Transition from microstructures to nanostructures and ultimate hardening

Regularities of change in the dependence of the yield stress on grain size in transition from the microstructured to the nanostructured state are discussed. It is shown that, using S-functions, a generalized equation for the yield strength dependence on the grain size with regard to changes in the h...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2009
Автори: Firstov, S.A., Rogul, T.G., Shut, O.A.
Формат: Стаття
Мова:English
Опубліковано: НТК «Інститут монокристалів» НАН України 2009
Назва видання:Functional Materials
Теми:
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/138928
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:Transition from microstructures to nanostructures and ultimate hardening // S.A. Firstov, T.G. Rogul, O.A. Shut // Functional Materials. — 2009. — Т. 16, № 4. — С. 364-373. — Бібліогр.: 40 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-138928
record_format dspace
spelling irk-123456789-1389282018-06-20T03:03:26Z Transition from microstructures to nanostructures and ultimate hardening Firstov, S.A. Rogul, T.G. Shut, O.A. Characterization and properties Regularities of change in the dependence of the yield stress on grain size in transition from the microstructured to the nanostructured state are discussed. It is shown that, using S-functions, a generalized equation for the yield strength dependence on the grain size with regard to changes in the hardening mechanisms of polycrystals in the vicinity of critical grain sizes dcr₁ and dcr₂ can be obtained. This equation enables to describe the softening effects in transition to nanostructures (the so-called "negative" trend of the Hall-Petch relationship) and an abrupt hardening under conditions of increased intergranular cohesive strength. Обговорюються закономірності зміни залежності напруги плинності при переході від мікро- до наноструктурованого стану. Показано, що за допомогою 8-функцій можна отримати узагальнене рівняння залежності границі плинності від розміру зерна з урахуванням зміни механізмів зміцнення полікристалів в околі критичних розмірів зерен dкр₁ і dкр₂. Це рівняння дозволяє описати як ефекти знеміцнення при переході до наноструктур (так званий "негативний" хід залежності Холла-Петча), так і, навпаки, різке зміцнення за умови підвищеної міцності межзеренного зчеплення. Обсуждаются закономерности изменения зависимости напряжения течения при переходе от микро- к наноструктурированному состоянию. Показано, что с помощью 8-функций можно получить обобщенное уравнение зависимости предела текучести от размера зерна с учетом изменения механизмов упрочнения поликристаллов в окрестности критических размеров зерен dкр₁ и dкр₂. Это уравнение позволяет описать как эффекты разупрочнения при переходе к наноструктурам (так называемый "отрицательный" ход зависимости Холла-Петча), так и, напротив, резкое упрочнение при условии повышенной прочности межзеренного сцепления. 2009 Article Transition from microstructures to nanostructures and ultimate hardening // S.A. Firstov, T.G. Rogul, O.A. Shut // Functional Materials. — 2009. — Т. 16, № 4. — С. 364-373. — Бібліогр.: 40 назв. — англ. 1027-5495 http://dspace.nbuv.gov.ua/handle/123456789/138928 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
topic Characterization and properties
Characterization and properties
spellingShingle Characterization and properties
Characterization and properties
Firstov, S.A.
Rogul, T.G.
Shut, O.A.
Transition from microstructures to nanostructures and ultimate hardening
Functional Materials
description Regularities of change in the dependence of the yield stress on grain size in transition from the microstructured to the nanostructured state are discussed. It is shown that, using S-functions, a generalized equation for the yield strength dependence on the grain size with regard to changes in the hardening mechanisms of polycrystals in the vicinity of critical grain sizes dcr₁ and dcr₂ can be obtained. This equation enables to describe the softening effects in transition to nanostructures (the so-called "negative" trend of the Hall-Petch relationship) and an abrupt hardening under conditions of increased intergranular cohesive strength.
format Article
author Firstov, S.A.
Rogul, T.G.
Shut, O.A.
author_facet Firstov, S.A.
Rogul, T.G.
Shut, O.A.
author_sort Firstov, S.A.
title Transition from microstructures to nanostructures and ultimate hardening
title_short Transition from microstructures to nanostructures and ultimate hardening
title_full Transition from microstructures to nanostructures and ultimate hardening
title_fullStr Transition from microstructures to nanostructures and ultimate hardening
title_full_unstemmed Transition from microstructures to nanostructures and ultimate hardening
title_sort transition from microstructures to nanostructures and ultimate hardening
publisher НТК «Інститут монокристалів» НАН України
publishDate 2009
topic_facet Characterization and properties
url http://dspace.nbuv.gov.ua/handle/123456789/138928
citation_txt Transition from microstructures to nanostructures and ultimate hardening // S.A. Firstov, T.G. Rogul, O.A. Shut // Functional Materials. — 2009. — Т. 16, № 4. — С. 364-373. — Бібліогр.: 40 назв. — англ.
series Functional Materials
work_keys_str_mv AT firstovsa transitionfrommicrostructurestonanostructuresandultimatehardening
AT rogultg transitionfrommicrostructurestonanostructuresandultimatehardening
AT shutoa transitionfrommicrostructurestonanostructuresandultimatehardening
