Eletrodeposição de nanoestruturas de cobalto em alumina anódica porosa e sua caracterização magnética

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s

❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❡ ❚❡❝♥♦❧♦❣✐❛

❉❡♣❛rt❛♠❡♥t♦ ❞❡ ◗✉í♠✐❝❛

Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ◗✉í♠✐❝❛

❊❧❡tr♦❞❡♣♦s✐çã♦ ❞❡ ◆❛♥♦❡str✉t✉r❛s ❞❡ ❈♦❜❛❧t♦

❡♠ ❆❧✉♠✐♥❛ ❆♥ó❞✐❝❛ P♦r♦s❛ ❡ s✉❛

❈❛r❛❝t❡r✐③❛çã♦ ▼❛❣♥ét✐❝❛

❈r✐st✐❛♥❡ P♦♥t❡s ❞❡ ❖❧✐✈❡✐r❛

❚❡s❡ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❈✐ê♥❝✐❛s✱ ár❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝♦✲◗✉í♠✐❝❛✳

❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❊r♥❡st♦ ❈❤❛✈❡s P❡r❡✐r❛ ❈♦✲♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❆❞✐❧s♦♥ ❏✳ ❆✳ ❞❡ ❖❧✐✈❡✐r❛

✯_{❇♦❧s✐st❛✿ ❋❛♣❡s♣ Pr♦❝❡ss♦✿ ✷✵✵✻✴✺✵✺✽✶✲✻}

❙ã♦ ❈❛r❧♦s ✲ ❙P

Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária/UFSCar

O48en

Oliveira, Cristiane Pontes de.

Eletrodeposição de nanoestruturas de cobalto em alumina anódica porosa e sua caracterização magnética / Cristiane Pontes de Oliveira. -- São Carlos : UFSCar, 2009.

239 p.

Tese (Doutorado) -- Universidade Federal de São Carlos, 2009.

1. Eletroquímica. 2. Anodização. 3. Eletrodeposição. 4. Simulação computacional. 5. Magnetismo. 6. Nanofios. I. Título.

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✳✳✳❋♦r ♥♦t❤✐♥❣ ❝♦✉❧❞ ❜❡ ❜❡tt❡r t❤❛♥ ❧✐✈✐♥❣ ❛ ♠♦❞❡st✱ s✐♠♣❧❡✱ ❛♥❞ ❢r❡❡ ❧✐❢❡ ✐♥ ❛♥ ❡❣❛❧✐t❛r✐❛♥ s♦❝✐❡t②✳ ■t t♦♦❦ s♦♠❡ t✐♠❡ ❜❡❢♦r❡ ■ r❡❝♦❣♥✐③❡❞ t❤✐s ❛s ♥♦ ♠♦r❡ t❤❛♥ ❛ ❜❡❛✉t✐❢✉❧ ❞r❡❛♠❀ t❤❛t ❢r❡❡❞♦♠ ✐s ♠♦r❡ ✐♠♣♦rt❛♥t t❤❛♥ ❡q✉❛❧✐t②❀ t❤❛t t❤❡ ❛tt❡♠♣t② t♦ r❡❛❧✐③❡ ❡q✉❛❧✐t② ❡♥❞❛♥❣❡rs ❢r❡❡❞♦♠❀ ❛♥❞ t❤❛t✱ ✐❢ ❢r❡❡❞♦♠ ✐s ❧♦st✱ t❤❡r❡ ✇✐❧❧ ♥♦t ❡✈❡♥ ❜❡ ❡q✉❛❧✐t② ❛♠♦♥❣ t❤❡ ✉♥❢r❡❡✳

❑❛r❧ P♦♣♣❡r ❡♠ ❯♥❡♥❞❡❞ ◗✉❡st✱ ✶✾✼✺

✳✳✳✳ ➱ ✐♠♣r❡s❝✐♥❞í✈❡❧ r❡❛❧✐③❛r ✉♠ ❡①♣❡r✐♠❡♥t♦ ❝♦♠ ✐♥t❡❣r✐❞❛❞❡ ❝✐❡♥tí✜❝❛✳✳✳✳ ❊♥tã♦✱ só ♣♦ss♦ ❞❡s❡❥❛r ✉♠❛ ❝♦✐s❛ ♣❛r❛ ✈♦❝ês ✲ ❛ ❜♦❛ s♦rt❡ ❞❡ ❡st❛r❡♠ ❡♠ ✉♠ ❧✉❣❛r ♦♥❞❡ s❡❥❛♠ ❧✐✈r❡s ♣❛r❛ ♠❛♥t❡r ♦ t✐♣♦ ❞❡ ✐♥t❡❣r✐❞❛❞❡ q✉❡ ❞❡s❝r❡✈✐ ❡ ♦♥❞❡ ♥ã♦ s❡ s✐♥t❛♠ ❢♦rç❛❞♦s ❛ ♣❡r❞❡r s✉❛ ✐♥t❡❣r✐❞❛❞❡ ♣♦r ✉♠❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠❛♥t❡r s✉❛ ♣♦s✐çã♦ ♥❛ ♦r❣❛♥✐③❛çã♦✱ ♦✉ ♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✱ ♦✉ ❝♦✐s❛s ❛ss✐♠✳ ◗✉❡ ✈♦❝ês ♣♦ss❛♠ t❡r ❡ss❛ ❧✐❜❡r❞❛❞❡✳

❆♦s ♠❡✉s ♣❛✐s✱

❏♦ã♦ ❡ ❖❧✐♥❞❛✳

P❘❊❋➪❈■❖

❊st❛ t❡s❡ é ♦ r❡s✉❧t❛❞♦ ❞❛s ♣❡sq✉✐s❛s s♦❜r❡ ❛ ♣r❡♣❛r❛çã♦ ❞❡ ❡❧❡tr♦❞❡♣ós✐t♦s ❞❡ ❝♦❜❛❧t♦ ❡♠ t❡♠♣❧❛t❡s ❞❡ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛ ❡ s✉❛ ❝❛r❛❝t❡r✐③❛çã♦ ♠❛❣♥ét✐❝❛ q✉❡ ❞❡s❡♥✈♦❧✈✐ ♥♦ ●r✉♣♦ ❞❡ ❊❧❡tr♦q✉í♠✐❝❛ ❞♦ ▲❛❜♦r❛tór✐♦ ■♥t❡r❞✐s❝✐♣❧✐♥❛r ❞❡ ❊❧❡tr♦q✉í♠✐❝❛ ❡ ❈❡râ♠✐❝❛ ✲ ▲■❊❈ ❡ ♥♦ ●r✉♣♦ ❞❡ ❙✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ ❡ ▼❛❣♥❡t✐s♠♦ ✲ ●❙▼ ✭❉❋✮ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s✳ ❉✉r❛♥t❡ ❡st❡ ♣❡rí♦❞♦✱ r❡❝❡❜✐ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦ ❞❛ ❋✉♥❞❛çã♦ ❞❡ ❆♠♣❛r♦ à P❡sq✉✐s❛ ❞♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦ ✭❋❆P❊❙P✮ ❛tr❛✈és ❞❛s ❜♦❧s❛s ❞❡ ♠❡str❛❞♦ ❡ ❞♦✉t♦r❛❞♦ ❞✐r❡t♦ ❝♦♠ ♦s s❡❣✉✐♥t❡s ♥ú♠❡r♦s ❞❡ ♣r♦❝❡ss♦s ✷✵✵✹✴✶✷✻✵✸✲✷ ❡ ✷✵✵✻✴✺✵✺✽✶✲✻✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳

❚✉❞♦ ❝♦♠❡ç♦✉ ❝♦♠ ❛ ♠✐♥❤❛ ♣r♦❢❡ss♦r❛ ❞❡ ❝✐ê♥❝✐❛✱ ❊❧③❛ ❖r✐t❛✱ q✉❡ ♠❛♥t✐♥❤❛ ❝♦♠ r❡❝✉rs♦s ♣ró♣r✐♦s ✉♠ ✧❧❛❜♦r❛tór✐♦✧✳ ◆❡ss❡ ✧❧❛❜♦r❛tór✐♦✧ ❡♥❝♦♥tr❛✈❛✲s❡ ❞❡ t✉❞♦✱ ❞❡s❞❡ ♠❛q✉❡t❡s tr❛t❛♥❞♦ ❞❡ q✉❡stõ❡s ❛♠❜✐❡♥t❛✐s ❛té ❢❡t♦ ❤✉♠❛♥♦✦ ◆❛ ❣r❛❞✉❛çã♦ ❡♥❝♦♥tr❡✐ ♦ ♣r♦❢✳ ❉r✳ ▼❛✉r♦ ❈❤✐❡r✐❝✐ ▲♦♣❡s ❝♦♠ q✉❡♠ ❡✉ ❛♣r❡♥❞✐ q✉❡✱ ♠❛✐s ✐♠♣♦rt❛♥t❡ q✉❡ ❛❧❝❛♥ç❛r ❡①❝❡❧❡♥t❡s r❡s✉❧t❛❞♦s✱ é ❢✉♥❞❛♠❡♥t❛❧ ❝✉rt✐r ♦ ♣r♦❝❡ss♦ ❞❡ ❢❛③❡r ❝✐ê♥❝✐❛✳ ❙✉❛ ❝✉✐❞❛❞♦s❛ ♦r✐❡♥t❛çã♦ ❞❡ ✐♥✐❝✐❛çã♦ ❝✐❡♥tí✜❝❛ ♠❡ ❛✉①✐❧✐♦✉ ♥❛ ❡s❝♦❧❤❛ q✉❡ r❡s✉❧t♦✉ ♥❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞♦✉t♦r❛❞♦ s♦❜ ❛ ♦r✐❡♥t❛çã♦ ❞♦ ♣r♦❢✳ ❉r✳ ❊r♥❡st♦ ❈❤❛✈❡s P❡r❡✐r❛ ❡ ❝♦✲♦r✐❡♥t❛çã♦ ❞♦ ♣r♦❢✳ ❉r✳ ❆❞✐❧s♦♥ ❞❡ ❖❧✐✈❡✐r❛✳ ◆❛ ♣ós✲❣r❛❞✉❛çã♦✱ ❛tr❛✈és ❞♦s ♣r♦❢✳✬s ❊r♥❡st♦ ❡ ❆❞✐❧s♦♥✱ ❢✉✐ ❛♣r❡s❡♥t❛❞❛ ❛ ♣r♦❢❡ss♦r❡s ✐♥❝rí✈❡✐s✿ ♣r♦❢✳ ❉r✳ ❈❛r❧♦s ❱❡♥t✉r❛ ❉✬❆❧❦❛✐♥❡✱ ♣r♦❢✳ ❉r✳ ❏♦❛q✉✐♠ ◆ó❜r❡❣❛✱ ♣r♦❢✳ ❉r✳✭❛✮■✈❛♥✐ ❈❛r❧♦s ❡ ♣r♦❢✳ ❉r✳✭❛✮▲✉❝✐❛ ▼❛s❝❛r♦✳ ❆ t♦❞♦s✿ ♣r♦❢✳✭❛✮

❊❧③❛✱ ♣r♦❢✳ ▼❛✉r♦✱ ♣r♦❢✳ ❊r♥❡st♦✱ ♣r♦❢✳ ❆❞✐❧s♦♥✱ ♣r♦❢✳ ❉✬❆❧❦❛✐♥❡✱ ♣r♦❢✳ ❏♦❛q✉✐♠✱ ♣r♦❢✳✭❛✮

■✈❛♥✐ ❡ ♣r♦❢✳✭❛✮ ▲✉❝✐❛✱ ▼✉✐t♦ ❖❜r✐❣❛❞❛ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s✦

