Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds

The modern theoretical approaches to investigation of polymorphism and structure phase transitions in inorganic compounds are reviewed. The emphasis is made on new ideas of solid state thermodynamics, structure and energy simulation of polymorphs, and results of application thereof to simple substan...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2004
Автор: Grebenyuk, A.G.
Формат: Стаття
Мова:English
Опубліковано: НТК «Інститут монокристалів» НАН України 2004
Назва видання:Functional Materials
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/138787
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds / A.G. Grebenyuk // Functional Materials. — 2004. — Т. 11, № 2. — С. 367-371. — Бібліогр.: 47 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-138787
record_format dspace
spelling irk-123456789-1387872018-06-20T03:06:30Z Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds Grebenyuk, A.G. The modern theoretical approaches to investigation of polymorphism and structure phase transitions in inorganic compounds are reviewed. The emphasis is made on new ideas of solid state thermodynamics, structure and energy simulation of polymorphs, and results of application thereof to simple substances and binary compounds. Статья содержит обзор современных теоретических подходов к исследованию полиморфизма и структурных фазовых переходов неорганических соединений. Основное внимание уделено новым идеям в термодинамике твердого тела, методам моделирования структуры и энергетики полиморфных форм и результаты их применения к простым веществам и бинарным соединениям. Стаття містить огляд сучасних теоретичних підходів до дослідження поліморфізму та структурних фазових переходів неорганічних сполук. Основну увагу приділено новим ідеям у термодинаміці твердого тіла, методам моделювання структури і енергетики поліморфних форм та результатам їхнього застосування до простих речовин і бінарних сполук. 2004 Article Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds / A.G. Grebenyuk // Functional Materials. — 2004. — Т. 11, № 2. — С. 367-371. — Бібліогр.: 47 назв. — англ. 1027-5495 http://dspace.nbuv.gov.ua/handle/123456789/138787 en Functional Materials НТК «Інститут монокристалів» НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The modern theoretical approaches to investigation of polymorphism and structure phase transitions in inorganic compounds are reviewed. The emphasis is made on new ideas of solid state thermodynamics, structure and energy simulation of polymorphs, and results of application thereof to simple substances and binary compounds.
format Article
author Grebenyuk, A.G.
spellingShingle Grebenyuk, A.G.
Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds
Functional Materials
author_facet Grebenyuk, A.G.
author_sort Grebenyuk, A.G.
title Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds
