Editing Neutron diffraction

{{Short description|Technique to investigate atomic structures using neutron scattering}}
{{Science with neutrons}}

'''Neutron diffraction''' or '''elastic neutron scattering''' is the application of [[neutron scattering]] to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of [[Neutron temperature|thermal or cold]] [[neutron radiation|neutrons]] to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to [[X-ray diffraction]] but due to their different scattering properties, [[neutron]]s and [[X-ray]]s provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from [[synchrotron radiation]] are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.<ref name="iaea">[http://www-pub.iaea.org/MTCD/publications/PDF/te_1457_web.pdf Measurement of residual stress in materials using neutrons], [[IAEA]], 2003</ref>

== History ==
=== Discovery of the neutron ===
{{main|Neutron#Discovery}}

In 1921, American chemist and physicist [[William Draper Harkins|William D. Harkins]] introduced the term "[[neutron]]" while studying [[atomic structure]] and [[Nuclear reaction|nuclear reactions]]. He proposed the existence of a neutral particle within the [[atomic nucleus]], though there was no experimental evidence for it at the time.<ref>{{Cite journal |last=Harkins |first=William D. |date=1917 |title=The evolution of the elements and the stability of complex atoms. A new periodic system which shows a relation between the abundance of the elements and structure of the nuclei of atoms. |url=https://pubs.acs.org/doi/abs/10.1021/ja02250a002 |journal=Journal of the American Chemical Society |language=en |volume=39 |issue=5 |pages=856–879 |doi=10.1021/ja02250a002 |issn=0002-7863|url-access=subscription }}</ref> In 1932, British physicist [[James Chadwick]] provided experimental proof of the neutron's existence. His discovery confirmed the presence of this neutral [[subatomic particle]], earning him the [[Nobel Prize in Physics]] in 1935. Chadwick's research was influenced by earlier work from [[Irène Joliot-Curie|Irène]] and [[Frédéric Joliot-Curie]], who had detected unexplained neutral [[radiation]] but had not recognized it as a distinct particle.<ref>{{Cite journal |date=1932 |title=The existence of a neutron |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1932.0112 |journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character |language=en |volume=136 |issue=830 |pages=692–708 |doi=10.1098/rspa.1932.0112 |bibcode=1932RSPSA.136..692C |issn=0950-1207 |last1=Chadwick |first1=J. |doi-access=free }}</ref> Neutrons are subatomic particles that exist in the nucleus of the atom, it has higher mass than protons but no electrical charge.

In the 1930s [[Enrico Fermi]] and colleagues gave theoretical contributions establishing the foundation of [[neutron scattering]]. Fermi developed a framework to understand how neutrons interact with atomic nuclei.<ref>{{Cite journal |last1=Amaldi |first1=E. |last2=Fermi |first2=E. |date=1936-11-15 |title=On the Absorption and the Diffusion of Slow Neutrons |url=https://link.aps.org/doi/10.1103/PhysRev.50.899 |journal=Physical Review |language=en |volume=50 |issue=10 |pages=899–928 |doi=10.1103/PhysRev.50.899 |bibcode=1936PhRv...50..899A |issn=0031-899X|url-access=subscription }}</ref>

===Early diffraction work===
Diffraction was first observed in 1936<ref>{{Cite journal |last1=Mason |first1=T. E. |last2=Gawne |first2=T. J. |last3=Nagler |first3=S. E. |last4=Nestor |first4=M. B. |last5=Carpenter |first5=J. M. |date=2013-01-01 |title=The early development of neutron diffraction: science in the wings of the Manhattan Project |url=https://journals.iucr.org/a/issues/2013/01/00/wl5168/index.html |journal=Acta Crystallographica Section A: Foundations of Crystallography |language=en |volume=69 |issue=1 |pages=37–44 |doi=10.1107/S0108767312036021 |issn=0108-7673 |pmc=3526866 |pmid=23250059}}</ref> by two groups, von Halban and Preiswerk <ref>{{Cite journal |last=H |first=Von Halban |date=1936 |title=Preuve Experimentale de la Diffraction des Neutrons |url=https://cir.nii.ac.jp/crid/1571135650793736832 |journal=Acad. Sci. Paris |volume=203 |pages=73–75}}</ref> and by Mitchell and Powers.<ref>{{Cite journal |last1=Mitchell |first1=Dana P. |last2=Powers |first2=Philip N. |date=1936-09-01 |title=Bragg Reflection of Slow Neutrons |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.50.486.2 |journal=Physical Review |volume=50 |issue=5 |pages=486–487 |doi=10.1103/PhysRev.50.486.2|bibcode=1936PhRv...50..486M |url-access=subscription }}</ref> In 1944, [[Ernest O. Wollan]], with a background in X-ray scattering from his PhD work<ref name="PhysicsTodayObit">
{{cite journal |last1=Snell |first1=A. H. |last2=Wilkinson |first2=M. K. |last3=Koehler |first3=W. C. |year=1984 |title=Ernest Omar Wollan |journal=[[Physics Today]] |volume=37 |issue=11 |page=120 |bibcode=1984PhT....37k.120S |doi=10.1063/1.2915947 |doi-access=free}}</ref> under [[Arthur Compton]], recognized the potential for applying thermal neutrons from the newly operational [[X-10 Graphite Reactor|X-10 nuclear reactor]] to [[crystallography]]. Joined by [[Clifford G. Shull]] they developed<ref>
{{cite book |last=Shull |first=C. G. |title=Nobel Lectures, Physics 1991–1995 |date=1997 |publisher=[[World Scientific Publishing]] |editor-last=Ekspong |editor-first=G. |pages=145–154 |chapter=Early Development of Neutron Scattering |chapter-url=https://www.nobelprize.org/nobel_prizes/physics/laureates/1994/shull-lecture.pdf |archive-url=https://web.archive.org/web/20170519024556/https://www.nobelprize.org/nobel_prizes/physics/laureates/1994/shull-lecture.pdf |archive-date=2017-05-19}}</ref> neutron diffraction throughout the 1940s. 

