Editing Crystallography

{{short description|Scientific study of crystal structures}}
{{for|the book of poetry|Crystallography (book)}}
{{more citations needed|date=July 2024}}
[[File:Stohrem.jpg|thumb|A crystalline solid: atomic resolution image of [[strontium titanate]]. Brighter spots are columns of [[strontium]] atoms and darker ones are [[titanium]]-[[oxygen]] columns.]]
[[File:Sites interstitiels cubique a faces centrees.svg|thumb|Octahedral and tetrahedral [[interstitial site]]s in a face centered cubic structure]]
[[File:EBSD_(001)_Si.png|thumb|[[Kikuchi lines (physics)|Kikuchi lines]] in an [[electron backscatter diffraction]] pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source]]

'''Crystallography''' is the branch of science devoted to the study of molecular and crystalline structure and properties.<ref>{{Cite web |editor-last=Chapuis |editor-first=Gervais |title=Online Dictionary of Crystallography |url=https://dictionary.iucr.org/Main_Page |access-date=2024-05-22 |website=Online dictionary of crystallography |publisher=[[International Union of Crystallography]]}}</ref> The word ''crystallography'' is derived from the [[Ancient Greek]] word {{wikt-lang|grc|κρύσταλλος}} ({{grc-transl|κρύσταλλος}}; "clear ice, rock-crystal"), and {{wikt-lang|grc|γράφειν}} ({{grc-transl|γράφειν}}; "to write").<ref>{{Cite web |date=2021-10-21 |title=Online Dictionary of Crystallography |url=https://dictionary.iucr.org/Main_Page |access-date=2024-03-11 |website=International Union of Crystallography}}</ref> In July 2012, the [[United Nations]] recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.<ref name="UN Resolution">[http://www.iycr2014.org/about/resolution UN announcement "International Year of Crystallography"]. iycr2014.org. 12 July 2012</ref>

Crystallography is a broad topic, and many of its subareas, such as [[X-ray crystallography]], are themselves important scientific topics. Crystallography ranges from the fundamentals of [[crystal structure]] to the mathematics of [[Crystal system|crystal geometry]], including those that are [[Aperiodic crystal|not periodic]] or [[quasicrystal]]s. At the atomic scale it can involve the use of [[X-ray diffraction]] to produce experimental data that the tools of [[X-ray crystallography]] can convert into detailed positions of atoms, and sometimes electron density. At larger scales it includes experimental tools such as [[Orientation imaging microscopy|orientational imaging]] to examine the relative orientations at the [[grain boundary]] in materials. Crystallography plays a key role in many areas of biology, chemistry, and physics, as well new developments in these fields.

== History and timeline ==
{{Main|Timeline of crystallography}}

Before the 20th century, the study of [[crystal]]s was based on physical measurements of their geometry using a [[goniometer]].<ref>{{Cite journal|date=1915-07-01|title=The Evolution of the Goniometer|journal=Nature|language=en|volume=95|issue=2386|pages=564–565|doi=10.1038/095564a0|bibcode=1915Natur..95..564.|issn=1476-4687|doi-access=free}}</ref> This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the [[Symmetry (physics)|symmetry]] of the crystal in question. The position in 3D space of each crystal face is plotted on a [[Stereographic projection|stereographic]] net such as a [[Wulff net]] or [[Lambert azimuthal equal-area projection|Lambert net]]. The [[pole figure|pole]] to each face is plotted on the net. Each point is labelled with its [[Miller index]]. The final plot allows the symmetry of the crystal to be established.<ref>{{Cite journal |last1=Molčanov |first1=Krešimir |last2=Stilinović |first2=Vladimir |date=2014-01-13 |title=Chemical Crystallography before X-ray Diffraction |url=https://onlinelibrary.wiley.com/doi/10.1002/anie.201301319 |journal=Angewandte Chemie International Edition |language=en |volume=53 |issue=3 |pages=638–652 |doi=10.1002/anie.201301319 |pmid=24065378 |issn=1433-7851}}</ref><ref>{{Cite journal |last=Mascarenhas |first=Yvonne Primerano |date=2020-03-02 |title=Crystallography before the Discovery of X-Ray Diffraction |journal=Revista Brasileira de Ensino de Física |language=en |volume=42 |pages=e20190336 |doi=10.1590/1806-9126-RBEF-2019-0336 |issn=1806-1117|doi-access=free }}</ref>

