❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ ❞❡ ▼❛r✐♥❣á
Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛
❘♦❜s♦♥ ❋❡rr❛r✐ ▼✉♥✐③
❆♥á❧✐s❡ ❞♦ ❛♠❜✐❡♥t❡ q✉í♠✐❝♦ ❧♦❝❛❧ ❡♠ r❡❞❡
❛♠♦r❢❛ ❡ ❝r✐st❛❧✐♥❛✿ ❖ ❡❢❡✐t♦ ❞❡ s♦❧✐❝✐t❛çõ❡s
♠❡❝â♥✐❝❛s ❡ tér♠✐❝❛s
▼❛r✐♥❣á
❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ ❞❡ ▼❛r✐♥❣á
Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛
❘♦❜s♦♥ ❋❡rr❛r✐ ▼✉♥✐③
❆♥á❧✐s❡ ❞♦ ❛♠❜✐❡♥t❡ q✉í♠✐❝♦ ❧♦❝❛❧ ❡♠ r❡❞❡
❛♠♦r❢❛ ❡ ❝r✐st❛❧✐♥❛✿ ❖ ❡❢❡✐t♦ ❞❡ s♦❧✐❝✐t❛çõ❡s
♠❡❝â♥✐❝❛s ❡ tér♠✐❝❛s
❚❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐✲ ❞❛❞❡ ❊st❛❞✉❛❧ ❞❡ ▼❛r✐♥❣á ♣❛r❛ ♦❜t❡♥✲ çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳
❖r✐❡♥t❛çã♦✿
Pr♦❢✳ ❉r✳ ❏✉r❛♥❞✐r ❍✐❧❧♠❛♥♥ ❘♦❤❧✐♥❣
▼❛r✐♥❣á
Dados Internacionais de Catalogação-na-Publicação (CIP) (Biblioteca Central - UEM, Maringá – PR, Brasil)
Muniz, Robson Ferrari
M966a Análise do ambiente químico local em rede amorfa e cristalina: o efeito de solicitações mecânicas e térmicas / Robson Ferrari Muniz. -- Maringá, 2016. 126 f. : il. col. figs. tabs. mapas
Orientador: Prof. Dr. Jurandir Hillmann Rohling. Tese (doutorado) - Universidade Estadual de Maringá, Centro de Ciências Exatas, Departamento de Física, Programa de Pós-Graduação em Física, 2016. 1. Vitro-cerâmicas. 2. Luminescência. 3. Európio.
I. Rohling, Jurandir Hillmann, orient. II.
Universidade Estadual de Maringá. Centro de Ciências Exatas. Departamento de Física. Programa de Pós Graduação em Física. III. Título.
CDD 23.ed. 535.3 MRP-003527
✐✐
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡❝❡r ♣♦❞❡ s❡ t♦r♥❛r ✉♠❛ t❛r❡❢❛ ✉♠ t❛♥t♦ q✉❛♥t♦ ❞✐❢í❝✐❧✳ P❛r❛ ♥ã♦ ❝♦rr❡r ♦ r✐s❝♦ ❞❛ ✐♥❥✉st✐ç❛✱ ❛❣r❛❞❡ç♦ ♣r❡✈✐❛♠❡♥t❡ ❛ t♦❞♦s q✉❡ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❛ ❝♦♥❝r❡t✐③❛çã♦ ❞❡ ♠❛✐s ❡ss❛ ❡t❛♣❛ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳ ❈♦♥t✉❞♦✱ ❞✐s❝♦rr♦ ♠❡✉s s✐♥❝❡r♦s ❛❣r❛❞❡❝✐♠❡♥t♦s àq✉❡❧❡s q✉❡ ❞✐r❡t❛♠❡♥t❡ t♦r♥❛r❛♠ ♣♦ssí✈❡❧ ❛ r❡❛❧✐③❛çã♦ ❞❡ss❡ tr❛❜❛❧❤♦✳
❖ ♣r✐♠❡✐r♦✱ ❞✐r❡❝✐♦♥♦ à ♠✐♥❤❛ q✉❡r✐❞❛ ❢❛♠í❧✐❛✱ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥♦✉ ❛♠❜✐❡♥t❡ ♣❛r❛ ❛s ❡①♣❡r✐ê♥❝✐❛s ❞❛ ♠✐♥❤❛ ✈✐❞❛✳ P❛rt✐❧❤❛♠♦s ❛❧❡❣r✐❛s ❡ tr✐st❡③❛s❀
➚ ♠✐♥❤❛ ♠ã❡✱ ❍é❧✐❛✱ ♥ã♦ ♣♦r s❡r ♠✐♥❤❛ ♠ã❡✱ ♠❛s ♣♦r s❡r ♠✐♥❤❛ ✈✐❞❛✳ ❆❣r❛❞❡ç♦ ❛♦s s❡✉s ❛❜r❛ç♦s q✉❡ ♠❡ ❛❝♦❧❤❡♠ ❡ ♠❡ ❝✉r❛♠✱ s❡✉ s♦rr✐s♦ ❡ ♦❧❤❛r q✉❡ s❡♠♣r❡ ♠❡ ❝❛t✐✈❛♠✳ ❖❜r✐❣❛❞♦ ♠ã❡ ♣❡❧♦s s❛❝r✐❢í❝✐♦s ❢❡✐t♦s ❡♠ ❢✉♥çã♦ ❞❛ ♠✐♥❤❛ ✈✐❞❛ ❡ ❡❞✉❝❛çã♦✳ ➱ ✐♠♣♦ssí✈❡❧ ❝♦❧♦❝❛r ❡♠ ♣❛❧❛✈r❛s ♦ q✉❡ s✐♥t♦ ♣♦r ✈♦❝ê✳
❆♦ ♠❡✉ ♣❛✐✱ ▼✐❧t♦♥✱ ❛♣♦✐♦ ❡ ❝♦♠♣r❡❡♥sã♦✳ ❖❜r✐❣❛❞♦ ♣❡❧♦ ❡①❡♠♣❧♦✱ ♣♦r ♠❡ ♠♦str❛r ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ s❡r ✉♠ ❤♦♠❡♠ ❞❡ ❜❡♠✱ ❤♦♥❡st♦ ❡ ❜❛t❛❧❤❛❞♦r✳
➚s ♠✐♥❤❛s ✐r♠ãs ❙✐♠♦♥❡ ❡ ❙✐❧✈❛♥❛ ♣♦r s❡♠♣r❡ t♦r❝❡r❡♠ ♣♦r ♠✐♠✳ P♦r t♦❞♦s ♦s ♠♦♠❡♥t♦s✱ q✉❡ ❤♦❥❡✱ só ❉❡✉s s❛❜❡ ♦ q✉❛♥t♦ s✐♥t♦ ❢❛❧t❛✳ ❆♦s ♠❡✉s q✉❡r✐❞♦s s♦❜r✐♥❤♦s ▲í✈✐❛✱ ▼✐❣✉❡❧ ❡ ❖tá✈✐♦✳
❆♦ ♣r♦❢✳ ❏✉r❛♥❞✐r ❍✐❧❧♠❛♥♥ ❘♦❤❧✐♥❣✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ✐♥❝❡♥t✐✈♦ ❡ ♣❡❧❛ ♦♣♦rt✉✲ ♥✐❞❛❞❡ ❞❛s ❡①♣❡r✐ê♥❝✐❛s ❛❝❛❞ê♠✐❝❛s✳ ❆ ❡❧❡ ❡①♣r❡ss♦ ♠❡✉ r❡s♣❡✐t♦✳
❆♦ ♣r♦❢✳ ❆♥t♦♥✐♦ ▼❡❞✐♥❛ ◆❡t♦✱ ♣❡❧❛ ❛t❡♥çã♦ ❝♦♥st❛♥t❡✱ ♣❛❝✐ê♥❝✐❛ ❡ ❡♥s✐♥❛♠❡♥✲ t♦s✳ ❈♦♥❤❡❝✐♠❡♥t♦ ❡st❡✱ q✉❡ ❧❡✈❛r❡✐ ♣❛r❛ ♦ r❡st♦ ✈✐❞❛✳
❆♦s ✐r♠ã♦s q✉❡ ❛ ✈✐❞❛ ♠❡ ♣r❡s❡♥t❡♦✉✱ ▲❡♦♥❛r❞♦✱ ❈❛♠✐❧❧❛ ❡ ▼❛②s❡✳ ❖❜r✐❣❛❞♦ ♣❡❧❛ ♣r❡s❡♥ç❛ ❝♦♥st❛♥t❡✱ ♣❡❧♦s ❝♦♥s❡❧❤♦s✱ ♣❡❧❛ ✈❡r❞❛❞❡✐r❛ ❛♠✐③❛❞❡✳
❆♦s ❛♠✐❣♦s ❞❡ ✐♥❢â♥❝✐❛ ❡ ♦✉tr♦r❛✱ ❉❡♥✐s❡ ✱ ❋á❜✐♦✱ ▼❛r❝✐♦ ❆♥❞ré✱ P❡❞r♦✱ ❘❛❢❛❡❧✱ ▼❛rq✉✐♥❤♦s✱ ●✉✐❧❤❡r♠❡✱ ❉✳ ▲✐♥❞❛✱ ❚❤✐❛❣♦✱ ❉❛♥✐❧♦✱ ❘♦❞♦❧❢♦✱ q✉❡ ♠✉✐t♦ ♣r♦✈❛✈❡❧✲ ♠❡♥t❡✱ ♥ã♦ ❧❡rã♦ ❡ss❡ tr❛❜❛❧❤♦✱ ♠❛s q✉❡ s❡♠♣r❡ ❡st❛rã♦ ❡♠ ♠✐♥❤❛s r❡❝♦r❞❛çõ❡s✳
❆♦ ❱✐t♦r✱ ❘❛❢❛❡❧❛✱ ▼❛r❝❡❧♦ ❡ ❘❛q✉❡❧ ♣❡❧❛ ❛♠✐③❛❞❡✱ ♥♦✐t❡s ●♦✉r♠❡t ✭❧❡✐❛✲s❡ ❣♦r❞✐❝❡s✮✱ ❡s♣♦rt❡s ✭❧❡✐❛✲s❡ ❯◆❖ ✴ ❈❆◆✲❈❆◆✮✱ ❡ t♦❞♦s ♦✉tr♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥✲ tr❛çã♦✳
❆♦s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞♦ P❋■✿ ●✐s❡❧❧②✱ ❉❡♥✐s❡✱ ❏♦sé ❘❡♥❛t♦✱ ❘♦❣ér✐♦✱ ●✉t✐❡rr❡③✱ ❆❞r✐❛♥❡✱ ❖tá✈✐♦✱ ❖❞❛✐r✱ ▲✉❞✐♠✐❧❛✱ ◆✐❝♦❧❛③ ❡ ❆♥❣❡❧❛ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❞✉r❛♥t❡ ♦s s❡✐s ❛♥♦s ❞❡ ♣ós✲❣r❛❞✉❛çã♦✳
✐✐✐
➚ ▼ô♥✐❝❛✱ ♣❡❧❛ ❛❥✉❞❛ ❡ ❛t❡♥çã♦✳
➚ ❈❆P❊❙✱ ✭❈❖❋❊❈❯❇ ✺✻✺✴✵✼✮ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✳
●r❛♥❞❡ ♣❛rt❡ ❞❡ss❡ tr❛❜❛❧❤♦ s❡ ❞❡✈❡ ❛ ❝♦❧❛❜♦r❛çã♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ❈❖❋❊❈❯❇✿ ❇r❛s✐❧✲ ❋r❛♥ç❛✱ ❝♦♦r❞❡♥❛❞❛ ♣❡❧♦ Pr♦❢✳ ▼❛✉r♦ ▲✉❝✐❛♥♦ ❇❛❡ss♦✱ ♦ q✉❛❧ ❡①♣r❡ss♦ ♠❡✉ s✐♥❝❡r♦ r❡s♣❡✐t♦ ❡ ❛❣r❛❞❡❝✐♠❡♥t♦✳ ❆♣r♦✈❡✐t♦ ❡ss❡ ♣❛rá❣r❛❢♦ ❡ ♣❡ç♦ ❧✐❝❡♥ç❛ ♣❛r❛ ✜♥❛❧✐③❛r ♦s ❛❣r❛❞❡❝✐♠❡♥t♦s ❡♠ ❋r❛♥❝ês✱ ❝♦♠♦ ❢♦r♠❛ ❞❡ ❛♣r❡ç♦ à t♦❞♦s ♣r♦❢❡ss♦r❡s ❡ ❝♦❧❡❣❛s ♦s q✉❛✐s ❝♦♥✈✐✈✐ ❡①❛t♦s ✸✻✹ ❞✐❛s ❞✉r❛♥t❡ ♠❡✉ ❡stá❣✐♦ ♥❛ ❋r❛♥ç❛✳
