Transições de fase em monocristais de DMetionina

❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙

0❘❖●❘❆▼❆ ❉❊ 03❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆

❲❆◆❊❙❙❆ ❉❆❱■❉ ❈❆◆❊❉❖ ▼❊▲❖

❚❘❆◆❙■➬'❊❙ ❉❊ ❋❆❙❊ ❊▼ ▼❖◆❖❈❘■❙❚❆■❙ ❉❊

❉✲▼❊❚■❖◆■◆❆

❲❆◆❊❙❙❆ ❉❆❱■❉ ❈❆◆❊❉❖ ▼❊▲❖

❚❘❆◆❙■➬'❊❙ ❉❊ ❋❆❙❊ ❊▼ ▼❖◆❖❈❘■❙❚❆■❙ ❉❊

❉✲▼❊❚■❖◆■◆❆

❚❡"❡ ❛♣%❡"❡♥'❛❞❛ ❛♦ *%♦❣%❛♠❛ ❞❡ *-"✲ ●%❛❞✉❛12♦ ❡♠ ❋4"✐❝❛ ❞❛ ❯♥✐✈❡%"✐❞❛❞❡ ❋❡❞❡%❛❧ ❞♦ ❈❡❛%; ♣❛%❛ ♦❜'❡♥12♦ ❞♦ ❣%❛✉ ❞❡ ❉♦✉'♦% ❡♠ ❋4"✐❝❛✳

❖%✐❡♥'❛❞♦%✿ *%♦❢✳ ❉%✳ ❏♦"✉C ▼❡♥❞❡" ❋✐❧❤♦ ❈♦✲❖%✐❡♥'❛❞♦%✿ *%♦❢✳ ❉%✳ *❛✉❧♦ ❞❡ ❚❛%"♦ ❈✳ ❋%❡✐%❡

▼❡❧♦✱ ❲❛♥❡((❛ ❉❛✈✐❞ ❈❛♥❡❞♦

❚/❛♥(✐01❡( ❞❡ ❢❛(❡ ❡♠ ♠♦♥♦❝/✐(5❛✐( ❞❡ ❉✲♠❡5✐♦♥✐♥❛ ✴ ❲❛♥❡((❛ ❉❛✈✐❞ ❈❛♥❡❞♦ ▼❡❧♦ ✲ ✷✵✶✷

✽✼ ❢✳

❚❡(❡ ✭❉♦✉5♦/❛❞♦✮ ✲ ❯♥✐✈❡/(✐❞❛❞❡ ❋❡❞❡/❛❧ ❞♦ ❈❡❛/C✱ ❉❡♣❛/5❛♠❡♥5♦ ❞❡ ❋E(✐❝❛✱ F/♦❣/❛♠❛ ❞❡ FH(✲●/❛❞✉❛0J♦ ❡♠ ❋E(✐❝❛✱ ❋♦/5❛❧❡③❛✱ ✷✵✶✷ ➪/❡❛ ❞❡ ❈♦♥❝❡♥5/❛0J♦✿ ❋E(✐❝❛ ❞❛ ▼❛5N/✐❛ ❈♦♥❝❡♥5/❛❞❛✳ ❖/✐❡♥5❛0J♦✿ F/♦❢✳ ❉/✳ ❏♦(✉N ▼❡♥❞❡( ❋✐❧❤♦✳

✶✳ ❉✲♠❡5✐♦♥✐♥❛✳ ✷✳ ❊(♣❡❝5/♦(❝♦♣✐❛ ❞❡ ❘❛♠❛♥✳ ✸✳ ❊(♣❡❝5/♦(❝♦♣✐❛ ■♥❢/❛✈❡/♠❡❧❤♦ ✹✳ ❚/❛♥(✐01❡( ❞❡ ❋❛(❡✳ ✺✳ ❆❧5❛( F/❡((1❡(✳ ■✳ ❚E5✉❧♦

❲❆◆❊❙❙❆ ❉❆❱■❉ ❈❆◆❊❉❖ ▼❊▲❖

❚!❛♥$✐&'❡$ ❞❡ ❢❛$❡ ❡♠ ♠♦♥♦❝!✐$.❛✐$ ❞❡ ❉✲♠❡.✐♦♥✐♥❛

❚❡"❡ ❛♣%❡"❡♥'❛❞❛ ❛♦ *%♦❣%❛♠❛ ❞❡ *-"✲ ●%❛❞✉❛12♦ ❡♠ ❋4"✐❝❛ ❞❛ ❯♥✐✈❡%"✐❞❛❞❡ ❋❡❞✲ ❡%❛❧ ❞♦ ❈❡❛%; ♣❛%❛ ♦❜'❡♥12♦ ❞♦ ❣%❛✉ ❞❡ ❉♦✉'♦% ❡♠ ❋4"✐❝❛✳

❆♣%♦✈❛❞❛ ❡♠ ✴ ✴

❇❆◆❈❆ ❊❳❆▼■◆❆❉❖❘❆

*%♦❢✳ ❉%✳ ❏♦"✉K ▼❡♥❞❡" ❋✐❧❤♦ ✭❖%✐❡♥'❛❞♦%✮ ❉❡♣❛%'❛♠❡♥'♦ ❞❡ ❋4"✐❝❛

❯♥✐✈❡%"✐❞❛❞❡ ❋❡❞❡%❛❧ ❞♦ ❈❡❛%;

*%♦❢✳ ❉%✳ *❛✉❧♦ ❞❡ ❚❛%"♦ ❈❛✈❛❧❝❛♥'❡ ❋%❡✐%❡ ✭❈♦✲♦%✐❡♥'❛❞♦%✮ ❉❡♣❛%'❛♠❡♥'♦ ❞❡ ❋4"✐❝❛

❯♥✐✈❡%"✐❞❛❞❡ ❋❡❞❡%❛❧ ❞♦ ❈❡❛%;

*%♦❢✳ ❉%✳ ❋%❛♥❝✐"❝♦ ❊%✐✈❛♥ ❞❡ ❆❜%❡✉ ▼❡❧♦ ❉❡♣❛%'❛♠❡♥'♦ ❞❡ ❋4"✐❝❛

!♦❢✳ ❉!✳ ❲❛❧❞❡❝✐ ❛!❛❣✉❛//✉ ❋❡✐♦ ❉❡♣❛!2❛♠❡♥2♦ ❞❡ ❋5/✐❝❛ ❯♥✐✈❡!/✐❞❛❞❡ ❋❡❞❡!❛❧ ❞♦ ❛!8

❉❡❞✐❝❛&'(✐❛

❆♦" ♠❡✉" ❛✈(" ✳

➚ ▼✐♥❤❛ ❚✐❛ ▼❛0❧❡♥❡ ✳

❆♦" ▼❡✉" 2❛✐"✳

❆♦ ♠❡✉ ❛♠❛❞♦ ❊"♣♦"♦✳✳✳

✧❖ ❡##❡♥❝✐❛❧ ) ✐♥✈✐#+✈❡❧ ❛♦# ♦❧❤♦#✧✳ ✭❙❛✐♥$✲❊①✉♣*+②✱ ✧❖ $❡&✉❡♥♦ $*+♥❝✐♣❡✧✮

❆❣"❛❞❡❝✐♠❡♥*♦,

➚ ❉❡✉$✳

❆♦ ♠❡✉ ♦)✐❡♥,❛❞♦)✱ ❏♦$✉1 ▼❡♥❞❡$ ❋✐❧❤♦ ❡ ❈♦✲♦)✐❡♥,❛❞♦)✱ 8❛✉❧♦ ❞❡ ❚❛)$♦ ❋)❡✐)❡ ❈❛✈❛❧❝❛♥,❡✱ ♣♦) ❛❝❡✐,❛)❡♠ ♠❡ ♦)✐❡♥,❛)✱ ♣❡❧❛ ❞❡❞✐❝❛=>♦ ❡ ❝♦♠♣❡,?♥❝✐❛ ❝♦♠ ❛ @✉❛❧ ♠❡ ♦)✐❡♥,❛)❛♠ ❡ ♣❡❧♦ ✈❛$,♦ ❝♦♥❤❡❝✐♠❡♥,♦ @✉❡ ♠❡ ,)❛♥$♠✐,✐)❛♠✳

❆♦ 8)♦❢✳ ■❧❞❡ ●✉❡❞❡$✱ @✉❡ ❢♦✐ ♠❡✉ ♣)✐♠❡✐)♦ ♦)✐❡♥,❛❞♦) ♥❡$$❛ ✐♥$,✐,✉✐=>♦✱ ❛❣)❛❞❡=♦ ♣❡❧♦ ❝♦♥❤❡❝✐♠❡♥,♦ ,)❛♥$♠✐,✐❞♦ ♥♦ ❝✉),♦ ♣❡)E♦❞♦ @✉❡ ♠❡ ♦)✐❡♥,♦✉✳

❆♦ ♠❡✉ ♦)✐❡♥,❛❞♦) ❞♦ ♠❡$,)❛❞♦✱ ❈❛)❧♦$ ❲✐❧❧✐❛♠ ❞❡ ❆)❛✉❥♦ 8❛$❝❤♦❛❧✱ ♣❡❧❛ ❡①❝❡❧❡♥,❡ ❢♦)♠❛=>♦ ❡ ✐♥❝❡♥,✐✈♦ ♣❛)❛ ❡❧❡✈❛) ♦ ♣❛,❛♠❛) ❞❛ ♠✐♥❤❛ ❢♦)♠❛=>♦✳

❆♦ 8)♦❢✳ ❏♦$1 ❆❧✈❡$ ▲✐♠❛✱ ♣❡❧❛ ❝♦♥,)✐❜✉✐=>♦ ♥❛$ ❞✐$❝✉$$K❡$ ❞❡$$❡ ,)❛❜❛❧❤♦✳ ❆♦$ ❞❡♠❛✐$ ♣)♦❢❡$$♦)❡$ ❞♦ 8)♦❣)❛♠❛ ❞❡ ❉♦✉,♦)❛❞♦ @✉❡ ❝♦♥,)✐❜✉E)❛♠ ♣❛)❛ ♠✐♥❤❛ ❢♦)♠❛=>♦✳

➚ 8)♦❢❛✳ ❙✐♠♦♥❡✱ ❡♥@✉❛♥,♦ ❈♦♦)❞❡♥❛❞♦)❛ ❞♦ ❈❡♥,)♦ ❞❡ ❈✐?♥❝✐❛$ ❡ ✐♥,❡✲ ❣)❛♥,❡ ❞♦ 8)♦♣❛❣✱ ♣❡❧❛$ ♣❛❧❛✈)❛$ ❞❡ ♠♦,✐✈❛=>♦✳

❆♦$ 8)♦❢❡$$♦)❡$ ▼❛)✐❛ ▼❛)❧M❝✐❛✱ ❆❧❡❥❛♥❞)♦ 8❡❞)♦ ❆②❛❧❛ ❡ ❈❛)❧♦$ ❆❧❜❡),♦✱ ♣❡❧❛ ♦)✐❡♥,❛=>♦ ❞♦ ♣)♦❥❡,♦ ❡$♣❡❝E✜❝♦ ❞♦ 8)♦♣❛❣✳

❆♦ ❈♦♦)❞❡♥❛❞♦) ❡ $❡❝)❡,P)✐❛$ ❞♦ 8)♦❣)❛♠❛ ❞❡ 8Q$✲❣)❛❞✉❛=>♦ ♣❡❧❛ ❛,❡♥=>♦ ❡ ♣)❡$,❡③❛✳

❆♦ ♠❡✉ ❝♦❧❡❣❛ ❈❧❡♥✐❧,♦♥✱ @✉❡ ,❛♥,♦ ♠❡ ❛✉①✐❧✐♦✉ ♥♦ ✐♥E❝✐♦ ❞❡$$❡ ❞♦✉,♦)❛❞♦✳ ➚ ❈❧❡S♥✐♦✱ ●❛)❞?♥✐❛ ❡ ❆❧❞✐❧❡♥❡✱ @✉❡ ♠❡ ❛✉①✐❧✐❛)❛♠ ♥♦ ✐♥E❝✐♦ ❞❛ ♠✐♥❤❛ ❡$,❛❞✐❛ ❡♠ ❋♦),❛❧❡③❛✳