The discovery of [[X-ray]]s and [[electron]]s in the last decade of the 19th century enabled the determination of crystal structures on the atomic scale, which brought about the modern era of crystallography. The first X-ray diffraction experiment was conducted in 1912 by [[Max von Laue]],<ref name="L1912">{{cite journal |vauthors=Friedrich W, Knipping P, von Laue M |date=1912 |title=Interferenz-Erscheinungen bei Röntgenstrahlen |url=https://commons.wikimedia.org/wiki/File:Interferenz-Erscheinungen_bei_Röntgenstrahlen.pdf |journal=Sitzungsberichte der Mathematisch-Physikalischen Classe der Königlich-Bayerischen Akademie der Wissenschaften zu München |volume=1912 |page=303 |trans-work=Interference phenomena in X-rays}}</ref> while electron diffraction was first realized in 1927 in the [[Davisson–Germer experiment]]<ref>{{Cite journal |last1=Davisson |first1=C. |last2=Germer |first2=L. H. |date=1927 |title=The Scattering of Electrons by a Single Crystal of Nickel |url=https://www.nature.com/articles/119558a0 |journal=Nature |language=en |volume=119 |issue=2998 |pages=558–560 |doi=10.1038/119558a0 |bibcode=1927Natur.119..558D |issn=1476-4687}}</ref> and parallel work by [[George Paget Thomson]] and Alexander Reid.<ref>{{Cite journal |last1=Thomson |first1=G. P. |last2=Reid |first2=A. |date=1927 |title=Diffraction of Cathode Rays by a Thin Film |url=https://www.nature.com/articles/119890a0 |journal=Nature |language=en |volume=119 |issue=3007 |pages=890 |doi=10.1038/119890a0 |bibcode=1927Natur.119Q.890T |issn=1476-4687}}</ref> These developed into the two main branches of crystallography, [[X-ray crystallography]] and [[Electron diffraction|electron]] diffraction. The quality and throughput of solving crystal structures greatly improved in the second half of the 20th century, with the developments of customized instruments and [[Phase problem|phasing algorithms]]. Nowadays, crystallography is an [[interdisciplinary field]], supporting theoretical and experimental discoveries in various domains.<ref>{{Cite journal |last1=Brooks-Bartlett |first1=Jonathan C. |last2=Garman |first2=Elspeth F. |date=2015-07-03 |title=The Nobel Science: One Hundred Years of Crystallography |url=https://journals.sagepub.com/doi/full/10.1179/0308018815Z.000000000116 |journal=Interdisciplinary Science Reviews |language=en |volume=40 |issue=3 |pages=244–264 |doi=10.1179/0308018815Z.000000000116 |bibcode=2015ISRv...40..244B |issn=0308-0188}}</ref> Modern-day scientific instruments for crystallography vary from laboratory-sized equipment, such as [[diffractometer]]s and [[electron microscope]]s, to dedicated large facilities, such as [[photoinjector]]s, [[synchrotron light source]]s and [[free-electron laser]]s.

== Methodology ==
{{Main|X-ray crystallography|Electron diffraction|Neutron crystallography|NMR crystallography}}

