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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Neutron diffraction</span></span>
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</style><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title" style="background-color: #cee0f2">Science with <a href="Neutron" title="Neutron">neutrons</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"></span></td></tr><tr><th class="sidebar-heading" style="background-color: #cee0f2">
Foundations</th></tr><tr><td class="sidebar-content" style="text-align: left">
<ul><li><a href="Neutron_temperature" title="Neutron temperature">Neutron temperature</a></li>
<li><a href="Neutron_flux" title="Neutron flux">Flux</a>, <a href="Neutron_radiation" title="Neutron radiation">Radiation</a>, <a href="Neutron_transport" title="Neutron transport">Transport</a></li>
<li><a href="Neutron_cross_section" title="Neutron cross section">Cross section</a>, <a href="Neutron_absorption" class="mw-redirect" title="Neutron absorption">Absorption</a>, <a href="Neutron_activation" title="Neutron activation">Activation</a></li></ul></td>
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<a href="Neutron_scattering" title="Neutron scattering">Neutron scattering</a></th></tr><tr><td class="sidebar-content" style="text-align: left">
<ul><li>
<ul><li><a href="Small-angle_neutron_scattering" title="Small-angle neutron scattering">Small-angle neutron scattering</a></li>
<li><a href="Grazing-incidence_small-angle_neutron_scattering" class="mw-redirect" title="Grazing-incidence small-angle neutron scattering">GISANS</a></li>
<li><a href="Neutron_reflectometry" title="Neutron reflectometry">Reflectometry</a></li></ul></li>
<li><a href="Inelastic_neutron_scattering" class="mw-redirect" title="Inelastic neutron scattering">Inelastic neutron scattering</a>
<ul><li><a href="Neutron_triple-axis_scattering" class="mw-redirect" title="Neutron triple-axis scattering">Triple-axis spectrometer</a></li>
<li><a href="Neutron_time-of-flight_scattering" title="Neutron time-of-flight scattering">Time-of-flight spectrometer</a></li>
<li><a href="Neutron_backscattering" title="Neutron backscattering">Backscattering spectrometer</a></li>
<li><a href="Neutron_spin_echo" title="Neutron spin echo">Spin-echo spectrometer</a></li></ul></li></ul></td>
</tr><tr><th class="sidebar-heading" style="background-color: #cee0f2">
Other applications</th></tr><tr><td class="sidebar-content" style="text-align: left">
<ul><li><a href="Neutron_tomography" title="Neutron tomography">Neutron tomography</a></li>
<li><a href="Neutron_activation_analysis" title="Neutron activation analysis">Activation analysis</a>, <a href="Prompt_gamma_neutron_activation_analysis" title="Prompt gamma neutron activation analysis">Prompt gamma activation analysis</a></li>
<li>Fundamental research with neutrons: <a href="Ultracold_neutrons" title="Ultracold neutrons">Ultracold neutrons</a>, <a href="Neutron_interferometer" title="Neutron interferometer">Interferometry</a></li>
<li><a href="Fast_neutron_therapy" title="Fast neutron therapy">Fast neutron therapy</a></li>
<li><a href="Neutron_capture_therapy_of_cancer" title="Neutron capture therapy of cancer">Neutron capture therapy</a></li></ul></td>
</tr><tr><th class="sidebar-heading" style="background-color: #cee0f2">
Infrastructure</th></tr><tr><td class="sidebar-content" style="text-align: left">
<ul><li><a href="Neutron_source" title="Neutron source">Neutron sources</a>: <a href="Research_reactor" title="Research reactor">Research reactor</a>, <a href="Spallation" title="Spallation">Spallation</a>, <a href="Neutron_moderator" title="Neutron moderator">Neutron moderator</a></li>
<li>Neutron optics: <a href="Neutron_reflector" title="Neutron reflector">Reflector</a>, <a href="Supermirror" class="mw-redirect" title="Supermirror">Supermirror</a></li>
<li><a href="Neutron_detection" title="Neutron detection">Detection</a></li></ul></td>
</tr><tr><th class="sidebar-heading" style="background-color: #cee0f2">
<a href="Neutron_facilities" class="mw-redirect" title="Neutron facilities">Neutron facilities</a></th></tr><tr><td class="sidebar-content" style="text-align: left">
<ul><li>America: <a href="High_Flux_Isotope_Reactor" title="High Flux Isotope Reactor">HFIR</a>, <a href="Los_Alamos_Neutron_Science_Center" title="Los Alamos Neutron Science Center">LANSCE</a>, <a rel="nofollow" class="external text" href="http://www.nist.gov/ncnr/">NIST CNR</a> -<a href="Spallation_Neutron_Source" title="Spallation Neutron Source">SNS</a></li>
<li>Oceania: <a href="Open-pool_Australian_lightwater_reactor" title="Open-pool Australian lightwater reactor">OPAL</a></li>
<li>Asia: <a href="J-PARC" title="J-PARC">J-PARC</a>, <a href="High-Flux_Advanced_Neutron_Application_Reactor" title="High-Flux Advanced Neutron Application Reactor">HANARO</a></li>
<li>Europe: <a href="Helmholtz-Zentrum_Berlin" title="Helmholtz-Zentrum Berlin">BER II</a>, <a href="FRM_II" title="FRM II">FRM II</a>, <a href="Institut_Laue%E2%80%93Langevin" title="Institut Laue–Langevin">ILL</a>, <a href="ISIS_Neutron_and_Muon_Source" title="ISIS Neutron and Muon Source">ISIS Neutron and Muon Source</a>, <a href="Joint_Institute_for_Nuclear_Research" title="Joint Institute for Nuclear Research">JINR</a>, <a href="Paul_Scherrer_Institute#Spallation_Neutron_Source_.28SINQ.29" title="Paul Scherrer Institute">SINQ</a></li>
<li>Historic: <a href="Intense_Pulsed_Neutron_Source" title="Intense Pulsed Neutron Source">IPNS</a>, <a rel="nofollow" class="external text" href="http://www.bnl.gov/bnlweb/history/HFBR_main.asp">HFBR</a></li>
<li>Under construction: <a href="European_Spallation_Source" title="European Spallation Source">ESS</a></li></ul></td>
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<p><b>Neutron diffraction</b> or <b>elastic neutron scattering</b> is the application of <a href="Neutron_scattering" title="Neutron scattering">neutron scattering</a> to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of <a href="Neutron_temperature" title="Neutron temperature">thermal or cold</a> <a href="Neutron_radiation" title="Neutron radiation">neutrons</a> to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to <a href="X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a> but due to their different scattering properties, <a href="Neutron" title="Neutron">neutrons</a> and <a href="X-ray" title="X-ray">X-rays</a> provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from <a href="Synchrotron_radiation" title="Synchrotron radiation">synchrotron radiation</a> are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.<sup id="cite_ref-iaea_1-0" class="reference"><a href="#cite_note-iaea-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p>
<meta property="mw:PageProp/toc">
<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>
<div class="mw-heading mw-heading3"><h3 id="Discovery_of_the_neutron">Discovery of the neutron</h3></div>
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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Neutron#Discovery" title="Neutron">Neutron § Discovery</a></div>
<p>In 1921, American chemist and physicist <a href="William_Draper_Harkins" title="William Draper Harkins">William D. Harkins</a> introduced the term "<a href="Neutron" title="Neutron">neutron</a>" while studying <a href="Atomic_structure" class="mw-redirect" title="Atomic structure">atomic structure</a> and <a href="Nuclear_reaction" title="Nuclear reaction">nuclear reactions</a>. He proposed the existence of a neutral particle within the <a href="Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a>, though there was no experimental evidence for it at the time.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In 1932, British physicist <a href="James_Chadwick" title="James Chadwick">James Chadwick</a> provided experimental proof of the neutron's existence. His discovery confirmed the presence of this neutral <a href="Subatomic_particle" title="Subatomic particle">subatomic particle</a>, earning him the <a href="Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> in 1935. Chadwick's research was influenced by earlier work from <a href="Ir%C3%A8ne_Joliot-Curie" title="Irène Joliot-Curie">Irène</a> and <a href="Fr%C3%A9d%C3%A9ric_Joliot-Curie" title="Frédéric Joliot-Curie">Frédéric Joliot-Curie</a>, who had detected unexplained neutral <a href="Radiation" title="Radiation">radiation</a> but had not recognized it as a distinct particle.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Neutrons are subatomic particles that exist in the nucleus of the atom, it has higher mass than protons but no electrical charge.