➚ ❆❧❝❡♠✐)❛ ❡ ▼❛♥♦❡❧✱ ♣❡❧❛ ❛♠✐③❛❞❡ $✐♥❝❡)❛✱ ♣❡❧♦$ ✈❛❧♦)♦$♦$ ❝♦♥$❡❧❤♦$✱ ♣❛❧❛✈)❛$ ❞❡ S♥✐♠♦✱ ❛❥✉❞❛ ♥♦ ❧❛❜♦)❛,Q)✐♦ ❡ ♣❡❧♦$ ♠♦♠❡♥,♦$ ❞❡ ❞❡$❝♦♥,)❛=>♦✳

❆♦ ♠❡✉ ❛♠✐❣♦ ❲❡❧❧❡)②✱ ♣❡❧❛ ❛❥✉❞❛ ❡♠ ♠❡✉ ,)❛❜❛❧❤♦ ❡ ♣❡❧♦$ ♠♦♠❡♥,♦$ ❛❣)❛❞P✈❡✐$ @✉❡ ❝♦♠♣❛),✐❧❤❛♠♦$✳

❆♦$ ♠❡✉$ ❛♠✐❣♦$ ❞❛ $❡❝)❡,❛)✐❛ ❞♦ ❞❡♣❛),❛♠❡♥,♦✱ ▼✐❝❤❡❧❡✱ ❈)❡✉③❛ ❡ ❏❛✐❧$♦♥ ♣❡❧♦$ ❛❧♠♦=♦$ ❞❡$❝♦♥,)❛E❞♦$ ♥♦ ❘❯✳

❆♦$ ♠❡✉$ ❝♦❧❡❣❛$ ❞❡ ♣)♦❥❡,♦ 8❘❖8❆●✳

❆♦$ ♠❡✉$ ❝♦❧❡❣❛$ ❞❡ $❛❧❛ ❈❛)❧♦$ ❆❧❡① ❡ ▼❛♥♦❡❧❛ ♣♦) ❛❝❡✐,❛)❡♠ ❛ ❞✐✈✐❞✐) ♦

❛♠❜✐❡♥&❡ ❞❡ &(❛❜❛❧❤♦ ❝♦♠✐❣♦✳

➚0 ♠✐♥❤❛0 ❛♠✐❣❛0 ❞❛ ❞❛♥1❛ 2✉❡ ❛❥✉❞❛(❛♠ ❛ 0✉♣(✐( ✉♠ ♣♦✉❝♦ ❛ 0❛✉❞❛❞❡ ❞❛ ♠✐♥❤❛ ❢❛♠7❧✐❛✳

❆♦0 ♣(♦❢❡00♦(❡0 ❞♦ ◆:❝❧❡♦ ❞❡ ;❡02✉✐0❛ ❡♠ ❋70✐❝❛ ✭◆;❋✮ ❞❛ ❯♥✐✈❡(0✐❞❛❞❡ ❈❛&B❧✐❝❛ ❞❡ ●♦✐D0 ✭❯❈●✮ ♣❡❧❛0 ❜♦❛0 (❡❝♦♠❡♥❞❛1E❡0 ❡ ❡①❝❡❧❡♥&❡ ❢♦(♠❛1G♦✳ ❊♠ ❡0♣❡❝✐❛❧ ❛♦ ;(♦❢✳ ❆♥❞(I✱ 2✉❡ 0❡♠♣(❡ ❡0&❡✈❡ ❞✐0♣♦♥7✈❡❧ ♣❛(❛ &✐(❛( ♠✐♥❤❛0 ❞:✈✐❞❛0 ❡ ♣❡❧♦ 0❡✉ ❡①❡♠♣❧♦ ❞❡ ♣(♦✜00✐♦♥❛❧❀ ❢❡③ ♣❛(&❡ ❞♦ ✐♥❝❡♥&✐✈♦ ❛♦ ♠❡✉ ❝(❡0❝✐♠❡♥&♦✳ ❆♦ ;(♦❢✳ ❉(✳ ❏✉❛♥ ♣❡❧♦ ❡①❡♠♣❧♦ &❛♥&♦ ♣(♦✜00✐♦♥❛❧ 2✉❛♥&♦ ♣❡00♦❛❧✳ ❆♦ ;(♦❢✳ ◆♦(&♦♥✱ ♣♦( 0✉❛ ❝♦♠♣❡&P♥❝✐❛ ❡ ❛♦ ;(♦❢✳ ❍❛♠✐❧&♦♥ ♣♦( 0❡✉0 ✈❛❧♦(♦0♦0 ❝♦♥0❡❧❤♦0✳

❆♦ ♠❡✉ ;(♦❢❡00♦( ❡ ❖(✐❡♥&❛❞♦( ❞❡ ■♥✐❝✐❛1G♦ ❈✐❡♥&7✜❝❛✱ ♥❛ ❯♥✐✈❡(0✐❞❛❞❡ ❈❛&B❧✐❝❛ ❞❡ ●♦✐D0✱ ❏❛❧❧❡0 ❋(❛♥❝♦ ❘✐❜❡✐(♦ ❞❛ ❈✉♥❤❛ ✭❯❈●✮✱ ♣♦( ❛❝(❡❞✐&❛( ❡♠ ♠❡✉ ♣♦&❡♥✲ ❝✐❛❧✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ 0✉❛ ❡①❝❡❧❡♥&❡ ❝♦♥&(✐❜✉✐1G♦ V ♠✐♥❤❛ ❢♦(♠❛1G♦✳

❆♦ ♣(♦❢❡00♦( ❘I❣✐0 2✉❡ ♠❡ ✐♥❝❡♥&✐✈♦✉ ❡ ❛♣♦✐♦✉ ❛ ❢❛③❡( ❛ ❣(❛❞✉❛1G♦ ❡♠ ❋70✐❝❛✳

❆♦ ♠❡✉ ❡0♣♦0♦ ❘❛✛❛❡❧✱ ♣♦( &♦❞❛ ♣❛❝✐P♥❝✐❛✱ ❝♦♠♣(❡❡♥00G♦✱ ❝❛(✐♥❤♦ ❡ ❛♣♦✐♦✱ ♥✉♥❝❛ ❞❡0❛❝(❡❞✐&❛♥❞♦ ❞❛ ♠✐♥❤❛ ❝❛♣❛❝✐❞❛❞❡✳

❆♦0 ♠❡✉0 2✉❡(✐❞♦0 ❛✈B0✱ ♣❡❧♦ ❝❛(✐♥❤♦✱ ✈❛❧♦(❡0 I&✐❝♦0 2✉❡ ♠❡ ♣❛00❛(❛♠ ❡ &♦❞♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐(♦✱ ❡0&❛♥❞♦ 0❡♠♣(❡ ♣(❡0❡♥&❡0 ❡ ❞✐0♣♦0&♦0 ❛ ♠❡ ❛❥✉❞❛( ♥♦0 ♠♦♠❡♥&♦0 ❞✐❢7❝❡✐0✳

❆♦0 ♠❡✉0 ♣❛✐0 ♣❡❧♦ ✐♥❝❡♥&✐✈♦ ❛♦ ♠❡✉ ❝(❡0❝✐♠❡♥&♦✳

➚ ♠✐♥❤❛ ❚✐❛ ▼❛(❧❡♥❡✱ 2✉❡ ❝♦♥&(✐❜✉✐✉ ♠✉✐&♦ ♣❛(❛ ♠✐♥❤❛ ❢♦(♠❛1G♦ ✐♥&❡❧❡❝✲ &✉❛❧✱ 0❡♥❞♦ ♠✉✐&♦ ❛&✉❛♥&❡ ♥♦0 ♠♦♠❡♥&♦0 2✉❡ ♥❡❝❡00✐&❡✐ ❞❡ ❛❥✉❞❛ ♣❛(❛ ♣(♦00❡❣✉✐( ❝♦♠ ♦0 ♠❡✉0 ❡0&✉❞♦0✳

➚ ❚✐❛ ▼❛(✐♥❛✱ ❚✐❛ ▼❛(❧❡✐❞❡✱ ❚✐❛ ❚✐♥❛✱ ❚✐♦ ❏Z♥✐♦✱ ♠❡✉0 ✐(♠G♦0 ❡ ❞❡♠❛✐0 ♠❡♠❜(♦0 ❞❛ ❢❛♠7❧✐❛✱ ♣♦( &❡(❡♠ 0❡♠♣(❡ ❛❝(❡❞✐&❛❞♦ ❡♠ ♠✐♠✱ ♠❡ ✐♥❝❡♥&✐✈❛❞♦✱ ❛♣♦✐❛❞♦ ❡ ❝♦♥0♦❧❛❞♦ ♥♦0 ♠♦♠❡♥&♦0 ❞✐❢7❝❡✐0✳

❆♦0 ♠❡✉0 ❛♠✐❣♦0✱ ❲❛♥❡00❛✱ ▼❛❜❡❧✱ ▲✉❝✐❛♥❛✱ ❲❡0❧❡②✱ ▲✉&&✱ ❩✉❧❡✐❞❡✱ ❘❛❢❛❡❧ ❆❧♠❡✐❞❛✱ ❏♦G♦✱ ❉✐❡❣♦✱ ❘♦❞♦❧♣❤♦✱ ❊❞✈❛♥ ❡ ■(❛♥✐❧❞♦✱ 2✉❡ ♠❡0♠♦ ❧♦♥❣❡✱ 0❡♠♣(❡ &✐✈❡(❛♠ ✉♠❛ ♣❛❧❛✈(❛ ❛♠✐❣❛✱ 2✉❡ ♠❡ ❛❥✉❞♦✉ ❛ ❡♥❢(❡♥&❛( ♦0 ♦❜0&D❝✉❧♦0 ❡ ❛❝(❡❞✐&❛( 2✉❡ ❡✉ ❡(❛ ❝❛♣❛③ ❞❡ 0✉♣❡(D✲❧♦0 ❡ 0❡❣✉✐( ❡♠ ❢(❡♥&❡✳

❆♦ ♠❡✉ ❙♦❣'♦ ❙'✳ ❏♦*♦ ❋✳ ,✐♥/♦✱ 1✉❡ ♥♦2 ❢♦'♥❡❝❡✉ ✉♠❛ ❛❥✉❞❛ 2✉❜2/❛♥❝✐❛❧✱ ♣❛'❛ 1✉❡ ❡✉ ❡ ♠❡✉ ❡2♣♦2♦ ♣✉❞;22❡♠♦2 ✐' ❢❛③❡' ♦ ♠❡2/'❛❞♦ ❡ = ♠✐♥❤❛ ❙♦❣'❛ ▼❛'✐❛ ❞❡ ❋@/✐♠❛ 1✉❡ /❛♥/♦ ♥♦2 ❛❥✉❞♦✉ ♥♦ ♣❡'A♦❞♦ 1✉❡ ❡2/✐✈❡♠♦2 ❝✉'2❛♥❞♦ ♦ ♠❡2/'❛❞♦✳

➚ /♦❞♦2 ♦2 ♠❡✉2 ❞❡♠❛✐2 ❛♠✐❣♦2 1✉❡ 2❡♠♣'❡ ♠❡ ❛♣♦✐❛'❛♠ ❡ ❛❝'❡❞✐/❛'❛♠ ❡♠ ♠✐♠✳

➚ ❈❛♣❡2 ♣❡❧❛ ❜♦❧2❛ ❝♦♥❝❡❞✐❞❛ ❞✉'❛♥/❡ ❛ ❡①❡❝✉F*♦ ❞♦ /'❛❜❛❧❤♦✳ . . .