title_short Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds
title_full Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds
title_fullStr Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds
title_full_unstemmed Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds
title_sort theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds
publisher НТК «Інститут монокристалів» НАН України
publishDate 2004
url http://dspace.nbuv.gov.ua/handle/123456789/138787
citation_txt Theoretical models for structural phase transitions in molecular clusters and crystals of inorganic compounds / A.G. Grebenyuk // Functional Materials. — 2004. — Т. 11, № 2. — С. 367-371. — Бібліогр.: 47 назв. — англ.
series Functional Materials
work_keys_str_mv AT grebenyukag theoreticalmodelsforstructuralphasetransitionsinmolecularclustersandcrystalsofinorganiccompounds
first_indexed 2025-07-10T06:34:38Z
last_indexed 2025-07-10T06:34:38Z
_version_ 1837240720322199552
fulltext 7KHRUHWLFDO�PRGHOV�IRU�VWUXFWXUDO�SKDVHWUDQVLWLRQV�LQ�PROHFXODU�FOXVWHUV�DQG�FU\VWDOVRI�LQRUJDQLF�FRPSRXQGV $�*�*UHEHQ\XN ,QVWLWXWH�RI�6XUIDFH�&KHPLVWU\��1DWLRQDO�$FDGHP\�RI�6FLHQFHV�RI�8NUDLQH����*HQ��1DXPRY�6W���������Ç\LY��8NUDLQH 7KH� PRGHUQ� WKHRUHWLFDO� DSSURDFKHV� WR� LQYHVWLJDWLRQ� RI� SRO\PRUSKLVP� DQG� VWUXFWXUHSKDVH�WUDQVLWLRQV�LQ�LQRUJDQLF�FRPSRXQGV�DUH�UHYLHZHG��7KH�HPSKDVLV�LV�PDGH�RQ�QHZ�LGHDVRI�VROLG�VWDWH�WKHUPRG\QDPLFV��VWUXFWXUH�DQG�HQHUJ\�VLPXODWLRQ�RI�SRO\PRUSKV��DQG�UHVXOWVRI�DSSOLFDWLRQ�WKHUHRI�WR�VLPSOH�VXEVWDQFHV�DQG�ELQDU\�FRPSRXQGV� fzjz�¹�xvlné qz�viové�xvkénuntt�}�znvénzq·nxrq}�wvl}vlvk�r�qxxsnlvkjtqí�wvsq�uvé{qouj� q� xzéyrzyét�}� {jovk�}� wnén}vlvk� tnvémjtq·nxrq}� xvnlqtntqp�� Ìxtvktvnktqujtqn�ylnsntv�tvk�u�qln¹u�k�znéuvlqtjuqrn�zknélvmv�znsj��unzvlju�uvlnsqévkj�tq¹�xzéyrzyé��q�ëtnémnzqrq�wvsquvé{t�}�{véu�q�énoys�zjz��q}�wéquntntq¹�r�wév�xz�u�kn�nxzkju�q�iqtjét�u�xvnlqtntq¹u�� 7KH� SRO\PRUSKLVP� RI� FKHPLFDO� VXE �VWDQFHV� KDV� EHHQ� NQRZQ� IRU� PRUH� WKDQ���� \HDUV� >�@�� 7KH� SKDVH� WUDQVLWLRQV� EH �WZHHQ�YDULRXV�VWUXFWXUHV�FDXVHG�E\�H[WHUQDOHIIHFWV�KDYH� EHHQ� VWXGLHG� IRU� D� JUHDW�QXP �EHU� RI� FRPSRXQGV� WKDW�PDGH� LW� SRVVLEOH� WRGHYHORS� D� FRQVLVWHQW� WKHRU\� RI� VXFK� SURF �HVVHV� >�@�� 7KH� WUDQVIRUPDWLRQV� FRQGLWLRQHGE\� WKH� FKDQJHV� LQ� DWRPLF� FRRUGLQDWLRQ� VXU �URXQGLQJ� DUH� RI� D� SDUWLFXODU� LQWHUHVW� EH �FDXVH� WKH\� DUH� GXH� WR� D� IXQGDPHQWDO� UHDU �UDQJHPHQW� RI� WKH� VXEVWDQFH� VSDWLDO� VWUXF �WXUH� DQG� DUH� DFFRPSDQLHG� E\� FRQVLGHUDEOHKHDW�HIIHFWV�>�@�7KH� FRQFHSW� RI� SUHIHUHQFH� HQHUJ\�� 7KHFRQVLGHUDEOH�JDS�EHWZHHQ�IDVW�DFFXPXODWLRQRI� WKH� VWUXFWXUDO� LQIRUPDWLRQ� RQ� FRPSOH[FRPSRXQGV� DQG� VORZ� UDWH� RI� WKH� ODERULRXVWKHUPRFKHPLFDO� VWXGLHV� VWLSXODWHG� D� GHYHO �RSPHQW� RI� QHZ� PHWKRGV� IRU� HVWLPDWLRQ� RIWKHUPRG\QDPLF� SURSHUWLHV� RI� VXEVWDQFHV�7KH� FKRLFH� RI� FRRUGLQDWLRQ� SRO\KHGURQ� DV� DVWUXFWXUH�IUDJPHQW�GHWHUPLQLQJ�WKHVH�SURS �HUWLHV�DOORZV�XV� WR�DSSO\�D�XQLWHG�DSSURDFKWR� WKH� FRQVLGHUDWLRQ� RI� DPRUSKRXV�� JODVV�OLNH��QDQR�FU\VWDOOLQH��DQG�FU\VWDOOLQH�VWDWHV>�@�� 7KH�SULPDU\�RFFXSDWLRQ� RI�GHILQLWH� SR �VLWLRQV� E\� FDWLRQV� LV� GHILQHG� E\� FU\VWDO �ORJUDSKLF� DQG� WKHUPRG\QDPLF� IDFWRUV�� WKDW EHFDPH�D�EDVH�IRU�WKH�FRQFHSW�RI�SUHIHUHQFHHQHUJ\� WR� D� FHUWDLQ� FRRUGLQDWLRQ� VXUURXQG �LQJ�� 7KH� $O�� LRQ� WUDQVLWLRQ� HQWKDOS\� IURPWHWUDKHGUDO� 2�± VXUURXQGLQJ� WR� RFWDKHGUDORQH� ZDV� ILUVW� GHWHUPLQHG� LQ� >�@� WR� EH� RI������N-�PRO��/DWHU��D�SUREOHP�ZDV�IRUPX �ODWHG� >�@� RI� WKH� FKRLFH� RI� NH\� ∆+�� ∆* DQG ∆6 YDOXHV� IRU� FKDQJH� LQ� FDWLRQLF� FRRUGLQD �WLRQ�QXPEHUV�UHODWHG� WR� WKH� WHWUDKHGURQ�WR�RFWDKHGURQ� WUDQVLWLRQV� ZLWKLQ� WKH� R[\JHQVXUURXQGLQJ�� ,Q� >�@�� WKH� YDOXHV� RI� WKHUPR �G\QDPLF� IXQFWLRQV� IRU� FKDQJHV� LQ�FRRUGLQD �WLRQ� RI� ERWK� WUDQVLWLRQ� DQG� QRQ�WUDQVLWLRQPHWDO� FDWLRQV� ZHUH� V\VWHPDWL]HG�� DQG� WKHVWUXFWXUDO�GHWDLOLQJ�WDNLQJ�LQWR�DFFRXQW�WKHW\SH�RI�R[LGH�RU�VXOILGH�FRRUGLQDWLRQ�SRO\KH �GURQ�ZDV� VKRZQ� WR� EH� DQ� RSWLPXP� RQH� IRUFRPSDULQJ� WKHUPRFKHPLFDO� DQG� VWUXFWXUDOFKDUDFWHULVWLFV� RI� FRRUGLQDWLRQ� FRPSRXQGV�5HFHQWO\� >�@�� D� YHUVDWLOH� HTXDWLRQ� ZDV� GH �GXFHG�UHODWLQJ�WKH�HQWKDOS\�RI�FDWLRQLF�SUHI �HUHQFH�WR�DOWHUQDWLYH�SRVLWLRQV�LQ�DQ\�DQLRQLFFORVHVW� SDFNLQJ�ZLWK� W\SLFDO� LQWHUDWRPLF� GLV �WDQFHV�DQG�D�VHOI�FRQVLVWHQW�V\VWHP�RI�WKH�FDW �LRQLF� SUHIHUHQFH� HQWKDOSLHV�ZDV� SURSRVHG� IRUVXOILGHV��VHOHQLGHV��DQG�K\GULGHV�7KH�FRQFHSW�RI�SUHIHUHQFH�HQHUJ\�SURYHGWR� EH� UDWKHU� IUXLWIXO�� 6R�� WKH� HQWKDOSLHV� RI )XQFWLRQDO�0DWHULDOV�����1R��������� �������²�,QVWLWXWH�IRU�6LQJOH�&U\VWDOV )XQFWLRQDO�PDWHULDOV������������� ��� FKDQJHV� LQ� FDWLRQLF� FRRUGLQDWLRQ� QXPEHUVDUH� XVHG� WR� FDOFXODWH� UHVSHFWLYH� YDOXHV� IRUWKH� SURFHVVHV� RI� VLPSOH�WR�FRPSOH[� R[LGHIRUPDWLRQ�� WR� DQDO\]H� WKHRUHWLFDOO\� WKH� VWD �ELOL]DWLRQ�RI�PHWDVWDEOH� R[LGH� IRUPV�GXH� WRPRGLI\LQJ�DGGLWLYHV��WR�VLPXODWH�SRZHU�FRQ �VXPLQJ�KLJK�WHPSHUDWXUH�SURFHVVHV��FU\VWDO �OL]DWLRQ� RI� DPRUSKRXV� R[LGHV� DQG� VHOI�VSUHDGLQJ� KLJK�WHPSHUDWXUH� V\QWKHVLV� RIPXOWL�HOHPHQWDO�R[LGHV��>�@�7KH� ILUVW� DWWHPSWV� WR� DSSO\� TXDQWXPFKHPLFDO�PHWKRGV� IRU� FDOFXODWLRQ� RI� HQHUJ\FKDQJH� YDOXHV� LQ� FDWLRQLF� FRRUGLQDWLRQ� VXU �URXQGLQJ�JDYH�RQO\�TXDOLWDWLYHO\�FRUUHFW�UH �VXOWV� ZKHUHDV� WKH� DEVROXWH� YDOXHV� H[FHHGHGWKH�H[SHULPHQWDO�RQHV�E\�VHYHUDO�WLPHV�>��@�1HYHUWKHOHVV�� IRU� H[DPSOH��PRGHUQ�QRQ�HP �SLULFDO�FDOFXODWLRQV�WDNLQJ�LQWR�DFFRXQW�HOHF �WURQ�HQHUJ\�FRUUHODWLRQ�IRU�WKH�SURFHVV� 0J2 + α−$O�2� <²> 0J$O�2� DFFRPSDQLHG� E\� WUDQVLWLRQ� RI� PDJQHVLXPLRQV� IURP� WKH� RFWDKHGUDO� FRRUGLQDWLRQ� VXU �URXQGLQJ�WR�WHWUDKHGUDO�RQH�>��@��UHSURGXFHWKH�H[SHULPHQWDO�GDWD�WR�ZLWKLQ���WR�����6WUXFWXUDO� WUDQVIRUPDWLRQV� LQ� FOXVWHUV�&OXVWHUV� ²� V\VWHPV� RI� ERXQG� DWRPV� DQGPROHFXOHV� ²� DUH� UDWKHU� FRQYHQLHQW� REMHFWVWR� VWXG\� VWUXFWXUDO� WUDQVIRUPDWLRQV� >��@�7KH� FOXVWHU� VWUXFWXUHV� PD\� GLIIHU� IXQGD �PHQWDOO\�IURP�WKRVH�RI�FU\VWDOV�ZKDW�LV�GLF �WDWHG� VLJQLILFDQWO\� E\� WKH� IRUP� RI� LQWHUD �WRPLF� SRWHQWLDO� >��@� DV� ZHOO� DV� E\� FOXVWHUVL]H��PXOWLDWRPLF�FOXVWHUV�PD\�EH�YHU\�VLPL �ODU� WR� FU\VWDOV� LQ� VWUXFWXUH�� DQG� WHPSHUD �WXUH�� $� VHDUFK� SURFHGXUH� ZDV� GHVFULEHG� LQ>��@� IRU� WUDQVLWLRQ� VWDWHV� EHWZHHQ� LVRPHULFIRUPV�RI�WKH�FOXVWHUV�XVLQJ�SRWHQWLDO�HQHUJ\VXUIDFHV�GHVFULEHG�E\�VLPSOH�DQDO\WLFDO�SDLUSRWHQWLDOV�� $V� H[DPSOHV�� DUJRQ� DQG� SRWDV �VLXP� FOXVWHUV� ZHUH� FRQVLGHUHG�� ,W� LV� WKHDXWKRUV¶� RSLQLRQ�� WKLV�PHWKRG� RSHQV� D� ZD\IRU�PRUH�GHWDLOHG� LQVLJKW� LQWR� UHODWLRQVKLSVEHWZHHQ� HQHUJ\�� UHDFWLYLW\�� DQG� SRWHQWLDO� HQ �HUJ\�VXUIDFHV�RI�VXFK�V\VWHPV��/DWHU��WKH�VWXG\PHWKRGV� RI� WKH� VWUXFWXUDO� WUDQVIRUPDWLRQV� LQFOXVWHUV�ZHUH�VXPPDUL]HG�LQ�WKH�UHYLHZ�>��@�6HYHUDO� ZRUNV� DUH� GHYRWHG� WR� LQYHVWLJD �WLRQ�LQ�WKH�HQHUJ\�RI�VWUXFWXUDO�WUDQVIRUPD �WLRQV�RI�PHWDO�FOXVWHUV��6R��LQ�>��@��GHSHQG �HQFH� RI� WKH� HQHUJ\� RI� VPDOO� FOXVWHUV� RI� WKHPHWDOV� SRVVHVVLQJ� IFF� ODWWLFH� LQ� WKH� EXONVWDWH� �$O�� &D�� 1L�� &X�� 6U�� 5K�� 3G�� $J�� &H�<E��,U��3W��$X��3E��DQG�7K��RQ�DWRPLF�FRRUGL�QDWLRQ� ZDV� VWXGLHG�� 7KH� HTXLOLEULXP� VWUXF �WXUHV�� WUDQVLWLRQ� VWDWHV� DQG� WUDQVIRUPDWLRQPHFKDQLVPV� LQ�WKH�WUDQVLWLRQ�PHWDO��QLFNHO�VLOYHU��DQG�JROG��FOXVWHUV�FRQVLVWLQJ�RI����WR ���� DWRPV� ZHUH� DOVR� H[DPLQHG� >��@�� WKH/HQQDUG�-RQHV�� 0RUVH�� 6DWWRQ�&KHQ�� DQG0DUUHOO�0RWWUDP� HPSLULFDO� LQWHUDWRPLF� SR �WHQWLDOV�EHLQJ�XVHG�6WUXFWXUDO�WUDQVIRUPDWLRQV�LQ�FU\VWDOV�RIVLPSOH�VXEVWDQFHV��3KDVH�WUDQVLWLRQV�LQ�VLP�SOH� ERGLHV� PD\� RFFXU� XQGHU� QRUPDO� RU� HOH �YDWHG� SUHVVXUH�� $� FU\VWDO� FKHPLFDO� HVWLPD �WLRQ� RI� WKH� SRO\PRUSKRXV� WUDQVIRUPDWLRQSUHVVXUHV� IRU� FRYDOHQW� VXEVWDQFHV� ZDV� SUR �SRVHG�LQ�>��@�WKDW�PDGH�LW�SRVVLEOH�WR�REWDLQTXDOLWDWLYHO\�FRUUHFW�FRQFOXVLRQV��7KH�SKDVHWUDQVLWLRQ�LQ�VLOLFRQ�XQGHU�K\GURVWDWLF�FRP �SUHVVLRQ��IURP�WKH�FXELF�GLDPRQG�VWUXFWXUHWR� WKDW� RI� β�WLQ�� DFFRPSDQLHG� E\� WKH� LQ�FUHDVH� LQ� DWRPLF� FRRUGLQDWLRQ�QXPEHU� IURPIRXU� WR� VL[� ZDV� VLPXODWHG� DV� GHSHQGHQW� RQWKH� DWRPLF� YROXPH� LQ� >��@� ZLWK� XVH� RI� WKH7HUVRII� HPSLULFDO� LQWHUDWRPLF� SRWHQWLDO� DVZHOO�DV�RQ�WKH�EDVH�RI�QRQ�HPSLULFDO�FDOFXOD �WLRQV�RI�WKH�WRWDO�HQHUJ\��7KH�H[LVWHQFH�SRV �VLELOLW\� RI�XQXVXDO�FU\VWDOOLQH� VWUXFWXUHV�RIHOHPHQWV�XQGHU�KLJK�SUHVVXUH�KDV�EHHQ�GLV �FXVVHG�LQ�WKH�UHYLHZ�>��@�6WUXFWXUDO� WUDQVIRUPDWLRQV� LQ� ELQDU\FRPSRXQGV�� )RU� WKH� PRVW� SDUW�� WKHRUHWLFDODUWLFOHV� DUH� GHYRWHG� WR� VLPXODWLRQ� RI� SKDVHWUDQVLWLRQV� LQ� $;�$%��� $;��$%���� DQG� $�%�FU\VWDOV�� 1RQ�HPSLULFDO� TXDQWXP� FKHPLFDOFDOFXODWLRQV� RI� VWUXFWXUDO� SURSHUWLHV� DQGSKDVH� WUDQVLWLRQ� SUHVVXUH� ZHUH� FDUULHG� RXWLQ� >��@� IRU� VRGLXP�FKORULGH�� FDOFXODWHG� YDO �XHV�EHLQJ� LQ�D�JRRG�DJUHHPHQW�ZLWK�H[SHUL �PHQWDO�RQHV��7KH�DXWKRUV�RI�>��@�KDYH�VWXG �LHG� WKH� SKDVH� WUDQVLWLRQ� WKHUPRG\QDPLFV�PHFKDQLVP�� DQG� NLQHWLF� DVSHFWV� LQ� DONDOLKDOLGHV� DQG� DONDOL� HDUWK� R[LGHV�ZLWK�XVH� RIERWK�WZR�ERG\�SRWHQWLDOV�DQG�DE�LQLWLR�SHUL �RGLF� FDOFXODWLRQV�� 7KH� UHVXOWV� REWDLQHG� WHV �WLI\�WKDW�ERWK�WKH�PHFKDQLVPV�SURSRVHG�EH �IRUH� �WKH� %XUJHU� DQG� :DWDQDEH�7RNRQDPL�0RULPRWR� RQHV�� FDQ� EH� UHDOL]HG�� VLQFH� WKHDFWLYDWLRQ� HQHUJ\� YDOXHV� IRU� WKHVH� WZRPHFKDQLVPV� DUH� YHU\� FORVH�� WKH� ZD\� RIWUDQVIRUPDWLRQ� EHLQJ� GHSHQGHQW� HVVHQWLDOO\RQ� WKH� H[WHUQDO�SUHVVXUH� YDOXH��$Q� LQYHVWL �JDWLRQ� RI� VWUXFWXUDO� SKDVH� WUDQVLWLRQV� LQ �GXFHG� E\� XOWUD�KLJK� SUHVVXUH� LQ� DONDOL� KDO �LGH�FU\VWDOV�ZDV�FDUULHG�RXW�LQ�>������@��7KHWUDQVLWLRQ� SUHVVXUH� IRU� FU\VWDO� RI� LQILQLWHVL]H� ZDV� FDOFXODWHG�� WKH� VHOI�FRQVLVWHQW� SR �WHQWLDOV�RI�SDLU�LQWHUDFWLRQ�RI�LRQV�REWDLQHGZLWKLQ� WKH� IUDPHZRUNV� RI� WKH� LQKRPRJHQH �RXV� HOHFWURQ� JDV� WKHRU\� EHLQJ� XVHG�� 7KHUHODWLYH� FKDQJHV� LQ� YROXPH� RI� %� DQG� %�PRGLILFDWLRQV�ZHUH� FDOFXODWHG� IRU�D�QXPEHURI� FRPSRXQGV� ZLWKLQ� WKH� DSSUR[LPDWLRQ� RIVHYHQ� FRRUGLQDWLRQ� VSKHUHV�� 7KH� DXWKRUV� RI>������@�KDYH�FDOFXODWHG�WKH�WUDQVLWLRQ�SUHV � $�*UHEHQ\XN���7KHRUHWLFDO�PRGHOV�IRU�VWUXFWXUDO���� ��� )XQFWLRQDO�PDWHULDOV������������� VXUH� IRU� OLPLWHG�VL]H� FU\VWDOV�� VKRZHG� D�GH �SHQGHQFH�RI�WKLV�YDOXH�RQ�WKH�LQLWLDO�FU\VWDOVL]H��DQG�DQDO\]HG�WKH�FRQWULEXWLRQ�IURP�YD �FDQFLHV� WR� WKH� FKDUDFWHU� RI� WKH� VL]H� HIIHFWGLVFRYHUHG�1RQ�HPSLULFDO� FDOFXODWLRQV�ZHUH�PDGH� LQ>��@�ZLWKLQ�WKH�IUDPHZRUNV�RI�GHQVLW\�IXQF �WLRQDO� WKHRU\� RQ� WKH� WUDQVLWLRQ� LQ� FHVLXPK\GULGH�IURP�FXELF�VWUXFWXUH�WR�RUWKRUKRP �ELF� RQH� WKDW� RFFXUV� XQGHU� SUHVVXUH� RI���*3D�� 7KH� TDXWKRUV� RI� >��@� FRQVLGHUHG� DVHULHV� RI� %� → %� → %� SKDVH� WUDQVLWLRQVLQ�EHU\OOLXP�R[LGH� WDNLQJ�SODFH�XQGHU�SUHV �VXUH�RI�XS�WR����*3D��DQG�LQ�>��@��D�UHODWLYHVWDELOLW\�RI�WKH�%� DQG�%� SKDVHV�ZDV�VWXG�LHG� WKHRUHWLFDOO\� IRU� PDJQHVLXP� R[LGH� DQGJDOOLXP�QLWULGH��7KH�HIIHFW�RI�KLJK�SUHVVXUHRQ� WKH� %� → %� VWUXFWXUDO� WUDQVIRUPDWLRQVLQ�VLOLFRQ�FDUELGH�ZDV�VWXGLHG�LQ�>��@�ZLWKLQWKH� IUDPH� RI� WKH� PROHFXODU� G\QDPLFVPHWKRG�� DQG� WKH� H[LVWHQFH�RI�DQ� LQWHUPHGL �DWH� RUWKRUKRPELF� SKDVH� ZDV� SUHGLFWHG� EH �VLGHV�RI�%� DQG�%� RQHV�>��@��7KH�HOHFWURQLFVWUXFWXUH�DQG�FKHPLFDO�VWDELOLW\�RI�ILYH�WLWD �QLXP� PRQRFDUELGH� SRO\PRUSKRXV� PRGLILFD �WLRQV� ZLWK� WKH� %�±%� DQG� %� VWUXFWXUHVZHUH�VWXGLHG�LQ�>��@��LW�ZDV�HVWDEOLVKHG�EDV �LQJ� RQ� FDOFXODWLRQV� RI� WRWDO� EDQG� HQHUJLHVWKDW�WKH�VWDELOLW\�RI�PRGLILFDWLRQV�GHFUHDVHVLQ�D�VHTXHQFH�RI�%� !�%� !�%� ≈ %� !