1,193 248 2MB
Pages 385 Page size 432 x 576 pts Year 2007
Phase Transformations of Elements Under High Pressure E. Yu Tonkov E. G. Ponyatovsky
CRC PR E S S Copyright © 2005 CRC Press, BocaLLC Raton London New York Washington, D.C.
3367 disclaimer.fm Page 1 Tuesday, October 5, 2004 9:48 AM
Library of Congress Cataloging-in-Publication Data Tonkov, E. Yu. Phase transformations of elements under high pressure / E. Yu Tonkov, E.G. Ponyatovsky. p. cm. — (Advances in metallic alloys ; 4) Includes bibliographical references and index. ISBN 0-8493-3367-9 (alk. paper) 1. Phase rule and equilibrium. 2. Phase diagrams. 3. High pressure (Science) I. Ponyatovsky, E. G. II. Title. III. Series. QD503.T63 2004 541'.363--dc22
2004056122
This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.
Visit the CRC Press Web site at www.crcpress.com © 2005 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-3367-9 Library of Congress Card Number 2004056122 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper
Copyright © 2005 CRC Press, LLC
3UHIDFH 7KHEHKDYLRURIPDWWHUXQGHUKLJKDQGXOWUDKLJKSUHVVXUHVLVRILQWHUHVWIRUUHVHDUFK ZRUNHUVDFWLYHLQVROLGVWDWHSK\VLFVJHRSK\VLFVFKHPLVWU\DVWURSK\VLFVPDWHULDOV VFLHQFH DQG PHWDOOXUJ\ $SSOLFDWLRQ RI GLDPRQG DQYLOFHOO WHFKQRORJ\ LQ FRPELQDWLRQ ZLWK ODVHU KHDWLQJ PDUNHGO\ KDV H[WHQGHG WKH UDQJH RI KLJKSUHVVXUH UHVHDUFKWR±*3D*3D DWP DQGIURPORZWHPSHUDWXUHVWR .7KHILUVWGHWDLOHGUHYLHZRQSKDVHGLDJUDPVRIWKHHOHPHQWVLQWKHUDQJHRI± *3DZDVZULWWHQLQ7RQNRY(±@XSWR*3D>@XSWR*3D>@XSWR*3D XS WR *3D E\ YLVXDO REVHUYDWLRQ RI WKH FKDQJH LQ VKDSH RI WKH VDPSOH XSRQ PHOWLQJ >±@ E\ FDOFXODWLRQ >@ 7KH PHOWLQJ FXUYH KDV DQ LQLWLDO VORSH RI .*3D1DPHOWVDWR&DQG*3DDWR&DQG*3D DQGDWaR& DQG*3D>@6WUXFWXUHRIOLTXLG1DZDVVWXGLHGXSWR*3D>@$QXPEHURI WKHRULVWV FDOFXODWHG WKH PHOWLQJ FXUYH XVLQJ DQ DFFXUDWH PRGHOV RI WKH VROLG DQG OLTXLG SKDVHV >±@ 7KHLU FDOFXODWLRQV KDYH D VHPLTXDQWLWDWLYH DJUHHPHQW ZLWK DQH[SHULPHQW7KHORZWHPSHUDWXUHVWXGLHVZHUHGHWHUPLQHGLQ>
Copyright © 2005 CRC Press, LLC
6RGLXP
@7KHEFF→KFSSKDVHWUDQVLWLRQOLQHKDVDQHJDWLYHG7G3DQGDW.LQWHUFHSWVDW 3 −*3D 6WDWLF FRPSUHVVLRQ RI WKH VROLG VWDWH VKRZQ QR SKDVH WUDQVLWLRQV XS WR *3DDQGURRPWHPSHUDWXUH>@1DKDVEHHQVWXGLHGDWR&E\;UD\GLIIUDFWLRQXS WRa*3D>@DQGE\DQJOHGLVSHUVLYH;UD\GLIIUDFWLRQXSWR*3D>@7KH EFF±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±.>@XSWR*3D>@ E\ 105 VWXG\ XS WR *3D >@ E\ WKH HTXDWLRQ RI VWDWH >@ E\ FDOFXODWLRQ>±@DQGLQ>@ 7KHSKDVHGLDJUDPRIVRGLXPLVVKRZQLQ)LJXUH
7. /LT
,EFF
,,KFS
3*3D
)LJXUH7KHSKDVHGLDJUDPRIVRGLXP
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
5HIHUHQFHV %ULGJPDQ3: &KDQJHRISKDVHXQGHUSUHVVXUH,,1HZPHOWLQJFXUYHVZLWKD JHQHUDOWKHUPRG\QDPLFGLVFXVVLRQRIPHOWLQJ3K\V5HY±± %ULGJPDQ3: 3UHVVXUHYROXPHUHODWLRQVIRUVHYHQWHHQHOHPHQWVWRDWP 3URF$P$FDG$UWV6FL± %ULGJPDQ 3 : 7KH FRPSUHVVLRQ RQVXEVWDQFHVWRDWP 3URF$P $FDG$UWV6FL± 3RQ\DWRYVN\(* 0HOWLQJFXUYHVRIOLWKLXPDQGVRGLXPXSWRDWP)L] 7YHUG7HOD± 1HZWRQ5&-D\DUDPDQ$DQG.HQQHG\*& 7KHIXVLRQFXUYHVRIWKHDONDOL PHWDOVXSWRNEDU-*HRSK\V5HV± 'XJGDOH - DQG *XJDQ ' (IIHFW RI SUHVVXUH RQ WKH HOHFWULFDO UHVLVWDQFH RI /L 1DDQG.DWORZWHPSHUDWXUHV3URF5R\DO6RF$± 6WDJHU 5 $ DQG 'ULFNDPHU + * (IIHFW RI WHPSHUDWXUH DQG SUHVVXUH RQ WKH UHVLVWDQFHRIIRXUDONDOLPHWDOV3K\V5HY± $QGHUVRQ ' 2WW 5 - % *RDWHV - 5 DQG +DOO + 7 +LJK SUHVVXUH SKDVH VWXGLHVRQVRGLXP±SRWDVVLXPDOOR\V-&KHP3K\V± 0DNDUHQNR,11LNRODHQNR$0DQG6WLVKRY60 7KHWKHUPRG\QDPLFVRI PHOWLQJ IRU DONDOL PHWDOV ,Q 3URF $,5$37 ,QW &RQI +LJK3UHVVXUH 6FLHQFH DQG 7HFKQRORJ\%RXOGHU HGV.'7LPPHUKDXVHWDOSS±1@ DQG XSWR*3D>@7KHPHOWLQJDQGWKH EHKDYLRURIOLTXLG.ZHUHFDOFXODWHG>±@7KHIXVLRQFXUYHKDVDQ LQLWLDO VORSH .*3D WKH WULSOH SRLQW EHWZHHQ WKH SKDVHV , ,, DQG OLTXLG ZDV GHWHUPLQHGDW*3DDQGR&>@7KHKLJKSUHVVXUHPRGLILFDWLRQ.,,PHOWVDW *3DDQGR&>@ 3KDVHWUDQVIRUPDWLRQVLQDVROLGVWDWHZHUHVWXGLHGDWURRPWHPSHUDWXUHE\ ;UD\ GLIIUDFWLRQ XS WR *3D >@ XS WR *3D >@ XS WR *3D >@ E\ RSWLFDO PHDVXUHPHQWV XS WR *3D >@ DQG E\ HOHFWURUHVLVWDQFH VWXG\ XS WR *3DIURP±WRR&>@7KHEHKDYLRURISRWDVVLXPZDVVWXGLHGH[SHULPHQWDOO\ >±@DQGDOVRE\FDOFXODWLRQ>±±@7KH,±,,SKDVH WUDQVLWLRQZDVREVHUYHGDWDERXW*3DDQGR&ZLWKFKDQJHLQFRORUIURPDVLOYHU WRDJROGDQGYROXPHUHGXFWLRQRI>@7KHSUHVVXUHLQGXFHGSKDVH,, KDVDIFFVWUXFWXUHZLWKD QPDW*3D7KH,,±,,,SKDVHWUDQVLWLRQZDV GHWHFWHGDWDERXW*3DDQGR&>@ 7. /LT
,EFF
,,IFF
,,,EFW
3*3D
)LJXUH7KHSKDVHGLDJUDPRISRWDVVLXP
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
0RGLILFDWLRQ,,,FU\VWDOOL]HVLQDERG\FHQWHUHGWHWUDJRQDOVWUXFWXUHZLWK= WKH XQLWFHOOGLPHQVLRQVDUHD QPF QPFD DW*3D>@ 3KDVH ,,, LV VWDEOH DW OHDVW WR *3D 7KH SKDVH GLDJUDP XS WR *3D ZDV SUHVHQWHGLQ>@ 7KHSKDVHGLDJUDPRISRWDVVLXPLVVKRZQLQ)LJXUH 5HIHUHQFHV %ULGJPDQ3: &KDQJHRISKDVHXQGHUSUHVVXUH,7KHSKDVHGLDJUDPRIHOHYHQ VXEVWDQFHVZLWKHVSHFLDOUHIHUHQFHWRWKHPHOWLQJFXUYH3K\V5HY± 3RQ\DWRYVN\ ( * 7KH PHOWLQJ WHPSHUDWXUH RI SRWDVVLXP XQGHU SUHVVXUH )L] 0HW0HWDOORYHG± 1HZWRQ5&-D\DUDPDQ$DQG.HQQHG\*& 7KHIXVLRQFXUYHVRIWKHDONDOL PHWDOVXSWRNEDU-*HRSK\V5HV± 0DNDUHQNR , 1 1LNRODHQNR $ 1 DQG 6WLVKRY 6 0 7KHUPRG\QDPLFV RI IXVLRQIRUDONDOLPHWDOV=K(NVS7HRU)L]± 0DNDUHQNR,11LNRODHQNR$1DQG6WLVKRY60 7KHWKHUPRG\QDPLFVRI PHOWLQJ IRU DONDOL PHWDOV ,Q 3URF ,QW &RQI $,5$37 +LJK3UHVVXUH 6FLHQFH DQG 7HFKQRORJ\ %RXOGHU HGV . ' 7LPPHUKDXV HW DO SS ± 1@XSWR*3D>@E\ HOHFWURUHVLVWDQFH XS WR *3D >@ XS WR *3D >±@ LQ >@ E\ FDOFXODWLRQ>@6WUXFWXUHRIOLTXLG5EZDVVWXGLHGXSWR*3D>@DQG LQ >@ 7KH IXVLRQ FXUYH RI 5E , KDV DQ LQLWLDO VORSH RI .*3D ZKLFK VKRZV D WHPSHUDWXUH PD[LPXP DW DERXW *3D DQG R& 7KH ,±,,±/LTXLG WULSOH SRLQW ZDV GHWHUPLQHG DW ± *3D DQG ±R& >@ 7KH PHOWLQJ FXUYH RI WKH KLJK SUHVVXUHSKDVH,,VKRZVDVHFRQGWHPSHUDWXUHPD[LPXPDWDERXW*3D>@7KH ,,±,,,±/LTXLGWULSOHSRLQWZDVGHWHFWHGDWa*3DDQGR&ZLWKDSRVLWLYHVORSH RIPHOWLQJFXUYHIRUSKDVH,9 6WDWLF FRPSUHVVLRQ LQ WKH VROLG VWDWH DW URRP WHPSHUDWXUH ZDV VWXGLHG E\ HOHFWURUHVLVWDQFH>±@E\;UD\GLIIUDFWLRQXSWR*3D>@XSWR*3D
Copyright © 2005 CRC Press, LLC
5XELGLXP
>@ LQ > @ E\ LQIUDUHG VSHFWUD XS WR *3D >@ E\ FDOFXODWLRQ >±±@ DQG LQ >@ 7KH ,±,, SKDVH WUDQVLWLRQ ZDV REVHUYHGDW*3DDQGR&ZKHUHWKHSUHVVXUHLQGXFHGSKDVH,,KDVDIFFVWUXFWXUH 7KH IROORZLQJ SKDVH WUDQVIRUPDWLRQV ZHUH REVHUYHG DW R& ,,±,,, DW ± *3D ,,,±,9DW*3D,9±9DW±*3DDQG9±9,DWDERXW*3DZLWKDK\VWHUHVLV IURP WR *3D 7KH VWUXFWXUHV RI SKDVHV ,,, ,9 9 DQG 9, KDYH QRW EHHQ LGHQWLILHGLQ>@ 0RGLILFDWLRQ ,,, ZDV LGHQWLILHG DW ± *3D DQG URRP WHPSHUDWXUH E\ TXDVLVLQJOH FU\VWDO ;UD\ VWXG\ >@ ,W KDV DQ RUWKRUKRPELF VWUXFWXUH ZLWK VSDFH JURXS & = DQG ODWWLFH FRQVWDQWV DUH D QP E QP F QP7KHSKDVHWUDQVLWLRQ,,±,,,ZDVDFFRPSDQLHGE\∆9 DQG,,,±,9E\ ∆9 >@3KDVH,9KDVDFRPSOH[WHWUDJRQDOVWUXFWXUHZLWKVSDFHJURXS,PFP DQG= >@,Q>@WKHSKDVH,9±*3DDWURRPWHPSHUDWXUH LVIRXQGWR KDYH DQ LQFRPPHQVXUDWH FRPSRVLWH VWUXFWXUH FRPSULVLQJ D WHWUDJRQDO KRVW IUDPHZRUN DQG D VLPSOH ERG\FHQWHUHG WHWUDJRQDO JXHVW 7KH UDWLR RI WKH FD[LV ODWWLFHSDUDPHWHUVLVVWURQJO\SUHVVXUHGHSHQGHQWDQGDSSURDFKHVWKHFRPPHQVXUDWH YDOXHRIDWWKHWUDQVLWLRQWRWKHSKDVH97KHSKDVH,9KDVODWWLFHFRQVWDQWVDK DJ QPFK QPFJ QP>@ 7.