</p><p>In the 1930s <a href="Enrico_Fermi" title="Enrico Fermi">Enrico Fermi</a> and colleagues gave theoretical contributions establishing the foundation of <a href="Neutron_scattering" title="Neutron scattering">neutron scattering</a>. Fermi developed a framework to understand how neutrons interact with atomic nuclei.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Early_diffraction_work">Early diffraction work</h3></div>
<p>Diffraction was first observed in 1936<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> by two groups, von Halban and Preiswerk<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and by Mitchell and Powers.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In 1944, <a href="Ernest_O._Wollan" title="Ernest O. Wollan">Ernest O. Wollan</a>, with a background in X-ray scattering from his PhD work<sup id="cite_ref-PhysicsTodayObit_8-0" class="reference"><a href="#cite_note-PhysicsTodayObit-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> under <a href="Arthur_Compton" title="Arthur Compton">Arthur Compton</a>, recognized the potential for applying thermal neutrons from the newly operational <a href="X-10_Graphite_Reactor" title="X-10 Graphite Reactor">X-10 nuclear reactor</a> to <a href="Crystallography" title="Crystallography">crystallography</a>. Joined by <a href="Clifford_G._Shull" class="mw-redirect" title="Clifford G. Shull">Clifford G. Shull</a> they developed<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> neutron diffraction throughout the 1940s.
</p><p>Neutron diffraction experiments were carried out in 1945 by <a href="Ernest_O._Wollan" title="Ernest O. Wollan">Ernest O. Wollan</a> using the Graphite Reactor at <a href="Oak_Ridge_National_Laboratory" title="Oak Ridge National Laboratory">Oak Ridge</a>. He was joined shortly thereafter (June 1946)<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> by <a href="Clifford_Glenwood_Shull" class="mw-redirect" title="Clifford Glenwood Shull">Clifford Shull</a>, 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 <a href="Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a>. (Wollan died in 1984). (The other half of the 1994 Nobel Prize for Physics went to <a href="Bertram_Brockhouse" title="Bertram Brockhouse">Bert Brockhouse</a> for development of the inelastic scattering technique at the <a href="Chalk_River_Laboratories" title="Chalk River Laboratories">Chalk River facility</a> of <a href="Atomic_Energy_of_Canada" class="mw-redirect" title="Atomic Energy of Canada">AECL</a>. This also involved the invention of the triple axis spectrometer).
</p>
<div class="mw-heading mw-heading3"><h3 id="1950–60s">1950–60s</h3></div>
<p>The development of neutron sources such as <a href="Nuclear_reactor" title="Nuclear reactor">reactors</a> and <a href="Spallation_source" class="mw-redirect" title="Spallation source">spallation sources</a> emerged. This allowed high-intensity <a href="Neutron_beam_activation_analysis" class="mw-redirect" title="Neutron beam activation analysis">neutron beams</a>, enabling advanced scattering experiments. Notably, the <a href="High_Flux_Isotope_Reactor" title="High Flux Isotope Reactor">high flux isotope reactor</a> (HFIR) at Oak Ridge and Institut Laue Langevin (ILL) in Grenoble, France, emerged as key institutions for neutron scattering studies.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="1970–1980s">1970–1980s</h3></div>
<p>This period saw major advancements in neutron scattering techniques by developing techniques to explore different aspects of material science, structure and behaviour.<sup id="cite_ref-Lovesey-2003_12-0" class="reference"><a href="#cite_note-Lovesey-2003-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>
</p><p><a href="Small-angle_neutron_scattering" title="Small-angle neutron scattering">Small angle neutron scattering (SANS)</a>:<i> 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 <a href="X-ray" title="X-ray">X-rays</a>.<sup id="cite_ref-Lovesey-2003_12-1" class="reference"><a href="#cite_note-Lovesey-2003-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </i>
</p><p><a href="Inelastic_neutron_scattering" class="mw-redirect" title="Inelastic neutron scattering">Inelastic neutron scattering (INS)</a><i>: Provides insights into the dynamic process at the microscopic level. Majorly used to examine atomic and molecular motions.<sup id="cite_ref-Lovesey-2003_12-2" class="reference"><a href="#cite_note-Lovesey-2003-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></i>
</p>
<div class="mw-heading mw-heading3"><h3 id="1990-present">1990-present</h3></div>
<p>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 <a href="ISIS_Neutron_and_Muon_Source" title="ISIS Neutron and Muon Source">ISIS Neutron</a> and Muon Source in the U.K., which can generate pulsed neutron beams for <a href="Time_of_flight" title="Time of flight">time-of-flight</a> experiments. <a href="Neutron_imaging" title="Neutron imaging">Neutron imaging</a> and <a href="Reflectometry" title="Reflectometry">reflectometry</a> were also developed, which are powerful tools to analyse surfaces, interfaces and thin film structures, thus providing valuable insights into the material properties.