Neutron diffraction experiments were carried out in 1945 by [[Ernest O. Wollan]] using the Graphite Reactor at [[Oak Ridge National Laboratory|Oak Ridge]]. He was joined shortly thereafter (June 1946)<ref>{{cite journal |last=Shull |first=Clifford G. |date=1995-10-01 |title=Early development of neutron scattering |journal=Reviews of Modern Physics |publisher=American Physical Society (APS) |volume=67 |issue=4 |pages=753–757 |bibcode=1995RvMP...67..753S |doi=10.1103/revmodphys.67.753 |issn=0034-6861}}</ref> by [[Clifford Glenwood Shull|Clifford Shull]], and together they established the basic principles of the technique, and applied it successfully to many different materials, addressing problems like the structure of ice and the microscopic arrangements of magnetic moments in materials. For this achievement, Shull was awarded one half of the 1994 [[Nobel Prize in Physics]]. (Wollan died in 1984). (The other half of the 1994 Nobel Prize for Physics went to [[Bertram Brockhouse|Bert Brockhouse]] for development of the inelastic scattering technique at the [[Chalk River Laboratories|Chalk River facility]] of [[Atomic Energy of Canada|AECL]]. This also involved the invention of the triple axis spectrometer).

=== 1950-60s === 
The development of neutron sources such as [[Nuclear reactor|reactors]] and [[Spallation source|spallation sources]] emerged. This allowed high-intensity [[Neutron beam activation analysis|neutron beams]], enabling advanced scattering experiments. Notably, the [[High Flux Isotope Reactor|high flux isotope reactor]] (HFIR) at Oak Ridge and Institut Laue Langevin (ILL) in Grenoble, France, emerged as key institutions for neutron scattering studies.<ref>{{Cite journal |last=Helliwell |first=John |date=2012 |title=My life in diffraction: an autobiographical review by George E. Bacon |url=http://www.tandfonline.com/doi/abs/10.1080/0889311X.2012.666976 |journal=Crystallography Reviews |language=en |volume=18 |issue=2 |pages=97–180 |doi=10.1080/0889311X.2012.666976 |bibcode=2012CryRv..18...97H |issn=0889-311X|url-access=subscription }}</ref>

===1970-80s === 
This period saw major advancements in neutron scattering techniques by developing techniques to explore different aspects of material science, structure and behaviour.<ref name="Lovesey-2003">{{Cite book |last=Lovesey |first=Stephen W. |title=Theory of neutron scattering from condensed matter. 2: Polarization effects and magnetic scattering |date=2003 |publisher=Clarendon Pr |isbn=978-0-19-852029-0 |edition=Repr |series=International series of monographs on physics |location=Oxford}}</ref>

[[Small-angle neutron scattering|Small angle neutron scattering (SANS)]]:'' Used to investigate large-scale structural features in materials. The works of Glatter and Kratky also helped in the advancements of this method, though it was primarily developed for [[X-ray|X-rays]].<ref name="Lovesey-2003" /> ''

[[Inelastic neutron scattering|Inelastic neutron scattering (INS)]]'': Provides insights into the dynamic process at the microscopic level. Majorly used to examine atomic and molecular motions.<ref name="Lovesey-2003" />''
[[File:Wollan_and_Shull_1949.jpg|thumb|In 1949, Ernest Wollan and Clifford Shull conducted experiments using a double-crystal [[neutron spectrometer]] positioned on the southern side of the ORNL graphite reactor to collect data. ]]

===1990-present === 
Recent advancements focus on improved sources, using sophisticated detectors and enhanced computational techniques. Spallation sources have been developed at SNS (Spallation Neutron Source) in the U.S. and [[ISIS Neutron and Muon Source|ISIS Neutron]] and Muon Source in the U.K., which can generate pulsed neutron beams for [[Time of flight|time-of-flight]] experiments. [[Neutron imaging]] and [[reflectometry]]<nowiki/>were also developed, which are powerful tools to analyse surfaces, interfaces and thin film structures, thus providing valuable insights into the material properties.

== Comparison of neutron scattering, XRD and electron scattering ==
{| class="wikitable"
|+
!'''Feature'''
![[Neutron scattering|Neutron diffraction]]
|'''[[X-ray diffraction]]'''
!'''[[Electron scattering]]'''
|-
|'''Principle'''
|Interacts with atomic nuclei and magnetic moments enabling nuclear and magnetic scattering <ref name="Bacon-1975">{{Cite book |last=Bacon |first=George E. |title=Neutron diffraction |date=1975 |publisher=Clarendon Pr |isbn=978-0-19-851353-7 |edition=3 |series=Monographs on the physics and chemistry of materials |location=Oxford}}</ref>
|Scatter off [[electron cloud]] thus allowing probing of electron density.<ref name="Cullity-2001">{{Cite book |last1=Cullity |first1=B. D.|title=Elements of X-ray diffraction |last2=Stock |first2=Stuart R. |date=2001 |publisher=Prentice Hall |isbn=978-0-201-61091-8 |edition=3rd |location=Upper Saddle River, NJ}}</ref><ref name="Authier-2004">{{Cite book |last=Authier |first=André|title=Dynamical theory of x-ray diffraction |date=2004 |publisher=Oxford University Press |isbn=978-0-19-852892-0 |edition=Revised |series=International Union of Crystallography monographs on crystallography |location=Oxford ; New York}}</ref>
|Scatter off electrostatic potential thus allowing probing of electron density.<ref name="Cowley-1995">{{Cite book |last=Cowley |first=J. M. |title=Diffraction physics |date=1995 |publisher=Elsevier |isbn=0-444-82218-6 |edition=3rd rev. |series=North-Holland personal library |location=New York}}</ref>
|-
|'''Penetration depth'''
|High (suitable to study bulk materials since neutrons penetrate deeply in)<ref name="Bacon-1975" />
|Moderate (good penetration but also absorption by heavy elements)<ref name="Cullity-2001" /><ref name="Authier-2004" />
|Low (suitable for surface studies since electrons are strongly absorbed) or quite deep depending upon the energy.<ref name="Cowley-1995" />
|-
|'''Sensitivity to light elements'''
|High (very sensitive to lighter elements like hydrogen or lithium) <ref name="Bacon-1975" />
|Low (poor sensitvity to lighter elements)<ref name="Cullity-2001" /><ref name="Authier-2004" />
|High (can detect lighter elements ).<ref name="Cowley-1995" />
|-
|'''Magnetic studies'''
|Excellent (can probe [[Magnetic structure|magnetic stucture]] and spin dynamics) <ref name="Bacon-1975" />
|Limited (require specialized techniques like resonance magnetic scattering)<ref name="Cullity-2001" /><ref name="Authier-2004" />
|Yields local information<ref name="Cowley-1995" />
|-
|'''Resolution'''
|High (depending on techniques and instrument) <ref name="Bacon-1975" />
|High (can yield very precise positions for crystal structure)<ref name="Cullity-2001" /><ref name="Authier-2004" />
|Very high (can achieve high resolution )<ref name="Squires">{{Cite book |last=Squires |first=Gordon Leslie |title=introduction to the Theory of Thermal Neutron Scattering}}</ref>
|-
|'''Sample environment'''
|Efficient (used to study samples in different environment) <ref name="Bacon-1975" />
|Efficient
|Limited (requires vacuum and thin samples)<ref name="Squires" />
|-
|'''Applications'''
|structure of materials and magnetic property of the material. <ref name="Bacon-1975" />
|[[X-ray crystallography]]<ref name="Cullity-2001" /><ref name="Authier-2004" />
|Used for bulk materials, surfaces, defects, see [[electron diffraction]]

