Crystallography: Difference between revisions

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[[File:EBSD_(001)_Si.png|thumb|[[Kikuchi lines (physics)|Kikuchi lines]] in an [[electron backscatter diffraction]] pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source]]

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

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

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

Crystallography is a broad topic, and many of its subareas, such as [[X-ray crystallography]], are themselves important scientific topics. Crystallography ranges from the fundamentals of [[crystal structure]] to the mathematics of [[Crystal system|crystal geometry]], including those that are [[Aperiodic crystal|not periodic]] or [[quasicrystal]]s. At the atomic scale it can involve the use of [[X-ray diffraction]] to produce experimental data that the tools of [[X-ray crystallography]] can convert into detailed positions of atoms, and sometimes electron density. At larger scales it includes experimental tools such as [[Orientation imaging microscopy|orientational imaging]] to examine the relative orientations at the [[grain boundary]] in materials. Crystallography plays a key role in many areas of biology, chemistry, and physics, as well as in emerging developments in these fields.<ref name="IUCrScope">International Union of Crystallography. "IUCrJ Scope." ''IUCr Journals''. https://journals.iucr.org/m/services/about.html</ref>

== History and timeline ==

{{Main|Timeline of crystallography|History of crystallography before X-rays}}

Before the 20th century, the study of [[crystal]]s was based on physical measurements of their geometry using a [[goniometer]].<ref>{{Cite journal|date=1915-07-01|title=The Evolution of the Goniometer|journal=Nature|language=en|volume=95|issue=2386|pages=564–565|doi=10.1038/095564a0|bibcode=1915Natur..95..564.|issn=1476-4687|doi-access=free}}</ref> This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the [[Symmetry (physics)|symmetry]] of the crystal in question. The position in 3D space of each crystal face is plotted on a [[Stereographic projection|stereographic]] net such as a [[Wulff net]] or [[Lambert azimuthal equal-area projection|Lambert net]]. The [[pole figure|pole]] to each face is plotted on the net. Each point is labelled with its [[Miller index]]. The final plot allows the symmetry of the crystal to be established.<ref name=":0">{{Cite journal |last1=Molčanov |first1=Krešimir |last2=Stilinović |first2=Vladimir |date=2014-01-13 |title=Chemical Crystallography before X-ray Diffraction |url=https://onlinelibrary.wiley.com/doi/10.1002/anie.201301319 |journal=Angewandte Chemie International Edition |language=en |volume=53 |issue=3 |pages=638–652 |doi=10.1002/anie.201301319 |pmid=24065378 |issn=1433-7851|url-access=subscription }}</ref><ref>{{Cite journal |last=Mascarenhas |first=Yvonne Primerano |date=2020-03-02 |title=Crystallography before the Discovery of X-Ray Diffraction |journal=Revista Brasileira de Ensino de Física |language=en |volume=42 |~~pages~~=e20190336 |doi=10.1590/1806-9126-RBEF-2019-0336 |issn=1806-1117|doi-access=free }}</ref>

Before the 20th century, the study of [[crystal]]s was based on physical measurements of their geometry using a [[goniometer]].<ref>{{Cite journal|date=1915-07-01|title=The Evolution of the Goniometer|journal=Nature|language=en|volume=95|issue=2386|pages=564–565|doi=10.1038/095564a0|bibcode=1915Natur..95..564.|issn=1476-4687|doi-access=free}}</ref> This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the [[Symmetry (physics)|symmetry]] of the crystal in question. The position in 3D space of each crystal face is plotted on a [[Stereographic projection|stereographic]] net such as a [[Wulff net]] or [[Lambert azimuthal equal-area projection|Lambert net]]. The [[pole figure|pole]] to each face is plotted on the net. Each point is labelled with its [[Miller index]]. The final plot allows the symmetry of the crystal to be established.<ref name=":0">{{Cite journal |last1=Molčanov |first1=Krešimir |last2=Stilinović |first2=Vladimir |date=2014-01-13 |title=Chemical Crystallography before X-ray Diffraction |url=https://onlinelibrary.wiley.com/doi/10.1002/anie.201301319 |journal=Angewandte Chemie International Edition |language=en |volume=53 |issue=3 |pages=638–652 |doi=10.1002/anie.201301319 |pmid=24065378 |bibcode=2014ACIE...53..638M |issn=1433-7851|url-access=subscription }}</ref><ref>{{Cite journal |last=Mascarenhas |first=Yvonne Primerano |date=2020-03-02 |title=Crystallography before the Discovery of X-Ray Diffraction |journal=Revista Brasileira de Ensino de Física |language=en |volume=42 |article-number=e20190336 |doi=10.1590/1806-9126-RBEF-2019-0336 |issn=1806-1117|doi-access=free }}</ref>

