Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor
We report the results of highly sensitive transmission X-ray scattering measurements performed at the Advanced Photon Source, Argonne National Laboratory, on nearly fully dense high-purity amorphous-silicon (a-Si) samples for the purpose of determining their degree of hyperuniformity. A perfectly hy...
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| Veröffentlicht in: | Proceedings of the National Academy of Sciences - PNAS 2013-08, Vol.110 (33), p.13250-13254 |
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| container_title | Proceedings of the National Academy of Sciences - PNAS |
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| creator | Xie, Ruobing Long, Gabrielle G. Weigand, Steven J. Moss, Simon C. Carvalho, Tobi Roorda, Sjoerd Hejna, Miroslav Torquato, Salvatore Steinhardt, Paul J. |
| description | We report the results of highly sensitive transmission X-ray scattering measurements performed at the Advanced Photon Source, Argonne National Laboratory, on nearly fully dense high-purity amorphous-silicon (a-Si) samples for the purpose of determining their degree of hyperuniformity. A perfectly hyperuniform structure has complete suppression of infinite-wavelength density fluctuations, or, equivalently, the structure factor S (q →0) = 0; the smaller the value of S (0), the higher the degree of hyperuniformity. Annealing was observed to increase the degree of hyperuniformity in a-Si where we found S (0) = 0.0075 (±0.0005), which is significantly below the computationally determined lower bound recently suggested by de Graff and Thorpe [de Graff AMR, Thorpe MF (2010) Acta Crystallogr A 66(Pt 1):22–31] based on studies of continuous random network models, but consistent with the recently proposed nearly hyperuniform network picture of a-Si. Increasing hyperuniformity is correlated with narrowing of the first diffraction peak and extension of the range of oscillations in the pair distribution function. |
| doi_str_mv | 10.1073/pnas.1220106110 |
| format | Article |
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A perfectly hyperuniform structure has complete suppression of infinite-wavelength density fluctuations, or, equivalently, the structure factor S (q →0) = 0; the smaller the value of S (0), the higher the degree of hyperuniformity. Annealing was observed to increase the degree of hyperuniformity in a-Si where we found S (0) = 0.0075 (±0.0005), which is significantly below the computationally determined lower bound recently suggested by de Graff and Thorpe [de Graff AMR, Thorpe MF (2010) Acta Crystallogr A 66(Pt 1):22–31] based on studies of continuous random network models, but consistent with the recently proposed nearly hyperuniform network picture of a-Si. Increasing hyperuniformity is correlated with narrowing of the first diffraction peak and extension of the range of oscillations in the pair distribution function.</description><identifier>ISSN: 0027-8424</identifier><identifier>EISSN: 1091-6490</identifier><identifier>DOI: 10.1073/pnas.1220106110</identifier><identifier>PMID: 23898166</identifier><language>eng</language><publisher>United States: National Academy of Sciences</publisher><subject>Amorphous silicon ; Annealing ; Correlation analysis ; Diffraction ; Energy gaps ; Glass ; Ion implantation ; Liquids ; Materials ; Measurement ; Microscopy, Electron ; Models, Chemical ; Photonics ; Physical Sciences ; Scattering ; Silicon ; Silicon - chemistry ; Solids ; Wave diffraction ; X-Ray Diffraction - methods</subject><ispartof>Proceedings of the National Academy of Sciences - PNAS, 2013-08, Vol.110 (33), p.13250-13254</ispartof><rights>copyright © 1993-2008 National Academy of Sciences of the United States of America</rights><rights>Copyright National Academy of Sciences Aug 13, 2013</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c492t-26651b6730648f6f58365c1416ad9384d9ec86c80dc8da9179b2f48b7d0f0c9d3</citedby><cites>FETCH-LOGICAL-c492t-26651b6730648f6f58365c1416ad9384d9ec86c80dc8da9179b2f48b7d0f0c9d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://www.pnas.org/content/110/33.cover.gif</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/42712893$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/42712893$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,727,780,784,803,885,27924,27925,53791,53793,58017,58250</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/23898166$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Xie, Ruobing</creatorcontrib><creatorcontrib>Long, Gabrielle G.