first_indexed 2025-07-10T06:52:04Z
last_indexed 2025-07-10T06:52:04Z
_version_ 1837241815746478080
fulltext 7UDQVLWLRQ�IURP�PLFURVWUXFWXUHVWR�QDQRVWUXFWXUHV�DQG�XOWLPDWH�KDUGHQLQJ 6�$�)LUVWRY��7�*�5RJXO��2�$�6KXW ,�)UDQWVHYLFK�,QVWLWXWH�IRU�3UREOHPV�RI�0DWHULDOV�6FLHQFH��1DWLRQDO $FDGHP\�RI�6FLHQFHV�RI�8NUDLQH��.\LY��8NUDLQH 5HFHLYHG�1RYHPEHU��������� 5HJXODULWLHV�RI�FKDQJH�LQ�WKH�GHSHQGHQFH�RI�WKH�\LHOG�VWUHVV�RQ�JUDLQ�VL]H�LQ�WUDQVLWLRQ IURP� WKH� PLFURVWUXFWXUHG� WR� WKH� QDQRVWUXFWXUHG� VWDWH� DUH� GLVFXVVHG�� ,W� LV� VKRZQ� WKDW� XVLQJ�6�IXQFWLRQV��D�JHQHUDOL]HG�HTXDWLRQ� IRU� WKH�\LHOG�VWUHQJWK�GHSHQGHQFH�RQ�WKH�JUDLQ VL]H�ZLWK�UHJDUG�WR�FKDQJHV�LQ�WKH�KDUGHQLQJ�PHFKDQLVPV�RI�SRO\FU\VWDOV�LQ�WKH�YLFLQLW\�RI FULWLFDO� JUDLQ� VL]HV� GFU�� DQG� GFU�� FDQ� EH� REWDLQHG�� 7KLV� HTXDWLRQ� HQDEOHV� WR� GHVFULEH� WKHVRIWHQLQJ� HIIHFWV� LQ� WUDQVLWLRQ� WR� QDQRVWUXFWXUHV� �WKH� VR�FDOOHG� �QHJDWLYH�� WUHQG� RI� WKH +DOO�3HWFK� UHODWLRQVKLS�� DQG� DQ� DEUXSW� KDUGHQLQJ� XQGHU� FRQGLWLRQV� RI� LQFUHDVHG� LQWHU� JUDQXODU�FRKHVLYH�VWUHQJWK� |­°�Î�È �°«� ÏÈ}ºÓºä˯Ӻ°�Ò� ÒÏäËÓËÓÒ«� ÏÈmÒ°Ò亰�Ò� Óȹ¯«ÎËÓÒ«� �Ë�ËÓÒ«� ¹¯Ò ¹Ë¯Ë²º�Ë� º�� äÒ}¯º�� }� ÓÈÓº°�¯�}��¯Ò¯ºmÈÓÓºä�� °º°�º«ÓÒ �� �º}ÈÏÈÓº�� ��º� °� ¹ºäº� 6�Á�Ó}�Ò®�äºÎÓº� ¹ºã��Ò� � º­º­�ËÓÓºË� �¯ÈmÓËÓÒË� ÏÈmÒ°Ò亰�Ò� ¹¯Ë�ËãÈ� �Ë}��˰�Ò� º� ¯ÈÏä˯È� Ï˯ÓÈ� °� ��Ë�ºä�ÒÏäËÓËÓÒ«�ä˲ÈÓÒÏäºm� �¹¯º�ÓËÓÒ«�¹ºãÒ}¯Ò°�Èããºm� m� º}¯Ë°�� Óº°�Ò� }¯Ò�Ò�˰}Ò²� ¯ÈÏä˯ºm� Ï˯ËÓ�G}¯�� Ò�G}¯��� w�º� �¯ÈmÓËÓÒË� ¹ºÏmºã«Ë�� º¹Ò°È� � }È}ªÁÁË}�©�¯ÈÏ�¹¯º�ÓËÓÒ«�¹¯Ò�¹Ë¯Ë²º�Ë�}�ÓÈÓº°�¯�}��¯Èä���È}�ÓÈÏ©mÈËä©®��º�¯Ò�È�Ëã � Ó©®��²º��ÏÈmÒ°Ò亰�Ò�tºããÈ��Ë��È����È}�Ò��Óȹ¯º�Òm��¯ËÏ}ºË��¹¯º�ÓËÓÒË�¹¯Ò��°ãºmÒÒ ¹ºm©�ËÓÓº®�¹¯º�Óº°�Ò�äËÎÏ˯ËÓÓº�º�°�˹ãËÓÒ«� 8QGRXEWHGO\��3URIHVVRU�/HY�3DODWQLN�FDQ EH� FDOOHG� DPRQJ� WKH� IRXQGHUV� RI� QDQRWHFK� QRORJLHV� DQG� WKH� LQYHVWLJDWLRQ� RI� WKH� PH� FKDQLFDO�SURSHUWLHV�RI�QDQRVWUXFWXUHG�PDWH� ULDOV� �WKRXJK� WKH� ZRUG� �QDQRPDWHULDO�� ZDV QRW�XVHG�DW�WKDW�WLPH��EHFDXVH�KH�VWXGLHG�LQ JUHDW� GHWDLO� WKH� PHFKDQLFDO� SURSHUWLHV� RI WKLQ� ILOPV� ZKHUH� HLWKHU� QDQROD\HUHG� VWUXF� WXUHV� RU� H[WUHPHO\� VPDOO� JUDLQ� VL]HV� XS� WR DPRUSKRXV� VWUXFWXUHV� FDQ� EH� REWDLQHG UDWKHU�HDVLO\��,Q�D�JHQHUDOL]LQJ�ZRUN�>�@��KH GLVFXVVHG�GLIIHUHQW�HIIHFWV�RI�FKDQJHV�LQ�WKH PHFKDQLFDO� SURSHUWLHV� RI� WKLQ� ILOP� REMHFWV� /�3DODWQLN� IRUPXODWHG� WKH� LGHD� WKDW� �WKH FODVVLILFDWLRQ�RI�ILOPV�LQWR��WKLQ��DQG��PDV� VLYH�� RQHV� LV� FRQYHQWLRQDO� DQG� DFTXLUHV� D FOHDU�SK\VLFDO�PHDQLQJ�RQO\�ZKHQ�D�VSHFLILF VWUXFWXUDO� VWDWH� DQG� D� VSHFLILF� SK\VLFDO SURSHUW\�DUH�FRQVLGHUHG��$�FULWLFDO�WKLFNQHVV KN� �RU� DQ� LQWHUYDO� RI� KN�� EHORZ� ZKLFK� WKHSDUDPHWHU� K� LQIOXHQFHV� GLUHFWO\� WKH� VWUXF� WXUH�RI�WKH�FRQGHQVDWH�FDQ�VHUYH�DV�D�FULWH� ULRQ�RI�WKH�WKLQ�ILOP�VWDWH���7KLV�LGHD�FRUUH� VSRQGV�WR�WKH�PRGHUQ�FRQFHSWV�RI�WKH�VSHFL� ILFLW\�RI�SURSHUWLHV�RI�QDQRVWUXFWXUHG�PDWH� ULDOV� LQ� FRQQHFWLRQ� ZLWK� WKH� PDQLIHVWDWLRQ RI�WKH�VSHFLILF��VL]H��HIIHFW� 7KH� LQYHVWLJDWLRQ� LQ� WKH� LQIOXHQFH� UHJX� ODULWLHV� RI� WKH� VWUXFWXUDO� HOHPHQW� VL]H�� LQ SDUWLFXODU�� WKH� JUDLQ� VL]H�� RQ� WKH� VWUHQJWK RI�PDWHULDOV�ZDV�DOZD\V� LQ� WKH� IRFXV�RI�DW� WHQWLRQ�� ,W� LV� ZHOO� HVWDEOLVKHG� WKDW�� LQ� D UDWKHU�ZLGH�UDQJH�RI�D�SRO\FU\VWDOOLQH�PDWH� ULDO� JUDLQ� VL]H�� WKH� +DOO�3HWFK� HTXDWLRQ� LV VDWLVILHG�>�Ü�@�ZKHUH�WKH�GHSHQGHQFH�RI�WKH \LHOG�VWUHQJWK�V\�RQ�WKH�JUDLQ�VL]H�G�FDQ�EH H[SUHVVHG�E\�WKH�IRUPXOD V\� �V����N\G��e�� ��� )XQFWLRQDO�0DWHULDOV�����1R��������� �������Û�67&��,QVWLWXWH�IRU�6LQJOH�&U\VWDOV� ��� )XQFWLRQDO�PDWHULDOV������������� ZKHUH� WKH� SDUDPHWHU� V�� FKDUDFWHUL]HV� WKHDYHUDJHG� UHVLVWDQFH� WR� GLVORFDWLRQ� PRWLRQ RYHU� WKH� JUDLQ� ERG\� DQG� WKH� FRHIILFLHQW� N\FKDUDFWHUL]HV� WKH� GLIILFXOW\� RI� VOLS� WUDQVIHU WKURXJK� WKH� JUDLQ� ERXQGDU\�� $� ODUJH� ERG\ RI�H[SHULPHQWDO�GDWD�FRQILUPV�WKDW�LQ�PDQ\ FDVHV��ERWK�SDUDPHWHUV��V��DQG�N\��DUH�SUDF�WLFDOO\�FRQVWDQW�LQ�WKH�JUDLQ�VL]H�UDQJH�IURP VHYHUDO� KXQGUHGV� RI�PLFURPHWHUV� WR� VHYHUDO PLFURPHWHUV�� ,I� GHYLDWLRQV� IURP� WKLV� GH� SHQGHQFH� DUH� REVHUYHG�� WKRVH�FDQ�EH�FDXVHG E\� HLWKHU� D� FKDQJH� LQ� WKH� VWDWH� RI� JUDLQ ERXQGDULHV�� ZKLFK� FDQ� EH� FKDUDFWHUL]HG� E\ WKH� FRHIILFLHQW� N\�� RU� E\� D� FKDQJH� LQ� WKHUHVLVWDQFH� WR� GLVORFDWLRQ� PRWLRQ� RYHU� WKH JUDLQ�ERG\�V��GXH�WR�UHGLVWULEXWLRQ�RI�LPSX�ULWLHV� RU� DOOR\LQJ� HOHPHQWV� EHWZHHQ� JUDLQV DQG�JUDLQ�ERXQGDULHV�ZKHQ�WKH�JUDLQ�VL]H�LV YDULHG� 0RUHRYHU�� LV� VRPH�ZRUNV� >�Ü��@� GHIRUPD� WLRQ�LQGXFHG�VWUXFWXUHV��WKH�H[SRQHQW�RI�G�LQ (T�����ZDV�UHSRUWHG�WR�YDU\�IURP�Ü����WR�Ü�� ,Q� UHFHQW� \HDUV�� WKH� LQWHUHVW� WR� WKH� GH� SHQGHQFHV� RI� WKH� VWUHQJWK� �\LHOG� VWUHQJWK� RQ�WKH�JUDLQ�VL]H�LV�LQFUHDVHG�GXH�WR�VWXGLHV RI� WKH� PHFKDQLFDO� SURSHUWLHV� RI� QDQRVWUXF� WXUHG� PDWHULDOV�� 7KH� PRVW� RIWHQ� GLVFXVVHG HIIHFW� OLHV� LQ� WKH� IDFW� WKDW�� LQVWHDG� RI� WKH VXFFHVVLYH� KDUGHQLQJ�� DQ� LQYHUVH� UHODWLRQ� VKLS��L�H���D��QHJDWLYH��VORSH��N\������RI�WKH +DOO�3HWFK� UHODWLRQ� LV� REVHUYHG� LQ� WKH QDQRPHWHU� JUDLQ� VL]H� UDQJH�� 7KLV� LQYHUVH +DOO�3HWFK� HIIHFW� ZDV� REVHUYHG� H[SHULPHQ� WDOO\� IRU� D� QXPEHU� RI� PDWHULDOV� >��Ü��� HWF�@�� DQG� D� VHW� RI� PRGHOV� ZDV� SURSRVHG� WR H[SODLQ�LW�>��Ü����HWF�@��� ,Q�RXU� LQYHVWLJDWLRQV� >������@�RQ�PDWHUL� DOV�REWDLQHG�E\�WKH�YDFXXP�GHSRVLWLRQ�PHWK� RGV�� WZR� HIIHFWV� ZHUH� REVHUYHG�� QDPHO\�� LQ WUDQVLWLRQ� IURP� WKH� PLFURVWUXFWXUHG� WR� WKH QDQRVWUXFWXUHG� VWDWH�� DW� OHDVW� WZR� FULWLFDO JUDLQ� VL]HV� �GFU�� DQG�GFU���ZHUH� UHYHDOHG� LQWKH�YLFLQLW\�RI�ZKLFK� WKH�KDUGHQLQJ�PHFKD� QLVP� FKDQJHV�� ,Q� SDUWLFXODU�� LQ� WKH� VXEPL� FURQ� JUDLQ� VL]H� UDQJH�GFU�d��PP�� WKH� H[SR�QHQW�RI�G�LQ�(T�����FKDQJHV�IURP�Ü����WR�Ü� RFFXUV��)LJ�����FXUYH���� ,W�IROORZV�IURP�)LJV����DQG���WKDW�LQ�WKH