Crystallographic methods depend mainly on analysis of the [[diffraction]] patterns of a sample targeted by a beam of some type. [[X-ray]]s are most commonly used; other beams used include [[electron]]s or [[neutron]]s. Crystallographers often explicitly state the type of beam used, as in the terms ''[[X-ray diffraction]], [[neutron diffraction]]'' and ''[[electron diffraction]]''. These three types of radiation interact with the specimen in different ways.
* X-rays interact with the [[Electron density|spatial distribution of electrons]] in the sample.<ref>{{Cite book |last1=Cullity |first1=B. D.|title=Elements of X-ray diffraction |last2=Stock |first2=Stuart R. |date=2001 |publisher=Prentice Hall |isbn=978-0-201-61091-8 |edition=3rd |location=Upper Saddle River, NJ}}</ref>
* Neutrons are scattered by the atomic nuclei through the [[strong nuclear force]]s, but in addition the [[magnetic moment]] of neutrons is non-zero, so they are also scattered by [[magnetic field]]s. When neutrons are scattered from [[hydrogen]]-containing materials, they produce diffraction patterns with high noise levels, which can sometimes be resolved by substituting [[deuterium]] for hydrogen.<ref>{{Cite web |title=ISIS Neutron Diffraction with Isotopic Substitution |url=https://www.isis.stfc.ac.uk/Pages/Neutron-Diffraction-with-Isotopic-Substitution.aspx |access-date=2024-07-02 |website=www.isis.stfc.ac.uk |language=en-GB}}</ref>
* Electrons are [[charged particle]]s and therefore interact with the total [[Charge density|charge distribution]] of both the [[atomic nuclei]] and the electrons of the sample.<ref>{{Cite book |last=Cowley |first=John Maxwell |author-link=John Maxwell Cowley|title=Diffraction physics |date=1995 |publisher=Elsevier Science B.V |isbn=978-0-444-82218-5 |edition=3rd |series=North-Holland personal library |location=Amsterdam; New York}}</ref>{{Rp|location=Chpt 4}}
It is hard to focus x-rays or neutrons, but since electrons are charged they can be focused and are used in [[electron microscope]] to produce magnified images. There are many ways that [[transmission electron microscopy]] and related techniques such as [[scanning transmission electron microscopy]], [[high-resolution electron microscopy]] can be used to obtain images with in many cases atomic resolution from which crystallographic information can be obtained. There are also other methods such as [[low-energy electron diffraction]], [[low-energy electron microscopy]] and [[reflection high-energy electron diffraction]] which can be used to obtain crystallographic information about surfaces.

== Applications in various areas ==

=== Materials science ===
Crystallography is used by materials scientists to characterize different materials. In single crystals, the effects of the crystalline arrangement of atoms is often easy to see macroscopically because the natural shapes of crystals reflect the atomic structure. In addition, physical properties are often controlled by crystalline defects. The understanding of crystal structures is an important prerequisite for understanding [[crystallographic defect]]s. Most materials do not occur as a single crystal, but are poly-crystalline in nature (they exist as an aggregate of small crystals with different orientations). As such, [[powder diffraction]] techniques, which take diffraction patterns of samples with a large number of crystals, play an important role in structural determination.

Other physical properties are also linked to crystallography. For example, the minerals in [[clay]] form small, flat, platelike structures. Clay can be easily deformed because the platelike particles can slip along each other in the plane of the plates, yet remain strongly connected in the direction perpendicular to the plates. Such mechanisms can be studied by crystallographic [[Texture (crystalline)|texture]] measurements. Crystallographic studies help elucidate the relationship between a material's structure and its properties, aiding in developing new materials with tailored characteristics. This understanding is crucial in various fields, including metallurgy, geology, and materials science. Advancements in crystallographic techniques, such as electron diffraction and X-ray crystallography, continue to expand our understanding of material behavior at the atomic level.

In another example, [[Iron#Allotropes|iron]] transforms from a [[body-centered cubic]] (bcc) structure called [[Allotropes of iron#Alpha iron (α-Fe)|ferrite]] to a [[face-centered cubic]] (fcc) structure called [[austenite]] when it is heated.<ref>{{Cite web |title=Materials Science and Engineering: An Introduction, 10th Edition {{!}} Wiley |url=https://www.wiley.com/en-us/Materials+Science+and+Engineering%3A+An+Introduction%2C+10th+Edition-p-9781119405498 |access-date=2022-09-10 |website=Wiley.com |language=en-us}}</ref> The fcc structure is a close-packed structure unlike the bcc structure; thus the volume of the iron decreases when this transformation occurs.

Crystallography is useful in phase identification. When manufacturing or using a material, it is generally desirable to know what compounds and what phases are present in the material, as their composition, structure and proportions will influence the material's properties. Each phase has a characteristic arrangement of atoms. X-ray or neutron diffraction can be used to identify which structures are present in the material, and thus which compounds are present. Crystallography covers the enumeration of the symmetry patterns which can be formed by atoms in a crystal and for this reason is related to [[group theory#Chemistry and materials science|group theory]].
{{Further|Oligocrystalline material}}