</creatorcontrib><creatorcontrib>Weigand, Steven J.</creatorcontrib><creatorcontrib>Moss, Simon C.</creatorcontrib><creatorcontrib>Carvalho, Tobi</creatorcontrib><creatorcontrib>Roorda, Sjoerd</creatorcontrib><creatorcontrib>Hejna, Miroslav</creatorcontrib><creatorcontrib>Torquato, Salvatore</creatorcontrib><creatorcontrib>Steinhardt, Paul J.</creatorcontrib><title>Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor</title><title>Proceedings of the National Academy of Sciences - PNAS</title><addtitle>Proc Natl Acad Sci U S A</addtitle><description>We report the results of highly sensitive transmission X-ray scattering measurements performed at the Advanced Photon Source, Argonne National Laboratory, on nearly fully dense high-purity amorphous-silicon (a-Si) samples for the purpose of determining their degree of hyperuniformity. A perfectly hyperuniform structure has complete suppression of infinite-wavelength density fluctuations, or, equivalently, the structure factor S (q →0) = 0; the smaller the value of S (0), the higher the degree of hyperuniformity. Annealing was observed to increase the degree of hyperuniformity in a-Si where we found S (0) = 0.0075 (±0.0005), which is significantly below the computationally determined lower bound recently suggested by de Graff and Thorpe [de Graff AMR, Thorpe MF (2010) Acta Crystallogr A 66(Pt 1):22–31] based on studies of continuous random network models, but consistent with the recently proposed nearly hyperuniform network picture of a-Si. Increasing hyperuniformity is correlated with narrowing of the first diffraction peak and extension of the range of oscillations in the pair distribution function.</description><subject>Amorphous silicon</subject><subject>Annealing</subject><subject>Correlation analysis</subject><subject>Diffraction</subject><subject>Energy gaps</subject><subject>Glass</subject><subject>Ion implantation</subject><subject>Liquids</subject><subject>Materials</subject><subject>Measurement</subject><subject>Microscopy, Electron</subject><subject>Models, Chemical</subject><subject>Photonics</subject><subject>Physical Sciences</subject><subject>Scattering</subject><subject>Silicon</subject><subject>Silicon - chemistry</subject><subject>Solids</subject><subject>Wave diffraction</subject><subject>X-Ray Diffraction - methods</subject><issn>0027-8424</issn><issn>1091-6490</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNpdkUuP0zAUhSMEYsrAmhVgiQ2bzFw_4tgbJDQCBmkkFjBry3Hs1lViFzsp6r_HoZ3yWNny_e7R8TlV9RLDFYaWXu-CzleYEMDAMYZH1QqDxDVnEh5XKwDS1oIRdlE9y3kLALIR8LS6IFRIgTlfVfvbw86mOXgX0-inA_IB6TGm3SbOGWU_eBMD6nS2PSqXaWPRaHWekx1tmFB0v598cD74ydY_9d4ONqynDRp80XsA8pRmM5Ut5LSZYnpePXF6yPbF6bys7j99_H5zW999_fzl5sNdbZgkU004b3DHWwqcCcddIyhvDGaY615SwXppjeBGQG9EryVuZUccE13bgwMje3pZvT_q7uZutL0pnpMe1C75UaeDitqrfyfBb9Q67hVtGRccF4F3J4EUf8w2T2r02dhh0MGWhBQu6dISp2gK-vY_dBvnFMr3FqppQMqWFer6SJkUc07Wnc1gUEunaulU_em0bLz--w9n_qHEAqATsGye5YoepQpT0iwar47INpf0zwwjLSZC0jJ_c5w7HZVeJ5_V_bfigAMU70WD_gKMZrzP</recordid><startdate>20130813</startdate><enddate>20130813</enddate><creator>Xie, Ruobing</creator><creator>Long, Gabrielle G.</creator><creator>Weigand, Steven J.</creator><creator>Moss, Simon C.</creator><creator>Carvalho, Tobi</creator><creator>Roorda, Sjoerd</creator><creator>Hejna, Miroslav</creator><creator>Torquato, Salvatore</creator><creator>Steinhardt, Paul J.</creator><general>National Academy of Sciences</general><general>National Acad Sciences</general><scope>FBQ</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QG</scope><scope>7QL</scope><scope>7QP</scope><scope>7QR</scope><scope>7SN</scope><scope>7SS</scope><scope>7T5</scope><scope>7TK</scope><scope>7TM</scope><scope>7TO</scope><scope>7U9</scope><scope>8FD</scope><scope>C1K</scope><scope>FR3</scope><scope>H94</scope><scope>M7N</scope><scope>P64</scope><scope>RC3</scope><scope>7X8</scope><scope>5PM</scope></search><sort><creationdate>20130813</creationdate><title>Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor</title><author>Xie, Ruobing ; Long, Gabrielle G. ; Weigand, Steven J. ; Moss, Simon C. ; Carvalho, Tobi ; Roorda, Sjoerd ; Hejna, Miroslav ; Torquato, Salvatore ; Steinhardt, Paul J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c492t-26651b6730648f6f58365c1416ad9384d9ec86c80dc8da9179b2f48b7d0f0c9d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Amorphous