QDQRVL]H�UDQJH��GdGFU����D�GUDVWLF�KDUGHQLQJLV� REVHUYHG� LQVWHDG�RI� D� FRPPRQ� WUDQVLWLRQ WR�WKH�QHJDWLYH�VORSH��GXH�WR�WKH�VHJUHJDWLRQ RI�XVHIXO�LPSXULWLHV�DW�WKH�JUDLQ�ERXQGDULHV LQ� WKLQ� FKURPLXP� ILOPV� >������@�� 7KLV� DO� ORZHG� WR� SURSRVH� D� FRQFHSW� RI� �XVHIXO�� LP� SXULWLHV� LQFUHDVLQJ� WKH� VWUHQJWK� OHYHO� RI QDQRVWUXFWXUHG�PDWHULDOV�>������@� 7KLV�ZRUN�LV�DLPHG�DW�WKH�DQDO\VLV�RI�WKH DERYH�PHQWLRQHG� HIIHFWV� DQG� DW� DQ� DWWHPSW WR� REWDLQ� D� JHQHUDOL]HG� GHSHQGHQFH� RI� WKH \LHOG�VWUHQJWK�RQ�WKH�JUDLQ�VL]H� ���7UDQVLWLRQ� IURP� Ü���� H[SRQHQW� WR� Ü� RQH� LQ� GHSHQGHQFH� ���� LQ� WKH� FDVH� RI� JUDLQ UHILQHPHQW��)RU�GHIRUPDWLRQ�LQGXFHG�PLFUR� VWUXFWXUHV�� VXFK� D� WUDQVLWLRQ� ZDV� QRWHG� D UDWKHU� ORQJ� WLPH� DJR� >�Ü��@�� ,Q� SDUWLFXODU� DIWHU� VHYHUH� SODVWLF� GHIRUPDWLRQV�� WKH� IRU� PDWLRQ� RI� GHIRUPDWLRQ�LQGXFHG� XOWUDILQH� JUDLQ� VWUXFWXUHV� LV� XVXDOO\� QRWHG� >��@�� WKH GLVRULHQWDWLRQ� RI� LQGLYLGXDO� HOHPHQWV� LQ VXFK� D� VWUXFWXUH� EHLQJ� TXLWH� FRPSDUDEOH ZLWK�FKDUDFWHULVWLF�GLVRULHQWDWLRQV�RI�JUDLQV LQ�D�FRQYHQWLRQDO�SRO\FU\VWDOOLQH�DJJUHJDWH� )LJ����� 6FKHPDWLF� GHSHQGHQFH� RI� WKH� \LHOG VWUHQJWK�RQ�WKH�JUDLQ�VL]H�LQ�WUDQVLWLRQ�IURP WKH� JUDLQ� PLFURVL]HV� WR� JUDLQ� QDQRVL]HV� &XUYH� �� FRUUHVSRQGV� WR� WKH� WUDQVLWLRQ� IURP WKH� +DOO�3HWFK� HTXDWLRQ� WR� D� GHFUHDVHG VWUHQJWK� LQ� WKH� QDQRVL]H� UDQJH� ��QHJDWLYH� VORSH��>��Ü����HWF�@��FXUYH����WR�WKH�WUDQVLWLRQ WR� WKH� GHSHQGHQFH� ZLWK� DQ� H[SRQHQW� RI�G� RI Ü�� DW� GFU�dGdGFU��� DQG� WR� DEUXSW� KDUGHQLQJIRU�WKH�JUDLQ�VL]H�GHFUHDVLQJ�EHORZ�GFU��LQ�WKHFDVH�RI�VWURQJ�ERXQGDULHV�>��Ü��@� )LJ�����7KH�\LHOG�VWUHQJWK�V�DV�D�IXQFWLRQ�RI WKH� JUDLQ� VL]H� G� LQ� FKURPLXP� REWDLQHG� E\ PDJQHWURQ�VSXWWHULQJ�>������@� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� )XQFWLRQDO�PDWHULDOV������������� ��� ,Q� >��@�� WKH� FRQFHSW� RI� WKH� FULWLFDO� JUDLQ� ERXQGDU\�DQJOH��TFU�!��Ü����ZDV�LQWURGXFHG�:KHQ� LW� LV� H[FHHGHG�� WKH� ERXQGDU\� RI� WKH GHIRUPDWLRQ� VXEVWUXFWXUH� H[HUWV� UHVLVWDQFH WR�VOLS�WUDQVIHU�ZKLFK�LV�SUDFWLFDOO\�HTXDO�WR WKDW�H[HUWHG�E\�WKH�ODUJH�DQJOH�JUDLQ�ERXQG� DU\�� /DWHU�� XVLQJ� WKH� LPSURYHPHQWV� LQ� WKH LQVWUXPHQWV�DQG�PHWKRGV�IRU�WKH�GHWHUPLQD� WLRQ� RI� VXFK� GLVRULHQWDWLRQV�� LW� ZDV� VKRZQ WKDW� WKRVH� FDQ� DWWDLQ� WHQV� RI� GHJUHHV� >��� ������@� $V� QRWHG� DERYH�� IRU� VXFK� VWUXFWXUHV� ZKHQ� WKH� JUDLQ� VL]HV� RI� GHIRUPDWLRQ� RULJLQ DUH� VPDOOHU� WKDQ� VHYHUDO� PLFURPHWHUV�� WKH H[SRQHQW�RI�WKH�JUDLQ�VL]H�LQ�GHSHQGHQFH���� LV� HTXDO� WR� Ü��� UDWKHU� WKDQ� WR� Ü����� 7KXV� DW�GdGFU��� WKH� IROORZLQJ�UHODWLRQ� LV�DFWXDOO\VDWLVILHG� V\� �V����N�G��� ��� ZKHUH�WKH�WHUP�V��KDV�WKH�VDPH�PHDQLQJ�DVLQ� (T����� DQG� WKH� FRHIILFLHQW� N��� WKRXJKFKDUDFWUHUL]LQJ� DOVR� WKH� GLIILFXOW\� RI� VOLS WUDQVIHU� WKURXJK� WKH� JUDLQ� ERXQGDU\�� KDV REYLRXVO\� RWKHU� GLPHQVLRQDOLW\� DQG�� WKHUH� IRUH�� D� VRPHZKDW� GLIIHUHQW� SK\VLFDO� PHDQ� LQJ� DV� FRPSDUHG� WR� WKRVH� RI� WKH� FRHIILFLHQW N\�LQ�(T�����&RQVLGHULQJ� WKLV� HIIHFW�� 7KRPSVRQ� >�@ SRVWXODWHG� DFWXDOO\� WKDW�� DW� JUDLQ� VL]HV VPDOOHU� WKDW� D� FHUWDLQ� FULWLFDO� YDOXH�� WKH KDUGHQLQJ�GHVFULEHG�E\�(T�����EHFRPHV�PRUH HIILFLHQW��7KLV�FULWLFDO�JUDLQ�VL]H�FDQ�EH�GH� WHUPLQHG� DW� WKH� LQWHUVHFWLRQ� SRLQW� RI� GH� SHQGHQFHV�����DQG������1DPHO\� GFU�� ��N��e�N\��� ��� ,Q�ZRUNV� RI� WKH� DXWKRUV� >��Ü��@�� LW�ZDV VKRZQ�WKDW�WKH�W\SH�����GHSHQGHQFH�LV�YDOLG QRW� RQO\� IRU�JUDLQV� RI� WKH�GHIRUPDWLRQ�RUL� JLQ�� EXW� DOVR� IRU� XOWUDILQH�JUDLQHG� VWUXF� WXUHV� REWDLQHG� XVLQJ� YDFXXP� GHSRVLWLRQ WHFKQRORJLHV�� ,Q� >��@�� LW� ZDV� DOVR� UHSRUWHG WKDW�� H�J��� IRU� D�&X±&U�PXOWLOD\HU� FRPSRVL� WLRQ��DW�D�FHUWDLQ�FULWLFDO�OD\HU�VL]HV��D�NQHH LV� REVHUYHG� LQ� WKH� GHSHQGHQFH� RI� WKH� \LHOG VWUHQJWK�RQ�WKH�JUDLQ�VL]H�LQ�WKH�FRRUGLQDWHV RI� (T������ ZKLOH� LQ� SURFHVVLQJ� RI� WKH� VDPH GDWD� LQ� WKH� V� �GÜ��� FRRUGLQDWHV�� GHSHQGHQFH ����LV�VDWLVILHG�ZHOO��,Q�>��@��LW�LV�VWDWHG�WKDW� LQ� WKH� VXEPLFURQ� JUDLQ� VL]H� UDQJH� �IRU VWUDLQHG�LURQ�DQG�WLWDQLXP���WKH�GHSHQGHQFH V�G��LV�GHVFULEHG�PXFK�EHWWHU�E\�(T�����WKDQ E\�(T����� ,Q�)LJ���D��YHU\� LQWHUHVWLQJ�UHVXOWV� IURP >��@� DUH� VKRZQ��7KH� DXWKRUV�SUHVHQWHG� WHVW GDWD�RI�VWUDLQHG�WLWDQLXP�LQ�WKH�V�GÜ�����FRRU� GLQDWHV�� ,Q� WKH�SORW�� WZR�UHJLRQV�RI� WKH� W\SH ����GHSHQGHQFH�FDQ�EH�GLVWLQJXLVKHG��1DPHO\� LQ� D� UHJLRQ� RI� UHODWLYHO\� ODUJH� JUDLQ� VL]HV� N\� �������ZKLOH�IRU�JUDLQ�VL]HV�VPDOOHU�WKDQD� FHUWDLQ� FULWLFDO� JUDLQ� VL]H�� N\� ������� 7KHFDXVH�RI�VXFK�D�VWHSZLVH�FKDQJH�LQ�WKH�FRHI� ILFLHQW� N\� LV� QRW� TXLWH� FOHDU��0RUHRYHU�� WKHDXWKRUV�QRWH�WKDW�IRU�WKH�VHFRQG�UHJLRQ��WKH WHUP�V��KDV�D�QHJDWLYH�YDOXH��ZKLFK�KDV�QRSK\VLFDO�PHDQLQJ��DQG�WKDW�WKH�YDOXH�RI�WKH FRHIILFLHQW� N\� ������03D�P���� VHHPV� WR� EH RYHUHVWLPDWHG�DQG�XQUHDOLVWLF� $�ZD\�RXW�FDQ�EH�IRXQG�LI� LW� LV�DVVXPHG WKDW�DW�D�JUDLQ�VL]H�GFU��d���PP��WKH�WUDQVL�WLRQ� IURP�GHSHQGHQFH� ���� WR�GHSHQGHQFH� ��� WDNHV� SODFH�� ,Q� )LJ���E�� WKH� GDWD� VKRZQ� LQ )LJ���D� DUH� DSSUR[LPDWHG� ZLWK� WZR� LQWHU� VHFWLQJ� FXUYHV� LQ� WKH� FRRUGLQDWHV� RI� WKH )LJ����� ([SHULPHQWDO� GHSHQGHQFH� RI� WKH� \LHOG� VWUHQJWK� �V�� IRU� ILQH�JUDLQHG� 97����� FRPPHUFLDOO\ SXUH� WLWDQLXP� RQ� WKH� JUDLQ� VL]H� �G�� LQ� WKH� V�GÜ����� FRRUGLQDWHV� >��@� �D��� RXU� DSSUR[LPDWLRQ� RI H[SHULPHQWDO�GDWD�SUHVHQWHG�LQ�)LJ���D�XVLQJ�V�GÜ�����DQG�V�GÜ���GHSHQGHQFHV��E�� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� ��� )XQFWLRQDO�PDWHULDOV������������� +DOO�3HWFK�HTXDWLRQ��,Q�WKLV�FDVH��LW�LV�QDWX� UDO� WKDW�GHSHQGHQFH� ���� KDV� WKH� IRUP� RI� DQ LQFUHDVLQJ�FXUYLOLQHDU�IXQFWLRQ� /HW� XV� FRQVLGHU� WKH� SK\VLFDO�PHDQLQJ� RI VXFK� D� WUDQVLWLRQ�� ,Q� WKH� UHJLRQ� RI� ODUJH JUDLQV� RI� G�!