Editing X-ray crystallography

{{Short description|Technique used for determining crystal structures and identifying mineral compounds}}
[[File:Freezed XRD.jpg|300px|thumb|upright=1.4|A [[Powder diffractometer|powder X-ray diffractometer]] in motion]]

'''X-ray crystallography''' is the experimental science of determining the atomic and molecular structure of a [[crystal]], in which the crystalline structure causes a beam of incident [[X-ray]]s to [[Diffraction|diffract]] in specific directions. By measuring the angles and intensities of the [[X-ray diffraction]], a [[crystallography|crystallographer]] can produce a three-dimensional picture of the density of [[electron]]s within the crystal and the positions of the atoms, as well as their [[chemical bond]]s, [[crystallographic disorder]], and other information.

X-ray crystallography has been fundamental in the development of many scientific fields. In its first decades of use, this method determined the size of [[atom]]s, the lengths and types of chemical bonds, and the atomic-scale differences between various materials, especially minerals and [[alloy]]s. The method has also revealed the structure and function of many biological molecules, including [[vitamin]]s, drugs, [[protein]]s and [[nucleic acid]]s such as [[DNA]]. X-ray crystallography is still the primary method for characterizing the atomic structure of materials and in differentiating materials that appear similar in other experiments. X-ray [[crystal structure]]s can also help explain unusual [[electronics|electronic]] or [[Elastic deformation|elastic]] properties of a material, shed light on chemical interactions and processes, or serve as the basis for [[drug design|designing pharmaceuticals against diseases]].

Modern work involves a number of steps all of which are important. The preliminary steps include preparing good quality samples, careful recording of the diffracted intensities, and processing of the data to remove artifacts. A variety of different methods are then used to obtain an estimate of the atomic structure, generically called direct methods. With an initial estimate further computational techniques such as those involving difference maps are used to complete the structure. The final step is a numerical refinement of the atomic positions against the experimental data, sometimes assisted by ''ab-initio'' calculations. In almost all cases new structures are deposited in databases available to the international community.

==History==
{{Multiple image|total_width=300
|image1=Kepler conjecture 1.jpg
|alt1=
|caption1=Drawing of square (A) and hexagonal (B) packing from [[Johannes Kepler|Kepler's]] work, ''Strena seu de Nive Sexangula''.
|image2=Snowflake8.png
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|caption2=The hexagonal symmetry of snowflakes results from the [[tetrahedron|tetrahedral]] arrangement of [[hydrogen bond]]s about each water molecule.
}}
Crystals, though long admired for their regularity and [[symmetry]], were not investigated scientifically until the 17th century. [[Johannes Kepler]] hypothesized in his work ''Strena seu de Nive Sexangula'' (A New Year's Gift of Hexagonal Snow) (1611) that the hexagonal symmetry of [[Snowflake|snowflake crystals]] was due to a regular packing of spherical water particles.<ref>{{cite book|vauthors= Kepler J|author-link= Johannes Kepler|date= 1611|title= Strena seu de Nive Sexangula|publisher= G. Tampach|location= Frankfurt|url= http://www.thelatinlibrary.com/kepler/strena.html|isbn= 3-321-00021-0|access-date= 2008-08-25|archive-date= 2011-09-19|archive-url= https://web.archive.org/web/20110919163249/http://www.thelatinlibrary.com/kepler/strena.html|url-status= live}}</ref> The Danish scientist [[Nicolas Steno]] (1669) pioneered experimental investigations of crystal symmetry. Steno showed that the angles between the faces are the same in every exemplar of a particular type of crystal ([[law of constancy of interfacial angles]]).<ref>{{cite book| vauthors = Steno N |author-link= Nicolas Steno|date= 1669|title= De solido intra solidum naturaliter contento dissertationis prodromus|publisher= Florentiae}}</ref> [[René Just Haüy]] (1784) discovered that every face of a crystal can be described by simple stacking patterns of blocks of the same shape and size ([[Law of rational indices|law of decrements]]). Hence, [[William Hallowes Miller]] in 1839 was able to give each face a unique label of three small integers, the [[Miller index|Miller indices]] which remain in use for identifying crystal faces. Haüy's study led to the idea that crystals are a regular three-dimensional array (a [[Bravais lattice]]) of atoms and [[molecule]]s; a single [[unit cell]] is repeated indefinitely along three principal directions. In the 19th century, a complete catalog of the possible symmetries of a crystal was worked out by [[Johann F. C. Hessel|Johan Hessel]],<ref>{{cite book| vauthors = Hessel JF |date= 1831|title= Kristallometrie oder Kristallonomie und Kristallographie|publisher= Leipzig}}</ref> [[Auguste Bravais]],<ref>{{cite journal| vauthors = Bravais A|author-link= Auguste Bravais|date= 1850|title= Mémoire sur les systèmes formés par des points distribués regulièrement sur un plan ou dans l'espace|journal= Journal de l'École Polytechnique|volume= 19|page=1}}</ref> [[Evgraf Fedorov]],<ref>{{Cite journal|vauthors= Shafranovskii II, Belov NV|title= E. S. Fedorov|journal= 50 Years of X-Ray Diffraction|editor= Paul Ewald|publisher= Springer|date= 1962|isbn= 90-277-9029-9|url= http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/fedorov.pdf|page= 351|access-date= 2007-09-25|archive-date= 2007-09-28|archive-url= https://web.archive.org/web/20070928070656/http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/fedorov.pdf|url-status= live}}</ref> [[Arthur Moritz Schönflies|Arthur Schönflies]]<ref>{{cite book| vauthors = Schönflies A|author-link= Arthur Moritz Schönflies|date= 1891|title= Kristallsysteme und Kristallstruktur|publisher= Leipzig}}</ref> and (belatedly) [[William Barlow (geologist)|William Barlow]] (1894). Barlow proposed several crystal structures in the 1880s that were validated later by X-ray crystallography;<ref>{{cite journal|vauthors= Barlow W|date= 1883|title= Probable nature of the internal symmetry of crystals|journal= Nature|volume= 29|page= 186|doi= 10.1038/029186a0|issue= 738|bibcode= 1883Natur..29..186B|url= https://zenodo.org/record/1429283|doi-access= free|access-date= 2019-09-10|archive-date= 2020-03-29|archive-url= https://web.archive.org/web/20200329132634/https://zenodo.org/record/1429283|url-status= live}} See also {{cite journal| vauthors =  Barlow W |title= Probable Nature of the Internal Symmetry of Crystals|journal= Nature|volume= 29|page=205|date= 1883|doi= 10.1038/029205a0|issue= 739|bibcode = 1883Natur..29..205B |doi-access= free}} {{cite journal|vauthors= Sohncke L|title= Probable Nature of the Internal Symmetry of Crystals|journal= Nature|volume= 29|page= 383|date= 1884|doi= 10.1038/029383a0|issue= 747|bibcode= 1884Natur..29..383S|s2cid= 4072817|url= https://zenodo.org/record/1429283|access-date= 2019-09-10|archive-date= 2020-03-29|archive-url= https://web.archive.org/web/20200329132634/https://zenodo.org/record/1429283|url-status= live}} {{cite journal|vauthors= Barlow WM|title= Probable Nature of the Internal Symmetry of Crystals|journal= Nature|volume= 29|page= 404|date= 1884|doi= 10.1038/029404b0|issue= 748|bibcode= 1884Natur..29..404B|s2cid= 4016086|url= https://zenodo.org/record/1429283|doi-access= free|access-date= 2019-09-10|archive-date= 2020-03-29|archive-url= https://web.archive.org/web/20200329132634/https://zenodo.org/record/1429283|url-status= live}}</ref> however, the available data were too scarce in the 1880s to accept his models as conclusive.

[[File:3D model hydrogen bonds in water.svg|thumb|Model of the arrangement of water molecules in ice, revealing the [[hydrogen bond]]s (1) that hold the solid together.]]

[[Wilhelm Röntgen]] discovered X-rays in 1895.<ref name="Stoddart">{{cite journal |vauthors=Stoddart C |title=Structural biology: How proteins got their close-up |journal=Knowable Magazine |date=1 March 2022 |doi=10.1146/knowable-022822-1 |doi-access=free |url=https://knowablemagazine.org/article/living-world/2022/structural-biology-how-proteins-got-their-closeup |access-date=25 March 2022 |archive-date=7 April 2022 |archive-url=https://web.archive.org/web/20220407231646/https://knowablemagazine.org/article/living-world/2022/structural-biology-how-proteins-got-their-closeup |url-status=live }}</ref> Physicists were uncertain of the nature of X-rays, but suspected that they were waves of [[electromagnetic radiation]]. The [[James Clerk Maxwell|Maxwell]] theory of [[electromagnetic radiation]] was well accepted, and experiments by [[Charles Glover Barkla]] showed that X-rays exhibited phenomena associated with electromagnetic waves, including transverse [[Polarization (waves)|polarization]] and [[spectral line]]s akin to those observed in the visible wavelengths. Barkla created the x-ray notation for sharp spectral lines, noting in 1909 two separate energies, at first naming them "A" and "B" and then supposing that there may be lines prior to "A", he started an alphabet numbering beginning with "K."<ref>Barkla, Charles G. (1911). "XXXIX.The spectra of the fluorescent Röntgen radiations". Philosophical Magazine. Series 6. 22 (129): 396–412. doi:10.1080/14786440908637137.</ref><ref name="Michael Eckert 2011">Michael Eckert, Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions, January 2011, Acta crystallographica. Section A, Foundations of crystallography 68(1):30–39 This Laue centennial article has also been published in Zeitschrift für Kristallographie [Eckert (2012). Z. Kristallogr. 227, 27–35].</ref> Single-slit experiments in the laboratory of [[Arnold Sommerfeld]] suggested that X-rays had a [[wavelength]] of about 1 [[angstrom]].<ref>Nisio, Sigeko. "The Formation of the Sommerfeld Quantum Theory of 1916." (1974) JSHS, No.12. pp39-78.</ref> X-rays are not only waves but also have particle properties causing Sommerfeld to coin the name [[Bremsstrahlung]] for the continuous spectra when they were formed when electrons bombarded a material.<ref name="Michael Eckert 2011" /> [[Albert Einstein]] introduced the photon concept in 1905,<ref>{{cite journal| vauthors = Einstein A|author-link= Albert Einstein|date= 1905|title= Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt |trans-title= A Heuristic Model of the Creation and Transformation of Light|journal= [[Annalen der Physik]]|volume= 17|page=132|bibcode= 1905AnP...322..132E |doi= 10.1002/andp.19053220607|issue= 6 |language= de|doi-access= free}}. An [[s:A Heuristic Model of the Creation and Transformation of Light|English translation]] is available from [[Wikisource]].</ref> but it was not broadly accepted until 1922,<ref>Compare: {{cite journal| vauthors = Einstein A|date= 1909|title= Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung |trans-title= The Development of Our Views on the Composition and Essence of Radiation |journal= Physikalische Zeitschrift|volume= 10|page=817|language= de}}. An [[s:The Development of Our Views on the Composition and Essence of Radiation|English translation]] is available from [[Wikisource]].</ref><ref>{{cite book| vauthors = Pais A |author-link= Abraham Pais|date= 1982|title= Subtle is the Lord: The Science and the Life of Albert Einstein|publisher= [[Oxford University Press]]|isbn= 0-19-853907-X|url= https://archive.org/details/subtleislordscie00pais}}</ref> when [[Arthur Compton]] confirmed it by the scattering of X-rays from electrons.<ref>{{cite journal|vauthors= Compton A|author-link= Arthur Compton|date= 1923|title= A Quantum Theory of the Scattering of X-rays by Light Elements|journal= Phys. Rev.|volume= 21|page= 483|doi= 10.1103/PhysRev.21.483|url= https://history.aip.org/history/exhibits/gap/PDF/compton.pdf|issue= 5|bibcode= 1923PhRv...21..483C|doi-access= free|access-date= 2019-09-15|archive-date= 2020-08-10|archive-url= https://web.archive.org/web/20200810055602/https://history.aip.org/history/exhibits/gap/PDF/compton.pdf|url-status= live}}</ref> The particle-like properties of X-rays, such as their ionization of gases, had prompted [[William Henry Bragg]] to argue in 1907 that X-rays were ''not'' electromagnetic radiation.<ref>{{cite journal| vauthors = Bragg WH|author-link= William Henry Bragg|date= 1907|title= The nature of Röntgen rays|journal= Transactions of the Royal Society of Science of Australia|volume= 31|page=94}}</ref><ref>{{cite journal|vauthors= Bragg WH|date= 1908|title= The nature of γ- and X-rays|journal= Nature|volume= 77|page= 270|doi= 10.1038/077270a0|issue= 1995|bibcode= 1908Natur..77..270B|s2cid= 4020075|url= https://zenodo.org/record/1429495|access-date= 2019-09-10|archive-date= 2020-03-29|archive-url= https://web.archive.org/web/20200329132644/https://zenodo.org/record/1429495|url-status= live}} See also {{cite journal|vauthors= Bragg WH|title= The Nature of the γ and X-Rays|journal= Nature|volume= 78|page= 271|date= 1908|doi= 10.1038/078271a0|issue= 2021|bibcode= 1908Natur..78..271B|s2cid= 4039315|url= https://zenodo.org/record/1429507|doi-access= free|access-date= 2020-06-03|archive-date= 2021-03-27|archive-url= https://web.archive.org/web/20210327105811/https://zenodo.org/record/1429507|url-status= live}} {{cite journal| vauthors = Bragg WH |title= The Nature of the γ and X-Rays|journal= Nature|volume= 78|page=293|date= 1908|doi= 10.1038/078293d0|issue= 2022|bibcode= 1908Natur..78..293B |s2cid= 3993814}} {{cite journal|vauthors= Bragg WH|title= The Nature of X-Rays|journal= Nature|volume= 78|page= 665|date= 1908|doi= 10.1038/078665b0|issue= 2035|bibcode= 1908Natur..78R.665B|s2cid= 4024851|url= https://zenodo.org/record/1429511|doi-access= free|access-date= 2020-08-27|archive-date= 2021-03-27|archive-url= https://web.archive.org/web/20210327105819/https://zenodo.org/record/1429511|url-status= live}}</ref><ref>{{cite journal|vauthors= Bragg WH|date= 1910|title= The consequences of the corpuscular hypothesis of the γ- and X-rays, and the range of β-rays|journal= Phil. Mag.|volume= 20|page= 385|doi= 10.1080/14786441008636917|issue= 117|url= https://zenodo.org/record/1430874|access-date= 2019-09-10|archive-date= 2020-03-29|archive-url= https://web.archive.org/web/20200329132633/https://zenodo.org/record/1430874|url-status= live}}</ref><ref>{{cite journal| vauthors = Bragg WH |date= 1912|title= On the direct or indirect nature of the ionization by X-rays|doi= 10.1080/14786440408637253 |journal= Phil. Mag.|volume= 23|page=647|issue= 136}}</ref>  Bragg's view proved unpopular and the observation of [[X-ray diffraction]] by [[Max von Laue]] in 1912<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%3AInterferenz-Erscheinungen_bei_R%C3%B6ntgenstrahlen.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 |access-date=2024-07-14 |archive-date=2024-05-21 |archive-url=https://web.archive.org/web/20240521103746/https://commons.wikimedia.org/wiki/File:Interferenz-Erscheinungen_bei_R%C3%B6ntgenstrahlen.pdf |url-status=live }}</ref> confirmed that X-rays are a form of electromagnetic radiation. [[File:Interferenz-Erscheinungen bei Röntgenstrahlen Tafel II Fig. 5.jpg|thumb|One of the copper sulfate X-ray interference patterns published in Von Laue's 1912 paper{{r|L1912}}.]]

