❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪ ❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❋❮❙■❈❆
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆
▼❆◆❖❊▲ ❈❆❘❱❆▲❍❖ ❈❆❙❚❘❖ ❏❯◆■❖❘
❚❘❆◆❙■➬Õ❊❙ ❉❊ ❋❆❙❊ ❊▼ P❊❘❖❱❙❑■❚❆❙
P❖▲■❚❮P■❈❆❙
▼❆◆❖❊▲ ❈❆❘❱❆▲❍❖ ❈❆❙❚❘❖ ❏❯◆■❖❘
❚❘❆◆❙■➬Õ❊❙ ❉❊ ❋❆❙❊ ❊▼ P❊❘❖❱❙❑■❚❆❙
P❖▲■❚❮P■❈❆❙
❚❡s❡ s✉❜♠❡t✐❞❛ ❛♦ ♣r♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳❉r✳❆❧❡❥❛♥❞r♦ P❡❞r♦ ❆②❛❧❛
❈♦♦r✐❡♥t❛❞♦r✿ Pr♦❢✳❉r✳❈❛r❧♦s ❲✐❧❧✐❛♠ ❞❡ ❆r❛✉❥♦ P❛s❝❤♦❛❧
Dados Internacionais de Catalogação na Publicação Universidade Federal do Ceará
Biblioteca do Curso de Física
C351t Castro Jr, Manoel Carvalho.
Transições de Fase em Perovskitas Politípicas/ Manoel Carvalho Castro Junior. – Fortaleza, 2013.
154 f.: il., enc.; 30 cm.
Tese (doutorado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Física, Fortaleza, 2013.
Área de Concentração: Física da Matéria Condensada. Orientador: Prof. Dr. Alejandro Pedro Ayala.
1. Transições de Fase. 2. Perovskita. 3. Espectroscopia Raman.
4. Propriedades Vibracionais. 5. Espectroscopia Infravermelha. I. Título. CDD 530.474
❉❡❞✐❝❛tór✐❛
❆♦s ♠❡✉s ♣❛✐s✳
❆♦s ♠❡✉s ❛✈ós✳
➚ ♠✐♥❤❛ ❡s♣♦s❛ ❙✉③✐ ❡ ❛♦ ♥♦ss♦ ✜❧❤♦✱ ❚✐❛❣♦✳
❆♦s ♠❡✉s ✐r♠ã♦s✳
✧❖ q✉❡ ❡✉ ♦✉ç♦✱ ❡sq✉❡ç♦✳ ❖ q✉❡ ✈❡❥♦✱ ❧❡♠❜r♦✳ ❖ q✉❡ ❢❛ç♦✱ ❛♣r❡♥❞♦✳✧✳ ❈♦♥❢ú❝✐♦
❆❣r❛❞❡❝✐♠❡♥t♦s
❆♦ Pr♦❢✳ ❉r✳ ❆❧❡❥❛♥❞r♦ P❡❞r♦ ❆②❛❧❛ ♣❡❧❛✱ ♦r✐❡♥t❛çã♦✱ ❞❡❞✐❝❛çã♦ ❡ ♣❛❝✐ê♥❝✐❛✳ ❆♦ Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❲✐❧❧✐❛♠✱ ♣♦r t♦❞❛ ❛❥✉❞❛ ♥❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❛s ♣❡r♦✈s❦✐t❛s ✻❍✱ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧♦ ❛✉①í❧✐♦ ♣r❡st❛❞♦ ❡ ❝♦♥s❡❧❤♦s ❞❛❞♦s ❡♠ t♦❞♦s ❡ss❡s ❛♥♦s ❞❡ ❡st✉❞♦s✳
❆♦ Pr♦❢✳ ❉r✳ ❏♦s✉é ▼❡♥❞❡s ❋✐❧❤♦✱ ♣♦r ❡♥s✐♥❛r✲♠❡ q✉❡ ❛ r❡s♣♦st❛ ♣❛r❛ ❛ ♠❛✐♦r✐❛ ❞♦s ♣r♦❜❧❡♠❛s ❢ís✐❝♦s✱ é ❡♥❝♦♥tr❛❞❛ ♥❛ ❝♦❡rê♥❝✐❛ ❞❛ s♦❧✉çã♦ q✉❡ s❡ ♣r♦♣õ❡ ❛ ❡st❡s ♣r♦❜❧❡♠❛s✳ ▼❛s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ✐♥✐❣✉❛❧á✈❡❧ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡✱ ♣❛❝✐ê♥❝✐❛ ❡ ❛❥✉❞❛✳
❆♦ ❛♠✐❣♦ ❘❛✛❛❡❧✱ ♣♦r ♠✉✐t❛s ✈❡③❡s ❞✐s♣♦r ❞❡ s❡✉ ♣r❡❝✐♦s♦ t❡♠♣♦ ✭❛té ❞❡ ♠❛❞r✉❣❛❞❛✮ ♣❛r❛ ❛✉①✐❧✐❛r✲♠❡ ♥❛ ♦❜t❡♥çã♦ ❞♦s ❡s♣❡❝tr♦s ❘❛♠❛♥ ❞❛s ❛♠♦str❛s ❞❡st❡ tr❛✲ ❜❛❧❤♦✳
➚ ❆❧❞✐❧❡♥❡✱ ♣♦r ♠❡ ❡♥s✐♥❛r ❛ tr❛❜❛❧❤❛r ❝♦♠ ♦ s♦❢t✇❛r❡ ❞❡ ❝á❧❝✉❧♦s ❞❡ ♣r✐✲ ♠❡✐r♦s ♣r✐♥❝í♣✐♦s✳
➚ ●❛r❞ê♥✐❛✱ ♣♦r t❡r r❡❛❧✐③❛❞♦ ❛s ♠❡❞✐❞❛s ❞❡ ❉❙❈ ♥♦ ♣♦❧✐❡t✐❧❡♥♦✱ ❧♦❣♦ ♥♦s ❡stá❣✐♦s ♣r❡❧✐♠✐♥❛r❡s ❞❛ ❝♦♥❢❡❝çã♦ ❞❡st❛s ♣❛st✐❧❤❛s ♣❛r❛ ❛s ♠❡❞✐❞❛s ❞❡ ❛❜s♦rçã♦ ❞❡ ✐♥❢r❛✲ ✈❡r♠❡❧❤♦✳
❆♦ ❋á❜✐♦✱ ♣♦r t❡r tr❛♥s♣♦st♦ t♦❞♦s ♦s r❛s❝✉♥❤♦s ❞❡ ♣r♦❥❡t♦s ♣❛r❛ ♦ ❆✉✲ t♦❈❆❉✳ ❆❧é♠ ❞❡ t❡r ❛✉①✐❧✐❛❞♦ ♥❛ ❝♦♥str✉çã♦ ❞♦s ♣r♦tót✐♣♦s ❞❡st❡s ♣r♦❥❡t♦s✱ ❡ t❡r ❞❛❞♦ ✈ár✐❛s ✐❞❡✐❛s ✈❛❧♦r♦s❛s ♣❛r❛ ✉♠❛ ♠❡❧❤♦r ♣❡r❢♦r♠❛♥❝❡✳
➚s ❛♠✐❣❛s ❲❛♥❡ss❛ ❡ ❆❧❝❡♠✐r❛✱ ♣♦r t♦❞❛ ❛❥✉❞❛ ❝♦♥❝❡❞✐❞❛✱ s❡♠ ♠❡❞✐r ❡s✲ ❢♦rç♦s ❞✉r❛♥t❡ ❛ ♣❡sq✉✐s❛ ❡ ❡❧❛❜♦r❛çã♦ ❞❡ss❡ tr❛❜❛❧❤♦✳
❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯❋❈✱ ♣❡❧❛ ❢♦r♠❛çã♦ ❞✉r❛♥t❡ ❡st❡ ♣❡rí♦❞♦ ❞❡ ❞♦✉t♦r❛❞♦✳
❆ t♦❞❛ ❡q✉✐♣❡ ❞❛ ♦✜❝✐♥❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛♦ ❙r✳ ■s♠❛❡❧✱ ❙r✳ ❘♦♥❛❧❞♦✱ ❙r✳ ❙❛❧❡s ❡ ❏♦❤♥♥②✱ ♣❡❧❛ ♣r❡st❡③❛ ❡ q✉❛❧✐❞❛❞❡ ♥❛ ✉s✐♥❛❣❡♠ ❡ ❝♦♥str✉çã♦ ❞❡ ✈ár✐♦s ❛❝❡ssór✐♦s ♥❡❝❡ssár✐♦s ♥❛ ♦❜t❡♥çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❡st❛ t❡s❡✳ ❆❧é♠ ❞✐ss♦✱ ♣❡❧♦s ♠✉✐t♦s ♠♦♠❡♥t♦s ❞❡ ❝♦♥✈❡rs❛ ❛❣r❛❞á✈❡❧✳
❆♦ ❆r✐❡❧✱ ❞❡✈✐❞♦ s✉❛ ❣r❛♥❞❡ ❛❥✉❞❛ ♥❛ ❡①❡❝✉çã♦ ❞♦s ❝á❧❝✉❧♦s ❝❧áss✐❝♦s✱ ♣❛r❛ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞♦s ♠♦❞♦s ❞❛s ♣❡r♦✈s❦✐t❛s ✻❍✳
➚ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ♣❡❧♦ ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦ ❡ ❛❧❡❣r✐❛✱ ❢❛t♦ q✉❡ ❢♦✐ ♣r✐♠♦r❞✐❛❧ ♣❛r❛ t❡r ♠❛✐s ❝❧❛r❡③❛ ❡ ❝❛❧♠❛ ♥❛ s♦❧✉çã♦ ❞❡ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ❡♥❝♦♥tr❛❞♦s
❞✉r❛♥t❡ ❛ ❝♦♥❢❡❝çã♦ ❞❡st❛ t❡s❡✳
❆♦ ❈◆Pq✱ ♣❡❧❛s ❜♦❧s❛ ❝♦♥❝❡❞✐❞❛ ♣❛r❛ ❡①❡❝✉çã♦ ❞♦ tr❛❜❛❧❤♦ ❡ ✜♥❛♥❝✐❛♠❡♥t♦ ❞❡ ♣r♦❥❡t♦s✳
➚ ❉❡✉s✱ ♣♦r t❡r ♠❡ ❧❡✈❛♥t❛❞♦ t♦❞❛s ❛s ✈❡③❡s q✉❡ ❝❛í✱ ❡ q✉❡ ♠❡ ♠♦str♦✉ ❛ tr✐❧❤❛ ❝❡rt❛ ❛ s❡r ❝❛♠✐♥❤❛❞❛✳
❘❡s✉♠♦
◆❡st❛ t❡s❡ ❛ ❡s♣❡❝tr♦s❝♦♣✐❛ ✈✐❜r❛❝✐♦♥❛❧ ❢♦✐ ❡♠♣r❡❣❛❞❛ ♣❛r❛ ✐♥✈❡st✐❣❛r ❛s tr❛♥s✐✲ çõ❡s ❡str✉t✉r❛✐s ❞❡ ♣❡r♦✈s❦✐t❛s ♣♦❧✐tí♣✐❝❛s✳ ❈♦♠♣♦st♦s r❡♣r❡s❡♥t❛t✐✈♦s ❞❡ ❞♦✐s ♣♦❧ít✐♣♦s ❢♦r❛♠ ❡st✉❞❛❞♦s✿ ❛ ♣❡r♦✈s❦✐t❛ ♠✉❧t✐❢❡rró✐❝❛ t✐♣♦ ✸❈ P❜✭❋❡1/2 ◆❜1/2✮❖3 ✭P❋◆✮ ❡ ❛s ♣❡✲
r♦✈s❦✐t❛s t✐♣♦ ✻❍ ❇❛3❇2+❙❜2❖9 ✭❇ ❂ ▼❣✱ ❈❛ ❡ ❙r✮✳ ❆ ♣❛rt✐r ❞❡ ❛♥♦♠❛❧✐❛s ♦✉ ❞❡s✈✐♦s
❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♥♦r♠❛❧ ❞♦s ♣❛râ♠❡tr♦s ❛❥✉stá✈❡✐s ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ❡s♣❡❝tr♦ ❞❡ ❢ô♥♦♥s ❞❡st❡s ❝♦♠♣♦st♦s ❢♦r❛♠ ✐❞❡♥t✐✜❝❛❞❛s tr❛♥s❢♦r♠❛çõ❡s ❡str✉t✉r❛✐s✳ ◆♦ P❋◆ ❢♦r❛♠ ♦❜s❡r✈❛❞♦s ✐♥❞í❝✐♦s ❞❡ ❞✉❛s tr❛♥s✐çõ❡s ❡♥tr❡ ❢❛s❡s ❢❡rr♦❡❧étr✐❝❛s✱ ❛❧é♠ ❞❡ ✉♠❛ tr❛♥s✐çã♦ ❡♥tr❡ ❞✐❢❡r❡♥t❡s ❢❛s❡s ❞❡ ♦r❞❡♥❛♠❡♥t♦ ♠❛❣♥ét✐❝♦ ✭❡st❛❞♦ ♣❛r❛♠❛❣♥ét✐❝♦ → ❡st❛❞♦ ❛♥t✐✲