P❛rt✐❡ ❞❡ ❝❡ tr❛✈❛✐❧ ❛ été ré❛❧✐sé ❛✉ s❡✐♥ ❞❡ ❧✬■♥st✐t✉t ▲✉♠✐èr❡ ▼❛t✐èr❡ ❞❡ ❧✬❯♥✐✈❡rs✐té ❈❧❛✉❞❡ ❇❡r♥❛r❞ ▲②♦♥ ■ ❡♥ ❋r❛♥❝❡✳ ❆✐♥s✐✱ ❝❡ tr❛✈❛✐❧ ❞♦✐t é♥♦r♠é♠❡♥t à ▼♦♥s✐❡✉r ❨❛♥♥✐❝❦ ●✉②♦t✱ ▼❛✐tr❡ ❞❡ ❝♦♥❢ér❡♥❝❡s✲❍❈ à ❧✬❯♥✐✈❡rs✐té ❞❡ ▲②♦♥ ■❀ ❉♦♠✐♥✐q✉❡ ❉❊ ▲✐❣♥②✱ Pr♦❢❡ss❡✉r à ❯♥✐✈❡rs✐tät ❊r❧❛♥❣❡♥✲◆ür♥❜❡r❣ ❡t ▼❛❞❛♠❡ ❈❤r✐st✐♥❡ ▼❛rt✐♥❡t✳ ▼✐❧❧❡ ♠❡r❝✐s à ✈♦✉s✦
➚ ▼♦♥s✐❡✉r ❨❛♥♥✐❝❦✱ ❥✬❡①♣r✐♠❡ ♠❛ ♣r♦❢♦♥❞❡ ❣r❛t✐t✉❞❡ ❞❡ ♠✬❛✈♦✐r ❛❝❝✉❡✐❧❧✐ ❛✉ ■▲▼✳ ❏❡ ❧❡ r❡♠❡r❝✐❡ ❛✉ss✐ ♣♦✉r s❡s ❝♦♥s❡✐❧s ♣ré❝✐❡✉① ❡t ❝♦♥st❛♥ts✱ s❛ ❝♦♥✜❛♥❝❡ ❡t s❡s ❡♥❝♦✉r❛❣❡♠❡♥ts✳
❏❡ r❡♠❡r❝✐❡ é❣❛❧❡♠❡♥t ❉♦♠✐♥✐q✉❡ ❉❡ ▲✐❣♥②✳ ▼❡r❝✐ ♣♦✉r ❧✬❡♥❝♦✉r❛❣❡♠❡♥t✱ ♣♦✉r s❛ très ❞✐s♣♦♥✐❜✐❧✐té ♠ê♠❡ ❛♣rès q✉❡ ❥❡ s✉✐s r❡✈❡♥✉ ❛✉ ❇rés✐❧✳ ▼❡r❝✐ ♣♦✉r ❧❡s ♥♦♠✲ ❜r❡✉s❡s ré✉♥✐♦♥s ✈✐❛ ❙❦②♣❡✳ ▼❡r❝✐ ❞✬❛✈♦✐r ♣r✐s ❧❡ t❡♠♣s ❞❡ ♠❡ ♠♦♥tr❡r ❧✬❛rt ❞✬êtr❡ ✉♥ ✈r❛✐ ❝❤❡r❝❤❡✉r✳
❏❡ t✐❡♥s à ❛❞r❡ss❡r ♠❛ r❡❝♦♥♥❛✐ss❛♥❝❡ à ❈❤r✐st✐♥❡✳ ❈❡tt❡ t❤ès❡ ♥✬❛✉r❛✐t ♣❛s été ré❛❧✐s❛❜❧❡ s❛♥s ❧✬❛ss✐st❛♥❝❡ ❞❡ ❈❤r✐st✐♥❡✳ ❏✬❡①♣r✐♠❡ ❞♦♥❝ t♦✉s ♠❡s r❡♠❡r❝✐❡♠❡♥ts✳ ❏❡ t✐❡♥s à ❧❡ r❡♠❡r❝✐❡r très ♣❛rt✐❝✉❧✐èr❡♠❡♥t ♣♦✉r ♠✬❛✈♦✐r ❢❛✐t ♣❛rt❛❣❡r s❛ ❣r❛♥❞❡ ❡①♣ér✐❡♥❝❡ ❞❛♥s ❧❡ ❞♦♠❛✐♥❡ ❞❡ ❧✬❡s♣❡❝tr♦s❝♦♣✐❡ ❘❛♠❛♥✳
❏✬❛❞r❡ss❡ ♠❡s r❡♠❡r❝✐❡♠❡♥ts très ❝❤❛❧❡✉r❡✉① à ♠❡s ❝♦♣❛✐♥s ❞❡ ❇✉r❡❛✉ ❑❛st❧❡r ✺❡✱ ◆♦r❛ ❡t ❆♥t♦✐♥❡✱ ❛✈❡❝ ❧❡sq✉❡❧s ❥✬❛✐ ♣❛rt❛❣é ❞✬❛❣ré❛❜❧❡s ♠♦♠❡♥ts ♣❡♥❞❛♥t ♠♦♥ st❛❣❡ à ■▲▼✳ ❏✬❛✐ ❡✉ ❧❡ ♣r✐✈✐❧è❣❡ ❞❡ ♠✬❡♥tr❡t❡♥✐r ré❣✉❧✐èr❡♠❡♥t ❛✈❡❝ ❡✉① ♣♦✉r ❜❛✈❛r❞❡r ❛✉t♦✉r ❞✬✉♥ ❝❛❢é✳ ▼❡r❝✐ ❞❡ ♠✬❛♣♣r❡♥❞r❡ ❛ ❥♦✉❡r ❧❡ ❜❡❧♦t❡✱ ❢❛✐r❡ ❞✉ s❦✐ ❡t ❞✉ r♦❧❧❡r✱ ♠❛✐s s✉rt♦✉t ♣♦✉r ♠❡ ❢❛✐r❡ s❡♥t✐r à ❧✬❛✐s❡✱ ♠ê♠❡ s✐ ❧♦✐♥ ❞❡ ♠❛ ❢❛♠✐❧❧❡✳ ❊t ♦✉✐ ❆♥t♦✐♥❡✱ ✈♦✉s ♣♦✉✈❡③ êtr❡ sûr q✉❡ ❥❡ t♦✉❥♦✉r ♣r♦✜t❡ ❞✬✉♥ ♣❡t✐t ✈❡rr❡ ❞❡ ❈❤❛rtr❡✉s❡ ❛✈❡❝ ♣❡♥sé❡s ♣♦✉r ♠❡s ❛♠✐s ▲②♦♥❡s✳
❏❡ ♥❡ ♣❡✉① ♣❛s ♦✉❜❧✐❡r ♠❡s ❝♦❧❡❣✉❡s à ▲②♦♥✿ ▼❛①✐♠❡✱ ❏✉❧✐❡♥✱ ❉❛♥✐❡❧✱ ▼✐❝❛❡❧✱ ❍❛♠♠❡❞✱ ❙❛♠❛♥t❤❛✱ ●❛r❞❡♥✐❛✱ ◆❛tá❧✐❛✱ ❆❧✐♥❡ ❡ P❡rr✐♥❡✳
❊♥❝♦r❡✱ ♠❡r❝✐ à t♦✉s✳✳✳
✐✈
❘❡s✉♠♦
✈
❆❜str❛❝t
❉❡✈❡❧♦♣✐♥❣ ♥❡✇ ♠❛t❡r✐❛❧s t♦ ❛❝t ❛s ❤♦st ❢♦r r❛r❡ ❡❛rt❤ ✐♦♥s ✐s st✐❧❧ ♦♥ t❤❡ ✉♣s✇✐♥❣✳ ❊✈❡♥ t❤♦✉❣❤ ❧✉♠✐♥❡s❝❡♥t ♣r♦♣❡rt✐❡s ♦❢ t❤❡s❡ ✐♦♥s ❛r❡ s✐❣♥✐✜❝❛♥t❧② ✐♥✢✉❡♥❝❡❞ ❜② t❤❡ ❧♦❝❛❧ ❡♥✈✐r♦♥♠❡♥t ✐♥ ✇❤✐❝❤ t❤❡② ❛r❡ ✐♥s❡rt❡❞✱ t❤❡ str✉❝t✉r❛❧ st✉❞✐❡s ♦❢ t❤❡s❡ ♠❛tr✐❝❡s ❛♥❞ ✐ts ✐♥✢✉❡♥❝❡ ♦♥ t❤❡ ♦♣t✐❝❛❧ ♣r♦♣❡rt✐❡s✱ ❛r❡ r❛r❡❧② ❝♦♥s✐❞❡r❡❞✳ ❚❤✐s t❤❡s✐s ❛✐♠❡❞ t♦ ❛♣♣❧② ♠♦❞❡❧s t♦ st✉❞② t❤❡ str✉❝t✉r❛❧ ♦❢ ❛♠♦r♣❤♦✉s ♥❡t✇♦r❦s ❛s ✇❡❧❧ ❛s t❤❡ ♠♦❞✐✜❝❛✲ t✐♦♥s ✐♥❞✉❝❡❞ ✈✐❛ ❜♦t❤ ❤❡❛t tr❡❛t♠❡♥t ♣r♦❝❡ss❡s ❛♥❞ ❤✐❣❤ ♣r❡ss✉r❡ s♦❧✐❝✐t❛t✐♦♥✳ ❚❤✐s ✇♦r❦ ❞❡s❝r✐❜❡s ❝❛❧❝✐✉♠ ❛❧✉♠✐♥♦s✐❧✐❝❛t❡ ❣❧❛ss❡s ✉♥❞♦♣❡❞ ❛♥❞ ❊✉✲❞♦♣❡❞ ✐♥ ✇❤✐❝❤ ✶✪
♦❢ t♦t❛❧ ♠❛tr✐① ♠❛ss ✇❛s r❡♣❧❛❝❡❞ ❜② ❊✉2❖3✳ ❋♦r t❤❡ ✜rst t✐♠❡✱ t❤❡ ❛✈❡r❛❣❡ ❛♥❣❧❡s
❙✉♠ár✐♦
❙✉♠ár✐♦ ✶
✶ ■♥tr♦❞✉çã♦ ✹
✷ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛✿ ❈♦♥❝❡✐t♦s ❣❡r❛✐s ✾
✷✳✶ Pr♦♣r✐❡❞❛❞❡s ❡str✉t✉r❛✐s ❞♦s ✈✐❞r♦s à ❝✉rt❛ ❡ ♠é❞✐❛ ❞✐stâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✶✳✶ ❱✐❞r♦ ❆❧✉♠✐♥♦s✐❧✐❝❛t♦ ❞❡ ❈á❧❝✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✷ ❊s♣❡❝tr♦s❝♦♣✐❛ ✈✐❜r❛❝✐♦♥❛❧✿ ❘❛♠❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✸ ❊st✉❞♦s t❡ór✐❝♦s ❞❡ í♦♥s ✐♥❝♦r♣♦r❛❞♦s ♥❛s ♠❛tr✐③❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✸✳✶ P❛râ♠❡tr♦s ❞❡ ❝❛♠♣♦ ❝r✐st❛❧✐♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✸✳✷ ❊str❡✐t❛♠❡♥t♦ ❞❛ ❧✐♥❤❛ ❞❡ ❋❧✉♦r❡s❝ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✹ ❚❡♦r✐❛ ❞❡ ❏✉❞❞✲❖❢❡❧t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✷✳✹✳✶ ❏✉❞❞✲❖❢❡❧t ♣❛r❛ ❡♠✐ssã♦✿ ❈❛s♦ ❞♦ ❊✉3+ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✷✳✹✳✷ ❆♥á❧✐s❡ ❞✐♥â♠✐❝❛ ❞♦s ♣r♦❝❡ss♦s ❞❡ tr❛♥s✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✺ ■♥❞❡♥t❛çã♦ ✐♥str✉♠❡♥t❛❞❛ ✲ ▼ét♦❞♦ ❞❡ ❖❧✐✈❡r ❡ P❤❛rr ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✸ ❊①♣❡r✐♠❡♥t❛❧ ✸✺
✸✳✶ ❙✐♥t❡t✐③❛çã♦ ❞❛s ❛♠♦str❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷ ❉✐s♣♦s✐t✐✈♦s ❞❡ ❝♦♥❞✐çõ❡s ❡①tr❡♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✷✳✶ ❈é❧✉❧❛ ❜✐❣♦r♥❛ ❞❡ ❞✐❛♠❛♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✷✳✷ Pr❡♥s❛ ❞♦ t✐♣♦ ❇❡❧t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✸ ❚é❝♥✐❝❛s ❞❡ ❡s♣❡❝tr♦s❝♦♣✐❛ ✉t✐❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✸✳✶ ❘❛♠❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✸✳✷ ▲✉♠✐♥❡s❝ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✹ ❉✉r❡③❛✿ ■♥❞❡♥t❛çã♦ ✐♥str✉♠❡♥t❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✹ ❈❛r❛❝t❡r✐③❛çã♦ ❡str✉t✉r❛❧ ❡ ♣r♦♣r✐❡❞❛❞❡s ❋ís✐❝❛s ❞♦s ✈✐❞r♦s ✹✽
✹✳✶ ❆♥á❧✐s❡ ❡str✉t✉r❛❧ ❞❛s ♠❛tr✐③❡s ✈✐❛ ❡s♣❡❝tr♦s❝♦♣✐❛ ❘❛♠❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
❙❯▼➪❘■❖ ✷