The idea that crystals could be used as a [[diffraction grating]] for [[X-ray]]s arose in 1912 in a conversation between [[Paul Peter Ewald]] and [[Max von Laue]] in the [[Englischer Garten|English Garden]] in Munich. Ewald had proposed a resonator model of crystals for his thesis, but this model could not be validated using [[visible light]], since the wavelength was much larger than the spacing between the resonators. Von Laue realized that electromagnetic radiation of a shorter wavelength was needed, and suggested that X-rays might have a wavelength comparable to the unit-cell spacing in crystals. Von Laue worked with two technicians, [[Walter Friedrich]] and his assistant Paul Knipping, to shine a beam of X-rays through a [[Copper(II) sulfate|copper sulfate]] crystal and record its diffraction on a [[photographic plate]]. After being developed, the plate showed a large number of well-defined spots arranged in a pattern of intersecting circles around the spot produced by the central beam. The results were presented to the [[Bavarian Academy of Sciences and Humanities]] in June 1912 as "Interferenz-Erscheinungen bei Röntgenstrahlen" (Interference phenomena in X-rays).<ref name="L1912"/><ref>{{cite journal |vauthors=von Laue M |date=1914 |title=Concerning the detection of x-ray interferences |url=http://nobelprize.org/nobel_prizes/physics/laureates/1914/laue-lecture.pdf |journal=Nobel Lectures, Physics |volume=1901–1921 |access-date=2009-02-18 |archive-date=2010-12-07 |archive-url=https://web.archive.org/web/20101207113911/http://nobelprize.org/nobel_prizes/physics/laureates/1914/laue-lecture.pdf |url-status=live }}</ref> Von Laue developed a law that connects the scattering angles and the size and orientation of the unit-cell spacings in the crystal, for which he was awarded the [[Nobel Prize in Physics]] in 1914.<ref>{{cite book |title=A Textbook of Mineralogy |vauthors=Dana ES, Ford WE |date=1932 |publisher=John Wiley & Sons |edition=fourth |location=New York |page=28}}</ref>

[[File:Diamond and graphite2.jpg|thumb|Although diamonds (top left) and [[graphite]] (top right) are identical in chemical composition—being both pure [[carbon]]—X-ray crystallography revealed the arrangement of their atoms (bottom). In diamond, the carbon atoms are arranged [[diamond cubic|tetrahedrally]] and held together by single [[covalent bond]]s. By contrast, graphite is composed of stacked sheets. Within the sheet, the bonding is covalent and has hexagonal symmetry, but there are no covalent bonds between the sheets.]]
After Von Laue's pioneering research, the field developed rapidly, most notably by physicists [[William Lawrence Bragg]] and his father [[William Henry Bragg]]. In 1912–1913, the younger Bragg developed [[Bragg's law]], which connects the scattering with evenly spaced planes within a crystal.<ref name="Stoddart"/><ref>{{cite journal|vauthors=Bragg WL|date=1912|title=The Specular Reflexion of X-rays|journal=Nature|volume=90|page=410|doi=10.1038/090410b0|issue=2250|bibcode=1912Natur..90..410B|s2cid=3952319|url=https://zenodo.org/record/1429558|doi-access=free|access-date=2019-09-10|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132707/https://zenodo.org/record/1429558|url-status=live}}</ref><ref>{{cite journal| vauthors = Bragg WL|date = 1913|title=The Diffraction of Short Electromagnetic Waves by a Crystal|journal=Proceedings of the Cambridge Philosophical Society|volume=17|page=43}}</ref><ref>{{cite journal| vauthors = Bragg WL |date = 1914|title=Die Reflexion der Röntgenstrahlen|journal=Jahrbuch der Radioaktivität und Elektronik|volume=11|page=350}}</ref> The Braggs, father and son, shared the 1915 Nobel Prize in Physics for their work in crystallography. The earliest structures were generally simple; as computational and experimental methods improved over the next decades, it became feasible to deduce reliable atomic positions for more complicated arrangements of atoms.

The earliest structures were simple inorganic crystals and minerals, but even these revealed fundamental laws of physics and chemistry. The first atomic-resolution structure to be "solved" (i.e., determined) in 1914 was that of [[sodium chloride|table salt]].<ref>{{cite journal| vauthors = Bragg WL |date=1913|title=The Structure of Some Crystals as Indicated by their Diffraction of X-rays|journal=Proc. R. Soc. Lond.|volume=A89|issue=610|jstor=93488|pages=248–277|bibcode=1913RSPSA..89..248B|doi=10.1098/rspa.1913.0083|doi-access=free}}</ref><ref>{{cite journal|vauthors=Bragg WL, James RW, Bosanquet CH|date=1921|title=The Intensity of Reflexion of X-rays by Rock-Salt|journal=Phil. Mag.|volume=41|page=309|doi=10.1080/14786442108636225|issue=243|url=https://zenodo.org/record/1430965|access-date=2019-09-10|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132638/https://zenodo.org/record/1430965|url-status=live}}</ref><ref>{{cite journal|vauthors=Bragg WL, James RW, Bosanquet CH|date=1921|title=The Intensity of Reflexion of X-rays by Rock-Salt. Part II|journal=Phil. Mag.|volume=42|page=1|doi=10.1080/14786442108633730|issue=247|url=https://zenodo.org/record/1430951|access-date=2019-09-10|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132627/https://zenodo.org/record/1430951|url-status=live}}</ref> The distribution of electrons in the table-salt structure showed that crystals are not necessarily composed of [[covalent bond|covalently bonded]] molecules, and proved the existence of [[ionic compound]]s.<ref>{{cite journal|vauthors=Bragg WL, James RW, Bosanquet CH|date=1922|title=The Distribution of Electrons around the Nucleus in the Sodium and Chlorine Atoms|journal=Phil. Mag.|volume=44|page=433|doi=10.1080/14786440908565188|issue=261|url=https://zenodo.org/record/1430852|access-date=2019-09-10|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132623/https://zenodo.org/record/1430852|url-status=live}}</ref> The structure of diamond was solved in the same year,<ref name=dia >{{cite journal|vauthors=Bragg WH, Bragg WL|date=1913|title=The structure of the diamond|journal=Nature|volume=91|page=557|doi=10.1038/091557a0|issue=2283|bibcode=1913Natur..91..557B|s2cid=3987932|url=https://zenodo.org/record/1429564|doi-access=free|access-date=2020-08-27|archive-date=2021-03-26|archive-url=https://web.archive.org/web/20210326103553/https://zenodo.org/record/1429564|url-status=live}}</ref><ref>{{cite journal| vauthors = Bragg WH, Bragg WL |date=1913|title=The structure of the diamond|journal= Proc. R. Soc. Lond.|volume=A89|page=277|doi=10.1098/rspa.1913.0084|issue=610|bibcode = 1913RSPSA..89..277B |doi-access=free}}</ref> proving the tetrahedral arrangement of its chemical bonds and showing that the length of C–C single bond was about 1.52 angstroms. Other early structures included copper,<ref>{{cite journal|vauthors=Bragg WL|date=1914|title=The Crystalline Structure of Copper|doi=10.1080/14786440908635219|journal=Phil. Mag.|volume=28|page=355|issue=165|url=https://zenodo.org/record/1430856|access-date=2019-09-10|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132712/https://zenodo.org/record/1430856|url-status=live}}</ref> [[calcium fluoride]] (CaF<sub>2</sub>, also known as ''fluorite''), [[calcite]] (CaCO<sub>3</sub>) and [[pyrite]] (FeS<sub>2</sub>)<ref name=carb >{{cite journal| vauthors = Bragg WL|date = 1914|title=The analysis of crystals by the X-ray spectrometer|doi=10.1098/rspa.1914.0015 |journal=Proc. R. Soc. Lond.|volume=A89|page=468|issue=613|bibcode=1914RSPSA..89..468B |doi-access=free}}</ref> in 1914; [[spinel]] (MgAl<sub>2</sub>O<sub>4</sub>) in 1915;<ref>{{cite journal|vauthors=Bragg WH|author-link=William Henry Bragg|date=1915|title=The structure of the spinel group of crystals|doi=10.1080/14786440808635400|journal=Phil. Mag.|volume=30|page=305|issue=176|url=https://zenodo.org/record/1430832|access-date=2019-09-10|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132637/https://zenodo.org/record/1430832|url-status=live}}</ref><ref>{{cite journal| vauthors = Nishikawa S |date=1915 |title=Structure of some crystals of spinel group|journal=Proc. Tokyo Math. Phys. Soc.|volume=8|page=199}}</ref> the [[rutile]] and [[anatase]] forms of [[titanium dioxide]] (TiO<sub>2</sub>) in 1916;<ref>{{cite journal|vauthors=Vegard L|date=1916|title=Results of Crystal Analysis|doi=10.1080/14786441608635544|journal=Phil. Mag.|volume=32|page=65|issue=187|url=https://zenodo.org/record/1430936|access-date=2019-09-10|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132659/https://zenodo.org/record/1430936|url-status=live}}</ref> [[Manganese(II) hydroxide|pyrochroite]] (Mn(OH)<sub>2</sub>) and, by extension, [[brucite]] (Mg(OH)<sub>2</sub>) in 1919.<ref>{{cite journal|vauthors=Aminoff G|date=1919|title=Crystal Structure of Pyrochroite|journal=Stockholm Geol. Fören. Förh.|volume=41|page=407|doi=10.1080/11035891909447000|url=https://zenodo.org/record/1532436|access-date=2019-09-10|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132707/https://zenodo.org/record/1532436|url-status=live}}</ref><ref>{{cite journal | vauthors = Aminoff G|date = 1921|title=Über die Struktur des Magnesiumhydroxids|journal=Z. Kristallogr.|volume=56|page=505}}</ref> Also in 1919, [[sodium nitrate]] (NaNO<sub>3</sub>) and caesium dichloroiodide (CsICl<sub>2</sub>) were determined by [[Ralph Walter Graystone Wyckoff]], and the [[wurtzite]] (hexagonal ZnS) structure was determined in 1920.<ref>{{cite journal|vauthors=Bragg WL|date=1920|title=The crystalline structure of zinc oxide|doi=10.1080/14786440608636079|journal=Phil. Mag.|volume=39|page=647|issue=234|url=https://zenodo.org/record/1430802|access-date=2020-06-03|archive-date=2021-10-25|archive-url=https://web.archive.org/web/20211025083928/https://zenodo.org/record/1430802|url-status=live}}</ref>

The structure of [[graphite]] was solved in 1916<ref>{{cite journal|date = 1916|title=Interferenz an regellos orientierten Teilchen im Röntgenlicht I|journal=Physikalische Zeitschrift|volume=17|page=277| vauthors = Debije P, Scherrer P |author-link1=Peter Debye}}</ref> by the related method of [[powder diffraction]],<ref>{{cite journal| vauthors = Friedrich W|date = 1913|title=Eine neue Interferenzerscheinung bei Röntgenstrahlen|journal=Physikalische Zeitschrift|volume=14|page=317}}</ref> which was developed by [[Peter Debye]] and [[Paul Scherrer]] and, independently, by [[Albert Hull]] in 1917.<ref>{{cite journal| vauthors = Hull AW|author-link=Albert Hull|date = 1917|title=A New Method of X-ray Crystal Analysis|journal=Phys. Rev.|volume=10|page=661|doi=10.1103/PhysRev.10.661|issue=6|bibcode = 1917PhRv...10..661H }}</ref> The structure of graphite was determined from single-crystal diffraction in 1924 by two groups independently.<ref>{{cite journal| vauthors = Bernal JD|author-link=John Desmond Bernal|date = 1924|title=The Structure of Graphite|jstor=94336|journal= Proc. R. Soc. Lond.|volume=A106|issue=740|pages=749–773}}</ref><ref>{{cite journal| vauthors = Hassel O, Mack H |date = 1924|title=Über die Kristallstruktur des Graphits|journal=Zeitschrift für Physik|volume=25|issue=1|page=317|doi=10.1007/BF01327534|bibcode = 1924ZPhy...25..317H |s2cid=121157442}}</ref> Hull also used the powder method to determine the structures of various metals, such as iron<ref>{{cite journal|author=Hull AW|date = 1917|title=The Crystal Structure of Iron|journal=Phys. Rev.|volume=9|issue = 1|page=84|doi= 10.1103/PhysRev.9.83|bibcode = 1917PhRv....9...83. }}</ref> and magnesium.<ref>{{cite journal | vauthors = Hull AW | title = The Crystal Structure of Magnesium | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 3 | issue = 7 | pages = 470–473 | date = July 1917 | pmid = 16576242 | pmc = 1091290 | doi = 10.1073/pnas.3.7.470 | doi-access = free | bibcode = 1917PNAS....3..470H }}</ref>

