Finite‐element simulation for crystals with surface undulations based on Takagi–Taupin theory
A finite‐element method based on a weak formulation of the Takagi–Taupin equations was adopted to study the X‐ray diffraction of crystals with surface undulations. A general diffraction geometry was simulated to investigate the diffraction features caused by the surface undulations. The numerical re...
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| Veröffentlicht in: | Journal of applied crystallography 2023-04, Vol.56 (2), p.391-400 |
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| container_title | Journal of applied crystallography |
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| creator | Wang, Yu-Hang Li, Ming Kang, Le Jia, Quan-Jie |
| description | A finite‐element method based on a weak formulation of the Takagi–Taupin equations was adopted to study the X‐ray diffraction of crystals with surface undulations. A general diffraction geometry was simulated to investigate the diffraction features caused by the surface undulations. The numerical results reveal that the effects of surface undulations on Bragg diffraction are local for those limited in the low‐frequency range and physically result from the refractive effect, brought on by the variation of the local asymmetry angle. Thus, a formula based on the local perfect flat crystal approximation was introduced to efficiently evaluate the change in the direction of the diffracted wave caused by surface undulations.
Takagi–Taupin dynamical X‐ray diffraction simulations of crystals with surface undulations show that the influence of the surface undulations is local for those in the low‐frequency range and can be predicted by classical X‐ray dynamical theory. |
| doi_str_mv | 10.1107/S1600576723000808 |
| format | Article |
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Takagi–Taupin dynamical X‐ray diffraction simulations of crystals with surface undulations show that the influence of the surface undulations is local for those in the low‐frequency range and can be predicted by classical X‐ray dynamical theory.</description><identifier>ISSN: 1600-5767</identifier><identifier>ISSN: 0021-8898</identifier><identifier>EISSN: 1600-5767</identifier><identifier>DOI: 10.1107/S1600576723000808</identifier><language>eng</language><publisher>5 Abbey Square, Chester, Cheshire CH1 2HU, England: International Union of Crystallography</publisher><subject>Crystals ; dynamical diffraction ; finite‐element method ; Frequency ranges ; Mathematical analysis ; surface morphologies ; Takagi–Taupin equations ; Wave diffraction</subject><ispartof>Journal of applied crystallography, 2023-04, Vol.56 (2), p.391-400</ispartof><rights>2023 Wang, Li, Kang and Jia. published by IUCr Journals.</rights><rights>Copyright Blackwell Publishing Ltd. Apr 2023</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2753-100ef10d5188da3f25ab3fc1e4849ca980246375b3d7ff55a4e9fc763371028d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1107%2FS1600576723000808$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1107%2FS1600576723000808$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>315,782,786,1419,27933,27934,45583,45584</link.rule.ids></links><search><creatorcontrib>Wang, Yu-Hang</creatorcontrib><creatorcontrib>Li, Ming</creatorcontrib><creatorcontrib>Kang, Le</creatorcontrib><creatorcontrib>Jia, Quan-Jie</creatorcontrib><title>Finite‐element simulation for crystals with surface undulations based on Takagi–Taupin theory</title><title>Journal of applied crystallography</title><description>A finite‐element method based on a weak formulation of the Takagi–Taupin equations was adopted to study the X‐ray diffraction of crystals with surface undulations. A general diffraction geometry was simulated to investigate the diffraction features caused by the surface undulations. The numerical results reveal that the effects of surface undulations on Bragg diffraction are local for those limited in the low‐frequency range and physically result from the refractive effect, brought on by the variation of the local asymmetry angle. Thus, a formula based on the local perfect flat crystal approximation was introduced to efficiently evaluate the change in the direction of the diffracted wave caused by surface undulations.
