5 |pages=213–232 |doi=10.1016/j.surfrep.2018.08.001|bibcode=2018SurSR..73..213A |s2cid=53137808 |doi-access=free }}</ref><ref>{{Cite book |title=Surface science: an introduction; with 16 tables |date=2003 |publisher=Springer |isbn=978-3-540-00545-2 |editor-last=Oura |editor-first=Kenjiro |edition= |series=Advanced texts in physics |location=Berlin Heidelberg |editor-last2=Lifšic |editor-first2=Viktor G. |editor-last3=Saranin |editor-first3=A. A. |editor-last4=Zotov |editor-first4=A. V. |editor-last5=Katayama |editor-first5=Masao}}</ref> Similar to a bulk superstructure there will be additional, weaker diffraction spots. One example is for the silicon (111) surface, where there is a supercell which is seven times larger than the simple bulk cell in two directions.<ref name=":15">{{Cite journal |last1=Takayanagi |first1=K. |last2=Tanishiro |first2=Y. |last3=Takahashi |first3=M. |last4=Takahashi |first4=S. |date=1985 |title=Structural analysis of Si(111)-7×7 by UHV-transmission electron diffraction and microscopy |url=http://dx.doi.org/10.1116/1.573160 |journal=Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films |volume=3 |issue=3 |pages=1502–1506 |doi=10.1116/1.573160 |bibcode=1985JVSTA...3.1502T |issn=0734-2101|url-access=subscription }}</ref> This leads to diffraction patterns with additional spots some of which are marked in [[#Figure 14|Figure 14]].<ref>{{Cite journal |last1=Ciston |first1=J. |last2=Subramanian |first2=A. |last3=Robinson |first3=I. K. |last4=Marks |first4=L. D. |date=2009 |title=Diffraction refinement of localized antibonding at the Si(111) 7 × 7 surface |url=https://link.aps.org/doi/10.1103/PhysRevB.79.193302 |journal=Physical Review B |language=en |volume=79 |issue=19 |pages=193302 |doi=10.1103/PhysRevB.79.193302 |arxiv=0901.3135 |bibcode=2009PhRvB..79s3302C |issn=1098-0121}}</ref> Here the (220) are stronger bulk diffraction spots, and the weaker ones due to the surface reconstruction are marked 7 × 7—see note{{efn|name=RecP}} for convention comments.