✹✳✷ ▼♦❞❡❧♦ ❞❡ ❋♦rç❛ ❈❡♥tr❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✸ Pr♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ❡ ♠❡❝â♥✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✸✳✶ ❉✉r❡③❛✿ ◆❛♥♦✐♥❞❡♥t❛çã♦ ✐♥str✉♠❡♥t❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✸✳✷ ❊❧❛st✐❝✐❞❛❞❡ ✲ ▼♦❞✉❧♦ ❞❡ ❨♦✉♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺ ❊s♣❡❝tr♦s❝♦♣✐❛ ❘❛♠❛♥ ✐♥ s✐t✉✿ ❝é❧✉❧❛ ❉❆❈ ✻✵
✺✳✶ ❈✐❝❧♦s ❞❡ ❝♦♠♣r❡ssã♦ ❡ ❞❡s❝♦♠♣r❡ssã♦ ❞♦ ✈✐❞r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✺✳✶✳✶ ▼❛tr✐③ ✈ítr❡❛ ▲❙❈❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✺✳✶✳✷ ▼❛tr✐③ ✈ítr❡❛ ❈❆❙✸✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✶✳✸ ▼❛tr✐③ ✈ítr❡❛ ❈❆❙✻✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✺✳✷ ❊✈♦❧✉çã♦ ❞❛ ❇❛♥❞❛ ♣r✐♥❝✐♣❛❧ ❚✲❖✲❚ ✭❚❂ ❆❧✱ ❙✐✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✸ ▼♦❞❡❧♦ ❞❡ ❢♦rç❛ ❝❡♥tr❛❧ ❡♠ ❢✉♥çã♦ ❞❛ ♣r❡ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✹ ❈♦♦r❞❡♥❛çã♦ ❞♦s í♦♥s ❞❡ ❆❧✉♠í♥✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✺✳✺ ❊st✉❞♦s ❞❛s ❡s♣é❝✐❡s ◗n✭s✮ ❡ ◆❇❖✭s✮ ❡♠ ❢✉♥çã♦ ❞❛ ♣r❡ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✺✳✻ ❉❡♥s✐✜❝❛çã♦ ♣❡r♠❛♥❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✻ Pr♦❝❡ss♦ ❞❡ ❙❍P❚ ♥❛ ♦❜t❡♥çã♦ ❞❡ ✈✐tr♦✲❝❡râ♠✐❝❛ ✼✻
✻✳✶ ❉✐❢r❛çã♦ ❞❡ ❘❛✐♦s✲❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✻✳✷ ❉❡♥s✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✻✳✸ ❱✐tr♦✲❝❡râ♠✐❝❛ ❈❆❙✸✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✻✳✸✳✶ ❊s♣❡❝tr♦ ❘❛♠❛♥ ❡ ♠❡❝â♥✐s♠♦ ❞❡ ❝r✐st❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✻✳✸✳✷ Pr♦♣r✐❡❞❛❞❡s ❧✉♠✐♥❡s❝❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✻✳✹ ❱✐tr♦✲❝❡râ♠✐❝❛ ▲❙❈❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✻✳✹✳✶ ▼❛♣❛s ❞❡ ❡①❝✐t❛çã♦✲❡♠✐ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
✻✳✹✳✷ ❊s♣❡❝tr♦ ❞❡ ❡①❝✐t❛çã♦ r❡s♦❧✈✐❞♦ ❡ ❧♦❝❛❧✐③❛❞♦ ♥❛ tr❛♥s✐çã♦ 7❋
0
→ 5❉
0 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
✻✳✹✳✸ ❚❡♦r✐❛ ❞❡ ❏✉❞❞✲❖❢❡❧t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸
✼ ❆♥á❧✐s❡ ❞♦ ❛♠❜✐❡♥t❡ q✉í♠✐❝♦✿ ❊✉3+ ❝♦♠♦ s♦♥❞❛ ❡str✉t✉r❛❧ ✾✼
✼✳✶ ❋▲◆ ✲ ❊str❡✐t❛♠❡♥t♦ ❞❛ ❧✐♥❤❛ ❞❡ ✢✉♦r❡s❝ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✼✳✶✳✶ ❋▲◆ ❛♣❧✐❝❛❞❛ ❛s ❛♠♦str❛s ❊✉✿▲❙❈❆❙ ❡ ❊✉✿▲❙❈❆❙✲❙❍P❚ ❞❡♥✲
tr♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ sít✐♦ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✼✳✷ P❛râ♠❡tr♦s ❞❡ ❈❛♠♣♦ ❝r✐st❛❧✐♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✼✳✸ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛s ♠❛tr✐③❛s ▲❙❈❆❙ ❡ ❈❆❙✸✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸
❙❯▼➪❘■❖ ✸
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✶✵✽
❆ ❆♣ê♥❞✐❝❡ ✶✶✾
❈❆P❮❚❯▲❖
✶
■♥tr♦❞✉çã♦
❖ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ s✉st❡♥tá✈❡❧ ❞❛ s♦❝✐❡❞❛❞❡ s❡ ❡♥❝♦♥tr❛ ❞✐r❡t❛♠❡♥t❡ ✐♥✢✉❡♥✲ ❝✐❛❞♦ ♣❡❧❛ ❝r✐s❡ ❡♥❡r❣ét✐❝❛ ❡ ♣♦❧✉✐çã♦ ❛♠❜✐❡♥t❛❧✳ P❛r❛ s✉♣❡r❛r ♦s ♣r♦❜❧❡♠❛s ❛t✉❛✐s✱ ♥♦✈❛s ❢♦♥t❡s ❞❡ ❡♥❡r❣✐❛ ❧✐♠♣❛ ❡ ❡❝♦♥ô♠✐❝❛s sã♦ ❝♦♥st❛♥t❡♠❡♥t❡ r❡q✉❡r✐❞❛s✳ ◆❡ss❡
s❡♥t✐❞♦✱ ♦s ❞✐♦❞♦s ❡♠✐ss♦r❡s ❞❡ ❧✉③ ✭▲❊❉✮✶ ❢♦r♠❛♠✱ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❛♠❜✐❡♥t❛❧
❡ ❡❝♦♥ô♠✐❝♦✱ ✉♠❛ ❣❛♠❛ ❞❡ ❞✐s♣♦s✐t✐✈♦s ✐❞❡❛✐s✳ ❖s ♠❛t❡r✐❛✐s ✐♥♦r❣â♥✐❝♦s ❞❡ ❢ós❢♦r♦ ❛t✐✈❛❞♦s ❝♦♠ í♦♥s ❞❡ t❡rr❛s r❛r❛s ✭❚❘✮ t❡♠ ❛tr❛í❞♦ ❝♦♥s✐❞❡rá✈❡❧ ❛t❡♥çã♦ ❞❛ ❝♦♠✉✲ ♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ❞❡✈✐❞♦ às ❛♠♣❧❛s ❛♣❧✐❝❛çõ❡s ♥♦ ❝❛♠♣♦ ❡♠❡r❣❡♥t❡ ❞♦s ❞✐s♣♦s✐t✐✈♦s ❧✉♠✐♥❡s❝❡♥t❡s ❬✶✕✸❪✳ ■ss♦ ✐♥❝❧✉✐ ✜❧tr♦s ó♣t✐❝♦s✱ ❧❛s❡r ❞❡ ❡st❛❞♦ só❧✐❞♦✱ ❧â♠♣❛❞❛s ✢✉♦✲ r❡s❝❡♥t❡s✱ t✉❜♦s ❞❡ r❛✐♦s ❝❛tó❞✐❝♦s✱ ♠♦♥✐t♦r❡s✱ t❡❧❛s ❞❡ ♣❧❛s♠❛ ❡ ❞✐♦❞♦s ❡♠✐ss♦r❡s ❞❡
❧✉③ ❜r❛♥❝❛ ✭❲▲❊❉✮✷✳
❖s ❲▲❊❉s ♣r❡♥❞❡♠ ❛♣r❡❝✐á✈❡❧ ❛t❡♥çã♦ ♥♦ s❡♥t✐❞♦ ❛ s❡r ✉♠❛ ❢♦♥t❡ ❞❡ ❧✉③ ❞❡ ú❧t✐♠❛ ❣❡r❛çã♦ ❞❡✈✐❞♦ à s✉❛ ❛❧t❛ ❡✜❝✐ê♥❝✐❛✱ ❜❛✐①♦ ❝♦♥s✉♠♦ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛✱ ❧♦♥❣❛ ✈✐❞❛ út✐❧ ❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❝♦♠ ♦ ❛♠❜✐❡♥t❡✳ ❖ ❛t✉❛❧ ❝❡♥ár✐♦ ✐♥❞✉str✐❛❧ r❡❢❡r❡♥t❡ ❛ ❧✉③ ❜r❛♥❝❛ é ❜❛s❡❛❞❛ ♥❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ✉♠ ❝❤✐♣ ❞❡ ▲❊❉ ❛③✉❧ ❝♦♠ ❢ós❢♦r♦s ❛♠❛r❡❧♦s
✭❨❆●✿❈❡3+✱ ♣♦r ❡①❡♠♣❧♦✮ ❬✹❪✳ ❖ ♣r✐♠❡✐r♦✱ ❡ ♠❛✐s ✉t✐❧✐③❛❞♦ ▲❊❉ ❛③✉❧✱ ❢♦✐ ❞❡s❡♥✈♦❧✲
✈✐❞♦ ♣♦r ❙❤✉❥✐ ◆❛❦❛♠✉r❛✱ ❡♠ ✶✾✾✵✱ ♦ q✉❛❧ ❝♦♥s✐st❡ ❞❡ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ✈ár✐❛s
❝❛♠❛❞❛s ❞❡ ♥✐tr❡t♦ ❞❡ ❣á❧✐♦ ✭●❛◆✮✸✳ ❊♠❜♦r❛ ❡st❡ ♠ét♦❞♦ ❞❡ ♠✐st✉r❛ t❡♠ s✐❞♦ ✉s❛❞❛
♣♦r ♠✉✐t♦s ❛♥♦s✱ ❛✐♥❞❛ ❡①✐st❡♠ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s sér✐♦s✱ t❛✐s ❝♦♠♦ ❡s❝❛ss❡③ ❞❛ ❡♠✐s✲ sã♦ ♥♦ ✈❡r♠❡❧❤♦ ❡ ♦ ❢❛t♦ ❞❛ ❧✉③ ❜r❛♥❝❛ ♦❜t✐❞❛ t❡r ❜❛✐①♦ r❡♥❞✐♠❡♥t♦ ❞❡ r❡♣r♦❞✉çã♦