|}

== Principle ==

=== Processes ===
Neutrons are produced through three major processes, fission, spallation, and Low energy nuclear reactions.{{cn|date=February 2025}}

==== Fission ====
In research reactors, fission takes place when a fissile nucleus, such as [[uranium-235]] (<sup>235</sup>U), absorbs a neutron and subsequently splits into two smaller fragments. This process releases energy along with additional neutrons. On average, each [[Nuclear fission|fission]] event produces about 2.5 neutrons. While one neutron is required to maintain the [[chain reaction]], the surplus neutrons can be utilized for various experimental applications.<ref>{{Cite book |last=LEMBO |first=MARY FRANCES |title=Nuclear engineering |year=2006 |isbn=9780429224515 |pages=15}}</ref>

==== Spallation ====
In spallation sources, high-energy protons (on the order of 1 [[Electronvolt|GeV]]) bombard a heavy metal target (e.g., [[uranium]] (U), [[tungsten]] (W), [[tantalum]] (Ta), [[lead]] (Pb), or [[Mercury (element)|mercury]] (Hg)). This interaction causes the nuclei to spit out neutrons. Proton interactions result in around ten to thirty neutrons per event, of which the bulk are known as "evaporation neutrons"(~2 MeV), while a minority are identified as "cascade neutrons" with energies reaching up to the GeV range. Although spallation is a very efficient technique of neutron production, the technique generates high energy particles, therefore requiring shielding for safety.<ref name="Carpenter-2015">{{Cite book |last=Carpenter |first=John M. |title=Elements of slow-neutron scattering: basics, techniques, and applications |date=2015 |publisher=Cambridge University Press |isbn=978-1-139-02931-5 |location=Cambridge}}</ref>
[[File:Three_major_process_for_neutron_production.png|thumb|Illustration of three major fundamental processes generating neutrons for scattering experiments:   Nuclear fission (Top), Spallation (middle),  Low energy reaction (bottom).<ref>{{Cite journal |last=Dronskowski |first=Richard |last2=Brückel |first2=Thomas |last3=Kohlmann |first3=Holger |last4=Avdeev |first4=Maxim |last5=Houben |first5=Andreas |last6=Meven |first6=Martin |last7=Hofmann |first7=Michael |last8=Kamiyama |first8=Takashi |last9=Zobel |first9=Mirijam |last10=Schweika |first10=Werner |last11=Hermann |first11=Raphaël P. |last12=Sano-Furukawa |first12=Asami |date=2024-06-25 |title=Neutron diffraction: a primer |url=https://www.degruyter.com/document/doi/10.1515/zkri-2024-0001/html |journal=Zeitschrift für Kristallographie - Crystalline Materials |language=en |volume=239 |issue=5-6 |pages=139–166 |doi=10.1515/zkri-2024-0001 |issn=2194-4946}}</ref>]]

==== Low energy nuclear reactions ====
Low-energy nuclear reactions are the basis of neutron production in accelerator-driven sources. The selected target materials are based on the energy levels; lighter metals such as [[lithium]] (Li) and [[beryllium]] (Be) can be used toachieve their maximum possible reaction rate under 30 MeV, while heavier elements such as tungsten (W) and [[carbon]] (C) provide better performance above 312 MeV. These Compact Accelerator-driven Neutron Sources (CANS) have matured and are now approaching the performance of fission and spallation sources.<ref>{{Cite journal |last1=Ashkar |first1=Rana |last2=Bilheux |first2=Hassina Z. |last3=Bordallo |first3=Heliosa |last4=Briber |first4=Robert |last5=Callaway |first5=David J. E. |last6=Cheng |first6=Xiaolin |last7=Chu |first7=Xiang-Qiang |last8=Curtis |first8=Joseph E. |last9=Dadmun |first9=Mark |last10=Fenimore |first10=Paul |last11=Fushman |first11=David |last12=Gabel |first12=Frank |last13=Gupta |first13=Kushol |last14=Herberle |first14=Frederick |last15=Heinrich |first15=Frank |date=2018-12-01 |title=Neutron scattering in the biological sciences: progress and prospects |url=https://journals.iucr.org/paper?S2059798318017503 |journal=Acta Crystallographica Section D Structural Biology |volume=74 |issue=12 |pages=1129–1168 |doi=10.1107/S2059798318017503 |pmid=30605130 |issn=2059-7983|hdl=2381/45684 |hdl-access=free }}</ref>

=== De-Broglie relation ===
Neutron scattering relies on the wave-particle dual nature of neutrons. The [[De Broglie relation|De-Broglie relation]] links the [[wavelength]] (''λ'') of a neutron to its energy (E)<ref name="Carpenter-2015" />

<math>\lambda=h/mv</math>

where: ''h'' is Planck's constant, ''p'' is the [[momentum]] of the neutron, ''m'' is the mass of the neutron, ''v'' is the [[velocity]] of the neutron.