�%��&DOFXODWLRQV�ZHUH�PDGH� LQ� >��@�RI�WKH� UX �WLOH�→ IOXRULWH� WUDQVLWLRQ�SUHVVXUH�XVLQJ� WKH+DUWUHH�)RFN� DQG� PROHFXODU� G\QDPLFV� PHWK �RGV�� WKH� ��� *3D� YDOXH� REWDLQHG� DJUHHV� ZHOOZLWK� H[SHULPHQWDO� RQH�� 1HYHUWKHOHVV�� LW� ZDVVKRZQ� ODWHU� >��@� WKDW� WKH� IOXRULWH� VWUXFWXUHVKRXOG� EH� DOZD\V� XQVWDEOH� DQG� LI� WKH� SUHV �VXUH� LQFUHDVHV�� WKH� FRPSRXQG� XQGHUJRHV� DQXPEHU�RI�WUDQVIRUPDWLRQV�LQ�D�VHTXHQFH RI�VWDEOHSKDVHV��UXWLOH�→ α�3E2� → 3G)� → α�3E&O��6LOLFRQ�LV�WHWUD�FRRUGLQDWHG�LQ�WKH�PDMRU �LW\� RI� VLOLFD� SRO\PRUSKV� H[FHSW� IRUVWLVKRYLWH�ZKHUH� LW� LV�VL[�FRRUGLQDWHG��3HUL �RGLF� FDOFXODWLRQV� RI� WKH� SUREDEOH� UHDFWLRQSDWK� EHWZHHQ� FU\VWREDOLWH� DQG� VWLVKRYLWHZHUH� FDUULHG� RXW� LQ� >��@�� 7KH� WUDQVLWLRQSUHVVXUH� FDOFXODWHG� ��� *3D�� LV� FRQVLVWHQWZLWK� WKH� H[SHULPHQWDO� FRQGLWLRQV� RI� WKHVWLVKRYLWH� V\VWKHVLV�� WKH� DFWLYDWLRQ� HQHUJ\DW���.�XQGHU�WKLV�SUHVVXUH�ZDV�IRXQG�WR�EH����N-�PRO��)XUWKHU�VWLVKRYLWH�WUDQVIRUPD �WLRQ� LQWR�D�SKDVH� RI� D� &D&O��W\SH� VWUXFWXUHXQGHU� SUHVVXUH� RI� DERYH� ����*3D�ZDV� FRQ �VLGHUHG� E\� WKH� VDPH� DXWKRUV� LQ� >��@� ZKHUHWKH� WUDQVLWLRQ�PHFKDQLVP�ZDV� VKRZQ� WR� LQ �FOXGH� D� URWDWLRQ� RI� WKH� 6L2� RFWDKHGUDDURXQG� WKHLU� &�� D[HV�� /DWHU�� LW� ZDV� VKRZQ>��@�WKDW�WKH�WUDQVLWLRQ�RI�VWLVKRYLWH�LQWR�D &D&O��OLNH�RUWKRUKRPELF�SKDVH�FDQ�RFFXU�DO �UHDG\� XQGHU� SUHVVXUH� ��� *3D�� WKHQ� DW��� *3D� D� VWUXFWXUH� RI� 3QF� VKRXOG� EHIRUPHG� WKDW� DW� ���� *3D� WUDQVIRUPV� LQWR� DS\ULWH�OLNH� SKDVH�� $� QRQ�K\GURVWDWLF� FRP �SUHVVLRQ� RI� VLOLFD� FDQ� UHVXOW� LQ� WKH� IRUPD �WLRQ�RI� D� VWUXFWXUH�ZKHUH�VLOLFRQ�DWRPV�DUHILYH�FRRUGLQDWHG�� 7KHRUHWLFDO� FDOFXODWLRQVKDYH� VKRZQ� >��@� WKDW� α�TXDUW]� XQGHU� WKHVHFRQGLWLRQV� WUDQVIRUPV� LQWR� D� SKDVH� SRVVHV �LQJ� WKH�3����� VSDWLDO� V\PPHWU\�JURXS�� WKHWUDQVLWLRQ� EHLQJ� UHYHUVLEOH�� $� JHQHUDOL]HGWKHRU\� RI� UHFRQVWUXFWLYH� SKDVH� WUDQVLWLRQVEHWZHHQ� VLOLFD� SRO\PRUSKV� ZDV� SURSRVHG� LQ>��@� FRQVLGHULQJ� WKH� SKDVHV� RI� VWLVKRYLWH�FRHVLWH�� β�TXDUW]�� WULGLPLWH�� β�FU\VWREDOLWHDV�ZHOO�DV�&D&O��OLNH�DQG�α�3E2� VWUXFWXUHVIURP� WKH� YLHZSRLQW� RI� D� GLVRUGHUHG� EFFVWUXFWXUH� ZKHUH� GLIIHUHQW� IUDFWLRQDO� RFFX �SDQF\�RI�R[\JHQ�DWRPLF�SRVLWLRQV�JHQHUDWHVDOO�WKH�SRO\PRUSKV�XQGHU�FRQVLGHUDWLRQ��$QLQYHVWLJDWLRQ� RI� SUHVVXUH�LQGXFHG� SKDVHWUDQVLWLRQV� LQ� FU\VWREDOLWH� E\� QRQ�HPSLULFDOPROHFXODU�G\QDPLFV�PHWKRG�KDV�VKRZQ� >��@WKH�FU\VWREDOLWH�VWLVKRYLWH�WUDQVLWLRQ�WR�EH�DWZR�VWDJH� SURFHVV� �ILUVW�� D� URWDWLRQ� RI� 6L2�WHWUDKHGUD� RFFXUV� IROORZHG�E\�D� ODWWLFH�GLV �WRUWLRQ� WR� \LHOG� WKH� VL[�FRRUGLQDWHG� VLOLFRQDWRPV��� DQG� IXUWKHU� FRPSUHVVLRQ� \LHOGV� WKH&D&O��OLNH� VWUXFWXUH� IROORZHG� E\� DQRWKHUVL[�FRRUGLQDWHG� VWUXFWXUH� ZLWK� 3���Q V\P�PHWU\�� ZKLFK� WKHQ� WUDQVIRUPV� LQWR� D� QLQH�FRRUGLQDWHG�3���P VWUXFWXUH�7KH� VWUXFWXUDO� SURSHUWLHV� DQG� UHODWLYHVWDELOLW\�RI�VL[�DOXPLQD�SRO\PRUSKV��FRUXQ �GXP�� SKDVHV� OLNH� 5K�2� �,,��� SHURYVNLWHV�DQG� UDUH� HDUWK� VHVTXLR[LGHV�� ZHUH� FRQVLG �HUHG� LQ� >������@� XVLQJ� QRQ�HPSLULFDOPHWKRG��7KH�FDOFXODWLRQV�WHVWLI\�WKDW�FRUXQ �GXP� WUDQVIRUPV� LQWR� D� VWUXFWXUH� RI� 5K�2��,,�� W\SH� DW� ��� *3D� DQG� WKHQ� LQWR� D� 3EQPSHURYVNLWH� DW� ���� *3D�� 7KHVH� UHVXOWV� ZHUHVXSSRUWHG� LQ� >��@�ZLWKLQ� WKH�IUDPH�RI�QRQ�HPSLULFDO� SHUWXUEHG� LRQ� PHWKRG�� DQG� WKHWUDQVLWLRQ�EHWZHHQ�FRUXQGXP�DQG�5K�2� �,,�W\SH� VWUXFWXUH� DW� URRP� WHPSHUDWXUH� ZDVVKRZQ� WR� EH� SUREDEOH� DOUHDG\� XQGHU� SUHV �VXUH�RI�DERXW���*3D��$�QXPEHU�RI�ZRUNV�LVGHYRWHG�WR�H[DPLQDWLRQ�RI�WKH�VWUXFWXUH�DQGVWDELOLW\� RI�GHIHFW� IRUPV�RI� DOXPLQD��6R�� LWZDV�IRXQG�LQ�>��@�WKDW�WKH�HQHUJ\�RI�θ�SKDVHLV� KLJKHU� WKDQ� WKDW� RI� FRUXQGXP� E\���N-�PRO��7KH�UROH�RI�DGPL[WXUH�K\GURJHQDWRPV�LQ� WKH� IRUPDWLRQ�RI��WUDQVLWLRQ��DOX �PLQD� IRUPV� �γ��� η��� DQG� δ�SKDVHV�� ZDV� DOVRVWXGLHG�>��@��7KH�UROH�RI�VXUIDFH�UHFRQVWUXF �WLRQ�LQ�WKH�IRUPDWLRQ�RI�VXUIDFH�DSURWLF�DFLGVLWHV�RI� WKH� γ�� DQG�η�PRGLILFDWLRQV�ZDV� GLV� $�*UHEHQ\XN���7KHRUHWLFDO�PRGHOV�IRU�VWUXFWXUDO���� )XQFWLRQDO�PDWHULDOV������������� ��� FXVVHG� LQ� >��@�� 7KH� HIIHFW� RI� WKH� VSHFLILFVXUIDFH� YDOXH� DQG� RI� ZDWHU� DGVRUSWLRQ� RQWKH� UHODWLYH� VWDELOLW\� RI� γ�� DQG� α�PRGLILFD�WLRQV� RI� DOXPLQD�ZDV�FRQVLGHUHG� LQ� >��@�� ,WZDV� VKRZQ�� LQ� SDUWLFXODU�� WKDW� LI� WKH� VSH �FLILF� VXUIDFH� ZDV� ���� P��J�� WKH� YDOXHV� RIIRUPDWLRQ� HQWKDOS\� IRU� WKHVH� PRGLILFDWLRQVEHFDPH�WKH�VDPH�,Q� FRQFOXVLRQ�� WKH� PRGHUQ� VWXGLHV� RQSRO\PRUSKLVP�RI�FKHPLFDO�FRPSRQGV�DQG�RQVWUXFWXUDO� SKDVH� WUDQVLWLRQV� XQGHU� H[WHUQDOHIIHFWV�DORQJ�ZLWK�XVH�RI�GLUHFW�H[SHULPHQ �WDO� PHWKRGV� �PRVWO\� FU\VWDOORJUDSK\� DQGFDORULPHWU\�� XWLOL]H� ZLGHO\� WKH� VLPXODWLRQPHWKRGV�EDVHG�RQ�WKH�HPSOR\PHQW�RI�XS�WR�GDWH�SURJUHVV�LQ�VROLG�VWDWH�WKHRU\��TXDQWXPPHFKDQLFV��DQG�PROHFXODU�G\QDPLFV��6XFK�DFRPELQHG� DSSURDFK�� SURYLGLQJ� WKH� SURJUHVVLQ� WKH� GHYHORSPHQW� RI� FRPSXWHUV� LV� XVHG�PDNHV�LW�SRVVLEOH�WR�REWDLQ�WKH�UHVXOWV�FKDU �DFWHUL]HG�E\�KLJK�DFFXUDF\�DQG�YDOLGLW\�5HIHUHQFHV���1�%�/HRQLGRY��5RVV��.KLP��=K��������������������<X�0�*XIDQ�� 6WUXFWXUDO� 3KDVH� 7UDQVLWLRQV�1DXND��0RVFRZ��������>LQ�5XVVLDQ@����/�$�5H]QLWVN\�� 6ROLG� 6WDWH� &DORULPHWU\�6WUXFWXUDO�� 0DJQHWLF�� (OHFWURQ� 7UDQVIRUPD�WLRQV��� 0*8� 3XEO��� 0RVFRZ� ������� >LQ� 5XV�VLDQ@����/�$�5H]QLWVN\�� &KHPLFDO� %RQG� DQG� 2[LGH7UDQVIRUPDWLRQV��0*8�3XEO���0RVFRZ� ������>LQ�5XVVLDQ@����$�1DYURWVN\�� 2�-�.OHSSD�� -��,QRUJ��1XFO�&KHP�����������������������/�$�5H]QLWVN\�� ,]Y��$1� 6665��1HRUJ��0DWHU����������������������/�$�5H]QLWVN\�� =K��)L]��.KLP��� ���� ��������������<D�$�.HVOHU�� '�6�)LOLPRQRY�� 1HRUJ��0DWHU����������������������/�$�5H]QLWVN\�� 6�(�)LOLSSRYD�� =K��1HRUJDQ�.KLP�����������������������0�6�6KXELQ�� *�3�3RSRY�� $�2�/LWLQVN\�$�1�0HQ¶�� =KXUQ��6WUXNW��.KLP��� ���� ���������������0�&DWWL��*�9DOHULR��5�'RYHVL��0�&DXVD��3K\V�5HY��%������������������������9�'�/DNKQR�� &OXVWHUV� LQ� 3K\VLFV�� &KHPLVWU\�DQG� %LRORJ\�� 65&� �5HJXODU� DQG� &KDRWLF� '\�QDPLFV���,]KHYVN��������>LQ�5XVVLDQ@�����-�3�.�'R\H�� '�-�:DOHV�� -��&KHP��3K\V��� ���������������������'�-�:DOHV��-��&KHP��3K\V������������������������5�6�%HUU\��&KHP��5HY������������������������/�<DQJ�� $�(�'H3ULVWR�� -��&DWDO��� ����� ���������������'�-�:DOHV�� /�-�0XQUR�� -�3�.�'R\H�� -��&KHP�6RF���'DOWRQ�7UDQV��������������� ����6�6�%DWVDQRY��=K��6WUXNW��.KLP����������������������.