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

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* Neutrons are scattered by the atomic nuclei through the [[strong nuclear force]]s, but in addition the [[magnetic moment]] of neutrons is non-zero, so they are also scattered by [[magnetic field]]s. When neutrons are scattered from [[hydrogen]]-containing materials, they produce diffraction patterns with high noise levels, which can sometimes be resolved by substituting [[deuterium]] for hydrogen.<ref>{{Cite web |title=ISIS Neutron Diffraction with Isotopic Substitution |url=https://www.isis.stfc.ac.uk/Pages/Neutron-Diffraction-with-Isotopic-Substitution.aspx |access-date=2024-07-02 |website=www.isis.stfc.ac.uk |language=en-GB}}</ref>

* Electrons are [[charged particle]]s and therefore interact with the total [[Charge density|charge distribution]] of both the [[atomic nuclei]] and the electrons of the sample.<ref>{{Cite book |last=Cowley |first=John Maxwell |author-link=John Maxwell Cowley|title=Diffraction physics |date=1995 |publisher=Elsevier Science B.V |isbn=978-0-444-82218-5 |edition=3rd |series=North-Holland personal library |location=Amsterdam; New York}}</ref>{{Rp|location=Chpt 4}}

It is hard to focus x-rays or neutrons, but since electrons are charged they can be focused and are used in [[electron ~~microscope~~]] to produce magnified images. There are many ways that [[transmission electron microscopy]] and related techniques such as [[scanning transmission electron microscopy]], [[high-resolution electron microscopy]] can be used to obtain images with in many cases atomic resolution from which crystallographic information can be obtained. There are also other methods such as [[low-energy electron diffraction]], [[low-energy electron microscopy]] and [[reflection high-energy electron diffraction]] which can be used to obtain crystallographic information about surfaces.

It is hard to focus x-rays or neutrons, but since electrons are charged they can be focused and are used in [[electron microscopes]] to produce magnified images. There are many ways that [[transmission electron microscopy]] and related techniques such as [[scanning transmission electron microscopy]], [[high-resolution electron microscopy]] can be used to obtain images with in many cases atomic resolution from which crystallographic information can be obtained. There are also other methods such as [[low-energy electron diffraction]], [[low-energy electron microscopy]] and [[reflection high-energy electron diffraction]] which can be used to obtain crystallographic information about surfaces.

== Applications in various areas ==

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=== Biology ===

[[X-ray crystallography]] is the primary method for determining the molecular conformations of biological [[macromolecule]]s, particularly [[protein]] and [[nucleic acid]]s such as [[DNA]] and [[RNA]]. The first crystal structure of a macromolecule was solved in 1958, a three-dimensional model of the myoglobin molecule obtained by X-ray analysis.<ref>{{Cite journal | doi = 10.1038/181662a0| title = A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-Ray Analysis| journal = Nature| volume = 181| issue = 4610| pages = 662–6| year = 1958| last1 = Kendrew | first1 = J. C.| last2 = Bodo | first2 = G.| last3 = Dintzis | first3 = H. M.| last4 = Parrish | first4 = R. G.| last5 = Wyckoff | first5 = H.| last6 = Phillips | first6 = D. C. | pmid=13517261|bibcode = 1958Natur.181..662K | s2cid = 4162786}}</ref> [[Neutron crystallography]] is often used to help refine structures obtained by X-ray methods or to solve a specific bond; the methods are often viewed as complementary, as X-rays are sensitive to electron positions and scatter most strongly off heavy atoms, while neutrons are sensitive to nucleus positions and scatter strongly even off many light isotopes, including hydrogen and deuterium.<ref>{{Cite journal |last=Meilleur |first=Flora |date=2020-11-20 |title=A ~~beginner’s~~ guide to neutron macromolecular crystallography ~~|url=https://doi.org/10.1042/BIO20200078~~ |journal=The Biochemist |volume=42 |issue=6 |pages=16–20 |doi=10.1042/BIO20200078 |issn=0954-982X|doi-access=free }}</ref>

