Convergence of the hyperspherical harmonic expansion for crystallographic texture
Advances in instrumentation allow a material texture to be measured as a collection of spatially resolved crystallite orientations rather than as a collection of pole figures. However, the hyperspherical harmonic expansion of a collection of spatially resolved crystallite orientations is subject to...
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| Veröffentlicht in: | Journal of applied crystallography 2013-12, Vol.46 (6), p.1722-1728 |
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| container_title | Journal of applied crystallography |
| container_volume | 46 |
| creator | Mason, Jeremy K. Johnson, Oliver K. |
| description | Advances in instrumentation allow a material texture to be measured as a collection of spatially resolved crystallite orientations rather than as a collection of pole figures. However, the hyperspherical harmonic expansion of a collection of spatially resolved crystallite orientations is subject to significant truncation error, resulting in ringing artifacts (spurious oscillations around sharp transitions) and false peaks in the orientation distribution function. This article finds that the ringing artifacts and the accompanying regions of negative probability density may be mitigated or removed entirely by modifying the coefficients of the hyperspherical harmonic expansion by a simple multiplicative factor. An addition theorem for the hyperspherical harmonics is derived as an intermediate result. |
| doi_str_mv | 10.1107/S0021889813022814 |
| format | Article |
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An addition theorem for the hyperspherical harmonics is derived as an intermediate result.</description><subject>Collection</subject><subject>Crystallites</subject><subject>Crystallography</subject><subject>Density</subject><subject>Harmonics</subject><subject>hyperspherical harmonics</subject><subject>Orientation</subject><subject>orientation distribution functions</subject><subject>Scientific apparatus & instruments</subject><subject>Surface layer</subject><subject>Texture</subject><issn>1600-5767</issn><issn>0021-8898</issn><issn>1600-5767</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqFkE1v1EAMhiNUJLaFH8AtEhcuaT2Z7yOK2i1oBdoCWm6jYeJsss1m0pkEmn_foFQVogdOtuTnsew3Sd4SOCcE5MVXgJwopRWhkOeKsBfJigiAjEshT_7qXyWnMR4AiJB5vkq2he9-Ydhj5zD1VTrUmNZTjyH2NYbG2TatbTj6rnEp3ve2i43v0sqH1IUpDrZt_T7Yvp7HA94PY8DXycvKthHfPNaz5PvV5bfiOtt8WX8sPmwyRzXlmdCsQq6FREkpVSUlgjmuaSkFZ1QxrrSg1P2UQDSUOVUEsFQlo445YJLRs-T9srcP_m7EOJhjEx22re3Qj9HMDxKuOTA-o-_-QQ9-DN18nSGM6xxAiHymyEK54GMMWJk-NEcbJkPA_AnZPAt5dtTi_G5anP4vmE_Fzc3u8ahsUZs4J_ek2nBrhKSSm93ntdlspdr-KJhR9AF98oyE</recordid><startdate>20131201</startdate><enddate>20131201</enddate><creator>Mason, Jeremy K.</creator><creator>Johnson, Oliver K.</creator><general>International Union of Crystallography</general><general>Blackwell Publishing Ltd</general><scope>BSCLL</scope><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>20131201</creationdate><title>Convergence of the hyperspherical harmonic expansion for crystallographic texture</title><author>Mason, Jeremy K. ; Johnson, Oliver K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3935-694fe5967e73338d3164c593d7654384589633cb70190d23810ed8d43c4c04743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Collection</topic><topic>Crystallites</topic><topic>Crystallography</topic><topic>Density</topic><topic>Harmonics</topic><topic>hyperspherical harmonics</topic><topic>Orientation</topic><topic>orientation distribution functions</topic><topic>Scientific apparatus & instruments</topic><topic>Surface layer</topic><topic>Texture</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mason, Jeremy K.</creatorcontrib><creatorcontrib>Johnson, Oliver K.</creatorcontrib><collection>Istex</collection><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>Mason, Jeremy K.</au><au>Johnson, Oliver K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence of the hyperspherical harmonic expansion for crystallographic texture</atitle><jtitle>Journal of applied crystallography</jtitle><addtitle>J. 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| fulltext | fulltext |
| identifier | ISSN: 1600-5767 |
| ispartof | Journal of applied crystallography, 2013-12, Vol.46 (6), p.1722-1728 |
| issn | 1600-5767 0021-8898 1600-5767 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1671595045 |
| source | Wiley Journals; Alma/SFX Local Collection |
| subjects | Collection Crystallites Crystallography Density Harmonics hyperspherical harmonics Orientation orientation distribution functions Scientific apparatus & instruments Surface layer Texture |
| title | Convergence of the hyperspherical harmonic expansion for crystallographic texture |
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