==Contributions in different areas==

=== Chemistry ===
X-ray crystallography has led to a better understanding of [[chemical bond]]s and [[noncovalent bonding|non-covalent interactions]]. The initial studies revealed the typical radii of atoms, and confirmed many theoretical models of chemical bonding, such as the tetrahedral bonding of carbon in the diamond structure,<ref name=dia /> the octahedral bonding of metals observed in ammonium hexachloroplatinate (IV),<ref>{{cite journal|vauthors=Wyckoff RW, Posnjak E|date=1921|title=The Crystal Structure of Ammonium Chloroplatinate|journal=J. Am. Chem. Soc.|volume=43|page=2292|doi=10.1021/ja01444a002|issue=11|url=https://zenodo.org/record/1428818|access-date=2020-06-03|archive-date=2021-04-13|archive-url=https://web.archive.org/web/20210413130753/https://zenodo.org/record/1428818|url-status=live}}</ref> and the resonance observed in the planar carbonate group<ref name=carb /> and in aromatic molecules.<ref name=antr /> [[Kathleen Lonsdale]]'s 1928 structure of [[hexamethylbenzene]]<ref>{{cite journal| vauthors = Lonsdale K|author-link=Kathleen Lonsdale|date=1928|title=The structure of the benzene ring|journal=Nature|volume=122|page=810|doi=10.1038/122810c0|issue=3082|bibcode=1928Natur.122..810L |s2cid=4105837|doi-access=free}}</ref> established the hexagonal symmetry of [[benzene]] and showed a clear difference in bond length between the aliphatic C–C bonds and aromatic C–C bonds; this finding led to the idea of [[resonance (chemistry)|resonance]] between chemical bonds, which had profound consequences for the development of chemistry.<ref>{{cite book| vauthors = Pauling L|author-link=Linus Pauling|title=The Nature of the Chemical Bond|edition=3rd|publisher=[[Cornell University Press]]|location=Ithaca, NY|isbn=0-8014-0333-2|year=1960}}</ref> Her conclusions were anticipated by [[William Henry Bragg]], who published models of [[naphthalene]] and [[anthracene]] in 1921 based on other molecules, an early form of [[molecular replacement]].<ref name=antr >{{cite journal|vauthors=Bragg WH|author-link=William Henry Bragg|date=1921|title=The structure of organic crystals|doi=10.1088/1478-7814/34/1/306|journal=Proc. R. Soc. Lond.|volume=34|issue=1|page=33|bibcode=1921PPSL...34...33B|s2cid=4098112|url=https://zenodo.org/record/1431507|access-date=2020-08-27|archive-date=2021-04-13|archive-url=https://web.archive.org/web/20210413130806/https://zenodo.org/record/1431507|url-status=live}}</ref><ref>{{cite journal|vauthors=Bragg WH|author-link=William Henry Bragg|date=1922|title=The crystalline structure of anthracene|doi=10.1088/1478-7814/35/1/320|journal=Proc. R. Soc. Lond.|volume=35|issue=1|page=167|bibcode=1922PPSL...35..167B|url=https://zenodo.org/record/1431515|access-date=2020-08-27|archive-date=2021-04-13|archive-url=https://web.archive.org/web/20210413130804/https://zenodo.org/record/1431515|url-status=live}}</ref>

The first structure of an organic compound, [[hexamethylenetetramine]], was solved in 1923.<ref>{{cite journal|vauthors=Dickinson RG, Raymond AL|date=1923|title=The Crystal Structure of Hexamethylene-Tetramine|journal=[[J. Am. Chem. Soc.]]|volume=45|page=22|doi=10.1021/ja01654a003|url=https://thesis.library.caltech.edu/756/1/Raymond_al_1923.pdf|access-date=2019-09-10|archive-date=2020-08-11|archive-url=https://web.archive.org/web/20200811125312/https://thesis.library.caltech.edu/756/1/Raymond_al_1923.pdf|url-status=live}}</ref> This was rapidly followed by several studies of different long-chain [[fatty acid]]s, which are an important component of [[biological membranes]].<ref>{{cite journal| vauthors = Müller A |date=1923|title=The X-ray Investigation of Fatty Acids|journal=Journal of the Chemical Society|volume=123|page=2043|doi=10.1039/ct9232302043}}</ref><ref>{{cite journal| vauthors = Saville WB, Shearer G |date=1925|title=An X-ray Investigation of Saturated Aliphatic Ketones|journal=Journal of the Chemical Society|volume=127|page=591|doi=10.1039/ct9252700591}}</ref><ref>{{cite journal | vauthors = Bragg WH |author-link=William Henry Bragg|date=1925|title=The Investigation of thin Films by Means of X-rays|journal=Nature|volume=115|page=266|doi=10.1038/115266a0|issue=2886|bibcode = 1925Natur.115..266B |doi-access=free}}</ref><ref>{{cite journal|date=1925|title=Sur l'interprétation physique des spectres X d'acides gras|journal=[[Comptes rendus hebdomadaires des séances de l'Académie des sciences]]|volume=180|page=1485| vauthors = de Broglie M, Trillat JJ |author-link1=Maurice de Broglie}}</ref><ref>{{cite journal| vauthors = Trillat JJ|date=1926|title=Rayons X et Composeés organiques à longe chaine. Recherches spectrographiques sue leurs structures et leurs orientations|journal=[[Annales de Physique]]|volume=10|issue=6|page=5|doi=10.1051/anphys/192610060005|bibcode=1926AnPh...10....5T}}</ref><ref>{{cite journal| vauthors = Caspari WA|date=1928|title=Crystallography of the Aliphatic Dicarboxylic Acids|journal=Journal of the Chemical Society|volume=?|page=3235|doi=10.1039/jr9280003235}}</ref><ref>{{cite journal| vauthors = Müller A|date = 1928|title=X-ray Investigation of Long Chain Compounds (n. Hydrocarbons)|journal= [[Proc. R. Soc. Lond.]]|volume=120|page=437|doi=10.1098/rspa.1928.0158|issue=785|bibcode = 1928RSPSA.120..437M |doi-access=free}}</ref><ref>{{cite journal| vauthors = Piper SH|date = 1929|title=Some Examples of Information Obtainable from the long Spacings of Fatty Acids|journal=[[Transactions of the Faraday Society]]|volume=25|page=348|doi=10.1039/tf9292500348}}</ref><ref>{{cite journal| vauthors = Müller A|date = 1929|title=The Connection between the Zig-Zag Structure of the Hydrocarbon Chain and the Alternation in the Properties of Odd and Even Numbered Chain Compounds|journal= Proc. R. Soc. Lond.|volume=124|page=317|doi=10.1098/rspa.1929.0117|issue=794|bibcode = 1929RSPSA.124..317M |doi-access=free}}</ref> In the 1930s, the structures of much larger molecules with two-dimensional complexity began to be solved. A significant advance was the structure of [[phthalocyanine]],<ref>{{cite journal| vauthors = Robertson JM|date=1936|title=An X-ray Study of the Phthalocyanines, Part II|journal=Journal of the Chemical Society|page=1195|doi=10.1039/jr9360001195}}</ref> a large planar molecule that is closely related to [[porphyrin|porphyrin molecules]] important in biology, such as [[heme]], [[corrin]] and [[chlorophyll]].

In the 1920s, [[Victor Moritz Goldschmidt]] and later [[Linus Pauling]] developed rules for eliminating chemically unlikely structures and for determining the relative sizes of atoms. These rules led to the structure of [[brookite]] (1928) and an understanding of the relative stability of the [[rutile]], [[brookite]] and [[anatase]] forms of [[titanium dioxide]].

The distance between two bonded atoms is a sensitive measure of the bond strength and its [[bond order]]; thus, X-ray crystallographic studies have led to the discovery of even more exotic types of bonding in [[inorganic chemistry]], such as metal-metal double bonds,<ref>{{cite journal| vauthors = Powell HM, Ewens RV |date=1939|title=The crystal structure of iron enneacarbonyl|journal=J. Chem. Soc.|page=286|doi=10.1039/jr9390000286}}</ref><ref>{{cite journal | vauthors = Bertrand JA, Cotton FA, Dollase WA |date=1963|title=The Metal-Metal Bonded, Polynuclear Complex Anion in CsReCl<sub>4</sub>|journal=J. Am. Chem. Soc.|volume=85|page=1349|doi=10.1021/ja00892a029|issue=9 }}</ref><ref>{{cite journal| vauthors = Robinson WT, Fergusson JE, Penfold BR|date=1963|title=Configuration of Anion in CsReCl<sub>4</sub>|journal=Proceedings of the Chemical Society of London|page=116}}</ref> metal-metal quadruple bonds,<ref>{{cite journal | vauthors = Cotton FA, Curtis NF, Harris CB, Johnson BF, Lippard SJ, Mague JT, Robinson WR, Wood JS | display-authors = 6 | title = Mononuclear and Polynuclear Chemistry of Rhenium (III): Its Pronounced Homophilicity | journal = Science | volume = 145 | issue = 3638 | pages = 1305–1307 | date = September 1964 | pmid = 17802015 | doi = 10.1126/science.145.3638.1305 | s2cid = 29700317 | bibcode = 1964Sci...145.1305C | author-link1 = F. Albert Cotton }}</ref><ref>{{cite journal|date=1965|title=The Crystal and Molecular Structure of Dipotassium Octachlorodirhenate(III) Dihydrate|journal=Inorganic Chemistry|volume=4|page=330|doi=10.1021/ic50025a015|issue=3 | vauthors = Cotton FA, Harris CB |author-link1 = F. Albert Cotton}}</ref><ref>{{cite journal| vauthors = Cotton FA|author-link= F. Albert Cotton|title=Metal-Metal Bonding in [Re<sub>2</sub>X<sub>8</sub>]<sup>2−</sup> Ions and Other Metal Atom Clusters|journal=Inorganic Chemistry|volume=4|page=334|doi=10.1021/ic50025a016|date=1965|issue=3}}</ref> and [[Three-center two-electron bond|three-center, two-electron bonds]].<ref>{{cite journal| vauthors = Eberhardt WH, Crawford Jr W, Lipscomb WN |date=1954|title=The valence structure of the boron hydrides|journal=J. Chem. Phys.|volume=22|page=989|doi=10.1063/1.1740320|issue=6|bibcode=1954JChPh..22..989E}}</ref> X-ray crystallography—or, strictly speaking, an inelastic [[Compton scattering]] experiment—has also provided evidence for the partly covalent character of [[hydrogen bond]]s.<ref>{{cite journal | vauthors = Martin TW, Derewenda ZS | title = The name is bond—H bond | journal = Nature Structural Biology | volume = 6 | issue = 5 | pages = 403–406 | date = May 1999 | pmid = 10331860 | doi = 10.1038/8195 | s2cid = 27195273 }}</ref> In the field of [[organometallic chemistry]], the X-ray structure of [[ferrocene]] initiated scientific studies of [[sandwich compounds]],<ref>{{cite journal| vauthors = Dunitz JD, Orgel LE, Rich A |date=1956|title=The crystal structure of ferrocene|journal=Acta Crystallographica|volume=9|page=373|doi=10.1107/S0365110X56001091|issue=4|bibcode=1956AcCry...9..373D |doi-access=free}}</ref><ref>{{cite journal| vauthors = Seiler P, Dunitz JD |date=1979|title=A new interpretation of the disordered crystal structure of ferrocene|doi=10.1107/S0567740879005598 |journal=Acta Crystallographica B|volume=35|page=1068|issue=5|bibcode=1979AcCrB..35.1068S }}</ref> while that of [[Zeise's salt]] stimulated research into "back bonding" and metal-pi complexes.<ref>{{cite journal| vauthors = Wunderlich JA, Mellor DP |date=1954 |title=A note on the crystal structure of Zeise's salt|journal=Acta Crystallographica|volume=7|issue=1 |page=130|doi=10.1107/S0365110X5400028X|bibcode=1954AcCry...7..130W |doi-access=free}}</ref><ref>{{cite journal| vauthors = Jarvis JA, Kilbourn BT, Owston PG |author-link3=P. G. Owston|date=1970|title=A re-determination of the crystal and molecular structure of Zeise's salt, KPtCl<sub>3</sub>.C<sub>2</sub>H<sub>4</sub>.H<sub>2</sub>O. A correction|journal=Acta Crystallographica B|volume=26|page=876|doi=10.1107/S056774087000328X|issue=6|bibcode=1970AcCrB..26..876J }}</ref><ref>{{cite journal| vauthors = Jarvis JA, Kilbourn BT, Owston PG |author-link3=P. G. Owston|date=1971|title=A re-determination of the crystal and molecular structure of Zeise's salt, KPtCl<sub>3</sub>.C<sub>2</sub>H<sub>4</sub>.H<sub>2</sub>O|doi=10.1107/S0567740871002231|journal=Acta Crystallographica B|volume=27|page=366|issue=2|bibcode=1971AcCrB..27..366J |doi-access=free}}</ref><ref>{{cite journal| vauthors = Love RA, Koetzle TF, Williams GJ, Andrews LC, Bau R|date=1975|title=Neutron diffraction study of the structure of Zeise's salt, KPtCl<sub>3</sub>(C<sub>2</sub>H<sub>4</sub>).H<sub>2</sub>O|journal=Inorganic Chemistry|volume=14|page=2653|doi=10.1021/ic50153a012|issue=11}}</ref> Finally, X-ray crystallography had a pioneering role in the development of [[supramolecular chemistry]], particularly in clarifying the structures of the [[crown ether]]s and the principles of [[host–guest chemistry]].{{cn|date=July 2024}}

===Materials science and mineralogy===
[[File:PIA16217-MarsCuriosityRover-1stXRayView-20121017.jpg|thumb|upright|left|First X-ray diffraction view of [[Martian soil]] – [[CheMin|CheMin analysis]] reveals [[feldspar]], [[pyroxenes]], [[olivine]] and more ([[Curiosity rover]] at "[[Rocknest (Mars)|Rocknest]]", October 17, 2012).<ref name="NASA-20121030" />]]
The application of X-ray crystallography to [[mineralogy]] began with the structure of [[garnet]], which was determined in 1924 by Menzer. A systematic X-ray crystallographic study of the [[silicate]]s was undertaken in the 1920s. This study showed that, as the [[silicon|Si]]/[[oxygen|O]] ratio is altered, the silicate crystals exhibit significant changes in their atomic arrangements. Machatschki extended these insights to minerals in which aluminium substitutes for the [[silicon]] atoms of the silicates. The first application of X-ray crystallography to [[metallurgy]] also occurred in the mid-1920s.<ref>{{cite journal| vauthors = Westgren A, Phragmén G |date=1925|title=X-ray Analysis of the Cu-Zn, Ag-Zn and Au-Zn Alloys|journal=Phil. Mag. |volume=50 |page=311 |doi=10.1080/14786442508634742}}</ref><ref>{{cite journal| vauthors = Bradley AJ, Thewlis J |date=1926 |title=The structure of γ-Brass|journal= Proc. R. Soc. Lond. |volume=112 |page=678 |doi=10.1098/rspa.1926.0134 |issue=762 |bibcode=1926RSPSA.112..678B |doi-access=free}}</ref><ref>{{cite journal| vauthors = Hume-Rothery W|date=1926|title=Researches on the Nature, Properties and Conditions of Formation of Intermetallic Compounds (with special Reference to certain Compounds of Tin)|journal=Journal of the Institute of Metals|volume=35|page=295}}</ref><ref>{{cite journal| vauthors = Bradley AJ, Gregory CH |date=1927|title=The Structure of certain Ternary Alloys|doi=10.1038/120678a0|journal=Nature|volume=120|page=678|issue=3027|bibcode = 1927Natur.120..678. |doi-access=free}}</ref><ref>{{cite journal| vauthors = Westgren A|date=1932|title=Zur Chemie der Legierungen|journal=Angewandte Chemie |volume=45|page=33|doi=10.1002/ange.19320450202|issue=2|bibcode=1932AngCh..45...33W}}</ref><ref>{{cite journal| vauthors = Bernal JD|author-link=John Desmond Bernal|date=1935|title=The Electron Theory of Metals|journal=Annual Reports on the Progress of Chemistry|volume=32|page=181|doi=10.1039/AR9353200181}}</ref> Most notably, [[Linus Pauling]]'s structure of the alloy Mg<sub>2</sub>Sn<ref>{{cite journal| vauthors = Pauling L|title=The Crystal Structure of Magnesium Stannide|journal=J. Am. Chem. Soc.|volume=45|page=2777|doi=10.1021/ja01665a001|date=1923|issue=12}}</ref> led to his theory of the stability and structure of complex ionic crystals.<ref>{{cite journal| vauthors = Pauling L|title=The Principles Determining the Structure of Complex Ionic Crystals|journal=J. Am. Chem. Soc.|volume=51|page=1010|doi=10.1021/ja01379a006|date=1929|issue=4}}</ref> Many complicated [[inorganic]] and [[organometallic]] systems have been analyzed using single-crystal methods, such as [[fullerene]]s, [[porphyrin|metalloporphyrins]], and other complicated compounds. Single-crystal diffraction is also used in the [[pharmaceutical industry]]. The [[Cambridge Structural Database]] contains over 1,000,000 structures as of June 2019; most of these structures were determined by X-ray crystallography.<ref>{{Cite web |title=The Cambridge Structural Database {{!}} CCDC |url=https://www.ccdc.cam.ac.uk/solutions/software/csd/ |access-date=2024-05-07 |website=www.ccdc.cam.ac.uk |archive-date=2024-05-07 |archive-url=https://web.archive.org/web/20240507084044/https://www.ccdc.cam.ac.uk/solutions/software/csd/ |url-status=live }}</ref>