❘❡"✉♠♦

◆❡""❡ #$❛❜❛❧❤♦ ✐♥✈❡"#✐❣❛♠♦" ❛" ♣$♦♣$✐❡❞❛❞❡" ✈✐❜$❛❝✐♦♥❛✐" ❡♠ ♠♦♥♦❝$✐"#❛✐" ❉✲ ▼❡#✐♦♥✐♥❛✱ ✉#✐❧✐③❛♥❞♦ ❛" ❡"♣❡❝#$♦"❝♦♣✐❛" ❘❛♠❛♥ ❡ ■♥❢$❛✈❡$♠❡❧❤♦✳ ❆" ♠❡❞✐❞❛" ❞❡ ❡"♣❡❝✲ #$♦"❝♦♣✐❛ ❘❛♠❛♥ ❢♦$❛♠ $❡❛❧✐③❛❞❛" "♦❜ ❛ ✈❛$✐❛=>♦ ❞❡ ♣$❡"">♦ ❤✐❞$♦"#?#✐❝❛ ♥♦ ✐♥#❡$✈❛❧♦ ❞❡ 0GP a❛#@ 7GP a✱ ♠♦"#$❛$❛♠ ❞✉❛" #$❛♥"✐=A❡" ❞❡ ❢❛"❡✱ ✉♠❛ ♣♦$ ✈♦❧#❛ 2.0GP a ❡ ♦✉#$❛ ❡♠ 2.5GP a✱ ❛" B✉❛✐" ❢♦$❛♠ ❞❡#❡❝#❛❞❛" ♥♦ ❡"♣❡❝#$♦ ❘❛♠❛♥ ❛#$❛✈@" ❞❛" ♠✉❞❛♥=❛" ❡①✐❜✐❞❛" ♣❡❧♦" ♣✐❝♦" ❛""♦❝✐❛❞♦" ♣$✐♥❝✐♣❛❧♠❡♥#❡ D" ✈✐❜$❛=A❡" ❛#$✐❜✉E❞❛" D ❝❛$❜♦①✐❧❛ ✭CO₂−✮✱ ❛♠✐♥❛ ✭N H₃+✮✱ ❧✐❣❛=A❡" ❈❙ ❡ ❈❙❈ ❡ ❣$✉♣♦" CH2 ❡ CH3✳ ❊""❡" ♠♦❞♦" ✈✐❜$❛❝✐♦♥❛✐" #❛♠❜@♠

❢♦$❛♠ "❡♥"✐❜✐❧✐③❛❞♦" ❡♠ ❜❛✐①❛" #❡♠♣❡$❛#✉$❛"✱ "❡♥❞♦ B✉❡ "✉❛" ♠✉❞❛♥=❛" "❡$✈✐$❛♠ ❝♦♠♦ $❡❢❡$K♥❝✐❛ ♣❛$❛ ✐❞❡♥#✐✜❝❛$ ❛ #$❛♥"✐=>♦ ❞❡ ❢❛"❡ ♥❛" ♠❡❞✐❞❛" ❞❡ ❡"♣❛❧❤❛♠❡♥#♦ ✐♥❢$❛✈❡$♠❡❧❤♦ ♥♦ ✐♥#❡$✈❛❧♦ ❞❡ #❡♠♣❡$❛#✉$❛ ❞❡ 298K ❛ 84K✳ ◆❛" ♠❡❞✐❞❛" ❞❡ ❡"♣❛❧❤❛♠❡♥#♦ ❘❛♠❛♥ ❞❡ 298K ❛ 13K✱ ❛ #$❛♥"✐=>♦ ❢♦✐ ✐❞❡♥#✐✜❝❛❞❛ ♣❡❧♦ "✉$❣✐♠❡♥#♦ ❞♦ ♠♦❞♦ #$❛♥"❧❛❝✐♦♥❛❧ ❡♠ 91 cm−1 _{♣♦$ ✈♦❧#❛ ❞❡ 84K✳ ❆❧@♠ ❞✐""♦✱ ♥❡""❡ #$❛❜❛❧❤♦ ❝♦♠♣❛$❛♠♦" ♦ ❝♦♠♣♦$#❛♠❡♥#♦}

❞❛" ♠✉❞❛♥=❛" ❛♣$❡"❡♥#❛❞❛" ♥❛ $❡❞❡ ❝$✐"#❛❧✐♥❛ ❞♦" ♠♦♥♦❝$✐"#❛✐" ❞❡ ❉✲♠❡#✐♦♥✐♥❛ ❡ ❞❡ ▲✲ ♠❡#✐♦♥✐♥❛ "♦❜ ❝♦♥❞✐=A❡" ❡①#$❡♠❛" ❞❡ ♣$❡"">♦✳

N❛❧❛✈$❛"✲❝❤❛✈❡✿ ❉✲♠❡#✐♦♥✐♥❛✳ ❊"♣❛❧❤❛♠❡♥#♦ ❘❛♠❛♥✳ ❊"♣❛❧❤❛♠❡♥#♦ ■♥❢$❛✈❡$♠❡❧❤♦✳ ❚$❛♥"✐=A❡" ❞❡ ❋❛"❡✳ ❆❧#❛" N$❡""A❡"✳ ❚❡♠♣❡$❛#✉$❛✳

❆❜"#$❛❝#

■♥ "❤✐% ✇♦(❦ ✇❡ ❤❛✈❡ ❜❡❡♥ ✐♥✈❡%"✐❣❛"❡❞ "❤❡ ✈✐❜(❛"✐♦♥❛❧ ♣(♦♣❡("✐❡% ♦❢ "❤❡ ❉✲ ♠❡"❤✐♦♥✐♥❡ %✐♥❣❧❡ ❝(②%"❛❧% ✉%✐♥❣ "❤❡ ❘❛♠❛♥ ❛♥❞ ■♥❢(❛(❡❞ %♣❡❝"(♦%❝♦♣✐❡%✳ ❚❤❡ ❘❛♠❛♥ %♣❡❝"(♦%❝♦♣② ♠❡❛%✉(❡♠❡♥"% ✇❡(❡ ♣❡(❢♦(♠❡❞ ✉♥❞❡( ✈❛(②✐♥❣ ❤②❞(♦%"❛"✐❝ ♣(❡%%✉(❡ ❢(♦♠ 0GP a✉♣ "♦7GP a✱ ✐♥❞✐❝❛"❡❞ "✇♦ "(❛♥%✐"✐♦♥%✱ ♦♥❡ ❛(♦✉♥❞2.0GP a❛♥❞ ❛♥♦"❤❡( ✐♥ 2.5GP a✱ ✇❤✐❝❤ ✇❡(❡ ❞❡"❡❝"❡❞ ❜② ❝❤❛♥❣❡% ♦❢ "❤❡ ✈✐❜(❛"✐♦♥❛❧% ♠♦❞❡% ♦❢ "❤❡ ❝❛(❜♦①✐❧✐❝ ✭CO−

2✮✱❛♠✐♥♦

✭N H+

3 ✮✱ ❈❙✱ ❈❙❈✱ CH2 ❛♥❞ CH3✱ (❡%♣❡❝"✐✈❡❧②✳ ❚❤❡%❡ ✈✐❜(❛"✐♦♥❛❧% ♠♦❞❡% ❛❧%♦ ❤❛✈❡ ❜❡❡♥

%❡♥%✐"✐③❡❞ ✉♥❞❡( ❧♦✇ "❡♠♣❡(❛"✉(❡%✱ ✇❤♦%❡ ❝❤❛♥❣❡% ❤❛✈❡ ❜❡❡♥ ❤❡❧♣❢✉❧ "♦ ✐❞❡♥"✐❢② "❤❡ ♣❤❛%❡ "(❛♥%✐"✐♦♥ ✇✐"❤ "❤❡ ♠❡❛%✉(❡♠❡♥"% ♦❢ "❤❡ ✐♥❢(❛(❡❞ %❝❛""❡(✐♥❣ ❢(♦♠ 298K ✉♣ "♦84K✳ ■♥ "❤❡ ♠❡❛%✉(❡♠❡♥"% ♦❢ "❤❡ ❘❛♠❛♥ %❝❛""❡(✐♥❣ (❡❛❧✐③❡❞ ❜❡"✇❡❡♥ 298K ❛♥❞ 84K✱ "❤❡ "(❛♥%✐"✐♦♥ ✇❛% ✐❞❡♥"✐✜❡❞ ❜② ❡♠❡(❣✐♥❣ ♦❢ "❤❡ "(❛♥%❧❛"✐♦♥❛❧ ♠♦❞❡ ✐♥ 91 cm−1 _{❛(♦✉♥❞ 84K✳ ❋✉(✲}

"❤❡(✱ ✐♥ "❤✐% ✇♦(❦ ✇❡ ❤❛✈❡ ❜❡❡♥ ❝♦♠♣❛(❡❞ ❝❤❛♥❣❡% ♣(❡%❡♥"❡❞ ❜② ❝(②%"❛❧ ❧❛""✐❝❡ ❜❡"✇❡❡♥ ❉✲♠❡"❤✐♦♥✐♥❡ ❛♥❞ ▲✲♠❡"❤✐♦♥✐♥❡ ✉♥❞❡( ❡①"(❡♠❡% ❝♦♥❞✐"✐♦♥% ♦❢ "❤❡ ♣(❡%%✉(❡✳

❑❡②✇♦(❞%✿ ❉✲♠❡"❤✐♦♥✐♥❡✳ ❘❛♠❛♥ ❙❝❛""❡(✐♥❣✳ ■♥❢(❛(❡❞ ❙❝❛""❡(✐♥❣✳ H❤❛%❡ ❚(❛♥%✐"✐♦♥%✳ ❍✐❣❤ H(❡%%✉(❡✳ ❚❡♠♣❡(❛"✉(❡✳

❈♦♥#❡%❞♦

✶ ■♥#$♦❞✉()♦ ✶

✷ ❆♠✐♥♦.❝✐❞♦0 ✸

✷✳✶ ❋✉♥❞❛♠❡♥*♦, ❚❡./✐❝♦, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✸ ❊0♣❡❝#$♦0❝♦♣✐❛ ❘❛♠❛♥ ✽

✸✳✶ ❋✉♥❞❛♠❡♥*♦, ❚❡./✐❝♦, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✸✳✶✳✶ ❆❜♦/❞❛❣❡♠ ❈❧9,,✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✸✳✶✳✷ ❆❜♦/❞❛❣❡♠ ◗✉<♥*✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✷ ▼♦♥*❛❣❡♠ ❡①♣❡/✐♠❡♥*❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✷✳✶ ❈❡❧❛ ❞❡ B/❡,,C♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✹ ❊0♣❡❝#$♦0❝♦♣✐❛ ■♥❢$❛✈❡$♠❡❧❤♦ ✷✸

✹✳✶ ❋✉♥❞❛♠❡♥*♦, ❚❡./✐❝♦, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✹✳✷ ▼♦♥*❛❣❡♠ ❊①♣❡/✐♠❡♥*❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻

✺ ❘❡0✉❧#❛❞♦0 ✷✾

✺✳✶ ❊,♣❡❝*/♦,❝♦♣✐❛ ❘❛♠❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✺✳✶✳✶ ❉✐,❝✉,,C♦ ,♦❜/❡ ❛ */❛♥,✐IC♦ ❡♠ ❛❧*❛, ♣/❡,,J❡, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✺✳✶✳✷ ▼❡❞✐❞❛, ❘❛♠❛♥ ❡♠ ❢✉♥IC♦ ❞❛ ❚❡♠♣❡/❛*✉/❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✺✳✷ ❊,♣❡❝*/♦,❝♦♣✐❛ ■♥❢/❛✈❡/♠❡❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✷✳✶ ❉✐,❝✉,,C♦ ,♦❜/❡ ❛ */❛♥,✐IC♦ ❡♠ ❜❛✐①❛, *❡♠♣❡/❛*✉/❛, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

✻ ❈♦♥❝❧✉0)♦ ✻✶

✼ !❡#$♣❡❝'✐✈❛$ ✻✹

▲✐"#❛ ❞❡ ❋✐❣✉*❛"

✷✳✶ ❊!"✉❡♠❛ ❞❛ ❊!()✉(✉)❛ ❇+!✐❝❛ ❞♦! ❆♠✐♥♦+❝✐❞♦!✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹

✷✳✷ ■❧✉!()❛45♦ ❞❛ ❈❧❛!!✐✜❝❛45♦ ❞♦! ❛♠✐♥♦+❝✐❞♦! !❡❣✉♥❞♦ ❛ ♣♦!✐45♦ ❞❛ ❛♠✐♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✷✳✸ ❆♠✐♥♦+❝✐❞♦! ❊♥❛♥(✐:♠❡)♦!✿ ▲✲❆♠✐♥♦+❝✐❞♦✲❛♠✐♥♦+❝✐❞♦ ❧❡✈?❣✐)♦❀ ❉✲❆♠✐♥♦+❝✐❞♦✲❛♠✐♥♦+❝✐❞♦ ❞❡①()?❣✐)♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✷✳✹ ❘❡❛45♦ ❡♥()❡ ❞♦✐! ♠♦♥♦♣❡♣(D❞❡♦! ♣❛)❛ ❢♦)♠❛) ✉♠ ❞✐♣❡♣(D❞❡♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✸✳✶ ■❧✉!()❛45♦ ❞♦ ❡❧✐♣!?✐❞❡ ❞❡ ♣♦❧❛)✐③❛❜✐❧✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✸✳✷ ❚✐♣♦! ❞❡ ♠♦❞♦! ✈✐❜)❛❝✐♦♥❛✐!✿ ❆ ♣)✐♠❡✐)❛ ✜❣✉)❛ ❡①❡♠♣❧✐✜❝❛ ✉♠❛ ♠♦❧I❝✉❧❛ ❡♠ "✉❡ ♦! +(♦♠♦! ❡!(5♦ ❛ ✉♠❛ ❞✐!(J♥❝✐❛ ❞❡ ❡"✉✐❧D❜)✐♦ re ❡ ❛ ✜❣✉)❛ ❛♦ !❡✉ ❧❛❞♦ ✐❧✉!()❛ ♦! +(♦♠♦!