/LT
,,IFF
,EFF
,,,
3*3D
)LJXUH7KHSKDVHGLDJUDPRIUXELGLXP
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
3KDVH9DGRSWVWKHWHWUDJRQDOVWUXFWXUH&V,9W\SH ZLWKVSDFHJURXS,DPGDQG = >@3KDVHWUDQVLWLRQ9±9,ZDVDFFRPSDQLHGE\∆9 DWDERXW*3D DQG URRP WHPSHUDWXUH 3KDVH 9, KDV DQ RUWKRUKRPELF VWUXFWXUH ZLWK VSDFH JURXS &PFD= DQGODWWLFHFRQVWDQWVD QPE QPF QP DW*3D>@ 6XSHUFRQGXFWLYLW\ RI 5E ZDV VWXGLHG LQ >@ 5E WUDQVIRUPHG WRDVXSHUFRQGXFWLQJVWDWHDW7F .DQG*3DDW7F .DQG*3D >@ 7KHSKDVHGLDJUDPRIUXELGLXPLVVKRZQLQ)LJXUH 5HIHUHQFHV %ULGJPDQ 3: 9DULRXVSK\VLFDOSURSHUWLHVRIUXELGLXPDQGFDHVLXPDQGWKH UHVLVWDQFHRISRWDVVLXPXQGHUSUHVVXUH3URF$P$FDG$UWV6FL± 1HZWRQ 5 & -D\DUDPDQ $ DQG .HQQHG\ * & 7KH IXVLRQ FXUYHV RI DONDOL PHWDOVXSWRNEDU-*HRSK\V5HV± /XHGHPDQQ+'DQG.HQQHG\*& 0HOWLQJFXUYHVRI/L1D.DQG5EWR NEDU-*HRSK\V5HV± 9HUHVKFKDJLQ/)6HPHUFKDQ$$.X]LQ11DQG6DGNRY@ XS WR *3D >@ XS WR *3D >@ DQG LQ >@ 7KH PHOWLQJ FXUYH LV XQLTXH LW VKRZV WZR WHPSHUDWXUH PD[LPD 7KH ILUVW PD[LPXP IRU SKDVH , ZDV REVHUYHG DW R& DQG *3D DQG WKH VHFRQG PD[LPXP IRU SKDVH ,, DW R& DQG *3D 7KH VWUXFWXUDO FKDQJHV LQ OLTXLG VWDWH ZHUH GHWHUPLQHG XS WR *3D >@7KHIXVLRQFXUYHZDVFDOFXODWHGLQ>±@ 7KHPHOWLQJFXUYHRI&V,9ZDVREVHUYHGDWR&DQG*3D>@DQGDWR& DQG *3D ZLWK G7G3 .*3D DW ± *3D >@ 7ZR FKDQJHV LQ OLTXLG VWDWH ZHUH GHWHUPLQHG DW DERXW *3D DQG ± *3D >@ 7KH OLTXLG FDQ EHFRPHPRUHGHQVHWKDQWKHVROLGLQWKHUHJLRQRIWKHWUDQVIRUPDWLRQ,,±,,,DWDERXW± *3D 7KH KLJKWHPSHUDWXUH SKDVH GLDJUDP ZDV VWXGLHG LQ >@ 7KH IROORZLQJ WULSOHSRLQWVZHUHGHWHFWHG,±,,±/LTXLGDW*3DDQGR&,,±,,,±/LTXLGDW *3DDQGR&DQG,,,±,9±/LTXLGDW*3DDQGR& 3KDVH WUDQVLWLRQV LQ &V DW URRP WHPSHUDWXUH DUH XVHG DV FDOLEUDQWV RI SUHVVXUH VFDOH >±@ 7KH ,±,, SKDVH WUDQVIRUPDWLRQ ZDV GHWHUPLQHGDW*3DDQGR&DQGDW*3DDQG±R&>@E\FDOFXODWLRQ >@ 3KDVH WUDQVLWLRQV QHDU *3D ZHUH LQYHVWLJDWHG E\ YROXPHWULF HOHFWURUHVLVWDQFHDQGVWUXFWXUDOVWXGLHV>±±@ $WURRPWHPSHUDWXUHWKH,,±,,,SKDVHWUDQVLWLRQZDVREVHUYHGDW*3D DQG WKH ,,,±,9 SKDVH WUDQVLWLRQ DW *3D 6ORSHV ZLWKLQ WKH WHPSHUDWXUH UDQJH EHWZHHQ WKH WULSOH SRLQWV ,,±,,,±/LTXLG ,,,±,9±/LTXLG DQG ,,±,,,±,9 H[FHHG DW
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
DERXW .*3D 7KH FRRUGLQDWHV RI WKH ,,±,,,±,9 WULSOH SRLQW ZHUH GHWHFWHG DW DERXW*3DDQG±R&>@ 7KHEHKDYLRURI&VLQWKHVROLGVWDWHDQGR&ZDVGHWHUPLQHGE\VWUXFWXUDO VWXGLHV >±@ RSWLFDO PHDVXUHPHQWV >@ XOWUDVRQLF VWXGLHV >@ DQG E\ FDOFXODWLRQ >±±± @7KH,±,,SKDVHWUDQVLWLRQLVDFFRPSDQLHGE\∆99 FPPRO3KDVH,,KDV DIFFVWUXFWXUHZLWKODWWLFHFRQVWDQWD QPDW*3DDQGD QPDW *3D>@7KH,,±,,,SKDVHWUDQVIRUPDWLRQUHSUHVHQWVWKHHOHFWURQLFVGSURPRWLRQ ZLWKQRFKDQJHLQODWWLFHV\PPHWU\7KHSKDVH,,,FU\VWDOOL]HVLQDIFFVWUXFWXUHZLWK D QP DW *3D DQG URRP WHPSHUDWXUH 7UDQVLWLRQ WR SKDVH ,,, LV DFFRPSDQLHGE\∆99 >@RU>@7KHSKDVH,,,ZDVGHWHUPLQHGDW *3DDQGR&E\;UD\GLIIUDFWLRQVWXG\>@8VLQJDVLQJOHFU\VWDO;UD\GDWD>@ WKHSKDVH,,,LGHQWLILHGLQDQRUWKRUKRPELFVWUXFWXUHZLWKVSDFHJURXS&= ODWWLFHFRQVWDQWVD QPE QPF QPQRHYLGHQFHFRXOG EH IRXQG IRU WKH IFF IRUPUHSRUWHGSUHYLRXVO\7KHSUHVVXUHLQGXFHGSKDVH,9ZDV IRXQGWRKDYHDWHWUDJRQDOVWUXFWXUHRIWKH β6QW\SHDQGVSDFHJURXS,DPGWKH XQLW FHOO GLPHQVLRQV DUH D QP F QP DW *3D DQG R& >@ 7KH SKDVH WUDQVLWLRQ ,,,±,9 ZDV DFFRPSDQLHG E\ ∆9 >@ RU >@ 7.
/LT
,EFF
,,IFF
,,,RUWK
,9WHWU
3*3D
)LJXUH7KHSKDVHGLDJUDPRIFHVLXP
Copyright © 2005 CRC Press, LLC
&HVLXP
$W DERXW *3D WKH ,9±9 SKDVH WUDQVLWLRQ ZDV REVHUYHG ZKHUH SKDVH 9 KDV D PRUHFRPSOLFDWHGVWUXFWXUHDVFRPSDUHGWRWKDWIRUSKDVH,9>@7KHSKDVH9KDV DQ RUWKRUKRPELF VWUXFWXUH ZLWK VSDFH JURXS &PFD DQG = RU LW LQGH[HG DV WKH GLVWRUWHG IFF VWUXFWXUH ODWWLFH SDUDPHWHUV DUH D QP E QP F QPDW*3D7KHSKDVHWUDQVLWLRQ,9±9ZDVDFFRPSDQLHGE\∆9a >@ 7KH SKDVH WUDQVLWLRQ 9±9, ZDV REVHUYHG DW DERXW *3D DQG R& ZLWK ∆99 >@ 7KH FU\VWDO VWUXFWXUH RI SKDVH 9, KDV D KFS W\SH ZLWK D QPF QPFD 7KHSKDVH9,LVVWDEOHXSWR*3D DQGURRPWHPSHUDWXUH>@ 6XSHUFRQGXFWLYLW\RI&VZDVVWXGLHGLQ>±@7KHSKDVH9WUDQVIRUPHG WRDVXSHUFRQGXFWLQJVWDWHDW7F .DQG±*3D>@ 7KHSKDVHGLDJUDPRIFHVLXPLVVKRZQLQ)LJXUH 5HIHUHQFHV %ULGJPDQ3: 9DULRXVSK\VLFDOSURSHUWLHVRI5EDQG&VDQGWKHUHVLVWDQFHRI. XQGHUSUHVVXUH3URF$P$FDG$UWV6FL± %ULGJPDQ3: 5RXJKFRPSUHVVLRQVRIVXEVWDQFHVWRDWP3URF$P $FDG$UWV6FL± %ULGJPDQ 3 : 7KH UHVLVWDQFH RI WKH HOHPHQWV DOOR\V DQG FRPSRXQGV WR DWP3URF$P$FDG$UWV6FL± %ULGJPDQ 3 : 7KH UHVLVWDQFH RI QLQHWHHQ PHWDOV WR DWP 3URF $P $FDG$UWV6FL± %ULGJPDQ 3 : 5RXJK FRPSUHVVLELOLWLHV RIIRXUWHHQVXEVWDQFHVWRDWP 3URF$P$FDG$UWV6FL± .HQQHG\*&DQG/D0RUL31 6RPHIL[HGSRLQWVRQWKHKLJKSUHVVXUHVFDOH ,Q3URJUHVVLQ9HU\+LJK3UHVVXUH5HVHDUFKSS±1@ WKH PHOWLQJ OLQH ZDV GHWHUPLQHG WR *3D DQG a . SRVVLEO\ WKH ,±,, WUDQVLWLRQ IURPKFSWRIFFVWUXFWXUHDWURRPWHPSHUDWXUH DQGXSWRa*3DDQG±. 7KH EHKDYLRU RI WKH HOHPHQW DW . ZDV VWXGLHG E\ HOHFWURUHVLVWDQFH >@ YROXPHWULFDOO\ >@ E\ ;UD\ GLIIUDFWLRQ XS WR *3D >@ DQG E\ 5DPDQ VSHFWUD XS WR *3D >@ 7UDQVLWLRQ IURP WKH SKDVH , WR WKH SUHVVXUHLQGXFHG PRGLILFDWLRQ,,KDYLQJDIFFVWUXFWXUHZDVREVHUYHGDW*SDQRIXUWKHUWUDQVLWLRQV DUH VHHQ WR *3D >@ 7KH KLJKSUHVVXUH VWUXFWXUDO SKDVH WUDQVIRUPDWLRQV DQG WKH SKDVHGLDJUDPZHUHFDOFXODWHG>±@7KHK\SRWHWLFDOWKHRUHWLFDOSKDVHGLDJUDP ZDVSUHVHQWHG>±@ZKHUHWKHWULSOHSRLQWEHWZHHQOLTXLGDQGSKDVHVZLWKKFS DQGEFFVWUXFWXUHVZDVGHWHUPLQHGDW*3DDQGa. 7KHSKDVHGLDJUDPRIPDJQHVLXPLVVKRZQLQ)LJXUH 7. /LT
,,,IFF
,,EFF
"
,KFS
)LJXUH7KHSKDVHGLDJUDPRIPDJQHVLXP
3*3D
5HIHUHQFHV
.HQQHG\*&DQG1HZWRQ5& 0HOWLQJDQGSKDVHWUDQVIRUPDWLRQVLQVROLGVWDWH RI VRPH SXUH PHWDOV DW KLJK WHPSHUDWXUHV DQG SUHVVXUHV ,Q 6ROLGV XQGHU 3UHVVXUH HGV :3DXODQG'0:DUVKDXHUSS±1±@ E\ WKH HODVWLF SURSHUWLHV >@ E\ ;UD\ GLIIUDFWLRQ XS WR *3D >@ XS WR *3D >@ XS WR *3D >@ LQ >±@E\WKHVXSHUFRQGXFWLQJSURSHUWLHVXSWR*3D>@E\ WKH +DOO HIIHFW >@ DQG FDOFXODWLRQ >±@ 7KH ,,±, WUDQVLWLRQ ZDV GHWHUPLQHG E\ '7$ DQG YROXPHWULFDOO\ DW *3D DQG R& >@ DW DERXW *3D DQG R& ZLWK ∆99 7KH ,±,,, SKDVH WUDQVIRUPDWLRQ ZDV REVHUYHG DW *3DDQGR&>@7KHSKDVHWUDQVLWLRQV,,±,DQG,±,,,ZHUHFRQILUPHG>@ 7KH GLIIUDFWLRQ OLQHV REVHUYHG DIWHU WKH ,±,,, SKDVH WUDQVLWLRQ DUH RI WKH GLIIHUHQW W\SHV ³VPRRWK´ RU ³VSRWW\´ VXJJHVWLQJ D PRUHFRPSOH[FU\VWDOORJUDSKLFEHKDYLRU 6WUXFWXUH RI ,,, ZDV GHWHUPLQHG EHWZHHQ DQG *3D DW R& >@ DQG E\ FDOFXODWLRQ>@,WKDVDQRUWKRUKRPELFERG\FHQWHUHGVWUXFWXUHZLWKDWRPVLQXQLW FHOO DQG ODWWLFH SDUDPHWHUV D QP E QP F QP DW *3D>@7KH,,,±,9SKDVHWUDQVLWLRQZDVGHWHUPLQHGDWDERXW±*3DDQG R& >@ DW DERXW ±R& E\ HOHFWURUHVLVWDQFH PHDVXUHPHQWV >@ 7KH GLIIUDFWLRQ OLQHV RI ,9 JUDGXDOO\ VWUHQJWKHQ ZLWK SUHVVXUH LQGLFDWLQJ D VOXJJLVK WUDQVIRUPDWLRQ7KH,9±9SKDVHWUDQVLWLRQZDVGHWHUPLQHGDW±*3DDQGR& >@ 7.