On October 17, 2012, the [[Curiosity rover]] on the [[Mars|planet Mars]] at "[[Rocknest (Mars)|Rocknest]]" performed the first X-ray diffraction analysis of [[Martian soil]]. The results from the rover's [[CheMin|CheMin analyzer]] revealed the presence of several minerals, including [[feldspar]], [[pyroxenes]] and [[olivine]], and suggested that the Martian soil in the sample was similar to the "weathered [[Basalt|basaltic soils]]" of [[Hawaii Volcanoes|Hawaiian volcanoes]].<ref name="NASA-20121030">{{cite web |vauthors=Brown D |title=NASA Rover's First Soil Studies Help Fingerprint Martian Minerals |url=http://www.nasa.gov/home/hqnews/2012/oct/HQ_12-383_Curiosity_CheMin.html |date=October 30, 2012 |publisher=[[NASA]] |access-date=October 31, 2012 |archive-date=June 3, 2016 |archive-url=https://web.archive.org/web/20160603091908/http://www.nasa.gov/home/hqnews/2012/oct/HQ_12-383_Curiosity_CheMin.html |url-status=dead }}</ref>

[[File:penicillin.png|thumb|The three-dimensional structure of [[penicillin]], solved by [[Dorothy Crowfoot Hodgkin]] in 1945. The green, red, yellow and blue spheres represent atoms of [[carbon]], [[oxygen]], [[sulfur]] and [[nitrogen]], respectively. The white spheres represent [[hydrogen]], which were determined mathematically rather than by the X-ray analysis.]]

=== Biological macromolecular crystallography ===
X-ray crystallography of biological molecules took off with [[Dorothy Crowfoot Hodgkin]], who solved the structures of [[cholesterol]] (1937), [[penicillin]] (1946) and [[vitamin B12|vitamin B<sub>12</sub>]] (1956), for which she was awarded the [[Nobel Prize in Chemistry]] in 1964. In 1969, she succeeded in solving the structure of [[insulin]], on which she worked for over thirty years.<ref>{{cite journal| vauthors = Hodgkin DC |author-link=Dorothy Crowfoot Hodgkin|date = 1935|title=X-ray Single Crystal Photographs of Insulin|journal=Nature|volume=135|page=591|doi=10.1038/135591a0|issue=3415|bibcode = 1935Natur.135..591C |s2cid=4121225|doi-access=free}}</ref>[[File:Myoglobin.png|thumb|right|[[Ribbon diagram]] of the structure of [[myoglobin]], showing [[alpha helix|alpha helices]]. Such [[protein]]s are long, linear [[molecule]]s with thousands of atoms; yet the relative position of each atom has been determined with sub-atomic resolution by X-ray crystallography. Since it is difficult to visualize all the atoms at once, the ribbon shows the rough path of the protein's [[Backbone chain#Proteins (polypeptides)|backbone]] from its N-terminus to its C-terminus.]]

Crystal structures of proteins (which are irregular and hundreds of times larger than cholesterol) began to be solved in the late 1950s, beginning with the structure of [[sperm whale]] [[myoglobin]] by [[John Kendrew|Sir John Cowdery Kendrew]],<ref>{{cite journal | vauthors = Kendrew JC, Bodo G, Dintzis HM, Parrish RG, Wyckoff H, Phillips DC | title = A three-dimensional model of the myoglobin molecule obtained by x-ray analysis | journal = Nature | volume = 181 | issue = 4610 | pages = 662–666 | date = March 1958 | pmid = 13517261 | doi = 10.1038/181662a0 | s2cid = 4162786 | author-link = John Kendrew | bibcode = 1958Natur.181..662K }}</ref> for which he shared the [[Nobel Prize in Chemistry]] with [[Max Perutz]] in 1962.<ref>{{Cite web|url=https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1962/|title=The Nobel Prize in Chemistry 1962|website=www.nobelprize.org|access-date=2018-01-31|archive-date=2018-01-31|archive-url=https://web.archive.org/web/20180131081517/https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1962/|url-status=live}}</ref> Since that success, 190,000 X-ray crystal structures of proteins, nucleic acids and other biological molecules have been determined.<ref>{{Cite web |last=Bank |first=RCSB Protein Data |title=PDB Statistics: PDB Data Distribution by Experimental Method and Molecular Type |url=https://www.rcsb.org/stats/summary |access-date=2025-02-02 |website=www.rcsb.org |language=en-US}}</ref> The nearest competing method in number of structures analyzed is [[Protein nuclear magnetic resonance spectroscopy|nuclear magnetic resonance (NMR) spectroscopy]], which has resolved less than one tenth as many.<ref>{{cite web|url=http://pdbbeta.rcsb.org/pdb/static.do?p=general_information/pdb_statistics/index.html|title=PDB Statistics|publisher=RCSB Protein Data Bank|access-date=2010-02-09|archive-date=2009-09-05|archive-url=https://web.archive.org/web/20090905005231/http://pdbbeta.rcsb.org/pdb/static.do?p=general_information%2Fpdb_statistics%2Findex.html|url-status=dead}}</ref> Crystallography can solve structures of arbitrarily large molecules, whereas solution-state NMR is restricted to relatively small ones (less than 70 k[[atomic mass unit|Da]]). X-ray crystallography is used routinely to determine how a pharmaceutical drug interacts with its protein target and what changes might improve it.<ref>{{cite journal | vauthors = Scapin G | title = Structural biology and drug discovery | journal = Current Pharmaceutical Design | volume = 12 | issue = 17 | pages = 2087–2097 | date = 2006 | pmid = 16796557 | doi = 10.2174/138161206777585201 }}</ref> However, intrinsic [[membrane protein]]s remain challenging to crystallize because they require detergents or other [[Denaturation (biochemistry)|denaturant]]s to solubilize them in isolation, and such detergents often interfere with crystallization. Membrane proteins are a large component of the [[genome]], and include many proteins of great physiological importance, such as [[ion channel]]s and [[receptor (biochemistry)|receptors]].<ref>{{cite journal | vauthors = Lundstrom K | title = Structural genomics for membrane proteins | journal = Cellular and Molecular Life Sciences | volume = 63 | issue = 22 | pages = 2597–2607 | date = November 2006 | pmid = 17013556 | doi = 10.1007/s00018-006-6252-y | s2cid = 13432321 | doi-access = free | pmc = 11136435 }}</ref><ref>{{cite journal | vauthors = Lundstrom K | title = Structural genomics on membrane proteins: mini review | journal = Combinatorial Chemistry & High Throughput Screening | volume = 7 | issue = 5 | pages = 431–439 | date = August 2004 | pmid = 15320710 | doi = 10.2174/1386207043328634 }}</ref> [[Helium cryogenics]] are used to prevent radiation damage in protein crystals.<ref>{{cite journal | vauthors = Chinte U, Shah B, Chen YS, Pinkerton AA, Schall CA, Hanson BL | title = Cryogenic (<20 K) helium cooling mitigates radiation damage to protein crystals | journal = Acta Crystallographica. Section D, Biological Crystallography | volume = 63 | issue = Pt 4 | pages = 486–492 | date = April 2007 | pmid = 17372353 | doi = 10.1107/s0907444907005264 | bibcode = 2007AcCrD..63..486C }}</ref>

==Methods==

===Overview===
{{See also|Resolution (electron density)}}[[File:X ray diffraction.png|thumb|Workflow for solving the structure of a molecule by X-ray crystallography.]]

Two limiting cases of X-ray crystallography—"small-molecule" (which includes continuous inorganic solids) and "macromolecular" crystallography—are often used. Small-molecule crystallography typically involves crystals with fewer than 100 atoms in their [[crystal structure|asymmetric unit]]; such crystal structures are usually so well resolved that the atoms can be discerned as isolated "blobs" of electron density. In contrast, macromolecular crystallography often involves tens of thousands of atoms in the unit cell. Such crystal structures are generally less well-resolved; the atoms and chemical bonds appear as tubes of electron density, rather than as isolated atoms. In general, small molecules are also easier to crystallize than macromolecules; however, X-ray crystallography has proven possible even for viruses and proteins with hundreds of thousands of atoms, through improved crystallographic imaging and technology.<ref>{{cite journal |vauthors=Jones N |date=January 2014 |title=Crystallography: Atomic secrets |journal=Nature |volume=505 |issue=7485 |pages=602–603 |bibcode=2014Natur.505..602J |doi=10.1038/505602a |pmid=24476871 |doi-access=free}}</ref>

The technique of single-crystal X-ray crystallography has three basic steps. The first—and often most difficult—step is to obtain an adequate crystal of the material under study. The crystal should be sufficiently large (typically larger than 0.1&nbsp;mm in all dimensions), pure in composition and regular in structure, with no significant internal [[crystal defect|imperfections]] such as cracks or [[crystal twinning|twinning]].<ref>{{cite book |last1=Ladd |first1=M. F. C. |last2=Palmer |first2=Rex A. |title=Structure Determination by X-ray Crystallography: Analysis by X-rays and Neutrons |date=2013 |publisher=Springer |location=Boston, MA |isbn=978-1-4614-3956-1 |pages=228-229 |edition=5th 2013}}</ref>

In the second step, the crystal is placed in an intense beam of X-rays, usually of a single wavelength (''monochromatic X-rays''), producing the regular pattern of reflections. The angles and intensities of diffracted X-rays are measured, with each compound having a unique diffraction pattern.<ref>{{Cite web|url=https://www.imrtest.com/tests/morphology-xrd-analysis|title=Morphology XRD Analysis {{!}} IMR TEST LABS|website=www.imrtest.com|access-date=2018-04-30}}{{Dead link|date=July 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> As the crystal is gradually rotated, previous reflections disappear and new ones appear; the intensity of every spot is recorded at every orientation of the crystal. Multiple data sets may have to be collected, with each set covering slightly more than half a full rotation of the crystal and typically containing tens of thousands of reflections.<ref>{{cite book |last1=Ladd |first1=M. F. C. |last2=Palmer |first2=Rex A. |title=Structure Determination by X-ray Crystallography: Analysis by X-rays and Neutrons |date=2013 |publisher=Springer |location=Boston, MA |isbn=978-1-4614-3956-1 |page=200 |edition=5th 2013}}</ref>

In the third step, these data are combined computationally with complementary chemical information to produce and refine a model of the arrangement of atoms within the crystal. The final, refined model of the atomic arrangement—now called a ''[[crystal structure]]''—is usually stored in a public database.<ref>{{cite book |last1=Ladd |first1=Mark F. c |title=Structure determination by x-ray crystallography: analysis by x-rays and neutrons |date=2012 |publisher=Springer |location=New York |isbn=978-1-4614-3956-1 |page=417}}</ref>

===Crystallization===
{{further|Crystallization|Recrystallization (chemistry)#Single perfect crystals (for X-ray analysis)|Protein crystallization}}
[[File:Protein crystal.jpg|thumb|left|A protein crystal seen under a [[microscope]]. Crystals used in X-ray crystallography may be smaller than a millimeter across.]]
Although crystallography can be used to characterize the disorder in an impure or irregular crystal, crystallography generally requires a pure crystal of high regularity to solve the structure of a complicated arrangement of atoms. Pure, regular crystals can sometimes be obtained from natural or synthetic materials, such as samples of metals, minerals or other macroscopic materials. The regularity of such crystals can sometimes be improved with macromolecular crystal [[annealing (metallurgy)|annealing]]<ref>{{cite journal | vauthors = Harp JM, Timm DE, Bunick GJ | title = Macromolecular crystal annealing: overcoming increased mosaicity associated with cryocrystallography | journal = Acta Crystallographica. Section D, Biological Crystallography | volume = 54 | issue = Pt 4 | pages = 622–628 | date = July 1998 | pmid = 9761858 | doi = 10.1107/S0907444997019008 | bibcode = 1998AcCrD..54..622H }}</ref><ref>{{cite journal | vauthors = Harp JM, Hanson BL, Timm DE, Bunick GJ | title = Macromolecular crystal annealing: evaluation of techniques and variables | journal = Acta Crystallographica. Section D, Biological Crystallography | volume = 55 | issue = Pt 7 | pages = 1329–1334 | date = July 1999 | pmid = 10393299 | doi = 10.1107/S0907444999005442 | bibcode = 1999AcCrD..55.1329H }}</ref><ref>{{cite book | vauthors = Hanson BL, Harp JM, Bunick GJ | title = Macromolecular Crystallography, Part C | chapter = The well-tempered protein crystal: annealing macromolecular crystals | volume = 368|pages=217–35 | date = 2003 | pmid = 14674276 | doi = 10.1016/S0076-6879(03)68012-2 | isbn = 978-0-12-182271-2 | series = Methods in Enzymology }}</ref> and other methods. However, in many cases, obtaining a diffraction-quality crystal is the chief barrier to solving its atomic-resolution structure.<ref>{{cite journal | vauthors = Geerlof A, Brown J, Coutard B, Egloff MP, Enguita FJ, Fogg MJ, Gilbert RJ, Groves MR, Haouz A, Nettleship JE, Nordlund P, Owens RJ, Ruff M, Sainsbury S, Svergun DI, Wilmanns M | display-authors = 6 | title = The impact of protein characterization in structural proteomics | journal = Acta Crystallographica. Section D, Biological Crystallography | volume = 62 | issue = Pt 10 | pages = 1125–1136 | date = October 2006 | pmid = 17001090 | pmc = 7161605 | doi = 10.1107/S0907444906030307 | bibcode = 2006AcCrD..62.1125G | doi-access = free }}</ref>