❢❡rr♦♠❛❣♥ét✐❝♦✮ ❡ ✉♠❛ tr❛♥s✐çã♦ ❡♥tr❡ ✉♠ ❡st❛❞♦ ♣❛r❛❡❧étr✐❝♦ ❡ ✉♠ ❢❡rr♦❡❧étr✐❝♦✳ ❊st❡s r❡s✉❧t❛❞♦s sã♦ ❡①♣♦st♦s ❞❡ ❢♦r♠❛ ❜❡♠ ♠❛✐s ❝❧❛r❛ ❞♦ q✉❡ ❡♠ tr❛❜❛❧❤♦s ❞❡ ❡s♣❡❝tr♦s❝♦♣✐❛ ❘❛♠❛♥ ❛♥t❡r✐♦r♠❡♥t❡ ✐♥❢♦r♠❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❞❡✈✐❞♦ ❛ ♠❡❧❤♦r r❡s♦❧✉çã♦ ♦❜t✐❞❛✱ ♦ q✉❡ ♣r♦♣✐❝✐♦✉ ❛té ❛ ♦❜s❡r✈❛çã♦ ❞❛ ♦r✐❣❡♠ ❞❡ ✉♠ ♥♦✈♦ ♠♦❞♦ ♥♦ ❡♥t♦r♥♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❞❡ ◆é❡❧✳ ◆❛s ♣❡r♦✈s❦✐t❛s ✻❍✱ ❛❧é♠ ❞❛ ♦❜s❡r✈❛çã♦ ✉s✉❛❧ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦s ❢ô♥♦♥s ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✱ ♦ q✉❡ r❡♥❞❡✉ ❛ ♦❜s❡r✈❛çã♦ ❞❛ tr❛♥s✐çã♦ ❞❡ ✉♠❛ ❢❛s❡ ❤❡①❛❣♦♥❛❧ ♣❛r❛ ✉♠❛ ❢❛s❡ ♠♦♥♦❝❧í♥✐❝❛ ❡♠ ✶✹✵❑ ♥♦ ❇❛3▼❣❙❜2❖9 ✭❇▼❙✮ ❡ ❞❡ ✉♠❛ ❢❛s❡ ♠♦♥♦❝❧í♥✐❝❛
♣❛r❛ ✉♠❛ ❢❛s❡ tr✐❝❧í♥✐❝❛ ❡♠ ✷✹✵ ❑ ♥♦ ❇❛3❈❛❙❜2❖9 ✭❇❈❙✮✱ ♣r♦❝✉r♦✉✲s❡ ❝❧❛ss✐✜❝❛r ♦s ❢ô♥♦♥s
❞♦s três ❝♦♠♣♦st♦s ✉t✐❧✐③❛♥❞♦ ❞♦✐s ♠ét♦❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳ Pr✐♠❡✐r❛♠❡♥t❡ ✉t✐❧✐③♦✉✲ s❡ ♦ ♠ét♦❞♦ ❛❜ ✐♥✐t✐♦ ❞❡ ❍❛rtr❡❡✲❋♦❝❦ ♣❛r❛ ❝❛❧❝✉❧❛r ♦s ♠♦❞♦s ♥♦r♠❛✐s ❞♦ ❞í♠❡r♦ ❙❜2❖9❀
❡ ❛ss✉♠✐♥❞♦ q✉❡ ❛ ❝é❧✉❧❛ ✉♥✐tár✐❛ ❞♦ ❇▼❙ é ❢♦r♠❛❞❛ ❞❡ ❞í♠❡r♦s ❙❜2❖9 ❡ í♦♥s ✐s♦❧❛❞♦s
❞❡ ❇❛ ❡ ▼❣✱ ❝♦♥s❡❣✉✐✉✲s❡ ❝♦rr❡❧❛❝✐♦♥❛r✱ ✉t✐❧✐③❛♥❞♦ t❡♦r✐❛ ❞❡ ❣r✉♣♦s✱ ♦s ♠♦❞♦s ❝❛❧❝✉❧❛❞♦s ❞♦ ❙❜2❖9 ❝♦♠ ♦s ♠♦❞♦s ✐♥t❡r♥♦s ❞♦ ❇▼❙✳ P♦st❡r✐♦r♠❡♥t❡ ✉t✐❧✐③♦✉✲ s❡ ♦ ♠ét♦❞♦ ❋● ❞❡
❲✐❧s♦♥ ♣❛r❛ ❝♦rr♦❜♦r❛r ♦s r❡s✉❧t❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡ ♦❜t✐❞♦s✱ s❡♥❞♦ ♦❜s❡r✈❛❞♦ ✉♠ ❜♦♠ ❛❝♦r❞♦ ❡♥tr❡ ❛♠❜♦s ♠ét♦❞♦s✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❊s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥✱ ■♥❢r❛✈❡r♠❡❧❤♦✱ ♣❡r♦✈s❦✐t❛s✱ ♠✉❧t✐❢❡rró✐❝♦s✳
❆❜str❛❝t
■♥ t❤✐s t❤❡s✐s ✈✐❜r❛t✐♦♥❛❧ s♣❡❝tr♦s❝♦♣② ✇❛s ✉s❡❞ t♦ ✐♥✈❡st✐❣❛t❡ t❤❡ str✉❝t✉r❛❧ tr❛♥s✐✲ t✐♦♥s ♦❢ ♣♦❧②t②♣✐❝ ♣❡r♦✈s❦✐t❡s✳ ❘❡♣r❡s❡♥t❛t✐✈❡ ❝♦♠♣♦✉♥❞s ♦❢ t✇♦ ♣♦❧②t②♣❡s ✇❡r❡ st✉❞✐❡❞✿ t❤❡ ♠✉❧t✐❢❡rr♦✐❝ ✸❈✲t②♣❡ ♣❡r♦✈s❦✐t❡ P❜✭❋❡1/2◆❜1/2✮❖3✭P❋◆✮ ❛♥❞ t❤❡ ✻❍✲t②♣❡ ♣❡r♦✈s❦✐t❡s
❇❛3❇2+❙❜2❖9 ✭❇ ❂ ▼❣✱ ❈❛✱ ❙r✮✳ ❇❛s❡❞ ♦♥ ❛♥♦♠❛❧✐❡s ♦r ❞❡✈✐❛t✐♦♥s ❢r♦♠ ♥♦r♠❛❧ ❜❡❤❛✈✐♦r
♦❢ t❤❡ ❛❞❥✉st❛❜❧❡ ♣❛r❛♠❡t❡rs ♦❢ t❤❡ t❡♠♣❡r❛t✉r❡ ❞❡♣❡♥❞❡♥❝❡ ♦❢ t❤❡ ♣❤♦♥♦♥ s♣❡❝tr❛ ♦❢ t❤❡s❡ ❝♦♠♣♦✉♥❞s✱ ✐t ✇❛s ♣♦ss✐❜❧❡ t♦ ✐❞❡♥t✐❢② str✉❝t✉r❛❧ tr❛♥s❢♦r♠❛t✐♦♥s✳ ■♥ P❋◆✱ ✐t ✇❛s ♦❜s❡r✈❡❞✱ ❡✈✐❞❡♥❝❡s ♦❢ t✇♦ tr❛♥s✐t✐♦♥s ❜❡t✇❡❡♥ ❢❡rr♦❡❧❡❝tr✐❝ ♣❤❛s❡s✱ ✐♥ ❛❞❞✐t✐♦♥ t♦ ❛ tr❛♥s✐✲ t✐♦♥ ❜❡t✇❡❡♥ ❞✐✛❡r❡♥t ♠❛❣♥❡t✐❝ ♦r❞❡r✐♥❣ st❛t❡s ✭♣❛r❛♠❛❣♥❡t✐❝ →❛♥t✐❢❡rr♦♠❛❣♥❡t✐❝✮ ❛♥❞
❞✐✛❡r❡♥t ♣♦❧❛r st❛t❡s ✭♣❛r❛❡❧❡❝tr✐❝ → ❢❡rr♦❡❧❡❝tr✐❝✮✳ ❚❤❡s❡ r❡s✉❧ts ♣r♦✈✐❞❡ str♦♥❣❡r ❡✈✐✲
❞❡♥❝❡s t❤❛♥ ♣r❡✈✐♦✉s ❘❛♠❛♥ ❙♣❡❝tr♦s❝♦♣② r❡♣♦rts ✐♥ ❧✐t❡r❛t✉r❡ ❞✉❡ t♦ ❛ ❜❡tt❡r r❡s♦❧✉t✐♦♥✱ ✇❤✐❝❤ ❛❧❧♦✇❡❞ ✉s t♦ ♦❜s❡r✈❡✱ ❢♦r ❡①❛♠♣❧❡✱ ❛ ♥❡✇ ♣❤♦♥♦♥ ❛t t❤❡ ◆é❡❧ t❡♠♣❡r❛t✉r❡✳ ■♥ t❤❡ ❝❛s❡ ♦❢ t❤❡ ✻❍ ♣❡r♦✈s❦✐t❡s✱ ❜❡s✐❞❡s t♦ t❤❡ ✉s✉❛❧ ♦❜s❡r✈❛t✐♦♥ ♦❢ t❡♠♣❡r❛t✉r❡ ❞❡♣❡♥❞❡♥❝❡ ♦❢ t❤❡ ♣❤♦♥♦♥ s♣❡❝tr❛✱ ✇❤✐❝❤ ♣r♦✈✐❞❡s ❡✈✐❞❡♥❝❡s ♦❢ t❤❡ tr❛♥s✐t✐♦♥ ♦❢ ❛ ❤❡①❛❣♦♥❛❧ t♦ ♠♦♥♦✲ ❝❧✐♥✐❝ ♣❤❛s❡ ❛t ✶✹✵ ❑ ✐♥ t❤❡ ❇❛3▼❣❙❜2❖9 ✭❇▼❙✮ ❛♥❞ ♦❢ ❛ ♠♦♥♦❝❧✐♥✐❝ t♦ tr✐❝❧✐♥✐❝ ♣❤❛s❡ ❛t
✷✹✵ ❑ ✐♥ t❤❡ ❇❛3❈❛❙❜2❖9 ✭❇❈❙✮✱ ✇❡ ❝❧❛ss✐❢② t❤❡ ♣❤♦♥♦♥s ♦❢ t❤❡ t❤r❡❡ ❝♦♠♣♦✉♥❞s ✉s✐♥❣
t✇♦ ♠❡t❤♦❞s✳ ❋✐rst ✇❡ ❛♣♣❧✐❡❞ t❤❡ ❍❛rtr❡❡✲❋♦❝❦ ❛❜✲✐♥✐t✐♦ ♠❡t❤♦❞ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ♥♦r♠❛❧ ♠♦❞❡s ♦❢ t❤❡ ❙❜2❖9 ❞✐♠❡r❀ ❛♥❞ ❛ss✉♠✐♥❣ t❤❛t t❤❡ ✉♥✐t ❝❡❧❧ ♦❢ ❇▼❙ ✐s ❝♦♥st✐t✉t❡❞ ♦❢ ❙❜2❖9
❞✐♠❡rs ❛♥❞ ✐s♦❧❛t❡❞ ✐♦♥s ♦❢ ❇❛ ❛♥❞ ▼❣✱ ✇❡ ❝♦rr❡❧❛t❡✱ ✉s✐♥❣ ❣r♦✉♣ t❤❡♦r② ♠❡t❤♦❞s✱ t❤❡ ❝❛❧❝✉❧❛t❡❞ ♠♦❞❡s ♦❢ ❙❜2❖9 ✇✐t❤ t❤❡ ✐♥t❡r♥❛❧ ♠♦❞❡s ♦❢ ❇▼❙✳ ▲❛t❡r ✇❡ ✉s❡❞ t❤❡ ❋● ❲✐❧s♦♥
♠❡t❤♦❞ t♦ ❝♦♥✜r♠ t❤❡ ♣r❡✈✐♦✉s r❡s✉❧ts✱ ❜❡✐♥❣ ♦❜t❛✐♥❡❞ ❛ ❣♦♦❞ ❛❣r❡❡♠❡♥t ❜❡t✇❡❡♥ t❤❡ t✇♦ ♠❡t❤♦❞s✳
❑❡②✇♦r❞s✿ ❘❛♠❛♥ s❝❛tt❡r✐♥❣✱ ■♥❢r❛r❡❞✱ ♣❡r♦✈s❦✐t❡s✱ ♠✉❧t✐❢❡rr♦✐❝s✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ♣✳ ✐①
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ♣✳ ①✈✐✐✐
✶ ■♥tr♦❞✉çã♦ ♣✳ ✶
✶✳✶ P❡r♦✈s❦✐t❛s P♦❧✐tí♣✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶ ✶✳✷ ▼✉❧t✐❢❡rró✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼ ✶✳✷✳✶ P❡r♦✈s❦✐t❛s ♠✉❧t✐❢❡rró✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶ ✶✳✷✳✷ ❉✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ♠✉❧t✐❢❡rró✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷ ✶✳✷✳✷✳✶ ▼✉❧t✐❢❡rró✐❝♦s ❞♦ t✐♣♦ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷ ✶✳✷✳✷✳✷ ▼✉❧t✐❢❡rró✐❝♦s ❞♦ t✐♣♦ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✹ ✶✳✷✳✸ P❜❋❡1/2 ◆❜1/2❖3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✻
✶✳✷✳✹ ❖❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹ ✶✳✸ P❡r♦✈s❦✐t❛s ✻❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹ ✶✳✸✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✸
✷ ▼❛t❡r✐❛✐s ❡ ▼ét♦❞♦s ♣✳ ✸✹
✷✳✸✳✶ ❈♦♥❢❡❝çã♦ ❞❡ ♣❛st✐❧❤❛s ♣❛r❛ ♠❡❞✐❞❛s ❞❡ ❛❜s♦rçã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✶ ✷✳✸✳✷ ■♥s❡rçã♦ ❞❡ ✉♠❛ ❛t♠♦s❢❡r❛ ❞❡ ♥✐tr♦❣ê♥✐♦ ♥♦ ❡s♣❡❝trô♠❡tr♦ ❞❡
✐♥❢r❛✈❡r♠❡❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻
✸ ◆✐♦❜❛t♦ ❞❡ ❋❡rr♦ ❡ ❈❤✉♠❜♦ ♣✳ ✹✾