/LT
,IFF ,,EFF
,,, RUWK
,9
9WHWU
)LJXUH7KHSKDVHGLDJUDPRIVWURQWLXP
3*3D
Copyright © 2005 CRC Press, LLC
6WURQWLXP
7KH LQFRPPHQVXUDWH SKDVH 6U 9 KDV D ERG\FHQWHUHG WHWUDJRQDO VWUXFWXUH FORVHO\ VLPLODU WR WKDW RI WKH %D ,9 W\SH ZLWK ODWWLFH SDUDPHWHUV D, QP F, QPF,D, DW*3D>@ $ FRPSOH[ SKDVH GLDJUDP RI 6U KDV EHHQ SHUIRUPHG XVLQJ D ODVHUKHDWHG GLDPRQG DQYLOFHOO XS WR *3D DQG ± R& >@ 7KH PHOWLQJ FXUYH ZDV GHWHUPLQHG WR a *3D DQG aR& SRVVLEOH ,±,,, 7KH PHOWLQJ FXUYH DEUXSWO\ LQFUHDVHGWRa*3DDQGR&DQGGHFUHDVHGWRa*3DDQGaR&SRVVLEOH ,,,±,9±/LTXLG WULSOH SRLQW 7KH PHOWLQJ ERXQGDU\ KDV EHHQ VWXGLHG XS WR *3D DQG±R& 7KH KLJKSUHVVXUH PRGLILFDWLRQV WUDQVIRUPHG WR WKH VXSHUFRQGXFWLQJ VWDWH DW 7F .DQG*3DDW7F .DQG*3DDSSDUHQWO\6U,9 DQGDOVRDW 7F ±.DQG±*3DDSSDUHQWO\6U9 ZLWKVOLJKWK\VWHUHVLV>@ 7KHSKDVHGLDJUDPRIVWURQWLXPLVVKRZQLQ)LJXUH 5HIHUHQFHV -D\DUDPDQ$.OHPHQW:DQG.HQQHG\*& 3KDVHGLDJUDPVRI&DDQG6UDW KLJKSUHVVXUHV3K\V5HY± %ULGJPDQ 3 : 5RXJK FRPSUHVVLELOLWLHV RIIRXUWHHQVXEVWDQFHVWRDWP 3URF$P$FDG$UWV6FL± %ULGJPDQ 3 : &RPSUHVVLRQV DQG SRO\PRUSKLF WUDQVLWLRQV RI VHYHQWHHQ HOHPHQWVWRDWP3K\V5HY± %ULGJPDQ3: 3UHVVXUH±YROXPHUHODWLRQVIRUVHYHQWHHQHOHPHQWVWRDWP 3URF$P$FDG$UWV6FL± %ULGJPDQ 3 : 7KH UHVLVWDQFH RI HOHPHQWV DOOR\V DQG FRPSRXQGV WR DWP3URF$P$FDG$WUV6FL± 6WDJHU 5 + DQG 'ULFNDPHU + * (IIHFW RI WHPSHUDWXUH DQG SUHVVXUH RQ WKH HOHFWULFDOUHVLVWDQFHRIIRXUDONDOLQHHDUWKPHWDOV3K\V5HY± %XQG\ )3DQG'XQQ.- (OHFWULFDOEHKDYLRURI&D6U%DDQG(XDWYHU\ KLJK SUHVVXUHV DQG ORZ WHPSHUDUXUHV ,Q 3K\VLFV RI 6ROLGV XQGHU +LJK 3UHVVXUH HGV -66FKLOOLQJDQG6KHOWRQ51SS±1RUWK±+ROODQG3XEO&R 'XQQ . - DQG %XQG\ ) 3 3UHVVXUHLQGXFHG VXSHUFRQGXFWLYLW\ LQ VWURQWLXP DQGEDULXP3K\V5HY%± %XQG\ ) 3 %ULGJPDQ DZDUG OHFWXUH 'LDPRQG V\QWKHVLV DQG KLJK SUHVVXUH UHVHDUFK,Q3URF,QW&RQI$,5$37+LJK3UHVVXUH6FLHQFHDQG7HFKQRORJ\.LHY SS±.LHY1DXNRYD'XPND
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
0F:KDQ'%5LFH70DQG6FKPLGW3+ 0HWDO±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
Copyright © 2005 CRC Press, LLC
%DULXP
SKDVH,WUDQVIRUPHGWRDVXSHUFRQGXFWLQJVWDWHDW.DQG*3DDQGDW. DQG*3D>@)RUSKDVH,,VXSHUFRQGXFWLQJWUDQVLWLRQZDVGHWHUPLQHGDW. DQG *3D >@ DW . DQG *3D DQG DW . DQG *3D >@6XSHUFRQGXFWLQJWUDQVLWLRQZDVGHWHUPLQHGDW.DQG*3DDQGDOVR DIWHUWKHUHOHDVLQJSUHVVXUHDWDERXW.DQG*3D 7KHSKDVHGLDJUDPVRIEDULXPDUHVKRZQLQ)LJXUHVDQG 7. /LT
,,KFS
,,,KH[
,9EFW
,EFF
3*3D
)LJXUH9DULDQWRIWKHSKDVHGLDJUDPRIEDULXP
7.
/LT
,,,FXE
, EFF
,, KFS
,9 9 KFS
3*3D
)LJXUH9DULDQWRIWKHSKDVHGLDJUDPRIEDULXP
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
5HIHUHQFHV %ULGJPDQ 3 : 7KH UHVLVWDQFH RI QLQHWHHQ PHWDOV WR DWP 3URF $P $FDG$UWV6FL± %ULGJPDQ 3 : 5RXJK FRPSUHVVLELOLWLHV RIIRXUWHHQVXEVWDQFHVWRDWP 3URF$P$FDG$UWV6FL± %ULGJPDQ 3 : &RPSUHVVLRQV DQG SRO\PRUSKLF WUDQVLWLRQV RI VHYHQWHHQ HOHPHQWVWRDWP3K\V5HY± %ULGJPDQ 3 : 7KH UHVLVWDQFH RI HOHPHQWV DOOR\V DQG FRPSRXQGV WR DWP3URF$P$FDG$UWV6FL± .HQQHG\*&DQG/D0RUL31 7KHSUHVVXUHRIVRPHVROLG±VROLGWUDQVLWLRQV -*HRSK\V5HV± -D\DUDPDQ$.OHPHQW:DQG.HQQHG\*& 0HOWLQJDQGSRO\PRUSKLVPRI EDULXPDWKLJKSUHVVXUHV3K\V5HY/HWW± 6WURPEHUJ + ' DQG 6WHSKHQV ' 5 (IIHFW RI SUHVVXUH RQ WKH HOHFWULFDO UHVLVWDQFHRIFHUWDLQPHWDOV-3K\V&KHP6ROLGV± *LDUGLQL$$3RLQGH[WHU(+DQG6DPDUD*$ +LJKSUHVVXUHSRO\PRUSKLF WUDQVLWLRQV VWXGLHG E\ DXGLR DQG UDGLRIUHTXHQF\ WHFKQLTXHV 5HY 6FL ,QVWUXP ± 9HUHVKFKDJLQ/)=XERYD(9%XLQRYD,3DQG%XUGLQD.3 0HDVXULQJ RIWKHSUHVVXUHXSWRNEDUXVLQJJDXJHPDQRPHWHU'RNO$NDG1DXN6665± -HIIHU\51%DUQHWW-'9DQIOHHW+%DQG+DOO+7 3UHVVXUHFDOLEUDWLRQ WRNEDUEDVHGRQWKHFRPSUHVVLRQRI1D&O-$SSO3K\V± +D\JDUWK-&*HWWLQJ,&DQG.HQQHG\*& 'HWHUPLQDWLRQRIWKHSUHVVXUH RQWKHEDULXP,±,,WUDQVLWLRQZLWKVLQJOHVWDJHSLVWRQF\OLQGHUDSSDUDWXV-$SSO3K\V ± :LWWLJ-DQG0DWWKLDV%7 6XSHUFRQGXFWLYLW\RIEDULXPXQGHUSUHVVXUH3K\V 5HY/HWW± =HWR 5 - DQG 9DQIOHHW + % 3UHVVXUH FDOLEUDWLRQ WR NEDU EDVHG RQ WKH UHVLVWDQFH FKDQJH RI D PDQJDQLQ FRLO XQGHU K\GURVWDWLF SUHVVXUH - $SSO 3K\V ± 9HUHVKFKDJLQ / ) 6HPHUFKDQ $ $ .X]LQ 1 1 DQG 6DGNRY @ XS WR *3D >@ E\ '7$ XS WR *3D >@ XS WR *3D >@ E\ VKRFNZDYH FRPSUHVVLRQ XS WR *3D >@ XS WR *3D >@ LQ >@ E\ FDOFXODWLRQ >@ DQG LQ >@ 7KH PHOWLQJ FXUYH ZDV REVHUYHG E\VWDWLFFRPSUHVVLRQXSWRR&DQG*3DZLWKDQLQLWLDOVORSH.*3D>@ XSWRa*3DDQGa±R&>@$OPHOWVDWDERXWR&DQG*3D E\VKRFNORDGLQJ>@ 7KHEHKDYLRURI$OLQWKHVROLGVWDWHZDVVWXGLHGDOVRE\VWDWLFSUHVVXUHDQG URRPWHPSHUDWXUH>±@E\VKRFNORDGLQJXSWR*3D>@XSWR*3D >@XSWR*3D>@E\PHDVXULQJRIGLIIHUHQWSK\VLFDOSURSHUWLHV> @DQGLQ>@7KHEHKDYLRURIWKHHOHPHQWZDVFDOFXODWHG >±@ ,Q >@ WKH VHTXHQFH RI D IFF→KFS→EFF VWUXFWXUH LV H[SHFWHG DW DERYH *3D DQG D IFF→KFS WUDQVIRUPDWLRQ DW ± *3D,WKDVQRWEHHQREVHUYHGH[SHULPHQWDOO\ 7.
/LT
,EFF
3*3D
)LJXUH7KHSKDVHGLDJUDPRIDOXPLQLXP
Copyright © 2005 CRC Press, LLC
$OXPLQLXP
7KHVXSHUFRQGXFWLQJSURSHUWLHVZHUHVWXGLHG>@ZLWK7F .DW *3DDQG7F .DW*3D>@ 7KHSKDVHGLDJUDPRIDOXPLQLXPLVVKRZQLQ)LJXUH 5HIHUHQFHV 0LWFKHOO $ & DQG 6KDQHU - : 0HOWLQJ DOXPLQLXP DW 0EDU %XOO $P 3K\V6RF 0LWFKHOO$&DQG1HOOLV:- 6KRFNFRPSUHVVLRQRI$O&XDQG7D-$SSO 3K\V± 0RULDUW\-$DQG0F0DKDQ$. +LJKSUHVVXUHVWUXFWXUDOSKDVHWUDQVLWLRQVLQ 1D0JDQG$O3K\V5HY/HWW± 0RULDUW\-$@DQG XSWR*3D>@7KHPHOWLQJFXUYHZDVREVHUYHGDWR&ZLWKDQLQLWLDOVORSH .*3D>@ 7KH ,,±, SKDVH WUDQVIRUPDWLRQ KDV D FRQVWDQW VORSH ± .*3D >@ 7KH ,,±,,,SKDVHWUDQVIRUPDWLRQLVZLGHO\XVHGDVDFDOLEUDQWRIWKHKLJKSUHVVXUHGHYLFHV DW URRP WHPSHUDWXUH 7KLV WUDQVLWLRQ ZDV VWXGLHG DW DERXW *3D YROXPHWULFDOO\ >±@E\HOHFWURUHVLVWDQFH>@DQGDOVRLQ>±±@7KHSUHVVXUH GHSHQGHQFH RI WKH ,±,,, SKDVH WUDQVLWLRQ ZDV GHWHFWHG DW KLJK WHPSHUDWXUHV > @ DQG WKH ,,±,,, WUDQVLWLRQ DW ORZ WHPSHUDWXUHV >@ 7KH ,,±,,, SKDVH WUDQVLWLRQ LV DFFRPSDQLHG E\ ∆99 DW R& 7KH VORSH RI WKH WUDQVLWLRQ OLQH FKDQJHV IURP D SRVLWLYH DW DERYH R& WR DQHJDWLYHDWORZWHPSHUDWXUHV7KH ,±,,±,,,WULSOHSRLQWZDVGHWHUPLQHGDW*3DDQGR&>±@7KH,,,±,SKDVH
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
WUDQVLWLRQZDVGHWHUPLQHGDWR&DQG*3D>@DWR&DQG*3D>@DQGLQ >@7KHSUHVVXUHLQGXFHGSKDVH,,,KDVDIFFVWUXFWXUHDQGD QPDW*3D DQGR&>@*HQVKDIW>@ILUVWSUHGLFWHGWKHH[LVWHQFHRI7O,,,KDYLQJDIFF VWUXFWXUH IURP WKH EHKDYLRU RI WKH 7O±+J 7O±%L DQG 7O±6Q DOOR\V DW DWPRVSKHULF SUHVVXUH7ODWR&ZDVVWXGLHGE\HODVWLFSURSHUWLHV>@E\QHXWURQGLIIUDFWLRQ >@ E\ ;UD\ GLIIUDFWLRQ XS WR *3D >@ DQG XS WR *3D >@ 3KDVH ,,, LV VWDEOHDWOHDVWWR*3D>@ 7KH VXSHUFRQGXFWLQJ SURSHUWLHV ZHUH VWXGLHG XS WR *3D >@ XS WR *3D >@ XS WR *3D >@ DQG LQ >@ 3KDVH ,, EHFRPHV VXSHUFRQGXFWLQJ DW . DQG *3D DQG DW . DQG *3D 3KDVH ,,, WUDQVIRUPV WR WKH VXSHUFRQGXFWLQJVWDWHDW.DQG*3DDQGDW.DQG*3D 7KHSKDVHGLDJUDPRIWKDOOLXPLVVKRZQLQ)LJXUH 7. /LT
,EFF
,,,IFF
,,KFS
3*3D
)LJXUH7KHSKDVHGLDJUDPRIWKDOOLXP
5HIHUHQFHV 0F'DQLHO0/%DEE6(DQG6FRWW*- 0HOWLQJFXUYHVRIILYHPHWDOVXQGHU KLJKSUHVVXUH-&KHP3K\V± %XWX]RY933RQ\DWRYVN\(*DQG6KDNKRYVNRL*3 0HOWLQJWHPSHUDWXUHV RI =Q &G 7O DQG 6E XQGHU SUHVVXUH WR DWP 'RNO $NDG 1DXN 6665 ±
Copyright © 2005 CRC Press, LLC
7KDOOLXP
