Universal Scherrer equation for graphene fragments
Graphene fragments spanning a wide range of size and shape were studied computationally using the Debye scattering equation. The calculated diffraction patterns were analysed using the Scherrer equation to infer the fragment size, La. Comparison with the known fragment sizes reveals a strong affine...
Gespeichert in:
| Veröffentlicht in: | Carbon (New York) 2020-06, Vol.162, p.475-480 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 480 |
|---|---|
| container_issue | |
| container_start_page | 475 |
| container_title | Carbon (New York) |
| container_volume | 162 |
| creator | Lim, Daniel J. Marks, Nigel A. Rowles, Matthew R. |
| description | Graphene fragments spanning a wide range of size and shape were studied computationally using the Debye scattering equation. The calculated diffraction patterns were analysed using the Scherrer equation to infer the fragment size, La. Comparison with the known fragment sizes reveals a strong affine relationship between La and the Scherrer quantity λ/(Bcosθ). To preserve this relationship, we propose modifying the Scherrer equation to include an empirical additive constant. Our approach solves the well-known problem of size-dependence in the shape factor and yields a universal expression by defining La as the square-root of the fragment area. The relationship between observed diffraction peak positions and unit cell parameters is also discussed.
[Display omitted] |
| doi_str_mv | 10.1016/j.carbon.2020.02.064 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2442320862</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0008622320302104</els_id><sourcerecordid>2442320862</sourcerecordid><originalsourceid>FETCH-LOGICAL-c380t-87f4913e07846700b03f648cff05878a3544296ebf79a7e5f803a0f52875d3203</originalsourceid><addsrcrecordid>eNp9kE1Lw0AQhhdRsFb_gYeA58TZj2Q3F0GKX1DwoD0v2-1sm9Am7Wxa8N-7JZ49DQPv8w7zMHbPoeDAq8e28I6WfVcIEFCAKKBSF2zCjZa5NDW_ZBMAMHklhLxmNzG2aVWGqwkTi645IUW3zb78BomQMjwc3dD0XRZ6ytbk9hvsMAvk1jvshnjLroLbRrz7m1O2eH35nr3n88-3j9nzPPfSwJAbHVTNJYI2qtIAS5ChUsaHAKXRxslSKVFXuAy6dhrLYEA6CKUwulxJAXLKHsbePfWHI8bBtv2RunTSioSmiKlESqkx5amPkTDYPTU7Rz-Wgz3bsa0d7dizHQvCJjsJexoxTB-cGiQbfYOdx1VD6Ae76pv_C34Bia1tdA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2442320862</pqid></control><display><type>article</type><title>Universal Scherrer equation for graphene fragments</title><source>Elsevier ScienceDirect Journals</source><creator>Lim, Daniel J. ; Marks, Nigel A. ; Rowles, Matthew R.</creator><creatorcontrib>Lim, Daniel J. ; Marks, Nigel A. ; Rowles, Matthew R.</creatorcontrib><description>Graphene fragments spanning a wide range of size and shape were studied computationally using the Debye scattering equation. The calculated diffraction patterns were analysed using the Scherrer equation to infer the fragment size, La. Comparison with the known fragment sizes reveals a strong affine relationship between La and the Scherrer quantity λ/(Bcosθ). To preserve this relationship, we propose modifying the Scherrer equation to include an empirical additive constant. Our approach solves the well-known problem of size-dependence in the shape factor and yields a universal expression by defining La as the square-root of the fragment area. The relationship between observed diffraction peak positions and unit cell parameters is also discussed.
[Display omitted]</description><identifier>ISSN: 0008-6223</identifier><identifier>EISSN: 1873-3891</identifier><identifier>DOI: 10.1016/j.carbon.2020.02.064</identifier><language>eng</language><publisher>New York: Elsevier Ltd</publisher><subject>Diffraction ; Diffraction patterns ; Empirical equations ; Fragments ; Graphene ; Molecules ; Nonlinear equations ; Scattering ; Shape factor ; Studies ; Unit cell</subject><ispartof>Carbon (New York), 2020-06, Vol.162, p.475-480</ispartof><rights>2020 Elsevier Ltd</rights><rights>Copyright Elsevier BV Jun 2020</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c380t-87f4913e07846700b03f648cff05878a3544296ebf79a7e5f803a0f52875d3203</citedby><cites>FETCH-LOGICAL-c380t-87f4913e07846700b03f648cff05878a3544296ebf79a7e5f803a0f52875d3203</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0008622320302104$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Lim, Daniel J.</creatorcontrib><creatorcontrib>Marks, Nigel A.</creatorcontrib><creatorcontrib>Rowles, Matthew R.</creatorcontrib><title>Universal Scherrer equation for graphene fragments</title><title>Carbon (New York)</title><description>Graphene fragments spanning a wide range of size and shape were studied computationally using the Debye scattering equation. The calculated diffraction patterns were analysed using the Scherrer equation to infer the fragment size, La. Comparison with the known fragment sizes reveals a strong affine relationship between La and the Scherrer quantity λ/(Bcosθ). To preserve this relationship, we propose modifying the Scherrer equation to include an empirical additive constant. Our approach solves the well-known problem of size-dependence in the shape factor and yields a universal expression by defining La as the square-root of the fragment area. The relationship between observed diffraction peak positions and unit cell parameters is also discussed.