== Scattering ==
Neutron scattering is used to detect the distance between atoms and study the dynamics of materials. It involves two major principles: [[elastic scattering]] and [[inelastic scattering]].

Elastic scattering provides insight into the structural properties of materials by looking at the angles at which neutrons are scattered.  The resulting pattern of the scattering provides information regarding the atomic structure of crystals, liquids and amorphous materials.<ref name="Bacon-1975" />

Inelastic scattering focuses on material dynamics through the study of neutron energy and momentum changes during interactions. It is key to study phonons, magnons, and other excitations of solid materials.<ref>{{Cite journal |title=Introduction to the Theory of Thermal Neutron Scattering; Dover Publications |url= |journal=Dover Publications}}</ref>

== Neutron matter interaction ==
X- rays interact with matter through electrostatic interaction by interacting with the electron cloud of atoms, this limits their application as they can be scattered strongly from electrons. While being neutral, neutrons primarily interact with matter through the short-range strong force with atomic nuclei. Nuclei are far smaller than the electron cloud, meaning most materials are transparent to neutrons and allow deeper penetration. The interaction between neutrons and nuclei is described by the [[Fermi pseudopotential]], that is, neutrons are well above their [[meson]] mass threshold, and thus can be treated effectively as point-like [[Scatterer|scatterers]]. While most elements have a low tendency to absorb neutrons, certain ones such as [[cadmium]] (Cd), [[gadolinium]] (Gd), [[helium]] (<sup>3</sup>He), [[lithium]] (<sup>6</sup>Li), and [[boron]] ( <sup>10</sup>B) exhibit strong neutron absorption due to nuclear resonance effects. The likelihood of absorption increases with neutron wavelength (''σ<sub>a</sub> ∝ λ''), meaning slower neutrons are absorbed more readily than faster ones.<ref>{{Cite journal |last=Bucknall |first=David |date=2012 |title=Introduction to the Theory of Thermal Neutron Scattering, 3rd edn., by G.L. Squires: Scope: textbook. Level: early career researchers, researchers, specialists, scientists |url=http://www.tandfonline.com/doi/abs/10.1080/00107514.2012.745613 |journal=Contemporary Physics |language=en |volume=53 |issue=6 |pages=544–545 |doi=10.1080/00107514.2012.745613 |bibcode=2012ConPh..53..544B |issn=0010-7514|url-access=subscription }}</ref><ref>{{Cite book |title=Neutron data booklet |date=2003 |publisher=Old City |isbn=978-0-9704143-7-3 |editor-last=Dianoux |editor-first=A. J. |edition=2 |location=Institut Laue-Langevin Philadelphia, PA }}</ref>

==Instrumental and sample requirements==
The technique requires a source of neutrons. Neutrons are usually produced in a [[nuclear reactor]] or [[spallation source]]. At a [[research reactor]], other components are needed, including a [[crystal monochromator]] (in the case of thermal neutrons), as well as filters to select the desired neutron wavelength. Some parts of the setup may also be movable. For the long-wavelength neutrons, crystals cannot be used and gratings are used instead as diffractive optical components.<ref>{{Cite book |last1=Hadden |first1=Elhoucine |last2=Iso |first2=Yuko |last3=Kume |first3=Atsushi |last4=Umemoto |first4=Koichi |last5=Jenke |first5=Tobias |last6=Fally |first6=Martin |last7=Klepp |first7=Jürgen |last8=Tomita |first8=Yasuo |title=Photosensitive Materials and their Applications II |chapter=Nanodiamond-based nanoparticle-polymer composite gratings with extremely large neutron refractive index modulation |editor-first1=Robert R |editor-first2=Yasuo |editor-first3=John T |editor-first4=Inmaculada |editor-last1=McLeod |editor-last2=Tomita |editor-last3=Sheridan |editor-last4=Pascual Villalobos |date=2022-05-24 |chapter-url=https://www.spiedigitallibrary.org/conference-proceedings-of-spie/12151/1215109/Nanodiamond-based-nanoparticle-polymer-composite-gratings-with-extremely-large-neutron/10.1117/12.2623661.full |publisher=SPIE |volume=12151 |pages=70–76 |doi=10.1117/12.2623661|bibcode=2022SPIE12151E..09H |isbn=9781510651784 |s2cid=249056691 }}</ref>  At a spallation source, the time of flight technique is used to sort the energies of the incident neutrons (higher energy neutrons are faster), so no monochromator is needed, but rather a series of aperture elements synchronized to filter neutron pulses with the desired wavelength.

The technique is most commonly performed as [[powder diffraction]], which only requires a polycrystalline powder. Single crystal work is also possible, but the crystals must be much larger than those that are used in single-crystal [[X-ray crystallography]]. It is common to use crystals that are about 1&nbsp;mm<sup>3</sup>.<ref name="Picc">Paula M. B. Piccoli, Thomas F. Koetzle, Arthur J. Schultz "Single Crystal Neutron Diffraction for the Inorganic Chemist—A Practical Guide" Comments on Inorganic Chemistry 2007, Volume 28, 3-38. {{doi|10.1080/02603590701394741}}</ref>

The technique also requires a device that can [[Neutron detection|detect the neutrons]] after they have been scattered.

Summarizing, the main disadvantage to neutron diffraction is the requirement for a nuclear reactor. For single crystal work, the technique requires relatively large crystals, which are usually challenging to grow. The advantages to the technique are many - sensitivity to light atoms, ability to distinguish isotopes, absence of radiation damage,<ref name="Picc" /> as well as a penetration depth of several cm<ref name="iaea" />

==Nuclear scattering==
Like all [[quantum]] [[elementary particle|particles]], neutrons can exhibit wave phenomena typically associated with light or sound. [[Diffraction]] is one of these phenomena; it occurs when waves encounter obstacles whose size is comparable with the [[wavelength]]. If the wavelength of a quantum particle is short enough, atoms or their nuclei can serve as diffraction obstacles. When a beam of neutrons emanating from a reactor is slowed and selected properly by their speed, their wavelength lies near one [[angstrom]] (0.1 [[nanometer]]), the typical separation between atoms in a solid material. Such a beam can then be used to perform a diffraction experiment. Impinging on a crystalline sample, it will scatter under a limited number of well-defined angles, according to the same [[Bragg law|Bragg's law]] that describes X-ray diffraction.

