Recent X-ray diffraction theory for the structural analysis of carbon material and the next-generation perspective

Abstract

The diffraction profile of carbon materials has been quantitavely analyzed by many researchers for more than fifty years and the structural parameters such as lattice constants, crystallite sizes, graphitizability and Debye-Waller factor have been proposed together with their estimation method. In the present article, the conventional method ever proposed are reviewed and the next-generation analytical theory of carbon structure will be overviewed. KEYWORDS : X-ray diffraction, Fourier transform, Least square method, Scattering intensity 1.•@ •• OE¾ 'Y'f •Þ-¿ ‚ÌX•ü ‰ñ •Üƒvƒ•ƒt ƒ@ ƒCƒ‹‚Ì 'è-Ê "I ‚ÈŽae‚舵 ‚¢ ‚Í, Warren, Hirsch, Diamond, Franklin‚ç ‚É‚ae‚Á‚Ä"ñ•í ‚ÉOEà ‚-‚©‚ç•s ‚í ‚ê ‚Ä‚«‚½1)-9)•B ‚»‚Ì ‰ß 'ö ‚Å,Žå‚ÉŠiŽq'è •"ao, Co,OE‹ •»ŽqƒTƒC ƒYLa, Lc,•• ‰" ‰» "xP1,Ši Žq˜c,Debye-WallerˆöŽq,'I 'ð"zOEü "x‚È ‚Ç‚Ì •\ '¢ƒpƒ‰ ƒ••[ ƒ^‚ÉŠÖ‚µ‚Ä ‹c˜_‹c˜_ ‚³‚ê,"¯ Žž‚É‚»‚ê ‚ç‚ð'è-Ê "I ‚Ɉµ ‚¤‚½‚ß‚Ì Žè-@ ‚à'ñˆÄ‚³ ‚ê ‚½•B"-Žž‚Í,•¢ "ï ‚ð"º ‚Á‚½‚Å‚ ‚ë ‚¤•" 'l •ˆ-•‚àOE» •Ý‚Ì ƒp•[ ƒ\ƒi ƒ‹ƒRƒ"ƒsƒ… •[ ƒ^‚Å‚Í •"•b'ö "x‚Å‚ae‚蕳 Šm ‚ÉOEv ŽZ‚· ‚é ‚±‚AE ‚ª ‚Å‚«‚邾‚¯ ‚Å‚È‚-,‚± ‚ê ‚Ü‚Å‚É'ñˆÄ‚³ ‚ꂽ‰ð •Í •û-@ ‚Ì "K-p OEÀ ŠE‚È‚Ç‚ÉŠÖ‚µ‚Ä‚à‹c˜_ ‚Å‚«‚é ‚ae‚¤‚É‚È‚Á‚Ä‚«‚Ä‚¢ ‚é•B‚±‚±‚Å‚Í,'Y 'f ‚Ì •Å‚àŠî-{"I ‚È•\'¢ ƒpƒ‰ ƒ••[ ƒ^‚Å‚ ‚éŠiŽq'è •" ‚AE OE‹ •»ŽqƒTƒC ƒY ‚¨‚ae‚Ñ‚»‚Ì‚¨‚ae‚Ñ‚»‚Ì •ª •z ‚ðOE© •Ï ‚à‚é•û-@ ‚É•Å"_‚ð•i ‚è, ‰ß ‹Ž‚É'ñˆÄ‚³ ‚ê ‚½Žè-@ ‚ð•Ð‰î ‚· ‚é ‚± ‚AE ‚É‚· ‚é•B‚Ü‚½‚±‚ê ‚ç‚Ì ‹Z •p ‚ðƒx•[ ƒX‚É,OE» •s ‚Ì ƒp•[ ƒ\ƒiƒ‹ƒRƒ"ƒsƒ… •[ ƒ^‹Z•p ‚ð"±"ü‚· ‚é ‚± ‚AE ‚É‚ae‚Á‚ĉ "\ ‚AE ‚È‚é‚Å‚ ‚ë ‚¤ŽŸ •¢'ã ‚Ì •\ '¢‰ð •Í-• ˜_ ‚ɂ‚¢‚Ä "W-]‚· ‚é•B 2.