[Display omitted]</description><subject>Diffraction</subject><subject>Diffraction patterns</subject><subject>Empirical equations</subject><subject>Fragments</subject><subject>Graphene</subject><subject>Molecules</subject><subject>Nonlinear equations</subject><subject>Scattering</subject><subject>Shape factor</subject><subject>Studies</subject><subject>Unit cell</subject><issn>0008-6223</issn><issn>1873-3891</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1Lw0AQhhdRsFb_gYeA58TZj2Q3F0GKX1DwoD0v2-1sm9Am7Wxa8N-7JZ49DQPv8w7zMHbPoeDAq8e28I6WfVcIEFCAKKBSF2zCjZa5NDW_ZBMAMHklhLxmNzG2aVWGqwkTi645IUW3zb78BomQMjwc3dD0XRZ6ytbk9hvsMAvk1jvshnjLroLbRrz7m1O2eH35nr3n88-3j9nzPPfSwJAbHVTNJYI2qtIAS5ChUsaHAKXRxslSKVFXuAy6dhrLYEA6CKUwulxJAXLKHsbePfWHI8bBtv2RunTSioSmiKlESqkx5amPkTDYPTU7Rz-Wgz3bsa0d7dizHQvCJjsJexoxTB-cGiQbfYOdx1VD6Ae76pv_C34Bia1tdA</recordid><startdate>202006</startdate><enddate>202006</enddate><creator>Lim, Daniel J.</creator><creator>Marks, Nigel A.</creator><creator>Rowles, Matthew R.</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>8FD</scope><scope>JG9</scope></search><sort><creationdate>202006</creationdate><title>Universal Scherrer equation for graphene fragments</title><author>Lim, Daniel J. ; Marks, Nigel A. ; Rowles, Matthew R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c380t-87f4913e07846700b03f648cff05878a3544296ebf79a7e5f803a0f52875d3203</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Diffraction</topic><topic>Diffraction patterns</topic><topic>Empirical equations</topic><topic>Fragments</topic><topic>Graphene</topic><topic>Molecules</topic><topic>Nonlinear equations</topic><topic>Scattering</topic><topic>Shape factor</topic><topic>Studies</topic><topic>Unit cell</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lim, Daniel J.</creatorcontrib><creatorcontrib>Marks, Nigel A.</creatorcontrib><creatorcontrib>Rowles, Matthew R.</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><jtitle>Carbon (New York)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lim, Daniel J.</au><au>Marks, Nigel A.</au><au>Rowles, Matthew R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Universal Scherrer equation for graphene fragments</atitle><jtitle>Carbon (New York)</jtitle><date>2020-06</date><risdate>2020</risdate><volume>162</volume><spage>475</spage><epage>480</epage><pages>475-480</pages><issn>0008-6223</issn><eissn>1873-3891</eissn><abstract>Graphene fragments spanning a wide range of size and shape were studied computationally using the Debye scattering equation. The calculated diffraction patterns were analysed using the Scherrer equation to infer the fragment size, La. Comparison with the known fragment sizes reveals a strong affine relationship between La and the Scherrer quantity λ/(Bcosθ). To preserve this relationship, we propose modifying the Scherrer equation to include an empirical additive constant. Our approach solves the well-known problem of size-dependence in the shape factor and yields a universal expression by defining La as the square-root of the fragment area. The relationship between observed diffraction peak positions and unit cell parameters is also discussed.
[Display omitted]</abstract><cop>New York</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.carbon.2020.02.064</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0008-6223 |
| ispartof | Carbon (New York), 2020-06, Vol.162, p.475-480 |
| issn | 0008-6223 1873-3891 |
| language | eng |
| recordid | cdi_proquest_journals_2442320862 |
| source | Elsevier ScienceDirect Journals |
| subjects | Diffraction Diffraction patterns Empirical equations Fragments Graphene Molecules Nonlinear equations Scattering Shape factor Studies Unit cell |
| title | Universal Scherrer equation for graphene fragments |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-07T18%3A20%3A22IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Universal%20Scherrer%20equation%20for%20graphene%20fragments&rft.jtitle=Carbon%20(New%20York)&rft.au=Lim,%20Daniel%20J.&rft.date=2020-06&rft.volume=162&rft.spage=475&rft.epage=480&rft.pages=475-480&rft.issn=0008-6223&rft.eissn=1873-3891&rft_id=info:doi/10.1016/j.carbon.2020.02.064&rft_dat=%3Cproquest_cross%3E2442320862%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2442320862&rft_id=info:pmid/&rft_els_id=S0008622320302104&rfr_iscdi=true |