surface surface general process involving motion molecules atomic clusters solid material surfaces process generally thought terms particles jumping adjacent sites surface figure bulk motion typically promoted process rates increasing increasing temperature systems display behavior conventional model nearest neighbor jumps particularly interesting example unconventional mechanism hydrogen shown clean metal surfaces quantum effect tools surface mechanisms rates important field scanning principle process occur variety materials experiments performed metal surfaces experimental constraints studies surface limited melting point substrate discovered processes place higher temperatures surface rates mechanisms affected variety factors including strength surface bond orientation surface attraction surface species chemical potential important concept surface phase formation growth topics surface science principles surface critical chemical production industries real world applications relying heavily phenomena include integrated circuits electronic devices silver photographic film surface thought terms residing sites moving adjacent nearest neighbor sites jumping process jump rate characterized attempt frequency factor probability attempt resulting successful jump attempt frequency typically taken simply frequency factor factor dependent temperature potential energy barrier equation describes relationship formula described jump rate temperature constant smaller energy occur processes dominate importantly equation tells strongly jump rate varies temperature manner takes place dependent relationship given factor factor approaches unity meaningful barrier case known mobile relatively uncommon observed systems phenomena described article assumed case possible extract plot versus cases mechanism present relative distribution different processes change temperature random walk statistics describe mean squared displacement species terms number jumps distance jump number successful jumps simply multiplied time allowed basic model nearest neighbor jumps considered corresponds nearest neighbor sites root mean squared displacement goes formula given case channel regimes different general schemes place chemical differ level coverage surface mass transfer differ nature environment refer systems experience relatively environment chemical mass transfer strongly affected surroundings describes motion individual surface relatively low coverage levels low levels particle interaction low particle considered independently single figure nice example chemical describes process higher level coverage effects attraction important interactions serve alter mobility crude way figure serves interact higher coverage levels choice right adjacent block sites occurs uniform surface lacking steps single terrace traps sources present regime studied field terrace sharp sample tip case clean terrace process influenced non near edges terrace mass transfer takes place case sources traps steps present instead dependent jump potential barrier regime dependent formation energy mobile exact nature environment plays role rate formation energy different type surface feature described terrace model takes form difference rates mechanisms surface given material given material miller index plane display unique phenomena close packed surfaces tend higher rates open faces material directional refers difference mechanism rate particular direction given plane differences result surface rectangular presence steps surface dramatic examples directional surfaces channel faster channel mechanisms occur variety mechanisms manner important movement temperature dependence overall mobility surface species parameters following summary important processes jumping basic mechanism model reside sites surface motion occurs successive jumps adjacent sites number depends nature surface figures display undergoing process studies shown presence transition states sites possible temporarily reside atomic exchange involves exchange adjacent surface shown figure atomic exchange event taken place surface surface displaced process place self unclear theoretical point view atomic exchange mechanism predominant systems current theory points multiple possibilities including surface stresses surface increased stability intermediate fact involved maintain high levels coordination process physical manifestation quantum effect involving particles barriers occur case low particle mass low observed case hydrogen copper surfaces phenomenon unique regime mechanism dominates rate nearly temperature independent vacancy occur predominant method surface high coverage levels approaching complete coverage process akin manner pieces slide sliding puzzle difficult directly observe vacancy typically high rates low vacancy concentration figure shows basic theme mechanism albeit manner recent theoretical work experimental work performed late 1970s brought light remarkable variety surface phenomena regard mechanisms following summary notable phenomena long jumps consist displacement non nearest neighbor site include double triple longer jumps direction nearest neighbor jump travel entirely different directions shown figure predicted theory exist different systems shown experiment place temperatures low melting temperature cases data indicate long jumps dominating process single jumps elevated temperatures phenomena variable jump lengths expressed different characteristic atomic displacement time figure rebound jumps shown experiment place certain systems motion result net displacement involved experimental evidence rebound jumps comes statistical interpretation atomic rebound jump shown figure figure slightly misleading rebound jumps shown place case surface particular face cross channel occur case surfaces typically channel dominates lower energy barrier process certain cases cross channel shown occur taking place manner similar shown figure intermediate position lead variety final surface long range atomic exchange process involving surface normal atomic exchange mechanism instead nearest neighbor distance initial emerges shown figure process observed molecular dynamics confirmed spite long range atomic exchange variety exotic mechanisms anticipated contribute substantially temperatures currently high direct observation cluster cluster involves motion atomic clusters ranging size islands containing hundreds motion cluster occur displacement individual sections cluster entire cluster moving processes involve change cluster center mass individual mechanisms involve movement time edge involves movement edge sites shown figure mobile maintains proximity cluster process involves cluster terrace accompanied terrace cluster leading change cluster center mass figure appears indicate cluster fact different gas similar edge actually moves atop cluster settling different location starting position displacement refers process involving motion time moving free nearest neighbor sites mechanisms involve movement sections cluster entire cluster occurs adjacent sub units cluster row row fashion displacement shown figure process begins followed essentially displacement basis refers motion entire cluster figure snake like movement involving motion cluster sub units figure displacement sub unit cluster figure size dependence rate cluster strong dependence size cluster larger cluster size generally corresponding slower universal trend shown systems rate takes periodic tendency larger clusters faster smaller surface surface critically important concept reaction rates dictated ability find catalyst surface increased temperature molecules molecular fragments clusters tend greater mobility equation increased temperature lifetime decreases factor large species overcome barrier figure reaction aside increased rates decreased lifetime increased temperature cases decrease overall rate reaction experimental surface studied variety techniques including direct indirect observations experimental techniques proved useful area study field scanning displacement clusters time possible extract useful information manner relevant species rate related information order study surface scale unfortunately necessary perform studies clean surfaces ultra high vacuum conditions presence small amounts gas case imaging gas field experiments cited works review surface science introduction isbn theory applications inc isbn
Surface diffusion