3RQ\DWRYVN\(* 3±7GLDJUDPRIWKDOOLXP.ULVWDOORJUDIL\D± -D\DUDPDQ$.OHPHQW:1HZWRQ5&DQG.HQQHG\*& )XVLRQFXUYHV DQG SRO\PRUSKLF WUDQVLWLRQV RI WKH ,,, JURXS HOHPHQWV ± $O *D ,Q DQG 7O DW KLJK SUHVVXUHV-3K\V&KHP6ROLGV± $QWRQRYD7(%HODVK,7DQG,YDNKQHQNR6$ 3KDVHGLDJUDPRIWKDOOLXPWR *3D)L]0HW0HWDOORYHG± %ULGJPDQ 3 : 3RO\PRUSKLVP SULQFLSDOO\ RI WKH HOHPHQWV XS WR DWP 3K\V5HY± .HQQHG\ * & DQG /D0RUL 3 1 6RPH IL[HG SRLQWV RQ WKH KLJK SUHVVXUH VFDOH ,Q 3URJUHVV LQ 9HU\ +LJK 3UHVVXUH 5HVHDUFK SS ± 1±@7KHWKUHVKROGRIYHU\IDVWDQG FRPSOHWHWUDQVLWLRQRIGLDPRQGWRJUDSKLWHZDVGHWHUPLQHGDWDERXW±*3DDQGDW DERXW . DQG WKHQ KHDWLQJ WKH DVVHPEO\ ZLWK D SXOVH RI HOHFWULF FXUUHQW 1R JUDSKLWL]DWLRQ RI WKH GLDPRQG RFFXUV XQOHVV WKH FULWLFDO WHPSHUDWXUH LV UHDFKHG DW ZKLFKJUDSKLWL]DWLRQLVFRPSOHWH7KHKH[DJRQDOW\SHGLDPRQGZDVILUVWGLVFRYHUHG LQ PHWHRULWLF PDWWHU >@ )RUPDWLRQ RI GLDPRQG ZDV VWXGLHG E\ VWDWLF SUHVVXUH >±@ LQ FRPELQDWLRQ ZLWK VKHDU VWUHVV KLJK SUHVVXUH DQG KLJK WHPSHUDWXUH>@DQGE\VKRFNZDYHORDGLQJDW±*3DDQGDERYH>±@ 7KH GLUHFW FRQYHUVLRQ JUDSKLWH±GLDPRQG OLQH H[WHQGV IURP WKH JUDSKLWH±GLDPRQG± OLTXLGWULSOHSRLQWDW*3DDQG.WR*3DDQG.ZLWKQHJDWLYHVORSH ,W PDNHV D VKDUS WXUQ DQG ZDV REVHUYHG DW *3D DQG . $W WKLV WUDQVLWLRQ KH[DJRQDO JUDSKLWH RU KH[DJRQDOW\SH GLDPRQG WUDQVIRUPV WR FXELFW\SH GLDPRQG 7KHGLUHFWFRQYHUVLRQJUDSKLWH±GLDPRQGERXQGDU\PD\H[WHQGWRURRPWHPSHUDWXUH DWDERXW*3D$FFRUGLQJWR>@WKHEHKDYLRURIFDUERQLVDQDORJRXVWRWKDWRIWKH LVRHOHFWURQLFFDVHRIERURQQLWULGHZKLFKZDVVWXGLHGLQ>@7KHVHVWXGLHVRIERURQ QLWULGH LQGLFDWHG D UHDFWLRQ UDWHFRQWUROOHG ³WKUHVKROG OLQH´ EHWZHHQ ZXUW]LWH %1 OLNH KH[DJRQDO GLDPRQG DQG ]LQFEOHQGH %1 OLNH FXELFW\SH GLDPRQG ZKLFK LV YHU\ VLPLODU WKDW RI WUDQVLWLRQ IRU FDUERQ 7KH EHKDYLRU RI FDUERQ ZDV VWXGLHG DW URRPWHPSHUDWXUHRSWLFDOO\E\5DPDQDQG;UD\GLIIUDFWLRQLQVLWXDWKLJKSUHVVXUH >±@ 7KH REVHUYHGEHKDYLRURIVSHFLPHQGXULQJFRPSUHVVLRQGHSHQGVXSRQLWV LQLWLDOGHJUHHRIFU\VWDOOLQLW\WKHGLUHFWLRQDQGKRPRJHQHLW\RIWKHSUHVVXUHILHOGWKH
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
UDSLGLW\ RI FRPSUHVVLRQ DQG WKH W\SH RI PHDVXUHPHQW SHUIRUPHG 7UDQVLWLRQ IURP VLQJOHFU\VWDO JUDSKLWH WR DQ RSWLFDOO\ WUDQVSDUHQW VWDWH ZDV REVHUYHG DW URRP WHPSHUDWXUH DW DERXW *3D XQGHU XQLD[LDO VWUHVV GLUHFWHG DORQJ WKH FD[LV RI WKH FU\VWDO >@ 7KLV EHKDYLRU RI JUDSKLWH ZDV GHWHUPLQHG E\ 5DPDQ DQG RSWLFDO H[SHULPHQWV DQG E\ ;UD\ GLIIUDFWLRQ VWXG\ >@ 'HFUHDVLQJ HOHFWULFDO FRQGXFWLYLW\ DQG RSWLFDO UHIOHFWLYLW\ DQG GHFUHDVLQJ RSWLFDO WUDQVPLWWDQFH ZHUH REVHUYHG DW KLJKHU SUHVVXUH 7KH PDWHULDO UHPDLQV WUDQVSDUHQW WR YLVLEOH OLJKW VXJJHVWLQJ WKDW LW UHPDLQV HOHFWULFDOO\ QRQFRQGXFWLQJ +HDWLQJ WKLV PDWHULDO FDXVHV WKH VDPSOH WR WUDQVIRUP LQWR FRKHUHQW KH[DJRQDO GLDPRQG FU\VWDOOLQLWLHV >@ $FFRUGLQJ WR WKHVH H[SHULPHQWV WKH WUDQVSDUHQW KLJKSUHVVXUH URRPWHPSHUDWXUH SKDVH SHUKDSV LV D QHZ DOORWURSH RI FDUERQ DQG KDV WKH SURSHUWLHV GHVFULEHG IRU UHDVRQV RWKHU WKDQ VS ERQGLQJ 'XULQJ VKRFN FRPSUHVVLRQ LQ WKH FRPPHUFLDO SURGXFWLRQRIGLDPRQGSRZGHUWKHERG\WREHVKRFNFRPSUHVVHGFRQVLVWVRIVPDOO SDUWLFOHV RI JUDSKLWH GLVSHUVHG LQ D PDWUL[ RI PHWDO 7KH W\SH DQG VL]H RI GLDPRQG SDUWLFOHV WKDW FDQ EH SURGXFHG E\ WKLV PHWKRG DUH OLPLWHG E\ WKH VKRUWQHVV RI WKH UHDFWLRQWLPH+H[DJRQDOW\SHGLDPRQGZDVSUHSDUHGLIWKHWRSRIWKHF\FOHJRHVWR ± . DQG *3D DQG PRVWO\ FXELFW\SH GLDPRQG LI WKH WRS RI WKH F\FOH JRHVWR±*3DDQG. 7.
/LT
GLDPRQGFXE
JUDSKLWH
3*3D
)LJXUH7KHSKDVHGLDJUDPRIFDUERQ
Copyright © 2005 CRC Press, LLC
&DUERQ
$WWKHSUHVHQWWLPHWKHVWDELOLW\RIFXELFW\SHGLDPRQGH[WHQGVWRDWOHDVW*3D DQGURRPWHPSHUDWXUH>@7KHPHOWLQJFXUYHRIFXELFW\SHGLDPRQGERXQGDU\DQG SKDVH VWDELOLW\ ZDV VWXGLHG H[SHULPHQWDOO\ >@ DQG WKHRUHWLFDOO\ > ±@7KHSKDVHGLDJUDPZDVFDOFXODWHGWR*3DDQG.>@$FFRUGLQJ WR WKHVH VWXGLHV WKH PHOWLQJ FXUYH RI GLDPRQG KDV D SRVLWLYH VORSH 7KH SKDVH GLDJUDPGLDPRQG±JUDSKLWH±IXOOHUHQHZDVFDOFXODWHG>@([LVWHQFHRIQHZPHWDOOLF SKDVHVLQSRO\FU\VWDOOLQHGLDPRQGLVGLVFXVVHGLQ>±@ 7KH SKDVH GLDJUDP RI FDUERQ LV VKRZQ LQ )LJXUH ZKHUHLVUHJLRQRI FRPPHUFLDO V\QWKHVLV RI GLDPRQG IURP JUDSKLWH E\ FDWDO\VLV LV WKH SKDVH ERXQGDU\RIYHU\IDVWOHVVWKDQPV GLUHFWWUDQVIRUPDWLRQRIJUDSKLWHWRGLDPRQG LV WKH ERXQGDU\ RI YHU\ IDVW WUDQVIRUPDWLRQ RI GLDPRQG WR JUDSKLWH LV WKH ERXQGDU\ WUDQVLWLRQ IURP JUDSKLWH RI KH[DJRQDOW\SH GLDPRQG LQWR FXELFW\SH GLDPRQGLVWKHWUDQVWLRQWRWUDQVSDUHQWPHWDVWDEOHJUDSKLWH 5HIHUHQFHV
%XQG\)3 3UHVVXUHWHPSHUDWXUHSKDVHGLDJUDPRIHOHPHQWDOFDUERQ3K\VLFD$ ± %XQG\)3 3KDVHWUDQVLWLRQVLQH[WHQGHGUHJLRQVRISUHVVXUHDQGWHPSHUDWXUH,Q 0HWDOOXUJ\+LJK3UHVVXUHDQG+LJK7HPSHUDWXUHSS±1@ 'LVRUGHUHG PROHFXODU FU\VWDO VWDWHV ZHUH SUHSDUHG DW ± *3D DQG ± . ZLWK GHQVLW\ ± JFP DQG KDUGQHVV ± *3D >±@ 8OWUDKDUGDPRUSKRXVFDJHQDQRVWUXFWXUHVZHUHSURGXFHGDWa*3DDQG± .ZLWKGHQVLW\±JFP>@+DUGQHVVRIXOWUDKDUG&KDYLQJ±*3D ZDVVWXGLHG>@(ODVWLFDQGVWUXFWXUDOSURSHUWLHVRIFURVVOLQNHGOD\HUHGVWUXFWXUHV DQG XOWUDKDUG IXOOHULWHV ZHUH V\QWKHVL]HG DW ± *3D DQG ± . DQG ZHUH PHDVXUHG>±@+LJKSUHVVXUHV\QWKHVLVVWUXFWXUHVDQGPHFKDQLFDOSURSHUWLHVRI & KDYH DOVR EHHQ VWXGLHG LQ ZLGH UDQJHV RI WKH VWDWLF DQG G\QDPLF SUHVVXUHV DQG WHPSHUDWXUHV >±@ $ VWURQJ PDJQHWLF VLJQDO LQ UKRPERKHGUDO & DIWHU KLJKSUHVVXUHDQGKLJKWHPSHUDWXUHWUHDWPHQWZDVREVHUYHG>@ 7KH H[SHULPHQWDO UHVXOWV SXEOLVKHG XS WR ZHUH UHYLHZHG DW OHQJKE\ 6XQGTYLVW >@ )LJXUH VKRZV WKH YDULDQWRIWKHSKDVHGLDJUDPRIIXOOHUHQH& XVLQJGDWDIURP>@7KH7±3GLDJUDPRI&DQGSURGXFWVRIWUDQVIRUPDWLRQVLQ& DW3!*3DDQG7XSWR.DUHGHVFULEHGLQ>@ 7.
DWRPLFIRUPV
'SRO\PHU UKRPE
'SRO\PHUV
)&&
' SRO\PHU WHWU
'SRO\PHU RUWK
6&
)LJXUH7KHYDULDQWRIWKHSKDVHGLDJUDPRI IXOOHUHQH&
3*3D
Copyright © 2005 CRC Press, LLC
)XOOHUHQH&
7. JUDSKLWH JUDSKLWHGLDPRQG
DPRUSKRXV VS
DPRUSKRXV VS
'SRO\PHUV
'SRO\PHUV PROHFXODUFU\VWDOV
)LJXUHD7KHK\SRWHWLFDOYDULDQWRIWKHSKDVH GLDJUDPRQIXOOHUHQH&
3*3D
7KH FU\VWDO VWUXFWXUHV RI 'SRO\PHULF SKDVHV RI & ZHUH ODWHU UHILQHG >±@YLDWKHPHDVXUHPHQWVRQVLQJOHFU\VWDOV,WLVVKRZQWKDWVXFFHVVLYHSRO\PHU OD\HUV LQ WKH WHWUDJRQDO SKDVH DUH URWDWHG E\ R DERXW WKH VWDFNLQJ D[LV >@ 7KH VSDFHJURXSHRIV\PPHWU\RIWKLVSKDVHLV3PPF>@7KHUKRPERKHGUDO'± SRO\PHUSKDVHKDVVSDFHJURXS5P= ZLWKODWWLFHFRQVWDQWVD QPF QP >@ 7KH VHFRQG YDULDQW RI WKH 7±3 SKDVH GLDJUDP RI IXOOHUHQH & LV VKRZQLQ)LJXUHD
5HIHUHQFHV 5XRII56DQG5XRII$/ 7KHEXONPRGXOXVRI&PROHFXOHVDQGFU\VWDOV $PROHFXODUPHFKDQLFVDSSURDFK$SSO3K\V/HWW± :DQJ@E\LQGHQWDWLRQ>@DQGLQ>±@ 6LOLFRQZDVVWXGLHGDWURRPWHPSHUDWXUHE\;UD\GLIIUDFWLRQXSWR*3D >@XSWR*3D>@XSWR*3D>@E\VKRFNORDGLQJ>@ E\LQGHQWDWLRQ>±@DQGLQ>±@DQGE\ FDOFXODWLRQ >±@ 3KDVH ;, KDYLQJ DQ RUWKRUKRPELF VWUXFWXUH VSDFH JURXS ,PPD = DQG ODWWLFH FRQVWDQWV D QPE QPF QPZDVGHWHUPLQHGDW±*3DDQG R& >@ 7KH ,,→9 SKDVH WUDQVLWLRQ ZDV REVHUYHG DW *3D DQG R& 3KDVH 9 KDV D VLPSOH KH[DJRQDO VWUXFWXUH DQG VSDFH JURXS 3PPP = ZLWK ODWWLFHFRQVWDQWVD QPF QPDW*3D>@3KDVHWUDQVLWLRQWR WKHSUHVVXUHLQGXFHGPRGLILFDWLRQ9,ZDVGHWHUPLQHGDWDERXW*3DDQGR&WKH SKDVH KDV DQ RUWKRUKRPELF VWUXFWXUH ZLWK VSDFH JURXS &PFD = ODWWLFH FRQVWDQWVD QPE QPF QPDW*3D>@ 3KDVH 9,, ZDV SUHSDUHG DW *3D DQG URRP WHPSHUDWXUH LW FU\VWDOOL]HV LQ D KH[DJRQDO FORVHSDFNHG VWUXFWXUH VSDFH JURXS 3PPF = ZLWK ODWWLFH SDUDPHWHUV D QP F QP DW ± *3D >@ 7KH 9,,→; SKDVH WUDQVIRUPDWLRQ ZDV GHWHUPLQHG DW DERXW *3D DQG R& 3KDVH ; KDV D IFF VWUXFWXUHVSDFHJURXS3PP= DQGD QPDW*3DWKLVSKDVHLVVWDEOH XSWR*3DDQGURRPWHPSHUDWXUHZKHUH99R >@ 7KHVXSHUFRQGXFWLQJSURSHUWLHVRIWKHKLJKSUHVVXUHSKDVHV6LZHUHVWXGLHG LQ >±@ 3KDVH ,, WUDQVIRUPHG WR WKH VXSHUFRQGXFWLQJ VWDWH DW ± . XS WR
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
*3D 'LVFUHSDQW UHVXOWV ZHUH REWDLQHG RI WKH VXSHUFRQGXFWLYLW\ RI SKDVH ,,, $FFRUGLQJWR>@WKHVXSHUFRQGXFWLYLW\ZDVREVHUYHGDW.DQG±*3DEXW SKDVH,,,GRHVQRWH[KLELWWKHVXSHUFRQGXFWLYLW\GRZQWR.>@ 7KH KLJKSUHVVXUH SUHSDUDWLRQ RI DPRUSKRXV 6L WKH EHKDYLRU RI LW LQ DQ DPRUSKRXV VWDWH DQG WKH VXSHUFRQGXFWLQJ WUDQVLWLRQ WHPSHUDWXUHV ZHUH VWXGLHG >±@ $W VWXGLHV RI FU\VWDOOLQH DQG DPRUSKRXV VDPSOHV XSWR *3DDQG±R&LWKDVEHHQIRXQGWKDWWKHVWUXFWXUHVDIWHUWKHSKDVHWUDQVLWLRQV VWURQJO\GHSHQGRQWKHSDWKLQWKHSUHVVXUH±WHPSHUDWXUHGLDJUDPWKURXJKZKLFKWKH V\VWHP XQGHUJRHV WKH SKDVH WUDQVLWLRQV >@ 6LQJOHFU\VWDO 6L FRQYHUWHG WR DQ DPRUSKRXV VWDWH DW URRP WHPSHUDWXUH GLUHFWO\ XQGHU LQGHQWDWLRQ > @&U\VWDOOL]DWLRQRIWKHDPRUSKRXVQHWZRUNSUHGLFWHGDW*3DDQGD ILUVWRUGHU DPRUSKRXV±DPRUSKRXV SKDVH WUDQVLWLRQ DW *3D >@ $ SUHVVXUH LQGXFHGKLJKGHQVLW\DPRUSKL]DWLRQRIFU\VWDOOLQHGLDPRQGSKDVH6LZDVFDOFXODWHG DURXQG *3D >@ &ODWKUDWH 6L WUDQVIRUPHG IURP D FXELF WR WKH β6Q W\SH VWUXFWXUHDW±*3DE\;UD\GLIIUDFWLRQ>@ 7KHSKDVHGLDJUDPRIVLOLFRQLVVKRZQLQ)LJXUH 7.