silicon</topic><topic>Annealing</topic><topic>Correlation analysis</topic><topic>Diffraction</topic><topic>Energy gaps</topic><topic>Glass</topic><topic>Ion implantation</topic><topic>Liquids</topic><topic>Materials</topic><topic>Measurement</topic><topic>Microscopy, Electron</topic><topic>Models, Chemical</topic><topic>Photonics</topic><topic>Physical Sciences</topic><topic>Scattering</topic><topic>Silicon</topic><topic>Silicon - chemistry</topic><topic>Solids</topic><topic>Wave diffraction</topic><topic>X-Ray Diffraction - methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xie, Ruobing</creatorcontrib><creatorcontrib>Long, Gabrielle G.</creatorcontrib><creatorcontrib>Weigand, Steven J.</creatorcontrib><creatorcontrib>Moss, Simon C.</creatorcontrib><creatorcontrib>Carvalho, Tobi</creatorcontrib><creatorcontrib>Roorda, Sjoerd</creatorcontrib><creatorcontrib>Hejna, Miroslav</creatorcontrib><creatorcontrib>Torquato, Salvatore</creatorcontrib><creatorcontrib>Steinhardt, Paul J.</creatorcontrib><collection>AGRIS</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Animal Behavior Abstracts</collection><collection>Bacteriology Abstracts (Microbiology B)</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>Chemoreception Abstracts</collection><collection>Ecology Abstracts</collection><collection>Entomology Abstracts (Full archive)</collection><collection>Immunology Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Nucleic Acids Abstracts</collection><collection>Oncogenes and Growth Factors Abstracts</collection><collection>Virology and AIDS Abstracts</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Engineering Research Database</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>Algology Mycology and Protozoology Abstracts (Microbiology C)</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Genetics Abstracts</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Proceedings of the National Academy of Sciences - PNAS</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xie, Ruobing</au><au>Long, Gabrielle G.</au><au>Weigand, Steven J.</au><au>Moss, Simon C.</au><au>Carvalho, Tobi</au><au>Roorda, Sjoerd</au><au>Hejna, Miroslav</au><au>Torquato, Salvatore</au><au>Steinhardt, Paul J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor</atitle><jtitle>Proceedings of the National Academy of Sciences - PNAS</jtitle><addtitle>Proc Natl Acad Sci U S A</addtitle><date>2013-08-13</date><risdate>2013</risdate><volume>110</volume><issue>33</issue><spage>13250</spage><epage>13254</epage><pages>13250-13254</pages><issn>0027-8424</issn><eissn>1091-6490</eissn><abstract>We report the results of highly sensitive transmission X-ray scattering measurements performed at the Advanced Photon Source, Argonne National Laboratory, on nearly fully dense high-purity amorphous-silicon (a-Si) samples for the purpose of determining their degree of hyperuniformity. A perfectly hyperuniform structure has complete suppression of infinite-wavelength density fluctuations, or, equivalently, the structure factor S (q →0) = 0; the smaller the value of S (0), the higher the degree of hyperuniformity. Annealing was observed to increase the degree of hyperuniformity in a-Si where we found S (0) = 0.0075 (±0.0005), which is significantly below the computationally determined lower bound recently suggested by de Graff and Thorpe [de Graff AMR, Thorpe MF (2010) Acta Crystallogr A 66(Pt 1):22–31] based on studies of continuous random network models, but consistent with the recently proposed nearly hyperuniform network picture of a-Si. Increasing hyperuniformity is correlated with narrowing of the first diffraction peak and extension of the range of oscillations in the pair distribution function.</abstract><cop>United States</cop><pub>National Academy of Sciences</pub><pmid>23898166</pmid><doi>10.1073/pnas.1220106110</doi><tpages>5</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Amorphous silicon Annealing Correlation analysis Diffraction Energy gaps Glass Ion implantation Liquids Materials Measurement Microscopy, Electron Models, Chemical Photonics Physical Sciences Scattering Silicon Silicon - chemistry Solids Wave diffraction X-Ray Diffraction - methods |
| title | Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor |
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