✶❉♦ ✐♥❣❧ês✿ ▲✐❣❤t ❡♠✐ss✐♦♥ ❞✐♦❞❡✳ ✷❉♦ ✐♥❣❧ês✿ ❲❤✐t❡ ❧✐❣❤t ❡♠✐ss✐♦♥ ❞✐♦❞❡✳
✸▼❡s♠♦ ❛♣ós ✈✐♥t❡ ❛♥♦s ❞❛ ❞❡s❝♦❜❡rt❛ ❞♦ ▲❊❉ ❛③✉❧✱ ❛ ❛t❡♥çã♦ ❞❛❞❛ ♥❡ss❛ ❧✐♥❤❛ ❞❡ ♣❡sq✉✐s❛ ♣❡r♠❛♥❡❝❡ ❡♠ ❛❧t❛✳ ❯♠❛ ♣r♦✈❛ ❞✐ss♦ é ♣r❡♠✐❛çã♦ ❞♦ r❡❝❡♥t❡ ◆♦❜❡❧ ❞❡ ❋ís✐❝❛ ✭✷✵✶✹✮✱ ♦ q✉❛❧ ❢♦✐ ❝♦♠♣❛rt✐❧❤❛❞♦ ♣♦r ■s❛♠✉ ❆❦❛s❛❦✐✱ ❍✐r♦s❤✐ ❆♠❛♥♦ ❡ ♦ ♣ró♣r✐♦ ◆❛❦❛♠✉r❛✱ ❡①❛t❛♠❡♥t❡ ♣♦r s✉❛s ❝♦♥tr✐❜✉✐çõ❡s ♥❛ ♦❜t❡♥çã♦ ❞❛ ♣r✐♠❡✐r❛ ❢♦♥t❡ ❞❡ ❧✉③ ❜r❛♥❝❛✱ ❡♠ ♣❛rt✐❝✉❧❛r ♣❡❧❛ ✐♥✈❡♥çã♦ ❞♦ ▲❊❉ ■♥◆●❛✳
✶✳ ■♥tr♦❞✉çã♦ ✺
❞❡ ❝♦r ✭❈❘■✮✹ ❬✶❪✳
❆ ❡♥❡r❣✐❛ ❝♦♥s✉♠✐❞❛ ♣❛r❛ ❡♠✐t✐r ❧✉③ é ♠✉✐t♦ ♠❡♥♦r ❡♠ ❧â♠♣❛❞❛s ❞❡ ▲❊❉✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛s ❝♦♠ ♦✉tr❛s ❢♦♥t❡s✳ ❖ ✢✉①♦ ❧✉♠✐♥♦s♦ é ❞❡✜♥✐❞♦ ❝♦♠♦ r❛❞✐❛çã♦ t♦t❛❧ ❡♠✐t✐❞❛ ❡♠ t♦❞❛s ❛s ❞✐r❡çõ❡s ♣♦r ✉♠❛ ❢♦♥t❡ ❧✉♠✐♥♦s❛ q✉❡ ♣r♦❞✉③ ❡stí♠✉❧♦ ✈✐s✉❛❧✱ ❝✉❥❛ ✉♥✐❞❛❞❡ é ♦ ❧✉♠❡♥ ✭❧♠✮✳ ❆ ❡✜❝✐ê♥❝✐❛ é ♦❜t✐❞❛ ♣❡❧♦ ✢✉①♦ ❧✉♠✐♥♦s♦ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ♣♦tê♥❝✐❛ ✭♠❡❞✐❞♦ ❡♠ ✇❛tts✮✳ ❆ ✜❣✉r❛ ✶✳✶ r❡♣r❡s❡♥t❛ ❛ ❡✜❝✐ê♥❝✐❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❢♦♥t❡s ❞❡ ❧✉③ ❞❡s❡♥✈♦❧✈✐❞❛s ❛♦ ❧♦♥❣♦ ❞❛ ❤✐stór✐❛✳
❋✐❣✉r❛ ✶✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❡✜❝✐ê♥❝✐❛ ❧✉♠✐♥♦s❛ ❞❡ ❛❧❣✉♠❛s ❢♦♥t❡ ❞❡ ❧✉③✳ ❆❞❛♣t❛❞♦ ❞❡ ❘♦s❡ ❬✺❪✳
◆♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ❢ós❢♦r♦s ♣❛r❛ ❣❡r❛çã♦ ❞❡ ❧✉③✱ ✉♠ ❞♦s ❢❛t♦r❡s q✉❡ ❛♣r❡✲ s❡♥t❛ ♣❛♣❡❧ ❝r✉❝✐❛❧ é ❛ ❡s❝♦❧❤❛ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛s ♠❛tr✐③❡s ♥❛s q✉❛✐s ❡ss❡s í♦♥s sã♦ ✐♥s❡r✐❞♦s✳ ❆ss✐♠✱ ❛ ❡❧❛❜♦r❛çã♦ ❞❡ ♥♦✈♦s ♠❛t❡r✐❛✐s ❝❛♥❞✐❞❛t♦s à ❛t✉❛r❡♠ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ✐♥❝♦r♣♦r❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s ❚❘s✱ ❝♦♥t✐♥✉❛ ❡♠ ❝♦♥st❛♥t❡ ❛s❝❡♥sã♦✳ ❉✉r❛♥t❡
♠✉✐t♦s ❛♥♦s✱ ✈✐❞r♦s ❛❧✉♠✐♥♦ss✐❧✐❝❛t♦ ❞❡ ❝á❧❝✐♦ ✭❈❆❙✮✺ ❞♦♣❛❞♦s ❝♦♠ ❚❘s ❡ ♠❡t❛✐s
❞❡ tr❛♥s✐çã♦ tê♠ s✐❞♦ s✐♥t❡t✐③❛❞♦s ♣❛r❛ ❡st❛ ✜♥❛❧✐❞❛❞❡✳ ❊st❡s ✈✐❞r♦s✱ ♣r❡♣❛r❛❞♦s ❡♠ ❛t♠♦s❢❡r❛ ❞❡ ✈á❝✉♦✱ ♣♦ss✉❡♠ ❡♥❡r❣✐❛ ❞❡ ❢ô♥♦♥s r❡❧❛t✐✈❛♠❡♥t❡ ❜❛✐①❛ ❡ ❛♣r❡s❡♥t❛♠✱ ♣♦rt❛♥t♦✱ ♣♦t❡♥❝✐❛✐s ❛♣❧✐❝❛çõ❡s ❝♦♠♦ ❧❛s❡r ❞❡ ❡st❛❞♦ só❧✐❞♦ ❡ ❞✐s♣♦s✐t✐✈♦s ❲▲❊❉s✳ ❆♦ ❧♦♥❣♦ ❞♦s ú❧t✐♠♦s ❛♥♦s✱ ✉♠❛ ❣❛♠❛ ❞❡ tr❛❜❛❧❤♦s ❢♦✐ ♣r♦❞✉③✐❞❛ ❛ ✜♠ ❞❡ ❛♣r❡s❡♥t❛r ♦s r❡s✉❧t❛❞♦s ❛❧❝❛♥ç❛❞♦s ♥❡st❡ ❝❛♠♣♦ ❬✻✕✶✶❪✳ ❊♠❜♦r❛ ❛s ♣r♦♣r✐❡❞❛❞❡s ❧✉♠✐♥❡s❝❡♥t❡s ❞❡ss❡s í♦♥s ❡st❡❥❛♠ ✐♥t✐♠❛♠❡♥t❡ ❧✐❣❛❞❛s ❛♦ ❛♠❜✐❡♥t❡ ❧♦❝❛❧ ❡♠ q✉❡ sã♦ ✐♥s❡r✐❞♦s✱ ❡s✲ t✉❞♦s ❡str✉t✉r❛✐s ❞❡ss❛s ♠❛tr✐③❡s✱ ❜❡♠ ❝♦♠♦ s✉❛s ✐♥✢✉ê♥❝✐❛s s♦❜r❡ ❛s ♣r♦♣r✐❡❞❛❞❡s
✶✳ ■♥tr♦❞✉çã♦ ✻
ó♣t✐❝❛s✱ sã♦ ♦❝❛s✐♦♥❛❧♠❡♥t❡ ❡❢❡t✐✈❛❞♦s✳ ❆❝r❡❞✐t❛♠♦s q✉❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❛❞✐❝✐♦♥❛❧ ❛❝❡r❝❛ ❞❛ ❡str✉t✉r❛ ❞❡ss❡s ♠❛t❡r✐❛✐s ♣♦ss❛ s❡r ❛ ❝❤❛✈❡ ♣❛r❛ ♦❜t❡r♠♦s ♦s ♠❡❧❤♦r❡s ♣❛râ♠❡tr♦s ❧✉♠✐♥❡s❝❡♥t❡s ❛ ❡❧❡s r❡❧❛❝✐♦♥❛❞♦s✳ ◆❛ ♠❛✐♦r✐❛ ❞♦s ❡st✉❞♦s ❛s ♠♦❞✐✜❝❛✲ çõ❡s ❞❛s ♠❛tr✐③❡s sã♦ ❢❡✐t❛s ❛❧t❡r❛♥❞♦ ❛ ❝♦♠♣♦s✐çã♦ q✉í♠✐❝❛✳ ❊ss❡ t✐♣♦ ❞❡ ❡st✉❞♦ é ❞❡♥♦♠✐♥❛❞❛ ❆❜♦r❞❛❣❡♠ ◗✉í♠✐❝❛ ✭❈❤❡♠✐❝❛❧ ❆♣♣r♦❛❝❤✮✱ ♦♥❞❡ ❛ ♣r❡♣❛r❛çã♦ ❞❡ ✉♠❛ sér✐❡ ❝♦♠ ✐♥ú♠❡r❛s ❛♠♦str❛s é ♥❡❝❡ssár✐❛✳
◆❡ss❡ tr❛❜❛❧❤♦ ♣r♦♣♦♠♦s ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ♠ét♦❞♦s ❛❧t❡r♥❛t✐✈♦s ♣❛r❛ ♠♦✲ ❞✐✜❝❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ♠❛tr✐③❡s ✈ítr❡❛s✳ ❊♠ ❡s♣❡❝✐❛❧✱ ✉t✐❧✐③❛♠♦s ❛❧t❛s ♣r❡ssõ❡s ❝♦♠♦ ♣❛râ♠❡tr♦ t❡r♠♦❞✐♥â♠✐❝♦ ♣r♦♠♦t♦r ❞❡ ❛❧t❡r❛çõ❡s ❡str✉t✉r❛✐s✳ ❚❛✐s ♠♦❞✐✜❝❛✲ çõ❡s ❡✈♦❧✈❡♠ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ❛❧tíss✐♠❛s ♣r❡ssõ❡s q✉❡ ♣♦❞❡♠ ❧❡✈❛r ❛ ✉♠❛ ❞❡♥s✐✜❝❛çã♦ ♣❡r♠❛♥❡♥t❡ ❞♦ ♠❛t❡r✐❛❧✱ r❡s✉❧t❛♥❞♦ ❡♠ ✉♠ ♥♦✈♦ ❝♦♠ ♣r♦♣r✐❡❞❛❞❡s ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐❢❡r❡♥t❡s✳ ❊ss❡ ♠ét♦❞♦ ♣r♦✈♦❝♦✉✱ ♣♦r ❡①❡♠♣❧♦✱ ♠✉❞❛♥ç❛s ❞❛s ❧✐❣❛çõ❡s ❡ â♥❣✉❧♦s
❞♦s t❡tr❛❡❞r♦s ❚❖4✳ ❆s ♠♦❞✐✜❝❛çõ❡s ✐♥❞✉③✐❞❛s ♣❡❧❛ ❛♣❧✐❝❛çã♦ ❞❡ ❛❧t❛s ♣r❡ssõ❡s é
❞❡♥♦♠✐♥❛❞❛ ❆❜♦r❞❛❣❡♠ ❋ís✐❝❛ ✭P❤②s✐❝❛❧ ❆♣♣r♦❛❝❤✮✳ ❆ ✈❛♥t❛❣❡♠ ❞❡ss❡ ♠ét♦❞♦ é ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞♦ ❡st✉❞♦ ❞❛s ✈❛r✐❛çõ❡s ♥❛ ❡str✉t✉r❛ s❡♠ ❛❧t❡r❛çã♦ ❞❛ ❝♦♠♣♦s✐çã♦ q✉í♠✐❝❛ ❞♦ ✈✐❞r♦ ❬✶✷❪✳
❖ ❡st✉❞♦ ❞❛s ♠♦❞✐✜❝❛çõ❡s ❡str✉t✉r❛✐s ✐♥❞✉③✐❞❛s ❡♠ ✈✐❞r♦s ✈✐❛ s♦❧✐❝✐t❛çõ❡s ♠❡✲ ❝â♥✐❝❛s é ❢✉♥❞❛♠❡♥t❛❧ ♥ã♦ só ♣❛r❛ ❡st✉❞❛r ❛s ✈❛r✐❛çõ❡s ♥♦s â♥❣✉❧♦s ✐♥t❡r✲t❡tr❛é❞r✐❝♦s✱ ♠❛s t❛♠❜é♠ ♣❛r❛ ♦❜t❡r ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❞❛s r❡❞❡s✳ ❆♣❡s❛r ❞✐ss♦✱ ❡①❝❡t♦ ♣❛r❛ ✈✐❞r♦s ❝♦♠♦ ❙✐❖2 ❬✶✸❪✱ ❈❛❆❧2❖3 ❬✶✹❪ ❡ ❈❛▼❣❙✐2❖6 ❬✶✺❪✱ ♠❡❞✐❞❛s ✐♥ s✐t✉
❘❛♠❛♥✱ sã♦ r❛r❛♠❡♥t❡ r❡♣♦rt❛❞❛s✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ♦ ✈✐❞r♦ ❞❡ ❙✐❖2 t❡♠ s✐❞♦ ❡①t❡♥✲
s✐✈❛♠❡♥t❡ ❡st✉❞❛❞♦ ♥❛s ú❧t✐♠❛s ❞é❝❛❞❛s ❬✶✸✱ ✶✻✕✶✽❪✳ ❆ ✈❡r✐✜❝❛çã♦ r❡❝♦rr❡♥t❡ é q✉❡ ♠♦❞✐✜❝❛çõ❡s ✐rr❡✈❡rsí✈❡✐s ♥❛ ❡str✉t✉r❛ ❞♦ ♠❛t❡r✐❛❧ ♣♦❞❡♠ s❡r ✐♥❞✉③✐❞❛s ♣❡❧❛ ♣r❡s✲ sã♦✳ P❛r❛ ❡ss❡ ✈✐❞r♦ ✉♠❛ ♠♦❞✐✜❝❛çã♦ ♣❡r♠❛♥❡♥t❡ ♦❝♦rr❡ ❡♠ ♣r❡ssõ❡s s✉♣❡r✐♦r❡s ❛ ✾ ●P❛ ❬✶✾❪✳