Neutrons and X-rays interact with matter differently. X-rays interact primarily with the [[electron]] cloud surrounding each atom. The contribution to the diffracted x-ray intensity is therefore larger for atoms with larger [[Z (Atomic number)|atomic number (Z)]]. On the other hand, neutrons interact directly with the ''nucleus'' of the atom, and the contribution to the diffracted intensity depends on each [[isotope]]; for example, regular hydrogen and deuterium contribute differently. It is also often the case that light (low Z) atoms contribute strongly to the diffracted intensity, even in the presence of large Z atoms. The scattering length varies from isotope to isotope rather than linearly with the atomic number. An element like [[vanadium]] strongly scatters X-rays, but its nuclei hardly scatters neutrons, which is why it is often used as a container material. Non-magnetic neutron diffraction is directly sensitive to the positions of the nuclei of the atoms.

The nuclei of atoms, from which neutrons scatter, are tiny. Furthermore, there is no need for an [[atomic form factor]] to describe the shape of the electron cloud of the atom and the scattering power of an atom does not fall off with the scattering angle as it does for X-rays. [[Diffractogram]]s therefore can show strong, well-defined diffraction peaks even at high angles, particularly if the experiment is done at low temperatures. Many neutron sources are equipped with liquid helium cooling systems that allow data collection at temperatures down to 4.2 K. The superb high angle (i.e. high ''resolution'') information means that the atomic positions in the structure can be determined with high precision. On the other hand, [[Fourier map]]s (and to a lesser extent [[difference Fourier map]]s) derived from neutron data suffer from series termination errors, sometimes so much that the results are meaningless.

==Magnetic scattering==
Although neutrons are uncharged, they carry a [[magnetic moment]], and therefore interact with magnetic moments, including those arising from the electron cloud around an atom. Neutron diffraction can therefore reveal the microscopic [[magnetic structure]] of a material.<ref>Neutron diffraction of magnetic materials / Yu. A. Izyumov, V.E. Naish, and R.P. Ozerov; translated from Russian by Joachim Büchner. New York : Consultants Bureau, c1991.{{ISBN|0-306-11030-X}}</ref>

Magnetic scattering does require an [[atomic form factor#Magnetic scattering|atomic form factor]] as it is caused by the much larger electron cloud around the tiny nucleus. The intensity of the magnetic contribution to the diffraction peaks will therefore decrease towards higher angles.

==Uses==
Neutron diffraction can be used to determine the [[static structure factor]] of [[gas]]es, [[liquid]]s or [[amorphous solid]]s. Most experiments, however, aim at the structure of crystalline solids, making neutron diffraction an important tool of [[crystallography]].

Neutron diffraction is closely related to X-ray [[powder diffraction]].<ref>''Neutron powder diffraction'' by Richard M. Ibberson and William I.F. David, Chapter 5 of Structure determination form powder diffraction data IUCr monographphs on crystallography, Oxford scientific publications 2002, {{ISBN|0-19-850091-2}}</ref> In fact, the single crystal version of the technique is less commonly used because currently available neutron sources require relatively large samples and large single crystals are hard or impossible to come by for most materials. Future developments, however, may well change this picture. Because the data is typically a 1D powder diffractogram they are usually processed using [[Rietveld refinement]]. In fact the latter found its origin in neutron diffraction (at Petten in the Netherlands) and was later extended for use in X-ray diffraction.

One practical application of elastic neutron scattering/diffraction is that the [[lattice constant]] of [[metal]]s and other crystalline materials can be very accurately measured. Together with an accurately aligned micropositioner a map of the lattice constant through the metal can be derived. This can easily be converted to the [[Stress (physics)|stress]] field experienced by the material.<ref name="iaea" /> This has been used to analyse stresses in [[aerospace]] and [[automotive]] components to give just two examples. The high penetration depth permits measuring residual stresses in bulk components as crankshafts, pistons, rails, gears. This technique has led to the development of dedicated stress diffractometers, such as the [[ENGIN-X]] instrument at the [[ISIS neutron source]].

Neutron diffraction can also be employed to give insight into the 3D structure any material that diffracts.<ref name="ojeda">{{citation|author= Ojeda-May, P.|display-authors= 4|author2= Terrones, M.|author3= Terrones, H.|author4= Hoffman, D.|author5= Proffen, T.|author6= Cheetham, A. |title=Determination of chiralities of single-walled carbon nanotubes by neutron powder diffraction technique|journal=Diamond and Related Materials|date=2007|volume=16|issue= 3|pages=473–476|bibcode = 2007DRM....16..473O |doi = 10.1016/j.diamond.2006.09.019 }}</ref><ref name="page">{{citation|author= Page, K.|author2= Proffen, T.|author3= Niederberger, M.|author4= Seshadri, R. |title=Probing Local Dipoles and Ligand Structure in BaTiO3 Nanoparticles|journal=Chemistry of Materials|date=2010|volume=22|issue= 15|pages=4386–4391|doi=10.1021/cm100440p}}</ref>

Another use is for the determination of the [[solvation shell|solvation number]] of ion pairs in electrolytes solutions.

The magnetic scattering effect has been used since the establishment of the neutron diffraction technique to quantify magnetic moments in materials, and study the magnetic dipole orientation and structure.  One of the earliest applications of neutron diffraction was in the study of magnetic dipole orientations in [[Antiferromagnetism|antiferromagnetic]] transition metal oxides such as manganese, iron, nickel, and cobalt oxides.  These experiments, first performed by Clifford Shull, were the first to show the existence of the antiferromagnetic arrangement of magnetic dipoles in a material structure.<ref>{{cite journal | last1=Shull | first1=C. G. | last2=Strauser | first2=W. A. | last3=Wollan | first3=E. O. | title=Neutron Diffraction by Paramagnetic and Antiferromagnetic Substances | journal=Physical Review | publisher=American Physical Society (APS) | volume=83 | issue=2 | date=1951-07-15 | issn=0031-899X | doi=10.1103/physrev.83.333 | pages=333–345| bibcode=1951PhRv...83..333S }}</ref> Now, neutron diffraction continues to be used to characterize newly developed magnetic materials.