❢♦)❛ ❞❛ !❡♣❛)❛45♦ ❞❡ ❡"✉✐❧D❜)✐♦✳ ❆! !❡(❛! ✐♥❞✐❝❛♠ ♦ !❡♥(✐❞♦ ❞❡ ❞❡!❧♦❝❛♠❡♥(♦ ❞♦! +(♦♠♦!

❡ ♦ !✐♥❛✐! ❞❡+❡−✐♥❞✐❝❛♠ ♦ !❡♥(✐❞♦ ❞❡ ❞❡!❧♦❝❛♠❡♥(♦ ❞♦! +(♦♠♦! ❛❝✐♠❛ ♦✉ ❛❜❛✐①♦ ❞♦ ♣❧❛♥♦✱ ❢❛③❡♥❞♦ ✉♠❛ ♦❜!❡)✈❛45♦ "✉❛♥(♦ ❛ ✈✐❜)❛45♦ ❞❡ ❞❡❢♦)♠❛45♦ ❢♦)❛ ❞♦ ♣❧❛♥♦✱ ❡♠ "✉❡

♦ ❞❡!❧♦❝❛♠❡♥(♦ ❞♦! +(♦♠♦! ♦❝♦))❡ ❡♠ )❡❧❛45♦ ❛ ❡!()✉(✉)❛ ❞♦ ❡!"✉❡❧❡(♦ ♠♦❧❡❝✉❧❛)✳ ✳ ✳ ✶✺ ✸✳✸ ❊!(❛❞♦! ❱✐❜)❛❝✐♦♥❛✐! ❞♦ M♦♥(♦ ❞❡ ✈✐!(❛ ❞❡ ✉♠ M♦(❡♥❝✐❛❧ ❍❛)♠:♥✐❝♦ ❡ M♦(❡♥❝✐❛❧ ❞❡

▼♦)!❡✱ ❡♠ "✉❡re✱ )❡♣)❡!❡♥(❛ ❛ !❡♣❛)❛45♦ ❞❡ ❡"✉✐❧D❜)✐♦ ❞❛ ❧✐❣❛45♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✸✳✹ ■❧✉!()❛45♦ ❞♦! ❞✐❢❡)❡♥(❡! (✐♣♦! ❞❡ ❡!♣❛❧❤❛♠❡♥(♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✸✳✺ ❊)*✉❡♠❛ ❞❛ ❝♦♥✜❣✉5❛67♦ ❞♦ ❊)♣❡❝95:♠❡95♦ ❏♦❜✐♥ ❨✈♦♥ ♠♦❞❡❧♦ ❚✻✹✵✵✵ ✉9✐❧✐③❛❞♦ ♥❡)9❡ 95❛❜❛❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✻ ❉❡9❛❧❤❛♠❡♥9♦ ❞♦) )✉❜95❛9♦5❡) ❡ ❡)♣❡❝95G❣5❛❢♦ ❞♦ ❊)♣❡❝95:♠❡95♦ ❏♦❜✐♥

❨✈♦♥ ♠♦❞❡❧♦ ❚✻✹✵✵✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✼ ❈❡❧❛ ❞❡ ♣)❡!!5♦✿ ✭❛✮ ✈✐!5♦ ❡①(❡)♥❛ ❡ ✭❜✮ ✈✐!5♦ ✐♥(❡)♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

✹✳✶ ❋)❡"✉T♥❝✐❛! ✈✐❜)❛❝✐♦♥❛✐! ♥❛(✉)❛✐! ❞❡ ❛❧❣✉♥! ♠♦❧I❝✉❧❛!✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✹✳✷ ❊!"✉❡♠❛ ❞♦ ❊!♣❡❝():♠❡()♦ ❱❡)(❡① ✼✵ ❞❛ ❇)✉❦❡) ❖♣(✐❝!✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻

✹✳✸ ❊!"✉❡♠❛ ❞♦ ❊!♣❡❝+,-♠❡+,♦ ❱❡,+❡① ✼✵ ❞❛ ❇,✉❦❡, ❖♣+✐❝!✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✺✳✶ ■♠❛❣❡♠ ❞♦! ♠♦♥♦❝,✐!+❛✐! ❞❡ ❉✲♠❡+✐♦♥✐♥❛ ❝,❡!❝✐❞♦! ♣❡❧♦ ♠=+♦❞♦ ❞❡ ❡✈❛♣♦,❛?@♦ ❧❡♥+❛✳ ✷✾ ✺✳✷ ❊!♣❡❝+,♦ ❘❛♠❛♥ ❞❛ ❉✲▼❡+✐♦♥✐♥❛ C +❡♠♣❡,❛+✉,❛ ❛♠❜✐❡♥+❡✳ ✭❛✮ ,❡❣✐@♦ ❞❡50❛150cm−1

✭♠❡❞✐❞❛ ,❡❛❧✐③❛❞❛ ♥♦ ❡!♣❡❝+,-♠❡+,♦ T64000✮✳ ✭❜✮ ,❡❣✐@♦150 ❛ 600cm−1✱ ✭❝✮ ,❡❣✐@♦ ❞❡

600❛1200cm−1✱ ✭❞✮ ,❡❣✐@♦ ❞❡1200❛1800cm−1❡ ✭❡✮ ,❡❣✐@♦18000 ❛3200cm−1✱ !❡♥❞♦

❡!!❛! I❧+✐♠❛! ,❡❣✐J❡! ,❡❢❡,❡♥+❡! C! ♠❡❞✐❞❛! ,❡❛❧✐③❛❞❛! ♥♦! ❡!♣❡❝+,-♠❡+,♦ ❈♦♥❢♦❝❛❧ ✳ ✳ ✸✷ ✺✳✸ ▼❡❞✐❞❛! ❞❡ ❡!♣❛❧❤❛♠❡♥+♦ ❘❛♠❛♥ ♥❛ ❉✲♠❡+✐♦♥✐♥❛ ♥♦ ❡!♣❡❝+,-♠❡+,♦ T64000 ❞❡ ❝♦♠✲

♣,❡!!@♦ ✭❛✮ ❡ ❞❡!❝♦♠♣,❡!!@♦ ✭❜✮ ,❡❢❡,❡♥+❡! C ,❡❣✐@♦ ❞❡50❛ 600cm−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✺✳✹ ▼❡❞✐❞❛! ❞❡ ❡!♣❛❧❤❛♠❡♥+♦ ❘❛♠❛♥ ♥❛ ❉✲♠❡+✐♦♥✐♥❛ ♥♦ ❡!♣❡❝+,-♠❡+,♦ T6400 ❞❡ ❝♦♠✲

♣,❡!!@♦ ✭❛✮ ❡ ❞❡!❝♦♠♣,❡!!@♦ ✭❜✮ ,❡❢❡,❡♥+❡! C ,❡❣✐@♦ ❞❡600 ❛1200cm−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✺✳✺ ✭❛✮ ❊!♣❡❝+,♦! ❘❛♠❛♥ ❞❡ ❝♦♠♣,❡!!@♦ ❞❛ ❉✲♠❡+✐♦♥✐♥❛ ♦❜+✐❞♦! ❞♦ ❡!♣❡❝+,-♠❡+,♦ T64000

,❡❢❡,❡♥+❡! C ,❡❣✐@♦ ❞❡ 50❛ 150 cm−1 ❡ ♣,♦✈❡♥✐❡♥+❡! ❞❛! ♠❡❞✐❞❛! ,❡❛❧✐③❛❞❛! ♥♦ ❡!♣❡❝✲

+,-♠❡+,♦ ❈♦♥❢♦❝❛❧ ✭❜✮ ,❡❣✐@♦ ❞❡150C 600cm−1 ❡ ✭❝✮ ,❡❣✐@♦ ❞❡600 C1200cm−1✳ ✳ ✳ ✸✻

✺✳✻ ▼♦❞♦! ❞❛ ❉✲♠❡+✐♦♥✐♥❛ ,❡❢❡,❡♥+❡! C ,❡❣✐@♦ 150❛600cm−1✱ !✉❜❞✐✈✐❞✐❞♦! ❡♠ ✭❛✮ ❞❡140

❛ 300 cm−1 ❡ ✭❜✮ ❞❡ 300 ❛ 600 cm−1❀ !❡♥❞♦ "✉❡ ♦! !O♠❜♦❧♦! +♦+❛❧♠❡♥+❡ ♣,❡❡♥❝❤✐❞♦!

,❡♣,❡!❡♥+❛♠ ♦! ❞❛❞♦! ♦❜+✐❞♦! ❞♦ ❡!♣❡❝+,-♠❡+,♦ ❈♦♥❢♦❝❛❧ ❡ ♦! !O♠❜♦❧♦! !❡♠✐✲♣,❡❡♥❝❤✐❞♦!

,❡♣,❡!❡♥+❛♠ ♦! ❞❛❞♦! ♦❜+✐❞♦! ✈✐❛ ❡!♣❡❝+,-♠❡+,♦T64000✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼

✺✳✼ ▼♦❞♦! ❞❛ ❉✲♠❡+✐♦♥✐♥❛ ,❡❢❡,❡♥+❡! C ,❡❣✐@♦640❛1200cm−1✱ !✉❜❞✐✈✐❞✐❞♦! ❡♠ ✭❝✮ ❞❡640

❛ 840cm−1 ❡ ✭❞✮ ❞❡ 840 ❛ 1200cm−1❀ !❡♥❞♦ "✉❡ ♦! !O♠❜♦❧♦! +♦+❛❧♠❡♥+❡ ♣,❡❡♥❝❤✐❞♦!

,❡♣,❡!❡♥+❛♠ ♦! ❞❛❞♦! ♦❜+✐❞♦! ❞♦ ❡!♣❡❝+,-♠❡+,♦ ❈♦♥❢♦❝❛❧ ❡ ♦! !O♠❜♦❧♦! !❡♠✐✲♣,❡❡♥❝❤✐❞♦!