•@ ‰ð •Í •û-@ Še˜_ 2.1•@ Šw •U-@10)-12) 'Y'f ‚Ì •\'¢ ƒpƒ‰ ƒ••[ ƒ^‚Ì ' †‚Å‚à,•Å ‚àŠî-{‚AE ‚È‚é ‚à‚Ì ‚Í ŠiŽq'è •" ‚AE OE‹•»ŽqƒTƒC ƒY ‚Å‚ ‚é•B‚±‚ê ‚ç‚Ì ƒpƒ‰ ƒ••[ ƒ^‚ð‹• ‚ß ‚é•û-@ ‚AE ‚µ‚Ä,"ú-{Šw •p•U‹»‰ï 'ae117ˆÏˆõ‰ïae117ˆÏˆõ‰ï ‚É‚ae‚Á‚Ä1963"N ‚É• §'è ‚³ ‚ꂽ •u •l '¢•• ‰" ‚Ì ŠiŽq'è •" ‚¨‚ae‚Ñ‚¨‚ae‚Ñ OE‹•»Žq‚Ì 'å ‚«‚³ 'ª 'è •û-@ •v('Ê•Ì,Šw •U-@)‚ª‚ ‚é10)•B ‚±‚Ì •û-@ ‚Í,2003"N‚É‹ß"N‚Ì ‰ñ •Ü'• 'u‚Ì ‹Z•p "I ‚ȉü-Ç,X•ü‰ñ •Ü-• ˜_ ‚Ì •i •à ‚È‚Ç‚ð•l-¶ ‚µ‚ĉü 'ù ‚³ ‚ê ‚½11),12)•B-{•e ‚ÅŽae‚è•ã ‚° ‚é‚ae‚è‚à,•Ú ‚µ‚¢‰ð •à ‚ðŽQ •l ‚É‚³‚ê ‚é ‚Ù‚¤‚ª ‚ae‚¢‚AE Žv‚í ‚ê ‚é‚Ì ‚Å,• ¶OE£ ‚ð•Ð‰î ‚· ‚é ‚É‚AE ‚Ç‚ß‚Ä‚¨‚‚Ç‚ß‚Ä‚¨‚-‚±‚AE ‚É‚· ‚é10)-12)•B 2.2•@-Ô-ʃTƒC ƒY •ª •z‰ð •Í-@(Diamond‚Ì •û-@) 2.2.1•@OE´-@OE´-• ‚±‚Ì •û-@ ‚Í,•Î 'Y‚â ƒsƒbƒ`‚Ì ‚ae‚¤‚È"äŠr "I-Ô-ʃTƒC ƒY ‚Ì •¬‚³ ‚È ŽŽ-¿ ' †‚Ì 'Y'f-Ô-Ê‚Ì •½‹Ï ƒTƒC ƒY ‚¨‚ae‚Ñ‚»‚Ì‚¨‚ae‚Ñ‚»‚Ì •ª •z ‚ð•] ‰¿ ‚· ‚邽‚ß ‚ÉDiamond‚É‚ae‚Á‚Ä1956"N ‚É'ñˆÄ‚³ ‚ê ‚½•û-@ ‚Å‚ ‚é5)-8)•B •\ '¢ ‚ª-¢'m‚Ì 'Y'f ŽŽ-¿ ‚Í,Fig.1‚É Ž¦‚· ‚ae‚¤‚È•\ '¢ ‚ª Šù'm‚Ì •" Ží-Þ ‚Ì ƒ‚ƒfƒ‹'Y'f-Ô-Ê‚Ì •W • ‡'Ì ‚Å‚ ‚é ‚AE ‚Ì ‰¼ 'è ‚Ì ‰º ‚É,-¢'mŽŽ-¿ ‚ÌX•ü ‰ñ •Üƒvƒ•ƒt ƒ@ ƒCƒ‹‚É‚¨‚¯ƒCƒ‹‚É‚¨‚¯ ‚é11ƒo ƒ"ƒh‚Ì ŽÀ 'ª ‹-"xIos‚ðƒ‚ƒfƒ‹-Ô-Ê ‚Ì-• ˜_X•ü ŽU-• ‹-"xBi (S)‚É•d-Ê •ª-¦Wi‚ð •ae‚ ¶‚½‚à‚Ì ‚̘a‚̘a ‚Å•\ OE»‚µ,•Å•¬"ñ•ae-@ ‚É‚ae‚Á‚ÄŠe•X‚Ì •d-Ê •ª-¦ ‚ð‹• ‚ß,-Ô-ʃTƒC ƒY ‚Ì •ª •z ‚ð•] ‰¿ ‚· ‚é•û-@ ‚Å‚ ‚é•B‚· ‚È‚í ‚¿,OEë •· ‚ðv(S)‚AE ‚· ‚é ‚AE,‰ñ •Ü Fig.