</p>
<div class="mw-heading mw-heading2"><h2 id="Comparison_of_neutron_scattering,_XRD_and_electron_scattering">Comparison of neutron scattering, XRD and electron scattering</h2></div>
<table class="wikitable">
<caption>
</caption>
<tbody><tr>
<th><b>Feature</b>
</th>
<th><a href="Neutron_scattering" title="Neutron scattering">Neutron diffraction</a>
</th>
<td><b><a href="X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a></b>
</td>
<th><b><a href="Electron_scattering" title="Electron scattering">Electron scattering</a></b>
</th></tr>
<tr>
<td><b>Principle</b>
</td>
<td>Interacts with atomic nuclei and magnetic moments enabling nuclear and magnetic scattering <sup id="cite_ref-Bacon-1975_13-0" class="reference"><a href="#cite_note-Bacon-1975-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</td>
<td>Scatter off <a href="Electron_cloud" class="mw-redirect" title="Electron cloud">electron cloud</a> thus allowing probing of electron density.<sup id="cite_ref-Cullity-2001_14-0" class="reference"><a href="#cite_note-Cullity-2001-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Authier-2004_15-0" class="reference"><a href="#cite_note-Authier-2004-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>
</td>
<td>Scatter off electrostatic potential thus allowing probing of electron density.<sup id="cite_ref-Cowley-1995_16-0" class="reference"><a href="#cite_note-Cowley-1995-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>
</td></tr>
<tr>
<td><b>Penetration depth</b>
</td>
<td>High (suitable to study bulk materials since neutrons penetrate deeply in)<sup id="cite_ref-Bacon-1975_13-1" class="reference"><a href="#cite_note-Bacon-1975-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</td>
<td>Moderate (good penetration but also absorption by heavy elements)<sup id="cite_ref-Cullity-2001_14-1" class="reference"><a href="#cite_note-Cullity-2001-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Authier-2004_15-1" class="reference"><a href="#cite_note-Authier-2004-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>
</td>
<td>Low (suitable for surface studies since electrons are strongly absorbed) or quite deep depending upon the energy.<sup id="cite_ref-Cowley-1995_16-1" class="reference"><a href="#cite_note-Cowley-1995-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>
</td></tr>
<tr>
<td><b>Sensitivity to light elements</b>
</td>
<td>High (very sensitive to lighter elements like hydrogen or lithium) <sup id="cite_ref-Bacon-1975_13-2" class="reference"><a href="#cite_note-Bacon-1975-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</td>
<td>Low (poor sensitivity to lighter elements)<sup id="cite_ref-Cullity-2001_14-2" class="reference"><a href="#cite_note-Cullity-2001-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Authier-2004_15-2" class="reference"><a href="#cite_note-Authier-2004-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>
</td>
<td>High (can detect lighter elements ).<sup id="cite_ref-Cowley-1995_16-2" class="reference"><a href="#cite_note-Cowley-1995-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>
</td></tr>
<tr>
<td><b>Magnetic studies</b>
</td>
<td>Excellent (can probe <a href="Magnetic_structure" title="Magnetic structure">magnetic structure</a> and spin dynamics) <sup id="cite_ref-Bacon-1975_13-3" class="reference"><a href="#cite_note-Bacon-1975-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</td>
<td>Limited (require specialized techniques like resonance magnetic scattering)<sup id="cite_ref-Cullity-2001_14-3" class="reference"><a href="#cite_note-Cullity-2001-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Authier-2004_15-3" class="reference"><a href="#cite_note-Authier-2004-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>
</td>
<td>Yields local information<sup id="cite_ref-Cowley-1995_16-3" class="reference"><a href="#cite_note-Cowley-1995-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>
</td></tr>
<tr>
<td><b>Resolution</b>
</td>
<td>High (depending on techniques and instrument) <sup id="cite_ref-Bacon-1975_13-4" class="reference"><a href="#cite_note-Bacon-1975-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</td>
<td>High (can yield very precise positions for crystal structure)<sup id="cite_ref-Cullity-2001_14-4" class="reference"><a href="#cite_note-Cullity-2001-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Authier-2004_15-4" class="reference"><a href="#cite_note-Authier-2004-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>
</td>
<td>Very high (can achieve high resolution)<sup id="cite_ref-Squires_17-0" class="reference"><a href="#cite_note-Squires-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>
</td></tr>
<tr>
<td><b>Sample environment</b>
</td>
<td>Efficient (used to study samples in different environment) <sup id="cite_ref-Bacon-1975_13-5" class="reference"><a href="#cite_note-Bacon-1975-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</td>
<td>Efficient
</td>
<td>Limited (requires vacuum and thin samples)<sup id="cite_ref-Squires_17-1" class="reference"><a href="#cite_note-Squires-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>
</td></tr>
<tr>
<td><b>Applications</b>
</td>
<td>structure of materials and magnetic property of the material. <sup id="cite_ref-Bacon-1975_13-6" class="reference"><a href="#cite_note-Bacon-1975-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</td>
<td><a href="X-ray_crystallography" title="X-ray crystallography">X-ray crystallography</a><sup id="cite_ref-Cullity-2001_14-5" class="reference"><a href="#cite_note-Cullity-2001-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Authier-2004_15-5" class="reference"><a href="#cite_note-Authier-2004-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>
</td>
<td>Used for bulk materials, surfaces, defects, see <a href="Electron_diffraction" title="Electron diffraction">electron diffraction</a>
</td></tr></tbody></table>
<div class="mw-heading mw-heading2"><h2 id="Principle">Principle</h2></div>
<div class="mw-heading mw-heading3"><h3 id="Processes">Processes</h3></div>
<p>Neutrons are produced through three major processes, fission, spallation, and Low energy nuclear reactions.
</p>
<div class="mw-heading mw-heading4"><h4 id="Fission">Fission</h4></div>
<p>In research reactors, fission takes place when a fissile nucleus, such as <a href="Uranium-235" title="Uranium-235">uranium-235</a> (<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 <a href="Nuclear_fission" title="Nuclear fission">fission</a> event produces about 2.5 neutrons. While one neutron is required to maintain the <a href="Chain_reaction" title="Chain reaction">chain reaction</a>, the surplus neutrons can be utilized for various experimental applications.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading4"><h4 id="Spallation">Spallation</h4></div>
<p>In spallation sources, high-energy protons (on the order of 1 <a href="Electronvolt" title="Electronvolt">GeV</a>) bombard a heavy metal target (e.g., <a href="Uranium" title="Uranium">uranium</a> (U), <a href="Tungsten" title="Tungsten">tungsten</a> (W), <a href="Tantalum" title="Tantalum">tantalum</a> (Ta), <a href="Lead" title="Lead">lead</a> (Pb), or <a href="Mercury_(element)" title="Mercury (element)">mercury</a> (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.<sup id="cite_ref-Carpenter-2015_19-0" class="reference"><a href="#cite_note-Carpenter-2015-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading4"><h4 id="Low_energy_nuclear_reactions">Low energy nuclear reactions</h4></div>
<p>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 <a href="Lithium" title="Lithium">lithium</a> (Li) and <a href="Beryllium" title="Beryllium">beryllium</a> (Be) can be used toachieve their maximum possible reaction rate under 30 MeV, while heavier elements such as tungsten (W) and <a href="Carbon" title="Carbon">carbon</a> (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.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="De-Broglie_relation">De-Broglie relation</h3></div>
<p>Neutron scattering relies on the wave-particle dual nature of neutrons. The <a href="De_Broglie_relation" class="mw-redirect" title="De Broglie relation">De-Broglie relation</a> links the <a href="Wavelength" title="Wavelength">wavelength</a> (<i>λ</i>) of a neutron to its energy (<i>E</i>)<sup id="cite_ref-Carpenter-2015_19-1" class="reference"><a href="#cite_note-Carpenter-2015-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>
<span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda =h/mv}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>λ<!-- λ --></mi>
<mo>=</mo>
<mi>h</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>m</mi>
<mi>v</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lambda =h/mv}</annotation>
</semantics>
</math></span></span>
where <i>h</i> is the Planck constant, <i>p</i> is the <a href="Momentum" title="Momentum">momentum</a> of the neutron, <i>m</i> is the mass of the neutron, <i>v</i> is the <a href="Velocity" title="Velocity">velocity</a> of the neutron.
</p>
<div class="mw-heading mw-heading2"><h2 id="Scattering">Scattering</h2></div>
<p>Neutron scattering is used to detect the distance between atoms and study the dynamics of materials. It involves two major principles: <a href="Elastic_scattering" title="Elastic scattering">elastic scattering</a> and <a href="Inelastic_scattering" title="Inelastic scattering">inelastic scattering</a>.