,❡♣,❡!❡♥+❛♠ ♦! ❞❛❞♦! ♦❜+✐❞♦! ✈✐❛ ❡!♣❡❝+,-♠❡+,♦T64000✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼

✺✳✽ ❉❡+❛+❛❧❤❛♠❡♥+♦ ❞❛! ❧♦,❡♥+③✐❛♥❛! ❞♦! ♣✐❝♦! ❡①♣,❡!!✐✈♦! ,❡❢❡,❡♥+❡! ❛♦! ♠♦❞♦! ✈✐❜,❛❝✐♦♥❛✐! ❝❛,❛❝+❡,O!+✐❝♦! ❞❡ ❝❛❞❛ ✉♠❛ ❞❛! ❢❛!❡! ❞♦ ♠♦♥♦❝,✐!+❛❧ ❞❡ ❉✲♠❡+✐♦♥✐♥❛ "✉❛♥❞♦ !✉❜♠❡+✐❞♦

❛ ❛❧+❛! ♣,❡!!J❡!✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✺✳✾ ■❧✉!+,❛?@♦ ❞♦! ❡!+✐,❛♠❡♥+♦! !✐♠=+,✐❝♦! ❡ ❛!!✐♠=+,✐❝♦! ❞❛! ❧✐❣❛?J❡! C−S−C✳ ✳ ✳ ✳ ✳ ✹✶

✺✳✶✵ ■❧✉!+,❛?@♦ ❞❛ ❝=❧✉❧❛ ✉♥✐+P,✐❛ ❞♦ ♠♦♥♦❝,✐!+❛❧ ❞❡ ▲✲▼❡+✐♦♥✐♥❛✱ ❣❡,❛❞❛ ❞♦ ❛,"✉✐✈♦ ❝✐❢ ❞❡ ❚♦,✐ ❡+ ❛❧ ❬✺✷❪ ❡ ❞♦ ♠♦♥♦❝,✐!+❛❧ ❞❡ ❉✲♠❡+✐♦♥✐♥❛✱ ❣❡,❛❞❛ ❛+,❛✈=! ❞♦! ❞❛❞♦! ❞♦ ❛,"✉✐✈♦

❝✐❢ ❬✸✸❪✳ ❖! P+♦♠♦! ❞❡ ❝♦, ❝✐♥③❛ ,❡♣,❡!❡♥+❛♠ ♦! ❝❛,❜♦♥♦!✱ ♦! ❞❡ ❝♦, ❛♠❛,❡❧❛ ♦ ❡♥①♦❢,❡✱

♦! ❞❡ ❝♦, ✈❡,♠❡❧❤❛ ♦ ♦①✐❣X♥✐♦ ❡ ❞❡ ❝♦, ❜,❛♥❝❛ ♦ ❤✐❞,♦❣X♥✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✺✳✶✶ ❈♦♠♣❛%❛&'♦ ❞❛) ♠✉❞❛♥&❛) ♦❜)❡%✈❛❞❛) ♥♦ ❡)♣❡❝0%♦ ❘❛♠❛♥ ♦❜0✐❞♦ ❞❡ ♠❡❞✐❞❛) %❡❛❧✐③❛❞❛) )♦❜ ❛❧0❛) ♣%❡))5❡) ❡♠ ♠♦♥♦❝%✐)0❛✐) ❞❡ ❉✲ ▼❡0✐♦♥✐♥❛ ✭❛✮ ❡ ✭❜✮ ❡ ❞❡ ▲✲▼❡0✐♦♥✐♥❛ ✭❝✮ ❡

✭❞✮ ❬✶✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✺✳✶✷ ❊)♣❡❝0%♦ ❘❛♠❛♥ ♦❜0✐❞♦ ❛0%❛✈B) ❞♦ ❡)♣❡❝0%C♠❡0%♦T64000%❡❢❡%❡♥0❡ ❛ %❡❣✐'♦ ✶ ✭❛✮ ❞❡50

F600cm−1 ❡ %❡❣✐'♦ ✷ ✭❜✮ ❞❡600F 1200cm−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✺✳✶✸ ❊)♣❡❝0%♦ ❘❛♠❛♥ ♦❜0✐❞♦ ❛0%❛✈B) ❞♦ ❡)♣❡❝0%C♠❡0%♦ T64000 %❡❢❡%❡♥0❡ ❛ %❡❣✐'♦ ✸ ✭❛✮ ❞❡ 1200F 1700cm−1❡ %❡❣✐'♦ ✹ ✭❜✮ ❞❡2800F 3100cm−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✺✳✶✹ ▼♦❞♦) %❡❢❡%❡♥0❡) ❛ %❡❣✐'♦ ✶ J✉❡ ❝♦♠♣%❡❡♥❞❡ ❛♦ ✐♥0❡%✈❛❧♦ ❞❡50F600cm−1✱ )✉❜❞✐✈✐❞✐❞♦)

❡♠ ✭❛✮50F300 cm−1❡ ✭❜✮300 F560cm−1❀ ❡ ♠♦❞♦) %❡❢❡%❡♥0❡) ❛ %❡❣✐'♦ ✷ J✉❡ ❛❜%❛♥❣❡

❞❡600F1200cm−1✱ )✉❜❞✐✈✐❞✐❞♦) ❡♠ ✭❝✮ 600F900 _cm−1❡ ✭❞✮ 950F 1200_cm−1✳ ✳ ✳ ✺✶

✺✳✶✺ ▼♦❞♦) %❡❢❡%❡♥0❡) ❛ %❡❣✐'♦ ✸ J✉❡ ❝♦♠♣%❡❡♥❞❡ ❛♦ ✐♥0❡%✈❛❧♦ ❞❡ 1200F 1700cm−1✱ )✉❜❞✐✲

✈✐❞✐❞♦) ❡♠ ✭❛✮1220F1380cm−1❡✭❜✮1400F1690_cm−1❀ ❡ ✭❝✮ ♠♦❞♦) %❡❢❡%❡♥0❡) ❛ %❡❣✐'♦

✹ J✉❡ ❛❜%❛♥❣❡ ❞❡2800F 3100cm−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

✺✳✶✻ ❉✐❢%❛0♦❣%❛♠❛ ♣%♦✈❡♥✐❡♥0❡ ❞❛) ♠❡❞✐❞❛) ❞❡ ❞✐❢%❛&'♦ ❞❡ %❛✐♦)✲① ✉0✐❧✐③❛♥❞♦ ♦ ♠B0♦❞♦ ❞♦ ♣N ♥♦) ♠♦♥♦❝%✐)0❛✐) ❞❡ ❉✲♠❡0✐♦♥✐♥❛ ♥♦ ✐♥0❡%✈❛❧♦ ❞❡ 0❡♠♣❡%❛0✉%❛ ❞❡ ✸✵✼❑ F ✽✹❑✳ ✳ ✳ ✺✹

✺✳✶✼ ▼❡❞✐❞❛) ❞❡ ❛❜)♦%❜R♥❝✐❛ ♥♦ ✐♥❢%❛✈❡%♠❡❧❤♦ ❞❛ ❉✲♠❡0✐♦♥✐♥❛ ❞❡)❡♥✈♦❧✈✐❞❛) ♥♦ ❡)♣❡❝✲ 0%C♠❡0%♦ ❱❡0❡① ✼✵ ❞❛ ❇%✉❝❦❡%✱ ♥❛ %❡❣✐'♦ ❞❡400 F1200cm−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✺✳✶✽ ▼❡❞✐❞❛) ❞❡ ❛❜)♦%❜R♥❝✐❛ ♥♦ ✐♥❢%❛✈❡%♠❡❧❤♦ ❞❛ ❉✲♠❡0✐♦♥✐♥❛ ❞❡)❡♥✈♦❧✈✐❞❛) ♥♦ ❡)♣❡❝✲ 0%C♠❡0%♦ ❱❡0❡① ✼✵ ❞❛ ❇%✉❝❦❡%✱ ♥❛ %❡❣✐'♦ ❞❡1200F3600cm−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✺✳✶✾ ■❧✉)0%❛&'♦ ❞❡ ✉♠❛ ♠♦❧B❝✉❧❛ ♥'♦ ❞✐)0♦%❝✐❞❛ ❡♠ ❝♦♥❞✐&5❡) ❛♠❜✐❡♥0❡) ❞❡ 0❡♠♣❡%❛0✉%❛ ❡ ♣%❡))'♦ ❡ ❞❡ ✉♠❛ ♣♦))X✈❡❧ ❢♦%♠❛ ❞❡ ✉♠❛ ♠♦❧B❝✉❧❛ ❞✐)0♦%❝✐❞❛ ❞❡✈✐❞♦ ❛ ❝♦♥❞✐&5❡)

❡①0%❡♠❛) ❞❡ 0❡♠♣❡%❛0✉%❛ ❡ ♣%❡))'♦✱ ♦♥❞❡ ✐♥❞✐❝❛♠♦) ♦) ♠♦❞♦) J✉❡ ♣♦❞❡%'♦ ❛♣%❡)❡♥✲

0❛% ♠✉❞❛♥&❛)✳ ❊♠ J✉❡ ♦) Y0♦♠♦) ❡♠ ❝✐❛♥♦ %❡♣%❡)❡♥0❛♠ ♦) ❝❛%❜♦♥♦)✱ ❡♠ ✈❡%❞❡ ♦)

❤✐❞%♦❣Z♥✐♦)✱ ❡♠ ❛③✉❧ ♦ ♥✐0%♦❣Z♥✐♦✱ ❡♠ ✈❡%♠❡❧❤♦ ♦) ♦①✐❣Z♥✐♦) ❡ ❡♠ ❛♠❛%❡❧♦ ♦ ❡♥①♦❢%❡✳ ✳ ✺✾

▲✐"#❛ ❞❡ ❚❛❜❡❧❛"

✷✳✶ ❚❛❜❡❧❛ ❞❡ ❝❧❛''✐✜❝❛*+♦ ❞♦'20❛♠✐♥♦/❝✐❞♦' ♣1❡'❡♥2❡' ♥♦' '❡1❡' ✈✐✈♦'✿ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

✺✳✶ ❘❡♣1❡'❡♥2❛*6❡' ■11❡❞✉29✈❡✐' ♣❛1❛ ♦ ❣1✉♣♦' ♣♦♥2✉❛❧ C2❬✷✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✺✳✷ ❚❛❜❡❧❛ ❞❡ ❝❛1❛❝2❡1❡' ❞♦ ❣1✉♣♦ ♣♦♥2✉❛❧ C2 ❬✷✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✺✳✸ ❉✐'21✐❜✉✐*+♦ ❞♦ ♥A♠❡1♦ 2♦2❛❧ ❞❡ ♠♦❞♦' ❞♦ ❣1✉♣♦ ♣♦♥2✉❛❧C2❬✷✼❪✳ ❖♥❞❡χ1❡♣1❡'❡♥2❛ ♦

❝❛1❛❝2❡1 ❞❛ 1❡♣1❡'❡♥2❛*+♦ ❡nγ❛ C✉❛♥2✐❞❛❞❡ ❞❡ ♠♦❞♦'✱ '❡♥❞♦ ❛' ❛❜1❡✈✐❛*6❡'✱ 2♦2✱ ❛❝✉'2✱

21❛♥'✱ 1♦2 ❡ ✈✐❜✱ '✐❣♥✐✜❝❛♥❞♦ 2♦2❛✐'✱ ❛❝A'2✐❝♦'✱ 21❛♥'❧❛❝✐♦♥❛✐'✱ 1♦2❛❝✐♦♥❛✐' ❡ ✈✐❜1❛❝✐♦♥❛✐'✱

1❡'♣❡❝2✐✈❛♠❡♥2❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✺✳✹ ❚❛❜❡❧❛ ❞❡ ■❞❡♥2✐✜❝❛*+♦ ❞♦' ♠♦❞♦' ✈✐❜1❛❝✐♦♥❛✐' ❞♦ ❡'♣❡❝21♦ ❘❛♠❛♥✱ '❡♥❞♦ C✉❡ ❛' ❛❜1❡✲ ✈✐❛*6❡' ✉2✐❧✐③❛❞❛' ♣❛1❛ ❞❡'✐❣♥❛1 ♦' 2✐♣♦' ❞❡ ♠♦❞♦' '✐❣♥✐✜❝❛♠✱ ❞❡❢✿ ❞❡❢♦1♠❛*+♦✱ τ✿

2♦1*+♦✱ρ✿ 1♦❝❦✐♥❣✱ν✿ ❡'2✐1❛♠❡♥2♦✱ω✿ ✇❛❣❣✐♥❣✱ 2✇✿2✇✐'2✱ δ✿ ❞♦❜1❛♠❡♥2♦✱ ❇❈✳ ❡ ❙✉♣✳✿

❇❛♥❞❛' ❞❡ ❝♦♠❜✐♥❛*+♦ ❡ ❞❡ '♦❜1❡♣♦'✐*+♦❀ ❡ ♦' 9♥❞✐❝❡' ✧'✧❡ ✧❛'✧✱ ❞❡2❡1♠✐♥❛♠ '❡ ♦ ♠♦❞♦

O '✐♠O21✐❝♦ ❡ ❛''✐♠O21✐❝♦✱ 1❡'♣❡❝2✐✈❛♠❡♥2❡✳ ❊ ♦ '9♠❜♦❧♦ν¯'✐❣♥✐✜❝❛ ♦ ✐♥✈❡1'♦ ❞♦ ♥A♠❡1♦

❞❡ ♦♥❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✺✳✺ ❋1❡C✉R♥❝✐❛ ❞♦' ♠♦❞♦' ❞❡ 2♦1*+♦ ❞♦ N H₃+✱ ✭τ N H₃+✮✱ ♦❝❦✐♥❣ ❞♦ CO−