Small-molecule and macromolecular crystallography differ in the range of possible techniques used to produce diffraction-quality crystals. Small molecules generally have few degrees of conformational freedom, and may be crystallized by a wide range of methods, such as [[chemical vapor deposition]] and [[Recrystallization (chemistry)#Single perfect crystals (for X-ray analysis)|recrystallization]]. By contrast, macromolecules generally have many degrees of freedom and their crystallization must be carried out so as to maintain a stable structure. For example, proteins and larger [[RNA]] molecules cannot be crystallized if their tertiary structure has been [[Denaturation (biochemistry)|unfolded]]; therefore, the range of crystallization conditions is restricted to solution conditions in which such molecules remain folded.{{cn|date=July 2024}}

[[File:CrystalDrops.svg|thumb|upright|Three methods of preparing crystals, A: Hanging drop. B: Sitting drop. C: Microdialysis]] Protein crystals are almost always grown in solution. The most common approach is to lower the solubility of its component molecules very gradually; if this is done too quickly, the molecules will precipitate from solution, forming a useless dust or amorphous gel on the bottom of the container. Crystal growth in solution is characterized by two steps: ''nucleation'' of a microscopic crystallite (possibly having only 100 molecules), followed by ''growth'' of that crystallite, ideally to a diffraction-quality crystal.<ref>{{cite journal | vauthors = Chernov AA | title = Protein crystals and their growth | journal = Journal of Structural Biology | volume = 142 | issue = 1 | pages = 3–21 | date = April 2003 | pmid = 12718915 | doi = 10.1016/S1047-8477(03)00034-0 }}</ref><ref>{{Cite web|url=http://xray.bmc.uu.se/terese/tutorials.html|title=Protein crystallization Tutorial|vauthors=Bergfors T|date=2016|access-date=2020-01-17|archive-date=2019-12-25|archive-url=https://web.archive.org/web/20191225142449/http://xray.bmc.uu.se/terese/tutorials.html|url-status=live}}</ref> The solution conditions that favor the first step (nucleation) are not always the same conditions that favor the second step (subsequent growth). The solution conditions should ''disfavor'' the first step (nucleation) but ''favor'' the second (growth), so that only one large crystal forms per droplet. If nucleation is favored too much, a shower of small crystallites will form in the droplet, rather than one large crystal; if favored too little, no crystal will form whatsoever. Other approaches involve crystallizing proteins under oil, where aqueous protein solutions are dispensed under liquid oil, and water evaporates through the layer of oil. Different oils have different evaporation permeabilities, therefore yielding changes in concentration rates from different percipient/protein mixture.<ref name="Chayen">{{cite journal | vauthors = Chayen N |title=Limitations of crystallizing under oil |journal = Cell|year=1997 |volume=5 |issue=10 |pages=1269–1274 |doi=10.1016/s0969-2126(97)00279-7 |pmid=9351804 |doi-access=free }}</ref>

It is difficult to predict good conditions for nucleation or growth of well-ordered crystals.<ref>{{cite journal | vauthors = Rupp B, Wang J | title = Predictive models for protein crystallization | journal = Methods | volume = 34 | issue = 3 | pages = 390–407 | date = November 2004 | pmid = 15325656 | doi = 10.1016/j.ymeth.2004.03.031 }}</ref> In practice, favorable conditions are identified by ''screening''; a very large batch of the molecules is prepared, and a wide variety of crystallization solutions are tested.<ref>{{cite journal | vauthors = Chayen NE | title = Methods for separating nucleation and growth in protein crystallisation | journal = Progress in Biophysics and Molecular Biology | volume = 88 | issue = 3 | pages = 329–337 | date = July 2005 | pmid = 15652248 | doi = 10.1016/j.pbiomolbio.2004.07.007 | doi-access = free }}</ref> Hundreds, even thousands, of solution conditions are generally tried before finding the successful one. The various conditions can use one or more physical mechanisms to lower the solubility of the molecule; for example, some may change the pH, some contain salts of the [[Hofmeister series]] or chemicals that lower the dielectric constant of the solution, and still others contain large polymers such as [[polyethylene glycol]] that drive the molecule out of solution by entropic effects. It is also common to try several temperatures for encouraging crystallization, or to gradually lower the temperature so that the solution becomes supersaturated. These methods require large amounts of the target molecule, as they use high concentration of the molecule(s) to be crystallized. Due to the difficulty in obtaining such large quantities ([[milligrams]]) of crystallization-grade protein, robots have been developed that are capable of accurately dispensing crystallization trial drops that are in the order of 100 [[nanoliter]]s in volume. This means that 10-fold less protein is used per experiment when compared to crystallization trials set up by hand (in the order of 1 [[microliter]]).<ref>{{cite journal | vauthors = Stock D, Perisic O, Löwe J | title = Robotic nanolitre protein crystallisation at the MRC Laboratory of Molecular Biology | journal = Progress in Biophysics and Molecular Biology | volume = 88 | issue = 3 | pages = 311–327 | date = July 2005 | pmid = 15652247 | doi = 10.1016/j.pbiomolbio.2004.07.009 | doi-access = free }}</ref>

Several factors are known to inhibit crystallization. The growing crystals are generally held at a constant temperature and protected from shocks or vibrations that might disturb their crystallization. Impurities in the molecules or in the crystallization solutions are often inimical to crystallization. Conformational flexibility in the molecule also tends to make crystallization less likely, due to entropy. Molecules that tend to self-assemble into regular helices are often unwilling to assemble into crystals.{{citation needed|date=March 2014}} Crystals can be marred by [[Crystal twinning|twinning]], which can occur when a unit cell can pack equally favorably in multiple orientations; although recent advances in computational methods may allow solving the structure of some twinned crystals. Having failed to crystallize a target molecule, a crystallographer may try again with a slightly modified version of the molecule; even small changes in molecular properties can lead to large differences in crystallization behavior.{{cn|date=July 2024}}

===Data collection===

====Mounting the crystal====
[[File:Kappa goniometer animation.ogg|thumb|left|Animation showing the five motions possible with a four-circle kappa goniometer. The rotations about each of the four angles φ, κ, ω and 2θ leave the crystal within the X-ray beam, but change the crystal orientation. The detector (red box) can be slid closer or further away from the crystal, allowing higher resolution data to be taken (if closer) or better discernment of the Bragg peaks (if further away).]]

The crystal is mounted for measurements so that it may be held in the X-ray beam and rotated. There are several methods of mounting. In the past, crystals were loaded into glass capillaries with the crystallization solution (the [[mother liquor]]).  Crystals of small molecules are typically attached with oil or glue to a glass fiber or a loop, which is made of nylon or plastic and attached to a solid rod.  Protein crystals are scooped up by a loop, then flash-frozen with [[liquid nitrogen]].<ref>{{cite book | vauthors = Jeruzalmi D | title = Macromolecular Crystallography Protocols, Volume 2 | chapter = First analysis of macromolecular crystals: biochemistry and x-ray diffraction | series = Methods in Molecular Biology | volume = 364|pages=43–62 | date = 2006 | pmid = 17172760 | doi = 10.1385/1-59745-266-1:43 | isbn = 1-59745-266-1 }}</ref> This freezing reduces the radiation damage of the X-rays, as well as thermal motion (the Debye-Waller effect). However, untreated protein crystals often crack if flash-frozen; therefore, they are generally pre-soaked in a cryoprotectant solution before freezing.<ref>{{cite journal | vauthors = Helliwell JR | title = Protein crystal perfection and its application | journal = Acta Crystallographica. Section D, Biological Crystallography | volume = 61 | issue = Pt 6 | pages = 793–798 | date = June 2005 | pmid = 15930642 | doi = 10.1107/S0907444905001368 | bibcode = 2005AcCrD..61..793H | author-link = John R. Helliwell | doi-access = free }}</ref> This pre-soak may itself cause the crystal to crack, ruining it for crystallography. Generally, successful cryo-conditions are identified by trial and error.{{cn|date=July 2024}}

The capillary or loop is mounted on a [[goniometer]], which allows it to be positioned accurately within the X-ray beam and rotated. Since both the crystal and the beam are often very small, the crystal must be centered within the beam to within ~25 micrometers accuracy, which is aided by a camera focused on the crystal. The most common type of goniometer is the "kappa goniometer", which offers three angles of rotation: the ω angle, which rotates about an axis perpendicular to the beam; the κ angle, about an axis at ~50° to the ω axis; and, finally, the φ angle about the loop/capillary axis. When the κ angle is zero, the ω and φ axes are aligned. The κ rotation allows for convenient mounting of the crystal, since the arm in which the crystal is mounted may be swung out towards the crystallographer. The oscillations carried out during data collection (mentioned below) involve the ω axis only. An older type of goniometer is the four-circle goniometer, and its relatives such as the six-circle goniometer.{{cn|date=July 2024}}

==== Recording the reflections ====
[[File:X-ray diffraction pattern 3clpro.jpg|thumb|An X-ray diffraction pattern of a crystallized enzyme. The pattern of spots (''reflections'') and the relative strength of each spot (''intensities'') can be used to determine the structure of the enzyme.]]
The relative intensities of the reflections provides information to determine the arrangement of molecules within the crystal in atomic detail. The intensities of these reflections may be recorded with [[photographic film]], an area detector (such as a [[hybrid pixel detector|pixel detector]]) or with a [[charge-coupled device]] (CCD) image sensor. The peaks at small angles correspond to low-resolution data, whereas those at high angles represent high-resolution data; thus, an upper limit on the eventual resolution of the structure can be determined from the first few images. Some measures of diffraction quality can be determined at this point, such as the [[mosaicity]] of the crystal and its overall disorder, as observed in the peak widths. Some pathologies of the crystal that would render it unfit for solving the structure can also be diagnosed quickly at this point.{{cn|date=July 2024}}

One set of spots is insufficient to reconstruct the whole crystal; it represents only a small slice of the full three dimensional set. To collect all the necessary information, the crystal must be rotated step-by-step through 180°, with an image recorded at every step; actually, slightly more than 180° is required to cover [[reciprocal space]], due to the curvature of the [[Ewald sphere]]. However, if the crystal has a higher symmetry, a smaller angular range such as 90° or 45° may be recorded. The rotation axis should be changed at least once, to avoid developing a "blind spot" in reciprocal space close to the rotation axis. It is customary to rock the crystal slightly (by 0.5–2°) to catch a broader region of reciprocal space.{{cn|date=July 2024}}

Multiple data sets may be necessary for certain [[Phase problem|phasing]] methods. For example, [[multi-wavelength anomalous dispersion]] phasing requires that the scattering be recorded at least three (and usually four, for redundancy) wavelengths of the incoming X-ray radiation. A single crystal may degrade too much during the collection of one data set, owing to radiation damage; in such cases, data sets on multiple crystals must be taken.<ref>{{cite journal |vauthors=Ravelli RB, Garman EF |date=October 2006 |title=Radiation damage in macromolecular cryocrystallography |journal=Current Opinion in Structural Biology |volume=16 |issue=5 |pages=624–629 |doi=10.1016/j.sbi.2006.08.001 |pmid=16938450}}</ref>

=== Crystal symmetry, unit cell, and image scaling ===
{{further|Space group}}

The recorded series of two-dimensional diffraction patterns, each corresponding to a different crystal orientation, is converted into a three-dimensional set. Data processing begins with ''indexing'' the reflections. This means identifying the dimensions of the unit cell and which image peak corresponds to which position in reciprocal space. A byproduct of indexing is to determine the symmetry of the crystal, i.e., its ''[[space group]]''. Some space groups can be eliminated from the beginning. For example, reflection symmetries cannot be observed in chiral molecules; thus, only 65 space groups of 230 possible are allowed for protein molecules which are almost always chiral. Indexing is generally accomplished using an ''autoindexing'' routine.<ref>{{cite journal |vauthors=Powell HR |date=October 1999 |title=The Rossmann Fourier autoindexing algorithm in MOSFLM |journal=Acta Crystallographica. Section D, Biological Crystallography |volume=55 |issue=Pt 10 |pages=1690–1695 |bibcode=1999AcCrD..55.1690P |doi=10.1107/S0907444999009506 |pmid=10531518 |doi-access=free}}</ref> Having assigned symmetry, the data is then ''integrated''. This converts the hundreds of images containing the thousands of reflections into a single file, consisting of (at the very least) records of the [[Miller index]] of each reflection, and an intensity for each reflection (at this state the file often also includes error estimates and measures of partiality (what part of a given reflection was recorded on that image)).

A full data set may consist of hundreds of separate images taken at different orientations of the crystal. These have to be merged and scaled using peaks that appear in two or more images (''merging'') and scaling so there is a consistent intensity scale. Optimizing the intensity scale is critical because the relative intensity of the peaks is the key information from which the structure is determined. The repetitive technique of crystallographic data collection and the often high symmetry of crystalline materials cause the diffractometer to record many symmetry-equivalent reflections multiple times. This allows calculating the symmetry-related [[R-factor (crystallography)|R-factor]], a reliability index based upon how similar are the measured intensities of symmetry-equivalent reflections,{{clarify|date=February 2015}} thus assessing the quality of the data.