✸✳✶ ❊str✉t✉r❛s ❞♦ P❋◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾ ✸✳✷ ❊s♣❡❝tr♦s❝♦♣✐❛ ❞❡ ✐♠♣❡❞â♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✹ ✸✳✷✳✶ ❊s♣❡❝tr♦ ✈✐❜r❛❝✐♦♥❛❧ à t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼ ✸✳✸ ❊s♣❡❝tr♦ ✈✐❜r❛❝✐♦♥❛❧ ✈❛r✐❛♥❞♦ ❛ t❡♠♣❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✷
✹ P❡r♦✈s❦✐t❛s ✻❍✿ ❇❛3❇2+❙❜ 5+
2 ❖9 ✭❇ ❂ ▼❣✱ ❈❛ ❡ ❙r✮ ♣✳ ✼✸
✹✳✶ ❊str✉t✉r❛s ❝r✐st❛❧✐♥❛s ❡ t❡♦r✐❛ ❞❡ ❣r✉♣♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✸ ✹✳✶✳✵✳✶ ❊str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❞♦ ❇▼❙ ❡ ❛♥á❧✐s❡ ❞❛ t❡♦r✐❛ ❞❡ ❣r✉♣♦s ♣✳ ✼✻ ✹✳✶✳✵✳✷ ❊str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❞♦ ❇❈❙ ❡ ❛♥á❧✐s❡ ❞❛ t❡♦r✐❛ ❞❡ ❣r✉♣♦s ♣✳ ✽✵ ✹✳✶✳✵✳✸ ❊str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❞♦ ❇❙❙ ❡ ❛♥á❧✐s❡ ❞❛ t❡♦r✐❛ ❞❡ ❣r✉♣♦s ♣✳ ✽✷ ✹✳✶✳✶ ❈♦rr❡❧❛çã♦ ❡♥tr❡ ❛s ❢❛s❡s ❤❡①❛❣♦♥❛❧✱ ♠♦♥♦❝❧í♥✐❝❛ ❡ tr✐❝❧í♥✐❝❛ ✳ ✳ ♣✳ ✽✻ ✹✳✷ ❊s♣❡❝tr♦ ❞❡ ❢ô♥♦♥s ❞❛s ♣❡r♦✈s❦✐t❛s ✻❍ à t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡ ✳ ✳ ✳ ✳ ♣✳ ✽✾ ✹✳✷✳✶ ❈á❧❝✉❧♦ ❛❜ ✐♥✐t✐♦ ❞❛s ✈✐❜r❛çõ❡s ❞♦ ❞í♠❡r♦ ❙❜2❖9 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾ ✹
✹✳✷✳✷ ❈á❧❝✉❧♦ ❞♦s ❢ô♥♦♥s ❞❛ ♣❡r♦✈s❦✐t❛ ❇❛3▼❣❙❜2❖9 ✉s❛♥❞♦ ♦ ♠ét♦❞♦
●❋ ❞❡ ❲✐❧s♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾ ✾ ✹✳✸ ❉❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ❡s♣❡❝tr♦ ❞❡ ❢ô♥♦♥s ❞❛s ♣❡r♦✈s❦✐t❛s ✻❍♣✳ ✶✵✼
✺ ❈♦♥❝❧✉sõ❡s ♣✳ ✶✶✹
❆♣ê♥❞✐❝❡ ❆ ✲✲ ❉✐str✐❜✉✐çã♦ ❞♦s ♠♦❞♦s ❞❡ ✈✐❜r❛çã♦ ❞♦ ❞í♠❡r♦ ❙❜2❖9 ♣✳ ✶✶✼
❆♣ê♥❞✐❝❡ ❇ ✲✲ Pr♦❥❡t♦ ♣❛r❛ ✉s✐♥❛❣❡♠ ❞♦ ♣❛st✐❧❤❛❞♦r ❞❡ ❛❧t❛ t❡♠♣❡r❛✲
t✉r❛ ♣✳ ✶✷✵
❘❡❢❡rê♥❝✐❛s ♣✳ ✶✷✷
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶ ❈é❧✉❧❛ ✉♥✐tár✐❛ ❞❛ ❡str✉t✉r❛ ♣❡r♦✈s❦✐t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶ ✷ ❊♠♣✐❧❤❛♠❡♥t♦ ❞❡ ❡s❢❡r❛s s♦❜r❡ ❛ ❝❛♠❛❞❛ ❆✱ q✉❡ s❡❣✉❡ ♦ ♣❛❞rã♦ ❞❡ ✉♠
♣♦❧✐❡❞r♦ ❤❡①❛❣♦♥❛❧ ✭❛✮✳ ❆ ❝❛♠❛❞❛ ❇ é ❡♠♣✐❧❤❛❞❛ s♦❜r❡ ♦s ❜✉r❛❝♦s ❞❛ ❝❛♠❛❞❛ ❆ ❡ ❛ ❝❛♠❛❞❛ ❈ ♣♦❞❡ s❡r ❡♠♣✐❧❤❛❞❛ s♦❜r❡ ♦s ❜✉r❛❝♦s ❞❛ ❝❛♠❛❞❛ ❆ q✉❡ ♥ã♦ ❢♦r❛♠ ♣r❡❡♥❝❤✐❞♦s ♣❡❧❛ ❝❛♠❛❞❛ ❇ ✭❜✮ ✕ ❡♠♣❛❝♦t❛♠❡♥t♦ ❝ú❜✐❝♦ ✕ ♦✉ s❡r ❡♠♣✐❧❤❛❞❛ s♦❜r❡ ❛s ❡s❢❡r❛s ❞❛ ❝❛♠❛❞❛ ❆ ✭❝✮ ✕ ❡♠♣❛❝♦t❛♠❡♥t♦
❤❡①❛❣♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷ ✸ ❋♦r♠❛s ❞❡ ❧✐❣❛çã♦ ❞♦s ♦❝t❛❡❞r♦s ♥❛s ♣❡r♦✈s❦✐t❛s ♣♦❧✐tí♣✐❝❛s✿ ✭❛✮ ✸❈❀ ✭❜✮
✷❍❀✭❝✮ ✻❍❀✭❞✮ ✹❍ ❡ ✭❡✮ ✾❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸ ✹ P♦ssí✈❡✐s t✐♣♦s ❞❡ s✉❜st✐t✉✐çõ❡s ♥❛ ❡str✉t✉r❛ ♣❡r♦✈s❦✐t❛ ❞♦ ❝♦♠♣♦st♦
❇❛❚✐❖3✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✹✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹
✺ P♦❧✐♠♦r❢♦s ❝r✐st❛❧✐♥♦s ❞♦ t✐t❛♥❛t♦ ❞❡ ❜ár✐♦✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛
✭✽✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻ ✻ ❈♦♥st❛♥t❡ ✭❛✮ ❡ ♣❡r❞❛ ✭❜✮ ❞✐❡❧étr✐❝❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛
❛♠♦str❛ ❡st❡q✉✐♦♠étr✐❝❛ ❞❡ ❤✲❇❛❚✐❖3 ✭✻❍✲❇❛❚✐❖3✮✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛
r❡❢❡rê♥❝✐❛ ✭✷✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻ ✼ ❈♦♥st❛♥t❡ ✭❛✮ ❡ ♣❡r❞❛ ✭❜✮ ❞✐❡❧étr✐❝❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛
❛♠♦str❛ ♥ã♦✲❡st❡q✉✐♦♠étr✐❝❛ ❞❡ ❤✲❇❛❚✐❖3 ✭✻❍✲❇❛❚✐❖3✮ ❝♦♠ ❞✐❢❡r❡♥t❡s
❡s♣❡ss✉r❛s✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✷✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼ ✽ ❈✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❢❡rró✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽ ✾ ❊♠ ✉♠ ♠✉❧t✐❢❡rró✐❝♦ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ✭❊✮✱ ♠❛❣♥ét✐❝♦ ✭❍✮ ❡ str❡ss ✭σ✮
♣♦❞❡♠ ❝♦♥tr♦❧❛r ❛ ♣♦❧❛r✐③❛çã♦ ✭P✮✱ ❛ ♠❛❣♥❡t✐③❛çã♦ ✭▼✮ ♦✉ ♦ str❛✐♥ ✭❡✮✳
❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✸✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾ ✶✵ ❖r❞❡♠ ❞❡ ❞✐♣♦❧♦s ♠❛❣♥ét✐❝♦s ❡♠ ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s✳ ❋✐❣✉r❛ ❡①tr❛í❞❛
✶✶ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣✉❜❧✐❝❛çõ❡s ♣♦r ❛♥♦ ♣❡sq✉✐s❛❞❛s ❝♦♠ ❛ ♣❛❧❛✈r❛✲❝❤❛✈❡
✬♠❛❣♥❡t♦❡❧étr✐❝♦✬ ♥❛ ❲❡❜ ♦❢ ❙❝✐❡♥❝❡✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✸✻✮ ♣✳ ✶✶ ✶✷ ❉✐❢❡r❡♥t❡s ♠❡❝❛♥✐s♠♦ ♠✐❝r♦s❝ó♣✐❝♦s q✉❡ ❞✐❢❡r❡♥❝✐❛♠ ♦s s✉❜❣r✉♣♦s ❞♦s
♠✉❧t✐❢❡rró✐❝♦s ❞♦ t✐♣♦ ■✿ ✭❛✮ ♣❡r♦✈s❦✐t❛s ❝♦♠ ❢❡rr♦❡❧❡tr✐❝✐❞❛❞❡ ✐♥❞✉③✐❞❛ ♣♦r í♦♥s ❞0 ✭s❡t❛s ✈❡r❞❡s✮ ❡ ♦r❞❡♠ ♠❛❣♥ét✐❝❛ ♣♦r í♦♥s ❞n ✭s❡t❛s ✈❡r♠❡✲ ❧❤❛s✮✳ ✭❜✮❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ♣❛r ❞❡ ❡❧étr♦♥s s♦❧✐tár✐♦s ❡♠ q✉❡ ❛t✐✈❛♠ ✉♠ ♠♦♠❡♥t♦ ❞❡ ❞✐♣♦❧♦ ♥♦ í♦♥ ❞❡ ❇✐ ♥♦ sít✐♦ ❆ ❞❛s ♣❡r♦✈s❦✐t❛s✳ ✭❝✮ ❊♠ s✐st❡♠❛s ❝♦♠ ♦r❞❡♥❛♠❡♥t♦ ❞❡ ❝❛r❣❛ ❛ ❝♦❡①✐stê♥❝✐❛ ❞❡ sít✐♦s ♥ã♦ ❡q✉✐✈❛✲ ❧❡♥t❡s ❝♦♠ ❞✐❢❡r❡♥t❡s ❝❛r❣❛s ❡ ❧✐❣❛çõ❡s ♥ã♦ ❡q✉✐✈❛❧❡♥t❡s✱ ✐♥❞✉③ ❛ ❢❡rr♦❡✲ ❧❡tr✐❝✐❞❛❞❡✳ ✭❞✮❆ ❞✐st♦rçã♦ ❞♦ ♣r✐s♠❛ ❜✐♣✐r❛♠✐❞❛❧ ❛♣r♦①✐♠❛ ♦s í♦♥s ❞❡ ♦①✐❣ê♥✐♦s ❞♦s í♦♥s ❞❡ ítr✐♦ ❣❡r❛♥❞♦ ❞✐♣♦❧♦s ✭s❡t❛s ✈❡r❞❡s✮ ♥♦ ❝♦♠♣♦st♦ ❨▼♥❖3 ♣♦r ✉♠ ♠❡❝❛♥✐s♠♦ ✧❣❡♦♠étr✐❝♦✧✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛
✭✹✼✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✹ ✶✸ ❖♥❞❛ s✐♥✉s♦✐❞❛❧ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ s♣✐♥s q✉❡ ✭❛✮♥ã♦ ✐♥❞✉③ ♣♦❧❛r✐③❛çã♦ ❡❧é✲
tr✐❝❛ ✉♥✐❢♦r♠❡ ✭❜✮P é ♦rt♦❣♦♥❛❧ ❛♦ ❡✐①♦ ❡3 ❞❡ r♦t❛çã♦ ❞❡ s♣✐♥ ❡ ❛♦ ✈❡t♦r
❞❡ ♦♥❞❛ ◗✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❡ ♠♦❞✐✜❝❛❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✺✻✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✺ ✶✹ ❖♥❞❛ s✐♥✉s♦✐❞❛❧ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ s♣✐♥s✱ ❡♠ q✉❡ ♦s s♣✐♥s ❛♣♦♥t❛♠ ❡♠ ✉♠❛
❞✐r❡çã♦ ♠❛s ✈❛r✐❛s ❡♠ ♠❛❣♥✐t✉❞❡✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✹✼✮✳ ✳ ♣✳ ✶✺ ✶✺ ✭❛✮❞✉❛s ❢♦r♠❛s ❞❡ ❝♦♠❜✐♥❛r ❛ ♦r❞❡♠ ♠❛❣♥ét✐❝❛ ✉♣✲✉♣✲❞♦✇♥✲❞♦✇♥ ❝♦♠
❛ ♦r❞❡♠ ❞❛s ❝❛r❣❛s ✐ô♥✐❝❛s✳ ❆s ♣♦s✐çõ❡s ❛tô♠✐❝❛s ♥❛ ❝❛❞❡✐❛ ♥ã♦ ❞✐st♦r✲ ❝✐❞❛ sã♦ ♠♦str❛❞❛s ❝♦♠ ❝ír❝✉❧♦s tr❛❝❡❥❛❞♦s✳ ✭❜✱❝✮❊str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❞♦
❈❛3❈♦▼♥❖6✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✻✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✻
✶✻ ▼❡❝❛♥✐s♠♦ ❞❡ s✉♣❡rtr♦❝❛ ❡♠ ❋❡❖✳ ❋✐❣✉r❛ ♠♦❞✐✜❝❛❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✸✽✮✳ ♣✳ ✶✼ ✶✼ ❊str✉t✉r❛s ♠❛❣♥ét✐❝❛s ❝♦♠ s❡✉s r❡s♣❡❝t✐✈♦s rót✉❧♦s✳ ❖s s✐♥❛✐s ❞❡ ✧+✧❡
✧−✧r❡♣r❡s❡♥t❛♠ ♣r♦❥❡çõ❡s ♥♦ ❡✐①♦ ❝ ❞❡ s♣✐♥s ✉♣ ❡ ❞♦✇♥✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✼✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✼ ✶✽ ❈✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❞❡ ✉♠❛ ❛♠♦str❛ ❝❡râ♠✐❝❛ ❞❡ P❋◆✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛
r❡❢❡rê♥❝✐❛ ✭✻✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽ ✶✾ ✭❛✮ P❛rt❡ r❡❛❧ ❞❛ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛❀ ✭❜✮
❆ ❞❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ❢❛t♦r ❞❡ ♣❡r❞❛ ❞✐❡❧étr✐❝❛✳ ❋✐❣✉r❛
❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✻✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✾
✷✵ ❉❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞❛ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ✭❛✮ ❡ ❞♦ ❢❛t♦r ❞❡
♣❡r❞❛ ✭❜✮ ❡♠ ❞✐❢❡r❡♥t❡s ❢r❡q✉ê♥❝✐❛s✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✼✺✮✳ ♣✳ ✷✶ ✷✶✭❛✮ ❈♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ❡♠ ✶✵4 ❍③ ❡ s✉❛ ❡①tr❛♣♦❧❛çã♦ ❞♦ ❡st❛❞♦ ♣❛r❛✲
♠❛❣♥ét✐❝♦✳ ✭❜✮ ❘❡❧❛çã♦ ❡♥tr❡ δε ❡ M2✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛
✭✼✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶ ✷✷ Pr♦❥❡çã♦ ❁✶✶✶❃ ❞♦s ❝❧✉st❡rs ❛♥t✐❢❡rr♦♠❛❣♥ét✐❝♦s ❞❡ s♣✐♥s ❞❡ ❋❡3+✱ ✈✐st♦s
♥❛ s❡çã♦ ✭✵✵✶✮ ❡♠ ❞✐❢❡r❡♥t❡s ❡s❝❛❧❛s✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✽✶✮✳ ♣✳ ✷✷ ✷✸ ❙✉s❝❡t✐❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ✭▼✴❍✮ ❡ ❛ ❞❡r✐✈❛❞❛ ❞❛ s✉s❝❡t✐❜✐❧✐❞❛❞❡ ♠✉❧✲
t✐♣❧✐❝❛❞❛ ♣❡❧❛ t❡♠♣❡r❛t✉r❛ ✭❞✭▼❚✴❍✮✴❞t✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✳
❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✽✻✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸ ✷✹ ❊sq✉❡♠❛ ❡str✉t✉r❛❧ ❞❛ ♣❡r♦✈s❦✐t❛s ✻❍ ❞♦ ❣r✉♣♦ ■✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛
r❡❢❡rê♥❝✐❛ ✭✾✷✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹ ✷✺ ❊str✉t✉r❛ ♠❛❣♥ét✐❝❛ ❞♦ ❇❛3❈♦❙❜2❖9 ❡ ❇❛3▼♥❙❜2❖9✿ ✭❛✮ ❝é❧✉❧❛ ✉♥✐tár✐❛
♠❛❣♥ét✐❝❛ ♥♦ ♣❧❛♥♦ ❛❜✱ ❝♦♠ ♦s í♦♥s ❞✐❛♠❛❣♥ét✐❝♦s ♦♠✐t✐❞♦s❀ ✭❜✮ ❞✐r❡çã♦ ❞♦s ♠♦♠❡♥t♦s ♠❛❣♥ét✐❝♦s ❈♦2+ ❡ ▼♥2+✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛
✭✾✷✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✺ ✷✻ ❱✐st❛ ♣❧❛♥❛r ❞❛ ❞✐❢❡r❡♥ç❛ ❞❛s ❝é❧✉❧❛s ✉♥✐tár✐❛s ❤❡①❛❣♦♥❛❧✱ ♠♦♥♦❝❧í♥✐❝❛ ❡
♠❛❣♥ét✐❝❛✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✾✷✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✻ ✷✼ ❉✐❢r❛t♦❣r❛♠❛s ❞❡ r❛✐♦s ① ❡♠ ✷✾✺ ❑ ♣❛r❛ ♦s ♣♦❧✐t✐♣♦s ❞❡ ❇❛3◆✐❙❜2❖9✿ ✭❛✮
✻❍✲❆✱ ✭❜✮ ✻❍✲❇ ❡ ✭❝✮ ✸❈✳ ❊sq✉❡♠❛ ❡str✉t✉r❛❧ ❞♦s ♣♦❧✐t✐♣♦s ❞❡ ❇❛3◆✐❙❜2❖9✿
✭❞✮ ✻❍✲❆✱ ✭❡✮ ✻❍✲❇ ❡ ✭❢✮ ✸❈✳ ❘❡❞❡ ♠❛❣♥ét✐❝❛ ❢♦r♠❛❞❛ ♣♦r í♦♥s ❞❡ ◆✐2+
♣❛r❛ ♦s ♣♦❧✐t✐♣♦s ❞❡ ❇❛3◆✐❙❜2❖9✿ ✭❣✮ ✻❍✲❆✱ ✭❤✮ ✻❍✲❇ ❡ ✭✐✮ ✸❈✳ ❋✐❣✉r❛
❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✾✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✼ ✷✽ ❉❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞❛ ✭❛✮ s✉s❝❡t✐❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ✭χ✮ ❞❝✱
♠♦str❛♥❞♦ ♦ ❛❥✉st❡ ♣♦r ❈✉r✐❡✲❲❡✐ss ♠♦❞✐✜❝❛❞♦ ♣❛r❛ t❡♠♣❡r❛t✉r❛s ❛❝✐♠❛ ❞❡ ❚∗ =✼✹ ❑ ✭❧✐♥❤❛ ❛③✉❧✮ ❡ ♣♦r ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ s♣✐♥✲❣❛♣ ✭❧✐♥❤❛ ✈❡r✲
♠❡❧❤❛✮ ❛❜❛✐①♦ ❞❡ ❚∗✱ ❞❡❝♦♠♣♦st❛ ♥♦ ✐♥s❡t ♣❛r❛ s❡♣❛r❛r ❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡
s♣✐♥✲❣❛♣ ✭❧✐♥❤❛ ❛③✉❧✮ ❞❛ ❝❛❧❞❛ ♣❛r❛♠❛❣♥ét✐❝❛ ✭❧✐♥❤❛ ✈❡r❞❡✮❀ ✭❜✮ ❝❛♣❛❝✐✲ ❞❛❞❡ tér♠✐❝❛ s♦❜r❡ t❡♠♣❡r❛t✉r❛❀ ❡ ✭❝✮ r❡s✐st✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ρ❥✉♥t❛♠❡♥t❡
❝♦♠ ♦ ❛❥✉st❡✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✾✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✵