[[X-ray crystallography]] is the primary method for determining the molecular conformations of biological [[macromolecule]]s, particularly [[protein]] and [[nucleic acid]]s such as [[DNA]] and [[RNA]]. The first crystal structure of a macromolecule was solved in 1958, a three-dimensional model of the myoglobin molecule obtained by X-ray analysis.<ref>{{Cite journal | doi = 10.1038/181662a0| title = A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-Ray Analysis| journal = Nature| volume = 181| issue = 4610| pages = 662–6| year = 1958| last1 = Kendrew | first1 = J. C.| last2 = Bodo | first2 = G.| last3 = Dintzis | first3 = H. M.| last4 = Parrish | first4 = R. G.| last5 = Wyckoff | first5 = H.| last6 = Phillips | first6 = D. C. | pmid=13517261|bibcode = 1958Natur.181..662K | s2cid = 4162786}}</ref> [[Neutron crystallography]] is often used to help refine structures obtained by X-ray methods or to solve a specific bond; the methods are often viewed as complementary, as X-rays are sensitive to electron positions and scatter most strongly off heavy atoms, while neutrons are sensitive to nucleus positions and scatter strongly even off many light isotopes, including hydrogen and deuterium.<ref>{{Cite journal |last=Meilleur |first=Flora |date=2020-11-20 |title=A beginner's guide to neutron macromolecular crystallography |journal=The Biochemist |volume=42 |issue=6 |pages=16–20 |doi=10.1042/BIO20200078 |issn=0954-982X|doi-access=free }}</ref>

[[Electron diffraction]] has been used to determine some protein structures, most notably [[membrane protein]]s and [[viral capsid]]s.

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== Reference literature ==

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

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

:Vol A - ''Space Group Symmetry'',

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* [[Fractional coordinates]]

* [[Low-energy electron diffraction]]

* [[Materials science]]

* [[Neutron crystallography]]

* [[Open-pool Australian lightwater reactor|Neutron diffraction at OPAL]]