P❛r❛ ✈✐❞r♦s ♠❛✐s ❝♦♠♣❧❡①♦s✱ ❉❛♥✐❡❧ ❡t ❛❧✳ ❬✶✹❪ ❢♦r❛♠ ♦s ♣r✐♠❡✐r♦s ❛ r❡♣♦rt❛r❡♠ ❛s ♠✉❞❛♥ç❛s ❞♦ ❡s♣❡❝tr♦ ❘❛♠❛♥ ❞✉r❛♥t❡ ✉♠ ❝✐❝❧♦ ❞❡ ❝♦♠♣r❡ssã♦ ❞♦ ✈✐❞r♦ ❛❧✉♠✐♥❛t♦ ❞❡ ❝á❧❝✐♦✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ❡❧❡s ❝♦♥st❛t❛r❛♠ q✉❡ q✉❛♥❞♦ ❡st❡ ✈✐❞r♦ é ❝♦♠♣r✐♠✐❞♦ à ✉♠❛
♣r❡ssã♦ ❞❡∼✽✲✶✵ ●P❛✱ ♦s át♦♠♦s ❞❡ ❛❧✉♠í♥✐♦✱ q✉❡ ♣♦ss✉❡♠ ✐♥✐❝✐❛❧♠❡♥t❡ ❝♦♦r❞❡♥❛çã♦
✹ ✭[4]❆❧✮✱ sã♦ tr❛♥s❢♦r♠❛❞♦s ❡♠ [5]❆❧ ❡✴♦✉ [6]❆❧✳ ❊ss❛s ♦❜s❡r✈❛çõ❡s ♥♦s ♠♦t✐✈❛r❛♠ ❛
❡st✉❞❛r ❛s ♠✉❞❛♥ç❛s ❡str✉t✉r❛✐s ✐♥❞✉③✐❞❛s ♥♦s ✈✐❞r♦s ❈❆❙✳ ❙❛❜❡♥❞♦ q✉❡ ♣❛r❛ ❛❧❣✉♥s í♦♥s ❛ ❡♠✐ssã♦ ❞❡♣❡♥❞❡ ❢♦rt❡♠❡♥t❡ ❞♦ ❧♦❝❛❧ q✉í♠✐❝♦ ♦♥❞❡ sã♦ ✐♥s❡r✐❞♦s✱ ❡s♣❡rá✈❛♠♦s ❛❧t❡r❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ❧✉♠✐♥❡s❝❡♥t❡s ❞❡ss❡s ♠❛t❡r✐❛✐s s❡♠ ♠♦❞✐✜❝❛r ❛ ❝♦♠♣♦s✐çã♦ ❞♦s ♠❡s♠♦s✳
✶✳ ■♥tr♦❞✉çã♦ ✼
✭❉❆❈✮✻ t❡♠ s✐❞♦ ❛ ♠❛✐s ✉t✐❧✐③❛❞❛✳ ❊st❛ ❝é❧✉❧❛ é ✉♠ ✐♥str✉♠❡♥t♦ q✉❡ ♣❡r♠✐t❡ ❛t✐♥❣✐r
♣r❡ssõ❡s ❞❛ ♦r❞❡♠ ❞❡ ●P❛✱ ♦ q✉❡ ✈✐❛❜✐❧✐③❛ r❡❝r✐❛r ❡♠ ❧❛❜♦r❛tór✐♦ ♣r❡ssõ❡s ❝♦♠♣❛✲ rá✈❡✐s ❛ ❞♦ ♠❛♥t♦ ❡ ❞❛ ❝r♦st❛ t❡rr❡str❡✳ P♦r ❡ss❡ ♠♦t✐✈♦✱ ❞✉r❛♥t❡ ♠✉✐t♦ t❡♠♣♦ ❡❧❛ t❡♠ s✐❞♦ ✉t✐❧✐③❛❞❛ ♣♦r ❣❡ó❧♦❣♦s q✉❡ ❡st✉❞❛♠ ✈❛r✐❛çõ❡s ❞♦s ó①✐❞♦s q✉❡ ❝♦♠♣õ❡♠ ♦ ♠❛❣♠❛ t❡rr❡str❡✳
❯♠❛ ♦✉tr❛ ♠❛♥❡✐r❛ ❞❡ ♠♦❞✐✜❝❛r ❛ ❡str✉t✉r❛ ✐♥✐❝✐❛❧ ❞♦s ♠❛t❡r✐❛✐s ✈ítr❡♦s é ♦ tr❛t❛♠❡♥t♦ tér♠✐❝♦✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ❝r✐st❛❧✐③❛çã♦ ❞♦ ✈✐❞r♦ ❈❆❙ ✈✐❛ tr❛t❛♠❡♥t♦ tér♠✐❝♦ ❝♦♥✈❡♥❝✐♦♥❛❧ é ❞✐❢í❝✐❧ ❞❡ s❡r ❛❧❝❛♥ç❛❞❛✳ ❆ ♥✉❝❧❡❛çã♦ ✐♥✐❝✐❛❧ é s✉♣❡r✜❝✐❛❧ ❡ ♣r♦✈♦❝❛ ✉♠ ❝r❡s❝✐♠❡♥t♦ ❤❡t❡r♦❣ê♥❡♦ ❞❡ ❝r✐st❛✐s✱ ✐♠♣♦ss✐❜✐❧✐t❛♥❞♦ ❛ ♦❜t❡♥çã♦ ❞❡ ✈✐tr♦✲❝❡râ♠✐❝❛s ❤♦♠♦❣ê♥❡❛s ❡ tr❛♥s♣❛r❡♥t❡s✳ ❖✉tr♦s ❡st✉❞✐♦s♦s ❥á r❡♣♦rt❛r❛♠ ❡ss❛ ❞✐✜❝✉❧❞❛❞❡ ♣❛r❛ s✐st❡♠❛s ❙✐❖2✲❆❧2❖3✲❈❛❖✲▼❣❖✭❘2❖✮ ❬✷✵❪✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ♦s ❛✉t♦r❡s✱ ❛ ✐♥✐❝✐❛❧✐③❛çã♦
❞❡ ✉♠❛ ❝r✐st❛❧✐③❛çã♦ ❞♦ t✐♣♦ ❜✉❧❦ ✭❡♠ t♦❞♦ ✈♦❧✉♠❡✮ é ❛ ♣r✐♥❝✐♣❛❧ ❜❛rr❡✐r❛ ♥❛ ♣r♦❞✉çã♦ ❞❡ ✈✐tr♦✲❝❡râ♠✐❝❛s✳
▼✉✐t♦s ♣❡sq✉✐s❛❞♦r❡s r❡♣♦rt❛r❛♠ r❡s✉❧t❛❞♦s s♦❜r❡ ❛ ❛❞✐çã♦ ❞❡ ❛❣❡♥t❡s ♥✉❝❧❡❛♥✲ t❡s ♣❛r❛ ❢❛❝✐❧✐t❛r ❛ ❝r✐st❛❧✐③❛çã♦ ❞❡ ♠❛tr✐③❡s ✈ítr❡❛s ❬✷✵✕✷✷❪✳ ❘❡③✈❛♥✐ ❡t ❛❧✳ ✈❡r✐✜❝❛r❛♠ q✉❡ ❛ ❛❞✐çã♦ s✐♠✉❧tâ♥❡❛ ❞❡ ❈r2❖3✱ ❋❡2❖3✱ ❡ ❚✐❖2 ❢♦✐ ❛ ❝♦♠❜✐♥❛çã♦ ♠❛✐s ❡❢❡t✐✈❛ ❡♠
♣r♦♠♦✈❡r ❛ ❝r✐st❛❧✐③❛çã♦ ✈♦❧✉♠étr✐❝❛s ❬✷✵❪✳ ❲❛♥❣ ❡t ❛❧✳ ❬✷✶❪ ❞❡s❡♥✈♦❧✈❡r❛♠ ✈✐tr♦✲
❝❡râ♠✐❝❛s tr❛♥s♣❛r❡♥t❡s ❝♦♥t❡♥❞♦ ❢❛s❡s ❝r✐st❛❧✐♥❛s ❞❡✈✐❞♦ ❛ ❛❞✐çã♦ ❞❡ ❈❞❋2✱ P❜❋2✱
▲❛❋3✳ ◆♦ ❡♥t❛♥t♦✱ ❡ss❡s ♠❛t❡r✐❛✐s ❡♥✈♦❧✈✐❛♠ ❡❧❡♠❡♥t♦s tó①✐❝♦s ✭❈❞❋2 ❡ P❜❋2✮ ♦✉
❝❛r♦s ✭▲❛❋3✮✳ P❛r❛ q✉❡ ❤❛❥❛ ✉♠❛ ❝r✐st❛❧✐③❛çã♦ ✈♦❧✉♠étr✐❝❛✱ é ❞❡ s✉♠❛ ✐♠♣♦rtâ♥❝✐❛
✐♥❞✉③✐r ❛ ❞✐❢✉sã♦ ✐♥t❡r✐♦r✳ ❊ss❛ ❞✐❢✉sã♦ é ♥♦r♠❛❧♠❡♥t❡ ❛❧❝❛♥ç❛❞❛ ♣♦r tr❛t❛♠❡♥t♦s à ❜❛✐①❛s t❡♠♣❡r❛t✉r❛s ❡ ❧♦♥❣♦s t❡♠♣♦s ❬✷✸❪✳ ◆♦ ❡♥t❛♥t♦✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ❞✉r❛çã♦ ♦ ✈✐❞r♦ ♣♦❞❡ ♣❡r❞❡r ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❡ ♠❡❝â♥✐❝❛s✳
❋r❡♥t❡ ❛ ❡ss❛ ❞✐✜❝✉❧❞❛❞❡✱ s✉❣❡r✐♠♦s ❛ ❛♣❧✐❝❛çã♦ ❞♦ ♣r♦❝❡ss♦ tr❛t❛♠❡♥t♦ tér♠✐❝♦
❡ ♣r❡ssã♦ s✐♠✉❧tâ♥❡♦ ✭❙❍P❚✮✼ ❝♦♠♦ ✉♠❛ t❡♥t❛t✐✈❛ ❞❡ ♦❜t❡r ✉♠❛ ❝❡râ♠✐❝❛ ✈ítr❡❛
tr❛♥s♣❛r❡♥t❡✱ ♦❜t✐❞❛ ♣♦r ❝r✐st❛❧✐③❛çã♦ ❤♦♠♦❣ê♥❡❛✳ ❖ ♠ét♦❞♦ ❞❡ ❙❍P❚ ❝♦♥s✐st❡ ❡♠ s✉❜♠❡t❡r ❛ ❛♠♦str❛ à ❛❧t❛ t❡♠♣❡r❛t✉r❛ ❡ ♣r❡ssã♦ ❞❡ ❢♦r♠❛ s✐♥❝rô♥✐❝❛✳ P❛r❛ ✐ss♦✱ ✉t✐❧✐③❛♠♦s ✉♠❛ ♣r❡♥s❛ ❞❡ ❛❧t❛ ♣r❡ssã♦ ❞♦ t✐♣♦ ❇❡❧t✳ ❉❡s❞❡ ✶✾✺✹✱ q✉❛♥❞♦ ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❚r❛❝② ❍❛❧❧✱ ❡ss❡ ❡q✉✐♣❛♠❡♥t♦ t❡♠ s❡ ♠♦str❛❞♦ ♦ ❞✐s♣♦s✐t✐✈♦ ♠❛✐s ❛❞❡q✉❛❞♦ ♣❛r❛ ❛t✐♥❣✐r✱ ❝♦♥❝♦♠✐t❛♥t❡♠❡♥t❡✱ ❡❧❡✈❛❞❛s ♣r❡ssõ❡s ❡ t❡♠♣❡r❛t✉r❛s ❬✷✹✱✷✺❪✳
❉✐❢❡r❡♥t❡ ❞♦s ♠❛t❡r✐❛✐s ❝r✐st❛❧✐♥♦s✱ ❛ ❢❛❧t❛ ❞❡ ♣❡r✐♦❞✐❝✐❞❛❞❡ ♥❛ ❡str✉t✉r❛ ❞♦ ✈✐✲ ❞r♦ ❧✐♠✐t❛ ❛ ❛♣❧✐❝❛çã♦ ❞❛s té❝♥✐❝❛s ❝♦♥✈❡♥❝✐♦♥❛✐s ❝♦♠♦ ❞✐❢r❛çã♦ ❞❡ ❘❛✐♦s✲❳ ✭❉❘❳✮ ❡✴♦✉ ❡s♣❡❝tr♦s❝♦♣✐❛ ✈✐❜r❛❝✐♦♥❛❧✳ P♦r ♦✉tr♦ ❧❛❞♦✱ s✐❣♥✐✜❝❛♥t❡ ♣r♦❣r❡ss♦ ♣ô❞❡ s❡r ♦❜✲
✻❉♦ ✐♥❣❧ês✿ ❉✐❛♠♦♥❞ ❆♥✈✐❧ ❈❡❧❧✳
✶✳ ■♥tr♦❞✉çã♦ ✽
s❡r✈❛❞♦ ♥♦s ú❧t✐♠♦s q✉❛r❡♥t❛ ❛♥♦s✳ ◆❡ss❡ â♠❜✐t♦✱ ❞❡st❛❝❛♠♦s ✉s♦ ❞❡ ❚❘s✱ ♠❛✐s
❡s♣❡❝✐✜❝❛♠❡♥t❡ í♦♥ ❧❛♥t❛♥í❞❡♦s tr✐✈❛❧❡♥t❡s ✭▲♥3+✮✱ ❝♦♠♦ s♦♥❞❛ ❡str✉t✉r❛❧ ❬✷✻✕✷✽❪✳
❆ ✐♥✈❡st✐❣❛çã♦ ❞♦ ❛♠❜✐❡♥t❡ ❧♦❝❛❧✱ ✈✐❛ ❡①❝✐t❛çã♦ s❡❧❡t✐✈❛ ❞❡ ✉♠ ✭▲♥3+✮✱ t❡♠ s❡ ♠♦s✲
tr❛❞❛ ✉♠❛ ❢❡rr❛♠❡♥t❛ ♣♦❞❡r♦s❛ ♣❛r❛ ❛♥❛❧✐s❛r ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝❛r❣❛s ❡ ❞✐stâ♥❝✐❛s ✐♥t❡r❛tô♠✐❝❛s ❞♦s ❧✐❣❛♥t❡s q✉❡ ❢♦r♠❛♠ ❛ r❡❞❡ ❞❡ ✉♠❛ ♠❛tr✐③✳ ❆ ❞❡s♦r❞❡♠ ✐♥❡r❡♥t❡ ❞❛ ❡str✉t✉r❛ ♥♦s ✈✐❞r♦s ✐♠♣❧✐❝❛ ❡♠ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❛♠❜✐❡♥t❡s ❧♦❝❛✐s ✭sít✐♦s✮ ❞♦
❧❛♥t❛♥í❞❡♦ ❝♦♠ ♣❡q✉❡♥❛s ❞✐❢❡r❡♥ç❛s ♥❛s ❞✐stâ♥❝✐❛s ❡ ♥♦s â♥❣✉❧♦s ❞❛ ❧✐❣❛çã♦ ✭▲♥3+✮✲
❧✐❣❛♥t❡ ❬✷✾❪✳ ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❡①♣❡r✐♠❡♥t❛❧✱ ♦ ❡❢❡✐t♦ ❞✐r❡t♦ ❞❡ss❛ ✐♥❡rê♥❝✐❛ é ♦ ❛❧❛r❣❛♠❡♥t♦ ❞❛s ❜❛♥❞❛s ❞❡ ❛❜s♦rçã♦✴❡①❝✐t❛çã♦ ❡ ❡♠✐ssã♦✱ r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ❛s tr❛♥✲