❆♦ ❧♦♥❣♦ ❞❡ ♠✐♥❤❛ ❢♦r♠❛çã♦ t✐✈❡ ❢♦rt❡ ✐♥✢✉ê♥❝✐❛ ❞❡ ♠✉✐t❛s ♣❡ss♦❛s✱ ❛❧❣✉♠❛s ❝✐❡♥t✐s✲ t❛s✱ ♦✉tr❛s ♥ã♦✳ ❊ sã♦ ❡st❛s ❝♦♥tr✐❜✉✐çõ❡s q✉❡ ❣♦st❛r✐❛ ❞❡ r❡❣✐str❛r ❛q✉✐✳ ❚♦❞❛s ❡ss❛s ❡①♣❡r✐ê♥❝✐❛s s❡r✈✐r❛♠ ♣❛r❛ q✉❡✱ ❞❡ ❝❡rt❛ ❢♦r♠❛✱ ❡✉ ❛t❡♥❞❡ss❡ ❛ ♠✐♥❤❛ ♣r❡♦❝✉♣❛çã♦ ❞❡ q✉❡ ♦ ♠❛✐s ✐♠♣♦rt❛♥t❡ é ❝♦♠♦ s❡r ❡✱ ♥ã♦✱ ♦ q✉❡ s❡r✳ ❊st♦✉ ❡♥❝❡rr❛♥❞♦ ❡st❛ ❡t❛♣❛ ❝♦♠ ❛ ❝❡rt❡③❛ ❞❡ t❡r ❢❡✐t♦ ❛ ❡s❝♦❧❤❛ ❝❡rt❛ ❡✱ ♠✉✐t♦ ❢❡❧✐③✱ ♣♦r t❡r ❡♥❝♦♥tr❛❞♦ ❛s ♣❡ss♦❛s q✉❡ ❡♥❝♦♥tr❡✐✳ P♦r t♦❞♦s ❡ss❡s ❡♥❝♦♥tr♦s✱ ✈❛❧❡ s❡♠♣r❡ ♠✉✐t♦ à ♣❡♥❛✱ t♦♠❛r ✉♠ ♥♦✈♦ ❝❛♠✐♥❤♦✳

❊♥tã♦✱ s✐❣♦ ❝♦♠ ♠❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s✳✳✳

❡ ♣❛❝✐ê♥❝✐❛ ❛♦ ❧♦♥❣♦ ❞❡ss❡s ❛♥♦s✳

❉✐✈✐❞✐ ❡st❡s q✉❛tr♦ ❛♥♦s ❝♦♠ ♠✉✐t♦s ❝♦♠♣❛♥❤❡✐r♦s ❞❡ ♣❡sq✉✐s❛✳ ◗✉❛♥t♦s ♣r♦❜❧❡♠❛s r❡s♦❧✈❡♠♦s ♥♦s ❝♦rr❡❞♦r❡s ❞♦ ❧❛❜♦r❛tór✐♦ ❡ ♥❛ ✧♠❡s❛ r❡❞♦♥❞❛✧✦❄ ▼❡✉s s✐♥❝❡r♦s ❛❣r❛✲ ❞❡❝✐♠❡♥t♦s à t✉r♠❛ ❞♦ ▲■❊❈✿ ♣r♦❢✳ ❉r❛✳ ▲✉❝✐❛ ▼❛s❝❛r♦✱ ❆❞r✐❛♥❡ ❱✳ ❘♦sár✐♦✱ ❏❛♥❛✐♥❛ ❙♦❛r❡s ❙❛♥t♦s✱ P❛♦❧❛ ▼❛rr❡t♦✱ ❋r❛♥❝✐s❝♦ ❙tr✐①✐♥♦✱ ❙❤❡r❧❛♥ ▲❡♠♦s✱ ▼✉r✐❧♦ ●r♦♠❜♦♥✐✱ ❆❧✐♥❡ ❞❡ ❖❧✐✈❡✐r❛✱ ❘♦❜❡rt♦ ❞❡ ▼❛t♦s✱ ❘❡♥❛t♦ ❋r❡✐t❛s✱ ▲❡❛♥❞r♦ P♦❝r✐❢❦❛✱ ❊❧✈✐r❛ ❇❡❧❧♦✱ ❋r❛♥❝✐✲ ❡❧❡ ❋r❡✐t❛s✱ ❋❡r♥❛♥❞♦ ❈r✐st♦✈❛♥✱ ▼❛r✐❛♥❛ ❙✐❦♦r❛✱ ❋❛❜✐♦ ❇❡♥t♦✱ ▲✉❝✐❛♥❛ ❩✐❞♦✐✱ ❉❥❡♥❛✐♥❡ ❙♦✉s❛✱ ▲✉❝✐❛♥❛ ❙❛♥❝❤❡s✱ ❱❛❧ér✐❛ ❋❡r♥❛♥❞❡s✱ ❆❧❡①s❛♥❞r♦ ❩✐♠♠❡r✱ ❊♠❡rs♦♥ ❈♦st❛ ❘✐♦s✱ ❈❧❛✉❞✐❛♥❡ ❞❡ ❆❜r❡✉✱ ▲✉✐s ❋❡r♥❛♥❞♦ ▼❛r❝❤❡s✐✱ ❆❞r✐❛♥♦ ❘❛❜❡❧♦✱ ❩✐❧❡♥❡ ❆❧✈❡s✱ ▼❛r❝♦✱ ❋❧❛✲ ✈✐♦✱ ❊r❧♦♥✱ Pr✐s❝✐❧❛✱ ✳✳✳❊✱ à t✉r♠❛ ❞♦ ●❙▼ ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛✱ q✉❡ ♠❡ r❡❝❡❜✐❛♠ ❝♦♠ ✉♠❛ ❤♦s♣✐t❛❧✐❞❛❞❡ ✐♥❝rí✈❡❧✿ ❋❛❜✐❛♥♦ ❈♦❧❛✉t♦✱ ❏✉❧✐❛♥❛ ❑❛♣♣✱ ❋❡r♥❛♥❞♦ ❞❡ P❛✉❧❛✱ ❈❡✲ s❛r ❉❡✐♠❧✐♥❣✱ ❆♥❞ré ❱❛r❡❧❛✱ ❘❛❢❛❡❧ ❩❛❞♦r♦s♥②✱ ❆♥❛ ❞❡ ❖❧✐✈❡✐r❛✱ P❡❞r♦ ❙❝❤✐♦✱ ♣r♦❢✳ ❉r✳ ❖rt✐③✱ ❆❧❡①❛♥❞r❡ ●✉❛❧❞✐✱ ❈❧❛✉❞✐♦ ✭♦ ❤♦♠❡♠ ❞♦ ❤é❧✐♦✮✱ ▼❛r❝✐❛ ▲♦✉r❡♥ç♦ ✭❛ ♣✐♦♥❡✐r❛✮✳✳✳ ❊ à t✉r♠✐♥❤❛ ❡①tr❛✲❧❛❜✿ ❊♠❡rs♦♥ ❇♦s❝❤❡tt♦✱ ❆♥❞r❡ss❛ ▼♦t❛✱ ❆♥❛ ❈❧❛✉❞✐❛✱ ❍❡❧t♦♥ ❲✐❣❣❡rs✱ ❈❡r✐③❡✱ ▼✐❝❤❡❧❡✱ ❊✈❡❧✐③❡✱ ❙❛❜r✐♥❛✱ P♦❧✐❛♥❛✱ ❘❡❜❡❝❛ ❡ ❛ t✉r♠❛ t♦❞❛ ❞♦ ❧❛❜♦r❛tór✐♦ ❞♦ ♣r♦❢✳ ❉r✳ ❉✬❆❧❦❛✐♥❡✳ ❱♦❝ês s❡♠♣r❡ ❢♦r❛♠ tã♦ ♣r❡st❛t✐✈♦s✱ q✉❡ q✉❛❧q✉❡r ❝♦✐s❛ q✉❡ ❡✉ ❞✐❣❛ s❡rá ♣♦✉❝♦✱ ♠❛s ❛✐♥❞❛ ❛ss✐♠ q✉❡r♦ ❞✐③❡r ▼✉✐tíss✐♠♦ ❖❜r✐❣❛❞❛ ♣❡❧♦ ❛♣♦✐♦✱ ❝♦♠♣r❡❡♥sã♦✱ t♦❧❡râ♥❝✐❛✱ ♣❛❝✐ê♥❝✐❛✳✳✳ q✉❛♥t❛ ♣❛❝✐ê♥❝✐❛✦

❙❡r❡✐ ❡t❡r♥❛♠❡♥t❡ ❣r❛t❛ ❛♦s ♠❡✉s ✐r♠ã♦s✱ ❘♦❞r✐❣♦ ❡ ▲✉❝❛s✱ ♣❡❧❛ ♥♦ss❛ ✉♥✐ã♦✳ ❱♦❝ês s❡♠♣r❡ ❢♦r❛♠ ✉♠ ♣♦rt♦ s❡❣✉r♦ ♣❛r❛ ♠✐♠✳ ❆♦s ♠❡✉s ♣❛✐s✱ ❏♦ã♦ ❡ ❖❧✐♥❞❛✱ s✐♠♣❧❡s♠❡♥t❡ ▼✉✐t♦ ❖❜r✐❣❛❞❛ ♣♦r t✉❞♦ q✉❡ ✜③❡r❛♠ ❡✱ ❛✐♥❞❛✱ ❢❛③❡♠ ♣♦r ♥ós✳ ❊s♣❡r♦✱ ✉♠ ❞✐❛✱ s❡r ❝❛♣❛③ ❞❡ t❛♠❛♥❤❛ ❞♦❛çã♦✦

❯♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ❡s♣❡❝✐❛❧ ❛♦ ❊r✐❝✳ ▼✉✐t♦ ♦❜r✐❣❛❞❛ ♣❡❧♦ s❡✉ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❡ ♣r❡✲ s❡♥ç❛ ❝❛r✐♥❤♦s❛ ❝♦♥st❛♥t❡✳ ❖❜r✐❣❛❞❛ ♣❡❧❛ r❡✈✐sã♦ ❞♦ tr❛❜❛❧❤♦✱ ♣♦r ♦✉✈✐r ❛s ♠✐♥❤❛s ❞✐✈❛✲ ❣❛çõ❡s s♦❜r❡ ❡st❡ ♦✉ ❛q✉❡❧❡ r❡s✉❧t❛❞♦✱ ♣❡❧❛s s✉❣❡stõ❡s s♦❜r❡ ♠ét♦❞♦s ♥✉♠ér✐❝♦s✳✳✳ ❊✱ ❝❧❛r♦✱ ♣♦r s❡✉s ❡✲♠❛✐❧s ❞✐ár✐♦s✱ ❛s ♥♦ss❛s ✈✐❛❣❡♥s✱ ♦s s❡✉s ♣♦❡♠❛s ❡ ♦s ❞❡ P❛❜❧♦ ◆❡r✉❞❛✳✳✳❝♦♠♦ ❛ ♣❧❛♥t❛ q✉❡ ♥ã♦ ✢♦r❡s❝❡ ❡ ❧❡✈❛ ❞❡♥tr♦ ❞❡ s✐✱ ♦❝✉❧t❛✱ ❛ ❧✉③ ❞❛q✉❡❧❛s ✢♦r❡s✳✳✳▼✉✐t♦ ♦❜r✐❣❛❞❛✱ ▼♦♥ P❡t✐t✦

❢❛③❡r❡♠ r✐r✳ ❆❤✦ ❊✉ ♣r❡❝✐s♦ ❞✐③❡r q✉❡ ♥❛❞❛ s❡ ❝♦♠♣❛r❛ ❛♦ ❜♦♠ ❣♦st♦ ♠✉s✐❝❛❧ ❞❛ ❉r✐✱ ❛ ❛❧❡❣r✐❛ ❞❛ ▼❛r✐✱ ❛ ♣r❡t✐♥❤❛ ❞❛ ❏❛♥❛ ♦♥❞❡ ♥ã♦ s❡ ♦✉✈❡ s❛♠❜❛✱ ❛ ❢❡✐❥♦❛❞❛ ❞❛ ❋r❛♥ q✉❡ ❡✉ ♥✉♥❝❛ ❡①♣❡r✐♠❡♥t❡✐✱ ❛ s❛❧❛❞❛ ❞❡ ❜❡r✐♥❣❡❧❛ ❞❛ ❉❥❡♥❛✐♥❡ ❡ ❛ ❜rô❛ ❞❡ ♠✐❧❤♦ ❝♦♠ ❡r✈❛ ❞♦❝❡ ❞❛ P❛♦❧❛✳