�GFU�� VL]H�� WKH� RUGLQDU\� +DOO�3HWFK�HTXDWLRQ�LV�VDWLVILHG��,W�LV�NQRZQ�WKDW WKHUH� DUH� DW� OHDVW� WKUHH�PRGHOV� >�@� H[SODLQ� LQJ� WKH� H[LVWHQFH� RI� D� W\SH� ���� GHSHQGHQFH� 7KH�PRGHO� RI�KDQGRYHU� WUDQVIHU��ZKHUH� WKH DFWXDWLRQ�RI�D�GLVORFDWLRQ�VRXUFH�LQ�D�QHLJK� ERULQJ� JUDLQ� LV� LQLWLDWHG� E\� VWUHVV� FRQFHQ� WUDWLRQ� DW� WKH� KHDG� RI� D� GLVORFDWLRQ� FOXVWHU LQ� WKH� ILUVW� JUDLQ�� LV� PRVW� JHQHUDOO\� DF� FHSWHG��$FFRUGLQJ�WR�WKLV�PRGHO�>�@� N\� ��VQU��e���� ��� ZKHUH�VQ� �D*E�O�LV�WKH�VWUHVV�RI�WKH�VRXUFH DFWXDWLRQ� LQ�WKH�QHLJKERULQJ�JUDLQ��D�EHLQJ D�FRHIILFLHQW�RI�DQ�RUGHU�RI����*�� WKH�VKHDU PRGXOXV��E��WKH�%XUJHUV�YHFWRU��O��WKH�FKDU� DFWHULVWLF� OHQJWK� RI� D� )UDQN�5HHG� VRXUFH�� DQG�U�LV�WKH�GLVWDQFH�RI�WKH�VRXUFH�IURP�WKH KHDG�RI�WKH�GLVORFDWLRQ�FOXVWHU�� ,Q� )LJ���D�� D� W\SLFDO� VWUXFWXUH� LOOXVWUDW� LQJ�WKH�VOLS�WUDQVIHU�WKURXJK�D�JUDLQ�ERXQG� DU\� DQG� REWDLQHG� IRU� D� SRO\FU\VWDOOLQH� PR� O\EGHQXP� VDPSOH� DIWHU� LQVLJQLILFDQW�SODVWLF GHIRUPDWLRQ�E\� UROOLQJ� �H�|�����DW����&�� LV VKRZQ�� )LJ���E� VKRZV� D� VWUXFWXUH� REWDLQHG LQ� WKH� VDPH�PDWHULDO� DIWHU� D� VHYHUH� SODVWLF GHIRUPDWLRQ� �H� ���� ���� ,W� LV� LPSRUWDQW WKDW� ZLWKLQ� JUDLQV� RI� WKH� GHIRUPDWLRQ� RUL� JLQ�� GLVORFDWLRQV� DUH� KDUGO\� REVHUYHG� ZKHQ WKHLU�VL]H�EHFRPHV�VPDOOHU�WKDQ�����PP� 1DWXUDOO\�� D� FHUWDLQ� GLVWULEXWLRQ� RI VRXUFHV� LQ� VWDUW� VWUHVVHV� DQG� GLVWDQFHV� �U� H[LVWV�� EXW�� LQ� SRO\FU\VWDOOLQH� PDWHULDOV� WKHVH�YDOXHV�EHFRPH�DYHUDJHG��VR�N\� �FRQVW LQ� WKH�JUDLQ�VL]H�UDQJH�ZKHUH�(T����� LV�VDW� LVILHG��7KH�FRHIILFLHQW�N\�DSSHDUV�WR�EH�VHQ�VLWLYH�WR�EORFNLQJ�RI�GLVORFDWLRQV�GXH�WR�LP� SXULWLHV� DQG� PD\� YDU\� UDWKHU� VXEVWDQWLDOO\ GHSHQGLQJ� RQ� WKH� LPSXULW\� FRQWHQW�� KHDW WUHDWPHQW��DQG��LQ�VRPH�FDVHV��DW�FKDQJHV�LQ WKH�JUDLQ�VL]H�>�@� ,Q� >��@�� DWWHQWLRQ� ZDV� JLYHQ� WR� WKH� IDFW WKDW�ZKHQ�WKH�JUDLQ�VL]H�GHFUHDVHV�WR�YDOXHV FORVH� LQ� WKH� RUGHU� WR� U� DQG� O� RQHV�� WKHVH YDOXHV� DUH� QR� ORQJHU� FRQVWDQW� DQG�� VLQFH WKHLU� VL]H� FDQQRW� EH� ODUJHU� WKDQ� G�� ZH� FDQ DVVXPH� WKDW� DV� WKH� JUDLQ� VL]H� GHFUHDVHV� WR YDOXHV� VPDOOHU� WKDQ� GFU��� WKH� U� DQG� O� RQHVDUH� SURSRUWLRQDO� WR� G�� 7KHQ� LW� LV� HDV\� WR REWDLQ�IURP�H[SUHVVLRQ�����WKDW��LQ�WKLV�FDVH �IRU�G���GFU���� WKH�N\�YDOXH�DOVR�GHSHQGV�RQWKH�JUDLQ�VL]H�DV�IROORZV� N\� �D�*E�e�G�e�� �N��e�G�e�� ��� ,W� LV� MXVW� WKLV�N\�G��GHSHQGHQFH� WKDW�ZDVREWDLQHG�LQ�>��@�IRU�D�QXPEHU�RI�PLFURFU\V� WDOOLQH�PDWHULDOV�LQ�WKH�FRUUHVSRQGLQJ�JUDLQ VL]H�UDQJH��)LJ����� 7KXV�� VWULFWO\� VSHDNLQJ�� WKH�GHSHQGHQFHV ����DQG� ����DUH�HTXLYDOHQW� LQ�WKH�VHQVH� WKDW ERWK�GHSHQGHQFHV�UHIOHFW�WKH�KDQGRYHU�FKDU� DFWHU� RI� VOLS� WUDQVIHU� WKURXJK� D� JUDLQ ERXQGDU\�� 2QO\� DW� G�!�GFU��� WKH� FRHIILFLHQWN\�LV�FRQVWDQW��ZKLOH�DW�G���GFU���LW�EHFRPHVGHSHQGHQW� RQ� WKH� JUDLQ� VL]H� DFFRUGLQJ� WR H[SUHVVLRQ� ����� &RUUHVSRQGLQJO\�� VXEVWLWXW� LQJ�H[SUHVVLRQ�����LQ�IRUPXOD������ZH�REWDLQ GHSHQGHQFH����� ,Q� >������@�� WKH� IROORZLQJ� SUREOHP� ZDV DOVR�GLVFXVVHG��$V� WKH�JUDLQ�VL]H�GHFUHDVHV� WKH�SRVVLEOH�QXPEHU�RI�GLVORFDWLRQV�LQ�D�IODW FOXVWHU�DQG��WKHUHIRUH��WKH�VWUHVV�FRQFHQWUD� WLRQ� DW� WKH� KHDG� RI� VXFK� D� FOXVWHU� PXVW GLPLQLVK��7KHQ��IRU�D�VRXUFH�LQ�D�QHLJKERXU� LQJ�JUDLQ� WR� EH� DFWXDWHG�� WKH� VWUHVVHV�PXVW )LJ�����'HSHQGHQFHV�RI�N\�RQ�WKH�JUDLQ�VL]H�>��@� )LJ����� (OHFWURQ� PLFURJUDSKV� RI� SRO\FU\VWDO� OLQH�PRO\EGHQXP�GHIRUPHG�DW�URRP�WHPSHUD� WXUH���H�|������D���H� �������E�� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� )XQFWLRQDO�PDWHULDOV������������� ��� LQFUHDVH�� WKDW� LV� ZKDW� GHILQHV� WKH� FDXVH� RI \LHOG�VWUHVV�ULVH�DFFRUGLQJ�WR�H[SUHVVLRQ����� ,W� LV� FOHDU�� KRZHYHU�� WKDW� WKHUH� H[LVWV� D JUDLQ� VL]H� DW�ZKLFK� QR� FOXVWHUV� DUH� IRUPHG ZLWKLQ� WKH�JUDLQ��DQG�WKH�\LHOG�VWUHVV�PXVW EH� SURSRUWLRQDO� WR� WKH� DFWLYDWLRQ� VWUHVV� RI WKH�)UDQN�5HHG�VRXUFH��L�H�� V\� �V����D�*E�e�G�� ��� $FWXDOO\��LQ�>��@��VXFK�D�VWUHVV�QHFHVVDU\ IRU� WKH� GHIRUPDWLRQ� RI� VHYHUHO\� GHIRUPHG LURQ� KDV� EHHQ� GHWHUPLQHG� DQG� LW� KDV� EHHQ VKRZQ� WKDW� D�� ����Ü����� 6LQFH� WKH� )UDQN�5HHG�VRXUFH�FKDUDFWHULVWLF� OHQJWK� O�PXVW�EH HTXDO�WR�D�FHUWDLQ�SDUW�RI�WKH�JUDLQ�VL]H�G�LQ RUGHU�WKDW�WKH�VRXUFH�FDQ�ZRUN��LW�LV�XVXDOO\ DVVXPHG�WKDW�Ot���G���WKH�SUHVHQWHG�HVWLPD� WLRQ�RI�D��VHHPV�WR�EH�UHDOLVWLF�,Q�FRQFOXVLRQ�RI�WKLV�VHFWLRQ��ZH�FDQ�QRWH ZKDW� IROORZV�� 7KH� WUDQVLWLRQ� IURP� GHSHQG� HQFH� ���� WR� ���� WDNHV� SODFH� QRW� RQO\� LQ� WKH FDVH� RI�JUDLQ� UHILQHPHQW�E\�PHWKRGV� RI� VH� YHUH� DQG� LQWHQVH� GHIRUPDWLRQV�� EXW� DOVR� LQ SRO\FU\VWDOOLQH� PDWHULDOV� ZKHUH� WKH� JUDLQ VL]H� LV� YDULHG� XVLQJ� RWKHU� WHFKQRORJLHV�� LQ SDUWLFXODU�� ZKHQ� VXFK� PLFURFU\VWDOOLQH� PD� WHULDOV�DUH�REWDLQHG�E\�JDV�SKDVH�GHSRVLWLRQ >��Ü������@�� $V� WKH� FULWLFDO� JUDLQ� VL]H� GFU�LV� DWWDLQHG�� HVVHQWLDOO\� QR� GLVORFDWLRQ� FOXV� WHUV� DUH� QXFOHDWHG� LQVLGH� VXFK� ILQH� JUDLQV� ZKLFK� LV� FRQILUPHG� E\� HOHFWURQ� PLFURVFRS\ VWXGLHV� ,W� LV� FOHDU�� KRZHYHU�� WKDW�� DV� WKH� JUDLQ VL]H� IXUWKHU� GHFUHDVHV�� WKHUH� FRPHV� D� PR� PHQW� ZKHQ�� IRU� D� GLVORFDWLRQ� VRXUFH� WR� EH DFWXDWHG� ZLWKLQ� D� JUDLQ�� D� VWUHVV� RI� WKH RUGHU� RI� WKH� WKHRUHWLFDO� VKHDU� VWUHQJWK� LV UHTXLUHG��7KXV��WKH�PHFKDQLVP�RI�KDQGRYHU VOLS� WUDQVIHU� PXVW� EH� H[KDXVWHG�� DQG� WKH \LHOG� VWUHVV� PXVW� DWWDLQ� WKH� WKHRUHWLFDO VWUHQJWK�� 7KLV�� KRZHYHU�� GRHV� QRW� RFFXU� 0RUHRYHU�� LQ� PDQ\� FDVHV�� WKH� \LHOG� VWUHVV