✷✾ ▼❡❞✐❞❛s ❞❛ s✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❥✉♥✲ t❛♠❡♥t❡ ❝♦♠ ♦ ❛❥✉st❡ ❞❛ ❝✉r✈❛ ♣❛r❛ ❛❧t❛ t❡♠♣❡r❛t✉r❛ ✭❧✐♥❤❛ ✈❡r♠❡❧❤❛✮ ❡ ❜❛✐①❛ t❡♠♣❡r❛t✉r❛ ✭❧✐♥❤❛ ❛③✉❧✮✳❖ ✐♥s❡t ✐♥❢❡r✐♦r ❞✐r❡✐t♦ ♠♦str❛ ❛ ❞❡♣❡♥✲ ❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞❛ ❞❡r✐✈❛❞❛ dχ/dT✳❖ ✐♥s❡t s✉♣❡r✐♦r ❡sq✉❡r❞♦
❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ ♠❛❣♥ét✐❝❛ ❝♦♠ ♦s ♣r✐♠❡✐r♦s ✭J0✱ ♥♦ ❞í♠❡r♦✮ ❡ s❡✲
❣✉♥❞♦s ✭Ji✱ i= 1, ...,5✮ ✈✐③✐♥❤♦s✳❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✾✻✮✳ ✳✳ ♣✳✸✶ ✸✵ ❉❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ✭❛✮ ✈♦❧✉♠❡ ❞❛ ❝é❧✉❧❛ ✉♥✐tár✐❛✱ ✭❜✮
♣❛râ♠❡tr♦ ❞❡ r❡❞❡ a✱ b/√3❡ ❝✱ ✭❝✮ ❞✐stâ♥❝✐❛ ■r✲■r ✐♥tr❛✲❞í♠❡r♦ ❡ â♥❣✉❧♦ ♠é❞✐♦ ❞❛ ❧✐❣❛çã♦ ■r✲❖✲■r ❡ ✭❞✮ s♦♠❛s ❞❛s ❧✐❣❛çõ❡s ❞❡ ✈❛❧ê♥❝✐❛ ✭❇❱❙✮ ♣❛r❛
♦ ■r ❡ ❇✐ ♥♦ ❇❛3❇✐■r2❖9✳❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✾✺✮✳✳✳✳✳✳✳✳ ♣✳✸✶
✸✶ ❉❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ✭❛✮ ✈♦❧✉♠❡ ❞❛ ❝é❧✉❧❛ ✉♥✐tár✐❛✱ ✭❜✮ ♣❛râ♠❡tr♦ ❞❡ r❡❞❡a✱b/√3❡ ❝✱ ✭❝✮ ❞✐stâ♥❝✐❛ ✐♥tr❛✲❞í♠❡r♦ dRu−Ru❡ ✭❞✮ s♦✲ ♠❛s ❞❛s ❧✐❣❛çõ❡s ❞❡ ✈❛❧ê♥❝✐❛ ✭❇❱❙✮ ✭✶✵✵✮ ♣❛r❛ ♦ ❘✉ ❡ ❇✐ ♥♦ ❇❛3❇✐❘✉2❖9✳
❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✾✻✮✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳ ♣✳✸✷ ✸✷ ❉✐❢r❛t♦❣r❛♠❛ ♦❜t✐❞♦ ♣❛r❛ ❛ ❛♠♦str❛ ❞❡ P❋◆✱ s✐♥t❡r✐③❛❞♦ ♣❡❧♦ ♠ét♦❞♦
❝♦♥✈❡♥❝✐♦♥❛❧✳❖ ❛st❡r✐s❝♦ ❞❡st❛❝❛ ♦ ♣✐❝♦ ❝♦rr❡❧❛❝✐♦♥❛❞♦ à ❢❛s❡ ♣✐r♦❝❧♦r♦✳
❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✶✶✮ ✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳ ♣✳✸✺ ✸✸ ❉✐❢r❛t♦❣r❛♠❛ ✉t✐❧✐③❛♥❞♦ r❛❞✐❛çã♦ sí♥❝r♦tr♦♥ ♦❜t✐❞♦ ♣❛r❛ ❛♠♦str❛s ❞❡
❇❛3❈❛❙❜2❖9✭❇❈❙✮ ❝♦♠λ❂ ✶✱✶✽✷✸ ➴✳❖s ♠❛r❝❛❞♦r❡s ❞❡ r❡✢❡①ã♦ r❡❢❡r❡♠✲
s❡ ❛♦ ❇❈❙ ✭♣❛rt❡ ✐♥❢❡r✐♦r✮✱ à ✐♠♣✉r❡③❛ t✐♣♦ ❇❛2❨◆❜❖6 ✭♣❛rt❡ ❝❡♥tr❛❧✮ ❡
à ✐♠♣✉r❡③❛ ❞❡ ❈❛❖ ✭♣❛rt❡ s✉♣❡r✐♦r✮✳❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✵✹✮ ♣✳✸✻ ✸✹ ❉✐❢r❛t♦❣r❛♠❛ ❞❡ ♥ê✉tr♦♥s ❞♦ ❇❙❙ ♦❜s❡r✈❛❞♦ ✭❝r✉③❡s✮✱ ❝❛❧❝✉❧❛❞♦ ✭❧✐♥❤❛
❝♦♥tí♥✉❛✮ ❡ ❛ ❞✐❢❡r❡♥ç❛ ✭✜❣✉r❛ ❛❜❛✐①♦✮ ❝♦♠ λ ❂ ✶✱✺✾✼✷ ➴✳❋✐❣✉r❛ ♦❜t✐❞❛
❞❛ r❡❢❡rê♥❝✐❛ ✭✶✵✹✮ ✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳ ♣✳✸✼ ✸✺ ❊sq✉❡♠❛ ❞❡ ❈♦♥✜❣✉r❛çã♦ ❞♦ ❊s♣❡❝trô♠❡tr♦ ❏♦❜✐♥✲❨✈♦♥ ♠♦❞❡❧♦ ❚✻✹✵✵✵ ♣✳✸✽ ✸✻ ❉✐❛❣r❛♠❛ ❞❡ ✐♥st❛❧❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❝♦♥tr♦❧❡ ♣❛r❛ ❛s ♠❡❞✐❞❛s ❘❛♠❛♥
❡♠ ❛❧t❛ t❡♠♣❡r❛t✉r❛ ✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳ ♣✳✹✵ ✸✼ Pr♦❥❡t♦ ❞❛ ♣❧❛❝❛ ❞❡ ❝✐r❝✉✐t♦ ❞♦ r❡❣✉❧❛❞♦r ❞❡ t❡♥sã♦ ✳✳✳✳✳✳✳✳✳✳✳ ♣✳✹✵ ✸✽ ❈❛♠✐♥❤♦ ót✐❝♦ ♥♦ ❡s♣❡❝trô♠❡tr♦ ❞❡ ✐♥❢r❛✈❡r♠❡❧❤♦ ❱❡rt❡① ✼✵ ✳✳✳✳✳✳ ♣✳✹✶ ✸✾ ❍♦♠♦❣❡♥❡✐③❛çã♦ ❞❛ ♠✐st✉r❛ ♥♦ ❣r❛❧✳ ✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳✳ ♣✳✹✷ ✹✵ ❆ ✐♠❛❣❡♠ ❞❛ ❡sq✉❡r❞❛ ♠♦str❛ ♦ ♣r❡❡♥❝❤✐♠❡♥t♦ ❞♦ ♣❛st✐❧❤❛❞♦r ❡ ❛ ✐♠❛✲
✹✶ ❆ ❢♦t♦ ❞❛ ❡sq✉❡r❞❛ ♠♦str❛ ♦ ♣❛st✐❧❤❛❞♦r ❝♦♠❡r❝✐❛❧ ✭♣❛rt❡ s✉♣❡r✐♦r✮ ❡ ♦ ❞❡ ❢❛❜r✐❝❛çã♦ ♣ró♣r✐❛ ✭♣❛rt❡ ✐♥❢❡r✐♦r✮✱ ♥❛ ✜❣✉r❛ ❝❡♥tr❛❧ ❛ ♣ré✲❢♦r♠❛ ❥á ❡♥❝♦♥tr❛✲s❡ ❛❝♦♠♦❞❛❞❛ ♥♦ ♥✐❝❤♦ ❝❡♥tr❛❧✱ ❡ ♥❛ ✜❣✉r❛ ❞❛ ❞✐r❡✐t❛ ♦❜s❡r✈❛✲s❡
❛ ❝♦❧♦❝❛çã♦ ❞♦s ♣❛r❛❢✉s♦s ♥♦ ♣❛st✐❧❤❛❞♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✸ ✹✷ ❖ ♣❛st✐❧❤❛❞♦r ❡♥❝♦♥tr❛✲s❡ ❡♠ ✉♠ ❢♦r♥♦ ♣r❡❛q✉❡❝✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✸ ✹✸ ▼❡❞✐❞❛ ❞❡ ❚❡r♠♦❣r❛✈✐♠❡tr✐❛ ✭❚●✮ ❡ ❝❛❧♦r✐♠❡tr✐❛ ❡①♣❧♦r❛tór✐❛ ❞✐❢❡r❡♥❝✐❛❧
✭❉❙❈✮✱ ♠♦str❛♥❞♦ ♦ ♣♦♥t♦ ❞❡ ❢✉sã♦ ✭♣✐❝♦ ❞❛ ❧✐♥❤❛ ❛③✉❧ ❝♦♥tí♥✉❛✮ ❞♦
P❊❆❉✱ ✉t✐❧✐③❛❞♦ ❝♦♠♦ ♠❛tr✐③ ❞✐s♣❡rs✐✈❛✱ ❡♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✶✸✺o❈✳ ✳ ♣✳ ✹✹ ✹✹ ❆ ✐♠❛❣❡♠ ❞❛ ❡sq✉❡r❞❛ ♠♦str❛ ♦ ♣❛st✐❧❤❛❞♦r r❡❝é♠ r❡t✐r❛❞♦ ❞♦ ❢♦r♥♦ ❡
♥❛ ✜❣✉r❛ ❞❛ ❞✐r❡✐t❛ ♦ r❡❛♣❡rt♦ ❞♦s ♣❛r❛❢✉s♦s ❛♣ós ✜①❛r ♦ ♣❛st✐❧❤❛❞♦r✳ ✳ ♣✳ ✹✹ ✹✺ ❊♠ s❡q✉ê♥❝✐❛ ❛s ✐♠❛❣❡♥s ♠♦str❛♠ ♦ ♣❛st✐❧❤❛❞♦r ❥á ❞❡s♠♦♥t❛❞♦ ❡ ❛ ❛r✲
r✉❡❧❛ ❝❡♥tr❛❧ ❝♦♠ ✉♠❛ ♣❛st✐❧❤❛ ♣r♦♥t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✺ ✹✻ P❛st✐❧❤❛s ❞❡ P❊❆❉ ♠❛✐s ❛♠♦str❛s ❞❡ P❋◆✱ ❇▼❙✱ ❇❈❙ ❡ ❇❙❙ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✺ ✹✼ ❊s♣❡❝tr♦s ❞❡ ❛❜s♦r❜â♥❝✐❛ ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦ ❞♦ ♣♦❧✐❡t✐❧❡♥♦ ❞❡ ❛❧t❛ ❞❡♥s✐✲
❞❛❞❡ ✭P❊❆❉✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻ ✹✽ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛ ❛❜s♦rçã♦ ❞❛ ♠❛tr✐③ ♣♦❧✐♠ér✐❝❛ ❡ ❞♦ ❇▼❙✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻ ✹✾ ❙✐st❡♠❛ ❞❡ ♣✉r❣❛ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❡❧✐♠✐♥❛r ❛ ❤✉♠✐❞❛❞❡ ✐♥t❡r♥❛ ❞♦ ❡s♣❡❝✲
trô♠❡tr♦ ❞❡ ✐♥❢r❛✈❡r♠❡❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼ ✺✵ P❡r✜❧ ❞❛ ❡✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞❛ ❛❜s♦rçã♦ s♦❜r❡ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ✷✵✸ ❝♠−1✳ ♣✳ ✹✽
✺✶ P❛râ♠❡tr♦s ❞❡ r❡❞❡ ❞♦ P❋◆ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✱ ❝♦♠ Te2 ❡ Te1
s❡♥❞♦ ❛ tr❛♥s✐çã♦ ❞❛ ❢❛s❡ ❝ú❜✐❝❛ ♣❛r❛ ❛ ❢❛s❡ t❡tr❛❣♦♥❛❧ ❡ ❞❛ t❡tr❛❣♦♥❛❧ ♣❛r❛ ❛ ♠♦♥♦❝❧í♥✐❝❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ ❛♥♦♠❛❧✐❛ Ta❢♦✐ ❛ss♦❝✐❛❞❛ ❛ ✉♠❛ r❡❣✐ã♦ ❞❡ ❝♦❡①✐stê♥❝✐❛ ❞❡ ✈ár✐♦s ❞♦♠í♥✐♦s ♦r✐❡♥t❛❝✐♦♥❛✐s✳ ❋✐❣✉r❛ ❡①tr❛í❞❛