/LT ,GLDPRQG
,,WHWU
3*3D
)LJXUH7KHSKDVHGLDJUDPRIVLOLFRQ
Copyright © 2005 CRC Press, LLC
6LOLFRQ
5HIHUHQFHV -D\DUDPDQ $ .OHPHQW : DQG .HQQHG\ * & 0HOWLQJ DQG SRO\PRUSKLVP DW KLJK SUHVVXUHV LQ VRPH JURXS ,9 HOHPHQWV DQG ,,,±9 FRPSRXQGV ZLWK WKH GLDPRQG]LQFEOHQGHVWUXFWXUH3K\V5HY± /HHV-DQG:LOOLDPVRQ%+- &RPELQHGYHU\KLJKSUHVVXUH±KLJKWHPSHUDWXUH FDOLEUDWLRQRIWKHWHWUDKHGUDODQYLOFHOODSSDUDWXVIXVLRQFXUYHVRI=Q$O*HDQG6LWR NEDU1DWXUH± %XQG\)3 3KDVHGLDJUDPVRI6LDQG*HWRNEDUR&-&KHP3K\V ± 6RPD7DQG0DWVXR+ /LQGHPDQ¶VPHOWLQJODZDQGWKHHIIHFWRISUHVVXUHRQ WKHPHOWLQJSRLQWRI6LDQG*H3K\V6WDWXV6ROLGL%± 6RPD7DQG0DWVXR+ 3UHVVXUHGHULYDWLYHVRIWKHPHOWLQJSRLQWIRU6LDQG*H -3K\V&± 6RPD7DQG0DWVXR+ 9ROXPHGHSHQGHQFHRIWKHPHOWLQJWHPSHUDWXUHVZLWK 'HED\PRGHOIRU6LDQG*H6ROLG6WDWH&RPPXQ± 0LQRPXUD6DQG'ULFNDPHU+* 3UHVVXUHLQGXFHGSKDVHWUDQVLWLRQVLQ6L*H DQGVRPH,,,±9FRPSRXQGV-3K\V&KHP6ROLGV± 0LQRPXUD 6 6DPDUD * $ DQG 'ULFNDPHU + * 7HPSHUDWXUH FRHIILFLHQW RI UHVLVWDQFHRIWKHKLJKSUHVVXUHSKDVHVRI6L*HDQGVRPH,,,±9DQG,,±9,FRPSRXQGV -$SSO3K\V± .DVSHU-&DQG5LFKDUGV60 &U\VWDOVWUXFWXUHVRIQHZILRUPVRI6LDQG*H $FWD&U\VWDOORJU± :LWWLJ - =XU 6XSUDOHLWXQJ YRQ *H DQG 6L XQWHU KRKHP 'UXFN = 3K\V ± 0LQRPXUD 6 6KLPRPXUD 2 6DNDL 1 $VDXPL . (QGR + 7DPXUD . )XNXVKLPD-DQG7VXML. 3UHVVXUHLQGXFHGVHPLFRQGXFWRU±PHWDOWUDQVLWLRQVLQ DPRUSKRXV6L*HDQG,Q6E,Q3URF,QW&RQI7HWUDKHGUDO%RQG$PRUSK6HPLFRQG @ RSWLFDOO\>@E\5DPDQVSHFWURVFRS\RIWKHPHWDVWDEOHSKDVHV >@E\LQHODVWLF QHXWURQ VFDWWHULQJ XS WR *3D >@ E\ FDOFXODWLRQ >±
Copyright © 2005 CRC Press, LLC
*HUPDQLXP
@LQ>±@DQGLQUHYLHZV>@ 3KDVH WUDQVLWLRQ IURP SKDVH ,, WR WKH KLJKSUHVVXUH SKDVH 9 KDYLQJ D SULPLWLYH KH[DJRQDO VWUXFWXUH ZDV GHWHUPLQHG DW *3D DQG R& >@ 7KH KLJKSUHVVXUH SKDVH ZLWK DQ RUWKRUKRPELF VWUXFWXUH DQG VSDFH JURXS ,PPD ZDV REVHUYHG DERYH *3D DQG R& EHWZHHQ WKH *H ,, DQG WKH *H 9 >@ 3KDVH WUDQVIRUPDWLRQ9→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→9,,, ZDV GHWHUPLQHG DW ± *3D SKDVH 9,,, KDV D KH[DJRQDO FORVHSDFNHG VWUXFWXUH ZLWK ODWWLFH FRQVWDQWV D QP F QP FD DW *3D >@ 3KDVH WUDQVLWLRQV 9,±9,, DQG 9,,±9,,, FDOFXODWHGLQ>@ 7KHVXSHUFRQGXFWLQJSURSHUWLHVRI*HZHUHVWXGLHGLQ>±@ 3KDVH ,, WUDQVIRUPHG WR WKH VXSHUFRQGXFWLQJ VWDWH DW . DQG *3D DQG DW . DQG *3D >@ 3KDVH ,,, ZLOO QRW EHFRPH VXSHUFRQGXFWLQJ XQWLO D WHPSHUDWXUH RI . LV UHDFKHG >@ 6XSHUFRQGXFWLYLW\ RI SKDVH 9 ZDV FDOFXODWHGLQWKHUDQJH±.>@ 7KHEHKDYLRURI*HDQGWUDQVLWLRQIURPDPRUSKRXVWRFU\VWDOOLQHVWDWHZHUH VWXGLHG E\ ;UD\ GLIIUDFWLRQ E\ HOHFWURUHVLVWDQFH E\ PHDVXULQJ VXSHUFRQGXFWLQJ SURSHUWLHV >±±@ DQG E\ FDOFXODWLRQ >@ 7KH DPRUSKRXV VHPLFRQGXFWRU WUDQVIRUPHG WR WKH DPRUSKRXV PHWDO RU WR SKDVH , RU WR SKDVH ,, > @ 7KH DPRUSKRXV *H EHFRPHV VXSHUFRQGXFWLQJ DW . DQG *3D ZLWKG7FG3 ±.*3DH[WUDSRODWLRQWRDWPRVSKHULFSUHVVXUHJLYHV7F . 7UDQVLWLRQ IURP DPRUSKRXV WR FU\VWDOOLQH VWDWH ZDV QRW IRXQG XS WR *3D XVLQJ ;UD\DEVRUSWLRQILQHVWUXFWXUH>@ 7KHSKDVHGLDJUDPRIJHUPDQLXPLVVKRZQLQ)LJXUH
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
7.
/LT
,GLDPRQG
,,WHWU
3*3D
)LJXUH7KHSKDVHGLDJUDPRIJHUPDQLXP
5HIHUHQFHV +DOO+7 7KHPHOWLQJSRLQWRI*HDVDIXQFWLRQRISUHVVXUHWRDWP-3K\V &KHP± -D\DUDPDQ $ .OHPHQW : DQG .HQQHG\ *& 0HOWLQJ DQG SRO\PRUSKLVP DW KLJK SUHVVXUHV LQ VRPH JURXS ,9 HOHPHQWV DQG ,,,±9 FRPSRXQGV ZLWK WKH GLDPRQG]LQFEOHQGHVWUXFWXUH3K\V5HY± /HHV - DQG :LOOLDPVRQ % + - &RPELQHG YHU\ KLJK SUHVVXUH KLJK WHPSHUDWXUH FDOLEUDWLRQRIWKHWHWUDKHGUDODQYLODSSDUDWXVIXVLRQFXUYHVRI=Q$O*H DQG6LWRNEDU1DWXUH± &RKHQ / + .OHPHQW : DQG .HQQHG\ * & ,QYHVWLJDWLRQ RI SKDVH WDQVIRUPDWLRQVDWHOHYDWHGWHPSHUDWXUHVDQGSUHVVXUHVE\GLIIHUHQWLDOWKHUPDODQDO\VLVLQ SLVWRQF\OLQGHUDSSDUDWXV-3K\V&KHP6ROLGV± &DQQRQ - 5 %HKDYLRU RI WKH HOHPHQWV DW KLJK SUHVVXUHV - 3K\V &KHP 5HI 'DWD± 7RQNRY (@XSWR*3D>@DQGLQ>@7KH PHOWLQJFXUYHKDVDQLQLWLDOVORSH.*3DDQGZDVREVHUYHGDWR&DQG*3D >@ 7KH EHKDYLRU RI OLTXLG 3E ZDV VWXGLHG LQ >@ 7KH IXVLRQ FXUYH DW XOWUDKLJKSUHVVXUHVZDVLQYHVWLJDWHGXVLQJDGLDPRQGDQYLOFHOOZLWKODVHUKHDWLQJRI WKHVDPSOHWR*3D>@,WZDVGHWHFWHGDW*3DDQGaR&DW*3DDQG aR&DQGDW*3DDQGaR&>@7KHPHDVXUHGFXUYHZDVIRXQGWREHLQ
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
VDWLVIDFWRU\ DJUHHPHQW ZLWK PHOWLQJ RQ WKH VKRFNZDYH ORDGLQJ DW a *3D DQG aR&>±@DQGZLWKWKHSUHGLFWLRQRIWKHFDOFXODWLRQ>@ /HDG LQ WKH VROLG VWDWH ZDV VWXGLHG DW R& E\ HOHFWURUHVLVWDQFH YROXPHWULFDOO\ DQG E\ ;UD\ GLIIUDFWLRQ >±@ 7KH ,→,, SKDVH WUDQVLWLRQ ZDVHVWDEOLVKHGDW*3DZLWKDYROXPHUHGXFWLRQRI7KHSUHVVXUHLQGXFHG SKDVH,,KDVDKFSVWUXFWXUHZLWKODWWLFHFRQVWDQWVD QPF QPDW *3DDQGVSDFHJURXS3PPF/HDGZDVVWXGLHGE\;UD\GLIIUDFWLRQDWR& DQGXOWUDKLJKSUHVVXUHVWR*3D>@XSWR*3D>@XSWR*3D>@ DQGE\VKRFNZDYHORDGLQJ>±@7KH,,→,,,SKDVHWUDQVLWLRQZDVGHWHUPLQHGDW DERXW *3D ZLWK ∆99 3KDVH ,,, FU\VWDOOL]HV LQ D EFF VWUXFWXUH ZLWK D QPDW*3DDQGD QPDW*3D>@ 7KHSUHVVXUHGHSHQGHQFHRIWKHVXSHUFRQGXFWLQJWUDQVLWLRQWHPSHUDWXUHIRU 3E,LVXVHGDVDPDQRPHWULFFDOLEUDQWLQWKHORZWHPSHUDWXUHKLJKSUHVVXUHGHYLFHV 7KHVXSHUFRQGXFWLQJSURSHUWLHVZHUHVWXGLHGXSWR*3D>@XSWR*3D>± @ XS WR*3D>±@XSWR*3D>@XSWR*3D>@DQGLQ>± @3KDVH,WUDQVIRUPVWRWKHVXSHUFRQGXFWLQJVWDWHDW.DQG*3DDQGDW . DQG *3D 3KDVH ,, WUDQVIRUPV WR WKH VXSHUFRQGXFWLQJ VWDWH DW . DQG *3D>±@DQGDW.DQG*3D>@ 7KHSKDVHGLDJUDPRIOHDGLVVKRZQLQ)LJXUH 7.
/LT
,IFF
,,KFS
)LJXUH7KHSKDVHGLDJUDPRIOHDG
3*3D
Copyright © 2005 CRC Press, LLC
/HDG
5HIHUHQFHV
0F'DQLHO 0 / %DEE 6 ( DQG 6FRWW * - 0HOWLQJ FXUYHV RI ILYH PHWDOV XQGHUKLJKSUHVVXUH-&KHP3K\V± %XWX]RY93DQG*RQLNEHUJ0* 0HOWLQJWHPSHUDWXUHRIWLQDQGOHDGXSWR DWP'RNO$NDG1DXN6665± %XWX]RY 9 3 DQG *RQLNEHUJ 0 * 0HOWLQJ FXUYHV RI VRPH PHWDOV DW KLJK SUHVVXUHV=K1HRUJDQ.KLP± 'HFNHU ' / -RUJHQVHQ - ' DQG @ XS WR *3D>@E\FDOFXODWLRQ>±@DQGLQ>@7KHIXVLRQFXUYHZDVPHDVXUHG
Copyright © 2005 CRC Press, LLC
;HQRQ
DW*3DDQG.DQGDW*3DDQG.,WZDVGHWHUPLQHGXSWR*3D DQGa.>@DQGLQODVHUKHDWHGGLDPRQGDQYLOFHOOPHDVXUHPHQWV>@8SWR DERXW ± *3D WKH GDWD DJUHHG ZLWK WKH PHOWLQJ FXUYH SUHGLFWHG IURP WKH FRU UHVSRQGLQJVWDWHVHTXDWLRQ7KHPHOWLQJVORSHG7G3H[KLELWVDVKDUSGHFUHDVHDERYH *3D 6LQFH VROLG ;H DW URRP WHPSHUDWXUH KDV EHHQ UHSRUWHG WR WUDQVIRUP IURP SKDVH , IFF WR D GLVRUGHUHG SKDVH ,, QHDU *3D DXWKRUVKDYHUHDVRQWREHOLHYH WKDW WKH FKDQJH LQ VORSH UHSUHVHQWV WKH RQVHW RI OLTXLG±JODVV WUDQVLWLRQ >@ $FFRUGLQJWR>@WKHPHOWLQJFXUYHKDVDEUHDNDWa*3DDQGa.WKHQLW LQFUHDVHGWR*3DDQGa.XSWR*3DDQG±. 7KHEHKDYLRURIVROLGVWDWHLQ;HZDVVWXGLHGE\WKHRSWLFDOPHWKRGXSWR *3D>@WR*3D>@LQ>@E\;UD\GLIIUDFWLRQDERYH*3D >@ WR *3D >@ WR*3D>@WR*3D>@WR*3D>@WR *3D >@ E\ VKRFNZDYH FRPSUHVVLRQ >@ E\ FDOFXODWLRQ >±± @DQGDOVRLQ>±@$FFRUGLQJWRWKHVHPHDVXUHPHQWVSKDVH,ZLWKDIFF VWUXFWXUHWUDQVIRUPHGPDUWHQVLWLFDOO\WRSKDVH,,WKDWLVNLQHWLFDOO\VOXJJLVKEHWZHHQ DQG *3D ZLWK ∆9 3KDVH ,, KDV D KFS VWUXFWXUH ZLWK D QP F QPDW*3D>@3KDVH,,ZLWKDKFSVWUXFWXUHZDVREVHUYHGDW*3D DWKHDWLQJ>@ 7.