s✐çõ❡s ✐♥tr❛✲❝♦♥✜❣✉r❛❝✐♦♥❛✐s ❡♥tr❡ ♦s ♠✉❧tí♣❧❡t♦s ❞♦s í♦♥s ▲♥3+✳ ❊ss❛ ❞✐str✐❜✉✐çã♦
❞❡♣❡♥❞❡✱ ❜❛s✐❝❛♠❡♥t❡✱ ❞♦ t✐♣♦ ❞❡ ❧✐❣❛♥t❡ ❝♦♠ q✉❡ ♦s í♦♥s ❡stã♦ ❝♦♥❡❝t❛❞♦s✳
❊♥q✉❛♥t♦ ❛ ❧✉♠✐♥❡s❝ê♥❝✐❛ ❝♦♥✈❡♥❝✐♦♥❛❧ ♥♦s ❢♦r♥❡❝❡ ❛♣❡♥❛s ✉♠❛ ♠é❞✐❛ ❣❧♦❜❛❧ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s sít✐♦s✱ ❛ té❝♥✐❝❛ ❞❡ ❡str❡✐t❛♠❡♥t♦ ❞❛ ❧✐♥❤❛ ❞❡ ✢✉♦r❡❝ê♥❝✐❛
✭❋▲◆✮✽ ♥♦s ♣r♦♣♦r❝✐♦♥❛ ✐♥❢♦r♠❛çõ❡s ❛❝❡r❝❛ ❞♦s sít✐♦s ✐♥❞✐✈✐❞✉❛✐s✳ ❊①❝✐t❛♥❞♦✱ s❡❧❡✲
t✐✈❛♠❡♥t❡✱ ♦s í♦♥s ❞❡ ✉♠ sít✐♦ ♣❛rt✐❝✉❧❛r✱ ❛ té❝♥✐❝❛ ♥♦s ♣❡r♠✐t❡ ♦❜t❡r ♦s ♣❛râ♠❡tr♦s
❞❡ ❈❛♠♣♦ ❈r✐st❛❧✐♥♦ ✭❈❋✮✾ ❡ s♦♠❛r ✐♥❢♦r♠❛çõ❡s r❡❧❛t✐✈❛s ❛s ❢♦rç❛s ❡ ❞✐stâ♥❝✐❛s ❞❛s
❧✐❣❛çõ❡s ▲♥✲❧✐❣❛♥t❡✳
◆❛ r❡❞❛çã♦ ❞❡st❛ t❡s❡✱ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❢♦r❛♠ ❛rt✐❝✉❧❛❞♦s ❡♠ três ♣❛rt❡s ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦s ♦❜❥❡t✐✈♦s✳ ❆ ♣r✐♠❡✐r❛ ❝♦♠♣r❡❡♥❞❡✉ ✉♠ ❡st✉❞♦ ❞❡t❛❧❤❛❞♦ ❞❛ ❡str✉t✉r❛ ✈ítr❡❛✱ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ sí❧✐❝❛✳ ❈♦♠♣❛r❛♠♦s ♥♦ss❛s ♠❛tr✐③❡s ❝♦♠ ✈✐❞r♦s ❞❡ sí❧✐❝❛ ♣✉r❛ ♣❛r❛ ♠❡❧❤♦r ❡♥t❡♥❞❡r ❛ ❢✉♥çã♦ ❞❡ ❝❛❞❛ ❝♦♠♣♦♥❡♥t❡ ✭❙✐✱ ❆❧✱ ❈❛ ❡ ▼❣✮ ♥❛ r❡❞❡ ❡str✉t✉r❛❧ ❞♦ ✈✐❞r♦✳ ◆✉♠ s❡❣✉♥❞♦ ♠♦♠❡♥t♦✱ ❛♥❛❧✐s❛♠♦s ❛s ✐♥✢✉ê♥❝✐❛s ❞❡ s♦❧✐❝✐t❛çõ❡s ♠❡❝â♥✐❝❛s ♥❛ ❡str✉t✉r❛ ❞❡ss❡s ♠❛t❡r✐❛✐s✳ ❋✐♥❛❧♠❡♥t❡✱ ❛♣r❡s❡♥t❛♠♦s ♦s r❡s✉❧t❛❞♦s ♣❡rt✐♥❡♥t❡s ❛♦ ♣r♦❝❡ss♦ ❝♦♥❝♦♠✐t❛♥t❡ ❞❡ ❛❧t❛s ♣r❡ssõ❡s ❡ t❡♠♣❡r❛t✉r❛s ♣❛r❛ ♦❜t❡♥çã♦ ❞❛s ✈✐tr♦✲❝❡râ♠✐❝❛s tr❛♥s♣❛r❡♥t❡s✳
❈❆P❮❚❯▲❖
✷
❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛✿ ❈♦♥❝❡✐t♦s ❣❡r❛✐s
◆❡ss❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛♠♦s✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ♦s ❝♦♥❝❡✐t♦s t❡ór✐❝♦s r❡❧❛❝✐♦♥❛❞♦s ❛ ✏❡str✉t✉r❛✑ ❞♦s ✈✐❞r♦s à ❝✉rt❛ ❡ ♠é❞✐❛ ❞✐stâ♥❝✐❛✱ ❜❡♠ ❝♦♠♦ ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ ❞♦s ✈✐❞r♦s ❞❛ ❢❛♠í❧✐❛ ❛❧✉♠✐♥♦ss✐❧✐❝❛t♦ ❞❡ ❝á❧❝✐♦✳ ◆✉♠ s❡❣✉♥❞♦ ✐♥st❛♥t❡✱ ❞✐s❝✉t✐♠♦s ❛ t❡♦r✐❛ ❡♥✈♦❧✈✐❞❛ ♥❛ ❡s♣❡❝tr♦s❝♦♣✐❛ ❘❛♠❛♥✱ ✉♠❛ ✈❡③ q✉❡ ❡st❛ té❝♥✐❝❛ ❢♦✐ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛ ♥♦ ❞❡❝♦rr❡r ❞❡ss❡ tr❛❜❛❧❤♦✳ ❚❛♠❜é♠ ❛♣r❡s❡♥t❛♠♦s ❛ ❞❡s❝r✐çã♦ ❞❛ t❡♦r✐❛ ❡♥✈♦❧✈✐❞❛ ♥♦s ❡st✉❞♦s ❞❛s tr❛♥s✐çõ❡s ❡❧❡trô♥✐❝❛s ❞♦s ❚❘s✱ ❡♠ ❡s♣❡❝✐❛❧ ❞❛ t❡♦r✐❛ ❞❡ ❏✉❞❞✲❖❢❡❧t✳ ❊♠ s❡❣✉✐❞❛✱ ❛❜♦r❞❛♠♦s ♦s ❝♦♥❝❡✐t♦s ❞❡ ❝❛♠♣♦ ❝r✐st❛❧✐♥♦✳ P♦r ✜♠✱ ❛ t❡♦✲ r✐❛ ❡♥✈♦❧✈✐❞❛ ♥♦ ❝á❧❝✉❧♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ♠❡❝â♥✐❝❛s✱ ♥❛♥♦✐♥❞❡♥t❛çã♦ ✐♥str✉♠❡♥t❛❞❛✱ ❢♦✐ ❞✐s❝✉t✐❞❛✳
✷✳✶ Pr♦♣r✐❡❞❛❞❡s ❡str✉t✉r❛✐s ❞♦s ✈✐❞r♦s à ❝✉rt❛ ❡
♠é❞✐❛ ❞✐stâ♥❝✐❛
❆♥t❡s ❞❡ ❝♦♥s✐❞❡r❛r♠♦s ♦ ❡❢❡✐t♦ ❞❛ ♣r❡ssã♦ ❡ t❡♠♣❡r❛t✉r❛ ♥❛s ♣r♦♣r✐❡❞❛❞❡s ❡s✲ tr✉t✉r❛✐s ❡ ó♣t✐❝❛s ❞♦s ✈✐❞r♦s✱ ✉♠❛ ❞✐s❝✉ssã♦ ♣ré✈✐❛ s♦❜r❡ ❛s ✉♥✐❞❛❞❡s ❡❧❡♠❡♥t❛r❡s ❞❛ r❡❞❡ ❞❡ss❡s s✐st❡♠❛s ❢❡③✲s❡ ♥❡❝❡ssár✐♦✳ ❙❡♥❞♦ ❛ss✐♠✱ ❡ss❛ s❡ssã♦ t❡✈❡ ❝♦♠♦ ♣r♦♣ós✐t♦ ✐♥✐❝✐❛❧ ❞✐s❝✉t✐r ❛ t❡♦r✐❛ ❡✈♦❧✈✐❞❛ ❛❝❡r❝❛ ❞♦s ♠♦❞❡❧♦s ✉t✐❧✐③❛❞♦s t❛♥t♦ ♥❛s ❛♥á❧✐s❡s ❞♦ ❛♠❜✐❡♥t❡ q✉í♠✐❝♦ ❧♦❝❛❧ ❞♦ ✈✐❞r♦ ❞❡ sí❧✐❝❛✱ t❛♥t♦ ❝♦♠♦ s✉❛ ❡①t❡♥sã♦ ❡ ❛♣❧✐❝❛çã♦ ♣❛r❛ ✈✐❞r♦s ♠❛✐s ❝♦♠♣❧❡①♦s✱ ❝♦♠♦ é ♦ ❝❛s♦ ❞♦ ❛❧✉♠✐♥♦ss✐❧✐❝❛t♦ ❞❡ ❝á❧❝✐♦✳
P♦r ❞❡✜♥✐çã♦✱ à ❧♦♥❣❛ ❞✐stâ♥❝✐❛✱ ♥❡♥❤✉♠❛ ♦r❞❡♠ ❡str✉t✉r❛❧ é ♦❜s❡r✈❛❞❛ ♥♦s s✐st❡♠❛s ✈ítr❡♦s✳ ◆♦ ❡♥t❛♥t♦✱ ✉♠❛ ❝❡rt❛ ✏❡str✉t✉r❛✑✱ ♥✉♠❛ ❡s❝❛❧❛ ❞❡ ♣r✐♠❡✐r♦s ✈✐③✐✲ ♥❤♦s✱ ❞❡✈❡ s❡r ❝♦♥s✐❞❡r❛❞❛✳ ◆❡ss❛ ♣❡rs♣❡❝t✐✈❛✱ ❞✉❛s ❡s❝❛❧❛s ❞❡ ♦r❞❡♠ sã♦ ❞❡✜♥✐❞❛s❀ ❛ ❝✉rt❛ ✭✶ ✲ ✺ ➴✮ ❡ ♠é❞✐❛ ✭✺ ✲ ✷✵ ➴✮ ❞✐stâ♥❝✐❛ ❬✸✵✱✸✶❪✳
✷✳ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛✿ ❈♦♥❝❡✐t♦s ❣❡r❛✐s ✶✵
P❛r❛ ✜♥s ❞❡ ❞✐s❝✉ssã♦✱ ❛ ✜❣✉r❛ ✷✳✶ ❛♣r❡s❡♥t❛ ❛ ✉♥✐❞❛❞❡ ❡❧❡♠❡♥t❛r ❞♦s t❡tr❛❡❞r♦s
❞❡ ❙✐❖4 ❡♠ ✉♠ ✈✐❞r♦ ❞❡ sí❧✐❝❛ ♣✉r❛✱ à ❝✉rt❛ ❞✐stâ♥❝✐❛✳
❋✐❣✉r❛ ✷✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✉♥✐❞❛❞❡ ❡❧❡♠❡♥t❛r ❞❛ sí❧✐❝❛ ❬✸✶❪✳
❆ ✉♥✐❞❛❞❡ ❡❧❡♠❡♥t❛r ❞❛ sí❧✐❝❛✱ ❝♦♠♦ ❛♣r❡s❡♥t❛❞❛ ♥❛ ✜❣✉r❛ ✷✳✶✱ é ❞❡✜♥✐❞❛ ♣♦r ✉♠ ❝♦♠♣r✐♠❡♥t♦ ❧Si−O ❡ ✉♠ â♥❣✉❧♦ ❞❡ ❧✐❣❛çã♦ΨO−Si−O✱ ❞❡♥♦♠✐♥❛❞♦ â♥❣✉❧♦ ❞✐❡❞r♦✳ ❆s ❝♦♥❡①õ❡s ❡♥tr❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ss❡s t❡tr❛❡❞r♦s sã♦ ❞❡s❝r✐t♦s ♣❡❧❛ ♦r❞❡♠ à ♠é❞✐♦ ❛❧❝❛♥❝❡✳ ◆❛ sí❧✐❝❛ ♣✉r❛✱ ♣♦r ❡①❡♠♣❧♦✱ t♦❞♦s ♦s t❡tr❛❡❞r♦s sã♦ ❝♦♥❡❝t❛❞♦s ✭❝♦r♥❡r s❤❛r✐♥❣✮ ❡ ❝❛❞❛ ♦①✐❣ê♥✐♦ é ❧✐❣❛❞♦ ❝♦♠ ❞♦✐s t❡tr❛❡❞r♦s ✈✐③✐♥❤♦s✳ ❉❡ss❛ ❢♦r♠❛✱ ♦ át♦♠♦ ❞❡ s✐❧í❝✐♦ é ❞✐t♦ t❡tr❛✲❝♦♦r❞❡♥❛❞♦✱ s❡♥❞♦ ❝❛r❛❝t❡r✐③❛❞♦ ❝♦♠♦ ✉♠ ❢♦r♠❛❞♦r ❞❡ r❡❞❡✳ ❊st❛ ❧✐❣❛çã♦✱ ♣♦r s✉❛ ✈❡③✱ ♣♦❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧♦ â♥❣✉❧♦ ✐♥t❡r✲t❡tr❛é❞r✐❝♦
θ✱ ❝♦♥❢♦r♠❡ ✜❣✉r❛ ✷✳✷✳❛✮✳
✷✳ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛✿ ❈♦♥❝❡✐t♦s ❣❡r❛✐s ✶✶
❆ ♠é❞✐❛ ❞✐stâ♥❝✐❛ ♣♦❞❡ s❡r✱ ❛✐♥❞❛✱ s✉❜❞✐✈✐❞✐❞❛ ❡♠ ❞✉❛s r❡❣✐õ❡s✿