===Hydrogen, null-scattering and contrast variation===
Neutron diffraction can be used to establish the structure of low atomic number materials like proteins and surfactants much more easily with lower flux than at a synchrotron radiation source. This is because some low atomic number materials have a higher cross section for neutron interaction than higher atomic weight materials.

One major advantage of neutron diffraction over X-ray diffraction is that the latter is rather insensitive to the presence of [[hydrogen]] (H) in a structure, whereas the nuclei <sup>1</sup>H and <sup>2</sup>H (i.e. [[Deuterium]], D) are strong scatterers for neutrons. The greater scattering power of protons and deuterons means that the position of hydrogen in a crystal and its thermal motions can be determined with greater precision by neutron diffraction.  The structures of [[metal hydride complex]]es, e.g., [[Magnesium iron hexahydride|Mg<sub>2</sub>FeH<sub>6</sub>]] have been assessed by neutron diffraction.<ref>Robert Bau, Mary H. Drabnis "Structures of transition metal hydrides determined by neutron diffraction" Inorganica Chimica Acta 1997, vol. 259, pp/ 27-50. {{doi|10.1016/S0020-1693(97)89125-6}}</ref>

The neutron scattering lengths ''b''<sub>H</sub> = −3.7406(11) fm <ref name="Sears">{{citation|author=Sears, V. F.|title=Neutron scattering lengths and cross sections|journal=Neutron News|date=1992|volume=3|issue=3|pages=26–37|doi=10.1080/10448639208218770}}</ref> and ''b''<sub>D</sub> = 6.671(4) fm,<ref name="Sears" /> for H and D respectively, have opposite sign, which allows the technique to distinguish them.  In fact there is a particular [[isotope]] ratio for which the contribution of the element would cancel, this is called null-scattering.

It is undesirable to work with the relatively high concentration of H in a sample. The scattering intensity by H-nuclei has a large inelastic component, which  creates a large continuous background that is more or less independent of scattering angle. The elastic pattern typically consists of sharp [[Bragg reflections]] if the sample is crystalline. They tend to drown in the inelastic background. This is even more serious when the technique is used for the study of liquid structure. Nevertheless, by preparing samples with different isotope ratios, it is possible to vary the scattering contrast enough to highlight one element in an otherwise complicated structure. The variation of other elements is possible but usually rather expensive. Hydrogen is inexpensive and particularly interesting, because it plays an exceptionally large role in biochemical structures and is difficult to study structurally in other ways.

== Applications ==

=== Study of hydrogen storage materials ===
Since neutron diffraction is particularly sensitive to lighter elements like [[hydrogen]], it can be used for its detection. It can play a role in determining the [[crystal structure]] and hydrogen binding sites within [[Hydride|metal hydrides]], a class of materials of interest for hydrogen storage applications. The order of hydrogen atoms in the [[Lattice (order)|lattice]] reflects the storage capacity and kinetics of the material.<ref>{{Cite journal |last1=Ravnsbæk |first1=Dorthe B. |last2=Filinchuk |first2=Yaroslav |last3=Cerný |first3=Radovan |last4=Jensen |first4=Torben R. |date=2010 |title=Powder diffraction methods for studies of borohydride-based energy storage materials |url=https://www.degruyter.com/document/doi/10.1524/zkri.2010.1357/html |journal=Zeitschrift für Kristallographie |language=en |volume=225 |issue=12 |pages=557–569 |doi=10.1524/zkri.2010.1357 |bibcode=2010ZK....225..557R |issn=0044-2968}}</ref>

=== Magnetic structure determination ===
Neutron diffraction is also a useful technique for determining magnetic structures in materials, as neutrons can interact with magnetic moments. It can be used to determine the [[Antiferromagnetism|antiferromagnetic]] structure of [[manganese oxide]] (MnO) using neutron diffraction. Neutron Diffraction Studies can be used to measure the [[magnetic moment]]. Orientation study demonstrates how neutron diffraction can detect the precise alignment of the magnetic moment in materials, something that is much more challenging with X-rays.<ref>{{Cite journal |last1=Lines |first1=M. E. |last2=Jones |first2=E. D. |date=1965 |title=Antiferromagnetism in the Face-Centered Cubic Lattice. II. Magnetic Properties of MnO |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.139.A1313 |journal=Physical Review |language=en |volume=139 |issue=4A |pages=A1313–A1327 |doi=10.1103/PhysRev.139.A1313 |bibcode=1965PhRv..139.1313L |issn=0031-899X|url-access=subscription }}</ref>

=== Phase transition in ferroelectrics ===
Neutron diffraction has been widely employed to understand phase transitions in materials including [[ferroelectrics]], which show the transition of crystal structure with [[temperature]] or [[pressure]]. It can be utilised to study the ferroelectric [[phase transition]] in [[lead titanate]] (PbTiO<sub>3</sub>). It can be used to analyse [[Atomic displacement parameter|atomic displacements]] and corresponding lattice distortions. <ref>{{Cite journal |last1=Jorio |first1=A. |last2=Currat |first2=R. |last3=Myles |first3=D. A. A. |last4=McIntyre |first4=G. J. |last5=Aleksandrova |first5=I. P. |last6=Kiat |first6=J. M. |last7=Saint-Grégoire |first7=P. |date=2000 |title=Ferroelastic phase transition in Cs 3 Bi 2 I 9 : A neutron diffraction study |url=https://journals.aps.org/prb/abstract/10.1103/PhysRevB.61.3857 |journal=Physical Review B |language=en |volume=61 |issue=6 |pages=3857–3862 |doi=10.1103/PhysRevB.61.3857 |issn=0163-1829|url-access=subscription }}</ref>