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 [[File:EBSD_(001)_Si.png|thumb|[[Kikuchi lines (physics)|Kikuchi lines]] in an [[electron backscatter diffraction]] pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source]]
-'''Crystallography''' is the branch of science devoted to the study of molecular and crystalline structure and properties.<ref>{{Cite web |editor-last=Chapuis |editor-first=Gervais |title=Online Dictionary of Crystallography |url=https://dictionary.iucr.org/Main_Page |access-date=2024-05-22 |website=Online dictionary of crystallography |publisher=[[International Union of Crystallography]]}}</ref> The word ''crystallography'' is derived from the [[Ancient Greek]] word {{wikt-lang|grc|κρύσταλλος}} ({{grc-transl|κρύσταλλος}}; "clear ice, rock-crystal"), and {{wikt-lang|grc|γράφειν}} ({{grc-transl|γράφειν}}; "to write").<ref>{{Cite web |date=2021-10-21 |title=Online Dictionary of Crystallography |url=https://dictionary.iucr.org/Main_Page |access-date=2024-03-11 |website=International Union of Crystallography}}</ref> In July 2012, the [[United Nations]] recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.<ref name="UN Resolution">[http://www.iycr2014.org/about/resolution UN announcement "International Year of Crystallography"]. iycr2014.org. 12 July 2012</ref>
+'''Crystallography''' is the branch of science devoted to the study of molecular and [[Crystal structure|crystalline structure]] and properties.<ref>{{Cite web |editor-last=Chapuis |editor-first=Gervais |title=Online Dictionary of Crystallography |url=https://dictionary.iucr.org/Main_Page |access-date=2024-05-22 |website=Online dictionary of crystallography |publisher=[[International Union of Crystallography]]}}</ref> The word ''crystallography'' is derived from the [[Ancient Greek]] word {{wikt-lang|grc|κρύσταλλος}} ({{grc-transl|κρύσταλλος}}; "clear ice, rock-crystal"), and {{wikt-lang|grc|γράφειν}} ({{grc-transl|γράφειν}}; "to write").<ref>{{Cite web |date=2021-10-21 |title=Online Dictionary of Crystallography |url=https://dictionary.iucr.org/Main_Page |access-date=2024-03-11 |website=International Union of Crystallography}}</ref> In July 2012, the [[United Nations]] recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.<ref name="UN Resolution">[http://www.iycr2014.org/about/resolution UN announcement "International Year of Crystallography"]. iycr2014.org. 12 July 2012</ref>
-Crystallography is a broad topic, and many of its subareas, such as [[X-ray crystallography]], are themselves important scientific topics. Crystallography ranges from the fundamentals of [[crystal structure]] to the mathematics of [[Crystal system|crystal geometry]], including those that are [[Aperiodic crystal|not periodic]] or [[quasicrystal]]s. At the atomic scale it can involve the use of [[X-ray diffraction]] to produce experimental data that the tools of [[X-ray crystallography]] can convert into detailed positions of atoms, and sometimes electron density. At larger scales it includes experimental tools such as [[Orientation imaging microscopy|orientational imaging]] to examine the relative orientations at the [[grain boundary]] in materials. Crystallography plays a key role in many areas of biology, chemistry, and physics, as well new developments in these fields.
+Crystallography is a broad topic, and many of its subareas, such as [[X-ray crystallography]], are themselves important scientific topics. Crystallography ranges from the fundamentals of [[crystal structure]] to the mathematics of [[Crystal system|crystal geometry]], including those that are [[Aperiodic crystal|not periodic]] or [[quasicrystal]]s. At the atomic scale it can involve the use of [[X-ray diffraction]] to produce experimental data that the tools of [[X-ray crystallography]] can convert into detailed positions of atoms, and sometimes electron density. At larger scales it includes experimental tools such as [[Orientation imaging microscopy|orientational imaging]] to examine the relative orientations at the [[grain boundary]] in materials. Crystallography plays a key role in many areas of biology, chemistry, and physics, as well as in emerging developments in these fields.<ref name="IUCrScope">International Union of Crystallography. "IUCrJ Scope." ''IUCr Journals''. https://journals.iucr.org/m/services/about.html</ref>
 == History and timeline ==
-{{Main|Timeline of crystallography}}
+{{Main|Timeline of crystallography|History of crystallography before X-rays}}