✭✐✮ ▼é❞✐❛ ✐♥t❡r♠❡❞✐ár✐❛ ✭✺ ✲ ✽ ➴✮✿ ❖r❞❡♠ ❛ss♦❝✐❛❞❛ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❛♥é✐s ❞❛ r❡❞❡ ✭♠❡♠❜❡r❡❞ r✐♥❣s✮✳ ❊ss❡s ❛♥é✐s✱ ♦✉ ❝✐❝❧♦s✱ sã♦ ❢♦r♠❛❞♦s ♣❡❧❛ ❝♦♠❜✐♥❛çã♦ ❞♦s t❡tr❛❡❞r♦s q✉❡ ♣❛rt✐❝✐♣❛♠ ❞❛ r❡❞❡✳ ◆♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞♦ ✈✐❞r♦ ❞❡ sí❧✐❝❛ ♣✉r❛✱ s✐♠✉❧❛çõ❡s ♥✉♠ér✐❝❛s ♠♦str❛♠ q✉❡ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ t❡tr❛❡❞r♦s ♥♦s ❛♥é✐s ❛♣r❡s❡♥t❛ ✉♠❛ ❣r❛♥❞❡ ❞✐str✐❜✉✐çã♦✿ ❡♥tr❡ ✸ ❡ ✶✵ ❞❡ t❡tr❛❡❞r♦s✱ ❝♦♠ ♠❛✐♦r ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✻ ❛♥é✐s ✭✻✲♠❡♠❜❡r❡❞ r✐♥❣s✮✶✳
✭✐✐✮ ▼é❞✐❛ ❧♦♥❣í♥q✉❛ ✭✽ ❡ ✷✵ ➴✮✿ ➱ ❞❡s❝r✐t❛ ♣♦r ✈ár✐♦s ♠♦❞❡❧♦s✱ s❡♥❞♦ ♦ ❞❡ ❩❛❝❤❛r✐❛s❡♥ ♦ ♠❛✐s ❛❝❡✐t♦✳ ❆ ✜❣✉r❛ ✷✳✷✳❜✮ é ✉♠❛ ❛❞❛♣t❛çã♦ ❞❡ss❡ ♠♦❞❡❧♦✱ ♦ q✉❛❧ é ❜❛s❡❛❞♦ ♥❛ ✐❞❡✐❛ ❞❡ ✉♠❛ r❡❞❡ ❛❧❡❛tór✐❛ ❡ ❝♦♥tí♥✉❛ ❞❡ ✉♥✐❞❛❞❡s ❡❧❡♠❡♥t❛r❡s✳ ❖ ♠♦❞❡❧♦ ❝♦♥s✐st❡ ❞❡ t❡tr❛❡❞r♦s ❞❡ ❙✐❖4✱ ♥♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞❛ sí❧✐❝❛ ♣✉r❛✳
❆ ❞✐str✐❜✉✐çã♦ ♠é❞✐❛ ❞♦ â♥❣✉❧♦ ✐♥t❡r✲t❡tr❛é❞r✐❝♦θ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ❡♠ t❡r♠♦s
❞♦ ♠♦❞❡❧♦ ❞❡ ❢♦rç❛ ❝❡♥tr❛❧✱ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❙❡♥ ❡ ❚❤♦r♣❡ ✭❙❚✮ ❬✸✷❪✳ ◆♦ ❛rt✐❣♦ ♦r✐❣✐♥❛❧✱ ♦s ❛✉t♦r❡s ✐♥✈❡st✐❣❛r❛♠ ❛ ❞❡♥s✐❞❛❞❡ ✈✐❜r❛❝✐♦♥❛❧ ❞❡ ❡st❛❞♦s ♥❛s r❡❞❡s ✈ítr❡❛s
❞♦ t✐♣♦ ❆❳2✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠♦❞❡❧♦✱ ♦ ♠♦❞♦ ✈✐❜r❛❝✐♦♥❛❧ ❞❡✈✐❞♦ ❛ ✉♠❛ ❧✐❣❛çã♦
❆✲❳✲❆ ♣♦❞❡ s❡r r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ♦ â♥❣✉❧♦θ✭✈❡r ✜❣✉r❛ ✷✳✸✮✳ ❊♠ s✉❛ ❢♦r♠✉❧❛çã♦ ♠❛✐s
s✐♠♣❧❡s✱ ❝❛s♦ ❞♦ ✈✐❞r♦ ❞❡ sí❧✐❝❛ ♣✉r❛✱ ♦ ♠♦❞❡❧♦ r❡❧❛❝✐♦♥❛ ❛ ❜❛♥❞❛ ♣r✐♥❝✐♣❛❧ ✭▼❇✮✷
❞♦ ❡s♣❡❝tr♦ ❘❛♠❛♥ ❞♦ ✈✐❞r♦ ✭❧✐❣❛çã♦ ❙✐✲❖✲❙✐✮ ❝♦♠ ♦ â♥❣✉❧♦ θ ♣♦r ♠❡✐♦ ❞❛ s❡❣✉✐♥t❡
❡①♣r❡ssã♦ ❬✶✻✱✶✼❪✿
ω2
BP =
αSi−O
mO
(1 +cosθSi−O−Si), ✭✷✳✶✮
❡♠ q✉❡ ωM B é ❛ ❢r❡q✉ê♥❝✐❛ ❞❛ ▼❇ ✭❡♠ s−1✮✱ α é ❛ ❝♦♥st❛♥t❡ ❞❡ ❢♦rç❛ ❞❛ ❧✐❣❛çã♦
✭◆✴♠✮✱ mO é ❛ ♠❛ss❛ ❞♦ át♦♠♦ ❞❡ ♦①✐❣ê♥✐♦ ❡ θ ♦ â♥❣✉❧♦ ✐♥t❡r✲t❡tr❛é❞r✐❝♦✳
P❛r❛ ♦ ✈✐❞r♦ ❞❡ sí❧✐❝❛ ♣✉r❛✱ θ t❡♠ ✉♠❛ ❛♠♣❧❛ ❞✐str✐❜✉✐çã♦✱ q✉❡ s❡ ❡st❡♥❞❡ ❞❡
120◦❛
180◦✱ ❝♦♠ ✉♠ ✈❛❧♦r ♠é❞✐♦ ♠❛✐s ♣r♦✈á✈❡❧ ❞❡
144◦✳ ❊ss❡ â♥❣✉❧♦ ♣♦❞❡ ✈❛r✐❛r ❝♦♠ ❛ ✐♥s❡rçã♦ ❞❡ ♥♦✈♦s ❝♦♠♣♦♥❡♥t❡s ♥❛ ♠❛tr✐③ ♦✉ ❝♦♠ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ❡str❡ss❡s ♠❡❝â♥✐❝♦s ❡✴♦✉ tér♠✐❝♦s✳ ❉❡✈✐♥❡ ❡t ❛❧✳ ❬✸✸❪✱ ♣♦r ❡①❡♠♣❧♦✱ ❞❡t❡r♠✐♥❛r❛♠ q✉❡ ♦ â♥❣✉❧♦ ♠é❞✐♦ ❞❡ ✉♠❛ ♠❛tr✐③ ❞❡ sí❧✐❝❛ ✈ítr❡❛ ✈❛r✐♦✉ ❞❡ ✶✹✸◦
à ✶✸✽◦
q✉❛♥❞♦ ❡ss❛ ❢♦✐ ❞❡♥s✐✜❝❛❞❛ ❛ ✉♠❛
t❡♠♣❡r❛t✉r❛ ❞❡ ✻✵✵ ◦
❈ ❡ ♣r❡ssã♦ ❞❡ ✺ ●P❛✳
✶❆ ❞✐str✐❜✉✐çã♦ ❞❡ ❛♥é✐s q✉❡ ❢♦r♠❛♠ ❛ ❡str✉t✉r❛ ♥ã♦ ♣♦❞❡ s❡r ❛❝❡ss❛❞❛s ✈✐❛ ❡①♣❡r✐♠❡♥t♦s✱ ♠❛s s✐♠ ♣♦r ♠❡✐♦ ❞❡ s✐♠✉❧❛çõ❡s✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ❡s♣❡❝tr♦s❝♦♣✐❛ ❘❛♠❛♥ ❢♦r♥❡❝❡ ✐♥❢♦r♠❛çõ❡s ✐♠♣♦rt❛♥t❡s s♦❜r❡ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝✐❝❧♦s ❝♦♠ ✸ ❡ ✹ t❡tr❛❡❞r♦s ✭✸✲ ❛♥❞ ✹✲♠❡♠❜❡r❡❞ r✐♥❣s✮✱ r❡❧❛❝✐♦♥❛❞❛s ❛ ❜❛♥❞❛s ❞❡ ❞❡❢❡✐t♦s ✭❉1✱ ❉2 ✲ ❞❡❢❡❝s ❧✐♥❡s✮ ❛t✐✈♦s ♥♦ ❡s♣❡❝tr♦s ❘❛♠❛♥
✷✳ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛✿ ❈♦♥❝❡✐t♦s ❣❡r❛✐s ✶✷
❋✐❣✉r❛ ✷✳✸✿ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❛ ♦r❞❡♠ ❧♦❝❛❧ ❛ss✉♠✐❞❛ ♣❛r❛ ✉♠ ✈✐❞r♦
t❡tr❛é❞r✐❝♦ ❞♦ t✐♣♦ AX2✳ ❆❞❛♣t❛❞♦ ❞❡ ❬✸✷❪✳
❆ ❡q✉❛çã♦ ✷✳✶ é✱ ♥❛ ✈❡r❞❛❞❡✱ ✉♠❛ ❛❞❛♣t❛çã♦ r❡❞✉③✐❞❛ ❞❡r✐✈❛❞❛ ❞♦ ♠♦❞❡❧♦ ♦r✐❣✐♥❛❧✳ ❉❡ ❢♦r♠❛ ♠❛✐s ♣r❡❝✐s❛✱ ❛ ❢♦rç❛ ❞❡ ❧✐❣❛çã♦ ❝❡♥tr❛❧ ♣♦❞❡ ✈❛r✐❛r✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ q✉❛♥❞♦ ♦✉tr♦s ❝♦♠♣♦♥❡♥t❡s q✉í♠✐❝♦s sã♦ ❛❞✐❝✐♦♥❛❞♦s ❛♦ ✈✐❞r♦ ❞❡ sí❧✐❝❛ ♣✉r❛✳
P❛r❛ ✉♠❛ ❞❡s❝r✐çã♦ ❝♦♠♣❧❡t❛ ❞♦ ♠♦❞❡❧♦ ♦r✐❣✐♥❛❧ ❞❡ ❢♦rç❛ ❝❡♥tr❛❧✱ r❡❝♦♥s✐❞❡r❡✲
♠♦s ❛ ✜❣✉r❛ ✷✳✸✳ ❖s t❡tr❛❡❞r♦s ❆❳4 sã♦ ❢♦r♠❛❞♦s ♣❡❧♦s át♦♠♦s ❆ ❡ ❳ ❝♦♠ ♠❛ss❛s
✐❣✉❛✐s ❛ ▼ ❡ ♠✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖s ❞❡s❧♦❝❛♠❡♥t♦s ❞♦s át♦♠♦s ✐♥❞✐✈✐❞✉❛✐s sã♦ ❞❡✜✲ ♥✐❞♦s ❝♦♠♦ ✉i✱ ❛ ❞✐stâ♥❝✐❛ ❡❧❡s ❝♦♠♦ rij ❡ ❢❛③❡♥❞♦ α ❛ ❢♦rç❛ ❝❡♥tr❛❧ ❡♥tr❡ ♦s át♦♠♦s
❆ ❡ ❳✱ ♣♦❞❡♠♦s ❡s❝r❡✈❡r ❛ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞♦ s✐st❡♠❛ ❝♦♠♦ ❬✸✷❪✿
V = α
2
X
i,j
[(ui−uj)rij]2 ✭✷✳✷✮
P❛r❛ ❞❡t❡r♠✐♥❛r ❛ ❡q✉❛çã♦ ❞❡ ♠♦✈✐♠❡♥t♦ ❞❡✈✐❞♦ ❛ ❢♦rç❛ r❡st❛✉r❛❞♦r❛ ♣r❡s❡♥t❡ ♥♦ s✐st❡♠❛✱ ❝♦♥s✐❞❡r❛♠♦s ❛♣❡♥❛s ✉♠❛ ❧✐❣❛çã♦ ♣❛rt✐❝✉❧❛r✳ ❉❡ ❢❛t♦✱ s❡ ❝♦♥s✐❞❡r❛r♠♦s ♦ ❡✐①♦ r❡❢❡r❡♥❝✐❛❧ ❇❙✱ ❛ ❝♦♠♣♦♥❡♥t❡ ♣❡r♣❡♥❞✐❝✉❧❛r ♥ã♦ t❡rá ❛ ❡❧❛ ✉♠❛ ❢♦rç❛ ❛ss♦❝✐❛❞❛✳ ❆s ❡q✉❛çõ❡s ❞❡ ♠♦✈✐♠❡♥t♦ sã♦✱ ♣♦rt❛♥t♦✱ ❡s❝r✐t❛s ❝♦♠♦✿
(M ω2−α)u
1 =−((αsen(θ/2) ˆS+ (αcos(θ/2)) ˆB) ✭✷✳✸✮
✷✳ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛✿ ❈♦♥❝❡✐t♦s ❣❡r❛✐s ✶✸
(mω2−2αcos2(θ/2) ˆB =−(αcos(θ/2)u1+ (αcos(θ/2)u2 ✭✷✳✺✮
❘❡s♦❧✈❡♥❞♦ ♦s s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s ♣❛r❛ ❙ ❡ ❇✱ t❡♠♦s✿
M ω2−α−αsen(θ/2)
mω2−2αsen2(θ/2) −
(αcos(θ/2))2
mω2−2αcos2(θ/2)
u1 =
(αcos(θ/2))2
2αcos2(θ/2) −
(αsen(θ/2))2
mω2−2αsen2(θ/2)
u2 ✭✷✳✻✮
❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ✜❣✉r❛ ✷✳✸✱ ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ❞✐♥â♠✐❝❛ ❞❛s ❧✐❣❛çõ❡s ❆✲❳✲❆✱ ♣♦❞❡♠♦s ❝♦♥❡❝t❛r ♦s ✈❡t♦r❡s ✉i❞❡✜♥✐♥❞♦ ❛s ❝♦♥st❛♥t❡s ❞❡ ❢♦rç❛ ❡❢❡t✐✈❛ ✭α′✮ ❡ ❞✐❛❣♦♥❛❧