▼❡✉s s✐♥❝❡r♦s ❛❣r❛❞❡❝✐♠❡♥t♦s à t✉r♠❛✱ ❛♠✐❣♦s ❡ ❢❛♠✐❧✐❛r❡s✱ q✉❡ ♠❡ ❛❝♦❧❤❡✉ ❡♠ ●✉❛r❛♣✉❛✈❛✲ P❘ tr❛♥s❢♦r♠❛♥❞♦ ❛q✉❡❧❡s ❞✐❛s t❡rrí✈❡✐s ❞❡ ✐♥✈❡r♥♦ ❡♠ ♠♦♠❡♥t♦s ♠✉✐t♦ ❛❣r❛❞á✈❡✐s✳ ❉❡♥✲ tr❡ ❡❧❡s ❣♦st❛r✐❛ ❞❡ ❝✐t❛r ❛ ▲❛♥❞❛ ❡ ♦ ❆❧❡♠ã♦ ✭♠❡✉ ♣❛✐ ❜r❛♥❝♦✮✱ ❡①❡♠♣❧♦s ❞❡ ✈✐❞❛ ♣r❛ ♠✐♠✳ ❊ ❛s ♣❡ss♦❛s ♠❛✐s ❣❡♥♦r♦s❛s q✉❡ ❝♦♥❤❡❝✐✿ ❆❞♥✐❧s♦♥✱ ❙✐❧✈❛♥❛✱ ▼❛t❤❡✉s ❡ ❋❡✲ ❧✐♣❡✳ ▼✉✐t♦ ♦❜r✐❣❛❞❛ ♣❡❧♦s ❝❤♦❝♦❧❛t❡s ❞❡✐①❛❞♦s ♣ró①✐♠♦s à ♠✐♥❤❛ ❝❛♠❛ ♥❛s ✈és♣❡r❛s ❞❡ Pás❝♦❛✱ ♣♦r ❝♦♠♣r❡❡♥❞❡r❡♠ ♠❡✉ s✐❧ê♥❝✐♦✱ ♠✐♥❤❛ ❛✉sê♥❝✐❛✳✳✳✳ ❛s ♠✐♥❤❛s ❧á❣r✐♠❛s✳

▼❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s ❛♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ◗✉í♠✐❝❛ ❡ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ◗✉í♠✐❝❛ ♣♦r t♦❞♦s ♦s s❡r✈✐ç♦s ♣r❡st❛❞♦s✳ ❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ▲■❊❈ ❡ ●❙▼ ♣❡❧❛ ♣r❡st❛t✐✈✐❞❛❞❡✳ ❊✱ ✜♥❛❧♠❡♥t❡✱ ❛♦s ór❣ã♦s✿ ❈◆Pq✱ ❈❛♣❡s ❡ ❋❛♣❡s♣ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✳

▼✉✐t♦ ♦❜r✐❣❛❞❛✱

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✷✳✶ ❈♦♥❞✐çõ❡s ❡①♣❡r✐♠❡♥t❛✐s ❡♠♣r❡❣❛❞❛s ♥❛ ♣r❡♣❛r❛çã♦ ❞❛s ♠❡♠❜r❛♥❛s ❞❡ ❆❆P✳ ❚♦❞♦s ♦s ❡①♣❡r✐♠❡♥t♦s ❛❜❛✐①♦ ❢♦r❛♠ r❡❛❧✐③❛❞♦s ❡♠ ❍3P❖4 ✵✱✶ ♠♦❧

▲−1 _{❡ ✹ ♠❆ ❝♠}−2_{✳ ❆s r♦t✐♥❛sB✱C✱D❡E❝♦♠♣õ❡♠ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❢❛t♦r✐❛❧}

✷2_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸}

✷✳✷ ❋r❛çã♦ ❞❛ ár❡❛ ♦❝✉♣❛❞❛ ♣❡❧❛s r❡❞❡s ♣♦r♦s❛s s✉♣❡r✐♦r ✭As✮ ❡ ✐♥❢❡r✐♦r ✭AO✮✱

❡ ♦ ❣r❛✉ ❞❡ s♦❜r❡♣♦s✐çã♦ ✭S✮✳ ❆s ♠❡♠❜r❛♥❛s ❢♦r❛♠ ♣r❡♣❛r❛❞❛s ❞❡ ❛❝♦r❞♦

❝♦♠ ❛s r♦t✐♥❛s B✱ C✱ D❡ E✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼

✸✳✶ ❉❡✜♥✐çõ❡s ❞❛s ✈❛r✐á✈❡✐s ❞✐♠❡♥s✐♦♥❛✐s ❡ ❛❞✐♠❡♥s✐♦♥❛✐s ♣r❡s❡♥t❡s ♥♦ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✸✳✷ ❊q✉❛çõ❡s ❞✐❢❡r❡♥❝✐❛✐s ❛❞✐♠❡♥s✐♦♥❛✐s ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞❛s tr❛♥s❢♦r♠❛çõ❡s ❞❡

✈❛r✐á✈❡✐s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❚❛❜❡❧❛ ✸✳✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✸✳✸ ❈♦♥st❛♥t❡s ❞❡ t❡♠♣♦ ❝❛r❛❝t❡ríst✐❝❛s ♦❜t✐❞❛s ♥♦ ❛❥✉st❡ ❡①♣♦♥❡♥❝✐❛❧ ❞❛s ❝✉r✲

✈❛s ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✸✳✹ P❧❛♥❡❥❛♠❡♥t♦ ❋❛t♦r✐❛❧25_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸}

✸✳✺ ▼❛tr✐③ ❞♦ P❧❛♥❡❥❛♠❡♥t♦ ❋❛t♦r✐❛❧25_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹}

✸✳✼ ▼❛tr✐③ ❞♦ P❧❛♥❡❥❛♠❡♥t♦ ❋❛t♦r✐❛❧25_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼}

✺✳✶ ❘♦t✐♥❛s ❞❡ Pr❡♣❛r❛çã♦ ❞❛s ❆♠♦str❛sA ❡B✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✻

✺✳✷ ❘♦t✐♥❛s ❞❡ Pr❡♣❛r❛çã♦ ❞❛s ❆♠♦str❛sC ❡D✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✼

✺✳✸ ❘♦t✐♥❛s ❞❡ Pr❡♣❛r❛çã♦ ❞❛s ❆♠♦str❛sF❡ G✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✻

❆✳✶ ❊❢❡✐t♦s ❝❛❧❝✉❧❛❞♦s ♣❛r❛ ✉♠ ♣❧❛♥❡❥❛♠❡♥t♦ 24 _{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸✵}

❆✳✷ ❈♦rr❡s♣♦♥❞ê♥❝✐❛ ❡♥tr❡ ♦s ❡❢❡✐t♦s✱ ❡♠ ♦r❞❡♠ ❝r❡s❝❡♥t❡✱ ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❢❛✲ t♦r✐❛❧24 _{❛♣r❡s❡♥t❛❞♦ ♥❛ ❚❛❜❡❧❛ ❆✳✶ ❡ ♦s ✈❛❧♦r❡s ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛❝✉♠✉❧❛❞❛✳✷✸✷}

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✷✳✶ ❈✉r✈❛ tí♣✐❝❛ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ❡♠ ❢✉♥çã♦ ❞♦ ♣♦t❡♥❝✐❛❧✱ ❛♣r❡s❡♥t❛♥❞♦ ❛s r❡❣✐õ❡s ❛t✐✈❛✱ ♣❛ss✐✈❛ ❡ tr❛♥s♣❛ss✐✈❛ q✉❡ ♣♦❞❡♠ ❡st❛r ♣r❡s❡♥t❡s ❞✉r❛♥t❡ ❛ ♣♦❧❛r✐③❛çã♦ ❞❡ ♠❡t❛✐s ❬✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❈✉r✈❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♣♦t❡♥❝✐❛❧ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ♣❛r❛ ❞✐❢❡r❡♥t❡s

❝♦♥❞✐çõ❡s ❞❡ ❛♥♦❞✐③❛çã♦ ❣❛❧✈❛♥♦stát✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸ ❊sq✉❡♠❛ ❞❡ ✉♠❛ ❝é❧✉❧❛ ❡❧❡tr♦q✉í♠✐❝❛ ❝♦♥✈❡♥❝✐♦♥❛❧ ❝♦♥t❡♥❞♦ três ❡❧❡tr♦❞♦s✱

s❡♥❞♦ ❞♦✐s ❝♦♥tr❛ ❡❧❡tr♦❞♦s ✭❈❊✮ ❡ ✉♠ ❡❧❡tr♦❞♦ ❞❡ tr❛❜❛❧❤♦ ✭❊❚✮✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✹ ▼✐❝r♦❣r❛✜❛s ❞♦s ✜❧♠❡s ❞❡ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛ ♦❜t✐❞♦s ❛ ♣❛rt✐r ❞❛ ❛♥♦✲

❞✐③❛çã♦ ❞❡ s✉❜str❛t♦ ❞❡ ❆❧ ♥ã♦ ❡❧❡tr♦♣♦❧✐❞♦✳ ❆♥♦❞✐③❛çõ❡s ❢♦r❛♠ r❡❛❧✐③❛❞❛s ❡♠ ❍3P❖4 ✵✱✶ ♠♦❧ ▲−1 ❛ ✹ ♠❆ ❝♠−2 ✭❛✮ 100❈ ❡ ✭❜✮ 250❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷

✷✳✺ ❋❧✉①♦❣r❛♠❛ ❡sq✉❡♠❛t✐③❛♥❞♦ ❛s ❡t❛♣❛s ❡♥✈♦❧✈✐❞❛s ♥❛ ♣r❡♣❛r❛çã♦ ❞❡ ♠❡♠✲ ❜r❛♥❛s ❞❡ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛ ❡♠ ❞✉❛s ❡t❛♣❛s ❞❡ ❛♥♦❞✐③❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✻ ❊t❛♣❛s ❡♥✈♦❧✈✐❞❛s ♥♦ ♣r♦❝❡ss♦ ❞❡ q✉❛♥t✐✜❝❛çã♦ ❞❛ ár❡❛ ♠é❞✐❛ ❞❡ ❝❛❞❛

♣♦r♦ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❡❧❡trô♥✐❝❛ ❞❡ ✈❛rr❡❞✉r❛✳ ❊♠✿ ✭❛✮ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧❀ ✭❜✮ ❞❡✜♥✐çã♦ ❞❛ ❡s❝❛❧❛ ❞❡ t♦♥s ❞❡ ❝✐♥③❛❀ ✭❝✮ ✐♠❛❣❡♠ ❜✐♥❛r✐③❛❞❛ ❡ ✭❞✮ ❝♦♥t❛❣❡♠ ❞♦s ♣♦r♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✼ ▼✐❝r♦❣r❛✜❛ ❞❛ ✈✐st❛ s✉♣❡r✐♦r ❞❡ ✉♠❛ ♠❡♠❜r❛♥❛ ❞❡ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛

q✉❡ ❛♣r❡s❡♥t❛ ❛s ❞✉❛s r❡❞❡s ♣♦r♦s❛s s♦❜r❡♣♦st❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✽ ❋❧✉①♦❣r❛♠❛ ❡sq✉❡♠❛t✐③❛♥❞♦ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛ s❡♣❛r❛çã♦ ❞❛

❝❛♠❛❞❛ ♣♦r♦s❛ s✉♣❡r✐♦r ❞❛ ✐♥❢❡r✐♦r✳ ✭❛✮ ■♠❛❣❡♠ ♦r✐❣✐♥❛❧ tr❛t❛❞❛✳ ✭❜✮ ■♠❛✲ ❣❡♠ ❜✐♥ár✐❛ ❞❛ ❝❛❞❡✐❛ ♣♦r♦s❛ s✉♣❡r✐♦r✳ ✭❝✮ ■♠❛❣❡♠ r❡s✉❧t❛♥t❡ ❞❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧ ❡ ❛ ✐♠❛❣❡♠ ❜✐♥ár✐❛ ♠♦str❛❞❛ ❡♠ ✭❜✮✳ ✭❞✮ ■♠❛❣❡♠ ❜✐♥ár✐❛ ❞❛ ❝❛♠❛❞❛ ♣♦r♦s❛ ✐♥❢❡r✐♦r✳ ✭❡✮ ■♠❛❣❡♥s ✏❜✑ ❡ ✏❞✑ s♦❜r❡♣♦st❛s✳ ✳ ✳ ✳ ✶✼

✷✳✾ ❉✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ✈❡rs✉s ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ tí♣✐❝❛ ❞❛ ❛♥♦❞✐③❛çã♦ ❞♦ ❛❧✉♠í♥✐♦ ❡♠ á❝✐❞♦ ❢♦s❢ór✐❝♦ ✭❍3P❖4✮ 0,1 ♠♦❧ ▲−1✱ ❛ 4 ♠❆ ❝♠−2 ❡ t❡♠♣❡✲

r❛t✉r❛ ❞❡ 300❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✷✳✶✵ ❈✉r✈❛ ❞❡ ♣♦t❡♥❝✐❛❧ ✈❡rs✉s ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❛ ❛♥♦❞✐③❛çã♦ r❡❛❧✐③❛❞❛ ❡♠ á❝✐❞♦ ❢♦s❢ór✐❝♦ ✭❍3P❖4✮ 0,1 ♠♦❧ ▲−1✱ 8 ♠❆ ❝♠−2 ❡ 100❈✳ ◆♦ ❞❡t❛❧❤❡✱