2✱ ✭ρCO−2✮ ❡ ❞♦

❡'2✐1❛♠❡2♦ ❞♦ ❈❙✱ ✭νCS✮ ♦❜'❡1✈❛❞♦' ❡♠ ❛❧❣✉♥' ❛♠✐♥♦/❝✐❞♦' 1❡❧❛2❛❞♦' ♥❛ ❧✐2❡1❛2✉1❛✳ ❊♠

C✉❡ ▲✲❆'♣❛1❛❣✐♥❛ ▼✳ O ❛ ▲✲❆'♣❛1❛❣✐♥❛ ♠♦♥♦❤✐❞1❛2❛❞❛ ❡ ▲✲❍✐'2✐❞✐♥❛ ❍✳ ▼✳ ❝♦11❡'♣♦♥❞❡

❛ ▲✲❍✐'2✐❞✐♥❛ ❤✐❞1♦❝❧♦1❡2♦ ♠♦♥♦❤✐❞1❛2❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✺✳✻ ❱❛❧♦1❡' ❡①♣❡1✐♠❡♥2❛✐' ω0exp✱ ✈❛❧♦1❡' ❝❛❧❝✉❧❛❞♦' ω0calc ❡ ❝♦❡✜❝✐❡♥2❡' ❞♦ ❛❥✉'2❡ ❧✐♥❡❛1

ω=ω0+αP ♣❛1❛ ❛ 1❡❣✐+♦ ❞❡150❛1200cm−1 ♥♦ ✐♥2❡1✈❛❧♦ ❞❡ ♣1❡''+♦ ❞❡0❛ 7,0GP a✳ ✸✽

✺✳✼ ❱❛❧♦1❡' ❡①♣❡1✐♠❡♥2❛✐' ω0exp✱ ✈❛❧♦1❡' ❝❛❧❝✉❧❛❞♦' ω0calc ❡ ❝♦❡✜❝✐❡♥2❡' ❞♦ ❛❥✉'2❡ ❧✐♥❡❛1

ω=ω0+αT ♣❛1❛ ❛ 1❡❣✐+♦ ❞❡ 150] 1200cm−1 ♥♦ ✐♥2❡1✈❛❧♦ ❞❡ 2❡♠♣❡1❛2✉1❛ ❞❡ 298K

]13K✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✺✳✽ ❚❛❜❡❧❛ ❞❡ ✐❞❡♥(✐✜❝❛+,♦ ❞♦ ♠♦❞♦/ ✈✐❜1❛❝✐♦♥❛✐/ ❞♦ ❡/♣❡❝(1♦ ✐♥❢1❛✈❡1♠❡❧❤♦ ❞❛ ❉✲♠❡(✐♦♥✐♥❛✱ ❡♠ 8✉❡ ❛/ ❛❜1❡✈✐❛+:❡/ ❡♠♣1❡❣❛❞❛/ /,♦✱ ❞❡❢✿ ❞❡❢♦1♠❛+,♦✱ τ✿ (♦1+,♦✱ ρ✿ ♦❝❦✐♥❣✱ν✿ ❡/(✐✲

1❛♠❡♥(♦✱ω✿ ✇❛❣❣✐♥❣✱ (✇✿ )✇✐*)✱δ✿ ❞♦❜1❛♠❡♥(♦✱❇❈✳ ❡ ❙✉♣✳✿ ❜❛♥❞❛/ ❞❡ ❝♦♠❜✐♥❛+,♦ ❡ ❞❡

/♦❜1❡♣♦/✐+,♦❀ ❡ ♦/ C♥❞✐❝❡/ ✧/✧❡ ✧❛/✧✱ ❞❡(❡1♠✐♥❛♠ /❡ ♦ ♠♦❞♦ E /✐♠E(1✐❝♦ ❡ ❛//✐♠E(1✐❝♦✱

1❡/♣❡❝(✐✈❛♠❡♥(❡✳ ❊ ♦ /C♠❜♦❧♦ν¯/✐❣♥✐✜❝❛ E ♦ ✐♥✈❡1/♦ ❞♦ ♥G♠❡1♦ ❞❡ ♦♥❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

❈❛♣#$✉❧♦ ✶

■♥$+♦❞✉-.♦

❖! ❛♠✐♥♦'❝✐❞♦! !*♦ ♠♦❧,❝✉❧❛! ♠✉✐.♦ ✐♠♣♦0.❛♥.❡! ♥❛ ♥❛.✉0❡③❛✱ ❡♠ 4✉❡ ❛ ✉♥✐*♦ ❞♦! ♠❡!♠♦! 0❡!✉❧.❛♠ ❡♠ ♠❛❝0♦♠♦❧,❝✉❧❛! ❡!!❡♥❝✐❛✐! ♣❛0❛ ♠❛♥✉.❡♥5*♦ ❞♦! !❡0❡! ✈✐✈♦!✱ ❛! ♣0♦.❡7♥❛!✱ ❢♦0♠❛❞❛! 9 ♣❛0.✐0 ❞❡ ❧✐❣❛5;❡! ♣❡♣.7❞✐❝❛! 4✉❡ ♦❝♦00❡♠ ❡♥.0❡ ♦ ❣0✉♣♦ ❛♠✐♥♦ ❡ ♦ ❣0✉♣♦ ❝❛0❜♦①7❧✐❝♦ ❞♦! ❛♠✐♥♦'❝✐❞♦!✳ ❆♣❡!❛0 ❞❛ ❝♦♥!.✐.✉✐5*♦ ❞❛! ♣0♦.❡7♥❛! !❡0 ✉♠ ❞♦! ♣❛♣,✐! ❢✉♥❞❛♠❡♥.❛✐! ❞❡!❡♠♣❡♥❤❛❞♦! ♣❡❧♦! ❛♠✐♥♦'❝✐❞♦!✱ ♦! ♠❡!♠♦! .❛♠❜,♠ ♣♦❞❡♠ ❛.✉❛0 ❝♦♠♦ ♥❡✉0♦.0❛♥!♠✐!!♦0❡!✱ ♣0❡❝✉0!♦0❡! ♦✉ ♠❡❞✐❛❞♦0❡! ❞❡ ♥❡✉0♦.0❛♥!♠✐!!♦0❡! ❡ ❤♦0♠A♥✐♦!✳ B♦0 ❡①❡♠♣❧♦✱ ♦ '❝✐❞♦ ❣❧✉.C♠✐❝♦ ❛.✉❛ ❝♦♠♦ ✉♠ .0❛♥!♠✐!!♦0 ❡!.✐♠✉❧❛♥.❡ ❞♦ !✐!.❡♠❛ ♥❡0✈♦!♦ ❝❡♥.0❛❧ ❡ ❛ ❣❧✐❝✐♥❛ , ✉♠ ♥❡✉0♦.0❛♥!♠✐!!♦0 ✐♥✐❜✐.D0✐♦ ❝♦♠ ❡❢❡✐.♦ ♥❛ ♠❡❞✉❧❛ ❡!♣✐♥❤❛❧ ❡ ♣❛0.❡! ❞♦ ❝,0❡❜0♦ ❬✶❪✳

❈♦♥.✉❞♦✱ ❛! ♣0♦.❡7♥❛! !*♦ ❡①❝❧✉!✐✈❛♠❡♥.❡ ❢♦0♠❛❞❛! ♣❡❧♦! ▲✲❛♠✐♥♦'❝✐❞♦! ❬✶❪✱ ✉♠❛ ❝❧❛!!❡ ❞❡ ❛♠✐♥♦'❝✐❞♦! 4✉❡ !✉0❣❡ ❞❡✈✐❞♦ ❛ ♣0♦♣0✐❡❞❛❞❡ ❞❡ ✐!♦♠❡0✐❛ D♣.✐❝❛ ❬✷❪ 4✉❡ ♦! ❛♠✐♥♦'❝✐❞♦! ♣♦!!✉❡♠✱ ❛ 4✉❛❧ .❛♠❜,♠ ❞❡0✐✈❛ ♦✉.0❛ ❝❧❛!!❡✱ ❛! ❞♦! ❉✲❛♠✐♥♦'❝✐❞♦!✱ ♦! 4✉❛✐! ♥*♦ ♦❝♦00❡♠ ♥♦! !❡0❡! ✈✐✈♦!✱ !❡♥❞♦ ❡♥❝♦♥.0❛❞♦! ❡♠ ❜❛❝.,0✐❛! ❡ !*♦ ❝♦♠✉♠❡♥.❡ ✉.✐❧✐③❛❞♦! ♥❛ ♣0♦❞✉5*♦ ❞❡ ❛♥.✐❜✐D.✐❝♦!❬✹❪❬✸❪✳

❖ ❛♠✐♥♦'❝✐❞♦ 4✉❡ ✐♥✈❡!.✐❣❛0❡♠♦! ❡♠ ♥♦!!♦ .0❛❜❛❧❤♦ , ❛ ❉✲▼❡.✐♦♥✐♥❛✱ ❝✉❥♦ !❡✉ ❡♥❛♥.✐A♠❡0♦✱ ❛ ▲✲♠❡.✐♦♥✐♥❛✱ , ✉♠ ❛♠✐♥♦'❝✐❞♦ ♣0❡❝✉0!♦0 ❞♦ ❛♠✐♥♦'❝✐❞♦ ▲✲ ❍♦♠♦❝✐!.❡7♥❛✱ 4✉❡ ♣♦!!✉✐ ♣0♦♣0✐❡❞❛❞❡! ♥❡✉0♦❡①❝✐.❛.D0✐❛! ❬✺❪✳ ❆ ❉✲▼❡.✐♦♥✐♥❛ ♥*♦ ❞❡!❡♠✲ ♣❡♥❤❛ ♥❡♥❤✉♠❛ ❢✉♥5*♦ ✈✐.❛❧✱ ❡♥.0❡.❛♥.♦✱ ❡!.✉❞♦! 0❡✈❡❧❛0❛♠ 4✉❡ !❡ ❛❞♠✐♥✐!.0❛❞❛ ❛♥.❡! ❞❡ .0❛.❛♠❡♥.♦! 4✉✐♠✐♦.❡0'♣✐❝♦! 9 ❜❛!❡ ❞❛ ❞0♦❣❛ ❝✐!♣❧❛.✐♥❛ ✭❞✐❛♠✐♥♦❞✐❝❧♦0♦♣❧❛.✐♥❛✮✱ ❞✐♠✐♥✉✐ !✐❣♥✐✜❝❛.✐✈❛♠❡♥.❡ ♦! ❞❛♥♦! ❛♦ ❛♣❛0❡❧❤♦ ❛✉❞✐.✐✈♦ ❡ 0✐♥! 4✉❡ ♦ ♠❡❞✐❝❛♠❡♥.♦ ♣0♦✈♦❝❛✱

❡♥❞♦ ❡ ❛ ♣'❡ ❡'✈❛)*♦ ❞♦ +❡❝✐❞♦ ❝♦♥ ❡.✉0♥❝✐❛ ❞❛ ✐♥+❡'❛)*♦ ❞♦ 1+♦♠♦ ❞❡ ❡♥①♦❢'❡ ❞❛ ❉✲♠❡+✐♦♥✐♥❛ ❝♦♠ ❛ ❝✐ ♣❧❛+✐♥❛ ❬✻❪✱ ❬✼❪✳