=== Biology ===
[[X-ray crystallography]] is the primary method for determining the molecular conformations of biological [[macromolecule]]s, particularly [[protein]] and [[nucleic acid]]s such as [[DNA]] and [[RNA]]. The double-helical structure of DNA was deduced from crystallographic data. The first crystal structure of a macromolecule was solved in 1958, a three-dimensional model of the myoglobin molecule obtained by X-ray analysis.<ref>{{Cite journal | doi = 10.1038/181662a0| title = A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-Ray Analysis| journal = Nature| volume = 181| issue = 4610| pages = 662–6| year = 1958| last1 = Kendrew | first1 = J. C.| last2 = Bodo | first2 = G.| last3 = Dintzis | first3 = H. M.| last4 = Parrish | first4 = R. G.| last5 = Wyckoff | first5 = H.| last6 = Phillips | first6 = D. C. | pmid=13517261|bibcode = 1958Natur.181..662K | s2cid = 4162786}}</ref> The [[Protein Data Bank]] (PDB) is a freely accessible repository for the structures of proteins and other biological macromolecules. Computer programs such as [[RasMol]], [[Pymol]] or [[Visual Molecular Dynamics|VMD]] can be used to visualize biological molecular structures.
[[Neutron crystallography]] is often used to help refine structures obtained by X-ray methods or to solve a specific bond; the methods are often viewed as complementary, as X-rays are sensitive to electron positions and scatter most strongly off heavy atoms, while neutrons are sensitive to nucleus positions and scatter strongly even off many light isotopes, including hydrogen and deuterium.
[[Electron diffraction]] has been used to determine some protein structures, most notably [[membrane protein]]s and [[viral capsid]]s.
==Notation==<!-- This section is linked from [[Ion implantation]] -->
{{Main|Miller index}}
* Coordinates in ''square [[bracket]]s'' such as '''<nowiki>[100]</nowiki>''' denote a direction vector (in real space).
* Coordinates in ''angle brackets'' or ''chevrons'' such as '''&lt;100&gt;''' denote a ''family'' of directions which are related by symmetry operations. In the cubic [[crystal system]] for example, '''<100>''' would mean <nowiki>[100], [010], [001]</nowiki> or the negative of any of those directions.
* [[Miller Index|Miller indices]] in ''parentheses'' such as '''(100)''' denote a plane of the crystal structure, and regular repetitions of that plane with a particular spacing. In the cubic system, the [[Normal (geometry)|normal]] to the (hkl) plane is the direction [hkl], but in lower-symmetry cases, the normal to (hkl) is not parallel to [hkl].
* Indices in ''curly brackets'' or ''braces'' such as '''<nowiki>{100}</nowiki>''' denote a family of planes and their normals. In cubic materials the symmetry makes them equivalent, just as the way angle brackets denote a family of directions. In non-cubic materials, <hkl> is not necessarily perpendicular to {hkl}.

== Reference literature ==
The ''International Tables for Crystallography''<ref>{{Cite book |last=Prince |first=E. |url=https://openlibrary.org/books/OL9332669M/Complete_Printed_Set_of_International_Tables_for_Crystallography |title=International Tables for Crystallography Vol. C: Mathematical, Physical and Chemical Tables |publisher=Wiley |year=2006 |isbn=978-1-4020-4969-9 |ol=9332669M |oclc=166325528 |archive-url=https://web.archive.org/web/20220506075232/https://openlibrary.org/books/OL9332669M/Complete_Printed_Set_of_International_Tables_for_Crystallography |archive-date=6 May 2022 |url-status=live}}</ref> is an eight-book series that outlines the standard notations for formatting, describing and testing crystals. The series contains books that covers analysis methods and the mathematical procedures for determining organic structure through x-ray crystallography, electron diffraction, and neutron diffraction. The International tables are focused on procedures, techniques and descriptions and do not list the physical properties of individual crystals themselves. Each book is about 1000 pages and the titles of the books are:

:Vol A -  ''Space Group Symmetry'',
:Vol A1 - ''Symmetry Relations Between Space Groups'',
:Vol B -  ''Reciprocal Space'',
:Vol C - ''Mathematical, Physical, and Chemical Tables'',
:Vol D - ''Physical Properties of Crystals'',
:Vol E - ''Subperiodic Groups'',
:Vol F - ''Crystallography of Biological Macromolecules'', and
:Vol G - ''Definition and Exchange of Crystallographic Data''.