❛♠♣❧✐❛çã♦ ❞❛ r❡❣✐ã♦ ❞❡ tr❛♥s✐çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✶✶ ❉✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ✈❡rs✉s ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❛ ❛♥♦❞✐③❛çã♦ r❡❛❧✐③❛❞❛

♥❛s s❡❣✉✐♥t❡s ❝♦♥❞✐çõ❡s✿ ❍3P❖4 0,1 ♠♦❧ ▲−1 ❛4 ♠❆ ❝♠−2 ❡100❈✳ ✳ ✳ ✳ ✳ ✷✵

✷✳✶✷ ❉✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ✈❡rs✉s ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ r❡❢❡r❡♥t❡ às ❛♥♦❞✐③❛çõ❡s r❡❛❧✐③❛❞❛s ❛ 100_{❈✱ 20}0_{❈ ❡ 25}0_{❈ ❡♠ ❍}

3P❖4 0,1 ♠♦❧ ▲−1 ❛ 4♠❆ ❝♠−2✳ ✳ ✳ ✷✶

✷✳✶✸ ▼✐❝r♦❣r❛✜❛s ❞❛ ❡str✉t✉r❛ ♣♦r♦s❛ ❞❛ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛✿ ✭❛✮ s♦❜r❡ ❛ ❝♦rr♦sã♦ ❧♦❝❛❧✐③❛❞❛ ❡ ✭❜✮ r❡❣✐ã♦ ❞❛ ❛♠♦str❛ ♦♥❞❡ ♥ã♦ ❤♦✉✈❡ ❝♦rr♦sã♦ ❧♦❝❛❧✐③❛❞❛✳ ❆♥♦❞✐③❛çã♦ r❡❛❧✐③❛❞❛ ❡♠ ❍3P❖4 0,1 ♠♦❧ ▲−1 ❛ 8 ♠❆ ❝♠−2 ❡

100_{❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷}

✷✳✶✹ ❈✉r✈❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❛ ❛♥♦❞✐③❛çã♦ r❡❛❧✐✲ ③❛❞❛ ❡♠ á❝✐❞♦ ♦①á❧✐❝♦ ✭❈2❍2❖4✮ 0,1♠♦❧ ▲−1 ❛ 4♠❆ ❝♠−2 ❡ 100❈✳ ✳ ✳ ✳ ✳ ✷✷

✷✳✶✺ ❈✉r✈❛s ❞❡ ♣♦t❡♥❝✐❛❧ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ r❡❢❡r❡♥t❡s às ❛♥♦❞✐✲ ③❛çõ❡s r❡❛❧✐③❛❞❛s ❛ 200_❈✱300_❈✱400_{❈ ❡ 50}0_{❈ ❡♠ ❍}

3P❖4 0,1 ♠♦❧ ▲−1 ❛4

♠❆ ❝♠−2_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸}

✷✳✶✻ ❱❛r✐❛çã♦ ❞❡δE_/δq ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❞❡ ❛♥♦❞✐③❛çã♦✳ ❊st❛ ❣r❛♥❞❡③❛

❢♦✐ ❝❛❧❝✉❧❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ✐♥í❝✐♦ ❞❛ ❛♥♦❞✐③❛çã♦ ❛té 70s ✭✷✽✵ ♠❈ ❝♠✲✷✮ ✳ ✷✹

✷✳✶✼ P♦t❡♥❝✐❛❧ ♠á①✐♠♦ ❛t✐♥❣✐❞♦ ❞✉r❛♥t❡ ❛ ❛♥♦❞✐③❛çã♦ ❡♠ ❍✸P❖✹ 0,1♠♦❧ ▲✲✶❡4

♠❆ ❝♠✲✷ _{❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ◆♦ ❞❡t❛❧❤❡✱E}

max ✈❡rs✉s ✈✐s❝♦s✐❞❛❞❡

❞❛ á❣✉❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✶✽ ❱❛r✐❛çã♦ ❞❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ♣♦t❡♥❝✐❛❧ ♠á①✐♠♦ ✭Emax✮ ❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❡

❡st❛❞♦ ❡st❛❝✐♦♥ár✐♦ ✭Eest✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❞❡ ❛♥♦❞✐③❛çã♦✳ ✳ ✳ ✳ ✳ ✷✻

✷✳✶✾ ❈✉r✈❛s ❞❡ ♣♦t❡♥❝✐❛❧ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ r❡❢❡r❡♥t❡ às ❛♥♦❞✐✲ ③❛çõ❡s r❡❛❧✐③❛❞❛s ❡♠ ❍3P❖4✱ ❍✷❙❖✹ ❡ ❍✷❈2❖4 0,1 ♠♦❧ ▲✲✶ ❛ 8 ♠❆ ❝♠✲✷ ❡

✷✳✷✵ ❈✉r✈❛s ❞❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ r❡❢❡✲ r❡♥t❡s à ♣r✐♠❡✐r❛ ❡ s❡❣✉♥❞❛ ❛♥♦❞✐③❛çõ❡s ❞♦ s✐st❡♠❛ ❆❧✴❆❧2❖3✳ ❆s ❞✉❛s

❛♥♦❞✐③❛çõ❡s ❢♦r❛♠ r❡❛❧✐③❛❞❛s ♥❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s✿ ❍3P❖4 0,1♠♦❧ ▲✲✶ ❛

4 ♠❆ ❝♠✲✷ ❡ 200_{❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽}

✷✳✷✶ ▼✐❝r♦❣r❛✜❛s ❞❛ ❡str✉t✉r❛ ♣♦r♦s❛ ❞❛ ♠❡♠❜r❛♥❛ ❛♣ós ❝❛❞❛ ✉♠❛ ❞❛s ❡t❛♣❛s✿ ✭❛✮ ❛♣ós ❛ ✶➟ ❛♥♦❞✐③❛çã♦ ❡ ❡♠ ✭❜✮ ❛♣ós ❛ ✷➟ ❛♥♦❞✐③❛çã♦✳ ❈♦♥❞✐çõ❡s ❞❡ ❛♥♦❞✐③❛çã♦✿ ❍3P❖4 0,1 ♠♦❧ ▲✲✶ ❛ 4 ♠❆ ❝♠✲✷ ❡ 200❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

✷✳✷✷ ✭❛✮ ❈✉r✈❛s ❞❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ r❡❢❡r❡♥t❡ à ❛♥♦❞✐③❛çã♦ ❞♦ ❛❧✉♠í♥✐♦ r❡❛❧✐③❛❞❛ ❡♠ ❞✉❛s ❡t❛♣❛s ✐❞ê♥t✐❝❛s ❡♠ ❍3P❖4 0,1 ♠♦❧ ▲✲✶✱ 4 ♠❆ ❝♠✲✷ ❡ 300❈✳ ✭❜✮ ▼✐❝r♦❣r❛✜❛ ❞❛ ♠❡♠❜r❛♥❛

r❡s✉❧t❛♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✷✸ ❈✉r✈❛s ❞♦ ♣♦t❡♥❝✐❛❧ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ r❡❢❡r❡♥t❡s à ♣r✐♠❡✐r❛

❛♥♦❞✐③❛çã♦ ✭❝✉r✈❛ ♣r❡t❛✮ r❡❛❧✐③❛❞❛ ❛ 400_{❈ ❡ s❡❣✉♥❞❛ ❛♥♦❞✐③❛çã♦ ✭❝✉r✈❛}

✈❡r♠❡❧❤❛✮ r❡❛❧✐③❛❞❛ ❛ 200_{❈✱ ❛♠❜❛s ❡♠ ❍}

3P❖4 0,1♠♦❧ ▲✲✶ ❡4 ♠❆ ❝♠✲✷✳ ✳ ✸✶

✷✳✷✹ ▼✐❝r♦❣r❛✜❛s ❞❛ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛ ♦❜t✐❞❛ ✉t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ❞❡ ❛♥♦❞✐③❛çã♦ ❡♠ ❞✉❛s ❡t❛♣❛s ❡♠ ❍3P❖4 0,1 ♠♦❧ ▲−1 ❛ 4 ♠❆ ❝♠−2✱ s❡♥❞♦

q✉❡ ❛ ✶➟ ❛♥♦❞✐③❛çã♦ ❢♦✐ r❡❛❧✐③❛❞❛ ❛400_{❈ ❡ ❛ ✷➟ ❛♥♦❞✐③❛çã♦ ❛20}0_{❈✳✭❛✮ ✈✐st❛}

s✉♣❡r✐♦r ❡ ✭❜✮ ✈✐st❛ ❧❛t❡r❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✷✺ ▼✐❝r♦❣r❛✜❛s ❞❛s ♠❡♠❜r❛♥❛s ❞❡ ❛❧✉♠✐♥❛ ❛♥♦❞✐❝❛ ♣r❡♣❛r❛❞❛s ❡♠ ❞✉❛s ❡t❛✲

♣❛s ✐❞ê♥t✐❝❛s ❞❡ ❛♥♦❞✐③❛çã♦ ❣❛❧✈❛♥♦stát✐❝❛✳ ✭❛✮ ♠❡♠❜r❛♥❛ ❝♦♠ ✉♠❛ ú♥✐❝❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦r♦s✳ ✭❜✮ ♠❡♠❜r❛♥❛ ❝♦♠ ❞✉❛s r❡❞❡s ♣♦r♦s❛s s♦❜r❡♣♦st❛s✳ ▼❡♠❜r❛♥❛s ♣r❡♣❛r❛❞❛s ❡♠ ❍3P❖4 ✵✱✶ ♠♦❧ ▲−1 s❡❣✉♥❞♦ ♦s ♣r♦❝❡❞✐♠❡♥t♦s

A ❡B ❛♣r❡s❡♥t❛❞♦s ♥❛ ❚❛❜❡❧❛ ✷✳✶✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✷✳✷✻ ▼✐❝r♦❣r❛✜❛s ❞❛s ♠❡♠❜r❛♥❛s ❞❡ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛ ♣r❡♣❛r❛❞❛s s❡✲ ❣✉♥❞♦ ❛s r♦t✐♥❛s B✱ C✱ D ❡ E✳ ❈♦♥❞✐çõ❡s ❡①♣❡r✐♠❡♥t❛✐s✿ ❍₃P❖_{4 0,1} ♠♦❧

▲−1_{✱ 4 ♠❆ ❝♠}−2_{✳ ✭❛✮ 20}0_{❈ ❡ t}

1a = 40 ♠✐♥✱ ✭❜✮ 300❈ ❡ t1a = 40 ♠✐♥✱ ✭❝✮

200_{❈ ❡ t}

✷✳✷✼ ❉✐str✐❜✉✐çã♦ ❞❡ ♣♦r♦s ❞❛ r❡❞❡ ♣♦r♦s❛ s✉♣❡r✐♦r ✭❤✐st♦❣r❛♠❛ ❤❛❝❤✉r❛❞♦✮ ❡ ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦r♦ ❛♣❛r❡♥t❡ ❞❛ r❡❞❡ ♣♦r♦s❛ ✐♥❢❡r✐♦r ✭❤✐st♦❣r❛♠❛ ❧✐s♦✮ ❞❛s ♠❡♠❜r❛♥❛s ♣r❡♣❛r❛❞❛s ❡♠ ❍3P❖4 ✵✱✶ ♠♦❧ ▲−1✱ ✹ ♠❆ ❝♠−2 ❛200❈✱ ❝✉❥❛s

♠✐❝r♦❣r❛✜❛s sã♦ ❛♣r❡s❡♥t❛❞❛s ♥❛ ❋✐❣✉r❛ ✷✳✷✻❛ ❡ ✷✳✷✻❝✱ ♥♦s s❡❣✉✐♥t❡s t❡♠♣♦s ❞❛ ♣r✐♠❡✐r❛ ❛♥♦❞✐③❛çã♦✿ ✭❛✮ t1a= 40♠✐♥ ❡ ✭❜✮ 120♠✐♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

✷✳✷✽ ❉✐❛❣r❛♠❛ ❞❡ ❘❡s♣♦st❛ ♣❛r❛ ♦ P❧❛♥❡❥❛♠❡♥t♦ ❋❛t♦r✐❛❧22_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽}

