David M. Kelly , Eric E. Fullerton , Jacobo Santa-Maria , Ivan K. Schuller
{"title":"具有累积粗糙度的多层材料x射线反射率的简单封闭表达式","authors":"David M. Kelly , Eric E. Fullerton , Jacobo Santa-Maria , Ivan K. Schuller","doi":"10.1016/0956-716X(95)00391-8","DOIUrl":null,"url":null,"abstract":"<div><p>We present a simple closed-form expression for the reflectivity from a multilayer which includes the effects of absorption, refraction, surface and substrate reflections but neglects dynamical effects. This expression reproduces the exact dynamical calculation except for the regions near the critical angle and for intense Bragg reflections. The expression is generalized to include cumulative interface roughness which follows a <span><math><mtext>t</mtext><msup><mi></mi><mn><mtext>1</mtext><mtext>2</mtext></mn></msup></math></span> power-law growth.</p></div>","PeriodicalId":101150,"journal":{"name":"Scripta Metallurgica et Materialia","volume":"33 10","pages":"Pages 1603-1608"},"PeriodicalIF":0.0000,"publicationDate":"1995-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0956-716X(95)00391-8","citationCount":"23","resultStr":"{\"title\":\"A simple closed-form expression for the X-ray reflectivity from multilayers with cumulative roughness\",\"authors\":\"David M. Kelly , Eric E. Fullerton , Jacobo Santa-Maria , Ivan K. Schuller\",\"doi\":\"10.1016/0956-716X(95)00391-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a simple closed-form expression for the reflectivity from a multilayer which includes the effects of absorption, refraction, surface and substrate reflections but neglects dynamical effects. This expression reproduces the exact dynamical calculation except for the regions near the critical angle and for intense Bragg reflections. The expression is generalized to include cumulative interface roughness which follows a <span><math><mtext>t</mtext><msup><mi></mi><mn><mtext>1</mtext><mtext>2</mtext></mn></msup></math></span> power-law growth.</p></div>\",\"PeriodicalId\":101150,\"journal\":{\"name\":\"Scripta Metallurgica et Materialia\",\"volume\":\"33 10\",\"pages\":\"Pages 1603-1608\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1995-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0956-716X(95)00391-8\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Scripta Metallurgica et Materialia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0956716X95003918\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scripta Metallurgica et Materialia","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0956716X95003918","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A simple closed-form expression for the X-ray reflectivity from multilayers with cumulative roughness
We present a simple closed-form expression for the reflectivity from a multilayer which includes the effects of absorption, refraction, surface and substrate reflections but neglects dynamical effects. This expression reproduces the exact dynamical calculation except for the regions near the critical angle and for intense Bragg reflections. The expression is generalized to include cumulative interface roughness which follows a power-law growth.