❞❛ r❡❢❡rê♥❝✐❛ ✭✻✼✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✵ ✺✷ ❉✐❢❡r❡♥t❡s ♣r♦❥❡çõ❡s ❞❛s ♠♦❞✐✜❝❛çõ❡s ❡str✉t✉r❛✐s s♦❢r✐❞❛s ♣❡❧♦ P❋◆✳ ❋✐✲
❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✶✼✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✶ ✺✸ ❉❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦s ♣❛râ♠❡tr♦s ❞❡ r❡❞❡ ❡ ✈♦❧✉♠❡ ❞♦
P❋◆✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✶✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸ ✺✹ ❊sq✉❡♠❛ ❞❡s❝r❡✈❡♥❞♦ ♦r❞❡♥s ♠❛❣♥ét✐❝❛✱ ❡❧étr✐❝❛ ❡ ❡str✉t✉r❛❧ ❞❛ ♣❡r♦✈s✲
❦✐t❛ P❜✭❋❡1/2 ◆❜1/2✮❖3✳ ❆❋▼ = ❛♥t✐❢❡rr♦♠❛❣♥ét✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✹
✺✺ P❛rt❡ r❡❛❧ ✭ǫ′✮ ❡ ✐♠❛❣✐♥ár✐❛ ✭ǫ′′✮❞❛ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ❡♠ ❢✉♥çã♦ ❞❛
t❡♠♣❡r❛t✉r❛ ❡♠ ❞✐❢❡r❡♥t❡s ❢r❡q✉ê♥❝✐❛s ❞♦ P b(F e1/2N b1/2)O3✱ ♠❡❞✐❞❛ ❞✉✲
r❛♥t❡ ♦ r❡s❢r✐❛♠❡♥t♦ ♥❛ r❛③ã♦ ❞❡2K/min✳ ❉❛❞♦s ❡①tr❛í❞♦s ❞❛ ❞✐ss❡rt❛çã♦
✭✶✶✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✻ ✺✻ P❛rt❡ r❡❛❧ ✭ǫ′✮ ❡ ✐♠❛❣✐♥ár✐❛ ✭ǫ′′✮❞❛ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ❡♠ ❢✉♥çã♦ ❞❛
t❡♠♣❡r❛t✉r❛ ❡♠ ❞✐❢❡r❡♥t❡s ❢r❡q✉ê♥❝✐❛s ❞♦ P b(F e1/2N b1/2)O3✱ ♠❡❞✐❞❛ ❞✉✲
r❛♥t❡ ♦ ❛q✉❡❝✐♠❡♥t♦✳ ❉❛❞♦s ❡①tr❛í❞♦s ❞❛ ❞✐ss❡rt❛çã♦ ✭✶✶✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼ ✺✼ ❆❥✉st❡ ❞♦ ❡s♣❡❝tr♦ ❘❛♠❛♥ ❞♦ P❋◆ ❡♠ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✽ ✺✽ ✭❛✮ ❊s♣❡❝tr♦s ❞❡ r❡✢❡tâ♥❝✐❛ ❡ ❛❜s♦r❜â♥❝✐❛ ❞♦ P❋◆✳ ✭❜✮ P❛rt❡s ✐♠❛❣✐♥ár✐❛s
❞❡ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ✭ε′′✮ ❡ s✉❛ ✐♥✈❡rs❛ ✭η′′✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✾
✺✾ ❊s♣❡❝tr♦ ❘❛♠❛♥ ❝♦♠ ❝❛rát❡r ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ♣❛r❛ ❛ ❢❛s❡ ♣❛r❛❡❧étr✐❝❛
❞♦ P❋◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✶ ✻✵ ❊s♣❡❝tr♦ ❘❛♠❛♥ ❡ ❞❡ ❛❜s♦rçã♦ ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦ ❞♦ P❋◆ à t❡♠♣❡r❛t✉r❛
❛♠❜✐❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✷ ✻✶ ●rá✜❝♦s ❞❡ ❛❜s♦rçã♦ ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦ ❞♦ P❋◆ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ♣✳ ✻✸ ✻✷ ❊s♣❡❝tr♦s ❘❛♠❛♥ ❞♦ P❋◆ ❡♥tr❡ ✶✶ ❡ ✼✵✵ ❑✱ ❝♦rr✐❣✐❞♦s ♣❡❧♦ ❢❛t♦r tér♠✐❝♦
♣♦♣✉❧❛❝✐♦♥❛❧ ❞❡ ❇♦❧t③♠❛♥♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✸ ✻✸ ❊s♣❡❝tr♦s ❘❛♠❛♥ ❞❛ ❘❊●✶ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✹ ✻✹ ❊s♣❡❝tr♦s ❘❛♠❛♥ ❞❛ ❘❊●✷ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✺ ✻✺ ❆❥✉st❡ ❞♦ ♥ú♠❡r♦ ❞❡ ♦♥❞❛ ❡ ❞❛ ❧❛r❣✉r❛ ❛ ♠❡✐❛ ❛❧t✉r❛ ❞♦ ♠♦❞♦ ❞❡ ✷✷✵
cm−1 ✭✶✶ ❑✮ ❡♠ ❢✉♥çã♦ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✻
✻✻ ❊✈♦❧✉çã♦ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ♣❛râ♠❡tr♦ ❞❡ r❡❞❡ ❢♦r❛ ❞♦ ♣❧❛♥♦ ♣❛r❛ ♦ ✜❧♠❡ ❞❡ P❋◆✳ ❚❛♠❜é♠ é ♠♦str❛❞♦ q✉❡ ♦ s✉❜str❛t♦ ❞❡ SrT iO3 ✭❙❚❖✮
♥ã♦ ❛♣r❡s❡♥t❛ ❛♥♦r♠❛❧✐❞❛❞❡ ♥❡ss❛ r❡❣✐ã♦ ❞❡ t❡♠♣❡r❛t✉r❛✳ T∗ r❡♣r❡s❡♥t❛
❛ t❡♠♣❡r❛t✉r❛ ❝♦♥❞❡♥s❛çã♦ ❞♦s ♠♦✈✐♠❡♥t♦s ❞✐♣♦❧❛r❡s ♥❛s ◆❘P ✭Tm✮✳
❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❡ r❡❢❡rê♥❝✐❛ ✭✶✸✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼ ✻✼ ❘❡s✐st✐✈✐❞❛❞❡ ❞♦ P❋◆ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛
r❡❢❡rê♥❝✐❛ ✭✶✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼ ✻✽ ❱❡❧♦❝✐❞❛❞❡ ❧♦♥❣✐t✉❞✐♥❛❧ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦ P❋◆ ♥❛ r❡❣✐ã♦
❞❛ tr❛♥s✐çã♦ ❡♥tr❡ ❢❛s❡s ❢❡rr♦❡❧étr✐❝❛s TF F2✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛
✭✶✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✽
✻✾ ◆ú♠❡r♦ ❞❡ ♦♥❞❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦ ♠♦❞♦ ❞❡ ❡st✐r❛♠❡♥t♦
s✐♠étr✐❝♦ ❞♦ ♦❝t❛❡❞r♦ ❞❡ N bO6✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✽
✼✵ ◆ú♠❡r♦ ❞❡ ♦♥❞❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦ ♠♦❞♦ ❞❡ ❡st✐r❛♠❡♥t♦
s✐♠étr✐❝♦ ❞♦ ♦❝t❛❡❞r♦ ❞❡ F eO6 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✾
✼✶ ◆ú♠❡r♦ ❞❡ ♦♥❞❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦s ♠♦❞♦ ❞❡ ❡st✐r❛♠❡♥t♦
F e−O ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✵
✼✷ ❱❡❧♦❝✐❞❛❞❡ ❧♦♥❣✐t✉❞✐♥❛❧ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦ P❋◆ ♥❛ r❡❣✐ã♦ ❞❛ tr❛♥s✐çã♦ ❡♥tr❡ ❛ ❢❛s❡ ♣❛r❛♠❛❣♥ét✐❝❛ ❡ ❛ ❛♥t✐❢❡rr♦♠❛❣ét✐❝❛✳ ❋✐❣✉r❛
❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✵ ✼✸ ◆ú♠❡r♦ ❞❡ ♦♥❞❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦s ♠♦❞♦ ❞❡ ❡st✐r❛♠❡♥t♦
❛ss✐♠étr✐❝♦ BO6 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✶
✼✹ ◆ú♠❡r♦ ❞❡ ♦♥❞❛ ❡ ❧❛r❣✉r❛ ❛ ♠❡✐❛ ❛❧t✉r❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛
♦s ♠♦❞♦ ❞❡ ❞♦❜r❛♠❡♥t♦ s✐♠étr✐❝♦ B−O−B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✶
✼✺ ❱❡❧♦❝✐❞❛❞❡ ❧♦♥❣✐t✉❞✐♥❛❧ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦ P❋◆ ❡♠ t♦❞❛
❛ r❡❣✐ã♦ ♠❡❞✐❞❛✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✷ ✼✻ ❊str✉t✉r❛s ❈r✐st❛❧✐♥❛s ❞❛s ♣❡r♦✈s❦✐t❛s ❇❛3❇2+❙❜5+2 ❖9 ❝♦♠ ❇ ❂ ▼❣ ✭✻✮✱