✷✳✷✾ ❈✉r✈❛ tí♣✐❝❛ ❞❡ ❛♥♦❞✐③❛çã♦✳ ❖s ❝❛r❛❝t❡r❡s ❡♠ ✈❡r♠❡❧❤♦ ❝♦rr❡s♣♦♥❞❡♠ ❛♦s t❡♠♣♦s ❞❡ ❛♥♦❞✐③❛çã♦ ♥❛ ♣r❡♣❛r❛çã♦ ❞❡ ❝❛❞❛ ❛♠♦str❛ ♣❛r❛ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ♠♦r❢♦❧ó❣✐❝❛✳ ❖s ❝❛r❛❝t❡r❡s ❡♠ ♣r❡t♦ ❞❡st❛❝❛♠ ❛s três r❡❣✐õ❡s ♣r✐♥❝✐♣❛✐s ❞❛ ❢♦r♠❛çã♦ ❞❛ ❡str✉t✉r❛ ♣♦r♦s❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✸✵ ▼✐❝r♦❣r❛✜❛s ❞❛ ❡str✉t✉r❛ ♣♦r♦s❛ ❞❛ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛ ♣r❡♣❛r❛❞❛ ❡♠

❍3P❖4 ✵✱✶ ♠♦❧ ▲−1 ❡ ✹ ♠❆ ❝♠−2❡ 300❈✳ ❈❛❞❛ ✐♠❛❣❡♠ ❝♦rr❡s♣♦♥❞❡ ❛

✉♠ t❡♠♣♦ ❞❡ ❛♥♦❞✐③❛çã♦ ✐♥❞✐❝❛❞♦ ♣❡❧♦s ❝❛r❛❝t❡r❡s ✈❡r♠❡❧❤♦s ♥❛ ❝✉r✈❛ ❞❡ ❛♥♦❞✐③❛çã♦ ❞❛ ❋✐❣✉r❛ ✷✳✷✾✿ ✭❛✮ 50s ✭❡stá❣✐♦ A✮✱ ✭❜✮ ₂₅₀s ✭❡stá❣✐♦ C✮✱ ✭❝✮

600s ✭❡stá❣✐♦ E✮✱ ✭❞✮₁₄₀₀s ✭❡stá❣✐♦ G✮ ❡ ✭❡✮₂₄₀₀s ✭❡stá❣✐♦ I✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

✷✳✸✶ ❱❛r✐❛çã♦ ❞❛ ❡s♣❡ss✉r❛ t♦t❛❧ ❞♦ ✜❧♠❡ ❞❡ ó①✐❞♦ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ❞❡ ❛♥♦❞✐③❛çã♦✳ ❆♥♦❞✐③❛çõ❡s r❡❛❧✐③❛❞❛s ❡♠ ❍3P❖4 ✵✱✶ ♠♦❧ ▲−1 ❡ ✹ ♠❆ ❝♠−2❡

300_{❈✳ ❆ ❧✐♥❤❛ é ❣✉✐❛ ♣❛r❛ ♦s ♦❧❤♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷}

✷✳✸✷ ▼✐❝r♦❣r❛✜❛ ❞❛ ✈✐st❛ ❧❛t❡r❛❧ ❞❛ ❡str✉t✉r❛ ♣♦r♦s❛ ❞❛ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣r❡♣❛✲ r❛❞❛ ❡♠ ❍3P❖4 ✵✱✶ ♠♦❧ ▲−1 ❡ ✹ ♠❆ ❝♠−2 ❡ 300❈ ❛♣ós ✭❛✮ 2000 s❡❣✉♥❞♦s

❡ ❡♠ ✭❜✮ 2400 s❡❣✉♥❞♦s ❞❡ ❛♥♦❞✐③❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✷✳✸✸ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ♣♦r♦ ❛♣ós ✉♠ t❡♠♣♦ ❞❡ ❛♥♦❞✐③❛çã♦ t

♠♦str❛♥❞♦ ❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❣r❛♥❞❡③❛s ❣❡♦♠étr✐❝❛s ❡ ♦s ♣❛râ♠❡tr♦s ❢ís✐❝♦✲ q✉í♠✐❝♦s ❞♦ ♠♦❞❡❧♦ ❞❡ P❛t❡r♠❛r❛❦✐s✳ ❊sq✉❡♠❛ ❛❞❛♣t❛❞♦ ❞❛s ♣r✐♥❝✐♣❛✐s ✐❞é✐❛s ❡ ❝♦♥❝❧✉sõ❡s ❞♦s tr❛❜❛❧❤♦s ❞❡ P❛t❡r♠❛r❛❦✐s ❡t ❛❧✳ ❬✸✷✲✸✹❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✸✹ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ♣♦r♦ ❡♠ três t❡♠♣♦s ❞✐st✐♥t♦s ❛♦ ❧♦♥❣♦

❞❛ ❛♥♦❞✐③❛çã♦✳ ❆ ❛❧t✉r❛ ♠á①✐♠❛ ✭❤max✮ ❛t✐♥❣✐❞❛ é ♠♦str❛❞❛ ♥♦ ❡sq✉❡♠❛✳

✷✳✸✺ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ✐♥t❡r❢❛❝❡ ♠❡t❛❧✴ó①✐❞♦✳ ❆s ❡s♣❡ss✉✲ r❛s ❞♦ ✜❧♠❡ ♣♦r♦s♦ ❡ ❞❛ ❝❛♠❛❞❛ ❜❛rr❡✐r❛ ❡stã♦ ✐♥❞✐❝❛❞❛s ♥♦ ❡sq✉❡♠❛✳ ✳ ✳ ✹✽

✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ❞♦♠í♥✐♦ ❡s♣❛❝✐❛❧ ❣❡♥ér✐❝♦ ✐❞❡♥t✐✜❝❛♥❞♦ ♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❡ ♦s r❡s♣❡❝t✐✈♦s ♥ós✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ❡str✉t✉r❛ ❞❛ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛✳ ■♠❛✲

❣❡♥s ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❡❧❡trô♥✐❝❛ ❞❛ ✈✐st❛ s✉♣❡r✐♦r ❡♠ ❞✐❢❡r❡♥t❡s ❝♦♥❞✐çõ❡s ❡①♣❡r✐♠❡♥t❛✐s ❡ ❞❛ ✈✐st❛ ❧❛t❡r❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✸ ❊t❛♣❛s ❡♥✈♦❧✈✐❞❛s ♥❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣r♦❜❧❡♠❛ ❢ís✐❝♦✳ ✳ ✳ ✳ ✻✽ ✸✳✹ ❆♣r❡s❡♥t❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❢ís✐❝♦✳ ✭❛✮ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ✈✐st❛

❧❛t❡r❛❧ ❞❛ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛ ♠♦str❛♥❞♦ ❛♣❡♥❛s ✉♠ ♣♦r♦✳✭❜✮ ❉❡t❛❧❤❡ ❞♦ ✐♥t❡r✐♦r ❞♦ ♣♦r♦✳ ✭❝✮ ■♥t❡r❢❛❝❡ ó①✐❞♦✴s♦❧✉çã♦✳ ❆ ❡s❝❛❧❛ ❡♠ q✉❡ ♦ ❡sq✉❡♠❛ ❢♦✐ ❝♦♥str✉í❞♦ ♥ã♦ r❡♣r❡s❡♥t❛ ❛s ❞✐♠❡♥sõ❡s r❡❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✸✳✺ ❉♦♠í♥✐♦ ❡s♣❛❝✐❛❧ ❞♦ ♣r♦❜❧❡♠❛ ❢ís✐❝♦ ❡♠ ❝♦♦r❞❡♥❛❞❛s ❝❛rt❡s✐❛♥❛s✳ ❆s ❣r❛♥✲

❞❡③❛s ❛♣r❡s❡♥t❛❞❛s ♥♦ ❡sq✉❡♠❛ ♥ã♦ ❡stã♦ r❡♣r❡s❡♥t❛❞❛s ❡♠ ❡s❝❛❧❛ r❡❛❧✳ ✳ ✳ ✼✸ ✸✳✻ ❉♦♠í♥✐♦ ❡s♣❛❝✐❛❧ ❞✐s❝r❡t✐③❛❞♦ ❡♠ ✉♠❛ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s tr✐❛♥❣✉✲

❧❛r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✸✳✼ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦t❡♥❝✐❛❧ ♥♦ s✐st❡♠❛ ❡♠ três

❝♦♥❞✐çõ❡s ❞✐❢❡r❡♥t❡s✳ ❖s ❝❛r❛❝t❡r❡s s✉❜s❝r✐t♦s ✐❞❡♥t✐✜❝❛♠ ❛s ❢❛s❡s✿ ♠❡t❛❧ ✭m✮✱ ó①✐❞♦ ✭o✮ ❡ s♦❧✉çã♦ ✭s✮✱ ❡ ❛ ✐♥t❡r❢❛❝❡ ó①✐❞♦✴s♦❧✉çã♦ ✭Ωo/s✮ ✳ ❖ ♣♦✲

t❡♥❝✐❛❧ ❞❛ s♦❧✉çã♦ ✭φs✮ ❢♦✐ ❛❞♦t❛❞♦ ❝♦♠♦ r❡❢❡rê♥❝✐❛ ❞❡ ♣♦t❡♥❝✐❛❧ ✭φref✮✳ ❖

❛st❡ríst✐❝♦ ✭✯✮ s♦❜r❡s❝r✐t♦ ✐❞❡♥t✐✜❝❛ ❛ ❝♦♥❞✐çã♦ ❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✸✳✽ ❊①❡♠♣❧♦ ❞❡ r❡✜♥❛♠❡♥t♦ ❞❡ ✉♠❛ ♠❛❧❤❛ ❜✐❞✐♠❡♥s✐♦♥❛❧✳ ❆ ❞❛ ❞✐r❡✐t❛ ❝♦r✲

✸✳✾ ❈✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ✭tr❛❝❡❥❛❞❛✮ ❡ ❛❧❣✉♠❛s ❧✐♥❤❛s ❞❡ ✢✉①♦ ✭só❧✐❞❛✮ ♥♦ ✐♥t❡r✐♦r ❞♦ ♣♦r♦ ♣❛r❛ ❞♦✐s ✈❛❧♦r❡s ❞❡ r❛③ã♦ ❞❡ ❛s♣❡❝t♦ ✭✭❛✮λ= 5❡

✭❜✮ λ= 500✮✳ ❖s ♥ú♠❡r♦s ♣ró①✐♠♦s às ❝✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦

✐♥❞✐❝❛♠ ♦s ✈❛❧♦r❡s ❛❞✐♠❡♥s✐♦♥❛✐s ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❛ ❡s♣é❝✐❡ ❡❧❡tr♦❛t✐✈❛✳ ❘❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ♦❜t✐❞♦s ❝♦♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s✿ Γ =

−1✱B = 0✱ Ψ_{→ ∞} ❡ χ= 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾

✸✳✶✵ ❈✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ✭❧✐♥❤❛s só❧✐❞❛s✮ ❡ ❧✐♥❤❛s ❞❡ ✢✉①♦ ❞❡♥✲ tr♦ ❞♦ ♣♦r♦ ❡♠ ❞✐❢❡r❡♥t❡s t❡♠♣♦ ❞❡ ♣♦❧❛r✐③❛çã♦✿ ✭❛✮ T = 0,0045❀ ✭❜✮

T = 0,029❀ ✭❝✮ T = 0,212 ❡ ✭❞✮ T = 3✳ ❖s ✈❛❧♦r❡s ❛❞✐♠❡♥s✐♦♥❛✐s ❞❛

❝♦♥❝❡♥tr❛çã♦ ❞❛s ❡s♣é❝✐❡s ❡❧❡tr♦❛t✐✈❛s sã♦ ✐♥❞✐❝❛❞♦s s♦❜r❡ ❛s ❧✐♥❤❛s ❞❡ ❝♦♥✲ t♦r♥♦✳ ❘❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ♦❜t✐❞♦s ❝♦♠ ♦s s❡❣✉✐♥t❡s ♣❛râ♠❡tr♦s✿ B = 0✱

χ= 1✱ Γ =₋0,25 ❡λ = 2.5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷

✸✳✶✶ ❈✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ♣❛r❛ ❞✐❢❡r❡♥t❡s r❛③õ❡s ❞❡ ❛s♣❡❝t♦✿ ✭❛✮

λ= 25❡χ= 1❀ ✭❜✮ λ= 300❡χ= 0,005✱ ❛♠❜❛s ♥♦ ✜♠ ❞❛ ♣♦❧❛r✐③❛çã♦ ✭T =

3✮✳ ❆ ❡s❝❛❧❛ ❞❡ ❝✐♥③❛ r❡♣r❡s❡♥t❛ ❛ ✈❛r✐r❛çã♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❛❞✐♠❡♥s✐♦♥❛❧