=== Initial phasing ===
{{further|Phase problem}}

The intensity of each diffraction 'spot' is proportional to the modulus squared of the [[structure factor]]. The structure factor  is a [[complex number]] containing information relating to both the [[amplitude]] and [[Phase (waves)|phase]] of a [[wave]]. In order to obtain an interpretable ''electron density map'', both amplitude and phase must be known (an electron density map allows a crystallographer to build a starting model of the molecule). The phase cannot be directly recorded during a diffraction experiment: this is known as the [[phase problem]]. Initial phase estimates can be obtained in a variety of ways:
* '''''[[Ab initio]]'' phasing''' or '''[[Direct methods (crystallography)|direct methods]]'''&nbsp;– This is usually the method of choice for small molecules (<1000 non-hydrogen atoms), and has been used successfully to solve the phase problems for small proteins. If the resolution of the data is better than 1.4&nbsp;Å (140&nbsp;[[picometre|pm]]), [[Direct methods (crystallography)|direct methods]] can be used to obtain phase information, by exploiting known phase relationships between certain groups of reflections.<ref>{{cite journal |vauthors=Hauptman H |date=October 1997 |title=Phasing methods for protein crystallography |journal=Current Opinion in Structural Biology |volume=7 |issue=5 |pages=672–680 |doi=10.1016/S0959-440X(97)80077-2 |pmid=9345626}}</ref><ref>{{cite journal |vauthors=Usón I, Sheldrick GM |date=October 1999 |title=Advances in direct methods for protein crystallography |journal=Current Opinion in Structural Biology |volume=9 |issue=5 |pages=643–648 |doi=10.1016/S0959-440X(99)00020-2 |pmid=10508770 |doi-access=free}}</ref>
* '''[[Molecular replacement]]'''&nbsp;– if a related structure is known, it can be used as a search model in molecular replacement to determine the orientation and position of the molecules within the unit cell. The phases obtained this way can be used to generate electron density maps.<ref name="Taylor">{{cite journal |vauthors=Taylor G |date=November 2003 |title=The phase problem |journal=Acta Crystallographica. Section D, Biological Crystallography |volume=59 |issue=Pt 11 |pages=1881–1890 |bibcode=2003AcCrD..59.1881T |doi=10.1107/S0907444903017815 |pmid=14573942 |doi-access=free}}</ref>
* '''[[Anomalous X-ray scattering]]''' (''[[Multi-wavelength anomalous dispersion|MAD]] or [[Single wavelength anomalous dispersion|SAD phasing]]'')&nbsp;– the X-ray wavelength may be scanned past an absorption edge{{efn|The absorption edge is originally known from [[X-ray absorption spectroscopy]]. See {{cite web |title=X-ray Anomalous Scattering |url=http://skuld.bmsc.washington.edu/scatter/ |website=skuld.bmsc.washington.edu}} for a guide to anomalous scattering.}} of an atom, which changes the scattering in a known way. By recording full sets of reflections at three different wavelengths (far below, far above and in the middle of the absorption edge) one can solve for the substructure of the anomalously diffracting atoms and hence the structure of the whole molecule. The most popular method of incorporating anomalous scattering atoms into proteins is to express the protein in a [[methionine]] auxotroph (a host incapable of synthesizing methionine) in a media rich in seleno-methionine, which contains [[selenium]] atoms. A multi-wavelength anomalous dispersion (MAD) experiment can then be conducted around the absorption edge, which should then yield the position of any methionine residues within the protein, providing initial phases.<ref>{{cite journal |vauthors=Ealick SE |date=October 2000 |title=Advances in multiple wavelength anomalous diffraction crystallography |journal=Current Opinion in Chemical Biology |volume=4 |issue=5 |pages=495–499 |doi=10.1016/S1367-5931(00)00122-8 |pmid=11006535|doi-access=free }}</ref>
* '''Heavy atom methods''' ([[multiple isomorphous replacement]])&nbsp;– If electron-dense metal atoms can be introduced into the crystal, [[Direct methods (crystallography)|direct methods]] or [[Patterson function|Patterson-space methods]] can be used to determine their location and to obtain initial phases. Such heavy atoms can be introduced either by soaking the crystal in a heavy atom-containing solution, or by co-crystallization (growing the crystals in the presence of a heavy atom). As in multi-wavelength anomalous dispersion phasing, the changes in the scattering amplitudes can be interpreted to yield the phases. Although this is the original method by which protein crystal structures were solved, it has largely been superseded by multi-wavelength anomalous dispersion phasing with selenomethionine.<ref name="Taylor" />

=== Model building and phase refinement ===
[[File:Helix electron density myoglobin 2nrl 17-32.jpg|thumb|Structure of a protein alpha helix, with stick-figures for the covalent bonding within electron density for the crystal structure at ultra-high-resolution (0.91&nbsp;Å). The density contours are in gray, the helix backbone in white, sidechains in cyan, O atoms in red, N atoms in blue, and hydrogen bonds as green dotted lines.<ref>From PDB file 2NRL, residues 17–32.</ref>]] [[File:Fitting a model into electron density.gif|thumb|3D depiction of electron density (blue) of a ligand (orange) bound to a binding site in a protein (yellow).<ref>{{cite web |title=Garman lab: Interconversion of lysosomal enzyme specificities – Proteopedia, life in 3D |url=http://proteopedia.org/wiki/index.php/Garman_lab:_Interconversion_of_lysosomal_enzyme_specificities |access-date=2018-11-28 |website=proteopedia.org |archive-date=2018-11-28 |archive-url=https://web.archive.org/web/20181128212454/http://proteopedia.org/wiki/index.php/Garman_lab:_Interconversion_of_lysosomal_enzyme_specificities |url-status=live }}</ref> The electron density is obtained from experimental data, and the ligand is modeled into this electron density.]]
{{further|Molecular modelling{{!}}Molecular modeling}}

Having obtained initial phases, an initial model can be built. The atomic positions in the model and their respective [[Debye-Waller factor]]s (or '''B'''-factors, accounting for the thermal motion of the atom) can be refined to fit the observed diffraction data, ideally yielding a better set of phases. A new model can then be fit to the new electron density map and successive rounds of refinement are carried out. This iterative process continues until the correlation between the diffraction data and the model is maximized. The agreement is measured by an [[R-factor (crystallography)|''R''-factor]] defined as

:<math>R = \frac{\sum_{\text{all reflections}} \left|F_\text{obs} - F_\text{calc} \right|}{\sum_{\text{all reflections}} \left|F_\text{obs} \right|},</math>

where ''F'' is the [[structure factor]]. A similar quality criterion is ''R''<sub>free</sub>, which is calculated from a subset (~10%) of reflections that were not included in the structure refinement. Both ''R'' factors depend on the resolution of the data. As a rule of thumb, ''R''<sub>free</sub> should be approximately the resolution in angstroms divided by 10; thus, a data-set with 2&nbsp;Å resolution should yield a final ''R''<sub>free</sub> ~ 0.2. Chemical bonding features such as stereochemistry, hydrogen bonding and distribution of bond lengths and angles are complementary measures of the model quality. In iterative model building, it is common to encounter phase bias or model bias: because phase estimations come from the model, each round of calculated map tends to show density wherever the model has density, regardless of whether there truly is a density. This problem can be mitigated by maximum-likelihood weighting and checking using ''omit maps''.<ref name="pmid25554228">{{cite journal |last1=Lamb |first1=AL |last2=Kappock |first2=TJ |last3=Silvaggi |first3=NR |date=April 2015 |title=You are lost without a map: Navigating the sea of protein structures. |journal=Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics |volume=1854 |issue=4 |pages=258–68 |doi=10.1016/j.bbapap.2014.12.021 |pmc=5051661 |pmid=25554228}}</ref>

It may not be possible to observe every atom in the asymmetric unit. In many cases, [[crystallographic disorder]] smears the electron density map. Weakly scattering atoms such as hydrogen are routinely invisible. It is also possible for a single atom to appear multiple times in an electron density map, e.g., if a protein sidechain has multiple (<4) allowed conformations. In still other cases, the crystallographer may detect that the covalent structure deduced for the molecule was incorrect, or changed. For example, proteins may be cleaved or undergo post-translational modifications that were not detected prior to the crystallization.

=== Disorder ===
{{main|Crystallographic disorder}}

A common challenge in refinement of crystal structures results from crystallographic disorder.  Disorder can take many forms but in general involves the coexistence of two or more species or conformations.  Failure to recognize disorder results in flawed interpretation.  Pitfalls from improper modeling of disorder are illustrated by the discounted hypothesis of [[bond stretch isomer]]ism.<ref>{{cite journal |vauthors=Parkin G |year=1993 |title=Bond-stretch isomerism in transition metal complexes: a reevaluation of crystallographic data |journal=Chem. Rev. |volume=93 |issue=3 |pages=887–911 |doi=10.1021/cr00019a003}}</ref>  Disorder is modelled with respect to the relative population of the components, often only two, and their identity.  In structures of large molecules and ions, solvent and counterions are often disordered.

=== Applied computational data analysis ===
The use of computational methods for the powder X-ray diffraction data analysis is now generalized. It typically compares the experimental data to the simulated diffractogram of a model structure, taking into account the instrumental parameters, and refines the structural or microstructural parameters of the model using [[least squares]] based minimization algorithm. Most available tools allowing phase identification and structural refinement are based on the [[Rietveld refinement|Rietveld method]],<ref>{{Cite journal |vauthors=Rietveld HM |date=1969-06-02 |title=A profile refinement method for nuclear and magnetic structures |journal=Journal of Applied Crystallography |volume=2 |issue=2 |pages=65–71 |bibcode=1969JApCr...2...65R |doi=10.1107/S0021889869006558 |doi-access=free}}</ref><ref>{{Cite book |title=The Rietveld Method |vauthors=Young RA |date=1993 |publisher=International Union of Crystallograhy |isbn=0198555776 |location=[Chester, England] |oclc=26299196}}</ref> some of them being open and free software such as FullProf Suite,<ref>{{Cite web |title=IUCr |url=https://www.iucr.org/resources/commissions/powder-diffraction/newsletter |access-date=2019-04-06 |website=www.iucr.org |archive-date=2019-04-06 |archive-url=https://web.archive.org/web/20190406103706/https://www.iucr.org/resources/commissions/powder-diffraction/newsletter |url-status=live }}</ref><ref>{{Cite web |title=Fullprof |url=https://www.ill.eu/sites/fullprof/ |access-date=2019-04-06 |website=www.ill.eu |archive-date=2019-04-02 |archive-url=https://web.archive.org/web/20190402200238/https://www.ill.eu/sites/fullprof/ |url-status=live }}</ref> Jana2006,<ref>{{Cite journal |vauthors=Petříček V, Dušek M, Palatinus L |date=2014-01-01 |title=Crystallographic Computing System JANA2006: General features |journal=Zeitschrift für Kristallographie – Crystalline Materials |volume=229 |issue=5 |pages=345–352 |doi=10.1515/zkri-2014-1737 |issn=2196-7105 |s2cid=101692863}}</ref> MAUD,<ref>{{Cite journal |vauthors=Lutterotti L |date=February 2010 |title=Total pattern fitting for the combined size–strain–stress–texture determination in thin film diffraction |journal=Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms |volume=268 |issue=3–4 |pages=334–340 |bibcode=2010NIMPB.268..334L |doi=10.1016/j.nimb.2009.09.053 |issn=0168-583X}}</ref><ref>{{Citation |title=Tenth European Powder Diffraction Conference |pages=125–130 |year=2007 |chapter=Rietveld texture analysis from diffraction images |publisher=OLDENBOURG WISSENSCHAFTSVERLAG |doi=10.1524/9783486992540-020 |isbn=9783486992540 |vauthors=Lutterotti L, Bortolotti M, Ischia G, Lonardelli I, Wenk HR}}</ref><ref>{{Cite journal |vauthors=Lutterotti L, Matthies S, Wenk HR, Schultz AS, Richardson Jr JW |date=1997-01-15 |title=Combined texture and structure analysis of deformed limestone from time-of-flight neutron diffraction spectra |journal=Journal of Applied Physics |volume=81 |issue=2 |pages=594–600 |bibcode=1997JAP....81..594L |doi=10.1063/1.364220 |issn=0021-8979}}</ref> Rietan,<ref>{{Cite web |title=Distribution Files for the RIETAN-FP-VENUS Package |url=http://fujioizumi.verse.jp/download/download_Eng.html |access-date=2019-04-06 |website=fujioizumi.verse.jp |archive-date=2019-08-10 |archive-url=https://web.archive.org/web/20190810120240/http://fujioizumi.verse.jp/download/download_Eng.html |url-status=live }}</ref> GSAS,<ref>{{Cite journal |vauthors=Toby BH, Von Dreele RB |date=2013-03-14 |title=GSAS-II: the genesis of a modern open-source all purpose crystallography software package |journal=Journal of Applied Crystallography |volume=46 |issue=2 |pages=544–549 |bibcode=2013JApCr..46..544T |doi=10.1107/s0021889813003531 |issn=0021-8898}}</ref> etc. while others are available under commercial licenses such as Diffrac.Suite TOPAS,<ref>{{Cite web |title=DIFFRAC.SUITE TOPAS - XRD Software, X-ray diffraction |url=https://www.bruker.com/products/x-ray-diffraction-and-elemental-analysis/x-ray-diffraction/xrd-software/topas.html |access-date=2019-04-06 |website=Bruker.com |archive-date=2019-04-02 |archive-url=https://web.archive.org/web/20190402174859/https://www.bruker.com/products/x-ray-diffraction-and-elemental-analysis/x-ray-diffraction/xrd-software/topas.html |url-status=live }}</ref> Match!,<ref>{{Cite web |title=Match! – Phase Identification from Powder Diffraction |url=http://www.crystalimpact.com/match/ |access-date=2019-04-06 |website=www.crystalimpact.com |archive-date=2019-04-02 |archive-url=https://web.archive.org/web/20190402175018/http://www.crystalimpact.com/match/ |url-status=live }}</ref> etc. Most of these tools also allow [[Le Bail method|Le Bail]] refinement (also referred to as profile matching), that is, refinement of the cell parameters based on the Bragg peaks positions and peak profiles, without taking into account the crystallographic structure by itself. More recent tools allow the refinement of both structural and microstructural data, such as the FAULTS program included in the FullProf Suite,<ref>{{Cite journal |vauthors=Casas-Cabanas M, Reynaud M, Rikarte J, Horbach P, Rodríguez-Carvajal J |date=2016-12-01 |title=FAULTS: a program for refinement of structures with extended defects |journal=Journal of Applied Crystallography |volume=49 |issue=6 |pages=2259–2269 |bibcode=2016JApCr..49.2259C |doi=10.1107/S1600576716014473 |issn=1600-5767}}</ref> which allows the refinement of structures with planar defects (e.g. stacking faults, twinnings, intergrowths).

=== Deposition of the structure ===
Once the model of a molecule's structure has been finalized, it is often deposited in a [[crystallographic database]] such as the [[Cambridge Structural Database]] (for small molecules), the [[Inorganic Crystal Structure Database (ICSD)]] (for inorganic compounds) or the [[Protein Data Bank]] (for protein and sometimes nucleic acids). Many structures obtained in private commercial ventures to crystallize medicinally relevant proteins are not deposited in public crystallographic databases.