❆ ❢✉♥)*♦ ❡ ❛ ❢♦'♠❛ ❞❛ ♣'♦+❡?♥❛ *♦ ❞❡+❡'♠✐♥❛❞❛ ♣❡❧❛ ♠❛♥❡✐'❛ .✉❡ ♦ ❛♠✐♥♦1❝✐❞♦ ❡ ❞✐ ♣@❡♠ ❡ ♣❛❝✐❛❧♠❡♥+❡ ❛♣A ❡ ❧✐❣❛'❡♠ ♣❛'❛ ❢♦'♠1✲❧❛ ❬✷❪✱❬✽❪✱❬✾❪✱ ✐ +♦ F✱ ❞❛ ❝♦♥✜❣✉'❛)*♦ ❡ ♣❛❝✐❛❧ ❞❛ ❧✐❣❛)@❡ ❞❡ ❤✐❞'♦❣0♥✐♦✳ ❆ ✐♠✱ ♦ ❡ +✉❞♦ ❞❡ ♠✉❞❛♥)❛ ❡ +'✉✲ +✉'❛✐ ❡♠ ❛♠✐♥♦1❝✐❞♦ ❝'✐ +❛❧✐♥♦ ❬✹✾❪ ✐♥❞✉③✐❞❛ ♣♦' ❝♦♥❞✐)@❡ ❡①+'❡♠❛ ❞❡ +❡♠♣❡'❛+✉'❛ ❡ ♣'❡ *♦✱ ❢♦'♥❡❝❡'*♦ ✐♥❞?❝✐♦ ❞❛ ❞✐♥K♠✐❝❛ ❞♦ ❝♦♠♣♦'+❛♠❡♥+♦ ❞❡ ❛ ❧✐❣❛)@❡ ✱ ♣'✐♥❝✐✲ ♣❛❧♠❡♥+❡ ❛ ❞♦ +✐♣♦ ❞❡ ❤✐❞'♦❣0♥✐♦ ❬✶✵❪✳ ◆♦ ❝❛ ♦ ❞♦ ❉✲❛♠✐♥♦1❝✐❞♦ ✱ ❛ ❧✐❣❛)@❡ ❞❡ ❛ ♠♦❧F❝✉❧❛ ❡ ❝♦♥✜❣✉'❛'✐❛♠ ♥♦ ❡ ♣❛)♦ ♣❛'❛ ❢♦'♠❛' ❛❧❣✉♠❛ ❡ +'✉+✉'❛ ♠✐❝'♦❜✐❛❧✱ +❛❧ ❝♦♠♦ ✉❛ ♣❛'❡❞❡ ❝❡❧✉❧❛' ❬✽❪✳

❆ ♣'♦♣'✐❡❞❛❞❡ ✈✐❜'❛❝✐♦♥❛✐ *♦ ✉♠ ❞♦ ♣♦♥+♦ ❞❡ ♣❛'+✐❞❛ ❞❡ ❛♥1❧✐ ❡ ❞❡ ♠✉❞❛♥)❛ ❡ +'✉+✉'❛✐ ♦❝♦''✐❞❛ ♥✉♠ ♠❡✐♦ ❝'✐ +❛❧✐♥♦✱ .✉❛♥❞♦ ✉❜♠❡+✐❞♦ ❛ ❛❧+❛ ♣'❡ @❡ ❡ ❜❛✐①❛ +❡♠♣❡'❛+✉'❛ ✳ ❙❡❣✉✐♥❞♦ ❡ ❛ ✈❡'+❡♥+❡✱ ♠✉✐+♦ ❛♠✐♥♦1❝✐❞♦ ❡ +✉❞❛❞♦ ✱ ❝✐+❛❞♦ ♥❛ ❧✐+❡'❛+✉'❛✱ ❛♣'❡ ❡♥+❛'❛♠ ♠✉❞❛♥)❛ '❡❧❡✈❛♥+❡ ❡♠ ❡✉ ♠♦❞♦ ✈✐❜'❛❝✐♦♥❛✐ ❛ ♦❝✐❛❞♦ ❛♦ ❣'✉♣♦ ❝❛'❜♦①✐❧?❝♦ ❡ ❛♠✐♥❛ ❬✶✷❪✱ ❬✶✸❪✱ ❬✶✹❪✱❬✶✺❪✳

❊♥+'❡+❛♥+♦✱ ❞❡♥+'❡ ♦ ❡ +✉❞♦ '❡❛❧✐③❛❞♦ ❡♠ ✈1'✐♦ ❛♠✐♥♦1❝✐❞♦ ✱ ❞❡✈❡♠♦ ❢♦❝❛' ♥♦ ❛♠✐♥♦1❝✐❞♦ .✉❡ ♣♦ ✉❡♠ ❡♥①♦❢'❡✳ ■♥✈❡ +✐❣❛)@❡ '❡❛❧✐③❛❞❛ ♥❛ ▲✲❝✐ +❡?♥❛✱ ❉❧✲ ❝✐ +❡?♥❛ ❬✹✺❪ ❡ ▲✲▼❡+✐♦♥✐♥❛ ❬✶✼❪✱ ♠♦ +'❛'❛♠ .✉❡ ❛❧F♠ ❞❡ ♠✉❞❛♥)❛ ✐❣♥✐✜❝❛+✐✈❛ ♥❛ ✈✐❜'❛)@❡ '❡❢❡'❡♥+❡ ❛ ❧✐❣❛)@❡ ❞♦ ❣'✉♣♦ ❢✉♥❝✐♦♥❛✐ ✱ +❛♠❜F♠ ❛♣'❡ ❡♥+❛'❛♠ ❛❧+❡'❛)@❡ ♥♦ ♠♦❞♦ ✈✐❜'❛❝✐♦♥❛✐ ❛+'✐❜✉?❞♦ ❛ ❧✐❣❛)@❡ .✉❡ ♦ ❡♥①♦❢'❡ ♣❛'+✐❝✐♣❛✳

◆♦ ❛ ✐♥✈❡ +✐❣❛)@❡ ✱ ❢♦'❛♠ ✐♠♣✉❧ ✐♦♥❛❞❛ ♣❡❧❛ ♠♦+✐✈❛)*♦ ✉♣'❛❝✐+❛❞❛✱ ❡♥✲ ❢❛+✐③❛♥❞♦ ❛ ❝♦♠♣❛'❛)*♦ ❡♥+'❡ ❛ ♣'♦♣'✐❡❞❛❞❡ ✈✐❜'❛❝✐♦♥❛✐ ❞❛ ❉✲▼❡+✐♦♥✐♥❛ ❡ ▲✲▼❡+✐♦♥✐♥❛ ❬✶✼❪✱ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❛♥❛❧✐ ❛' ❛ ✉❛ ❡♠❡❧❤❛♥)❛ ❡ ❞✐❢❡'❡♥)❛ ✳ ❉❡ ❡ ♠♦❞♦✱ ✉+✐❧✐③❛♠♦ ❛ +F❝♥✐❝❛ ❡ ♣❡❝+'♦ ❝A♣✐❝❛ ❘❛♠❛♥ ❡ ■♥❢'❛✈❡'♠❡❧❤♦✱ ♣❛'❛ +❡♥+❛' ❡❧✉❝✐❞❛' ♦ ❝♦♠♣♦'+❛✲ ♠❡♥+♦ ✈✐❜'❛❝✐♦♥❛❧ ❞❡ ❡ ❛♠✐♥♦1❝✐❞♦ ♦❜ ❛❧+❛ ♣'❡ @❡ ❡ ❜❛✐①❛ +❡♠♣❡'❛+✉'❛ ✳

❉❡ ❡ ♠♦❞♦✱ ♥♦ ❛ ❡①♣❧❛♥❛)@❡ *♦ ❞✐✈✐❞❛ ♥❛ ❛♣'❡ ❡♥+❛)*♦ ❞❛ ♣'♦✲ ♣'✐❡❞❛❞❡ ❞♦ ❛♠✐♥♦1❝✐❞♦ ✱ ♣♦ +❡'✐♦'♠❡♥+❡ ❞❡ ❝'❡✈❡♠♦ ♦ ❛ ♣❡❝+♦ ❝♦♥❝❡✐+✉❛✐ ❞❛ +F❝✲ ♥✐❝❛ ✐♥✈❡ +✐❣❛+✐✈❛ .✉❡ ✉+✐❧✐③❛♠♦ ✱ ❛ ❡ ♣❡❝+'♦ ❝♦♣✐❛ ❘❛♠❛♥ ❡ ❡ ♣❡❝+'♦ ❝♦♣✐❛ ■♥❢'❛✈❡'✲ ♠❡❧❤♦ ❡ ✜♥❛❧♠❡♥+❡ ❛♣'❡ ❡♥+❛♠♦ ♦ '❡ ✉❧+❛❞♦ ❡♥❝♦♥+'❛❞♦ ❡ ❝♦♥❝❧✉ *♦ .✉❡ ♦❜+✐✈❡♠♦ ❡♠ ♥♦ ♦ +'❛❜❛❧❤♦✳

❈❛♣#$✉❧♦ ✷

❆♠✐♥♦-❝✐❞♦0

✷✳✶ ❋✉♥❞❛♠❡♥*♦, ❚❡./✐❝♦,

❖! ❛♠✐♥♦'❝✐❞♦! ❞❡!❡♠♣❡♥❤❛♠ ✉♠ ✐♠♣♦./❛♥/❡ ♣❛♣❡❧ ❜✐♦❧2❣✐❝♦✱ ♣♦. !❡.❡♠ .❡✲ !♣♦♥!'✈❡✐! ♣❡❧❛ ❢♦.♠❛89♦ ❞❛! ♣.♦/❡:♥❛!✳ ❖! ❛♠✐♥♦'❝✐❞♦! ♣.❡!❡♥/❡! ♥♦! ♦.❣❛♥✐!♠♦! ✈✐✈♦!✱ /♦/❛❧✐③❛♠ 20✱ ♦! =✉❛✐! !9♦ ❝❧❛!!✐✜❝❛❞♦! =✉❛♥/♦ ❛ !✐♥/❡/✐③❛89♦ ❞♦! ♠❡!♠♦!✱ ❛=✉❡❧❡! !✐♥✲ /❡/✐③❛❞♦! ♥♦ ♣.2♣.✐♦ ♦.❣❛♥✐!♠♦ !9♦ ❞❡♥♦♠✐♥❛❞♦! ❛♠✐♥♦'❝✐❞♦! ♥9♦ ❡!!❡♥❝✐❛✐!✱ ❡♥=✉❛♥/♦ ❛=✉❡❧❡! ♥9♦ !✐♥/❡/✐③❛❞♦! ♣❡❧♦ ♦.❣❛♥✐!♠♦ !9♦ ❝❧❛!!✐✜❝❛❞♦! ❝♦♠♦ ❛♠✐♥♦'❝✐❞♦! ❡!!❡♥❝✐❛✐!✱ ♦! =✉❛✐! !9♦ ❛❞=✉✐.✐❞♦! ❛/.❛✈?! ❞♦! ❛❧✐♠❡♥/♦!✳ ❖! .❡❣✐!/.♦! ♥❛ ❧✐/❡.❛/✉.❛ ✐♥❞✐❝❛♠ =✉❡ ♦ ♣.✐♠❡✐.♦ ❛♠✐♥♦'❝✐❞♦ ❞❡!❝♦❜❡./♦ ❢♦✐ ❛ ❆!♣❛.❛❣✐♥❛ ❡♠ 1806 ❡ ♦ A❧/✐♠♦ ❢♦✐ ❛ ❚.❡♦♥✐♥❛ ❡♠ 1836 ❬✶✽❪✳