❛♦ ❧♦♥❣♦ ❞❛ r❡❣✐ã♦ ❞❛ s♦❧✉çã♦✳ ❖s ♥ú♠❡r♦s s♦❜r❡ ❛s ❧✐♥❤❛s ❞❡ ❝♦♥t♦r♥♦ ✐♥❞✐❝❛♠ ❛s ❝♦♥❝❡♥tr❛çõ❡s ❛❞✐♠❡♥s✐♦♥❛✐s✳ ❊♠ ❛♠❜♦s ♦s ❝❛s♦s Γ = ₋0,5 ❡

B = 0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸

✸✳✶✷ ✭❛✮ ◗✉❡❞❛ ❞❡ ♣♦t❡♥❝✐❛❧ r❡❧❛t✐✈❛ ♥❛ ❢❛s❡ ó①✐❞♦ ♥♦ ✐♥í❝✐♦ ❞❛ ❞❡♣♦s✐çã♦ ❡♠ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦Ψ✳ ✭❜✮ ❉✐str✐❜✉✐çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ❛❞✐♠❡♥✲

s✐♦♥❛❧ ❛♦ ❧♦♥❣♦ ❞❛ s✉♣❡r❢í❝✐❡ Ω0/s ❞❡♥tr♦ ❞♦ ♣♦r♦ ♥♦ ✐♥í❝✐♦ ❞❛ ❞❡♣♦s✐çã♦

♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞♦ ♣❛râ♠❡tr♦ Ψ ✐♥❞✐❝❛❞♦s ♥❛ ✜❣✉r❛✳ ❘❡s✉❧t❛❞♦s

♥✉♠ér✐❝♦s ♦❜t✐❞♦s ❝♦♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s✿ Γ =₋1✱B = 0

❡ χ= 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼

✸✳✶✸ ❈✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❡ ❛❧❣✉♠❛s ❧✐♥❤❛s ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦ ♥♦ ✭❛✮ ✐♥í❝✐♦ ❡ ♥♦ ✭❜✮ ✜♠ ❞♦ ❡①♣❡r✐♠❡♥t♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ ❆ ❡s❝❛❧❛ ❞❡ ❝✐♥③❛ r❡♣r❡s❡♥t❛ ♦s ❣r❛❞✐❡♥t❡s ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❛❞✐♠❡♥s✐♦♥❛❧ ❞❡ ✵ ❛ ✶✳ ❘❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ♦❜t✐❞♦s ❝♦♠ ♦s s❡❣✉✐♥t❡s ♣❛râ♠❡tr♦s✿ Γ =₋0,5✱χ= 1✱λ= 500✱

✸✳✶✹ ❉❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ♥❛ ❜❛s❡ ❞♦ ♣♦r♦ ♣❛r❛ três ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ ❡s✲ ♣❡ss✉r❛ ❞❛ ❝❛♠❛❞❛ ❜❛rr❡✐r❛ ✭B✮ ❡ ❞♦✐s ✈❛❧♦r❡s ❞✐❢❡r❡♥t❡s ❞❡ χ✳ ❘❡s✉❧t❛❞♦s

♥✉♠ér✐❝♦s ♦❜t✐❞♦s ❝♦♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s✿ Γ = ₋1.5✱

Ψ = 1000 ❡ λ= 50✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶

✸✳✶✺ ❉♦♠í♥✐♦ ❡s♣❛❝✐❛❧ ❞♦ ♣r♦❜❧❡♠❛ ❢ís✐❝♦ ❝♦♥t❡♥❞♦ ❞♦✐s ♣♦r♦s ❡♠ ❝♦♦r❞❡♥❛❞❛s ❝❛rt❡s✐❛♥❛s✳ ❖ ❡sq✉❡♠❛ ♥ã♦ ❡stá ❛♣r❡s❡♥t❛❞♦ ❡♠ ❡s❝❛❧❛ r❡❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✸✳✶✻ ❈✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ♣♦t❡♥❝✐❛❧✱ ♥♦ ✐♥í❝✐♦ ❞❛ ♣♦❧❛r✐③❛çã♦ ✭T = 10−3_{✮✱ ♥♦}

✐♥t❡r✐♦r ❞❛ t❡♠♣❧❛t❡ s❡♠ ❝❛♠❛❞❛ ❜❛rr❡✐r❛ ❝♦♥t❡♥❞♦ ❞♦✐s ♣♦r♦s✳ ❆ ❡s❝❛❧❛ ❞❡ ❝♦r ✐♥❞✐❝❛ ♦ ✈❛❧♦r ❞❛ q✉❡❞❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❞❡♥tr♦ ❞❛ t❡♠♣❧❛t❡✳ ❘❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ♦❜t✐❞♦s ❝♦♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s✿ B = 0✱ Ψ =

1_×10−3_{✱ χ= 0,005✱W = 0,04✱ λ}

1 = 5 ❡ λ2 = 5,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸

✸✳✶✼ ❈✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❞❛ ❡s♣é❝✐❡ ❡❧❡tr♦❛t✐✈❛ ❞❡♥tr♦ ❞❡ ❞♦✐s ♣♦r♦s ❡♠ ❞✐❢❡r❡♥t❡s t❡♠♣♦s ❞❡ s✐♠✉❧❛çã♦✿ ✭❛✮ T = 0,001✱ ✭❜✮ T = 0,004✱

✭❝✮T = 0,51❡ ✭❞✮T = 1✳ ❆ ❝♦♥❝❡♥tr❛çã♦ ❛✉♠❡♥t❛ ❞♦ ❧✐❧ás ♣❛r❛ ♦ ✈❡r♠❡❧❤♦✳

❘❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ♦❜t✐❞♦s ❝♦♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s✿ B =

0✱ Ψ = 1_×10−3_{✱ χ= 0,005✱ W = 0,04✱ λ}

1 = 5 ❡ λ2 = 5,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺

✸✳✶✽ ❈♦♥❝❡♥tr❛çã♦ ❛❞✐♠❡♥s✐♦♥❛❧ ❞❛ ❡s♣é❝✐❡ ❡❧❡tr♦❛t✐✈❛ ♥❛ ❞✐r❡çã♦Y ♣❛r❛ ❛♠❜♦s

♦s ♣♦r♦s ♥♦ ✐♥í❝✐♦ ✭T = 0,001✮ ❡ ♥♦ ✜♠ ✭T = 1✮ ❞❛ s✐♠✉❧❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻

✸✳✶✾ ❉✐str✐❜✉✐çã♦ ❞❡ ❝♦rr❡♥t❡ ❛❞✐♠❡♥s✐♦♥❛❧ ❛♦ ❧♦♥❣♦ ❞❛ ✐♥t❡r❢❛❝❡ r❡❛❣❡♥t❡ ♣❛r❛ ♦ ♣♦r♦1❡♠ ❢✉♥çã♦ ❞❡ ✉♠❛ ❞✐stâ♥❝✐❛ ❣❡♥❡r❛❧✐③❛❞❛ ✭δ✮✱ ♦♥❞❡ ❝❛❞❛ s❡❣♠❡♥t♦

❞♦ ❞♦♠í♥✐♦ ❡s♣❛❝✐❛❧ r❡♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✸✳✶✺ ❡stá ✐❞❡♥t✐✜❝❛❞♦ ♣❡❧♦s ✐♥t❡r✈❛❧♦s ♥❛ ❛❜❝✐ss❛✳ ❉✐str✐❜✉✐çã♦ ❞❡ ❝♦rr❡♥t❡ ❝♦rr❡s♣♦♥❞❡♥t❡ à s✐♠✉❧❛çõ❡s r❡❛❧✐③❛❞❛s ❝♦♠ ♦s s❡❣✉✐♥t❡s ♣❛râ♠❡tr♦s✿ B = 0✱ Ψ = 1_×103_{✱ χ = 0,005✱}

W = 0,004✱λ1 = 500 ❡λ2 = 550✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽

✸✳✷✵ ❉✐str✐❜✉✐çã♦ ❞❡ ♣♦t❡♥❝✐❛❧ ♥♦ ✐♥t❡r✐♦r ❞❛ t❡♠♣❧❛t❡ ♥❛ r❡❣✐ã♦ ♣ró①✐♠❛ ❛♦s ♣♦✲ r♦s ❡♠T = 0,001✳ ❆ ❡s❝❛❧❛ ❞❡ ❝♦r ✐♥❞✐❝❛ ♦ ✈❛❧♦r ❞❡ ♣♦t❡♥❝✐❛❧ ❛❞✐♠❡♥s✐♦♥❛❧

❡♠ ❝❛❞❛ ♣♦♥t♦ ❞♦ ❞♦♠í♥✐♦ ❡s♣❛❝✐❛❧ ❛♣r❡s❡♥t❛❞♦✳ ❙✐♠✉❧❛çõ❡s r❡❛❧✐③❛❞❛s ❝♦♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s✿ B = 0✱ Ψ = 1_×103_{✱ χ = 0,005✱}

✸✳✷✶ ◗✉❡❞❛ ❞❡ ♣♦t❡♥❝✐❛❧ r❡❧❛t✐✈❛ ❞❡♥tr♦ ❞❛ t❡♠♣❧❛t❡ ΓO

Γ ❡♠ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦

Ψ ❡♠ ❞✉❛s ♣♦s✐çõ❡s ❞✐st✐♥t❛s ❞♦ ❞♦♠í♥✐♦ ❛✐♥❞❛ ♥♦ ✐♥í❝✐♦ ❞❛ ♣♦❧❛r✐③❛çã♦✳ ✳ ✳ ✶✶✵

✸✳✷✷ ❉✐str✐❜✉✐çã♦ ❞❡ ❝♦rr❡♥t❡ ❛♦ ❧♦♥❣♦ ❞❛ ✐♥t❡r❢❛❝❡ r❡❛❣❡♥t❡ ❡♠ ❢✉♥çã♦ ❞❡ ✉♠❛ ❞✐stâ♥❝✐❛ ❣❡♥❡r❛❧✐③❛❞❛ ✭δ✮ ♦❜t✐❞❛s ♣❛r❛ três ✈❛❧♦r❡s ❞✐st✐♥t♦s ❞♦ ♣❛râ♠❡tr♦

χ✳ ❙✐♠✉❧❛çõ❡s r❡❛❧✐③❛❞❛s ❝♦♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s✿ B = 0✱

Ψ = 1✱ Γ =₋5✱ W = 0,004✱ λ1 = 5 ❡λ2 = 5,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶

✸✳✷✸ ◗✉❡❞❛ ❞❡ ♣♦t❡♥❝✐❛❧ r❡❧❛t✐✈❛ ❞❡♥tr♦ ❞❛ t❡♠♣❧❛t❡ ❡♠ ❢✉♥çã♦ ❞❛ r❡s✐st✐✈✐❞❛❞❡ ❞❛ t❡♠♣❧❛t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✸✳✷✹ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ❞♦♠í♥✐♦ ❡s♣❛❝✐❛❧ ❞♦ ♣r♦❜❧❡♠❛ ❢ís✐❝♦ s♦❜ ✐♥✲

✈❡st✐❣❛çã♦ ❝♦♥t❡♥❞♦ três ♣♦r♦s✳ ❆s ❞✐♠❡♥sõ❡s ❞♦ ❡sq✉❡♠❛ ♥ã♦ r❡♣r❡s❡♥t❛ ❛s ❞✐♠❡♥sõ❡s r❡❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✸✳✷✺ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❡ ❞✐str✐❜✉✐çã♦ ❞❡ ❝♦rr❡♥t❡✳ ❊①♣❡r✐♠❡♥t♦ ❝♦♠♣✉t❛❝✐♦♥❛❧

r❡❛❧✐③❛❞♦ ❝♦♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s✿ Γ = ₋10✱ Ψ = 1000✱

χ= 0,001✱λ = 10✱B = 0✱ W = 0,004✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷

✸✳✷✻ ✭❛✮ ❉✐str✐❜✉✐çã♦ ❞❡ ♣♦t❡♥❝✐❛❧ ❛♦ ❧♦♥❣♦ ❞❛ s✉♣❡r❢í❝✐❡ ✐♥t❡r♥❛ ❞♦ ♣♦r♦ ❝❡♥tr❛❧ ❡♠T = 0,001✳ ✭❜✮ ❈✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❡s♣é❝✐❡s ❡❧❡tr♦❛✲

t✐✈❛s ❛♦ ❧♦♥❣♦ ❞❛ s✉♣❡r❢í❝✐❡ ✐♥t❡r♥❛✳ ❆s s❡t❛s ✐♥❞✐❝❛♠ ♦ s❡♥t✐❞♦ ❞❛ ❡✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❡s♣é❝✐❡s ❡❧❡tr♦❛t✐✈❛s ♥❡st❛ r❡❣✐ã♦✳ P❛râ♠❡tr♦s✿