== Contribution of women to X-ray crystallography ==
A number of women were pioneers in X-ray crystallography at a time when they were excluded from most other branches of physical science.<ref>{{Cite journal|last=Kahr|first=Bart|date=2015|title=Broader Impacts of Women in Crystallography|url=https://doi.org/10.1021/acs.cgd.5b00457|journal=Crystal Growth & Design|volume=15|issue=10|pages=4715–4730|doi=10.1021/acs.cgd.5b00457|issn=1528-7483}}</ref>

[[Kathleen Lonsdale]] was a research student of [[William Henry Bragg]], who had 11 women research students out of a total of 18. She is known for both her experimental and theoretical work. Lonsdale joined his crystallography research team at the [[Royal Institution]] in London in 1923, and after getting married and having children, went back to work with Bragg as a researcher. She confirmed the structure of the benzene ring, carried out studies of diamond, was one of the first two women to be elected to the [[Royal Society]] in 1945, and in 1949 was appointed the first female tenured professor of chemistry and head of the Department of crystallography at [[University College London]].<ref>{{Cite journal|last=Ferry|first=Georgina|date=2014|title=History: Women in crystallography|journal=Nature|language=en|volume=505|issue=7485|pages=609–611|doi=10.1038/505609a|pmid=24482834|bibcode=2014Natur.505..609F |issn=1476-4687|doi-access=free}}</ref> Lonsdale always advocated greater participation of women in science and  said in 1970: "Any country that wants to make full use of all its potential scientists and technologists could do so, but it must not expect to get the women quite so simply as it gets the men.{{nbsp}}... It is utopian, then, to suggest that any country that really wants married women to return to a scientific career, when her children no longer need her physical presence, should make special arrangements to encourage her to do so?".<ref>{{Cite journal|last=Sanz-Aparicio|first=Julia|date=2015|title=Vista de El legado de las mujeres a la cristalografía {{!}} Arbor|url=http://arbor.revistas.csic.es/index.php/arbor/article/view/2019/2475|url-status=live|access-date=|journal=Arbor|volume=191 |issue=772 |pages=a216 |doi=10.3989/arbor.2015.772n2002 |archive-url=https://web.archive.org/web/20150907073131/http://arbor.revistas.csic.es:80/index.php/arbor/article/view/2019/2475 |archive-date=2015-09-07 |doi-access=free|hdl=10261/130728|hdl-access=free}}</ref> During this period, Lonsdale began a collaboration with William T. Astbury on a set of 230 space group tables which was published in 1924 and became an essential tool for crystallographers.
[[File:Molecular model of Penicillin by Dorothy Hodgkin (9663803982).jpg|thumb|Molecular model of penicillin by Dorothy Hodgkin, 1945]]
In 1932 [[Dorothy Hodgkin]] joined the laboratory of the physicist John Desmond Bernal, who was a former student of Bragg, in Cambridge, UK. She and Bernal took the first X-ray photographs of crystalline proteins. Hodgkin also played a role in the foundation of the [[International Union of Crystallography]]. She was awarded the Nobel Prize in Chemistry in 1964 for her work using X-ray techniques to study the structures of penicillin, insulin and vitamin B12. Her work on penicillin began in 1942 during the war and on vitamin B12 in 1948. While her group slowly grew, their predominant focus was on the X-ray analysis of natural products. She is the only [[List of female Nobel laureates|British woman ever to have won a Nobel Prize]] in a science subject.
[[File:Fig-1-X-ray-chrystallography-of-DNA.gif|thumb|Photograph of DNA (photo 51), Rosalind Franklin, 1952]]
[[Rosalind Franklin]] took the X-ray photograph of a DNA fibre that proved key to [[James Watson]] and [[Francis Crick]]'s  discovery of the double helix, for which they both won the Nobel Prize for Physiology or Medicine in 1962. Watson revealed in his autobiographic account of the discovery of the structure of DNA, ''The Double Helix'',<ref>{{Citation|last=Watson|first=James D.|title=Discovering the double helix|date=2000|url=http://worldcat.org/oclc/48554849|publisher=Cold Spring Harbor Laboratory|isbn=978-0-87969-622-1|oclc=48554849|access-date=}}</ref> that he had used Franklin's X-ray photograph without her permission. Franklin died of cancer in her 30s, before Watson received the Nobel Prize. Franklin also carried out important structural studies of carbon in coal and graphite, and of plant and animal viruses.

[[Isabella Karle]] of the United States Naval Research Laboratory developed an experimental approach to the mathematical theory of crystallography. Her work improved the speed and accuracy of chemical and biomedical analysis. Yet only her husband Jerome shared the 1985 Nobel Prize in Chemistry with Herbert Hauptman, "for outstanding achievements in the development of direct methods for the determination of crystal structures". Other prize-giving bodies have showered Isabella with awards in her own right.

Women have written many textbooks and research papers in the field of X-ray crystallography. For many years Lonsdale edited the ''International Tables for Crystallography'', which provide information on crystal lattices, symmetry, and space groups, as well as mathematical, physical and chemical data on structures. [[Olga Kennard]] of the [[University of Cambridge]], founded and ran the [[Cambridge Crystallographic Data Centre]], an internationally recognized source of structural data on small molecules, from 1965 until 1997. [[Jenny Pickworth Glusker]], a British scientist, co-authored ''Crystal Structure Analysis: A Primer'',<ref>{{Cite book|last1=Glusker|first1=Jenny Pickworth|url=https://www.worldcat.org/oclc/1241842166|title=Crystal structure analysis: a primer.|last2=Trueblood|first2=Kenneth N|last3=International Union of Crystallography|date=2020|isbn=978-0-19-191790-5|oclc=1241842166}}</ref> first published in 1971 and as of 2010 in its third edition. [[Eleanor Dodson]], an Australian-born biologist, who began as Dorothy Hodgkin's technician, was the main instigator behind [[CCP4 (file format)|CCP4]], the collaborative computing project that currently shares more than 250 software tools with protein crystallographers worldwide.

==Nobel Prizes involving X-ray crystallography==
{| class="wikitable collapsible sortable"
|-
! Year !! Laureate !! Prize !! Rationale
|-
|1914||[[Max von Laue]]||Physics||"For his discovery of the diffraction of X-rays by crystals"<ref>{{cite web |title=The Nobel Prize in Physics 1914 |publisher=Nobel Foundation |url=http://nobelprize.org/nobel_prizes/physics/laureates/1914/index.html |access-date=2008-10-09 |archive-date=2008-09-15 |archive-url=https://web.archive.org/web/20080915195235/http://nobelprize.org/nobel_prizes/physics/laureates/1914/index.html |url-status=live }}</ref>
|-
| rowspan="2" |1915||[[William Henry Bragg]]|| rowspan="2" |Physics|| rowspan="2" |"For their services in the analysis of [[crystal structure]] by means of X-rays"<ref name="The Nobel Prize in Physics 1915">{{cite web |title=The Nobel Prize in Physics 1915 |publisher=Nobel Foundation |url=http://nobelprize.org/nobel_prizes/physics/laureates/1915/index.html |access-date=2008-10-09 |archive-date=2008-10-19 |archive-url=https://web.archive.org/web/20081019182238/http://nobelprize.org/nobel_prizes/physics/laureates/1915/index.html |url-status=live }}</ref>
|-
|[[William Lawrence Bragg]]
|-
| rowspan="2" |1962||[[Max F. Perutz]]|| rowspan="2" |Chemistry|| rowspan="2" |"for their studies of the structures of [[myoglobin|globular proteins]]"<ref name="The Nobel Prize in Chemistry 1962">{{cite web | title = The Nobel Prize in Chemistry 1962 | publisher = Nobelprize.org | url = http://nobelprize.org/nobel_prizes/chemistry/laureates/1962/index.html | access-date = 2008-10-06 | archive-date = 2008-09-24 | archive-url = https://web.archive.org/web/20080924043552/http://nobelprize.org/nobel_prizes/chemistry/laureates/1962/index.html | url-status = live }}</ref>
|-
|[[John C. Kendrew]]
|-
| rowspan="3" |1962||[[James D. Watson|James Dewey Watson]]|| rowspan="3" |Medicine|| rowspan="3" |"For their discoveries concerning the molecular structure of [[nucleic acid]]s and its significance for information transfer in living material"<ref name="nobel-1962">{{cite web
 | url = http://nobelprize.org/nobel_prizes/medicine/laureates/1962/index.html
 | title = The Nobel Prize in Physiology or Medicine 1962
 | access-date = 2007-07-28
 | publisher = Nobel Foundation
 | archive-date = 2018-12-26
 | archive-url = https://web.archive.org/web/20181226094942/https://www.nobelprize.org/nobel_prizes/medicine/laureates/1962/index.html%0A%20
 | url-status = live
 }}</ref>
|-
|[[Francis Crick|Francis Harry Compton Crick]]
|-
|[[Maurice Wilkins|Maurice Hugh Frederick Wilkins]]
|-
|1964||[[Dorothy Hodgkin]]||Chemistry||"For her [[#Early organic and small biological molecules|determinations by X-ray techniques]] of the structures of important biochemical substances"<ref>{{cite web | title = The Nobel Prize in Chemistry 1964 | publisher = Nobelprize.org | url = http://nobelprize.org/nobel_prizes/chemistry/laureates/1964/index.html | access-date = 2008-10-06 | archive-date = 2008-10-15 | archive-url = https://web.archive.org/web/20081015033105/http://nobelprize.org/nobel_prizes/chemistry/laureates/1964/index.html | url-status = live }}</ref>
|-
| rowspan="2" |1972||[[Stanford Moore]]|| rowspan="2" |Chemistry|| rowspan="2" |"For their contribution to the understanding of the connection between chemical structure and catalytic activity of the active centre of the [[ribonuclease]] molecule"<ref name="n1972">{{cite web | title = The Nobel Prize in Chemistry 1972 | publisher = Nobelprize.org | url = http://nobelprize.org/nobel_prizes/chemistry/laureates/1972/index.html | access-date = 2008-10-06 | archive-date = 2008-10-11 | archive-url = https://web.archive.org/web/20081011142815/http://nobelprize.org/nobel_prizes/chemistry/laureates/1972/index.html | url-status = live }}</ref>
|-
|[[William Howard Stein|William H. Stein]]
|-
|1976||[[William Lipscomb|William N. Lipscomb]]||Chemistry||"For his studies on the structure of [[borane]]s illuminating problems of chemical bonding"<ref>{{cite web | title = The Nobel Prize in Chemistry 1976 | publisher = Nobelprize.org | url = http://nobelprize.org/nobel_prizes/chemistry/laureates/1976/index.html | access-date = 2008-10-06 | archive-date = 2008-12-25 | archive-url = https://web.archive.org/web/20081225083422/http://nobelprize.org/nobel_prizes/chemistry/laureates/1976/index.html | url-status = live }}</ref>
|-
| rowspan="2" |1985||[[Jerome Karle]]|| rowspan="2" |Chemistry|| rowspan="2" |"For their outstanding achievements in developing [[Hauptman-Karle method|direct methods]] for the determination of crystal structures"<ref name="The Nobel Prize in Chemistry 1985">{{cite web | title = The Nobel Prize in Chemistry 1985 | publisher = Nobelprize.org | url = http://nobelprize.org/nobel_prizes/chemistry/laureates/1985/index.html | access-date = 2008-10-06 | archive-date = 2008-12-25 | archive-url = https://web.archive.org/web/20081225083444/http://nobelprize.org/nobel_prizes/chemistry/laureates/1985/index.html | url-status = live }}</ref>
|-
|[[Herbert A. Hauptman]]
|-
| rowspan="3" |1988||[[Johann Deisenhofer]]||Chemistry|| rowspan="3" |"For their determination of the three-dimensional structure of a [[photosynthetic reaction center|photosynthetic reaction centre]]"<ref name="The Nobel Prize in Chemistry 1988">{{cite web | title = The Nobel Prize in Chemistry 1988 | publisher = Nobelprize.org | url = http://nobelprize.org/nobel_prizes/chemistry/laureates/1988/index.html | access-date = 2008-10-06 | archive-date = 2008-12-25 | archive-url = https://web.archive.org/web/20081225083746/http://nobelprize.org/nobel_prizes/chemistry/laureates/1988/index.html | url-status = live }}</ref>
|-
|[[Hartmut Michel]]||Chemistry
|-
|[[Robert Huber]]||Chemistry
|-
|1997||[[John E. Walker]]||Chemistry||"For their elucidation of the [[ATP synthase|enzymatic mechanism]] underlying the synthesis of adenosine triphosphate (ATP)"<ref name="n1997">{{cite web | title = The Nobel Prize in Chemistry 1997 | publisher = Nobelprize.org | url = http://nobelprize.org/nobel_prizes/chemistry/laureates/1997/index.html | access-date = 2008-10-06 | archive-date = 2008-10-21 | archive-url = https://web.archive.org/web/20081021222630/http://nobelprize.org/nobel_prizes/chemistry/laureates/1997/index.html | url-status = live }}</ref>
|-
| rowspan="2" |2003||[[Roderick MacKinnon]]|| rowspan="2" |Chemistry||"For discoveries concerning channels in cell membranes [...] for structural and mechanistic [[Potassium channel#Structure|studies of ion channels]]"<ref name="n2003"/>
|-
|[[Peter Agre]]||"For discoveries concerning channels in cell membranes [...] for the discovery of [[Aquaporin|water channels]]"<ref name="n2003">{{cite web| title = The Nobel Prize in Chemistry 2003| publisher = Nobelprize.org| url = http://nobelprize.org/nobel_prizes/chemistry/laureates/2003/index.html| access-date = 2008-10-06| archive-date = 2008-09-29| archive-url = https://web.archive.org/web/20080929075139/http://nobelprize.org/nobel_prizes/chemistry/laureates/2003/index.html| url-status = live}}</ref>
|-
|2006||[[Roger D. Kornberg]]||Chemistry||"For his studies of the molecular basis of [[Transcription (genetics)|eukaryotic transcription]]"<ref>{{cite web| title = The Nobel Prize in Chemistry 2006| publisher = Nobelprize.org| url = http://nobelprize.org/nobel_prizes/chemistry/laureates/2006/index.html| access-date = 2008-10-06| archive-date = 2008-10-17| archive-url = https://web.archive.org/web/20081017150038/http://nobelprize.org/nobel_prizes/chemistry/laureates/2006/index.html| url-status = live}}</ref>
|-
| rowspan="3" |2009||[[Ada E. Yonath]]|| rowspan="3" |Chemistry|| rowspan="3" |"For studies of the structure and function of the [[ribosome]]"<ref name="The Nobel Prize in Chemistry 2009">{{cite web| title = The Nobel Prize in Chemistry 2009| publisher = Nobelprize.org| url = http://nobelprize.org/nobel_prizes/chemistry/laureates/2009/index.html| access-date = 2009-10-07| archive-date = 2009-10-10| archive-url = https://web.archive.org/web/20091010063812/http://nobelprize.org/nobel_prizes/chemistry/laureates/2009/index.html| url-status = live}}</ref>
|-
|[[Thomas A. Steitz]]
|-
|[[Venkatraman Ramakrishnan]]
|-
|2012||[[Brian Kobilka]]||Chemistry||"For studies of [[G protein-coupled receptor|G-protein-coupled receptors]]"<ref name="nobel-2012">{{cite web| title = The Nobel Prize in Chemistry 2012| publisher = Nobelprize.org| url = http://nobelprize.org/nobel_prizes/chemistry/laureates/2012/index.html| access-date = 2012-10-13| archive-date = 2012-10-13| archive-url = https://web.archive.org/web/20121013000137/http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2012/index.html| url-status = live}}</ref>

|}

== See also ==
{{Div col|colwidth=30em}}
* [[Beevers–Lipson strip]]
* [[Bragg diffraction]]
* [[Crystallographic database]]
* [[Crystallographic point groups]]
* [[Difference density map]]
* [[Electron diffraction]]
* [[Energy-dispersive X-ray diffraction]]
* [[Flack parameter]]
* [[Grazing incidence diffraction]]
* [[Henderson limit]]
* [[International Year of Crystallography]]
* [[Multipole density formalism]]
* [[Neutron diffraction]]
* [[Powder diffraction]]
* [[Ptychography]]
* [[Scherrer equation]]
* [[Small angle X-ray scattering (SAXS)]]
* [[Structure determination]]
* [[Ultrafast x-ray]]
* [[Virus crystallisation]]
* [[Wide angle X-ray scattering]] (WAXS)
* [[X-ray diffraction]]
{{div col end}}