/LT
,IFF
)LJXUH7KHPHOWLQJFXUYHRI[HQRQ
3*3D
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
7KH WULSOH SRLQW /LTXLG±IFF±EFF ZDV FDOFXODWHG DW *3D DQG a . >@ 1R IXUWKHU VWUXFWXUDO WUDQVLWLRQ LV VHHQXSWR*3DDQGURRPWHPSHUDWXUH>@7KH RSWLFDODEVRUSWLRQVSHFWUDLQGLFDWHWKDWWKHLQVXODWRU±PHWDOWUDQVLWLRQLVLQWKHUDQJH ±*3D>@ZLWKFRORUFKDQJHWROLJKGDUNRUUHG >@ 7KHPHOWLQJFXUYHRI;HLVSUHVHQWHGLQ)LJXUH 5HIHUHQFHV 6WU\ODQG-&&UDZIRUG-(DQG0DVWRRU0$ 0HOWLQJWHPSHUDWXUHVRI.U ;H&+DWSUHVVXUHVXSWRDWP&DQDG-3K\V± 7RQNRY ( ±@ $W VKRFNZDYH ORDGLQJDQDQRPDO\RIWKH+XJRQLRWDGLDEDWZDVREVHUYHGDWDERXW*3D>@ 7KHEHKDYLRURI±@SKDVHWUDQVLWLRQIURP DIFFVWUXFWXUHWRD EFFZDVSUHGLFWHGDWDERXW*3D>@ 7KHVXSHUFRQGXFWLQJSURSHUWLHVZHUHVWXGLHGXSWR*3D>@DQGXSWR *3D >@ 6HYHUDO VXSHUFRQGXFWLQJ SKDVHV ZHUH GHWHUPLQHG:LWWLJ>@GHWHFWHG WKHVXSHUFRQGXFWLQJWUDQVLWLRQDW7F .DQG*3DXSWR7F .DW*3D IRUSKDVH,,7F .DW*3DDQG.DW*3D
7. /LT
,EFF
,,KFS
,,,6PW\SH
,9GKFS
)LJXUH7KHSKDVHGLDJUDPRI\WWULXP
9IFF 3*3D
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
%UDQGWHWDO>@GHWHUPLQHGWKUHHVXSHUFRQGXFWLQJPRGLILFDWLRQV7F ± .DW±*3D±.DW±*3DDQG.DW3!*3D 7KHSKDVHGLDJUDPRI@ E\ VWUHVV GHIRUPDWLRQ >@ DQG E\ FDOFXODWLRQ >±@ 7KH SKDVH WUDQVLWLRQ IURP ,,, ω WR PRGLILFDWLRQ , KDYLQJ D EFF VWUXFWXUH ZDV REVHUYHG DW 3 ! *3D DQG URRP
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
WHPSHUDWXUH >@ 'LIIHUHQW UHVXOWV ZHUH REVHUYHG LQ >@ 3KDVH WUDQVLWLRQ ZDV GHWHUPLQHG IURP SKDVH ,,, WR DQ LQWHUPHGLDWH SKDVH ,9 γ DW a *3D ZLWK ∆9 >@3KDVH,9KDVDQRUWKRUKRPELFVWUXFWXUHZLWKVSDFHJURXS&PFP DQG ODWWLFH SDUDPHWHUV D QP E QP F QP 3KDVH WUDQVLWLRQWRWKHSUHVVXUHLQGXFHGPRGLILFDWLRQ δ7L9 ZDVGHWHUPLQHGDWa*3D ZLWK ∆9 >@ 3KDVH 9 KDV DQ RUWKRUKRPELF VWUXFWXUH GLVWRUWHG EFF ZLWK VSDFH JURXS &PFP = DQG ODWWLFH FRQVWDQWV D QP E F QPDW*3DLWLVVWDEOHXSWR*3DDQGSKDVHV,9DQG9KDGD XQLTXH]LJ]DJFKDLQOLNHVWUXFWXUH>@ 7KHVXSHUFRQGXFWLQJSURSHUWLHVZHUHVWXGLHGLQ>@,QSKDVH,,WUDQVLWLRQ ZDVGHWHUPLQHGDW7F .DQG*3DDQGDW.DQG*3D6XSHUFRQGXF WLYLW\LQPHWDVWDEOHSKDVH,,,KDVQRWEHHQGHWHFWHGGRZQWR.DQG03D 7KHSKDVHGLDJUDPRIWLWDQLXPLVVKRZQLQ)LJXUH
7. /LT
, ( β )EFF
,,(α ) KFS
,,, ω KH[
)LJXUH7KHSKDVHGLDJUDPRIWLWDQLXP
3*3D
5HIHUHQFHV @7KHPHOWLQJFXUYHZDVGHWHUPLQHGXSWRa*3DDQG±.E\ODVHU KHDWHGGLDPRQGDQYLOFHOO>@DQGE\FDOFXODWLRQXSWRa*3D>@$EUHDNRQ WKH +XJRQLRW DGLDEDW ZDV IRXQG DW DERXW *3D LW KDV EHHQ DWWULEXWHG WR WKH PHOWLQJ SRLQW >@ 7KH PHOWLQJ WHPSHUDWXUH WKHRUHWLFDOO\ FRPSXWHG DW WKLV SRLQW LV DSSUR[LPDWHO\. 7KH EHKDYLRU RI 7D LQ VROLG VWDWH DW . ZDV VWXGLHG E\ PHDVXULQJ WKH HTXDWLRQRIVWDWHE\;UD\GLIIUDFWLRQXSWR*3D>@XSWR*3D>@XSWR *3D>@XSWR*3D>@XSWR*3DDQG.>@DQGE\VKRFN ZDYH FRPSUHVVLRQ >±@ 6WUXFWXUDO DQG PHFKDQLFDO SURSHUWLHV ZHUH FDOFXODWHGXSWR*3D>@DQGLQ>@$IWHUVKRFNFRPSUHVVLRQDW*3DD KLJKSUHVVXUHSKDVHZDVGHWHUPLQHGLWKDVDKH[DJRQDOVWUXFWXUHRIWKH ωW\SHDQG ODWWLFHFRQVWDQWVD QPF QPFD >@ 7KHVXSHUFRQGXFWLQJSURSHUWLHVZHUHVWXGLHGXSWR*3D XSWR*3D DQG 7F . >@ XS WR *3D >@ XS WR *3D DQG a . DQG LQ >@ 7KHPHOWLQJFXUYHRIWDQWDOXPLVVKRZQLQ)LJXUH
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
7.
/LT
,EFF
3*3D
)LJXUH7KHPHOWLQJFXUYHRIWDQWDOXP
5HIHUHQFHV )DWHHYD16DQG9HUHVKFKDJLQ/) 0HOWLQJFXUYHRI7DXSWRNEDU'RNO $NDG1DXN6665± 9HUHVKFKDJLQ/)DQG)DWHHYD16 0HOWLQJWHPSHUDWXUHVRIUHIUDFWRU\PHWDOV DWKLJKSUHVVXUHV+LJK7HPS+LJK3UHVVXUHV± 6KDQHU - : *DWKHUV * 5 DQG 0LQLFKLQR & 7KHUPRSK\VLFDO SURSHUWLHV RI OLTXLG7DDQG0R+LJK7HPS+LJK3UHVVXUHV± 0HU[ + DQG 0RXVVLQ & &RPSUHVVLELOLW\ PHDVXUHPHQWV RI KHDY\ PHWDOV E\ HQHUJ\GLVSHUVLYH ;UD\ GLIIUDFWLRQ LQ WKH GLDPRQGDQYLO FHOO ,Q 3URF ,QW $,5$37 &RQI +LJK 3UHVVXUH 6FLHQFH DQG 7HFKQRORJ\ /H &UHXVRW SS ± 2[IRUG 0LQJ / & DQG 0DQJKQDQL 0 + ,VRWKHUPDO FRPSUHVVLRQ RI EFF WUDQVLWLRQ PHWDOVWRNEDU-$SSO3K\V± ;X - 0DR + . DQG %HOO 3 0 3RVLWURQVHQVLWLYH ;UD\ GLIIUDFWLRQ K\GURVWDWLFFRPSUHVVLELOLW\RI$U7DDQG&XWRNEDU+LJK7HPS+LJK3UHVVXUHV ± 0LWFKHOO$&DQG1HOOLV:- 6KRFNFRPSUHVVLRQRI$O&XDQG7D-$SSO 3K\V±
Copyright © 2005 CRC Press, LLC
7DQWDOXP
7UXQLQ5)/DQRY19DQG0HGYHGHY$% &RPSUHVVLELOLW\RI)H$O0R 7LDQG7DXQGHUVKRFNZDYHVWR±73D3LV¶PD=K(NVS7HRU)L]± %URZQ-0 *UQHLVHQSDUDPHWHUVDQGSKDVHWUDQVLWLRQVIRUVKRFNHG)HDQG7D %XOO$P3K\V6RF -HQQLQJV / ' DQG 6ZHQVRQ & $ (IIHFW RI SUHVVXUH RQ WKH VXSHUFRQGXFWLQJ WUDQVLWLRQWHPSHUDWXUHVRI6Q,Q7D7ODQG+J3K\V5HY± %UDQGW 1 % DQG *LQ]EXUJ 1 , 3UHVVXUH GHSHQGHQFH RI VXSHUFRQGXFWLQJ WUDQVLWLRQIRU]LQF=K(NVS7HRU)L]± 0LQJ/&DQG0DQJKQDQL0+ ,VRWKHUPDOFRPSUHVVLRQRI91EDQG7DWR NEDUFRUUHODWLRQZLWKXOWUDVRQLFVKRFNZDYHDQGRWKHUVWDWLFGDWD,Q3URF$,5$37 ,QW&RQI+LJK3UHVVXUH6FLHQFHDQG7HFKQRORJ\%RXOGHU HGV.'7LPPHUKDXV HWDOSS±1@E\TXHQFKLQJXSWR*3D >@E\'7$XSWR*3D>@DQGLQ>@7KH,δ ±,,γ ±/LTXLGWULSOHSRLQWZDV REVHUYHGDW*3DDQGR&>@7KH,,±,SKDVHERXQGDU\KDVDFRQVWDQWG7G3 .*3DDQGPHOWLQJFXUYHRISKDVH,ZLWKG7G3 .*3D>@7KHPHOWLQJ FXUYH RI SKDVH ,, XS WR *3D PD\ EH UHSUHVHQWHG E\ WKH HTXDWLRQ 7 3± ±Â−3± Â−3± ZKHUH3LQ*3D7LQR& >@7KHIXVLRQFXUYHZDVGHWHUPLQHGRSWLFDOO\DW*3DDQGR&DQGDW*3D DQGR&7KHWKH&XULHSRLQW,,,±,,, ZDVREVHUYHG>±@7KHWULSOHSRLQW EHWZHHQWKH&XULHWHPSHUDWXUHDQGSKDVHV,,,DQG,,ZDVPHDVXUHGDWR&DQG
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
*3D ZLWK WKH &XULH WHPSHUDWXUH LQGHSHQGHQW RI SUHVVXUH 7KH ,,,±,, SKDVH WUDQVIRUPDWLRQ ZDV VWXGLHG E\ '7$ TXHQFKLQJ HOHFWURUHVLVWDQFH YROXPHWULFDOO\ DQGE\VKRFNZDYHORDGLQJ>@7KLVSKDVHERXQGDU\ KDVDQLQLWLDOVORSHG7G3 ±.*3DDQGG7G3 ±.*3DDW*3D 7KH ,,,→,9 SKDVH WUDQVLWLRQ ZDV GHWHUPLQHG DW DERXW *3D DQG URRP WHPSHUDWXUH7KLVWUDQVLWLRQLVVOXJJLVKDQGWKHSKDVHOLQHKDVDSRVLWLYHVORSHDQGLV VHQVLWLYH WR QRQK\GURVWDWLF SUHVVXUHV 7KH ,,,±,9 SKDVH WUDQVLWLRQ ZDV XVHG DV D FDOLEUDQW IRU KLJKSUHVVXUH GHYLFHV DQG ZDV VWXGLHG LQWHQVLYHO\ >± @7UDQVLWLRQWRSKDVH,9ε ZDVGHWHUPLQHGDOVRE\HOHFWURUHVLVWDQFH PHDVXUHPHQWV;UD\GLIIUDFWLRQ0|VVEDXHUVSHFWURVFRS\DQGVKRFNZDYHORDGLQJ LQ WKH UDQJH IURP KLJK WR ORZ WHPSHUDWXUHV >±@ 7KH ,,,±,9 SKDVH WUDQVLWLRQ LV DFFRPSDQLHG E\ ∆99 FPPRO 3KDVH ,9 ε KDV D KFS VWUXFWXUHDQGVSDFHJURXS3PPFZLWKODWWLFHFRQVWDQWVD QPF QPDW*3DDQGURRPWHPSHUDWXUH>@7KHEHKDYLRURISKDVH,9ZDVVWXGLHGE\ ;UD\ GLIIUDFWLRQ >±@ 0|VVEDXHU VSHFWURVFRS\ DW ORZ WHPSHUDWXUH >@ QHXWURQ GLIIUDFWLRQ >@ LQ >@ DQG E\ 5DPDQ VSHFWUD XS WR *3D>@7KHFRPSUHVVLRQRIQRQPDJQHWLFSKDVH,9DWURRPWHPSHUDWXUHXS WR *3D VKRZV QR SKDVH WUDQVLWLRQ >@ 7KH ,,±,,,±,9 WULSOH SRLQW ZDV GHWHUPLQHGEHWZHHQR&DW*3DDQGR&DW*3D>@ ,URQ LV QRW RQO\ LPSRUWDQW WHFKQRORJLFDOO\ EXW LV DOVR WKH PDLQ FRQVWLWXHQW RIWKH(DUWK¶VFRUH7KLVKDVVWLPXODWHGFRQWLQXLQJUHVHDUFKRIWKHPHOWLQJFXUYHDQG WKHSKDVHGLDJUDPLQWKHPHJDEDUUDQJH7KHVHKLJKSUHVVXUHPHDVXUHPHQWVLQYROYH KHDWLQJ WKH VDPSOH LQ D GLDPRQG DQYLOFHOO E\ IRFXVHG ODVHU OLJKW RU E\ HOHFWULFDO FXUUHQWDQGVRPHGLDJQRVWLFWHFKQLTXHIRUDFKDQJHRISKDVH7KHPHOWLQJFXUYHZDV VWXGLHGXSWR*3D>@XSWR*3D>@XSWR*3D>@DQGXSWR *3D>@,WZDVREVHUYHGDW*3DDQGR&DW*3DDQGR& >@ XS WR *3D DQG R& >@ DQG E\ VKRFN ORDGLQJ DW a *3D DQG aR& >@ 7KH PHOWLQJ FXUYH RI )H ZDV PHDVXUHG DQG FDOFXODWHG LQ >±@ 7KH ,,±,9 SKDVH WUDQVIRUPDWLRQ ZDV GHWHUPLQHGE\;UD\GLIIUDFWLRQDQGHOHFWURUHVLVWDQFHPHDVXUHPHQWVDW*3DDQG R&DW*3DDQGR&DW*3DDQGR&ZLWKG7G3 .*3D>@ DQG LQ >@ 7KH GLIIHUHQW YDULDQWV RI WKH KLJKSUHVVXUH SKDVH GLDJUDP LQWKHPHJDEDUUDQJHZHUHSUHVHQWHG> @
Copyright © 2005 CRC Press, LLC
,URQ
7KH WULSOH SRLQW ,,±,9±OLTXLG ZDV GHWHUPLQHG DW *3D DQG aR&
>@$QHZWULSOHSRLQW/LTXLG±,,±9θ ZDVREVHUYHGDWa*3DDQGaR& DQG WKH ,,±,9±9 WULSOH SRLQW DW DERXW *3D DQG aR& >@ 7KH ,9±9 SKDVH WUDQVIRUPDWLRQ ZDV GHWHFWHG DW a *3D DQG aR& DQG WKH PHOWLQJ FXUYH IRU SKDVH 9 θ DW a *3D DQG aR& >@ DQG DW ± *3D DQG aR& >@$QHZKLJKSUHVVXUHSKDVHZLWKDGRXEOHKFSGKFS VWUXFWXUHZDVREVHUYHG DW±*3DDQG±R&>@ZLWKODWWLFHFRQVWDQWVD QPF QP DW *3D DQG R& >@ $ QHZ SKDVH KDYLQJ DQ RUWKRUKRPELF VWUXFWXUHZLWKVSDFHJURXS3EFPDQGODWWLFHFRQVWDQWVD QPE QPF QPZDVGHWHUPLQHGDW*3DDQGR&WKHWULSOHSRLQW,,±,9± QHZSKDVHZDVGHWHFWHGDW*3DDQGR&DQGWKHPHOWLQJRILURQDW*3D DQGaR&>@1RVROLGSKDVHVRWKHUWKDQ,,,DQG,9ZHUHREVHUYHGLQVLWXE\ ;UD\ GLIIUDFWLRQ XS WR *3D DQG R& >@ DQG XS WR *3D DQG !R& >@ 6XSHUFRQGXFWLYLW\ RI )H ,9 ZDV GHWHUPLQHG DW 7F . ZLWK XSSHU FULWLFDO PDJQHWLF ILHOG +F RI 7HVOD XQGHU SUHVVXUH *3D ZKHUH )H LV LQ WKH FU\VWDOORJUDSKLFKFSSKDVHDQGQRQPDJQHWLF>@)XUWKHUFRQILUPDWLRQRIWKLV VXSHUFRQGXFWLQJ WUDQVLWLRQ ZDV REWDLQHG E\ WKH GHWHFWLRQ RI WKH GLDPDJQHWLF VLJQDO GXHWRWKH0HLVVQHUHIIHFWLQDFFRUGDQFHZLWKWKHUHVXOWVRIWKHHOHFWULFDOUHVLVWDQFH PHDVXUHPHQWV 7. /LT
,δ EFF
,,γ IFF
7F
,9ε KFS
,,,α EFF
)LJXUH7KHSKDVHGLDJUDPRILURQ
3*3D
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH 7.