=== Residual stress analysis in engineering materials ===
Neutron diffraction can be used as a technique for the nondestructive assessment of residual stresses in engineering materials, including [[Metal|metals]] and [[Alloy|alloys]]. Also used for measuring residual stresses in engineering materials.<ref>{{Cite journal |last1=Jacob |first1=Anais |last2=Oliveira |first2=Jeferson |last3=Mehmanparast |first3=Ali |last4=Hosseinzadeh |first4=Foroogh |last5=Kelleher |first5=Joe |last6=Berto |first6=Filippo |date=2018 |title=Residual stress measurements in offshore wind monopile weldments using neutron diffraction technique and contour method |url=https://linkinghub.elsevier.com/retrieve/pii/S0167844218300454 |journal=Theoretical and Applied Fracture Mechanics |language=en |volume=96 |pages=418–427 |doi=10.1016/j.tafmec.2018.06.001|hdl=11250/2578469 |hdl-access=free }}</ref>

=== Lithium-ion batteries ===
Neutron diffraction is especially useful for the investigation of [[lithium-ion battery]] materials, because lithium atoms are almost [[opaque]] to X-ray radiation. It can further be used to investigate the structural evolution of lithium-ion battery cathode materials during charge and discharge cycles.<ref>{{Cite journal |last1=Ziesche |first1=Ralf F. |last2=Kardjilov |first2=Nikolay |last3=Kockelmann |first3=Winfried |last4=Brett |first4=Dan J.L. |last5=Shearing |first5=Paul R. |date=2022 |title=Neutron imaging of lithium batteries |url=https://linkinghub.elsevier.com/retrieve/pii/S2542435121005766 |journal=Joule |language=en |volume=6 |issue=1 |pages=35–52 |doi=10.1016/j.joule.2021.12.007|bibcode=2022Joule...6...35Z }}</ref>

=== High temperature superconductors ===
Neutron diffraction has played an important role in revealing the crystal and magnetic structures in high-temperature [[Superconductivity|superconductors]]. A neutron diffraction study of magnetic order in the high-temperature superconductor YBa<sub>2</sub>Cu<sub>3</sub>O<sub>6</sub>+x was done. The work of each of these scientific teams together with others across the globe has revealed the origins of the relationship between [[magnetic ordering]] and [[superconductivity]], delivering crucial insights into the mechanism of [[high-temperature superconductivity]].<ref>{{Cite journal |last1=Moodenbaugh |first1=A. R. |last2=Cox |first2=D. E. |last3=Vining |first3=C. B. |last4=Segre |first4=C. U. |date=1984 |title=Neutron-diffraction study of magnetically ordered Er 2 Fe 3 Si 5 |url=https://link.aps.org/doi/10.1103/PhysRevB.29.271 |journal=Physical Review B |language=en |volume=29 |issue=1 |pages=271–277 |doi=10.1103/PhysRevB.29.271 |issn=0163-1829|url-access=subscription }}</ref>

=== Mechanical behaviour of alloys ===
Advancements in neutron diffraction have facilitated in situ investigations into the mechanical deformation of alloys under load, permitting observations on the mechanisms of [[Deformation (engineering)|deformation]]. The deformation behavior of [[titanium alloys]] under mechanical loads can be investigated using in situ neutron diffraction. This technique allows real-time monitoring of lattice strains and phase transformations throughout deformation.<ref>{{Cite journal |last1=Sun |first1=C. |last2=Brown |first2=D.W. |last3=Clausen |first3=B. |last4=Foley |first4=D.C. |last5=Yu |first5=K.Y. |last6=Chen |first6=Y. |last7=Maloy |first7=S.A. |last8=Hartwig |first8=K.T. |last9=Wang |first9=H. |last10=Zhang |first10=X. |date=2014 |title=In situ neutron diffraction study on temperature dependent deformation mechanisms of ultrafine grained austenitic Fe–14Cr–16Ni alloy |url=https://linkinghub.elsevier.com/retrieve/pii/S0749641913001447 |journal=International Journal of Plasticity |language=en |volume=53 |pages=125–134 |doi=10.1016/j.ijplas.2013.07.007|url-access=subscription }}</ref>[[File:Neutron diffraction; Ion channels (5888008521).jpg|thumb|Neutron diffraction, used along with molecular simulations, revealed that an ion channel's voltage sensing domain (red, yellow and blue molecule at center) perturbs the two-layered cell membrane that surrounds it (yellow surfaces), causing the membrane to thin slightly.]]
=== Neutron diffraction for ion channels ===
Neutron diffraction can be used to study ion channels, highlighting how neutrons interact with biological structures to reveal atomic details. Neutron diffraction is particularly sensitive to light elements like hydrogen, making it ideal for mapping water molecules, ion positions, and hydrogen bonds within the channel. By analysing neutron scattering patterns, researchers can determine ion binding sites, hydration structures, and conformational changes essential for ion transport and selectivity.




== Current developments in neutron diffraction ==

=== Advancements in Neutron Diffraction Research ===
Neutron diffraction has made significant progress, particularly at Oak Ridge National Laboratory (ORNL), which operates a suite of 12 diffractometers—seven at the [[Spallation Neutron Source]] (SNS) and five at the [[High Flux Isotope Reactor]] (HFIR). These instruments are designed for different applications and are grouped into three categories: [[powder diffraction]], single crystal diffraction, and advanced diffraction techniques.

To further enhance neutron diffraction research, ORNL is undertaking several key projects:
* Expansion of the SNS First Target Station: New beamlines equipped with state-of-the-art instruments are being installed to broaden the scope of scientific investigations.
* Proton Power Upgrade: This initiative aims to double the proton power used for neutron production, which will enhance research efficiency, allow for the study of smaller and more complex samples, and support the eventual development of a next-generation neutron source at SNS.
* Development of the SNS Second Target Station: A new facility is being constructed to house 22 beamlines, making it a leading source for cold neutron research, crucial for studying soft matter, biological systems, and quantum materials.
* Enhancements at HFIR: Planned upgrades include optimizing the cold neutron guide hall to improve experimental capabilities, expanding [[isotope]] production (including [[plutonium-238]] for space exploration), and enhancing the performance of existing instruments.