✭αd✮❀
α′
= −ω
2α2cos(θ)
(mω2−α)2−α2cos2(θ) ✭✷✳✼✮
αd =α+ −
α2(mω2−αsen2(θ))
(mω2−α)2−α2cos2(θ) ✭✷✳✽✮
❙❡♥ ❡ ❚❤♦r♣❡ ❬✸✷❪✱ ❝♦♠ ❜❛s❡ ♥♦ tr❛❜❛❧❤♦ ❞❡ ❲❡❛✐r❡ ❡ ❆❧❜❡♥ ❬✸✹❪✱ ❝♦♥❝❧✉ír❛♠ q✉❡ ♦s ♠♦❞♦s ✈✐❜r❛❝✐♦♥❛✐s ❞♦ át♦♠♦ ❞❡ s✐❧í❝✐♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛♣❡♥❛s ❛s ❢♦rç❛s ❝❡♥tr❛✐s ❞❡ ♣r✐♠❡✐r♦s ✈✐③✐♥❤♦s✱ é ❞❛❞❛ ♣♦r
M ω2 = 4
3(αd−α
′
ǫ) ✭✷✳✾✮
♥♦ q✉❛❧ ♦ ❛✉t♦✈❛❧♦r ǫ ✈❛r✐❛ ❞❡ ✲✶ à ✶✳
❙✉❜st✐t✉✐♥❞♦ ❛s ❢♦rç❛s ❝❡♥tr❛✐s ❡❢❡t✐✈❛ ❡ ❞✐❛❣♦♥❛❧ ✭❡q✉❛çõ❡s ✷✳✼ ❡ ✷✳✽✮✱ ❛❞✐❝✐♦✲ ♥❛❞❛s ❛ ♠❛tr✐③ ❞♦ s✐st❡♠❛✱ ❞❡✜♥❡✲s❡ ❛s ❛✉t♦✲❢r❡q✉ê♥❝✐❛s ❝♦♠♦✿
ω2 =
2α
3M +
α M ± s 2α 3M 2 +
αcos(θ) m
2
+4α
2ǫcos(θ)
3M m ✭✷✳✶✵✮
❯s❛♥❞♦ ♦s ❧✐♠✐t❡s ❞♦s ❛✉t♦✈❛❧♦r❡s ✭✲✶≤ ǫ ≤✶✮✱ ❞❡✜♥✐♠♦s q✉❛tr♦ ❧✐♠✐t❡s ❞❡
❛✉t♦✲❢r❡q✉ê♥❝✐❛s✿
ω12 = α
✷✳ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛✿ ❈♦♥❝❡✐t♦s ❣❡r❛✐s ✶✹
ω22 =
α
m(1−cosθ) ✭✷✳✶✷✮
ω32 = α
m(1 + cosθ) + 4α
3M ✭✷✳✶✸✮
ω24 = α
m(1−cosθ) + 4α
3M ✭✷✳✶✹✮
❆s ❡q✉❛çõ❡s ✷✳✶✶✲✷✳✶✹ ♥♦s ❢♦r♥❡❝❡♠ ❛ r❡❧❛çã♦ ❞❡α ❡ θ ❝♦♠ ❛s ❢r❡q✉ê♥❝✐❛s ❞♦s
♠♦❞♦s ❞❡ ✈✐❜r❛çã♦✱ ❡♠ q✉❡ ωi ✭✐❂✶✱ ✷✱ ✸✱ ✹✮ sã♦ ♦s ✈❛❧♦r❡s ❡①♣❡r✐♠❡♥t❛✐s ♦❜t✐❞❛s ♥❛s
r❡❣✐õ❡s ❞❡ ❜❛✐①❛✱ ✐♥t❡r♠❡❞✐ár✐❛ ❡ ❛❧t❛ ❢r❡q✉ê♥❝✐❛ ❞♦s ❡s♣❡❝tr♦s ❘❛♠❛♥✳
❆ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ❙❚ ❝♦♥s✐st❡ ❡♠ ❛♣❧✐❝❛r ♦s ✈❛❧♦r❡s ❡①♣❡r✐♠❡♥t❛✐s ❞❡ω3 ❡ω4♥❛s ❡q✉❛çõ❡s ✷✳✶✸ ❡ ✷✳✶✹ ♣❛r❛ ❞❡t❡r♠✐♥❛r✱ ♣r✐♠❡✐r❛♠❡♥t❡✱α❡θ✳ ❉❡♣♦✐s✱ ♦s
✈❛❧♦r❡s t❡ór✐❝♦s ❞❡ω1 ❡ω2 ♣♦❞❡♠ s❡r ❝❛❧❝✉❧❛❞♦s ❡ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s ❡①♣❡r✐♠❡♥t❛✐s✱
♦❜t✐❞♦s ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ❞❡❝♦♥✈♦❧✉çã♦ ●❛✉ss✐❛♥❛ ♥❛ r❡❣✐ã♦ ❞❡ ❜❛✐①❛ ❢r❡q✉ê♥❝✐❛ ❞♦ ❡s♣❡❝tr♦ ❘❛♠❛♥✳
❖ ♠♦❞❡❧♦ ❞❡ ❢♦rç❛ ❝❡♥tr❛❧ ❞❡ ❙❡♥ ❡ ❚❤♦r♣❡ ❢♦✐ ❡st❡♥❞✐❞♦ à ♦✉tr❛s ❝♦♦r❞❡♥❛✲ çõ❡s ❞❡ ❝át✐♦♥s ❡ â♥✐♦♥s ❬✸✺✱ ✸✻❪✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ✈✐❞r♦s ❞♦ t✐♣♦ ❛❧✉♠✐♥♦ss✐❧✐❝❛t♦s ✭❙✐❖2✲◆❛❆❧❖2✱ ❙✐❖2✲❈❛❆❧2❖✱ ❙✐❖2✲▼❣❆❧2❖✮ ❢♦r❛♠ ❡st✉❞❛❞♦s ♣♦r ❙❡✐❢❡rt ❡t ❛❧✳ ❬✸✼❪
❡ ▼❝▼✐❧❧❛♥ ❡t ❛❧✳ ❬✸✽❪✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ♦s ❛✉t♦r❡s✱ ♦ ♠♦❞❡❧♦ ♣♦❞❡ s❡r ❡st❡♥❞✐❞♦ ♣❛r❛ s✐st❡♠❛s ❞❡ s✐❧✐❝❛t♦s s✐♠♣❧❡s ❝♦♠ ❛♠❜❛s ❧✐❣❛çõ❡s ❙✐✲❖✲❙✐ ❡ ▼✲❖✲▼✱ ♥♦ q✉❛❧ ▼ é ✉♠ ❝át✐♦♥✱ ♣♦r ❡①❡♠♣❧♦✱ ❆❧ ♦✉ ◆❛✳ ❊ss❡s r❡s✉❧t❛❞♦s ♥♦s ♠♦t✐✈❛r❛♠ ❛ ❛♣❧✐❝❛r ♦ ♠♦✲ ❞❡❧♦ ❞❡ ❙❚ ♣❛r❛ ❛s ♠❛tr✐③❡s ❛❧✉♠✐♥♦ss✐❧✐❝❛t♦s ❞❡ ❝á❧❝✐♦✱ ❞❛ q✉❛❧ ❛ ❡str✉t✉r❛ é ♣♦✉❝♦ ❝♦♥❤❡❝✐❞❛✳
✷✳✶✳✶ ❱✐❞r♦ ❆❧✉♠✐♥♦s✐❧✐❝❛t♦ ❞❡ ❈á❧❝✐♦
P❛r❛ ♠♦❞✐✜❝❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ❡ ♠❡❝â♥✐❝❛s ❞♦s ✈✐❞r♦s✱ ♣♦r ❡①❡♠♣❧♦ ❞✐✲ ♠✐♥✉✐r ❛ t❡♠♣❡r❛t✉r❛ ❞❡ ❢✉sã♦ ♦✉ ♠❡❧❤♦r❛r ❛ q✉❛❧✐❞❛❞❡ ót✐❝❛✱ é ❝♦♠✉♠ ❛❞✐❝✐♦♥❛r ❛ r❡❞❡ ❞❛ sí❧✐❝❛ ♣✉r❛ r❡❛❣❡♥t❡s ❛❞✐t✐✈♦s ✭ó①✐❞♦s ♠♦❞✐✜❝❛❞♦r❡s ❡✴♦✉ ✐♥t❡r♠❡❞✐ár✐♦s✮✳ ◗✉❛♥❞♦ ❛❞✐❝✐♦♥❛❞♦s ❛ sí❧✐❝❛ ♣✉r❛✱ ❡ss❡s ó①✐❞♦s ♣❛rt✐❝✐♣❛♠ ❞❛ ❢♦r♠❛çã♦ ❞❛ r❡❞❡ ❡
♣r♦✈♦❝❛♠ ❛ r✉♣t✉r❛ ❞❛s ❧✐❣❛çõ❡s ❙✐✲❖✲❙✐✱ ❢♦r♠❛♥❞♦ ♣❛r❡s ❙✐✲❖−✳ ❆s ❝❛r❣❛s ♥❡❣❛✲
✷✳ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛✿ ❈♦♥❝❡✐t♦s ❣❡r❛✐s ✶✺
❞❡♥♦♠✐♥❛❞♦s ❞❡ ♦①✐❣ê♥✐♦s ♥ã♦ ❧✐❣❛❞♦s ✭◆❇❖✮✸✳ ❖s ◆❇❖s ♣♦❞❡♠ s❡r r❡♣r❡s❡♥t❛❞♦s
♣♦r ❡s♣é❝✐❡s ◗n✱ ❡♠ q✉❡ ♥ é ♦ ♥ú♠❡r♦ ❞❡ ♦①✐❣ê♥✐♦s ❧✐❣❛❞♦s r❡❢❡r❡♥t❡ ❛♦ t❡tr❛❡❞r♦
❚❖4 ❡♠ ❝♦♥s✐❞❡r❛çã♦ ✭✈❡r ✜❣✉r❛ ✷✳✹✮✳
❋✐❣✉r❛ ✷✳✹✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛s ❞✐❢❡r❡♥t❡s ❡s♣é❝✐❡s ◗n✭✵❁♥❁✹✮✱
r❡❧❛❝✐♦♥❛❞❛s ❛♦ ♥ú♠❡r♦ ❞❡ ◆❇❖s✳
❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ◗ns✱ ❞✐③❡♠♦s q✉❡ ❛ r❡❞❡ ✈ítr❡❛ é ♠❛✐s ♣♦❧✐♠❡✲
r✐③❛❞❛ q✉❛♥t♦ ♠❛✐♦r ❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ◗4✱ ♦✉ s❡❥❛✱ q✉❛♥t♦ ♠❡♥♦r ❛ q✉❛♥t✐❞❛❞❡ ❞❡
◆❇❖s✳
◆♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞♦ ✈✐❞r♦ ❈❆❙✱ ❛♠❜❛s ❛ sí❧✐❝❛ ❡ ❛ ❛❧✉♠✐♥❛ ❢♦r♠❛♠ ✉♠❛
r❡❞❡ t❡tr❛é❞r✐❝❛ ✭❚❖4✱ ❝♦♠ ❚ ❂ ❙✐✱ ❆❧✮ ❡ ♦s át♦♠♦s ❞❡ ❝á❧❝✐♦ sã♦ ❞✐str✐❜✉í❞♦s ❞❡
❢♦r♠❛ ❛❧❡❛tór✐❛✱ ❝♦♠♦ r❡♣r❡s❡♥t❛❞♦ ♥❛ ✜❣✉r❛ ✷✳✺✳ ❊st❡ ú❧t✐♠♦✱ ♣♦r s✉❛ ✈❡③✱ t❡♠ ❝♦♠♦ ♣r✐♠❡✐r❛ ❢✉♥çã♦ ❛ ❝♦♠♣❡♥s❛çã♦ ❞❡ ❝❛r❣❛ ♥❡❣❛t✐✈❛✳ P♦ré♠✱ ❡♠ ❛❧❣✉♥s ❝❛s♦s ❡❧❡ ♣♦❞❡ ❛t✉❛r ❝♦♠ ✉♠ ♠♦❞✐✜❝❛❞♦r❡s ❞❡ r❡❞❡✱ ❡ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ♣r♦✈♦❝❛r ❛ ❝r✐❛çã♦ ❞❡ ◆❇❖s✳ ▼❛✐s ♣r❡❝✐s❛♠❡♥t❡✱ s❡ ♦ ♥ú♠❡r♦ ❞❡ át♦♠♦s ❝á❧❝✐♦ ♣r❡s❡♥t❡ ♥❛ ❡str✉t✉r❛
❝♦♠♣❡♥s❛ t♦t❛❧♠❡♥t❡ ❛s ❝❛r❣❛s ❞❡✈✐❞♦ à ❆❧❖−
4✱ ♦s í♦♥s ❈❛+2 ❛t✉❛r❛♠ ❛♣❡♥❛s ❝♦♠♦
❝♦♠♣❡♥s❛❞♦r❡s ❞❡ ❝❛r❣❛✳ ◆❡ss❡ ❝❛s♦✱ ♥ã♦ ❤❛✈❡rá ♦①✐❣ê♥✐♦ ♥ã♦ ❧✐❣❛❞♦s✳ ❚♦❞❛✈✐❛✱ s❡
❤♦✉✈❡r ✉♠ ❡①❝❡ss♦ ❞❡ ❈❛+2 ✭❝❛s♦ ❞❛s ♠❛tr✐③❡s ✉t✐❧✐③❛❞❛s ♥❡ss❡ tr❛❜❛❧❤♦✮✱ ❡ss❡s t❡rã♦
❛ ❢✉♥çã♦ ❞❡ ♠♦❞✐✜❝❛r ❛ r❡❞❡✱ ❝r✐❛♥❞♦ ◆❇❖s✳ ❊ss❛s ❛✜r♠❛çõ❡s sã♦ ❢❡✐t❛s ❝♦♠ ❜❛s❡ ❡♠ ❛r❣✉♠❡♥t♦s ♣✉r❛♠❡♥t❡ ❡st❡q✉✐♦♠étr✐❝♦s✱ ♥♦ ❡♥t❛♥t♦ ❛❧❣✉♥s ❛✉t♦r❡s tê♠ r❡♣♦rt❛❞♦
❛ ♣r❡s❡♥ç❛ ❞❡ ◆❇❖s✱ ❡♠ ✈✐❞r♦s ❝♦♠ ❈❛+2 ❛t✉❛♥❞♦ ❛♣❡♥❛s ❝♦♠♦ ❝♦♠♣❡♥s❛❞♦r✱ ♦✉
s❡❥❛✱ s✉❜st✐t✉✐çã♦ ♣❡r❢❡✐t❛ ❞❡ ❆❧❖−
4 ♣♦r ❈❛+2 ❬✸✾❪✳