B = 0✱W = 0,004✱ λ= 10✱ χ= 0,001✱ Γ =₋10✱ Ψ = 0,001✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹

✸✳✷✼ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ♥♦ ❝❡♥tr♦ ❞❛ ❜❛s❡ ❞♦ ♣♦r♦ ❝❡♥tr❛❧✳ P❛râ♠❡tr♦s✿ B = 0✱ W = 0,004✱ λ = 10✱ χ = 0,001✱ Γ = ₋10✱

Ψ = 0,001✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺

✸✳✷✽ ●rá✜❝♦s ♥♦r♠❛✐s ♦✉ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❛❝✉♠✉❧❛❞❛s ❞♦s ❡❢❡✐t♦s ❞♦s ♣❛râ♠❡✲ tr♦s 1✱ 2✱ 3✱ 4 ❡ 5 s♦❜r❡ _T1 ❡ _T2 ❝❛❧❝✉❧❛❞♦s ♣❛r❛ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❢❛t♦r✐❛❧

✹✳✶ ❱♦❧t❛♠♦❣r❛♠❛ tí♣✐❝♦ ♣❛r❛ ❛ ❡❧❡tr♦❞❡♣♦s✐çã♦ ❞❡ ❈♦ s♦❜r❡ ❆❧ ❡♠ ❈♦❙❖✹

✵✱✵✶ ♠♦❧ ▲✲✶_{✰ ❍}

✸❇❖✸ ✵✱✵✶ ♠♦❧ ▲✲✶ ✰ ◆❛✷❙❖✹ ✵✱✵✺ ♠♦❧ ▲✲✶✱ ♣❍ ✹✱✼ ✭❡s✲

q✉❡r❞❛✮✳ ❱♦❧t❛♠♦❣r❛♠❛ tí♣✐❝♦ s♦❜r❡ ❛❧✉♠í♥✐♦ s❡♠ ♣ré✲tr❛t❛♠❡♥t♦ ❝❛tó❞✐❝♦ ❡♠ ❍✸❇❖✸ ✵✱✵✶ ♠♦❧ ▲✲✶ ✰ ◆❛✷❙❖✹ ✵✱✵✺ ♠♦❧ ▲✲✶ ✭❞✐r❡✐t❛✮✳ ❱❡❧♦❝✐❞❛❞❡ ❞❡

✈❛rr❡❞✉r❛ ✐❣✉❛❧ ❛ ✷✵ ♠❱ s✲✶_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺}

✹✳✷ ✭❛✮ ❘❡❣✐ã♦ ❝❛tó❞✐❝❛ ❞❛ ✈♦❧t❛♠❡tr✐❛ ❞❛ ❡❧❡tr♦❞❡♣♦s✐çã♦ ❞❡ ❈♦ ❞♦ ✈♦❧t❛♠♦✲ ❣r❛♠❛ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✹✳✶ ❡ ✭❜✮ ❈✐❝❧♦s ✈♦❧t❛♠étr✐❝♦s ❝♦♥s❡❝✉t✐✈♦s ♦❜t✐❞♦s ❡♠ ❈♦❙❖✹ ✵✱✵✶ ♠♦❧ ▲✲✶✰ ❍✸❇❖✸ ✵✱✵✶ ♠♦❧ ▲✲✶ ✰ ◆❛✷❙❖✹ ✵✱✵✺ ♠♦❧

▲✲✶_{✱ ♣❍ ✹✱✼✳ ❖s sí♠❜♦❧♦s ✐❞❡♥t✐✜❝❛♠ ♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❝r✉③❛♠❡♥t♦✱ E}

N✱ ❡♠

❝❛❞❛ ❝✐❝❧♦✳ ❱❡❧♦❝✐❞❛❞❡ ❞❡ ✈❛rr❡❞✉r❛✿ ✷✵ ♠❱ s✲✶_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼}

✹✳✸ ❘❡❣✐ã♦ ❛♥ó❞✐❝❛ ❞♦s ✈♦❧t❛♠♦❣r❛♠❛s ❝♦♥s❡❝✉t✐✈♦s ❛♣r❡s❡♥t❛❞♦s ♥❛ ❋✐❣✉r❛ ✹✳✷❜ ❞❡st❛❝❛♥❞♦ ♦s ♣r♦❝❡ss♦s ❛♥ó❞✐❝♦s ♣r❡s❡♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾ ✹✳✹ Pr✐♠❡✐r♦ ❡ ❞é❝✐♠♦ ❝✐❝❧♦s ✈♦❧t❛♠étr✐❝♦s ❞❛ ♣❛ss✐✈❛çã♦ ❞♦ ❆❧ ❡♠ ❍3❇❖3

✵✱✶♠♦❧✳▲✲✶_{✱ ♣❍ ❂ ✻✱✼ ❛ ✷✵ ♠❱s}✲✶_{✳ ❆s s❡t❛s ✐♥❞✐❝❛♠ ♦ s❡♥t✐❞♦ ❞❛ ✈❛rr❡❞✉r❛✳ ✶✹✵}

✹✳✺ ❱♦❧t❛♠♦❣r❛♠❛ tí♣✐❝♦ ❞❛ ❡❧❡tr♦❞❡♣♦s✐çã♦ ❞❡ ❈♦ s♦❜r❡ ❆❧ ♣❛ss✐✈❛❞♦ ❡❧❡tr♦✲ q✉✐♠✐❝❛♠❡♥t❡✳ ❱♦❧t❛♠♦❣r❛♠❛ r❡❛❧✐③❛❞♦ ❡♠ ❈♦❙❖✹ ✵✱✵✶ ♠♦❧ ▲✲✶ ✰ ❍✸❇❖✸

✵✱✵✶ ♠♦❧ ▲✲✶ _{✰ ◆❛}

✷❙❖✹ ✵✱✵✺ ♠♦❧ ▲✲✶ ♣❍ ✹✱✼✳ ❱❡❧♦❝✐❞❛❞❡ ❞❡ ✈❛rr❡❞✉r❛✿ ✷✵

♠❱ s✲✶_{✳ ❆s s❡t❛s ✐♥❞✐❝❛♠ ♦ s❡♥t✐❞♦ ❞❛ ✈❛rr❡❞✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶}

✹✳✻ ❊sq✉❡♠❛ ❞❡ ✉♠❛ ❝é❧✉❧❛ ❡❧❡tr♦q✉í♠✐❝❛ ❝♦♥✈❡♥❝✐♦♥❛❧ ❝♦♥t❡♥❞♦ q✉❛tr♦ ❡❧❡tr♦✲ ❞♦s✱ s❡♥❞♦ ❞♦✐s ❝♦♥tr❛ ❡❧❡tr♦❞♦s ✭❈❊✮✱ ❡❧❡tr♦❞♦ ❞❡ tr❛❜❛❧❤♦ ✭❊❚✮ ❡ ❡❧❡tr♦❞♦ ❞❡ r❡❢❡rê♥❝✐❛ ✭❊❘✮✳ ❖ ✢✉①♦ ❞❡ ◆2 ❡stá r❡♣r❡s❡♥t❛❞♦ ♥♦ ❡sq✉❡♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷

✹✳✽ ❘❡s♣♦st❛ ❞❛ ❡❧❡tr♦❞❡♣♦s✐çã♦ ♣✉❧s❛❞❛ ❞❡ ❈♦ s♦❜r❡ ❛❧✉♠✐♥❛ ❛♥ó❞✐❝❛ ♣♦r♦s❛✳ ❖s tr❛♥s✐❡♥t❡s ❛♣r❡s❡♥t❛❞♦s ❝♦rr❡s♣♦♥❞❡♠ à ✶✵ _{❡ à ✺✵}✵ _{s❡q✉ê♥❝✐❛ ❞❡ ♣✉❧s♦s✳}

❊①♣❡r✐♠❡♥t♦ r❡❛❧✐③❛❞♦ ♥❛s s❡❣✉✐♥t❡s ❝♦♥❞✐çõ❡s✿ ion =−30♠❆ ❝♠−2✱iof f =

0✱ ton = 10 ♠s✱ tof f = 10 s✱ ❡♠ ❈♦❙❖✹ ✵✱✶ ♠♦❧ ▲✲✶✰ ❍✸❇❖✸✵✱✶ ♠♦❧ ▲✲✶ ✰

◆❛✷❙❖✹ ✵✱✺ ♠♦❧ ▲✲✶ ❛ ✷✺0❈✳ ◆ú♠❡r♦ ❞❡ ♣✉❧s♦s ❛♥ó❞✐❝♦s✿ 1250❀ ♥ú♠❡r♦ ❞❡

♣✉❧s♦s ❝❛tó❞✐❝♦s✿ 1250✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✺

✺✳✶ ❊str✉t✉r❛s ❈r✐st❛❧✐♥❛s ❋❈❈ ✭❞✐r❡✐t❛✮ ❡ ❍❈P ✭❡sq✉❡r❞❛✮ ❞♦ ❝♦❜❛❧t♦ ♠❡tá❧✐❝♦✳ ❆s s❡t❛s ✈❡r❞❡✱ ❛♠❛r❡❧❛ ❡ ❜r❛♥❝❛ ✐♥❞✐❝❛♠ ❛s ❞✐r❡çõ❡s ❬✶✵✵❪✱ ❬✶✶✵❪ ❡ ❬✶✶✶❪ ♥❛ ❡str✉t✉r❛ ❋❈❈✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❊♠ ❍❈P✱ ❛s s❡t❛s ✈❡r❞❡ ❡ ❜r❛♥❝❛ ✐♥❞✐❝❛♠✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛s ❞✐r❡çõ❡s ❬✶✵✶✵❪ ❡ ❬✵✵✵✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✽ ✺✳✷ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❛ ♦❝✉♣❛çã♦ ❞♦s ♥í✈❡✐s ❡❧❡trô♥✐❝♦s ✈á❧✐❞♦ ♣❛r❛ ó①✐✲

❞♦s ❞❡ ♠❡t❛✐s ❞❡ tr❛♥s✐çã♦✱ ✐❧✉str❛♥❞♦ ❛ ♦r✐❣❡♠ ❞♦ ❛♥t✐❢❡rr♦♠❛❣♥❡t✐s♠♦ ❡♠ ó①✐❞♦s ❞❡ ♠❡t❛✐s ❞❡ tr❛♥s✐çã♦ ✸❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✺ ✺✳✸ ❊sq✉❡♠❛ r❡♣r❡s❡♥t❛t✐✈♦ ❞❛ ♠♦✈✐♠❡♥t❛çã♦ ❞❛s ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦ s♦❜ ❛

❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡①t❡r♥♦H✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✼

✺✳✹ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ tí♣✐❝❛ ♣❛r❛ ✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦✳ ❆s ❣r❛♥✲ ❞❡③❛s ❢ís✐❝❛s ♠❛✐s r❡❧❡✈❛♥t❡s ❡stã♦ ✐♥❞✐❝❛❞❛s ♥❛ ✜❣✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✽ ✺✳✺ ■❧✉str❛çã♦ ❝♦♥❝❡✐t✉❛❧ ❞♦ ♠❡❝❛♥✐s♠♦ ❞❛ ❡①❝❤❛♥❣❡ ❜✐❛s s❡❣✉♥❞♦ ▼❡✐❦❧❡❥♦❤♥

❡ ❇❡❛♥ ❬✶✻✺❪✳ ▼ é ❛ ♠❛❣♥❡t✐③❛çã♦ ❡ ❍ é ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦❀ ❚ é ❛ t❡♠♣❡r❛t✉r❛❀ TC é ❛ t❡♠♣❡r❛t✉r❛ ❞❡ ❈✉r✐❡✱ TN é ❛ t❡♠♣❡r❛t✉r❛ ❞❡

◆é❡❧❀ Hf c é ♦ ❝❛♠♣♦ ♥♦ q✉❛❧ ❛ ❛♠♦str❛ ❢♦✐ r❡s❢r✐❛❞❛✳ ✭❛✮ ◆❛ t❡♠♣❡r❛t✉r❛

TN < T < TC ♦ ❢❡rr♦♠❛❣♥❡t♦ ❡stá ♦r❞❡♥❛❞♦ ❡ ♦ ❛♥t✐❢❡rr♦♠❛❣♥❡t♦ ❡stá

❞❡s♦r❞❡♥❛❞♦✳ ✭❜✮ ❆❜❛✐①♦ ❞❡ TN ♦ ❛♥t✐❢❡rr♦♠❛❣♥❡t♦ ❡stá ♦r❞❡♥❛❞♦✱ ♦ q✉❡

❝❛✉s❛ ❛ ❡①❝❤❛♥❣❡ ❜✐❛s ❝♦♠♦ ❡sq✉❡♠❛t✐③❛❞♦ ❡♠ ✭❝✮✱ ✭❞✮✱ ❡ ✭❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✶ ✺✳✻ ▼❛❣♥❡t♦str✐❝çã♦ ❝❛✉s❛❞❛ ♣❡❧❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡ ❛ ✈❛r✐✲