These advancements are set to significantly improve neutron diffraction techniques, allowing for more precise and detailed analysis of material structures. By expanding research capabilities and increasing neutron production efficiency, these developments will support a wide range of scientific fields, from materials science to [[energy research]] and [[quantum physics]].<ref>{{Cite web |title=Future of Neutron Scattering at Oak Ridge National Laboratory: Three World Leading Neutron Scattering Facilities for Breakthrough Materials Science |url=https://neutrons.ornl.gov/future}}</ref>

=== Modern trends in neutron scattering information technology ===
Neutron diffraction technology is evolving rapidly, with a focus on improving beam intensity and instrument efficiency. Modern instruments are designed to produce smaller, more intense beams, enabling high-precision studies of smaller samples, which is particularly beneficial for new material research. Advanced detectors, such as [[boron]]-based alternatives to [[Helium|helium-3]], are being developed to address material shortages, while improved neutron spin manipulation enhances the study of magnetic and structural properties. Computational advancements, including [[Simulation|simulations]] and virtual instruments, are optimizing [[Neutron source|neutron sources]], streamlining experimental design, and integrating [[machine learning]] for data analysis. Multiplexing and event-based acquisition systems are enhancing data collection by capturing multiple datasets simultaneously. Additionally,next-generation spallation sources like the European Spallation Source (ESS) and Oak Ridge's Second Target Station (STS) are increasing neutron production efficiency. Lastly, the rise of remote-controlled experiments and automation is improving accessibility and precision in neutron diffraction research.<ref>{{Cite journal |last1=Ehlers |first1=Georg |last2=Crow |first2=Morris L. |last3=Diawara |first3=Yacouba |last4=Gallmeier |first4=Franz X. |last5=Geng |first5=Xiaosong |last6=Granroth |first6=Garrett E. |last7=Gregory |first7=Raymond D. |last8=Islam |first8=Fahima F. |last9=Knudson |first9=Robert O. |last10=Li |first10=Fankang |last11=Loyd |first11=Matthew S. |last12=Vacaliuc |first12=Bogdan |date=2022 |title=Modern Trends in Neutron Scattering Instrument Technologies |journal=Instruments |language=en |volume=6 |issue=3 |pages=22 |doi=10.3390/instruments6030022 |doi-access=free |issn=2410-390X}}</ref>

=== Current trends in structural biology ===
Modern advancements in neutron diffraction are enhancing data precision, broadening structural research applications, and refining experimental methodologies. A key focus is the improved visualization of hydrogen atoms in biological [[Macromolecule|macromolecules]], crucial for studying [[enzymatic activity]] and [[hydrogen bonding]]. The expansion of specialized [[Diffractometer|diffractometers]] has increased accessibility in structural biology, with techniques like [[Monochrome|monochromatic]], quasi-Laue, and time-of-flight methods being optimized for efficiency. Innovations in sample preparation, particularly protein deuteration, are minimizing [[background noise]] and reducing the need for large crystals. Additionally, [[Computational tools for artificial intelligence|computational tools]], including quantum chemical modeling, are aiding in the interpretation of complex molecular interactions. Improved neutron sources, such as spallation facilities, along with advanced detectors, are further boosting measurement accuracy and structural resolution. These developments are solidifying neutron diffraction as a critical technique for exploring the molecular architecture of biological systems.<ref>{{Cite journal |last1=Kono |first1=Fumiaki |last2=Kurihara |first2=Kazuo |last3=Tamada |first3=Taro |date=2022 |title=Current status of neutron crystallography in structural biology |url=https://www.jstage.jst.go.jp/article/biophysico/19/0/19_e190009/_article |journal=Biophysics and Physicobiology |language=en |volume=19 |pages=e190009 |doi=10.2142/biophysico.bppb-v19.0009 |issn=2189-4779 |pmc=9135615 |pmid=35666700}}</ref>

==See also==
* [[Crystallography]]
* [[Crystallographic database]]
* [[Electron diffraction]]
* [[Grazing incidence diffraction]]
* [[Inelastic neutron scattering]]
* [[X-ray diffraction computed tomography]]

== References ==
{{reflist}}

==Further reading==
* {{cite book
 | last = Lovesey
 | first = S. W.
 | date = 1984
 | title = Theory of Neutron Scattering from Condensed Matter; Volume 1: Neutron Scattering
 | publisher = [[Clarendon Press]]
 | location = Oxford
 | isbn = 0-19-852015-8
}}
* {{cite book
 | last = Lovesey
 | first = S. W.
 | date = 1984
 | title = Theory of Neutron Scattering from Condensed Matter; Volume 2: Condensed Matter
 | publisher = Clarendon Press
 | location = Oxford
 | isbn = 0-19-852017-4
}}
* {{cite book
 | last = Squires
 | first = G.L.
 | date = 1996
 | title = Introduction to the Theory of Thermal Neutron Scattering
 | edition = 2nd
 | publisher = Dover Publications Inc
 | location = Mineola, New York
 | isbn = 0-486-69447-X
}}

* {{cite book | editor = Young, R.A. | date = 1993 | title = The Rietveld Method | location = Oxford | publisher = Oxford University Press & International Union of Crystallography
 | isbn = 0-19-855577-6}}

== External links ==
* [http://www.ncnr.nist.gov/ National Institute of Standards and Technology Center for Neutron Research]
* [http://nmi3.eu/news-and-media/from-braggs-law-to-neutron-diffraction.html From Bragg's law to neutron diffraction]
* [http://nmi3.eu/ Integrated Infrastructure Initiative for Neutron Scattering and Muon Spectroscopy (NMI3)] - a European consortium of 18 partner organisations from 12 countries, including all major facilities in the fields of neutron scattering and muon spectroscopy
*[http://flnph.jinr.ru/en/facilities/ibr-2/instruments Frank Laboratory of Neutron Physics] of [[Joint Institute for Nuclear Research]] (JINR)
*[https://nucleus.iaea.org/sites/accelerators/Pages/Interactive-Map-of-NB-Instruments.aspx IAEA neutron beam instrument database]

{{Crystallography}}

[[Category:Diffraction]]
[[Category:Neutron scattering]]