</p><p>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.<sup id="cite_ref-Bacon-1975_13-7" class="reference"><a href="#cite_note-Bacon-1975-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</p><p>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.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Neutron_matter_interaction">Neutron matter interaction</h2></div>
<p>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 <a href="Fermi_pseudopotential" class="mw-redirect" title="Fermi pseudopotential">Fermi pseudopotential</a>, that is, neutrons are well above their <a href="Meson" title="Meson">meson</a> mass threshold, and thus can be treated effectively as point-like <a href="Scatterer" class="mw-redirect" title="Scatterer">scatterers</a>. While most elements have a low tendency to absorb neutrons, certain ones such as <a href="Cadmium" title="Cadmium">cadmium</a> (Cd), <a href="Gadolinium" title="Gadolinium">gadolinium</a> (Gd), <a href="Helium" title="Helium">helium</a> (<sup>3</sup>He), <a href="Lithium" title="Lithium">lithium</a> (<sup>6</sup>Li), and <a href="Boron" title="Boron">boron</a> (<sup>10</sup>B) exhibit strong neutron absorption due to nuclear resonance effects. The likelihood of absorption increases with neutron wavelength (<i>σ</i><sub>a</sub> ∝ <i>λ</i>), meaning slower neutrons are absorbed more readily than faster ones.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Instrumental_and_sample_requirements">Instrumental and sample requirements</h2></div>
<p>The technique requires a source of neutrons. Neutrons are usually produced in a <a href="Nuclear_reactor" title="Nuclear reactor">nuclear reactor</a> or <a href="Spallation_source" class="mw-redirect" title="Spallation source">spallation source</a>. At a <a href="Research_reactor" title="Research reactor">research reactor</a>, other components are needed, including a <a href="Crystal_monochromator" title="Crystal monochromator">crystal monochromator</a> (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.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> 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.
</p><p>The technique is most commonly performed as <a href="Powder_diffraction" title="Powder diffraction">powder diffraction</a>, 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 <a href="X-ray_crystallography" title="X-ray crystallography">X-ray crystallography</a>. It is common to use crystals that are about 1 mm<sup>3</sup>.<sup id="cite_ref-Picc_26-0" class="reference"><a href="#cite_note-Picc-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup>
</p><p>The technique also requires a device that can <a href="Neutron_detection" title="Neutron detection">detect the neutrons</a> after they have been scattered.
</p><p>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,<sup id="cite_ref-Picc_26-1" class="reference"><a href="#cite_note-Picc-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> as well as a penetration depth of several cm<sup id="cite_ref-iaea_1-1" class="reference"><a href="#cite_note-iaea-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Nuclear_scattering">Nuclear scattering</h2></div>
<p>Like all <a href="Quantum" title="Quantum">quantum</a> <a href="Elementary_particle" title="Elementary particle">particles</a>, neutrons can exhibit wave phenomena typically associated with light or sound. <a href="Diffraction" title="Diffraction">Diffraction</a> is one of these phenomena; it occurs when waves encounter obstacles whose size is comparable with the <a href="Wavelength" title="Wavelength">wavelength</a>. 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 <a href="Angstrom" title="Angstrom">angstrom</a> (<span class="nowrap">0.1 <a href="Nanometre" title="Nanometre">nm</a></span>), 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 <a href="Bragg_law" class="mw-redirect" title="Bragg law">Bragg law</a> that describes X-ray diffraction.
</p><p>Neutrons and X-rays interact with matter differently. X-rays interact primarily with the <a href="Electron" title="Electron">electron</a> cloud surrounding each atom. The contribution to the diffracted x-ray intensity is therefore larger for atoms with larger <a href="Z_(Atomic_number)" class="mw-redirect" title="Z (Atomic number)">atomic number (Z)</a>. On the other hand, neutrons interact directly with the <i>nucleus</i> of the atom, and the contribution to the diffracted intensity depends on each <a href="Isotope" title="Isotope">isotope</a>; 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-<i>Z</i> atoms. The scattering length varies from isotope to isotope rather than linearly with the atomic number. An element like <a href="Vanadium" title="Vanadium">vanadium</a> 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.
</p><p>The nuclei of atoms, from which neutrons scatter, are tiny. Furthermore, there is no need for an <a href="Atomic_form_factor" title="Atomic form factor">atomic form factor</a> 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. <a href="Diffractogram" class="mw-redirect" title="Diffractogram">Diffractograms</a> 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 <i>resolution</i>) information means that the atomic positions in the structure can be determined with high precision. On the other hand, <a href="Fourier_map" class="mw-redirect" title="Fourier map">Fourier maps</a> (and to a lesser extent difference Fourier maps) derived from neutron data suffer from series termination errors, sometimes so much that the results are meaningless.
</p>
<div class="mw-heading mw-heading2"><h2 id="Magnetic_scattering">Magnetic scattering</h2></div>
<p>Although neutrons are uncharged, they carry a <a href="Magnetic_moment" title="Magnetic moment">magnetic moment</a>, and therefore interact with magnetic moments, including those arising from the electron cloud around an atom. Neutron diffraction can therefore reveal the microscopic <a href="Magnetic_structure" title="Magnetic structure">magnetic structure</a> of a material.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup>
</p><p>Magnetic scattering does require an <a href="Atomic_form_factor#Magnetic_scattering" title="Atomic form factor">atomic form factor</a> 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.
</p>
<div class="mw-heading mw-heading2"><h2 id="Uses">Uses</h2></div>
<p>Neutron diffraction can be used to determine the <a href="Static_structure_factor" class="mw-redirect" title="Static structure factor">static structure factor</a> of <a href="Gas" title="Gas">gases</a>, <a href="Liquid" title="Liquid">liquids</a> or <a href="Amorphous_solid" title="Amorphous solid">amorphous solids</a>. Most experiments, however, aim at the structure of crystalline solids, making neutron diffraction an important tool of <a href="Crystallography" title="Crystallography">crystallography</a>.
</p><p>Neutron diffraction is closely related to X-ray <a href="Powder_diffraction" title="Powder diffraction">powder diffraction</a>.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> 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 <a href="Rietveld_refinement" title="Rietveld refinement">Rietveld refinement</a>. 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.
</p><p>One practical application of elastic neutron scattering/diffraction is that the <a href="Lattice_constant" title="Lattice constant">lattice constant</a> of <a href="Metal" title="Metal">metals</a> 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 <a href="Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a> field experienced by the material.<sup id="cite_ref-iaea_1-2" class="reference"><a href="#cite_note-iaea-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> This has been used to analyse stresses in <a href="Aerospace" title="Aerospace">aerospace</a> and <a href="Automotive" class="mw-redirect" title="Automotive">automotive</a> 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 <a href="ENGIN-X" title="ENGIN-X">ENGIN-X</a> instrument at the <a href="ISIS_neutron_source" class="mw-redirect" title="ISIS neutron source">ISIS neutron source</a>.
</p><p>Neutron diffraction can also be employed to give insight into the 3D structure any material that diffracts.<sup id="cite_ref-ojeda_29-0" class="reference"><a href="#cite_note-ojeda-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-page_30-0" class="reference"><a href="#cite_note-page-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup>
</p><p>Another use is for the determination of the <a href="Solvation_shell" title="Solvation shell">solvation number</a> of ion pairs in electrolytes solutions.
</p><p>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 <a href="Antiferromagnetism" title="Antiferromagnetism">antiferromagnetic</a> 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.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Now, neutron diffraction continues to be used to characterize newly developed magnetic materials.
</p>
<div class="mw-heading mw-heading3"><h3 id="Hydrogen,_null-scattering_and_contrast_variation">Hydrogen, null-scattering and contrast variation</h3></div>
<p>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.
</p><p>One major advantage of neutron diffraction over X-ray diffraction is that the latter is rather insensitive to the presence of <a href="Hydrogen" title="Hydrogen">hydrogen</a> (H) in a structure, whereas the nuclei <sup>1</sup>H and <sup>2</sup>H (i.e. <a href="Deuterium" title="Deuterium">Deuterium</a>, 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 <a href="Metal_hydride_complex" class="mw-redirect" title="Metal hydride complex">metal hydride complexes</a>, e.g., <a href="Magnesium_iron_hexahydride" title="Magnesium iron hexahydride">Mg<sub>2</sub>FeH<sub>6</sub></a> have been assessed by neutron diffraction.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup>
</p><p>The neutron scattering lengths <i>b</i><sub>H</sub> = −3.7406(11) fm <sup id="cite_ref-Sears_33-0" class="reference"><a href="#cite_note-Sears-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> and <i>b</i><sub>D</sub> = 6.671(4) fm,<sup id="cite_ref-Sears_33-1" class="reference"><a href="#cite_note-Sears-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> for H and D respectively, have opposite sign, which allows the technique to distinguish them. In fact there is a particular <a href="Isotope" title="Isotope">isotope</a> ratio for which the contribution of the element would cancel, this is called null-scattering.