GURSV�DEUXSWO\�� ,Q�ZKDW�IROORZV��WKH�FDXVHV RI�VXFK�D�EHKDYLRU�DUH�GLVFXVVHG� ��� <LHOG� VWUHQJWK� RI� SRO\FU\VWDOV� LQ� D QDQRPHWHU� JUDLQ� VL]H� UDQJH�� ,Q�)LJ����� SUH� VHQWHG� LV� D� GHSHQGHQFH� RI� WKH� QRUPDOL]HG \LHOG� VWUHVV� �V�Ü�V���N� RQ� WKH� VL]H� RIQDQRJUDLQV� �WR� D� JUDLQ� VL]H� RI� DERXW��� QP� IRU� VRPH�PDWHULDOV� WKDW�ZDV� JHQHUDOL]HG� LQ >��@�� ,Q� LV� VHHQ� WKDW� LQ� VRPH� FDVHV�� LQ� D JUDLQ� VL]H� UDQJH� VPDOOHU� WKDQ� D� FHUWDLQ FKDUDFWHULVWLF� FULWLFDO� VL]H� GFU�� �DV� D� UXOH���Ü��� QP��� D� IXUWKHU� JUDLQ� UHILQHPHQW�� LQ FRQWUDGLFWLRQ�WR�UHODWLRQ������HLWKHU�GRHV�QRW UHVXOW� LQ� KDUGHQLQJ� RU� LV� DFFRPSDQLHG� E\ VRIWHQLQJ��WKH�LQYHUVH�+DOO�3HWFK�HIIHFW��� $W� SUHVHQW�� QXPHURXV� ZRUNV� DUH� NQRZQ GHYRWHG� WR� WKH� GLVFXVVLRQ� RI� VLPLODU� GHYLD� WLRQV� >��Ü���� HWF�@�� ,W� LV� DVVXPHG� WKDW� WKH SODVWLF� VWUDLQLQJ� PHFKDQLVPV� LQ� PDWHULDOV ZLWK� QDQRJUDLQV� GLIIHU� IURP� WKRVH� LQ� WKH FRDUVH�JUDLQHG� DQDORJV�� ZKLFK� LV� FRQQHFWHG ZLWK� ERWK� WKH� VPDOO� VL]H� RI� VWUXFWXUDO� HOH� PHQWV� DQG� DQ� LQFUHDVH� LQ� WKH� YROXPH� IUDF� WLRQ� RI� WKH� VR�FDOOHG� �LPSHUIHFW�� PDWHULDO� QDPHO\�� JUDLQ� LQWHUIDFHV�� )RU� WKH� GHVFULS� WLRQ�RI�REWDLQHG�H[SHULPHQWDO�UHVXOWV��D�QX� PHURXV� WKHRUHWLFDO� PRGHOV� ZHUH� SURSRVHG IRU� SODVWLF� VWUDLQLQJ� LQ�QDQRFU\VWDOOLQH�PD� WHULDOV� $�JHQHUDO�FODVVLILFDWLRQ�RI�VXFK�PRGHOV�LV SUHVHQWHG� LQ� >��@�� ,W� LQFOXGHV� PRGHOV� GH� VFULELQJ� WKH� \LHOG� VWUHQJWK� RI� D� QDQRFU\V� WDOOLQH� PDWHULDO� EDVLQJ� RQ� GLIIHUHQW� �PL[� WXUH� UXOHV��� PRGHOV� ZKHUH� RUGLQDU\�PRWLRQ PHFKDQLVPV� RI� ODWWLFH� GLVORFDWLRQV� GRPL� QDWH�� PRGHOV� RI� JUDLQ�ERXQGDU\� SODVWLFLW\ PHFKDQLVPV� �JUDLQ�ERXQGDU\� VOLS�� GLIIXVLRQ SODVWLFLW\� DORQJ� JUDLQ� ERXQGDULHV��� PRGHOV RI� WZLQQLQJ�PHFKDQLVPV��6RPH�PRGHOV�WDNH LQWR� DFFRXQW� WKH� FRPSHWLWLRQ� RI� GLIIHUHQW VWUDLQLQJ� PHFKDQLVPV�� EHFDXVH�� DV� D� UXOH� VHYHUDO� PHFKDQLVPV� DFW� VLPXOWDQHRXVO\� LQ UHDO�PDWHULDOV�� ,Q�RXU�RSLQLRQ��DPRQJ�DOO�WKH�DERYH�PHQ� WLRQHG� PRGHOV�� WKH� PRVW� WKRURXJKO\� GHYHO� RSHG�DUH�WKRVH�EDVLQJ�RQ�PL[WXUH�UXOHV�DQG WKH�FRQFHSW�RI�D�QDQRFU\VWDOOLQH�PDWHULDO�LQ WKH� IRUP� RI� D� WZR�SKDVH� FRPSRVLWH� FRQVLVW� LQJ�RI� DQ� LQWUDJUDQXODU� DQG�DQ� LQWHUJUDQX� ODU� SKDVHV�� 6XFK� DQ� DSSURDFK� FDQ� EH� XVHG ERWK�ZLWKRXW�FRQFUHWL]LQJ�WKH�SODVWLF�VWUDLQ� LQJ� PHFKDQLVPV� RI� FU\VWDOOLWHV� DQG� LQWHU� JUDQXODU� ERXQGDULHV� DQG� WDNLQJ� WKRVH� LQWR DFFRXQW�� $W� WKH� VDPH� WLPH�� WKH� GLVORFDWLRQ PRGHOV� WKDW� DVVXPH� WKH� SUHVHQFH� RI� SODVWLF IORZ� FDUULHUV� LQ� WKH� IRUP� RI� ODWWLFH� DQG )LJ����� 'HSHQGHQFHV� RI� WKH� QRUPDOL]HG� \LHOG VWUHVV� RQ� WKH� JUDLQ� VL]H� IRU� VRPH� PDWHULDOV >��@�� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� ��� )XQFWLRQDO�PDWHULDOV������������� JUDLQ�ERXQGDU\� GLVORFDWLRQV�� MRLQW� GLVFOLQD� WLRQV�� DUH� FRQVLGHUHG� WR� EH� UDWKHU� SUREOHP� DWLF� EHFDXVH� GLUHFW� LQYHVWLJDWLRQV� LQGLFDWH WKDW� GLVORFDWLRQV� DUH� DEVHQW� LQ� QDQRJUDLQV� 1HYHUWKHOHVV�� WKH� DXWKRUV� RI� DOO� SURSRVHG PRGHOV�QRWHG� WKDW� WKH\� DJUHH�ZHOO�ZLWK� H[� SHULPHQWDO�UHVXOWV� +RZHYHU�� DORQJ� ZLWK� H[SHULPHQWDO� GDWD WHVWLI\LQJ� WR� WKH� SUHVHQFH� RI� WKH� LQYHUVH +DOO�3HWFK� HIIHFW� LQ� WKH� QDQRPHWHU� JUDLQ VL]H� UDQJH�� WKHUH� H[LVW� GDWD� RQ� DQ� LQFUHDVH LQ�WKH�VWUHQJWK��KDUGQHVV��LQ�WKH�VDPH�JUDLQ VL]H�UDQJH��H�J���UHVXOWV�SUHVHQWHG�LQ�>��@��$ GHSHQGHQFH� RI� WKH� \LHOG� VWUHQJWK� RQ� WKH JUDLQ� VL]H� G� LQ� GHSRVLWHG� FKURPLXP� �)LJ���� REWDLQHG� E\� WKH� DXWKRUV� LQGLFDWHV� DOVR� DQ DEUXSW� LQFUHDVH� LQ� WKH� \LHOG� VWUHQJWK� DW� D JUDLQ�VL]H�VPDOOHU�WKDQ�GFU��|�����PP�DQG�FDQ EH�GHVFULEHG�E\�WKH�UHODWLRQ�V� �V����N�GÜ��$FFRUGLQJ�WR�WKH�FRQFHSW�RI��XVHIXO��LP� SXULWLHV� SURSRVHG� E\� WKH� DXWKRUV� >��@�� WKH REVHUYHG� GUDVWLF� VWUHQJWK� �KDUGQHVV�� LQ� FUHDVH� RI� QDQRFU\VWDOOLQH� FKURPLXP� LV� GXH WR� WKH� LQIOXHQFH� RI� LQWHUVWLWLDO� R[\JHQ DWRPV�� ZKLFK� DUH� �XVHIXO�� LPSXULWLHV� IRU FKURPLXP� EHFDXVH� WKH\� H[KLELW� D� VWURQJHU FKHPLFDO� ERQG� ZLWK� FKURPLXP� DWRPV� WKDQ WKDW�EHWZHHQ�FKURPLXP�DWRPV��7KH�VHJUHJD� WLRQ�RI�R[\JHQ�UHVXOWV�LQ�WKH�IRUPDWLRQ�RI�D VWURQJHU� �KDUGHU�� VKHOO� IURP� LQWHUIDFHV� ZKLFK� IRUPV� D� KRQH\FRPE� VWUXFWXUH� ZLWK VRIWHU�SODVWLF�FKURPLXP�JUDLQV�EHLQJ�ORFDWHG ZLWKLQ�LW��)LJ������ ,W� VKRXOG� EH� QRWHG� WKDW� DQ� DEUXSW� \LHOG VWUHQJWK�ULVH�DV�D�UHVXOW�RI�WKH�JUDLQ�UHILQH� PHQW� WR�D� VL]H� VPDOOHU� WKDQ�GFU�� LV�SRVVLEOHRQO\� LQ� PXOWLFRPSRQHQW� V\VWHPV� DW� DQ� DS� SURSULDWH� FKRLFH� RI� FRPSRQHQWV�� ,Q� VLQJOH� FRPSRQHQW� PDWHULDOV�� D� GHFUHDVH� LQ� WKH JUDLQ� VL]H� UHVXOWV� LQ� DQ� LQFUHDVHG� YROXPH IUDFWLRQ� RI� LPSHUIHFW� PDWHULDO� LQ� JUDLQ ERXQGDULHV� DQG� DW� WULSOH� JUDLQ�ERXQGDU\ MXQFWLRQV� DQG�� WKHUHIRUH�� WR� D� GHFUHDVHG \LHOG�VWUHQJWK��KDUGQHVV�� 7R�GHVFULEH�WKH�\LHOG�VWUHVV�LQ�D�QDQRPH� WHU� JUDLQ� VL]H� UDQJH��ZH�XVHG� WKH� DSSURDFK EDVHG� RQ� D�PL[WXUH� UXOH��:H� DVVXPHG� WKDW WKH�YROXPH�IUDFWLRQ�RI�D�FU\VWDOOLQH�PDWHULDO LV� �G�Ü�W�G���� WKH� IUDFWLRQ� RI� JUDLQ� ERXQGD� ULHV� LV� ���Ü��G�Ü�W�G����� 7KH� \LHOG� VWUHVV YDOXH�RI�D�PDWHULDO�DW�JUDLQ�UHILQHPHQW�GH� SHQGV�RQ�WKH�VWUHQJWK�RI�WKHLU�ERXQGDULHV��LW LQFUHDVHV� DV� JUDLQ� ERXQGDULHV� DUH� VWUHQJWK� HQHG� E\� XVHIXO� LPSXULWLHV� DQG� GHFUHDVHV� LQ VLQJOH�FRPSRQHQW� PDWHULDOV��� 7DNLQJ� LQWR� DF� FRXQW�WKH�VKHDU�RFFXUV�LQ�D�SODQH��ZH�SURSRVH WKH�IROORZLQJ�UHODWLRQ�IRU�WKH�\LHOG�VWUHVV�DW�D JUDLQ�VL]H�VPDOOHU�WKDQ�GFU�� V�� ������§̈© G���W G ·̧ ¹ � �V%���§̈© G���W G ·̧ ¹ � V&5� ��� ZKHUH� W� LV� WKH� WKLFNQHVV� RI� JUDLQ� ERXQGD� ULHV�� V%�� WKH� VWUHQJWK� RI� JUDLQ� ERXQGDULHV� DQG�V&5��WKH�JUDLQ�WKHRUHWLFDO�VWUHQJWK�6LQFH� WKH� VWUHQJWK� RI� GLVORFDWLRQ�IUHH