❈❛ ❡ ❙r✭✶✵✹✮✱ ❡♠ ♣r♦❥❡çõ❡s ❡q✉✐✈❛❧❡♥t❡s✱ ♠♦str❛♥❞♦ ❛ r❡❞✉çã♦ ❞❛ s✐♠❡tr✐❛ ❞❛ ❝é❧✉❧❛ ✉♥✐tár✐❛ ❛ ♣❛rt✐r ❞❛s r♦t❛çõ❡s ❞♦s ♦❝t❛❡❞r♦s✳ ❖s ❞í♠❡r♦s ❞❡ ♦❝t❛❡❞r♦s SbO6 sã♦ ♠❛rr♦♥s✱ ♦s ♦❝t❛❡❞r♦s ❞❡ ▼❣✱ ❈❛ ❡ ❙r sã♦ ❛♠❛r❡❧♦s✱
❛③✉✐s ❡ ✈❡r❞❡s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❡ ♦s át♦♠♦s ❞❡ ❇❛ sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r
❡s❢❡r❛s r♦①❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✹ ✼✼ ❈✉r✈❛s ❞❡ ❉❙❈ ♦❜t✐❞❛s ♥♦ ❛q✉❡❝✐♠❡♥t♦ ♣❛r❛ ♦ ❇▼❙✱ ❇❈❙ ❡ ❇❙❙✱ ♠♦s✲
tr❛♥❞♦ tr❛♥s✐çõ❡s ❡♥❞♦tér♠✐❝❛s ❞❛ ❢❛s❡ ♠♦♥♦❝❧í♥✐❝❛ ♣❛r❛ ❛ ❤❡①❛❣♦♥❛❧ ✭❇▼❙✮ ❡ ❞❛ ❢❛s❡ tr✐❝❧í♥✐❝❛ ♣❛r❛ ❛ ♠♦♥♦❝❧í♥✐❝❛ ✭❇❈❙ ❡ ❇❙❙✮✳ ❉❛❞♦s ❡①✲
tr❛í❞♦s ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✵✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✺ ✼✽ ❱❛r✐❛çã♦ ❞♦ â♥❣✉❧♦ ♠♦♥♦❝❧í♥✐❝♦ β✱ ♦❜t✐❞♦ ♣♦r r❡✜♥❛♠❡♥t♦ ❘✐❡t✈❡❧❞ ❞♦s
❞❛❞♦s ❞❡ r❛✐♦s ❳✱ ♣❛r❛ ♦ ❇❈❙ ❡ ❇❙❙✳ ❆s ❜❛rr❛s ❞❡ ❡rr♦ sã♦ ♠❡♥♦r❡s q✉❡
♦s sí♠❜♦❧♦s✳ ●rá✜❝♦ ❡①tr❛í❞♦ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✵✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✺ ✼✾ ❈é❧✉❧❛ ✉♥✐tár✐❛ ❞♦ ❇❛3▼❣❙❜2❖9 ❝♦♥s✐❞❡r❛♥❞♦ ♦ ❞í♠❡r♦ ❙❜✷❖✾ ❝♦♠♦ ✉♠
❛rr❛♥❥♦ ✐ô♥✐❝♦ ✐s♦❧❛❞♦ ❝♦♠ ❡s❢❡r❛s ❛♠❛r❡❧❛s r❡♣r❡s❡♥t❛♥❞♦ ♦s í♦♥s ❞❡ ▼❣✱ r♦①❛s ✲ í♦♥s ❞❡ ❇❛✱ ♠❛rr♦♥s ✲ í♦♥s ❞❡ ❙❜ ❡ ♦ ✈ért✐❝❡ ❞❡ ❝❛❞❛ ♣♦❧í❣♦♥♦
r❡♣r❡s❡♥t❛♥❞♦ ✉♠ í♦♥ ❞❡ ♦①✐❣ê♥✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✽
✽✵ ▲♦❝❛❧✐③❛çã♦ ❞♦s ❡✐①♦s C2✱ r❡♣r❡s❡♥t❛❞♦s ♣♦r ❡❧✐♣s❡s r♦①❛s✱ ❞❛ ❝é❧✉❧❛ ✉♥✐✲
tár✐❛ ♠♦♥♦❝❧í♥✐❝❛ ✭C2/c (C6
2h) ✮✱ à ❞✐r❡✐t❛✱ ♥❛ ❝é❧✉❧❛ ♣r✐♠✐t✐✈❛ ❤❡①❛❣♦♥❛❧
✭P63/mmc (D46h) ✮✱ à ❡sq✉❡r❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✼ ✽✶ ❊s♣❡❝tr♦s ❘❛♠❛♥ ❡ ❞❡ ❛❜s♦rçã♦ ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦ à t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡
❞❛s ♣❡r♦✈s❦✐t❛s ❇▼❙✱ ❇❈❙ ❡ ❇❙❙✳ ❈❛❞❛ ♠♦❞♦ ✈✐❜r❛❝✐♦♥❛❧ ❡stá r♦t✉❧❛❞♦ ❝♦♠ s✉❛ r❡s♣❡❝t✐✈❛ ❢r❡q✉ê♥❝✐❛ ❡ ♦s ♠♦❞♦s r♦t✉❧❛❞♦s ❝♦♠ ✉♠ ❛st❡r✐s❝♦ ✭✯✮
r❡♣r❡s❡♥t❛♠ ❛ ✈✐❜r❛çã♦ ❞♦ ♣♦❧✐❡t✐❧❡♥♦ ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✵ ✽✷ ❉✐s♣♦s✐çã♦ ❛tô♠✐❝❛ ❞♦s í♦♥s ♥❛ ❝é❧✉❧❛ ✉♥✐tár✐❛ ❞♦ ❈s3❈r2❈❧9 ❝♦♠ ❡s❢❡r❛s
r♦s❛s r❡♣r❡s❡♥t❛♥❞♦ ♦s í♦♥s ❞❡ ❈s✱ ✈✐♦❧❡t❛s ✲ í♦♥s ❞❡ ❈r ❡ ✈❡r❞❡s ✲ í♦♥s ❞❡
❈❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✷ ✽✸ ❖s ❡s♣❡❝tr♦s ❡♠ ♠♦❞❡❧♦s ❞❡ r❛✐❛s ♣❛r❛ ♦ ❇▼❙✱ ❇❈❙ ❡ ❇❙❙ ♣♦ss✉❡♠
ót✐♠❛ ❝♦♥❝♦r❞â♥❝✐❛ ❝♦♠ ♦ ❈s3❈r2❈❧9✱ ♣♦ss✉✐♥❞♦ ❞í♠❡r♦s ❞❡ ❈r2❈❧9✳ ✳ ✳ ♣✳ ✾✸
✽✹ ▼♦❞♦s ❘❛♠❛♥ ❛t✐✈♦s A′
1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✹
✽✺ ▼♦❞♦s ❛t✐✈♦s ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦ A′′
2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✹
✽✻ ▼♦❞♦s E′ ❛t✐✈♦s t❛♥t♦ ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦ q✉❛♥t♦ ♥♦ ❘❛♠❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✺
✽✼ ▼♦❞♦s ❘❛♠❛♥ ❛t✐✈♦s E′′✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✻
✽✽ ▼♦❞♦sA′′
1(ν17)❡A2′(ν18)✱ q✉❡ sã♦ s✐❧❡♥❝✐♦s♦s ♣❛r❛ ♦ ❛rr❛♥❥♦ ✐ô♥✐❝♦ Sb2O9
❝♦♠ s✐♠❡tr✐❛ D3h✳ ❖ ♠♦❞♦ ν17 ❢♦✐ ♦ ú♥✐❝♦ ♠♦❞♦ ❝❛❧❝✉❧❛❞♦ q✉❡ ♦❜t❡✈❡
❝♦♠♦ r❡s✉❧t❛❞♦ ✉♠❛ ❢r❡q✉ê♥❝✐❛ ❝♦♠♣❧❡①❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✻ ✽✾ ■❧✉str❛çã♦ ❞❡ ✉♠ ♣♦♥t♦ ❞❡ ❝❡❧❛ ❡ ✉♠ ♣♦♥t♦ ❞❡ ♠í♥✐♠♦ ♥❛ s✉♣❡r❢í❝✐❡ ❞❡
❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞❡ ✉♠❛ ♠♦❧é❝✉❧❛✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✹✵✮✳ ♣✳ ✾✼ ✾✵ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦ ❡s♣❡❝tr♦ ❘❛♠❛♥ ❝❛❧❝✉❧❛❞♦ ♣❛r❛ ♦ ❙❜2❖9 ❡ ♦ ❡①♣❡r✐✲
♠❡♥t❛❧ ❞♦ ❇▼❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✽ ✾✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦ ❡s♣❡❝tr♦ ✐♥❢r❛✈❡r♠❡❧❤♦ ❝❛❧❝✉❧❛❞♦ ♣❛r❛ ♦ ❙❜2❖9 ❡ ♦
❡①♣❡r✐♠❡♥t❛❧ ❞♦ ❇▼❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✽ ✾✷ ❈♦♦r❞❡♥❛❞❛s ✐♥t❡r♥❛s ❛ss✉♠✐❞❛s ♥♦ ♠♦❞❡❧♦ ❞❡ ✈✐❜r❛çõ❡s ❞♦ ❇▼❙✳ ✳ ✳ ✳ ♣✳ ✶✵✵ ✾✸ ▼♦❞♦s A1g ❘❛♠❛♥ ❛t✐✈♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✶ ✾✹ ▼♦❞♦s E1g ❘❛♠❛♥ ❛t✐✈♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✹ ✾✺ ▼♦❞♦s E2g ❘❛♠❛♥ ❛t✐✈♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✹ ✾✻ ▼♦❞♦s A2u ❛t✐✈♦s ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✺
✾✼ ▼♦❞♦s A1u ❛t✐✈♦s ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✺ ✾✽ ❊s♣❡❝tr♦s ❘❛♠❛♥ ❞♦ ❇❛3▼❣❙❜2❖9 ❡♥tr❡ ✾ ❡ ✷ ✻✺ ❑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✼
✾✾ ❉❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ❢ô♥♦♥s ♦❜s❡r✈❛❞♦s
♣❛r❛ ♦ ❇▼❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✽ ✶✵✵ ❉❡♣❡♥❞ê♥❝✐❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞❛ ár❡❛ ♥♦r♠❛❧✐③❛❞❛ ❞♦s ♣r✐♥❝✐♣❛✐s ♣✐❝♦s
❞❡ s✐♠❡tr✐❛ Eg ❞♦ ❇▼❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✾ ✶✵✶ ◆ú♠❡r♦ ❞❡ ♦♥❞❛ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❘❛♠❛♥ ❡s♣❛❧❤❛❞❛ ❞♦ ❇❛3❈❛❙❜2❖9
♣❛r❛ ❞✐❢❡r❡♥t❡s t❡♠♣❡r❛t✉r❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✵ ✶✵✷❉❡♣❡♥❞ê♥❝✐❛ ❞♦ ♥ú♠❡r♦ ❞❡ ♦♥❞❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ♠♦❞♦ ❞❡ ✹✽✶