9Θ
/LT
,,γ IFF
,9ε KFS
)LJXUH7KHSKDVHGLDJUDPRILURQ
3*3D
7KH EHKDYLRU RI )H ZDV VWXGLHG E\ VKRFNZDYH FRPSUHVVLRQ >± @ XS WR *3D >@ E\ ;UD\ GLIIUDFWLRQ XS WR *3D DQG R&>@DQGDOVRLQ>@(OHFWURQLFVWUXFWXUHSKDVHVWDELOLW\ WKH HTXDWLRQ RI VWDWH DQG WKH SKDVH GLDJUDP ZHUH FDOFXODWHG >± @ 7KHSKDVHGLDJUDPVRILURQDUHVKRZQLQ)LJXUHVDQG 5HIHUHQFHV 6LPRQ)( 7KHPHOWLQJRILURQDWKLJKSUHVVXUHV1DWXUH± 6WURQJ+0 7KHH[SHULPHQWDOIXVLRQFXUYHRILURQWRDWP-*HRSK\V 5HV± 6WURQJ + 0 0HOWLQJ DQG RWKHU SKDVH WUDQVIRUPDWLRQV DW KLJK SUHVVXUH ,Q 3URJUHVV LQ 9HU\ +LJK 3UHVVXUH 5HVHDUFK HGV ) 3 %XQG\ HW DO SS ± 1@E\FDOFXODWLRQ>@DQGLQ>@7KHPHOWLQJFXUYHDQGSKDVH
Copyright © 2005 CRC Press, LLC
3ODWLQXP
WUDQVLWLRQV ZHUH QRW GHWHUPLQHG 7KH SKDVH WUDQVLWLRQ FXELF±PRQRFOLQLF ZDV GHWHUPLQHGXSWR*3DDQGR&>@ 5HIHUHQFHV 0DR + . %HOO 3 0 6KDQHU - DQG 6WHLQEHUJ ' $ V\VWHP RI SUHVVXUH FDOLEUDWLRQIRUWKHUDQJH±0EDUEDVHGRQVKRFNZDYHHTXDWLRQVRIVWDWHIRU&X 0R 3G DQG $J ,Q 3URF $,5$37 ,QW &RQI +LJK 3UHVVXUH 6FLHQFH 7HFKQRORJ\ %RXOGHU HGV.'7LPPHUKDXVHWDOSS±1@ E\ HOHFWURUHVLVWDQFH PHDVXUHPHQWV XS WR *3D >@LQ>@DQGE\FDOFXODWLRQ>@7KHIXVLRQFXUYHZDVGHWHUPLQHGXSWR R&DQG*3DZLWKG7G3 .*3D>@DQGXSWRR&DQG*3D >@$FFRUGLQJWR>@WKHVKRFNLQGXFHGPHOWLQJEHJLQVDWDERXW*3DZLWKDQ XQLGHQWLILHGWHPSHUDWXUH 7.
/LT
,IFF
)LJXUH7KHPHOWLQJFXUYHRIJROG
3*3D
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
*ROGLQDVROLGVWDWHZDVVWXGLHGE\FRPSUHVVLELOLW\DQGVWUXFWXUDOVWDELOLW\ >@E\WKHHTXDWLRQRIVWDWH>@XSWR±73DXVLQJODVHU GULYHQVKRFNZDYHV>@DQGE\FDOFXODWLRQ>±@$QHZEFFSKDVHZDV SUHGLFWHGE\FDOFXODWLRQ>@WREHDVVWDEOHDVWKHXOWLPDWHKLJKSUHVVXUHSKDVH%XW QR SUHVVXUHLQGXFHG PRGLILFDWLRQV ZHUH GHWHUPLQHG H[SHULPHQWDOO\ +HLQW] DQG -HDQOR] >@ KDYH SURSRVHG XVH RI $X DV D SUHVVXUH FDOLEUDWLRQ VWDQGDUG XS WR *3DDQGR&DQGXSWR±*3DLQ>@ 7KHSKDVHGLDJUDPRIJROGLVVKRZQLQ)LJXUH
5HIHUHQFHV 'HFNHU ' / DQG 9DQIOHHW + % 0HOWLQJ DQG KLJKWHPSHUDWXUH HOHFWULFDO UHVLVWDQFHRIJROGXQGHUSUHVVXUH3K\V5HY± &RKHQ / + .OHPHQW : DQG .HQQHG\ * & 0HOWLQJ RI &X $J DQG $X DW KLJKSUHVVXUHV3K\V5HY± 0LWUD15'HFNHU'/DQG9DQIOHHW+% 0HOWLQJFXUYHVRI&X$J$X DQG3WWRNEDU3K\V5HY± $NHOOD-DQG.HQQHG\*& 0HOWLQJRI$X$JDQG &X±SURSRVDOIRUDQHZ KLJKSUHVVXUHFDOLEUDWLRQVFDOH-*HRSK\V5HV± 6WURQJ + 0 7XIW 5 ( DQG +DQQHPDQ 5 ( 7KH LURQ IXVLRQ FXUYH DQG JDPPD±GHOWD±OLTXLGWULSOHSRLQW0HWDO7UDQV± +HLQW] ' / DQG -HDQOR] 5 7KH HTXDWLRQ RI VWDWH RI WKH JROG FDOLEUDWLRQ VWDQGDUG-$SSO3K\V± *RGZDO % . 1J $ DQG 'DVLOYD / 0HOWLQJ DQG +XJRQLRW FDOFXODWLRQV IRU JROG3K\V/HWW$± *RGZDO % . DQG -HDQOR] 5 )LUVWSULQFLSOHV HTXDWLRQ RI VWDWH RI JROG 3K\V 5HY%± 6FKORVVHU + 9LQHW 3 DQG )HUUDQWH - 3UHVVXUH GHSHQGHQFH RI WKH PHOWLQJ WHPSHUDWXUHRIPHWDOV3K\V5HY%± .XPDUL0DQG'DVV1 $QHTXDWLRQRIVWDWHDSSOLHGWRVROLGV,,-3K\V &RQG0DWW± 0LQJ/&;LRQJ'DQG0DQJKQDQL0+ ,VRWKHUPDOFRPSUHVVLRQRI$XDQG $OWR*3D3K\VLFD%± $NLPRWR6 +LJKSUHVVXUHKLJKWHPSHUDWXUHUHVHDUFKZLWKV\QFKURWURQUDGLDWLRQ 'UDPDWLF DGYDQFH LQVLWX REVHUYDWLRQ RI FU\VWDO VWUXFWXUH DQG SKDVH WUDQVIRUPDWLRQV -&U\VWDOORJU6RF-DS±
Copyright © 2005 CRC Press, LLC
*ROG
0LJDXOW$5DPDLQ-3DQG-DFTXHVVRQ- )XVLRQFXUYHVDWKLJKSUHVVXUHDQG SDUDPHWHU *UQHLVHQ RI PHWDOV ,Q 3URF ,QW $,5$37 &RQI +LJK 3UHVVXUH 6FLHQFH 7HFKQRORJ\/H&UHXVRW SS±2[IRUG +RIIEDXHU:YRQ%RUJHQ1(XOHU+DQG%RHKOHU5 7KHGLIIHUHQFHEHWZHHQ K\GURVWDWLFDQGQRQK\GURVWDWLFFRPSUHVVLRQRI$XDQG)H+LJK3UHV5HV± 0LUZDOG 3 : DQG .HQQHG\ * & 7KH PHOWLQJ FXUYH RI $X $J DQG &X WR NEDUSUHVVXUH$UHLQYHVWLJDWLRQ-*HRSK\V5HV%± @XSWR *3D >@ DQG E\ HOHFWURUHVLVWDQFH XS WR *3D >@ 7KH PHOWLQJ FXUYH ZDV PHDVXUHGXSWRR&DQG*3DZLWKDFRQVWDQWG7G3 .*3D>@ 7KH EHKDYLRU RI =Q DW R& ZDV GHWHUPLQHG E\ ;UD\ GLIIUDFWLRQ XS WR *3D >@ XS WR *3D >@ XS WR *3D >@ XS WR *3D >@ XS WR *3D >@E\0|VVEDXHUVSHFWURVFRS\DWORZWHPSHUDWXUH>@E\FDOFXODWLRQ>@ DQGLQ>@7KHYROXPHGHSHQGHQFHRIWKHFDUDWLRFKDQJHVDQGEHFRPHV H[DFWO\ DW *3D >@ 7KLV DQRPDO\ LV PRVW OLNHO\ UHODWHG WR WKH HOHFWURQLF WRSRORJLFDO WUDQVLWLRQ UHFHQWO\ IRXQG ZLWK WKH 0|VVEDXHU VSHFWURVFRS\ DW *3D DQG . DW LQHODVWLF QHXWURQ VFDWWHULQJ >@ DQG E\ FDOFXODWLRQ >@ ,Q >@ WKH DQRPDO\ LQ WKH YROXPH GHSHQGHQFH RI WKH FD D[LDO UDWLRFDQQRORQJHUEHRUVHUYHGE\;UD\GLIIUDFWLRQZLWKDKHOLXPSUHVVXUHPHGLXP XSWR*3DDWR&DQG±R&WKHDQRPDO\LVLQGXFHGE\WKHQRQK\GURVWDWLFLW\ DVVRFLDWHGZLWKVROLGLILFDWLRQRIWKHHWKDQRO−PHWKDQROPHGLXPLQ>@
7. /LT
,KFS
3*3D
)LJXUH7KHSKDVHGLDJUDPRI]LQF
Copyright © 2005 CRC Press, LLC
=LQF
7KH FD DQRPDO\ ZKLFK LV SUHGLFWHG WR DSSHDU DVVRFLDWHG ZLWK WKH HOHFWURQLFWRSRORJLFDOWUDQVLWLRQVZRXOGEHH[WUHPHO\VPDOO>@7KHFDUDWLRZDV GHWHUPLQHGDVDW*3DDQG99Ra>@7KHHOHFWURQLFVWUXFWXUHRI=QXS WR*3DKDVEHHQFDOFXODWHGXVLQJWKHVHOIFRQVLVWHQWO\PXIILQWLQRUELWDOPHWKRG >@&DOFXODWLRQVVKRZWKDWIRXUHOHFWURQLFWRSRORJLFDOWUDQVLWLRQVKDSSHQHGDW DQG *3D 7KHVH WUDQVLWLRQV H[SODLQ PDQ\ DQRPDOLHV RI HOHFWULFDO DQG WKHUPDO UHVLVWLYLW\ WKH UHVLVWDQFH PLQLPXP WKH WUDQVYHUVH H[SDQVLRQ FRHIILFLHQW VLJQ RVFLOODWLRQV DQG WKH DQRPDOLHV RI WKH 0|VVEDXHU DQGWKH5DPDQVSHFWUD>@ 6WUXFWXUDO SKDVH WUDQVLWLRQV KDYH QRW EHHQ REVHUYHG XS WR *3D >@ 7KH VXSHUFRQGXFWLQJSURSHUWLHVZHUHPHDVXUHGXSWR*3DDQG7F .>@XSWR *3DDQG7F .>@DQGLQ>@7KHSKDVHGLDJUDPRI]LQFLVVKRZQLQ )LJXUH 5HIHUHQFHV %XWX]RY933RQ\DWRYVN\(*DQG6KDNKRYVNRL*3 0HOWLQJWHPSHUDWXUHV RI =Q &G 7O DQG 6E XQGHU SUHVVXUHV WR DWP 'RNO $NDG 1DXN 6665 ± .HQQHG\ * & DQG 1HZWRQ 5 & 0HOWLQJ DQG SKDVH WUDQVIRUPDWLRQV LQ VROLG VWDWHRIVRPHSXUHPHWDOVDWKLJKWHPSHUDWXUHVDQGSUHVVXUHV,Q6ROLGVXQGHU3UHVVXUH HGV:3DXOHWDOSS±1@ XS WR *3D >@ XS WR *3D >@ E\ FDOFXODWLRQ >@ DQG LQ >@7KHPHOWLQJFXUYHLVXVHGIRUFDOLEUDWLRQRISUHVVXUHPDQJDQLQJDXJHV ,WZDVREVHUYHGDW*3DDQGR&7KHIXVLRQFXUYHZDVGHWHUPLQHGDWR& DQG*3DDQGDWR&DQG*3DZLWKDQLQLWLDOG7G3 .*3D>@ 7KHEHKDYLRURI+JLQDVROLGVWDWHZDVVWXGLHGE\;UD\GLIIUDFWLRQXSWR *3D >@ XS WR *3D >@ XS WR *3D >@ E\ FDOFXODWLRQ > @ DQG LQ >±@ 7KH ,,±, β±α SKDVH WUDQVLWLRQ KDV DQ LQLWLDO G7G3 .*3DLWZDVREVHUYHGDWR&DQG*3DDQGDWR&DQG*3D7KLV WUDQVLWLRQ LV RI WKH PDUWHQVLWLF W\SH DQG LV FKDUDFWHUL]HG E\ D PDUNHG K\VWHUHVLV >@ 3KDVH WUDQVLWLRQ IURP +J ,, WR WKH KLJKSUHVVXUH PRGLILFDWLRQ ,,, γ ZDV GHWHUPLQHG DW a *3D DQG URRP WHPSHUDWXUH >@ 3KDVH ,,, KDV D VLPSOH RUWKRUKRPELFVWUXFWXUHZLWK= DQGODWWLFHFRQVWDQWVD QPE QP
Copyright © 2005 CRC Press, LLC
0HUFXU\
F QPDW*3D7KH,,,±,9δ SKDVHWUDQVIRUPDWLRQZDVGHWHUPLQHGDW a *3D DQG R& >±@ 7KH VWUXFWXUH RISKDVH,9δ KDVQRWEHHQLGHQWLILHG 7KHVXSSRVHGSKDVHGLDJUDPKDVWKH,±,,±,,,WULSOHSRLQWQHDU*3DDQGR&DQG WKH,±,,,±,9WULSOHSRLQWQHDU*3DDQGR&>@ 7KH VXSHUFRQGXFWLQJ SURSHUWLHV RI SKDVHV , DQG ,, ZHUH LQYHVWLJDWHG LQ >@3KDVH,KDVWKH G7FG3 ±Â−.*3D3KDVH,,WUDQVIRUPVWR WKHVXSHUFRQGXFWLQJVWDWHDW7F .DQG*3DZLWKG7FG3 ±Â−.*3D 7KHVXSSRVHGSKDVHGLDJUDPRIPHUFXU\LVVKRZQLQ)LJXUH 7.