JUDLQV� WHQGV� WR� WKH�KLJKJHVW�SRVVLEOH� �WKHR� UHWLFDO�� VWUHQJWK� RI� D� PDWHULDO�� V&5� FDQ� EHDVVXPHG� WR� FRUUHVSRQG� WR� WKH� WKHRUHWLFDO VWUHQJWK�RI�WKH�PDWHULDO��)RU�LQVWDQFH��LW�LV VWDWHG� >��@�WKDW�WKHUH�H[LVWV�D�FHUWDLQ�FULWL� FDO� FU\VWDOOLWH� VL]H� DW� ZKLFK� FRQYHQWLRQDO PHFKDQLVPV�RI�SODVWLFLW\�DQG�KDUGHQLQJ�VWRS DFWLQJ� DQG� DQ� LGHDO� VWUHQJWK� LV� UHDOL]HG� LQ JUDLQV��DW�ZKLFK�WKH�PLFURKDUGQHVV�QR�ORQJHU GHSHQGV� RQ� WKH� JUDLQ� VL]H� DQG� UHPDLQV� FRQ� VWDQW��)RU�D�QXPEHU�RI�PHWDOV��WKH�YDOXHV�RI VXFK�FULWLFDO�JUDLQ�VL]H�HYDOXDWHG�LQ�>��@�VKRZ D�ODUJH�VSUHDG��)RU�H[DPSOH��WKLV�VL]H�UDQJHV IURP�����WR������QP�IRU�DOXPLQXP�DQG�IURP ����WR������QP�IRU�FRSSHU� ,W� LV�ZRUWK\� WR�QRWH� WKDW��ZKHQ�UHILQLQJ LQWHUJUDQXODU� VWUDLQLQJ� PHFKDQLVPV� RI� D PDWHULDO� LQ� D� QDQRPHWHU� JUDLQ� VL]H� UDQJH� ZH�FDQ�UHSUHVHQW�V%� LQ�H[SUHVVLRQ�����LQ�DQDQDO\WLF�IRUP� ���*HQHUDOL]HG�+DOO�3HWFK�HTXDWLRQ��7KXV� WKH�FRQVLGHUDWLRQ�RI�WKH�\LHOG�VWUHQJWK�YDUL� DWLRQV�LQ�D�ZLGH�JUDLQ�VL]H�UDQJH��LQFOXGLQJ WKH�QDQRPHWHU�UDQJH��LQGLFDWHV�WKH�SUHVHQFH RI� WZR� FULWLFDO� VL]HV� WKDW� GHILQH� FKDQJHV� LQ WKH� VWUDLQLQJ� PHFKDQLVP� ZKHQ� EHLQJ� DW� WDLQHG��:KHQ� WKH� JUDLQ� LV� UHILQHG� WR� GFU��WKH�\LHOG�VWUHQJWK�YDULDWLRQ�FKDUDFWHU�LV�GH� VFULEHG�E\�WKH�+DOO�3HWFK�UHODWLRQ������LQ�WKH JUDLQ� VL]H� LQWHUYDO� IURP� GFU�� WR� GFU��� LW� LVGHVFULEHG� E\� (T������ DQG� DW� JUDLQ� VL]HV VPDOOHU�WKDQ�GFU���E\�UHODWLRQVKLS����� )LJ����� (OHFWURQ� KLJK�UHVROXWLRQ� PLFURJUDSK RI� FKURPLXP� GHSRVLWHG� XVLQJ� D� PDJQHWURQ WHFKQRORJ\�>��@� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� )XQFWLRQDO�PDWHULDOV������������� ��� 2QH� FDQ� FRPELQH� WKH� LQGLFDWHG� GHSHQG� HQFHV�DQG�GHULYH�D�JHQHUDOL]HG�HTXDWLRQ�WKDW GHVFULEHV� WKH� \LHOG� VWUHQJWK� YDULDWLRQ� GH� SHQGLQJ� RQ� WKH� JUDLQ� VL]H� LQ� D� ZLGH� UDQJH ZLWK� UHJDUG� WR� WUDQVLWLRQV� WR� GLIIHUHQW� GH� SHQGHQFHV� DW� DWWDLQLQJ� WKH� FULWLFDO� VL]HV� XVLQJ�WKH�VR�FDOOHG�VLJPD�IXQFWLRQV��QDPHO\� 6�IXQFWLRQV� >��@�� $� IHDWXUH� RI� 6�IXQFWLRQV �WKH� *RPSHUW]� IXQFWLRQ�� 3HDUO� IXQFWLRQ� HWF��� LV� WKDW� LQ� WKH� YLFLQLW\� RI� WKH� FULWLFDO DUJXPHQW��WKHLU�YDOXH�FKDQJHV�IURP���WR��� WKDW�LV�ZK\�WKHLU�XVH�HQDEOHV�RQH�WR�FRPELQH IXQFWLRQV� I��[�� DQG� I��[�� KDYLQJ� WKH� SORWVLQWHUVHFWLQJ� DW� FHUWDLQ� FULWLFDO� YDOXHV�� LQ RQH�FRPPRQ�IXQFWLRQ� )�[�� �6�[�I��[���������6�[��I��[�� ��� 7KH� FKRVHQ� 6�IXQFWLRQ� PXVW� FRUUHVSRQG WR� WKH� SK\VLFDO� PHDQLQJ� RI� WUDQVLWLRQV� DW DWWDLQLQJ� WKH� FULWLFDO� YDOXHV�� 6LQFH� LW� LV NQRZQ� WKDW� LQ� WKH�PDWHULDO�� WKHUH� H[LVWV� D FHUWDLQ� JUDLQ�VL]H� GLVWULEXWLRQ� GHVFULEHG� E\ WKH�ORJ�QRUPDO�GLVWULEXWLRQ� I�G�� � $ V���G�CCC�S H[S��OQ�G����OQ�GFU��FU���V���� �� ��� ZKHUH�$� ��� �FRQVW� DQG� V���� LV� WKH� GLV�WULEXWLRQ� YDULDQFH� IRU� WKH� ILUVW� DQG� VHFRQG WUDQVLWLRQ��UHVSHFWLYHO\��WKHQ��WR�FRQVWUXFW�D JHQHUDOL]HG�HTXDWLRQ�� LW� LV� H[SHGLHQW� WR�XVH DQWLGHULYDWLYH�����DV�DQ�6�IXQFWLRQ 6�G�� ��³�I�G�G�G�� ������ � �HUI §̈ © OQ�G����OQ�GFU� V�CC� ·̧ ¹ � ���� ZKHUH�HUI�[�� � ��CCS ³�H[S��W��GW��W� �����[� $Q� HTXDWLRQ� FRQVWUXFWHG� XVLQJ� 6�IXQF� WLRQV�FKRVHQ� LQ� VXFK�D�ZD\� LV�D�JHQHUDOL]D� WLRQ� RI� (TV������ ����� DQG� ���� DQG� KDV� WKH IRUP V� �­®̄V�6��GFU�����V������6��GFU���½¾¿6��GFU���� ��V��G������6��GFU���� � ���� $FFRUGLQJ� WR� ������ LI� DOO� JUDLQV� FRUUH� VSRQGLQJ� WR� WKH� JLYHQ� GLVWULEXWLRQ� DUH� LQ WKH� UDQJH� RI� YDOXHV� DERYH� GFU��� WKHQ� WKH+DOO�3HWFK� GHSHQGHQFH� ���� KROGV�� IRU� JUDLQ VL]HV�O\LQJ�LQ�WKH�LQWHUYDO�IURP�GFU��WR�GFU��GHSHQGHQFH� ���� LV�YDOLG��DQG�IRU�JUDLQ�VL]HV VPDOOHU� WKDQ� GFU��� GHSHQGHQFH� ���� KROGV�)URP�������LW�DOVR�IROORZV�WKDW�DW�JUDLQ�VL]HV VPDOOHU� WKDQ� GFU��� WKH� \LHOG� VWUHQJWK� PD\LQFUHDVH� RU� GHFUHDVH� GHSHQGLQJ� RQ� WKH VWUHQJWK� RI� JUDLQ� ERXQGDULHV�� )LJXUH� �D VKRZV�D�GHSHQGHQFH�RI�WKH�QRUPDOL]HG�\LHOG VWUHQJWK� �WKH� \LHOG� VWUHQJWK� GLYLGHG� E\ <RXQJ�V� PRGXOXV�� RQ� WKH� JUDLQ� VL]H�� FRQ� VWUXFWHG�IRU�D�ZLGH�JUDLQ�VL]H�UDQJH�DFFRUG� LQJ�WR������DQG�ZLWK�DFFRXQW�IRU�WKH�IROORZ� LQJ�H[SHULPHQWDOO\�REWDLQHG�GDWD�IRU�GHSRV� LWHG� FKURPLXP�� V�� ������ *3D�� N\� ����NJ�PP����� GFU�� ������PP�� GFU�� � ������PP�� V�� ������ DQG� V�� ������� ,Q� WKH QDQRVL]H� UDQJH�� WKH� YDOXH� V&5� ����*3D� LVWDNHQ�� ZKLFK� LV� VRPHZKDW� KLJKHU� WKDQ� WKH ORZHUHVW� LPDWH�RI� WKH�FKURPLXP�WKHRUHWLFDO VWUHQJWK�� DQG� WKH� WKLFNQHVV� RI� JUDLQ ERXQGDULHV� LV� W� ��� QP�� ,Q� WKH� FDVH� RI� D VWURQJ� ERQG� DORQJ� JUDLQ� ERXQGDULHV ��VWURQJ�� ERXQGDULHV��� DW� V%�� ����*3D�V%��!�V&5���DQ�DEUXSW�LQFUHDVH�LQ�WKH�\LHOGVWUHQJWK� �FXUYH���� FRUUHVSRQGV� WR� WKH� WUDQ� VLWLRQ� WR� QDQRVL]HV��ZKLFK� DJUHHV�ZHOO�ZLWK DQ�H[SHULPHQWDO�FXUYH��)LJ������,Q�WKH�K\SR� WKHWLFDO�FDVH�RI�ZHDN�LQWHUJUDQXODU�FRKHVLRQ ��ZHDN�� ERXQGDULHV��� ZH� WDNH� V%�� ���*3D�V%��LV�PXFK�VPDOOHU�WKDQ�V&5��DQG�REVHUYHLWV�GHFUHDVH��FXUYH����� L�H���WKH�VR�FDOOHG�LQ� YHUVH�+DOO�3HWFK�UHODWLRQ� 7KXV�� LW� LV� VHHQ� WKDW� (T������ WDNHV� LQWR DFFRXQW� WKH� KDUGHQLQJ� PHFKDQLVP� FKDQJHV )LJ����� 'HSHQGHQFHV� RI� WKH� QRUPDOL]HG� \LHOG VWUHQJWK�RQ�WKH�JUDLQ�VL]H�IRU�GHSRVLWHG�FKUR� PLXP� LQ� WKH� FDVH� RI� �VWURQJ�� ERXQGDULHV �FXUYH����DQG��ZHDN��ERXQGDULHV��FXUYH�����D� DQG� 6�IXQFWLRQV� LQ� WKH� YLFLQLW\� RI� FULWLFDO JUDLQ�VL]HV��E�� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� ��� )XQFWLRQDO�PDWHULDOV������������� LQ�WKH�YLFLQLW\�RI�WKH�FULWLFDO�JUDLQ�VL]HV�DQG DJUHHV� ZHOO� ZLWK� WKH� H[SHULPHQWDO� GDWD� RE� WDLQHG� E\� WKH� DXWKRUV�� +RZHYHU�� LW� VKRXOG EH� QRWHG� WKDW� WKH� SODVWLFLW\� PHFKDQLVP� RI