== Notes ==
{{notelist}}

== References ==
{{Reflist|30em}}

== Further reading ==

===''International Tables for Crystallography''===
{{refbegin}}
* {{cite book|date=2002|title=International Tables for Crystallography. Volume A, Space-group Symmetry|edition = 5th|publisher=[[Kluwer Academic Publishers]], for the [[International Union of Crystallography]]|location=Dordrecht|isbn=0-7923-6590-9| veditors = Hahn T }}
* {{cite book|date=2001|title=International Tables for Crystallography. Volume F, Crystallography of biological molecules| veditors = Rossmann MG, Arnold E |publisher=Kluwer Academic Publishers, for the International Union of Crystallography|location=Dordrecht|isbn = 0-7923-6857-6}}
* {{cite book|date=1996|title=International Tables for Crystallography. Brief Teaching Edition of Volume A, Space-group Symmetry|edition = 4th|publisher=Kluwer Academic Publishers, for the International Union of Crystallography|location=Dordrecht|isbn=0-7923-4252-6| veditors = Hahn T }}
{{refend}}

===Bound collections of articles===
{{refbegin}}
* {{cite book|date=1997|title=Macromolecular Crystallography, Part A (Methods in Enzymology, v. 276)|publisher=Academic Press|location=San Diego|isbn=0-12-182177-3| veditors = Carter Jr CW, Sweet RM |url-access=registration|url=https://archive.org/details/macromolecularcr0000unse}}
* {{cite book|date=1997|title=Macromolecular Crystallography, Part B (Methods in Enzymology, v. 277)|publisher=Academic Press|location=San Diego|isbn=0-12-182178-1| veditors = Carter Jr CW, Sweet RM }}
* {{cite book|date=1999|title=Crystallization of Nucleic Acids and Proteins: A Practical Approach|edition = 2nd| veditors = Ducruix A, Giegé R |publisher=Oxford University Press|location=Oxford|isbn=0-19-963678-8}}
{{refend}}

===Textbooks===
{{refbegin}}
* {{cite book|vauthors=Birkholz M, Fewster PF, Genzel C|year=2005|title=Thin Film Analysis by X-Ray Scattering|publisher=Wiley-VCH|location=Weinheim|isbn=978-3-527-31052-4|chapter-url=https://www.researchgate.net/publication/260086423|chapter=Chapter 1: Principles of X-ray Diffraction|via=ResearchGate|url-access=registration|url=https://archive.org/details/thinfilmanalysis0000birk}}
* {{cite book | vauthors = Blow D|date=2002|title=Outline of Crystallography for Biologists|publisher=Oxford University Press|location=Oxford|isbn=0-19-851051-9}}
* {{cite book | vauthors = Burns G, Glazer AM | date = 1990 | title = Space Groups for Scientists and Engineers | edition = 2nd | location = Boston | publisher = Academic Press, Inc. | isbn = 0-12-145761-3 | url-access = registration | url = https://archive.org/details/spacegroupsforso0000burn }}
* {{cite book | vauthors = Clegg W|date=1998|title=Crystal Structure Determination (Oxford Chemistry Primer)|publisher=Oxford University Press|location=Oxford|isbn=0-19-855901-1}}
* {{cite book | vauthors = Cullity BD|date=1978|title=Elements of X-Ray Diffraction|edition = 2nd|publisher=Addison-Wesley Publishing Company|location=Reading, Massachusetts|isbn=0-534-55396-6}}
* {{cite book | vauthors = Drenth J|date=1999|title=Principles of Protein X-Ray Crystallography|publisher=Springer-Verlag|location=New York|isbn=0-387-98587-5}}
* {{cite book | vauthors = Giacovazzo C|date=1992|title=Fundamentals of Crystallography|publisher=Oxford University Press|location=Oxford|isbn=0-19-855578-4}}
* {{cite book| vauthors = Glusker JP, Lewis M, Rossi M |date=1994|title=Crystal Structure Analysis for Chemists and Biologists|publisher=VCH Publishers|location=New York|isbn=0-471-18543-4}}
* {{cite book| vauthors = Massa W |date=2004|title=Crystal Structure Determination|publisher=Springer|location=Berlin|isbn=3-540-20644-2}}
* {{cite book | vauthors = McPherson A|date=1999|title=Crystallization of Biological Macromolecules|publisher=Cold Spring Harbor Laboratory Press|location=Cold Spring Harbor, NY|isbn =0-87969-617-6}}
* {{cite book | vauthors = McPherson A|date=2003|title=Introduction to Macromolecular Crystallography|publisher=John Wiley & Sons|isbn=0-471-25122-4}}
* {{cite book|vauthors=McRee DE|date=1993|title=Practical Protein Crystallography|publisher=Academic Press|location=San Diego|isbn=0-12-486050-8|url=https://archive.org/details/practicalprotein00mcre_0}}
* {{cite book | vauthors = O'Keeffe M, Hyde BG |date=1996|title=Crystal Structures; I. Patterns and Symmetry|publisher=Mineralogical Society of America, Monograph Series|location=Washington, DC|isbn=0-939950-40-5}}
* {{cite book|vauthors=Rhodes G|date=2000|title=Crystallography Made Crystal Clear|publisher=Academic Press|location=San Diego|isbn=0-12-587072-8|url=http://www.chem.uwec.edu/Chem406_F06/Pages/lecture_notes/lect07/Crystallography_Rhodes.pdf|via=UW-Eau Claire, Chem 406, Fall 2005|access-date=2007-09-16|archive-date=2021-10-08|archive-url=https://web.archive.org/web/20211008172737/http://www.chem.uwec.edu/Chem406_F06/Pages/lecture_notes/lect07/Crystallography_Rhodes.pdf|url-status=live}}
* {{cite book | vauthors = Rupp B|date=2009|title=Biomolecular Crystallography: Principles, Practice and Application to Structural Biology|publisher=Garland Science|location=New York|isbn=978-0-8153-4081-2}}
* {{cite book | vauthors = Warren BE|date=1969|title=X-ray Diffraction |publisher=Dover Publications |location=New York|isbn=0-486-66317-5}}
* {{cite book | vauthors = Zachariasen WH|date=1945|title=Theory of X-ray Diffraction in Crystals|publisher=Dover Publications|location=New York|lccn=67026967}}
{{refend}}

===Applied computational data analysis===
{{refbegin}}
* {{cite book| veditors = Young RA|date=1993|title=The Rietveld Method|location=Oxford|publisher=Oxford University Press & International Union of Crystallography|isbn=0-19-855577-6}}
{{refend}}

===Historical===
{{refbegin}}
* {{cite book|date=1969|title=Early Papers on Diffraction of X-rays by Crystals|volume=I|publisher=published for the International Union of Crystallography by A. Oosthoek's Uitgeversmaatschappij N.V.|location=Utrecht| veditors = Bijvoet MJ, Burgers WG, Hägg G | editor1-link = Johannes Martin Bijvoet }}
* {{cite book | veditors = Bijvoet JM, Burgers WG, Hägg G |date=1972|title=Early Papers on Diffraction of X-rays by Crystals|volume=II|publisher=published for the International Union of Crystallography by A. Oosthoek's Uitgeversmaatschappij N.V.|location=Utrecht}}
* {{cite book|vauthors=Bragg WL, Phillips DC, Lipson H|date=1992|title=The Development of X-ray Analysis|publisher=Dover|location=New York|isbn=0-486-67316-2|url=https://archive.org/details/developmentofxra00brag_0}}
* {{cite book|date=1962|title=Fifty Years of X-ray Diffraction|publisher=published for the International Union of Crystallography by A. Oosthoek's Uitgeversmaatschappij N.V.|location=Utrecht| veditors = Ewald PP, etal | editor-link1=Paul Peter Ewald|doi=10.1007/978-1-4615-9961-6|isbn=978-1-4615-9963-0}}
* {{cite web | veditors = Ewald PP | url = http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/ | title = 50 Years of X-Ray Diffraction | quote = Reprinted in pdf format for the IUCr XVIII Congress, Glasgow, Scotland | publisher = International Union of Crystallography | access-date = 2006-12-11 | archive-date = 2008-03-23 | archive-url = https://web.archive.org/web/20080323071738/http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/ | url-status = live }}
* {{cite journal|vauthors=Friedrich W|date=1922|title=Die Geschichte der Auffindung der Röntgenstrahlinterferenzen|journal=Die Naturwissenschaften|volume=10|page=363|doi=10.1007/BF01565289|issue=16|bibcode=1922NW.....10..363F|s2cid=28141506|url=https://zenodo.org/record/2307864|access-date=2019-12-03|archive-date=2020-03-29|archive-url=https://web.archive.org/web/20200329132703/https://zenodo.org/record/2307864|url-status=live}}
* {{cite book | vauthors = Lonsdale K|date=1949|title=Crystals and X-rays|publisher=D. van Nostrand|location=New York}}
{{refend}}

== External links ==
{{Library resources box
 |onlinebooks=no
 |by=no
 |lcheading=X-ray crystallography}}
{{wikibooks|Xray Crystallography}}

===Tutorials===
* [https://www.xtal.iqf.csic.es/Cristalografia/index-en.html Learning Crystallography]
* [https://web.archive.org/web/20120303025301/http://stein.bioch.dundee.ac.uk/~charlie/index.php?section=1 Simple, non technical introduction]
* [http://richannel.org/collections/2013/crystallography The Crystallography Collection], video series from the [[Royal Institution]]
* [https://web.archive.org/web/20160303181456/http://acaschool.iit.edu/lectures04/JLiangXtal.pdf "Small Molecule Crystalization"] ([[PDF]]) at [[Illinois Institute of Technology]] website
* [http://iucr.org/ International Union of Crystallography]
* [http://www.ruppweb.org/Xray/101index.html Crystallography 101]
* [http://www.ysbl.york.ac.uk/~cowtan/sfapplet/sfintro.html Interactive structure factor tutorial], demonstrating properties of the diffraction pattern of a 2D crystal.
* [http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html Picturebook of Fourier Transforms], illustrating the relationship between crystal and diffraction pattern in 2D.
* [http://www.chem.uwec.edu/Chem406_F06/Pages/lectnotes.html#lecture7 Lecture notes on X-ray crystallography and structure determination]
* [http://nanohub.org/resources/5580 Online lecture on Modern X-ray Scattering Methods for Nanoscale Materials Analysis] by Richard J. Matyi
* [http://rigb.org/our-history/history-of-research/crystallography-timeline Interactive Crystallography Timeline] {{Webarchive|url=https://web.archive.org/web/20210630015448/https://www.rigb.org/our-history/history-of-research/crystallography-timeline |date=2021-06-30 }} from the [[Royal Institution]]

===Primary databases===
* [[Crystallography open database|Crystallography Open Database]] (COD)
* [https://web.archive.org/web/20150418160606/http://www.rcsb.org/pdb/home/home.do Protein Data Bank] ([[Protein Data Bank|PDB]])
* [http://ndbserver.rutgers.edu/ Nucleic Acid Databank] {{Webarchive|url=https://web.archive.org/web/20180714164436/http://ndbserver.rutgers.edu/ |date=2018-07-14 }} (NDB)
* [http://www.ccdc.cam.ac.uk/products/csd/ Cambridge Structural Database] ([[Cambridge Structural Database|CSD]])
* [http://www.fiz-karlsruhe.de/icsd.html Inorganic Crystal Structure Database] ([[Inorganic Crystal Structure Database|ICSD]])
* [https://web.archive.org/web/20070601170003/http://xpdb.nist.gov:8060/BMCD4/ Biological Macromolecule Crystallization Database] (BMCD)

===Derivative databases===
* [http://www.ebi.ac.uk/thornton-srv/databases/pdbsum/ PDBsum]
* [http://www.proteopedia.org/ Proteopedia&nbsp;– the collaborative, 3D encyclopedia of proteins and other molecules]
* [https://web.archive.org/web/20070426104437/http://www.rnabase.org/ RNABase]
* [http://xray.bmc.uu.se/hicup/ HIC-Up database of PDB ligands] {{Webarchive|url=https://web.archive.org/web/20200808155616/http://xray.bmc.uu.se/hicup/ |date=2020-08-08 }}
* [[Structural Classification of Proteins]] database
* [[CATH|CATH Protein Structure Classification]]
* [http://blanco.biomol.uci.edu/Membrane_Proteins_xtal.html List of transmembrane proteins with known 3D structure] {{Webarchive|url=https://web.archive.org/web/20110411070708/http://blanco.biomol.uci.edu/Membrane_Proteins_xtal.html |date=2011-04-11 }}
* [[Orientations of Proteins in Membranes database]]

===Structural validation===
* [http://molprobity.biochem.duke.edu/ MolProbity structural validation suite]
* [https://prosa.services.came.sbg.ac.at/prosa.php ProSA-web]
* [https://flipper.services.came.sbg.ac.at/ NQ-Flipper] (check for unfavorable rotamers of Asn and Gln residues)
* [http://ekhidna2.biocenter.helsinki.fi/dali/ DALI server] (identifies proteins similar to a given protein)

{{Crystallography}}
{{X-ray science}}
{{Protein structure determination}}

{{Authority control}}

{{DEFAULTSORT:X-Ray Crystallography}}
[[Category:X-ray crystallography| ]]
[[Category:Laboratory techniques in condensed matter physics]]
[[Category:Crystallography]]
[[Category:Diffraction]]
[[Category:Materials science]]
[[Category:Protein structure]]
[[Category:Protein methods]]
[[Category:Protein imaging]]
[[Category:Synchrotron-related techniques]]
[[Category:Articles containing video clips]]
[[Category:X-rays|Crystallography]]