/LT
,α UKRPE
,,,γ RUWK
,9σ
,,( β ) EFW
3*3D
)LJXUH7KHVXSSRVHGSKDVHGLDJUDPRIPHUFXU\
5HIHUHQFHV %ULGJPDQ3: 0HUFXU\OLTXLGDQGVROLGXQGHUSUHVVXUH3URF$P$FDG$UWV 6FL± %ULGJPDQ 3 : 3RO\PRUSKLVP SULQFLSDOO\ RI WKH HOHPHQWV XS WR DWP 3K\V5HY± %ULGJPDQ3: 7KHPHDVXUHPHQWRIK\GURVWDWLFSUHVVXUHWRDWP3URF $P$FDG$UWV6FL± %ULGJPDQ 3 : 7KH UHVLVWDQFH RI HOHPHQWV DOOR\V DQG FRPSRXQGV WR DWP3URF$P$FDG$UWV6FL±
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH =KRNKRYVNLL0. 0HOWLQJFXUYHRIPHUFXU\XQGHUSUHVVXUHXSWRDWP ,]PHULW7HNKQ1R± =KRNKRYVNLL 0 . DQG 5D]XPLNKLQ 9 1 0HOWLQJ FXUYH RI PHUFXU\ WR DWPDVDVFDOHRIWKHKLJKSUHVVXUHV,]PHULW7HNKQ1R± %XURYD//=KRNKRYVNLL0.=RORW\NK(9DQG5D]XPLNKLQ91 7KH WKHUPRG\QDPLF VFDOH RI KLJK SUHVVXUHV WR DWP 7UXG\ 0HWURORJ ,QVW 6665 1R ± %RJGDQRY96DQG0LURVKQLNRY$3 6WXG\RIPHOWLQJFXUYHIRUPHUFXU\XS WRDWP7UXG\0HWURORJ,QVW66651R ± .OHPHQW:-D\DUDPDQ$DQG.HQQHG\*& 7UDQVIRUPDWLRQVLQPHUFXU\DW KLJKSUHVVXUH3K\V5HY± 'DGVRQ56DQG*UHLJ5*3 )L[HGSRLQWVRQWKHVFDOHRIKLJKSUHVVXUHVWKH IUHH]LQJSUHVVXUHRIPHUFXU\DWR&-$SSO3K\V± *UDIWRQ5* $FRPSLODWLRQDQGDQDO\VLVRIPHOWLQJFXUYHGDWDIRUDUJRQ3K\V /HWW$± 'HFNHU ' / -RUJHQVHQ - ' DQG @ 7KH EHKDYLRU RI WKH γ DQG WKH α SKDVHV ZDV PHDVXUHG E\ SRVLWURQ DQQLJLODWLRQ VSHFWURVFRS\ >@ E\ XOWUDYLROHW DQG ;UD\ VSHFWURVFRS\>@E\/HGJH;UD\DEVRUSWLRQVSHFWUD>@E\&RPSWRQVFDWWHULQJ >±@ DQG E\ PXRQ VSLQ URWDWLRQ >@ 7KHRUHWLFDO ZRUNV RQ &H KDYH EHHQ FRQFHQWUDWHG RQ WKH α±γ LVRVWUXFWXUDO WUDQVLWLRQ WKH FULWLFDO SRLQW DQG WKH WHPSHUDWXUH PLQLPXP RQ WKH PHOWLQJ FXUYH >± ± ±@ $ ODUJH QXPEHU RI WKHRULHV KDYH EHHQ PDGH DERXW WKH ,,±,9 WUDQVLWLRQ $QGHUVRQ PL[LQJ .RQGRHIIHFW 0RWW WUDQVLWLRQ -DKQ 7HOOHUHIIHFWLQWHUFRQILJXUDWLRQDOPL[LQJRUPL[HGYDOHQFH7KHLVRVWUXFWXUDO,,±,9 SKDVH WUDQVLWLRQ DQG SRVLWLRQ RI WKH FULWLFDO SRLQW ZHUH VWXGLHG E\ GRSLQJ ZLWK WKH UDUHHDUWK PHWDV DQG 7K >@ 7KH FULWLFDO SRLQW IRU WKH &H7K DOOR\ ZDV PHDVXUHG DW 03D DQG DW DERXW ±R& 'RSLQJ ZLWK WKH UDUHHDUWK HOHPHQWVORZHUVWKHSUHVVXUHRIWKHFULWLFDOSRLQW $WKLJKHUSUHVVXUHWKHEHKDYLRURI&HZDVVWXGLHGE\;UD\GLIIUDFWLRQXS WR*3D>@XSWR*3D>@XSWR*3D>@XSWR*3D>@DQG LQ>±@3KDVHWUDQVIRUPDWLRQIURP&H,9WRWKHKLJKSUHVVXUHSKDVH 9 α ZDV GHWHUPLQHG DW a *3D DQG R& ZLWK ∆99 a DQG D QHJDWLYH G7G3 ±.*3DDW±R&7KLVWUDQVLWLRQZDVREVHUYHGE\HOHFWURUHVLVWDQFH PHDVXUHPHQWV WKH YROXPHWULF PHWKRG PHDVXULQJ RI WKH HODVWLF FRQVWDQWV DQG E\ WKHUPRHPI VWXG\ 7KHUH LV VRPH FRQWURYHUV\ IRU D VWUXFWXUH RI WKH α SKDVH ,W LGHQWLILHV DV DQ RUWKRUKRPELF VWUXFWXUH RI WKH α8 W\SH ZLWK ODWWLFH FRQVWDQWV
Copyright © 2005 CRC Press, LLC
&HULXP
D QPE QPF QPDW*3DDQGR&>±@3KDVH
α LGHQWLILHVLQDIFFVWUXFWXUH>@DQGLQDGLVWRUWHGKFSVWUXFWXUH>@$FFRUGLQJ WR >@ WKH PL[WXUH RI SKDVHα SKDVHα
DQG SKDVH ZLWK D IFF VWUXFWXUH ZDV REVHUYHG DW *3D DQG URRP WHPSHUDWXUH 3KDVH α
KDV D ERG\FHQWHUHG PRQRFOLQLFVWUXFWXUHDQGODWWLFHFRQVWDQWVD QPE QPF QP β R $XWKRUV >@ REVHUYHG D FU\VWDO JUDLQ JURZWK GXULQJ WKH SKDVH WUDQVLWLRQ WR 9 α ERWK GXULQJ FRPSUHVVLRQ DQG GHFRPSUHVVLRQ F\FOHV 3KDVH WUDQVLWLRQ IURP α WR PRGLILFDWLRQ 9, ε ZDV GHWHFWHG DW *3D DQG R& ZLWK D VORSH ± .*3D DW ±R& ZKHUH SKDVH 9, LV VWDEOH XS WR *3D >@ 0RGLILFDWLRQ 9, ε FU\VWDOOL]HV LQ D ERG\FHQWHUHG WHWUDJRQDO VWUXFWXUH ZLWK = DQG ODWWLFH SDUDPHWHUV D QP F QP DW *3D DQG URRP WHPSHUDWXUH>@3KDVH9,ZDVGHWHUPLQHGXSWR*3D99R ZLWKD FRQVWDQW FD >@ 6WUXFWXUHV RI WKH KLJKSUHVVXUH SKDVHV ZHUH VWXGLHGDOVRXSWR*3D>@DQGLQ>@7KHSKDVHZLWKDERG\FHQWHUHG PRQRFOLQLFVWUXFWXUHDQGVSDFHJURXS&P>SRVVLEO\α @ZDVREVHUYHGDW*3D DQG R& ,W KDV ODWWLFH FRQVWDQWV D QP E QP F QP
β R1RHYLGHQFHRIWKH α SKDVHDWR&ZDVREVHUYHG>@3KDVH α KDV REWDLQHG E\ KHDWLQJ WKH &P SKDVH α
DW R& IRU VHYHUDO KRXUV ZLWK ODWWLFH FRQVWDQWVD QPE QPF QP>@([WHQVLYHVWXG\ RI SKDVH GLDJUDP RQ &H ZDV SHUIRUPHG XS WR *3D DW ±R& E\ ;UD\ GLIIUDFWLRQ )LJXUH $ >@ $FFRUGLQJ WR WKLV VWXG\ WKH PHWDVWDEOH PRQRFOLQLF SKDVH α H[LVWV IURP *3D DQG R& XS WR *3D DQG R& LW GLVDSSHDUV RQ KHDWLQJ DWFRQVWDQWSUHVVXUHLWZDVQHYHUUHFRYHUHGRQFRROLQJ7KH SKDVH α
SRVVLEO\EHFRPHVVWDEOHDWORZWHPSHUDWXUHV,UUHYHUVLEOHGLVDSSHDUDQFHRI WKHPHWDVWDEOHSKDVH α
RQKHDWLQJDWDERXWR&DQG±*3DZDVREVHUYHGE\ UHVLVWDQFH DQRPDOLHV >@ 7KH SKDVH OLQHV ,9±9 9±9, DQG ,9±9, DUH SUHVHQWHGLQ)LJXUHD3KDVHVWDELOLW\DQGVWUXFWXUHVZHUHFDOFXODWHGLQ>@7KH ,9±9±9,α±α ±ε WULSOHSRLQWZDVGHWHUPLQHGDWR&DQGa*3D>@LW ZDV SUHYLRXVO\ GHULYHG IURP UHVLVWDQFH DQG '7$ PHDVXUHPHQWV >@ 7KH ,9±9, SKDVHWUDQVLWLRQZDVREVHUYHGDW±*3DDQG±R&ZLWKDSRVLWLYHVORSH 7KHH[LVWHQFHRIWULFULWLFDOSRLQWZDVGLVFXVVHGRQWKH,9±9,ERXQGDU\>@ 6XSHUFRQGXFWLYLW\ ZDV VWXGLHG LQ >± @ 3KDVH,9WUDQVIRUPV WRDVXSHUFRQGXFWLQJVWDWHDW7F .DQG*3DDQGDW.DQG*3D>± @7KHSUHVVXUHLQGXFHGSKDVHVWUDQVIRUPWRDVXSHUFRQGXFWLQJVWDWHDW.DQG
Copyright © 2005 CRC Press, LLC
3KDVHWUDQVIRUPDWLRQVRIHOHPHQWVXQGHUKLJKSUHVVXUH
*3D DQG DW . DQG *3D >±@ 7KH WHPSHUDWXUHV RI WKH VXSHUFRQ GXFWLQJWUDQVLWLRQZHUHGHFUHDVHGZLWKDFRQWDPLQDWLRQRIFHULXP 7KHSKDVHGLDJUDPVRIFHULXPDUHVKRZQLQ)LJXUHVDQGD 7.
/LT
,EFF
,,IFF
9,EFW
.
,9IFF
9RUWK
,,,GKFS
3*3D
)LJXUH7KHSKDVHGLDJUDPRIFHULXP.FULWLFDOSRLQW
7. /LT
,EFF IFF ,,γ
9,ε EFW 9 α RUWK
.
,9α
α α
PRQ
,,,GKFS
3*3D
)LJXUHD7KHK\SRWKHWLFDOYDULDQWRIWKHSKDVHGLDJUDP RIFHULXP.FULWLFDOSRLQW
Copyright © 2005 CRC Press, LLC
&HULXP
5HIHUHQFHV
%ULGJPDQ3: 7KHFRPSUHVVLELOLW\DQGSUHVVXUHFRHIILFLHQWRIUHVLVWDQFHRIWHQ HOHPHQWV3URF$P$FDG$UWV6FL± %ULGJPDQ3: 5RXJKFRPSUHVVLRQVRIVXEVWDQFHVWRDWP3URF$P $FDG$UWV6FL± %ULGJPDQ 3 : 7KH HIIHFW RI SUHVVXUH RQ WKH HOHFWULFDO UHVLVWDQFH RI FHUWDLQ VHPLFRQGXFWRUV3URF$P$FDG$UWV6FL± %ULGJPDQ 3 : 7KH UHVLVWDQFH RI HOHPHQWV DOOR\V DQG FRPSRXQGV WR DWP3URF$P$FDG$UWV6FL± /DZVRQ $ : DQG 7DQJ 7