==Notable scientists==
{{columns-list|colwidth=22em|
* [[William Astbury]]
* [[William Barlow (geologist)|William Barlow]]
* [[C. Arnold Beevers]]
* [[John Desmond Bernal]]
* [[William Henry Bragg]]
* [[William Lawrence Bragg]]
* [[Auguste Bravais]]
* [[Liquid Crystal Institute#Directors|Glenn H. Brown]]
* [[Martin Julian Buerger]]
* [[Ernest Gordon Cox|Sir Gordon Cox]]
* [[Francis Crick]]
* [[Durward William John Cruickshank|D. W. J. Cruickshank]]
* [[Pierre Curie]]
* [[Peter Debye]]
* [[Johann Deisenhofer]]
* [[Boris Delone]]
* [[Gautam R. Desiraju]]
* [[Eleanor Dodson]]
* [[Jack Dunitz]]
* [[David Eisenberg]]
* [[Paul Peter Ewald]]
* [[Yevgraf Fyodorov|Evgraf Stepanovich Fedorov]]
* [[Rosalind Franklin]]
* [[Georges Friedel]]
* [[Jenny Glusker]]
* [[Paul Heinrich von Groth]]
* [[Herbert A. Hauptman]]
* [[René Just Haüy]]
* [[Wayne Hendrickson]]
* [[Carl Hermann]]
* [[Johann Friedrich Christian Hessel]]
* [[Dorothy Crowfoot Hodgkin]]
* [[Judith Howard]]
* [[Robert Huber]]
* [[Louise Johnson]]
* [[Isabella Karle]]
* [[Jerome Karle]]
* [[Olga Kennard]]
* [[Aaron Klug]]
* [[Max von Laue]]
* [[Otto Lehmann (physicist)|Otto Lehmann]]
* [[Michael Levitt (biophysicist)|Michael Levitt]]
* [[Henry Lipson]]
* [[Kathleen Lonsdale]]
* [[Ernest-François Mallard]]
* [[Charles-Victor Mauguin]]
* [[William Hallowes Miller]]
* [[Friedrich Mohs]]
* [[Paul Niggli]]
* [[Louis Pasteur]]
* [[Arthur Lindo Patterson]]
* [[Max Perutz]]
* [[Friedrich Reinitzer]]
* [[Hugo Rietveld]]
* [[Jean-Baptiste L. Romé de l'Isle]]
* [[Michael Rossmann]]
* [[Paul Scherrer]]
* [[Arthur Moritz Schönflies]]
* [[Dan Shechtman]]
* [[George M. Sheldrick]]
* [[Tej P. Singh]]
* [[Nicolas Steno]]
* [[Constance Tipper]]
* [[Daniel Vorländer]]
* [[Christian Samuel Weiss]]
* [[Don Craig Wiley]]
* [[Michael Woolfson]]
* [[Ralph Walter Graystone Wyckoff]]
* [[Ada Yonath]]
}}

==See also==
{{div col|colwidth=22em}}
* [[Atomic packing factor]]
* [[Crystal structure]]
* [[Crystallographer]]
* [[Crystallographic database]]
* [[Crystallographic point group]]
* [[Crystallographic group]]
* [[Dana classification system]]
* [[Electron crystallography]]
* [[Electron diffraction]]
* [[Fractional coordinates]]
* [[Low-energy electron diffraction]]
* [[Neutron crystallography]]
* [[Open-pool Australian lightwater reactor|Neutron diffraction at OPAL]]
* [[Institut Laue–Langevin|Neutron diffraction at the ILL]]
* [[NMR crystallography]]
* [[Point group]]
* [[Precession electron diffraction]]
* [[Quasicrystal]]
* [[Reflection high-energy electron diffraction]]
* [[Space group]]
* [[Symmetric group]]
* [[Timeline of crystallography]]
* [[Transmission electron microscopy]]
* [[X-ray crystallography]]
{{div col end}}

==References==
{{reflist}}

==External links==
* [https://www.phase-trans.msm.cam.ac.uk/2020/Crystallography_book.pdf Free book, Geometry of Crystals, Polycrystals and Phase Transformations]
* [http://www.AmerCrystalAssn.org/ American Crystallographic Association]
* [https://www.xtal.iqf.csic.es/Cristalografia/index-en.html Learning Crystallography]
* [http://pd.chem.ucl.ac.uk/pdnn/pdindex.htm Web Course on Crystallography]
* [http://img.chem.ucl.ac.uk/sgp/large/sgp.htm Crystallographic Space Groups]

{{Crystallography}}
{{Branches of materials science}}
{{Geology}}
{{Branches of chemistry}}
{{Authority control}}

[[Category:Crystallography| ]]
[[Category:Chemistry]]
[[Category:Condensed matter physics]]
[[Category:Instrumental analysis]]
[[Category:Materials science]]
[[Category:Neutron-related techniques]]
[[Category:Synchrotron-related techniques]]