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...
Збережено в:
Дата: | 2004 |
---|---|
Автор: | |
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 Ukraineid |
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������������� ���
|