</p><p>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 <a href="Bragg_reflections" class="mw-redirect" title="Bragg reflections">Bragg reflections</a> 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.
</p>
<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>
<div class="mw-heading mw-heading3"><h3 id="Study_of_hydrogen_storage_materials">Study of hydrogen storage materials</h3></div>
<p>Since neutron diffraction is particularly sensitive to lighter elements like <a href="Hydrogen" title="Hydrogen">hydrogen</a>, it can be used for its detection. It can play a role in determining the <a href="Crystal_structure" title="Crystal structure">crystal structure</a> and hydrogen binding sites within <a href="Hydride" title="Hydride">metal hydrides</a>, a class of materials of interest for hydrogen storage applications. The order of hydrogen atoms in the <a href="Lattice_(order)" title="Lattice (order)">lattice</a> reflects the storage capacity and kinetics of the material.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Magnetic_structure_determination">Magnetic structure determination</h3></div>
<p>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 <a href="Antiferromagnetism" title="Antiferromagnetism">antiferromagnetic</a> structure of <a href="Manganese_oxide" title="Manganese oxide">manganese oxide</a> (MnO) using neutron diffraction. Neutron Diffraction Studies can be used to measure the <a href="Magnetic_moment" title="Magnetic moment">magnetic moment</a>. 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.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Phase_transition_in_ferroelectrics">Phase transition in ferroelectrics</h3></div>
<p>Neutron diffraction has been widely employed to understand phase transitions in materials including <a href="Ferroelectrics" class="mw-redirect" title="Ferroelectrics">ferroelectrics</a>, which show the transition of crystal structure with <a href="Temperature" title="Temperature">temperature</a> or <a href="Pressure" title="Pressure">pressure</a>. It can be utilised to study the ferroelectric <a href="Phase_transition" title="Phase transition">phase transition</a> in <a href="Lead_titanate" title="Lead titanate">lead titanate</a> (PbTiO<sub>3</sub>). It can be used to analyse <a href="Atomic_displacement_parameter" class="mw-redirect" title="Atomic displacement parameter">atomic displacements</a> and corresponding lattice distortions. <sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Residual_stress_analysis_in_engineering_materials">Residual stress analysis in engineering materials</h3></div>
<p>Neutron diffraction can be used as a technique for the nondestructive assessment of residual stresses in engineering materials, including <a href="Metal" title="Metal">metals</a> and <a href="Alloy" title="Alloy">alloys</a>. Also used for measuring residual stresses in engineering materials.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Lithium-ion_batteries">Lithium-ion batteries</h3></div>
<p>Neutron diffraction is especially useful for the investigation of <a href="Lithium-ion_battery" title="Lithium-ion battery">lithium-ion battery</a> materials, because lithium atoms are almost <a href="Opaque" class="mw-redirect" title="Opaque">opaque</a> 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.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="High_temperature_superconductors">High temperature superconductors</h3></div>
<p>Neutron diffraction has played an important role in revealing the crystal and magnetic structures in high-temperature <a href="Superconductivity" title="Superconductivity">superconductors</a>. 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 <a href="Magnetic_ordering" class="mw-redirect" title="Magnetic ordering">magnetic ordering</a> and <a href="Superconductivity" title="Superconductivity">superconductivity</a>, delivering crucial insights into the mechanism of <a href="High-temperature_superconductivity" title="High-temperature superconductivity">high-temperature superconductivity</a>.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Mechanical_behaviour_of_alloys">Mechanical behaviour of alloys</h3></div><p>
Advancements in neutron diffraction have facilitated in situ investigations into the mechanical deformation of alloys under load, permitting observations on the mechanisms of <a href="Deformation_(engineering)" title="Deformation (engineering)">deformation</a>. The deformation behavior of <a href="Titanium_alloys" title="Titanium alloys">titanium alloys</a> 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.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></p>
<div class="mw-heading mw-heading3"><h3 id="Neutron_diffraction_for_ion_channels">Neutron diffraction for ion channels</h3></div>
<p>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.
</p>
<div class="mw-heading mw-heading2"><h2 id="Current_developments_in_neutron_diffraction">Current developments in neutron diffraction</h2></div>
<div class="mw-heading mw-heading3"><h3 id="Advancements_in_Neutron_Diffraction_Research">Advancements in Neutron Diffraction Research</h3></div>
<p>Neutron diffraction has made significant progress, particularly at Oak Ridge National Laboratory (ORNL), which operates a suite of 12 diffractometers—seven at the <a href="Spallation_Neutron_Source" title="Spallation Neutron Source">Spallation Neutron Source</a> (SNS) and five at the <a href="High_Flux_Isotope_Reactor" title="High Flux Isotope Reactor">High Flux Isotope Reactor</a> (HFIR). These instruments are designed for different applications and are grouped into three categories: <a href="Powder_diffraction" title="Powder diffraction">powder diffraction</a>, single crystal diffraction, and advanced diffraction techniques.
</p><p>To further enhance neutron diffraction research, ORNL is undertaking several key projects:
</p>
<ul><li>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.</li>
<li>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.</li>
<li>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.</li>
<li>Enhancements at HFIR: Planned upgrades include optimizing the cold neutron guide hall to improve experimental capabilities, expanding <a href="Isotope" title="Isotope">isotope</a> production (including <a href="Plutonium-238" title="Plutonium-238">plutonium-238</a> for space exploration), and enhancing the performance of existing instruments.</li></ul>
<p>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 <a href="Energy_research" class="mw-redirect" title="Energy research">energy research</a> and <a href="Quantum_physics" class="mw-redirect" title="Quantum physics">quantum physics</a>.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Modern_trends_in_neutron_scattering_information_technology">Modern trends in neutron scattering information technology</h3></div>
<p>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 <a href="Boron" title="Boron">boron</a>-based alternatives to <a href="Helium" title="Helium">helium-3</a>, are being developed to address material shortages, while improved neutron spin manipulation enhances the study of magnetic and structural properties. Computational advancements, including <a href="Simulation" title="Simulation">simulations</a> and virtual instruments, are optimizing <a href="Neutron_source" title="Neutron source">neutron sources</a>, streamlining experimental design, and integrating <a href="Machine_learning" title="Machine learning">machine learning</a> 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.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Current_trends_in_structural_biology">Current trends in structural biology</h3></div>