�0L]XVKLPD��6�<LS��(�.D[LUDV��3K\V��5HY���%����������������������7�1�.RORE\DQLQD�� 8VS��)L]��1DXN�� ����� ����������������(�$SUD��0�&DXVD��0�3UHQFLSH�HW�DO���-��3K\V��&RQGHQV��0DWWHU����������������������&�(�6LPV��*�'�%DUUHUD��1�/�$OODQ��:�&�0DFN�URGW��3K\V��5HY���%�����������������������6�9�.DUSHQNR�� $�.�.\DURY�� $�,�7HPURNRY�,]Y��98=RY��)L]LND���������������������6�9�.DUSHQNR�� '�/�9LQRNXUVN\�� $�,�7HP�URNRY��0DWHULDORYHGHQLH��1R�����������������6�9�.DUSHQNR�� $�.�.\DURY�� $�,�7HPURNRY�'�/�9LQRNXURY�� .ULVWDOORJUDILD�� ���� ��������������6�9�.DUSHQNR�� $�.�.\DURY�� $�,�7HPURNRY�0DWHULDORYHGHQLH��1R�����������������$�0�6DLWWD��'�$OIH��6�'H�*LURQFROL��6�%DURQL�3K\V��5HY��/HWW������������������������-�%RHWWJHU��-�0�:LOOV��3K\V��5HY���%���������������������6�/LPSLMXPQRQJ�� :�5�/�/DPEUHFKW�� 3K\V�5HY���%��������������������������)�6LPRMR��,�6HEMR��5�.�.DOLD�HW�DO���3K\V��5HY�/HWW������������������������0�&DWWL��3K\V��5HY��/HWW���������������������������$�/�,YDQRYVN\�� $�$�6DIRQRY�� ,]Y��$1��6HU�.KLP��������������������*�'�%DUUHUD�� 0�%�7D\ORU�� 1�/�$OODQ�7�+�.�%DUURQ��-��&KHP��3K\V������������������������-�+DLQHV�� -�0�/HJHU�� )�*RUHOOL� HW� DO��� 3K\V�5HY���%�������������������������%�6LOYL�� /��+�-ROO\�� 3K�'¶$UFR�� -��0ROHF�6WUXFW���7KHRFKHP���������������������/��+�-ROO\��%�6LOYL��3K�'¶$UFR��-��&KLP��3K\V����������������������%�%�.DUNL�� 0�&�:DUHQ�� /�6WL[UXGH� HW� DO��3K\V��5HY���%���������������������-�%DGUR�� '�0�7HWHU��5�7�'RZQV� HW� DO��� 3K\V�5HY���%���������������������9�3�'PLWULHY�� 3�7ROHGDQR�� 9�,�7RUJDVKHY�(�.�+�6DOMH��3K\V��5HY���%����������������������'�'�.OXJ��5�5RXVVHDX��.�8HKDUD�HW�DO���3K\V�5HY���%�������������������������.�7�7KRPVRQQ��5�0�:HQW]FRYLWFK��0�6�7�%XNR�ZLQVNL��6FLHQFH�����������������������:�'XDQ�� 5�0�:HQW]FRYLWFK�� .�7�7KRPVRQ�3K\V��5HY���%����������������������5�)UDQFR�� -�0�5HFLR�� /�3XH\R�� -��0ROHF�6WUXFW���7KHRFKHP�����������������������$�3�%RURV\��%�6LOYL��0�$OODYHQD��3�1RUWLHU��-�3K\V��&KHP������������������������.�6RKOEHUJ��6�-�3HQQ\FRRN��6�7�3DQWHOLGHV��-�$PHU��&KHP��6RF������������������������.�6RKOEHUJ��6�7�3DQWHOLGHV��6�-�3HQQ\FRRN��-�$PHU��&KHP��6RF����������������������-�0�0F+DOH�� $�1DYURWVN\�� $�-�3HUURWWD�� -�3K\V��&KHP��%������������������ $�*UHEHQ\XN���7KHRUHWLFDO�PRGHOV�IRU�VWUXFWXUDO���� ��� )XQFWLRQDO�PDWHULDOV������������� Ònvénzq·tL�uvlnsL�xzéyrzyétq}�{jovkq}�wnén}vlLk�yuvsnrys¹étq}�rsjxznéj}�zj�réqxzjsj}�tnvémjtL·tq}xwvsyr k����¯Ë­ËÓ } fzjzz¹�uLxzqz��vms¹l�xy·jxtq}�znvénzq·tq}�wLl}vlLk�lv�lvxsLl ntt¹�wvsLuvé{Louyzj� xzéyrzyétq}� {jovkq}� wnén}vlLk� tnvémjtL·tq}� xwvsyr�� Ìxtvkty� ykjmy� wéqlLsntvtvkqu�Lln¹u�y�znéuvlqtjuL|L�zknélvmv�zLsj��unzvlju�uvlnsíkjtt¹�xzéyrzyéq�L�ntnémn�zqrq� wvsLuvé{tq}� {véu� zj� énoys�zjzju� ¢}t�vmv� ojxzvxykjtt¹� lv� wévxzq}� én·vkqt� LiLtjétq}�xwvsyr�� $�*UHEHQ\XN���7KHRUHWLFDO�PRGHOV�IRU�VWUXFWXUDO���� )XQFWLRQDO�PDWHULDOV������������� ���