Takagi–Taupin dynamical X‐ray diffraction simulations of crystals with surface undulations show that the influence of the surface undulations is local for those in the low‐frequency range and can be predicted by classical X‐ray dynamical theory.</description><subject>Crystals</subject><subject>dynamical diffraction</subject><subject>finite‐element method</subject><subject>Frequency ranges</subject><subject>Mathematical analysis</subject><subject>surface morphologies</subject><subject>Takagi–Taupin equations</subject><subject>Wave diffraction</subject><issn>1600-5767</issn><issn>0021-8898</issn><issn>1600-5767</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNqFkMFKw0AQhhdRsFYfwNuC5-jMbjabHKW0VikIGs9hm-zarWlSdxNKbn0EwTfsk5jSHgQPnmb4-b4Z-Am5RrhFBHn3ihGAkJFkHABiiE_IYB8F--z0135OLrxfAmCPsgFRE1vZRu-2X7rUK1011NtVW6rG1hU1taO563yjSk83tllQ3zqjck3bqjhCns6V1wXt8VR9qHe7236nql3bijYLXbvukpyZ3tdXxzkkb5NxOpoGs-eHx9H9LMiZFDxAAG0QCoFxXChumFBzbnLUYRwmuUpiYGHEpZjzQhojhAp1YnIZcS4RWFzwIbk53F27-rPVvsmWdeuq_mXGZNK7DJOwp_BA5a723mmTrZ1dKddlCNm-yexPk72THJyNLXX3v5A9jV5YOhaInP8Azjh4sQ</recordid><startdate>202304</startdate><enddate>202304</enddate><creator>Wang, Yu-Hang</creator><creator>Li, Ming</creator><creator>Kang, Le</creator><creator>Jia, Quan-Jie</creator><general>International Union of Crystallography</general><general>Blackwell Publishing Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope><scope>L7M</scope></search><sort><creationdate>202304</creationdate><title>Finite‐element simulation for crystals with surface undulations based on Takagi–Taupin theory</title><author>Wang, Yu-Hang ; Li, Ming ; Kang, Le ; Jia, Quan-Jie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2753-100ef10d5188da3f25ab3fc1e4849ca980246375b3d7ff55a4e9fc763371028d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Crystals</topic><topic>dynamical diffraction</topic><topic>finite‐element method</topic><topic>Frequency ranges</topic><topic>Mathematical analysis</topic><topic>surface morphologies</topic><topic>Takagi–Taupin equations</topic><topic>Wave diffraction</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Yu-Hang</creatorcontrib><creatorcontrib>Li, Ming</creatorcontrib><creatorcontrib>Kang, Le</creatorcontrib><creatorcontrib>Jia, Quan-Jie</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of applied crystallography</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Yu-Hang</au><au>Li, Ming</au><au>Kang, Le</au><au>Jia, Quan-Jie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Finite‐element simulation for crystals with surface undulations based on Takagi–Taupin theory</atitle><jtitle>Journal of applied crystallography</jtitle><date>2023-04</date><risdate>2023</risdate><volume>56</volume><issue>2</issue><spage>391</spage><epage>400</epage><pages>391-400</pages><issn>1600-5767</issn><issn>0021-8898</issn><eissn>1600-5767</eissn><abstract>A finite‐element method based on a weak formulation of the Takagi–Taupin equations was adopted to study the X‐ray diffraction of crystals with surface undulations. A general diffraction geometry was simulated to investigate the diffraction features caused by the surface undulations. The numerical results reveal that the effects of surface undulations on Bragg diffraction are local for those limited in the low‐frequency range and physically result from the refractive effect, brought on by the variation of the local asymmetry angle. Thus, a formula based on the local perfect flat crystal approximation was introduced to efficiently evaluate the change in the direction of the diffracted wave caused by surface undulations.
Takagi–Taupin dynamical X‐ray diffraction simulations of crystals with surface undulations show that the influence of the surface undulations is local for those in the low‐frequency range and can be predicted by classical X‐ray dynamical theory.</abstract><cop>5 Abbey Square, Chester, Cheshire CH1 2HU, England</cop><pub>International Union of Crystallography</pub><doi>10.1107/S1600576723000808</doi><tpages>10</tpages></addata></record> |
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| subjects | Crystals dynamical diffraction finite‐element method Frequency ranges Mathematical analysis surface morphologies Takagi–Taupin equations Wave diffraction |
| title | Finite‐element simulation for crystals with surface undulations based on Takagi–Taupin theory |
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