❛çã♦ ❞❛ ❞❡❢♦r♠❛çã♦ ✭△L

L ✮ ❡♠ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦✳ ✳ ✳ ✳ ✳ ✶✻✹

✺✳✽ ❱❛r✐❛çã♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✉♠❛ ❡s♣é❝✐❡ ❡♠ ❢✉♥çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣❛r❡❞❡ ❞❡ ❞♦♠í♥✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✼ ✺✳✾ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣❛r❡❞❡ ❞❡ ❞♦♠í♥✐♦ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠❛ t❡♥sã♦ s❡♥♦✐❞❛❧✳ ✳ ✶✻✾ ✺✳✶✵ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❛ r❡❣✐ã♦ ❛♠♦str❛❧ à ❡sq✉❡❞❛✳ ✶✮ ❙✉♣♦rt❡ ❞❡ ❛♠♦s✲

tr❛❀ ✷✮ ▼❡❝❛♥✐s♠♦ ♣❛r❛ ❣✐r❛r ❛ ❛♠♦str❛❀ ✸✮ ▼❡❝❛♥✐s♠♦ ♣❛r❛ ♣♦s✐❝✐♦♥❛r ❛ ❛♠♦str❛❀ ✹✮❱✐s♦r❀ ✺✮ ❙❡♥s♦r ❞❡ ♥í✈❡❧ ❞❡ ❍❡❀ ✻✮ ▼❛❣♥❡t♦ s✉♣❡r❝♦♥❞✉✲ t♦r❀ ✼✮ ■♠♣❡❞â♥❝✐❛ ❞❡ ✢✉①♦❀ ✽✮ ❈á♣s✉❧❛ ❞♦ s❡♥s♦r ❙◗❯■❉❀ ✾✮ P✐❝❦✲✉♣ ❈♦✐❧ ❙✉♣❡r❝♦♥❞✉t♦r✳ ➚ ❞✐r❡✐t❛✱ ❢♦t♦❣r❛✜❛ ❞♦ ♠❛❣♥❡tô♠❡tr♦ ❙◗❯■❉ ❝♦♠♣❧❡t♦✱ ✐♥❝❧✉✐♥❞♦ ❣❛❜✐♥❡t❡ ❞♦ ❞❡✇❛r✱ ❞❡✇❛r✱ ❢♦♥t❡ ❞♦ ♠❛❣♥❡t♦ s✉♣❡r❝♦♥❞✉t♦r✱ ❝♦♥✲ tr♦❧❛❞♦r ❞❡ t❡♠♣❡r❛t✉r❛✱ ❣❛❜✐♥❡t❡✱ ✉♥✐❞❛❞❡ ❞❡ ♣♦tê♥❝✐❛✱ ❝♦♥tr♦❧❛❞♦r ❣❡r❛❧✱ ✉♥✐❞❛❞❡ ❞❡ ❝♦♥tr♦❧❡ ❞♦ ✢✉①♦ ❞❡ ❣ás ❞♦ ♠❛❣♥❡t♦✱ ♠✐❝r♦❝♦♠♣✉t❛❞♦r✱ ♠♦♥✐t♦r ❡ ✐♠♣r❡ss♦r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✶ ✺✳✶✶ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛s ❝♦♥✜❣✉r❛çõ❡s ❞❡ ❛♣❧✐❝❛çã♦ ❞♦ ❝❛♠♣♦ ♠❛❣✲

♥ét✐❝♦ ❞✉r❛♥t❡ ❛s ♠❡❞✐❞❛s ❞❡ ❝❛r❛❝t❡r✐③❛çã♦ ♠❛❣♥ét✐❝❛✳ ✭❛✮ ❈❛♠♣♦ ♠❛❣♥é✲ t✐❝♦ ❛♣❧✐❝❛❞♦ ♣❛r❛❧❡❧❛♠❡♥t❡ à s✉♣❡r❢í❝✐❡ ❞❛ ❛♠♦str❛✱ ♦✉ s❡❥❛✱ ♣❡r♣❡♥❞✐❝✉❧❛r ❛♦ ❡✐①♦ ❞♦ ♥❛♥♦✜♦✳ ✭❜✮ ❈❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ ♣❡r♣❡♥❞✐❝✉❧❛r♠❡♥t❡ à s✉♣❡r❢í❝✐❡ ❞❛ ❛♠♦str❛✱ ♦✉ s❡❥❛✱ ♣❛r❛❧❡❧♦ ❛♦ ❡✐①♦ ❞♦ ♥❛♥♦✜♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✷ ✺✳✶✷ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ♥♦r♠❛❧✐③❛❞♦ ♣❡❧♦ s❡✉ ✈❛❧♦r ❞❡ s❛t✉r❛çã♦ (_µµ

sat✮ ❡♠

❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✭H✮ ❛♣❧✐❝❛❞♦ ♣❛r❛❧❡❧❛♠❡♥t❡ à s✉♣❡r❢í❝✐❡ ❞♦

❝♦♥❥✉♥t♦ ❈♦✴❆l2O3porosa✴❆❧✳ ❈✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ♦❜t✐❞♦ ❛ 5❑✳ ❆ ✐♥s❡rçã♦

♥❛ ✜❣✉r❛ ❛♣r❡s❡♥t❛ ♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❝♦♠♣❧❡t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✹ ✺✳✶✸ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ✭µ✮ ❡♠ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ ✭H✮ ❞♦

❝♦♥❥✉♥t♦ ❈♦✴❆l2O3porosa✴❆❧ ✐❞❡♥t✐✜❝❛❞♦ ❝♦♠♦ ❛♠♦str❛ A. ❈✐❝❧♦ ❞❡ ❤✐st❡✲

r❡s❡ ♦❜t✐❞♦ ❛5❑✳ ❆ ✐♥s❡rçã♦ ♥❛ ✜❣✉r❛ ❛♣r❡s❡♥t❛ ♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❝♦♠♣❧❡t♦✳✶✼✽

✺✳✶✹ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ✭µ✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ✭T✮ ❝♦♠ ❝❛♠♣♦ ♠❛❣✲

♥ét✐❝♦✱ 500❖❡ ❡ 1000❖❡✱ ❛♣❧✐❝❛❞♦ ♣❛r❛❧❡❧❛♠❡♥t❡ à s✉♣❡r❢í❝✐❡ ❞❛ ❛♠♦str❛

A✳ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s s❡❣✉♥❞♦ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ZFC✳ ❆♠♦str❛ A✳ ✳ ✳ ✳ ✳ ✳ ✶✼✾

✺✳✶✺ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ✭µ✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ✭T✮ s❡❣✉♥❞♦ ♦s ♣r♦❝❡❞✐✲

♠❡♥t♦sZFC_/FC❝♦♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ ♣❛r❛❧❡❧❛♠❡♥t❡ à s✉♣❡r❢í❝✐❡

✺✳✶✻ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ✭µ✮ ❡♠ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✭H✮ ❛♣❧✐❝❛❞♦ ♣❛✲

r❛❧❡❧❛♠❡♥t❡ à s✉♣❡r❢í❝✐❡ ❞❛ ❛♠♦str❛ A_. ❈✐❝❧♦s ❞❡ ❤✐st❡r❡s❡ ♦❜t✐❞♦s ❛ ✺ ❑

❛♣ós ♦ ♣r♦❝❡❞✐♠❡♥t♦ ZFC ❡ FC✳ ❖ ❝❛♠♣♦ ❞❡ ❡①❝❤❛♥❣❡ ✭_Hex✮✱ ❞❛❞♦ ♣♦r

HC1,ZF C−HC1,F C✱ ❡stá ✐♥❞✐❝❛❞♦ ♥♦ ❣rá✜❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✶

✺✳✶✼ ❈❛♠♣♦s ❝♦❡r❝✐✈♦s✱−H_{❈✶ ❡}H_{❈✷✱ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ✭}T✮ ❡♠ q✉❡ ♦s

❝✐❝❧♦s ❞❡ ❤✐st❡r❡s❡ ❢♦r❛♠ r❡❛❧✐③❛❞♦s✳ ✭❛✮ ❘❡s✉❧t❛❞♦s s❡❣✉♥❞♦ ♦ ♣r♦❝❡❞✐♠❡♥t♦

ZFC✳ ✭❜✮ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s s❡❣✉♥❞♦ ♦ ♣r♦❝❡❞✐♠❡♥t♦ FC✳ ❆s ❧✐♥❤❛s sã♦

❣✉✐❛s ♣❛r❛ ♦s ♦❧❤♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✸ ✺✳✶✽ ❈❛♠♣♦ ❞❡ ❡①❝❤❛♥❣❡ ✭❍ex✮ ❡ ❈♦❡r❝✐✈✐❞❛❞❡ ✭❍❈✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛

❡♠ q✉❡ ♦s ❝✐❝❧♦s ❞❡ ❤✐st❡r❡s❡ FC ❢♦r❛♠ r❡❛❧✐③❛❞♦s✳ ❆ t❡♠♣❡r❛t✉r❛ ❞❡ ❜❧♦✲

q✉❡✐♦✱ ❚❇✱ ❡stá ✐♥❞✐❝❛❞❛ ♥♦ ❣rá✜❝♦✳ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❛r❛ ❛ ❛♠♦str❛A✳

❆s ❧✐♥❤❛s sã♦ ❣✉✐❛s ♣❛r❛ ♦s ♦❧❤♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✺ ✺✳✶✾ s✉s❝❡t✐❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡✈❡rsí✈❡❧ ✭χrev✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ✭T✮

❡♠ q✉❡ ♦s ❝✐❝❧♦s ❞❡ ❤✐st❡r❡s❡ FC ❢♦r❛♠ r❡❛❧✐③❛❞♦s✳ ❆♠♦str❛ A✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✽

✺✳✷✵ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ✭µ✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ✭❚✮ ❛ 1❦❖❡ ❡ 5❦❖❡

♣❛r❛ ♦ ❝♦♥❥✉♥t♦ ❈♦✴❆l2O3porosa✴❆❧ ✐❞❡♥t✐✜❝❛❞♦ ❝♦♠♦ ❆♠♦str❛Bs❡❣✉♥❞♦ ♦

♣r♦❝❡❞✐♠❡♥t♦ ZFC✳ ❈❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ ♣❛r❛❧❡❧❛♠❡♥t❡ à s✉♣❡r❢í❝✐❡

❞❛ ❛♠♦str❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✾ ✺✳✷✶ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ✭µ✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ✭T✮ s❡❣✉♥❞♦ ♦s ♣r♦❝❡❞✐✲

♠❡♥t♦sZFC ❡FCr❡❛❧✐③❛❞❛s ❝♦♠ ❝❛♠♣♦ ❞❡₁₀₀❖❡ ❛♣❧✐❝❛❞♦ ♣❛r❛❧❡❧❛♠❡♥t❡

à s✉♣❡r❢í❝✐❡ ❞❛ ❛♠♦str❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✵ ✺✳✷✷ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ♥♦r♠❛❧✐③❛❞♦ ♣❡❧♦ s❡✉ ✈❛❧♦r ❞❡ s❛t✉r❛çã♦(_µµ_sat✮ ❡♠ ❢✉♥✲

çã♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ ✭❍✮ ❛♠♦str❛D❛♣ós tr❛t❛♠❡♥t♦ tér♠✐❝♦

❛ 5000_{❈ ❞✉r❛♥t❡ 2❤ ❡♠ ❛t♠♦s❢❡r❛ ❞❡ ❖}

2✳ ❈✐❝❧♦s ❞❡ ❤✐st❡r❡s❡ ♦❜t✐❞♦s ❛ ✺

❑ s❡❣✉♥❞♦ ♦s ♣r♦❝❡❞✐♠❡♥t♦s ZFC ❡FC✳ ❖ ❝✐❝❧♦ FC ❢♦✐ ♦❜t✐❞♦ ❛♣ós r❡s❢r✐✲

❛♠❡♥t♦ ❞❛ ❛♠♦str❛ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐❣✉❛❧ ❛50❦❖❡✳ ❖