<p>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 <a href="Macromolecule" title="Macromolecule">macromolecules</a>, crucial for studying <a href="Enzymatic_activity" class="mw-redirect" title="Enzymatic activity">enzymatic activity</a> and <a href="Hydrogen_bonding" class="mw-redirect" title="Hydrogen bonding">hydrogen bonding</a>. The expansion of specialized <a href="Diffractometer" title="Diffractometer">diffractometers</a> has increased accessibility in structural biology, with techniques like <a href="Monochrome" title="Monochrome">monochromatic</a>, quasi-Laue, and time-of-flight methods being optimized for efficiency. Innovations in sample preparation, particularly protein deuteration, are minimizing <a href="Background_noise" title="Background noise">background noise</a> and reducing the need for large crystals. Additionally, <a href="Computational_tools_for_artificial_intelligence" class="mw-redirect" title="Computational tools for artificial intelligence">computational tools</a>, 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.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Crystallography" title="Crystallography">Crystallography</a></li>
<li><a href="Crystallographic_database" title="Crystallographic database">Crystallographic database</a></li>
<li><a href="Electron_diffraction" title="Electron diffraction">Electron diffraction</a></li>
<li><a href="Grazing_incidence_diffraction" title="Grazing incidence diffraction">Grazing incidence diffraction</a></li>
<li><a href="Inelastic_neutron_scattering" class="mw-redirect" title="Inelastic neutron scattering">Inelastic neutron scattering</a></li>
<li><a href="X-ray_diffraction_computed_tomography" title="X-ray diffraction computed tomography">X-ray diffraction computed tomography</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><cite id="CITEREFRavnsbækFilinchukCernýJensen2010" class="citation journal cs1">Ravnsbæk, Dorthe B.; Filinchuk, Yaroslav; Cerný, Radovan; Jensen, Torben R. (2010). <a rel="nofollow" class="external text" href="https://www.degruyter.com/document/doi/10.1524/zkri.2010.1357/html">"Powder diffraction methods for studies of borohydride-based energy storage materials"</a>. <i>Zeitschrift für Kristallographie</i>. <b>225</b> (12): <span class="nowrap">557–</span>569. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010ZK....225..557R">2010ZK....225..557R</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1524%2Fzkri.2010.1357">10.1524/zkri.2010.1357</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2078.1%2F70808">2078.1/70808</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0044-2968">0044-2968</a>.</cite></span>
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<li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><cite id="CITEREFLinesJones1965" class="citation journal cs1">Lines, M. E.; Jones, E. D. (1965). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://journals.aps.org/pr/abstract/10.1103/PhysRev.139.A1313">"Antiferromagnetism in the Face-Centered Cubic Lattice. II. Magnetic Properties of MnO"</a></span>. <i>Physical Review</i>. <b>139</b> (4A): <span class="nowrap">A1313 –</span> <span class="nowrap">A1327</span>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1965PhRv..139.1313L">1965PhRv..139.1313L</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.139.A1313">10.1103/PhysRev.139.A1313</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-899X">0031-899X</a>.</cite></span>
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<li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><cite id="CITEREFJorioCurratMylesMcIntyre2000" class="citation journal cs1">Jorio, A.; Currat, R.; Myles, D. A. A.; McIntyre, G. J.; Aleksandrova, I. P.; Kiat, J. M.; Saint-Grégoire, P. (2000). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.61.3857">"Ferroelastic phase transition in Cs 3 Bi 2 I 9 : A neutron diffraction study"</a></span>. <i>Physical Review B</i>. <b>61</b> (6): <span class="nowrap">3857–</span>3862. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevB.61.3857">10.1103/PhysRevB.61.3857</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0163-1829">0163-1829</a>.</cite></span>
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<li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><cite id="CITEREFJacobOliveiraMehmanparastHosseinzadeh2018" class="citation journal cs1">Jacob, Anais; Oliveira, Jeferson; Mehmanparast, Ali; Hosseinzadeh, Foroogh; Kelleher, Joe; Berto, Filippo (2018). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0167844218300454">"Residual stress measurements in offshore wind monopile weldments using neutron diffraction technique and contour method"</a>. <i>Theoretical and Applied Fracture Mechanics</i>. <b>96</b>: <span class="nowrap">418–</span>427. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.tafmec.2018.06.001">10.1016/j.tafmec.2018.06.001</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/11250%2F2578469">11250/2578469</a></span>.</cite></span>
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<li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><cite id="CITEREFZiescheKardjilovKockelmannBrett2022" class="citation journal cs1">Ziesche, Ralf F.; Kardjilov, Nikolay; Kockelmann, Winfried; Brett, Dan J.L.; Shearing, Paul R. (2022). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S2542435121005766">"Neutron imaging of lithium batteries"</a>. <i>Joule</i>. <b>6</b> (1): <span class="nowrap">35–</span>52. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2022Joule...6...35Z">2022Joule...6...35Z</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.joule.2021.12.007">10.1016/j.joule.2021.12.007</a>.</cite></span>
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<li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><cite id="CITEREFMoodenbaughCoxViningSegre1984" class="citation journal cs1">Moodenbaugh, A. R.; Cox, D. E.; Vining, C. B.; Segre, C. U. (1984). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRevB.29.271">"Neutron-diffraction study of magnetically ordered Er 2 Fe 3 Si 5"</a></span>. <i>Physical Review B</i>. <b>29</b> (1): <span class="nowrap">271–</span>277. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevB.29.271">10.1103/PhysRevB.29.271</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0163-1829">0163-1829</a>.</cite></span>
</li>
<li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><cite id="CITEREFSunBrownClausenFoley2014" class="citation journal cs1">Sun, C.; Brown, D.W.; Clausen, B.; Foley, D.C.; Yu, K.Y.; Chen, Y.; Maloy, S.A.; Hartwig, K.T.; Wang, H.; Zhang, X. (2014). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0749641913001447">"In situ neutron diffraction study on temperature dependent deformation mechanisms of ultrafine grained austenitic Fe–14Cr–16Ni alloy"</a></span>. <i>International Journal of Plasticity</i>. <b>53</b>: <span class="nowrap">125–</span>134. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.ijplas.2013.07.007">10.1016/j.ijplas.2013.07.007</a>.</cite></span>
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<li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><cite id="CITEREFKonoKuriharaTamada2022" class="citation journal cs1">Kono, Fumiaki; Kurihara, Kazuo; Tamada, Taro (2022). <a rel="nofollow" class="external text" href="https://www.jstage.jst.go.jp/article/biophysico/19/0/19_e190009/_article">"Current status of neutron crystallography in structural biology"</a>. <i>Biophysics and Physicobiology</i>. <b>19</b>: e190009. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2142%2Fbiophysico.bppb-v19.0009">10.2142/biophysico.bppb-v19.0009</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2189-4779">2189-4779</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9135615">9135615</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/35666700">35666700</a>.</cite></span>
</li>
</ol></div></div>
<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>
<ul><li><cite id="CITEREFLovesey1984" class="citation book cs1">Lovesey, S. W. (1984). <i>Theory of Neutron Scattering from Condensed Matter; Volume 1: Neutron Scattering</i>. Oxford: <a href="Clarendon_Press" class="mw-redirect" title="Clarendon Press">Clarendon Press</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-19-852015-8</bdi>.</cite></li>
<li><cite id="CITEREFLovesey1984" class="citation book cs1">Lovesey, S. W. (1984). <i>Theory of Neutron Scattering from Condensed Matter; Volume 2: Condensed Matter</i>. Oxford: Clarendon Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-19-852017-4</bdi>.</cite></li>