QDQRVWUXFWXUHG� PDWHULDOV� IRU� JUDLQ� VL]HV WKDW� UXOHV� RXW� WKH� LQWUDJUDQXODU� VWUDLQLQJ FDQ�EH�IXUWKHU�UHILQHG��DQG��LQ�WKLV�FDVH��V�ZLOO�WDNH�D�PRUH�VSHFLILF�IRUP� ,Q� YLHZ� RI� WKH� IDFW� WKDW�� LQ�)LJ���D�� WKH \LHOG� VWUHQJWK� QRUPDOL]HG� ZLWK� UHVSHFW� WR <RXQJ�V�PRGXOXV�LV�ODLG�RII�RQ�WKH�RUGLQDWH D[LV��ZH�FRQVLGHU�WKDW�WKH�REWDLQHG�GHSHQG� HQFH� FDQ� EH� XVHG� LQ� WKH� IXWXUH� IRU� D� FRP� SDUDWLYH�DQDO\VLV�RI�WKH�KDUGHQLQJ�OHYHO�QRW RQO\�IRU�FKURPLXP��EXW�DOVR�IRU�RWKHU�PDWH� ULDOV�� +RZHYHU�� VLQFH� <RXQJ�V� PRGXOXV� RI QDQRVWUXFWXUHG� PDWHULDOV� PD\� GLIIHU� VXE� VWDQWLDOO\� IURP� WDEXODU� YDOXHV� �GXH� WR� WKH VWDWH� RI� JUDLQ� ERXQGDULHV�� WH[WXUH�� DQG RWKHU� IDFWRUV��� LW� LV� UHDVRQDEOH� WR� REWDLQ� D GHSHQGHQFH� RI� WKH� QRUPDOL]HG� KDUGQHVV� RQ WKH�JUDLQ�VL]H��7KLV�VHHPV�WR�EH�FRQYHQLHQW EHFDXVH��LQ�PDQ\�FDVHV��XVLQJ�WKH�PHWKRG�RI DXWRPDWLF� LQGHQWDWLRQ� �QDQRLQGHQWDWLRQ��� LW LV� UDWKHU� HDV\� WR� GHWHUPLQH� ERWK� WKH� KDUG� QHVV� DQG� <RXQJ�V� PRGXOXV� YDOXHV� DQG� KHQFH�� WKHLU� UDWLR�� LQ� RQH� H[SHULPHQW� DW HDFK�SRLQW�DW�ZKLFK�WKH�KDUGQHVV�LV�WHVWHG� :H�FDQ�SDVV�IURP�WKH�V�(�G��GHSHQGHQFH WR�+�(�G��RQH�XVLQJ�WKH�0DUVK�IRUPXOD�WKDW UHODWHV�WKH�KDUGQHVV�DQG�WKH�\LHOG�VWUHVV� +9 VV � ����OQ(VV �������������OQ � ����Q� ���� ZKHUH�(� LV�<RXQJ�V�PRGXOXV�DQG�Q� LV�3RLV� VRQ�V�UDWLR� ,Q�)LJ�����WKH�GHSHQGHQFH�RI�WKH�KDUGQHVV QRUPDOL]HG�ZLWK�UHVSHFW�WR�<RXQJ�V�PRGXOXV RQ�WKH�JUDLQ�VL]H�LV�SUHVHQWHG��WKH�KDUGQHVV YDOXHV� RI� WKH� JUDLQ�ERXQGDU\� PDWHULDO� DUH LQGLFDWHG�QHDU� WKH�FXUYHV��FDOFXODWHG� LQ� WKH PHQWLRQHG�ZD\��7KLV�GHSHQGHQFH�HQDEOHV�XV�WR GHVFULEH� ERWK� WKH� GHVFHQGLQJ� EUDQFK� IRU� WKH FDVH� RI� �ZHDN�� ERXQGDULHV� DQG� WKH� VWDELOL]D� WLRQ� RU� HYHQ� LQFUHDVH� LQ� WKH� VWUHQJWK� �KDUG� QHVV�� LQ� WKH� FDVH� RI� �VWURQJ�� ERXQGDULHV� LQ WKH�QDQRPHWHU�JUDLQ�VL]H�UDQJH� 7KH�GHSHQGHQFH�+�(�G�� FDQ�EH�DOVR�XVHG IRU�WKH�IDVW�HYDOXDWLRQ�RI�D�PDWHULDO�KDUGHQ� LQJ� GHJUHH� E\� FRPSDULQJ� LW� ZLWK� WKH� WKHR� UHWLFDO� KDUGQHVV� YDOXH� RI� WKH� PDWHULDO� DQG KHQFH�ZLWK�WKH�WKHRUHWLFDO�KDUGQHVV�YDOXH�RI WKH�PDWHULDO�ZKLFK�FRUUHVSRQGV�RI�WKH�KLJK� HVW� SRVVLEOH� KDUGHQLQJ� YDOXH� IRU� WKH� JLYHQ PDWHULDO�DQG��KHQFH��ZLWK�WKH�ODUJHVW�SRVVL� EOH�YDOXH�RI�WKH�+�(� �+WKHRU��(�UDWLR�7KH� FRQFHSW� RI� WKHRUHWLFDO� KDUGQHVV� ZDV LQWURGXFHG�E\�WKH�DXWKRUV�LQ�>��@��7KH�WKHR� UHWLFDO�KDUGQHVV�RI�D�PDWHULDO�LV�LWV�PD[LPDO KDUGQHVV� ZKLFK� FDQ� EH� DWWDLQHG� SURYLGHG WKDW� WKH� VWUHVV� WKDW� FDXVHV� SODVWLF� IORZ� LQ WKH�PDWHULDO�XQGHU�WKH�LQGHQWHU�FRUUHVSRQGV WR�WKH�WKHRUHWLFDO�VKHDU�VWUHQJWK�RI�WKLV�PD� WHULDO��7KH�WKHRUHWLFDO�KDUGQHVV�YDOXH�FDQ�EH FDOFXODWHG�XVLQJ�WKH�IRUPXOD +WKHRU�� �E(�e�D�����Q�� ���� ZKHUH�Q� LV�3RLVVRQ�V�UDWLR��WKH�D�YDOXHV�DUH ZLWKLQ�OLPLWV������D��������IRU�PHWDOOLF�PD� WHULDOV��ZH�FDQ�WDNH�&�|���� ,W� LV� VHHQ� WKDW� IRU� WKH�YDOXH�D� ����� WKH WKHRUHWLFDO� KDUGQHVV� FDQ� EH� +WKHRU��|�����(GHSHQGLQJ� RQ� 3RLVVRQ�V� UDWLR� RI� WKH� PDWH� ULDO��7KHVH�YDOXHV�DUH�WKH�ORZHU�OLPLW�RI�WKH SRVVLEOH�WKHRUHWLFDO�KDUGQHVV�� ,W�ZDV�QRWHG�>������@��WKDW��ZKHQ�WKH�LQ� GHQWDWLRQ� LV� GRQH� XVLQJ� D� %HUNRYLFK� LQ� GHQWHU��WKH�UDWLR�RI�WKH�KDUGQHVV�WR�WKH�HODV� WLFLW\�PRGXOXV�LV�GHVFULEHG�DV +�e�( � �����������KV�e�KF�� ���� ZKHUH� KF� LV� WKH� SHQHWUDWLRQ� GHSWK� ZLWKLQZKLFK�WKH�LQGHQWHU�FRQWDFWV�ZLWK�D�PDWHULDO DIWHU� FRPSOHWH� ORDGLQJ� XS� WR�3PD[�� KV�� WKHSDUW� RI� WKH� LQGHQWHU� SHQHWUDWLRQ� GHSWK ZLWKLQ�ZKLFK� WKH� FRQWDFW�ZLWK� WKH�PDWHULDO LV�DEVHQW�DV�D�UHVXOW�RI�D�VLQN�LQ�IRUPHG�LQ WKH�PDWHULDO�QHDU�WKH� LQGHQWHU��DQG�( �� WKH HIIHFWLYH�<RXQJ�V�PRGXOXV��( � �(����Ü�Q��� ZKHUH�Q�LV�3RLVVRQ�V�UDWLR�DQG�(�LV�<RXQJ�V PRGXOXV� $Q� H[SHULPHQWDOO\� REWDLQHG� GHSHQGHQFH +�( �RQ��KV�KF���)LJ������VKRZV�WKDW��DW�LQ�GHQWDWLRQ� ZLWK� D� %HUNRYLFK� LQGHQWHU�� IRU� D PDWHULDO�ZLWK� WKH� JLYHQ� HODVWLFLW\�PRGXOXV� )LJ����� 'HSHQGHQFHV� RI� WKH� KDUGQHVV� QRUPDO� L]HG�ZLWK�UHVSHFW�WR�<RXQJ�V�PRGXOXV�RQ�WKH JUDLQ� VL]H� IRU� VRPH�YDOXHV�RI� D�JUDLQ�ERXQG� DU\�PDWHULDO�VWUHQJWK� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� )XQFWLRQDO�PDWHULDOV������������� ��� WKH� UDWLR�+�( � FDQQRW� H[FHHG� �������� DQG WKH� ODUJHVW� VSHFLILF� KDUGQHVV� YDOXHV �+�( �|�����Ü������FRUUHVSRQG�WR�WKH�DPRU� SKRXV� RU� DPRUSKRXV�QDQRFU\VWDOOLQH� �TXDVL� FU\VWDOOLQH��VWDWHV� 7R�FRQFOXGH��DW�GHFUHDVLQJ�WKH�JUDLQ�VL]H �RU� WKH� VL]H� RI� DQRWKHU� VWUXFWXUDO� HOHPHQW� H�J��� WKH� OD\HU� WKLFNQHVV� LQ� OD\HUHG�PDWHUL� DOV���WKUHH�FKDUDFWHULVWLF�UHJLRQV�ZLWK�TXDOL� WDWLYHO\�GLIIHUHQW�LQIOXHQFH�RI�WKH�VWUXFWXUH RQ�WKH�\LHOG�VWUHVV�FDQ�EH�GLVWLQJXLVKHG�WKDW DUH� VHSDUDWHG� E\� WZR� FULWLFDO� JUDLQ� VL]HV� 5HVSHFWLYHO\�� DW� OHDVW� WKUHH� DQDO\WLFDO� GH� SHQGHQFHV�RI�WKH�\LHOG�VWUHVV�IRU�HDFK�UHJLRQ FDQ�EH�FRQVLGHUHG��7KH�ILUVW�WZR�UHJLRQV�DUH FKDUDFWHUL]HG� E\� KDQGRYHU� VOLS� WUDQVIHU WKURXJK� JUDLQ� ERXQGDULHV� ZLWK� D� FRQVWDQW FRHIILFLHQW�RI�WKH�+DOO�3HWFK�HTXDWLRQ�LQ�WKH ILUVW� UHJLRQ� �N\� �FRQVW�� DQG� ZLWK� D� FRHIIL�FLHQW� RI� WKH�+DOO�3HWFK� HTXDWLRQ� GHSHQGLQJ RQ� WKH� JUDLQ� VL]H� �N\� �N��G����� LQ� WKH� VHF�RQG� RQH�� 7KLV� UHVXOWV� LQ� D� FKDQJH� RI� WKH H[SRQHQW� LQ� WKH� +DOO�3HWFK� HTXDWLRQ� IURP Ü���� WR�Ü��DV� WKH�JUDLQ�VL]H�GHFUHDVHV�WR�D YDOXH� EHORZ� GFU��� :KHQ� SDVVLQJ� WR� WKH QDQRVL]H� UHJLRQ� WKURXJK� GFU��� WKH� GHSHQG�HQFH�RI�WKH�\LHOG�VWUHVV�RQ�WKH�JUDLQ�VL]H�FDQ EH�GHVFULEHG�XVLQJ�D�FRPSRVLWH�PRGHO� 7R�FRQVWUXFW�D�JHQHUDOL]HG�GHSHQGHQFH�RI WKH� \LHOG� VWUHVV� RQ� WKH� JUDLQ� VL]H�� LW� KDV EHHQ�SURSRVHG�WR�XVH�6�IXQFWLRQV��IRU�ZKLFK DQWLGHULYDWLYHV�RI�ORJ�QRUPDO�JUDLQ�VL]H�GLV� WULEXWLRQV� KDYH� EHHQ� FKRVHQ�� $� JHQHUDOL]HG