cm−1 ♦❜s❡r✈❛❞♦ ♣❛r❛ ♦ ❇❛
3❈❛❙❜2❖9 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✵
✶✵✸ ❊s♣❡❝tr♦ ❘❛♠❛♥ ❞❡♣❡♥❞❡♥t❡ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦ ❇❛3❙r❙❜2❖9 ✳ ✳ ✳ ♣✳ ✶✶✶
✶✵✹ ●rá✜❝♦s ❞❡ ✐♥❢r❛✈❡r♠❡❧❤♦s ❡♠ ❞✐❢❡r❡♥t❡s t❡♠♣❡r❛t✉r❛s ♣❛r❛ ♦ ❇❛3▼❣❙❜2❖9
✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✶ ✶✵✺ ❊s♣❡❝tr♦ ❞❡ ❛❜s♦rçã♦ ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦ ♠é❞✐♦ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛
♣❛r❛ ♦ ❇❈❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✷ ✶✵✻ ❊s♣❡❝tr♦ ❞❡ ❛❜s♦rçã♦ ♥♦ ✐♥❢r❛✈❡r♠❡❧❤♦ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛
♦ ❇❈❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✷ ✶✵✼ ❊s♣❡❝tr♦ ❞❡ ■❘ ❞❡♣❡♥❞❡♥t❡ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ♦ ❇❛3❙r❙❜2❖9 ✳ ✳ ✳ ✳ ♣✳ ✶✶✸
✶✵✽ ●r✉♣❛♠❡♥t♦ ✐ô♥✐❝♦(Sb2O9)8− ✐s♦❧❛❞♦ ♥❛ ❝❡❧❛ ✉♥✐tár✐❛ ❝♦♠ s✐♠❡tr✐❛ ♣♦♥✲
t✉❛❧ D3h ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✼
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶ ❈♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ❡①♣❡r✐♠❡♥t❛❧ ✭εmed✮✱ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ❝♦rr✐❣✐❞❛ ♣❛r❛ ♣♦r♦s✐❞❛❞❡ ✭εcorr✮✱ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ❝❛❧❝✉❧❛❞❛ ❝♦♠ ❛ ❡q✉❛çã♦ ❞❡ ❈❧❛✉s✐✉s✲▼♦ss♦tt✐ ✭εC−M✮ ❡ ♦ ♣r♦❞✉t♦ ❞♦ ❢❛t♦r ❞❡ q✉❛❧✐❞❛❞❡ ❡ ❞❛
❢r❡q✉ê♥❝✐❛ ❞❡ r❡ss♦♥â♥❝✐❛ ❢✳ ❚❛❜❡❧❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✵✶✮ ✳ ✳ ✳ ✳ ♣✳ ✸✸ ✷ ❉✐stâ♥❝✐❛s ❞❛s ❧✐❣❛çõ❡s ✭➴✮ ❡♠ ✺✷✸ ❑✱ ✸✻✸ ❑ ❡ ✷✺✵ ❑ ♦❜t✐❞♦s ♣❡❧♦ r❡✜✲
♥❛♠❡♥t♦ ❞❛ ❞✐❢r❛çã♦ ❞❡ ♥ê✉tr♦♥s✳ ♥❛ ❢❛s❡ ❝ú❜✐❝❛✱ ❛ ❞❡s♦r❞❡♠ ❞♦ P❜ ❡ ❖
♥ã♦ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞❛s✳ ❉❛❞♦s ❡①tr❛í❞♦s ❞❛ r❡❢❡rê♥❝✐❛ ✭✶✶✼✮ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷ ✸ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ♠♦❞♦s ♥♦r♠❛✐s ❞❡ ✈✐❜r❛çã♦ ♣❛r❛ ❛s ❞✐❢❡r❡♥t❡s ❢❛s❡s ❞♦
P❋◆✱ s❡♥❞♦ ♥ ♦ ♥ú♠❡r♦ ❞❡ ❢ór♠✉❧❛s ♣♦r ❝é❧✉❧❛ ✉♥✐tár✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✵ ✹ P❛râ♠❡tr♦s ❡str✉t✉r❛✐s ❞❛ ♣❡r♦✈s❦✐t❛ ❇❛3▼❣❙❜2❖9 à t❡♠♣❡r❛t✉r❛ ❛♠❜✐✲
❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✻ ✺ ❉✐str✐❜✉✐çã♦ ❞♦s ♠♦❞♦s ♥♦r♠❛✐s ❞❡ ✈✐❜r❛çã♦ ♣❛r❛ ❛ ♣❡r♦✈s❦✐t❛ ❇❛3▼❣❙❜2❖9
♣✳ ✼✼
✻ ❚❛❜❡❧❛ ❞❡ ❝♦rr❡❧❛çã♦ ♣❛r❛ ♦ ❇▼❙✳ ❖s ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡ tr❛♥s❧❛❝✐♦♥❛✐s ✭tr❛♥s✮ ❡ r♦t❛❝✐♦♥❛✐s ✭r♦t✮ t♦r♥❛♠✲s❡ ♠♦❞♦s tr❛♥s❧❛❝✐♦♥❛✐s ✭❚✮ ❡ ❧✐❜r❛❝✐✲
♦♥❛✐s ✭▲✮ ❞❛ r❡❞❡ ❝r✐st❛❧✐♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✾ ✼ P❛râ♠❡tr♦s ❡str✉t✉r❛✐s ❞❛ ♣❡r♦✈s❦✐t❛ ❇❛3❈❛❙❜2❖9 à t❡♠♣❡r❛t✉r❛ ❛♠❜✐✲
❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✶ ✽ ❉✐str✐❜✉✐çã♦ ❞♦s ♠♦❞♦s ♥♦r♠❛✐s ❞❡ ✈✐❜r❛çã♦ ♣❛r❛ ❛ ♣❡r♦✈s❦✐t❛ ✻❍ ❇❈❙ ♣✳ ✽✷ ✾ P❛râ♠❡tr♦s ❡str✉t✉r❛✐s ❞❛ ♣❡r♦✈s❦✐t❛ ❇❛3❙r❙❜2❖9 à t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡✳ ♣✳ ✽✸
✶✵ ❉✐str✐❜✉✐çã♦ ❞♦s ♠♦❞♦s ♥♦r♠❛✐s ❞❡ ✈✐❜r❛çã♦ ♣❛r❛ ❛ ♣❡r♦✈s❦✐t❛ ✻❍ ❇❛3❈❛❙❜2❖9
♣✳ ✽✹
✶✶ ❉✐stâ♥❝✐❛ ❞❛s ❧✐❣❛çõ❡s ❞♦ ❇❛ ❝♦♦r❞❡♥❛❞♦ ❛ ✶✷ ♦①✐❣ê♥✐♦s✱ â♥❣✉❧♦s ❡♥tr❡ ♦s ❛♥t✐♠ô♥✐♦s ❡ ♦s ♦①✐❣ê♥✐♦s ❞❡ ❝♦♥❡①ã♦ ✭❖✶✮ ❡ ❡♥tr❡ ♦s ❛♥t✐♠ô♥✐♦s ✭❙❜✮✱ ♦s
✶✷ ❈♦♠♣r✐♠❡♥t♦ ❞❛s ❧✐❣❛çõ❡s ♠❡t❛❧✲♦①✐❣ê♥✐♦✱ ♠❡t❛❧✲♠❡t❛❧ ❡ ♦①✐❣ê♥✐♦✲♦①✐❣ê♥✐♦
♣❛r❛ ❛s ♣❡r♦✈s❦✐t❛s ❇▼❙✱ ❇❈❙ ❡ ❇❙❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✻ ✶✸ ❚❛❜❡❧❛ ❞❡ ❝♦rr❡❧❛çã♦ ❞♦s ♠♦❞♦s ✈✐❜r❛❝✐♦♥❛✐s ❞❛s s✐♠❡tr✐❛s ♦❜t✐❞❛s ♣♦r
tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ♥❛s ♣❡r♦✈s❦✐t❛s ✻❍ ❇❛3▼❣❙❜2❖9✱ ❇❛3❈❛❙❜2❖9❡ ❇❛3❙r❙❜2❖9
✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✽ ✶✹ ❋r❡q✉ê♥❝✐❛s ❞♦s ❢ô♥♦♥s ♦❜t✐❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❡ s✉❛s ❝❧❛ss✐✜❝❛çõ❡s
♠❡❞✐❛♥t❡ ♦ ♠ét♦❞♦ ❞❡ ❍❛rtr❡❡✲❋♦❝❦ ✭❍❋✮ ❛♣❧✐❝❛❞♦ ♥♦ ❞í♠❡r♦ ❙❜2❖9✳ ✳ ♣✳ ✾✶
✶✺ ❚❛❜❡❧❛ ❞❡ ❝♦♥st❛♥t❡s ❞❡ ❢♦rç❛ ✉t✐❧✐③❛❞❛s ♣❛r❛ ♠♦❞❡❧❛r ♦ ❇▼❙ ♣❡❧♦ ♠ét♦❞♦
●❋ ❞❡ ❲✐❧s♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✶ ✶✻ ❋ô♥♦♥s ❝❛❧❝✉❧❛❞♦s ❡ ♦❜s❡r✈❛❞♦s✱ ❡♠ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡✱ ♣❛r❛ ❛ ❝é❧✉❧❛
✉♥✐tár✐❛ ❞♦ ❇▼❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✷ ✶✼ ❋r❡q✉ê♥❝✐❛s ❢ô♥♦♥s ♦❜t✐❞♦s ♣♦r ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ❡ ❛❜s♦rçã♦ ♥♦ ✐♥✲
❢r❛✈❡r♠❡❧❤♦✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❝❧❛ss✐✜❝❛çã♦ ❞♦s ♠♦❞♦s ✐♥t❡r♥♦s ❡ ❞❛ r❡❞❡
❞♦ ❇▼❙ ♣❡❧♦ ♠ét♦❞♦ ❋● ❞❡ ❲✐❧s♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✸ ✶✽ ▼♦❞♦s ❘❛♠❛♥ ❡ ✐♥❢r❛✈❡r♠❡❧❤♦s ♦❜s❡r✈❛❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❡ s✉❛ ♣♦s✲
sí✈❡❧ ❝❧❛ss✐✜❝❛çã♦ ♣❡❧♦ ♠ét♦❞♦ ❋● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✻ ✶✾ ❉✐✈❡r❣ê♥❝✐❛ ❡♥tr❡ ❛s ❝❧❛ss✐✜❝❛çõ❡s r❡❛❧✐③❛❞❛s ♣❡❧♦ ♠ét♦❞♦ ❞❡ ❍❛rtr❡❡✲
❋♦❝❦ ✭❍❋✮ ❡ ❋● ❞❡ ❲✐❧s♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✻ ✷✵ ❚❛❜❡❧❛ ❞❡ ❝❛r❛❝t❡r❡s ❞♦ ❣r✉♣♦ ♣♦♥t✉❛❧ D3h✱ ❝♦♠ n r❡♣r❡s❡♥t❛♥❞♦ ♦ ♥ú✲
♠❡r♦ ❞❡ r❡♣r❡s❡♥t❛çõ❡s ✐rr❡❞✉tí✈❡✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✽