<li><cite id="CITEREFSquires1996" class="citation book cs1">Squires, G.L. (1996). <i>Introduction to the Theory of Thermal Neutron Scattering</i> (2nd ed.). Mineola, New York: Dover Publications Inc. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-486-69447-X</bdi>.</cite></li>
<li><cite id="CITEREFYoung,_R.A.1993" class="citation book cs1">Young, R.A., ed. (1993). <i>The Rietveld Method</i>. Oxford: Oxford University Press & International Union of Crystallography. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-19-855577-6</bdi>.</cite></li></ul>
<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
<ul><li><a rel="nofollow" class="external text" href="http://www.ncnr.nist.gov/">National Institute of Standards and Technology Center for Neutron Research</a></li>
<li><a rel="nofollow" class="external text" href="http://nmi3.eu/news-and-media/from-braggs-law-to-neutron-diffraction.html">From Bragg's law to neutron diffraction</a></li>
<li><a rel="nofollow" class="external text" href="http://nmi3.eu/">Integrated Infrastructure Initiative for Neutron Scattering and Muon Spectroscopy (NMI3)</a> - a European consortium of 18 partner organisations from 12 countries, including all major facilities in the fields of neutron scattering and muon spectroscopy</li>
<li><a rel="nofollow" class="external text" href="http://flnph.jinr.ru/en/facilities/ibr-2/instruments">Frank Laboratory of Neutron Physics</a> of <a href="Joint_Institute_for_Nuclear_Research" title="Joint Institute for Nuclear Research">Joint Institute for Nuclear Research</a> (JINR)</li>
<li><a rel="nofollow" class="external text" href="https://nucleus.iaea.org/sites/accelerators/Pages/Interactive-Map-of-NB-Instruments.aspx">IAEA neutron beam instrument database</a></li></ul>
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<ul><li><a href="Timeline_of_crystallography" title="Timeline of crystallography">Timeline of crystallography</a>
<ul><li>Crystallographers</li></ul></li>
<li><a href="Metallurgy" title="Metallurgy">Metallurgy</a></li>
<li>Biocrystallography</li></ul>
</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Crystal_structure" title="Crystal structure">Structure</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Unit_cell" title="Unit cell">Unit cell</a>
<ul><li><a href="Bravais_lattice" title="Bravais lattice">Bravais lattice</a></li>
<li><a href="Miller_index" title="Miller index">Miller index</a></li>
<li><a href="Crystallographic_point_group" title="Crystallographic point group">Point group</a></li>
<li><a href="Reciprocal_lattice" title="Reciprocal lattice">Reciprocal lattice</a></li>
<li><a href="Crystallographic_restriction_theorem" title="Crystallographic restriction theorem">Restriction theorem</a></li></ul></li>
<li><a href="Periodic_table_(crystal_structure)" title="Periodic table (crystal structure)">Periodic table</a></li>
<li><a href="Crystal_structure_prediction" title="Crystal structure prediction">Structure prediction</a></li></ul>
</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Systems26" scope="row" class="navbox-group" style="width:1%"><a href="Crystal_system" title="Crystal system">Systems</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Cubic_crystal_system" title="Cubic crystal system">Cubic</a></li>
<li><a href="Hexagonal_crystal_family" title="Hexagonal crystal family">Hexagonal</a></li>
<li><a href="Monoclinic_crystal_system" title="Monoclinic crystal system">Monoclinic</a></li>
<li><a href="Orthorhombic_crystal_system" title="Orthorhombic crystal system">Orthorhombic</a></li>
<li><a href="Tetragonal_crystal_system" title="Tetragonal crystal system">Tetragonal</a></li>
<li><a href="Triclinic_crystal_system" title="Triclinic crystal system">Triclinic</a></li></ul>
</div></td></tr></tbody></table><div>
<ul><li><a href="Crystal_growth" title="Crystal growth">Growth</a>
<ul><li><a href="Crystallite" title="Crystallite">Crystallite</a></li>
<li><a href="Equiaxed_crystal" title="Equiaxed crystal">Equiaxed</a></li></ul></li>
<li><a href="Crystal_twinning" title="Crystal twinning">Twinning</a>
<ul><li><a href="Fiveling" title="Fiveling">Fiveling</a></li></ul></li>
<li><a href="Aperiodic_crystal" title="Aperiodic crystal">Aperiodic crystal</a>
<ul><li><a href="Quasicrystal" title="Quasicrystal">Quasicrystal</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Phase_transition" title="Phase transition">Phase<br>transition</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Phase_diagram" title="Phase diagram">Phase diagram</a>
<ul><li><a href="Eutectic_system" title="Eutectic system">Eutectic</a></li>
<li><a href="Miscibility_gap" title="Miscibility gap">Miscibility gap</a></li>
<li><a href="Crystal_polymorphism" title="Crystal polymorphism">Polymorphism</a></li>
<li><a href="Liquid_crystal" title="Liquid crystal">Liquid crystal</a></li></ul></li>
<li><a href="Phase_transformation_crystallography" title="Phase transformation crystallography">Phase transformation crystallography</a></li>
<li><a href="Precipitation_hardening" title="Precipitation hardening">Precipitation</a></li>
<li><a href="Segregation_(materials_science)" title="Segregation (materials science)">Segregation</a></li>
<li><a href="Spinodal_decomposition" title="Spinodal decomposition">Spinodal decomposition</a></li>
<li><a href="Supersaturation" title="Supersaturation">Supersaturation</a></li>
<li><a href="Guinier%E2%80%93Preston_zone" title="Guinier–Preston zone">GP-zone</a></li>
<li><a href="Ostwald_ripening" title="Ostwald ripening">Ostwald ripening</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Crystallographic_defect" title="Crystallographic defect">Defects</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Grain_boundary" title="Grain boundary">Grain boundary</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Disclination" title="Disclination">Disclination</a></li>
<li>CSL</li>
<li><a href="Grain_growth" title="Grain growth">Growth</a></li>
<li><a href="Abnormal_grain_growth" title="Abnormal grain growth">Abnormal growth</a></li></ul>
</div></td></tr></tbody></table><div>
<ul><li><a href="Perfect_crystal" title="Perfect crystal">Perfect crystal</a></li>
<li><a href="Stacking_fault" title="Stacking fault">Stacking fault</a></li>
<li><a href="Dislocation" title="Dislocation">Dislocation</a>
<ul><li><a href="Burgers_vector" title="Burgers vector">Burgers vector</a></li>
<li><a href="Partial_dislocation" title="Partial dislocation">Partial dislocation</a></li>
<li><a href="Kink_(materials_science)" title="Kink (materials science)">Kink</a></li>
<li><a href="Cross_slip" title="Cross slip">Cross slip</a></li>
<li><a href="Frank%E2%80%93Read_source" title="Frank–Read source">Frank–Read source</a></li>
<li><a href="Cottrell_atmosphere" title="Cottrell atmosphere">Cottrell atmosphere</a></li>
<li><a href="Peierls_stress" title="Peierls stress">Peierls stress</a></li>
<li><a href="Geometrically_necessary_dislocations" title="Geometrically necessary dislocations">GND</a></li>
<li><a href="Lomer%E2%80%93Cottrell_junction" title="Lomer–Cottrell junction">Lomer–Cottrell junction</a></li></ul></li>
<li><a href="Slip_(materials_science)" title="Slip (materials science)">Slip</a>
<ul><li><a href="Slip_bands_in_metals" title="Slip bands in metals">Slip bands</a></li></ul></li>
<li><a href="Interstitial_defect" title="Interstitial defect">Interstitials</a>
<ul><li><a href="Bjerrum_defect" title="Bjerrum defect">Bjerrum defect</a></li>
<li><a href="Frenkel_defect" title="Frenkel defect">Frenkel defect</a></li>
<li><a href="Wigner_effect" title="Wigner effect">Wigner effect</a></li></ul></li>
<li><a href="Vacancy_defect" title="Vacancy defect">Vacancy</a>
<ul><li><a href="Schottky_defect" title="Schottky defect">Schottky defect</a></li>
<li><a href="F-center" title="F-center">F-center</a></li></ul></li>
<li><a href="Stone%E2%80%93Wales_defect" title="Stone–Wales defect">Stone–Wales defect</a></li>
<li><a href="Crystallographic_defects_in_diamond" title="Crystallographic defects in diamond">Defects in diamond</a></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Laws</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<li><a href="Bragg's_law" title="Bragg's law">Bragg's law</a></li>
<li><a href="Friedel's_law" title="Friedel's law">Friedel's law</a></li>