-Before the 20th century, the study of [[crystal]]s was based on physical measurements of their geometry using a [[goniometer]].<ref>{{Cite journal|date=1915-07-01|title=The Evolution of the Goniometer|journal=Nature|language=en|volume=95|issue=2386|pages=564–565|doi=10.1038/095564a0|bibcode=1915Natur..95..564.|issn=1476-4687|doi-access=free}}</ref> This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the [[Symmetry (physics)|symmetry]] of the crystal in question. The position in 3D space of each crystal face is plotted on a [[Stereographic projection|stereographic]] net such as a [[Wulff net]] or [[Lambert azimuthal equal-area projection|Lambert net]]. The [[pole figure|pole]] to each face is plotted on the net. Each point is labelled with its [[Miller index]]. The final plot allows the symmetry of the crystal to be established.<ref name=":0">{{Cite journal |last1=Molčanov |first1=Krešimir |last2=Stilinović |first2=Vladimir |date=2014-01-13 |title=Chemical Crystallography before X-ray Diffraction |url=https://onlinelibrary.wiley.com/doi/10.1002/anie.201301319 |journal=Angewandte Chemie International Edition |language=en |volume=53 |issue=3 |pages=638–652 |doi=10.1002/anie.201301319 |pmid=24065378 |issn=1433-7851|url-access=subscription }}</ref><ref>{{Cite journal |last=Mascarenhas |first=Yvonne Primerano |date=2020-03-02 |title=Crystallography before the Discovery of X-Ray Diffraction |journal=Revista Brasileira de Ensino de Física |language=en |volume=42 |pages=e20190336 |doi=10.1590/1806-9126-RBEF-2019-0336 |issn=1806-1117|doi-access=free }}</ref>
+Before the 20th century, the study of [[crystal]]s was based on physical measurements of their geometry using a [[goniometer]].<ref>{{Cite journal|date=1915-07-01|title=The Evolution of the Goniometer|journal=Nature|language=en|volume=95|issue=2386|pages=564–565|doi=10.1038/095564a0|bibcode=1915Natur..95..564.|issn=1476-4687|doi-access=free}}</ref> This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the [[Symmetry (physics)|symmetry]] of the crystal in question. The position in 3D space of each crystal face is plotted on a [[Stereographic projection|stereographic]] net such as a [[Wulff net]] or [[Lambert azimuthal equal-area projection|Lambert net]]. The [[pole figure|pole]] to each face is plotted on the net. Each point is labelled with its [[Miller index]]. The final plot allows the symmetry of the crystal to be established.<ref name=":0">{{Cite journal |last1=Molčanov |first1=Krešimir |last2=Stilinović |first2=Vladimir |date=2014-01-13 |title=Chemical Crystallography before X-ray Diffraction |url=https://onlinelibrary.wiley.com/doi/10.1002/anie.201301319 |journal=Angewandte Chemie International Edition |language=en |volume=53 |issue=3 |pages=638–652 |doi=10.1002/anie.201301319 |pmid=24065378 |bibcode=2014ACIE...53..638M |issn=1433-7851|url-access=subscription }}</ref><ref>{{Cite journal |last=Mascarenhas |first=Yvonne Primerano |date=2020-03-02 |title=Crystallography before the Discovery of X-Ray Diffraction |journal=Revista Brasileira de Ensino de Física |language=en |volume=42 |article-number=e20190336 |doi=10.1590/1806-9126-RBEF-2019-0336 |issn=1806-1117|doi-access=free }}</ref>
 The discovery of [[X-ray]]s and [[electron]]s in the last decade of the 19th century enabled the determination of crystal structures on the atomic scale, which brought about the modern era of crystallography. The first X-ray diffraction experiment was conducted in 1912 by [[Max von Laue]],<ref name="L1912">{{cite journal |vauthors=Friedrich W, Knipping P, von Laue M |date=1912 |title=Interferenz-Erscheinungen bei Röntgenstrahlen |url=https://commons.wikimedia.org/wiki/File:Interferenz-Erscheinungen_bei_Röntgenstrahlen.pdf |journal=Sitzungsberichte der Mathematisch-Physikalischen Classe der Königlich-Bayerischen Akademie der Wissenschaften zu München |volume=1912 |page=303 |trans-work=Interference phenomena in X-rays}}</ref> while electron diffraction was first realized in 1927 in the [[Davisson–Germer experiment]]<ref>{{Cite journal |last1=Davisson |first1=C. |last2=Germer |first2=L. H. |date=1927 |title=The Scattering of Electrons by a Single Crystal of Nickel |url=https://www.nature.com/articles/119558a0 |journal=Nature |language=en |volume=119 |issue=2998 |pages=558–560 |doi=10.1038/119558a0 |bibcode=1927Natur.119..558D |issn=1476-4687|url-access=subscription }}</ref> and parallel work by [[George Paget Thomson]] and Alexander Reid.