GHSHQGHQFH�RI� WKH�\LHOG�VWUHVV�RQ� WKH�JUDLQ VL]H� QRUPDOL]HG� ZLWK� UHVSHFW� WR� <RXQJ�V PRGXOXV�� ZKLFK� GHVFULEHV� ERWK� WKH� �QHJD� WLYH�� +DOO�3HWFK� UHODWLRQ� �IRU� �ZHDN� ERXQGDULHV�� DQG� WKH� LQFUHDVLQJ� GHSHQGHQFH �IRU� �VWURQJ� ERXQGDULHV��� 8VLQJ� WKH� 0DUVK IRUPXOD�� D� JHQHUDOL]HG� GHSHQGHQFH� RI� WKH KDUGQHVV� QRUPDOL]HG� ZLWK� UHVSHFW� WR <RXQJ�V�PRGXOXV�RQ� WKH�JUDLQ�VL]H�ZDV�RE� WDLQHG�� ZKLFK� PDNHV� LW� SRVVLEOH� WR� XVH� WKH DXWRPDWLF� LQGHQWDWLRQ�PHWKRG� WR�DVVHVV� WKH VWUXFWXUDO� VHQVLWLYLW\� RI� KDUGHQLQJ� LQ� D ZLGH� YDULDWLRQ� UDQJH� RI� WKH� VWUXFWXUDO� HOH� PHQW� VL]HV�� $� IXUWKHU� UHILQHPHQW� RI� WKH SURSRVHG� WHFKQLTXH�PXVW� EH�FRQQHFWHG�ZLWK WKH� UHILQHPHQW� RI� WKH� SODVWLFLW\�PHFKDQLVP LQ�WKH�WKLUG�VWDJH�DQG��KHQFH��WKH�DQDO\WLFDO GHSHQGHQFH�RI�WKH�\LHOG�VWUHVV�LQ�WKH�UHJLRQ RI�QDQRFU\VWDOOLQH�DQG�DPRUSKRXV�QDQRFU\V� WDOOLQH�VWUXFWXUHV�� 5HIHUHQFHV � ���/�6�3DODWQLN��$�,�,O�LQVNLL��8VS��)L]��1DXN����� ����������� � ���(�2�+DOO��3URF��3K\V��6RF��%���������������� � ���1�-�3HWFK��-��,URQ�6WHHO�,QVW������������������ � ���$�+�&RWWUHOO�� 6WUXFWXUH� DQG� 0HFKDQLFDO� 3UR� SHUWLHV� RI� 0HWDOV�� 0HWDOOXUJL\D�� 0RVFRZ �������>LQ�5XVVLDQ@� � ���5�9�$UPVWURQJ�� 8OWUDILQH� *UDLQV� LQ� 0HWDOV� 0HWDOOXUJL\D��0RVFRZ��������>LQ�5XVVLDQ@�� � ���+�&RQUDG��8OWUDILQH�*UDLQV�LQ�0HWDOV��0HWDO� OXUJL\D��0RVFRZ��������>LQ�5XVVLDQ@� � ���9�,�7UHILORY��<X�,�0LOPDQ��6�$�)LUVWRY��3K\VL� FDO� )XQGDPHQWDOV� RI� 6WUHQJWK� RI� 5HIUDFWRU\ 0HWDOV��1DXNRYD�'XPND��.LHY��������>LQ�5XV� VLDQ@� � ���$�0�7KRPSVRQ��0HW��7UDQV����������������� � ���9�,�7UHILORY��9�)�0RLVHHY��(�3�3HFKNRYVNLL�HW DO��� 6WUDLQ� +DUGHQLQJ� DQG� )UDFWXUH� RI� 3RO\� FU\VWDOOLQH� 0HWDOV�� 1DXNRYD� 'XPND�� .LHY �������>LQ�5XVVLDQ@� ����1�$�*UDLYRURQVNLL��*�)�6DU]KDQ��6�$�)LUVWRY� 0HWDOORIL]��1RYHLVK��7HNKQRO���������������� ����5�$�$QGULHYVNLL��$�0�*OH]HU��)L]��0HW��0HWDO� ORYHG����������������� ����+�*OHLWHU�� 3URJUHVV� 0DWHU��6FL��� ���� ��� ������� ����+�*OHLWHU��1DQRVWUXFW��0DWHU��������������� ����5�$�0DVXPXUD�� 3�0�+D]]OHGLQH�� &�6�3DQGH� $FWD�0DWHU������������������� ����9�*�*U\D]QRY�� /�,�7UXVRY�� 3URJUHVV� 0DWHU� 6FL������������������� ����5�:�6LHJHO�� -��3K\V��&KHP��6ROLGV�� ���� ���� ������� ����*�3DOXPER�� 8�(UE�� .�7�$XVW�� 6FU��0HW� 0DWHU������������������� ����0�<X�*XWNLQ��,�$�2YLGNR��3K\VLFDO�0HFKDQLFV RI� 'HIRUPDEOH� 6WUXFWXUHV�� 9RO���� 1DQRFU\V� WDOOLQH� 0DWHULDOV�� ,QVWLWXWH� IRU� 3UREOHPV� RI 0DFKLQH�%XLOGLQJ��6DLQW�3HWHUVEXUJ��������>LQ 5XVVLDQ@� ����8�)�.RFNV��0HWDO��7UDQV������������������ ����9�*�*U\D]QRY�� 0�<X�*XWNLQ�� $�(�5RPDQRY� /�,�7UXVRY��-��0DWHU��6FL������������������� ����+�6�.LP�� <�(VWULQ�� 0�%�%XVK�� $FWD� 0DWHU�� ��������������� ����6�7DNHXFKL��6FU��0DWHU������������������� ����6�$�)LUVWRY��7�*�5RJXO��9�7�0DUXVKNR��9�$�6D� JD\GDN��9RSU��0DWHULDORYHG������������������� )LJ������ ([SHULPHQWDO� GHSHQGHQFH� RI� +�( UDWLR�RQ�WKH�UDWLR�RI�WKH�FKDUDFWHULVWLFV�KV�KFREWDLQHG�DW�LQGHQWDWLRQ�>��Ü��@� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� ��� )XQFWLRQDO�PDWHULDOV������������� ����6�$�)LUVWRY�� 7�*�5RJXO�� 9�/�6YHFKQLNRY� HW DO��� 0HWDOORIL]��1RYHLVK��7HNKQRO��� ���� ���� �������� ����6�$�)LUVWRY�� <X�)�/XJRYVNRL�� (OHNWURQ��0LN� URVNRS��3URFKQ��0DWHU���,VVXH��������������� ����6�9HSUHN�� -��9DF��6FL��7HFKQRO��� ���� ���� ������� ����9�$�0DQLORY�� 9�*�7NDFKHQNR�� 9�,�7UHILORY� 6�$�)LUVWRY�� ,]Y��$NDG��1DXN� 6665�� 0HWDOO\� 1R��������������� ����5�=�9DOLHY�� ,�9�$OHNVDQGURY�� 1DQRVWUXFWXUHG 0DWHULDOV�2EWDLQHG�E\�,QWHQVLYH�3ODVWLF�'HIRU� PDWLRQ��/RJRV��0RVFRZ��������>LQ�5XVVLDQ@� ����9�9�5\ELQ�� /DUJH� 3ODVWLF� 'HIRUPDWLRQV� DQG )UDFWXUH� RI� 0HWDOV�� 0HWDOOXUJL\D�� 0RVFRZ �������>LQ�5XVVLDQ@� ����$�,�,OLQVNLL�� 6WUXFWXUH� DQG� 6WUHQJWK� RI� /D\� HUHG�'LVSHUVLRQ�6WUHQJWKHQHG�)LOPV��0HWDOOXU� JL\D��0RVFRZ��������>LQ�5XVVLDQ@� ����-�*LO� 6HYLOODQR�� 3�YDQ� +RXWWH�� (�$HUQRXGW� 3URJUHVV�0DWHU��6FL����������������� ����$�9�1RNKULQ�� 9�1�&KXYLOGHHY�� (�6�6PLUQRYD HW� DO��� 0HFKDQLFDO� 3URSHUWLHV� RI� 1DQRFU\V� WDOOLQH� DQG� 0LFURFU\VWDOOLQH� 0HWDOV�� )HGHUDO $JHQF\� RI� (GXFDWLRQ� RI� WKH�5XVVLDQ� )HGHUD� WLRQ�� /REDFKHYVN\� 6WDWH� 8QLY��RI� 1L]KQ\ 1RYJRURG�� 1L]KQ\� 1RYJRURG� ������� >LQ� 5XV� VLDQ@� ����*�/DQJIRUG�� 0�&RKHQ�� 7UDQV��$PHU��6RV��0HW�� ��������������� ����%�$�0RYFKDQ�� $YWRPDW��6YDUND�� 1R����� ��� ������� ����'�9ROODWK��'�9�6]DER��1DQRVWUXFW��0DWWHU����� ����������� ����1�:DQJ�� =�:DQJ�� .�7�$XVW�� 8�(UE�� $FWD 0HWDOO��0DWHU������������������� ����6�$�)LUVWRY�� 7�*�5RJXO�� 2�$�6KXW��)L]��.KLP� 0HNK��0DWHU���1R������������� ����6�$�)LUVWRY��7�*�5RJXO��'RS��1DWV��$NDG��1DXN 8NU���1R���������������� ����6�$�)LUVWRY�� (�3�3HFKNRYVNLL�� 9�)�*RUEDQ� HW DO��� 'RS��1DWV��$NDG��1DXN� 8NU��� 1R����� ��� ������� ����6�$�)LUVWRY��7�*�5RJXO��9�)�*RUEDQ�HW�DO���LQ� .H\� (QJLQHHULQJ� 0DWHULDOV� �������� Y����� S����� �˯˲L��mL��äL}¯º���º�ÓÈÓº°�¯�}��¯���¯ÈÓÒ�ÓË�ÏäL�ÓËÓÓ« v�|�nL¯°�ºm������cº��ã ��|�|�b�� |­�ºmº¯ � °«� ÏÈ}ºÓºäL¯Óº°�L� ÏäLÓÒ� ÏÈãËÎÓº°�L� Óȹ¯��Ò� ¹ãÒÓÓº°�L� ¹¯Ò� ¹Ë¯Ë²º�L mL��äL}¯º���º�ÓÈÓº°�¯�}��¯ºmÈÓº�º�°�ÈÓ����º}ÈÏÈÓº���º�ÏÈ��º¹ºäº�º �6�Á�Ó}�L®�äºÎÓÈ º�¯ÒäÈ�Ò��ÏÈ�Èã ÓËÓË�¯LmÓ«ÓÓ«�ÏÈãËÎÓº°�L��¯ÈÓÒ�L�¹ãÒÓÓº°�L�mL��¯ºÏäL¯��Ï˯ÓÈ�Ï��¯È� ²�mÈÓÓ«ä�ÏäLÓÒ�ä˲ÈÓLÏäLm�ÏäL�ÓËÓÓ«�¹ºãL}¯Ò°�ÈãLm�m�º}ºãL�}¯Ò�Ò�ÓÒ²�¯ºÏäL¯Lm�Ï˯ËÓ G}¯�� L� G}¯��� ¡Ë� ¯LmÓ«ÓÓ«� �ºÏmºã«¼� º¹Ò°È�Ò� «}� ËÁË}�Ò� ÏÓËäL�ÓËÓÓ«� ¹¯Ò� ¹Ë¯Ë²º�L� �ºÓÈÓº°�¯�}��¯� ��È}� ÏmÈÓÒ®��ÓË�È�ÒmÓÒ®��²L�� ÏÈãËÎÓº°�L�tºããÈ��Ë��È��� �È}� L�� ÓÈm¹È}Ò� ¯LÏ}Ë�ÏäL�ÓËÓÓ«�ÏÈ��äºmÒ�¹L�mÒ�ËÓº��äL�Óº°�L�äËÎÏ˯ËÓÓº�º�Ï�˹ãËÓÓ«� 6�$�)LUVWRY�HW�DO����7UDQVLWLRQ�IURP�PLFURVWUXFWXUHV���� )XQFWLRQDO�PDWHULDOV������������� ���