<li><a href="Law_of_constancy_of_interfacial_angles" title="Law of constancy of interfacial angles">Steno's law (constancy of interfacial angles)</a></li>
<li><a href="Law_of_rational_indices" title="Law of rational indices">Law of rational indices</a></li>
<li><a href="Law_of_symmetry_(crystallography)" title="Law of symmetry (crystallography)">Law of symmetry</a></li>
</div></td></tr></tbody></table><div>
<ul><li><a href="Bragg_plane" title="Bragg plane">Bragg plane</a></li>
<li><a href="Ewald's_sphere" title="Ewald's sphere">Ewald's sphere</a></li>
<li><a href="Hermann%E2%80%93Mauguin_notation" title="Hermann–Mauguin notation">Hermann–Mauguin notation</a></li>
<li><a href="Structure_factor" title="Structure factor">Structure factor</a></li>
<li><a href="Thermal_ellipsoid" title="Thermal ellipsoid">Thermal ellipsoid</a></li></ul>
</div></td><td class="noviewer navbox-image" rowspan="9" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span><br></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Characterisation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Electron_crystallography" title="Electron crystallography">Electron</a>
<ul><li><a href="Electron_diffraction" title="Electron diffraction">Diffraction</a></li>
<li><a href="Electron_scattering" title="Electron scattering">Scattering</a></li></ul></li>
<li><a href="Neutron_crystallography" class="mw-redirect" title="Neutron crystallography">Neutron</a>
<ul>
<li><a href="Neutron_scattering" title="Neutron scattering">Scattering</a></li></ul></li>
<li><a href="Nuclear_magnetic_resonance_crystallography" title="Nuclear magnetic resonance crystallography">Nuclear magnetic resonance</a></li>
<li><a href="X-ray_crystallography" title="X-ray crystallography">X-ray</a>
<ul><li><a href="X-ray_diffraction" title="X-ray diffraction">Diffraction</a></li>
<li><a href="X-ray_scattering" class="mw-redirect" title="X-ray scattering">Scattering</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Algorithms</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Direct_methods_(crystallography)" title="Direct methods (crystallography)">Direct methods</a></li>
<li><a href="Isomorphous_replacement" title="Isomorphous replacement">Isomorphous replacement</a></li>
<li><a href="Molecular_replacement" title="Molecular replacement">Molecular replacement</a></li>
<li><a href="Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a></li>
<li><a href="Patterson_map" class="mw-redirect" title="Patterson map">Patterson map</a></li>
<li><a href="Phase_retrieval" title="Phase retrieval">Phase retrieval</a>
<ul><li><a href="Gerchberg%E2%80%93Saxton_algorithm" title="Gerchberg–Saxton algorithm">Gerchberg–Saxton</a></li></ul></li>
<li><a href="Single_particle_analysis" title="Single particle analysis">Single particle analysis</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Software</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Collaborative_Computational_Project_Number_4" title="Collaborative Computational Project Number 4">CCP4</a></li>
<li><a href="Coot_(software)" title="Coot (software)">Coot</a></li>
<li><a href="CrystalExplorer" title="CrystalExplorer">CrystalExplorer</a></li>
<li><a href="Disordered_Structure_Refinement" title="Disordered Structure Refinement">DSR</a></li>
<li><a rel="nofollow" class="external text" href="http://jana.fzu.cz/">JANA2020</a></li>
<li><a href="MTEX" title="MTEX">MTEX</a></li>
<li><a href="OctaDist" title="OctaDist">OctaDist</a></li>
<li><a href="Olex2" title="Olex2">Olex2</a></li>
<li><a href="ShelXle" title="ShelXle">SHELX</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;"><a href="Crystallographic_database" title="Crystallographic database">Databases</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Bilbao_Crystallographic_Server" title="Bilbao Crystallographic Server">Bilbao Crystallographic Server</a></li>
<li><a href="Cambridge_Structural_Database" title="Cambridge Structural Database">CCDC</a></li>
<li><a href="Crystallographic_Information_File" title="Crystallographic Information File">CIF</a></li>
<li><a href="Crystallography_Open_Database" title="Crystallography Open Database">COD</a></li>
<li><a href="Inorganic_Crystal_Structure_Database" title="Inorganic Crystal Structure Database">ICSD</a></li>
<li><a href="International_Centre_for_Diffraction_Data" title="International Centre for Diffraction Data">ICDD</a></li>
<li><a href="Protein_Data_Bank" title="Protein Data Bank">PDB</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Journals</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Crystal_Growth_%26_Design" title="Crystal Growth & Design">Crystal Growth & Design</a></li>
<li><a href="Crystallography_Reviews" title="Crystallography Reviews">Crystallography Reviews</a></li>
<li><a href="Journal_of_Chemical_Crystallography" title="Journal of Chemical Crystallography">Journal of Chemical Crystallography</a></li>
<li><a href="Journal_of_Crystal_Growth" title="Journal of Crystal Growth">Journal of Crystal Growth</a></li>
<li><a href="Kristallografija" title="Kristallografija">Kristallografija</a></li>
<li><a href="Zeitschrift_f%C3%BCr_Kristallographie_%E2%80%93_Crystalline_Materials" title="Zeitschrift für Kristallographie – Crystalline Materials">Zeitschrift für Kristallographie – Crystalline Materials</a></li>
<li><a href="Zeitschrift_f%C3%BCr_Kristallographie_%E2%80%93_New_Crystal_Structures" title="Zeitschrift für Kristallographie – New Crystal Structures">Zeitschrift für Kristallographie – New Crystal Structures</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Awards</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Carl_Hermann_Medal" title="Carl Hermann Medal">Carl Hermann Medal</a></li>
<li><a href="Ewald_Prize" title="Ewald Prize">Ewald Prize</a></li>
<li><a href="Gregori_Aminoff_Prize" title="Gregori Aminoff Prize">Gregori Aminoff Prize</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">History</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Chemical_crystallography_before_X-rays" title="Chemical crystallography before X-rays">Chemical crystallography before X-rays</a></li>
<li><a href="Physical_crystallography_before_X-rays" title="Physical crystallography before X-rays">Physical crystallography before X-rays</a></li>
<li><a href="Timeline_of_crystallography" title="Timeline of crystallography">Timeline of crystallography</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Organisation</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="International_Union_of_Crystallography" title="International Union of Crystallography">IUCr</a></li>
<li><a href="International_Organization_for_Biological_Crystallization" title="International Organization for Biological Crystallization">IOBCr</a></li>
<li><a href="Shubnikov_Institute_of_Crystallography_RAS" title="Shubnikov Institute of Crystallography RAS">RAS</a></li>
<li><a href="German_Mineralogical_Society" title="German Mineralogical Society">DMG</a></li></ul>
</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Associations12" scope="row" class="navbox-group" style="width:1%">Associations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="European_Crystallographic_Association" title="European Crystallographic Association">Europe</a>
<ul><li><a href="French_Crystallographic_Association" title="French Crystallographic Association">France</a></li>
<li><a href="German_Crystallographic_Society" title="German Crystallographic Society">Germany</a></li>
<li><a href="British_Crystallographic_Association" title="British Crystallographic Association">UK</a></li></ul></li>
<li><a href="American_Crystallographic_Association" title="American Crystallographic Association">US</a></li>
<li><a href="Crystallographic_Society_of_Japan" title="Crystallographic Society of Japan">Japan</a></li></ul>
</div></td></tr></tbody></table><div>
</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div>
<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> <b>Category</b></li>
<li><span class="noviewer" typeof="mw:File"><span title="Commons page"></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Crystallography" class="extiw external" title="commons:Category:Crystallography">Commons</a></b></li></ul>
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