<ref>{{Cite journal |last1=Thomson |first1=G. P. |last2=Reid |first2=A. |date=1927 |title=Diffraction of Cathode Rays by a Thin Film |url=https://www.nature.com/articles/119890a0 |journal=Nature |language=en |volume=119 |issue=3007 |pages=890 |doi=10.1038/119890a0 |bibcode=1927Natur.119Q.890T |issn=1476-4687|url-access=subscription }}</ref> These developed into the two main branches of crystallography, [[X-ray crystallography]] and [[Electron diffraction|electron]] diffraction. The quality and throughput of solving crystal structures greatly improved in the second half of the 20th century, with the developments of customized instruments and [[Phase problem|phasing algorithms]]. Nowadays, crystallography is an [[interdisciplinary field]], supporting theoretical and experimental discoveries in various domains.<ref>{{Cite journal |last1=Brooks-Bartlett |first1=Jonathan C. |last2=Garman |first2=Elspeth F. |date=2015-07-03 |title=The Nobel Science: One Hundred Years of Crystallography |url=https://journals.sagepub.com/doi/full/10.1179/0308018815Z.000000000116 |journal=Interdisciplinary Science Reviews |language=en |volume=40 |issue=3 |pages=244–264 |doi=10.1179/0308018815Z.000000000116 |bibcode=2015ISRv...40..244B |issn=0308-0188|url-access=subscription }}</ref> Modern-day scientific instruments for crystallography vary from laboratory-sized equipment, such as [[diffractometer]]s and [[electron microscope]]s, to dedicated large facilities, such as [[photoinjector]]s, [[synchrotron light source]]s and [[free-electron laser]]s.
@@ Line 24: / Line 23: @@
 * Neutrons are scattered by the atomic nuclei through the [[strong nuclear force]]s, but in addition the [[magnetic moment]] of neutrons is non-zero, so they are also scattered by [[magnetic field]]s. When neutrons are scattered from [[hydrogen]]-containing materials, they produce diffraction patterns with high noise levels, which can sometimes be resolved by substituting [[deuterium]] for hydrogen.<ref>{{Cite web |title=ISIS Neutron Diffraction with Isotopic Substitution |url=https://www.isis.stfc.ac.uk/Pages/Neutron-Diffraction-with-Isotopic-Substitution.aspx |access-date=2024-07-02 |website=www.isis.stfc.ac.uk |language=en-GB}}</ref>
 * Electrons are [[charged particle]]s and therefore interact with the total [[Charge density|charge distribution]] of both the [[atomic nuclei]] and the electrons of the sample.<ref>{{Cite book |last=Cowley |first=John Maxwell |author-link=John Maxwell Cowley|title=Diffraction physics |date=1995 |publisher=Elsevier Science B.V |isbn=978-0-444-82218-5 |edition=3rd |series=North-Holland personal library |location=Amsterdam; New York}}</ref>{{Rp|location=Chpt 4}}
-It is hard to focus x-rays or neutrons, but since electrons are charged they can be focused and are used in [[electron microscope]] to produce magnified images. There are many ways that [[transmission electron microscopy]] and related techniques such as [[scanning transmission electron microscopy]], [[high-resolution electron microscopy]] can be used to obtain images with in many cases atomic resolution from which crystallographic information can be obtained. There are also other methods such as [[low-energy electron diffraction]], [[low-energy electron microscopy]] and [[reflection high-energy electron diffraction]] which can be used to obtain crystallographic information about surfaces.
+It is hard to focus x-rays or neutrons, but since electrons are charged they can be focused and are used in [[electron microscopes]] to produce magnified images. There are many ways that [[transmission electron microscopy]] and related techniques such as [[scanning transmission electron microscopy]], [[high-resolution electron microscopy]] can be used to obtain images with in many cases atomic resolution from which crystallographic information can be obtained. There are also other methods such as [[low-energy electron diffraction]], [[low-energy electron microscopy]] and [[reflection high-energy electron diffraction]] which can be used to obtain crystallographic information about surfaces.
 == Applications in various areas ==
@@ Line 39: / Line 38: @@
 === Biology ===
-[[X-ray crystallography]] is the primary method for determining the molecular conformations of biological [[macromolecule]]s, particularly [[protein]] and [[nucleic acid]]s such as [[DNA]] and [[RNA]]. The first crystal structure of a macromolecule was solved in 1958, a three-dimensional model of the myoglobin molecule obtained by X-ray analysis.<ref>{{Cite journal | doi = 10.1038/181662a0| title = A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-Ray Analysis| journal = Nature| volume = 181| issue = 4610| pages = 662–6| year = 1958| last1 = Kendrew | first1 = J. C.| last2 = Bodo | first2 = G.| last3 = Dintzis | first3 = H. M.| last4 = Parrish | first4 = R. G.| last5 = Wyckoff | first5 = H.| last6 = Phillips | first6 = D. C. | pmid=13517261|bibcode = 1958Natur.181..662K | s2cid = 4162786}}</ref> [[Neutron crystallography]] is often used to help refine structures obtained by X-ray methods or to solve a specific bond; the methods are often viewed as complementary, as X-rays are sensitive to electron positions and scatter most strongly off heavy atoms, while neutrons are sensitive to nucleus positions and scatter strongly even off many light isotopes, including hydrogen and deuterium.<ref>{{Cite journal |last=Meilleur |first=Flora |date=2020-11-20 |title=A beginner’s guide to neutron macromolecular crystallography |url=https://doi.org/10.1042/BIO20200078 |journal=The Biochemist |volume=42 |issue=6 |pages=16–20 |doi=10.1042/BIO20200078 |issn=0954-982X|doi-access=free }}</ref>
+[[X-ray crystallography]] is the primary method for determining the molecular conformations of biological [[macromolecule]]s, particularly [[protein]] and [[nucleic acid]]s such as [[DNA]] and [[RNA]]. The first crystal structure of a macromolecule was solved in 1958, a three-dimensional model of the myoglobin molecule obtained by X-ray analysis.<ref>{{Cite journal | doi = 10.1038/181662a0| title = A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-Ray Analysis| journal = Nature| volume = 181| issue = 4610| pages = 662–6| year = 1958| last1 = Kendrew | first1 = J. C.| last2 = Bodo | first2 = G.| last3 = Dintzis | first3 = H. M.| last4 = Parrish | first4 = R. G.| last5 = Wyckoff | first5 = H.| last6 = Phillips | first6 = D. C. | pmid=13517261|bibcode = 1958Natur.181..662K | s2cid = 4162786}}</ref> [[Neutron crystallography]] is often used to help refine structures obtained by X-ray methods or to solve a specific bond; the methods are often viewed as complementary, as X-rays are sensitive to electron positions and scatter most strongly off heavy atoms, while neutrons are sensitive to nucleus positions and scatter strongly even off many light isotopes, including hydrogen and deuterium.<ref>{{Cite journal |last=Meilleur |first=Flora |date=2020-11-20 |title=A beginner's guide to neutron macromolecular crystallography |journal=The Biochemist |volume=42 |issue=6 |pages=16–20 |doi=10.1042/BIO20200078 |issn=0954-982X|doi-access=free }}</ref>
 [[Electron diffraction]] has been used to determine some protein structures, most notably [[membrane protein]]s and [[viral capsid]]s.
@@ Line 52: / Line 51: @@
 == Reference literature ==
-The ''International Tables for Crystallography''<ref>{{Cite book |last=Prince |first=E. |url=https://openlibrary.org/books/OL9332669M/Complete_Printed_Set_of_International_Tables_for_Crystallography |title=International Tables for Crystallography Vol. C: Mathematical, Physical and Chemical Tables |publisher=Wiley |year=2006 |isbn=978-1-4020-4969-9 |ol=9332669M |oclc=166325528 |archive-url=https://web.archive.org/web/20220506075232/https://openlibrary.org/books/OL9332669M/Complete_Printed_Set_of_International_Tables_for_Crystallography |archive-date=6 May 2022 |url-status=live}}</ref> is an eight-book series that outlines the standard notations for formatting, describing and testing crystals. The series contains books that covers analysis methods and the mathematical procedures for determining organic structure through x-ray crystallography, electron diffraction, and neutron diffraction. The International tables are focused on procedures, techniques and descriptions and do not list the physical properties of individual crystals themselves. Each book is about 1000 pages and the titles of the books are:
+The ''International Tables for Crystallography''<ref>{{Cite book |last=Prince |first=E. |title=International Tables for Crystallography Vol. C: Mathematical, Physical and Chemical Tables |publisher=Wiley |year=2006 |isbn=978-1-4020-4969-9 |ol=9332669M |oclc=166325528 }}</ref> is an eight-book series that outlines the standard notations for formatting, describing and testing crystals. The series contains books that covers analysis methods and the mathematical procedures for determining organic structure through x-ray crystallography, electron diffraction, and neutron diffraction. The International tables are focused on procedures, techniques and descriptions and do not list the physical properties of individual crystals themselves. Each book is about 1000 pages and the titles of the books are:
 :Vol A -  ''Space Group Symmetry'',
@@ Line 151: / Line 150: @@
 * [[Fractional coordinates]]
 * [[Low-energy electron diffraction]]
+* [[Materials science]]
 * [[Neutron crystallography]]
 * [[Open-pool Australian lightwater reactor|Neutron diffraction at OPAL]]
@@ Line 178: / Line 178: @@
 {{Crystallography}}
 {{Branches of materials science}}
+{{Branches of physics}}
 {{Geology}}
 {{Branches of chemistry}}

Crystallography: Difference between revisions

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