◆❛ ♥❛/✉.❡③❛✱ ♦! ❛♠✐♥♦'❝✐❞♦! ♣♦❞❡♠ ❛!!✉♠✐. ❞✉❛! ❢♦.♠❛!✱ ❛ ❢♦.♠❛ ▲ ❡ ❛ ❢♦.♠❛ ❉✳ ❈♦♥/✉❞♦✱ ♥♦! !❡.❡! ✈✐✈♦! ❛ ❢♦.♠❛ ▲ ? ♣.❡❞♦♠✐♥❛♥/❡ ❡♠ ❞❡/.✐♠❡♥/♦ ❞❛ ❢♦.♠❛ ❉✱ !❡♥❞♦ ❛! ♣.♦/❡:♥❛! ❢♦.♠❛❞❛! ❛ ♣❛./✐. ❞♦! ▲✲❛♠✐♥♦'❝✐❞♦!✳ ❆ ❡①♣❧✐❝❛89♦ ♣❛.❛ ❛ ❛❜✉♥❞L♥❝✐❛ ❞❡ ❛♠✐♥♦'❝✐❞♦! ❞♦ /✐♣♦ ▲ ❛✐♥❞❛ ♥9♦ ? ❝♦♥❝❧✉!✐✈❛✱ ❡①✐!/✐♥❞♦ ♥❛ ❧✐/❡.❛/✉.❛ ❛♣❡♥❛! ❤✐♣2/❡!❡!✱ /❛✐! ❝♦♠♦ ❛ ❞❡ ❨❛♠❛❣❛/❛ ❡ ❞❡ ❙❛❧❛♠✱ ❢✉♥❞❛♠❡♥/❛❞❛! ♥❛ .❡❧❛89♦ ❡♥❡.❣✐❛ ✈❡.✉! ❡!/❛❜✐❧✐✲ ❞❛❞❡✱ ❛✜.♠❛♥❞♦ =✉❡ ♦ ▲✲❛♠✐♥♦'❝✐❞♦ ? ♠❛✐! ❡!/'✈❡❧ ❞♦ =✉❡ ♦ ❉✲❡♥❛♥/✐O♠❡.♦ ♣♦. !❡. ♠❡♥♦! ❡♥❡.❣?/✐❝♦ ❬✶✾❪✳ ❊♠❜♦.❛✱ ♦! ❉✲❛♠✐♥♦'❝✐❞♦! .❡♣.❡!❡♥/❛.❡♠ ✉♠❛ ♠✐♥♦.✐❛ ♥❛ ♥❛/✉.❡③❛ ❡ ♥9♦ !❡.❡♠ ❝❛♣❛③❡! ❞❡ ❢♦.♠❛. ♣.♦/❡:♥❛!✱ ❡❧❡! ❡!/9♦ ♣.❡!❡♥/❡! ❡♠ ❛❧❣✉♠❛! ❜❛❝/?.✐❛!✱ ❝♦♠♣♦♥❞♦ !✉❛ ♣❛.❡❞❡ ❝❡❧✉❧❛. ❬✽❪ ❡ !9♦ ✉/✐❧✐③❛❞♦! ♣❛.❛ ♣.♦❞✉89♦ ❞❡ ❛❧❣✉♥! ❛♥/✐❜✐2/✐❝♦! !❡♠✐✲!✐♥/?/✐❝♦!✱ ❤♦.♠O♥✐♦! ❡ ♣❡!/✐❝✐❞❛! =✉:♠✐❝♦! ❬✸❪✳

❆ ❡"#$✉#✉$❛ ❞♦" ❛♠✐♥♦,❝✐❞♦" ❝♦♥"✐"#❡ ❞❡ ✉♠ $❛❞✐❝❛❧✱ ❝♦♠♣♦"#♦ ❞❡ ✉♠❛ ❝❛❞❡✐❛ ❛❧✐❢,#✐❝❛ ♦✉ ❛$♦♠,#✐❝❛ ❞❡ ❝❛$❜♦♥♦" ❡ ❞♦" ❣$✉♣♦" ❢✉♥❝✐♦♥❛✐" ❛♠✐♥❛ ❡ ❝❛$❜♦①✐❧❛ 5✉❡ ❡"#6♦ ❧✐❣❛❞♦" ❛ ❡""❡ $❛❞✐❝❛❧ ✭❋✐❣✉$❛ ✷✳✶✮❬✷❪✳ ❊①❝❡#♦✱ ♥♦" ❛♠✐♥♦,❝✐❞♦" ❈✐"#❡A♥❛ ❡ ▼❡#✐♦♥✐♥❛✱ ❡""❛ ❝❛❞❡✐❛ ❝❛$❜C♥✐❝❛ ❛♣$❡"❡♥#❛ ❡♥①♦❢$❡✱ ♦ 5✉❛❧ ♣❡$♠✐#❡ 5✉❡ ❡""❡" ❛♠✐♥♦,❝✐❞♦" ♣♦""❛♠ "❡ ❧✐❣❛$ ❛ ♠❡#❛✐" ❬✷✵❪✳

❋✐❣✉$❛ ✷✳✶✿ ❊!"✉❡♠❛ ❞❛ ❊!()✉(✉)❛ ❇+!✐❝❛ ❞♦! ❆♠✐♥♦+❝✐❞♦!✳

❆ ♥❛#✉$❡③❛ ❞❛" ❧✐❣❛GH❡" ❞♦" ❣$✉♣♦" ❢✉♥❝✐♦♥❛✐" N H₃+ ❡ COO− _{I ❞♦ #✐♣♦ ❞❡}

❤✐❞$♦❣K♥✐♦ ❬✶✵❪ ❛♣❡"❛$ ❞❡ "❡ ❧✐❣❛$❡♠ ❝♦✈❛❧❡♥#❡♠❡♥#❡ M ❝❛❞❡✐❛ ❝❛$❜C♥✐❝❛ ✱ ❡♥#$❡#❛♥#♦✱ ♦ 5✉❡ #♦$♥❛ ❡""❡" $❛❞✐❝❛✐" ♠❛✐" "✉"❝❡♣#A✈❡✐" ❛ ♠✉❞❛♥G❛" ❡"#$✉#✉$❛✐" ❞♦ 5✉❡ ❡"5✉❡❧❡#♦ ❝❛$❜C♥✐❝♦ ❞♦ ❛♠✐♥♦,❝✐❞♦ I ♦ ❢❛#♦ ❞❡ ❛♣$❡"❡♥#❛$❡♠ ✉♠ $❡❛#✐✈✐❞❛❞❡ "✐❣♥✐✜❝❛#✐✈❛✳

❆ ♣$❡"❡♥G❛ ❞♦" ❞♦✐" ❣$✉♣♦" ❢✉♥❝✐♦♥❛✐" ♥❛ ♠♦❧I❝✉❧❛ ❞❡ ❛♠✐♥♦,❝✐❞♦ ❛ #♦$♥❛ ❛♥❢O#❡$❛✱ ✐"#♦ I✱ 5✉❡ ♣♦❞❡ "❡ ❝♦♠♣♦$#❛$ #❛♥#♦ ❝♦♠♦ ✉♠❛ ❜❛"❡ 5✉❛♥#♦ ❝♦♠♦ ✉♠ ,❝✐❞♦ ❢$❛❝♦✱ ❡♠ ♣❍ ♥❡✉#$♦✱ "❡♥❞♦ ❝♦♥"✐❞❡$❛❞❛ ❛""✐♠ ✉♠❛ ❡"#$✉#✉$❛ ❞❡♥♦♠✐♥❛❞❛ ③✇✐#❡$✐C♥✐❝❛ ❬✷❪✳

❆ ♣♦❧❛$✐❞❛❞❡ ❞♦ $❛❞✐❝❛❧ ❞♦" ❛♠✐♥♦,❝✐❞♦" #❛♠❜I♠ "❡$, $❡❧❡✈❛♥#❡✱ ♣♦✐" ❞❡✲ #❡$♠✐♥❛$, "❡ ♦ ❛♠✐♥♦,❝✐❞♦ ♣♦❞❡$, "❡$ ❝❧❛""✐✜❝❛❞♦ ❝♦♠♦ ❤✐❞$♦❢O❜✐❝♦✱ "❡ ♦ "❡✉ $❛❞✐❝❛❧ ❢♦$ ❛♣♦❧❛$ ♦✉ ❝♦♠♦ ❤✐❞$♦❢A❧✐❝♦✱ ❝❛"♦ ❛♣$❡"❡♥#❡ $❛❞✐❝❛❧ ♣♦❧❛$✱ ♦ 5✉❛❧ ♣♦❞❡ ❡"#❛$ ♥❡✉#$♦✱ ♣♦"✐#✐✈❛♠❡♥#❡ ♦✉ ♥❡❣❛#✐✈❛♠❡♥#❡ ❝❛$$❡❣❛❞♦❬✽❪✱❬✾❪✳

❯♠❛" ❞❛" ❝❧❛""✐✜❝❛GH❡" ✐♠♣♦$#❛♥#❡" ❞♦" ❛♠✐♥♦,❝✐❞♦" I ❡♠ $❡❧❛G6♦ ❛ ♣♦"✐G6♦ ❞♦ ❣$✉♣♦ ❛♠✐♥❛ ❡♠ $❡❧❛G6♦ ❛♦ ❣$✉♣♦ ❝❛$❜♦❧A①✐❝♦ ♥✉♠❛ ❝❛❞❡✐❛ ❝❛$❜C♥✐❝❛✱ "❡♥❞♦ 5✉❡ ♦ ♣$✐♠❡✐$♦ ❝❛$❜♦♥♦ ❛♣O" ❛ ❝❛$❜♦①✐❧❛ I ❞❡♥♦♠✐♥❛❞♦ α✱ ♦ "❡❣✉♥❞♦ β ❡ ❛""✐♠ ♣♦$ ❞✐❛♥#❡ ✭❋✐❣✉$❛ ✷✳✷✮✳ ❖" ❛♠✐♥♦,❝✐❞♦" 5✉❡ ♣♦""✉❡♠ ❛ ❛♠✐♥❛ ♥♦ ❝❛$❜♦♥♦ α✱ ❛♣$❡"❡♥#❛♠ ✉♠❛ ✐♠♣♦$#❛♥#❡ ♣$♦♣$✐❡❞❛❞❡ O♣#✐❝❛✱ ❛ ✐"♦♠❡$✐❛ O♣#✐❝❛ ❬✷❪✳

❆ ✐"♦♠❡&✐❛ ( ✉♠ ❢❡♥,♠❡♥♦ ❡♠ -✉❡ ♠♦❧(❝✉❧❛" ❝♦♠♦ ♠❡"♠❛ ❢0&♠✉❧❛ ♠♦❧❡❝✲ ✉❧❛&✱ ♣♦&(♠ ❝♦♠ ❛&&❛♥❥♦ ❡"5&✉5✉&❛❧ ❞✐❢❡&❡♥5❡✱ "❡♥❞♦ -✉❡ ❡""❡ ❞✐❢❡&❡♥5❡ ❞♦ ❛&&❛♥❥♦ ❡"♣❛❝✐❛❧ ❞♦" 75♦♠♦" ( ❞❡5❡&♠✐♥❛♥5❡ ♣❛&❛ ❞❡✜♥✐& ❛" ♣&♦♣&✐❡❞❛❞❡" ❞❡ ❝❛❞❛ ♠♦❧(❝✉❧❛✳ ❆ ✐"♦♠❡&✐❛ -✉❡ ❛♣❛&❡❝❡ ♥♦" ❛♠✐♥♦7❝✐❞♦" ( ❛ ✐"♦♠❡&✐❛ 0♣5✐❝❛✱ ❝❛&❛❝5❡&✐③❛❞❛ ♣❡❧❛ ❢♦&♠❛ -✉❡ ✉♠❛ ♠♦❧(❝✉❧❛ ❞❡"✈✐❛ ❛ ❧✉③✳

❆ ✐"♦♠❡&✐❛ 0♣5✐❝❛ ♦❝♦&&❡ -✉❛♥❞♦ ❛ ♠♦❧(❝✉❧❛ ❛♣&❡"❡♥5❛& ✉♠ 75♦♠♦ ❛"✲ "✐♠(5&✐❝♦✱ ❞❡✜♥✐❞♦ ❝♦♠♦ -✉✐&❛❧✱ -✉❡ &❡"✉❧5❛ ♥✉♠ ❛&&❛♥❥♦ ♠♦❧❡❝✉❧❛& -✉❡ ♣♦❞❡ ❧❡✈❛& ❛ ❢♦&♠❛<=♦ ❞❡ ❞✉❛" ♠♦❧(❝✉❧❛" ❞❡ ✐♠❛❣❡♥" ♥=♦ "✉♣❡&♣♦♥?✈❡✐"✱ ♠❛" -✉❡ ❛♣&❡"❡♥5❛♠ ✉♠❛ &❡❧❛<=♦ "✐♠(5&✐❝❛ ❞❡ ❡"♣❡❧❤♦✱ ❞❡✜♥✐❞❛" ❝♦♠♦ ❡♥❛♥5✐,♠❡&♦" ✭❋✐❣✉&❛ ✷✳✸✮✱ ♦ ❧❡✈0❣✐&♦ -✉❡ ❞❡"✈✐❛ ❛ ❧✉③ ♣❛&❛ ❡"-✉❡&❞❛ ❡ ♦ ❞❡①5&0❣✐&♦✱ -✉❡ ❞❡"✈✐❛ ❛ ❧✉③ ♣❛&❛ ❞✐&❡✐5❛✱ ❞✐""♦ -✉❡ "✉&❣❡ ❛ 5❡&♠♦❧♦❣✐❛ "✉♣&❛❝✐5❛❞❛✱ -✉❡ ❞❡"❣✐♥❛ ♦ 5✐♣♦ ❞♦" ❛♠✐♥♦7❝✐❞♦" -✉❛♥5♦ ❛ ❢♦&♠❛ ❡♠ ▲✲ ❛♠✐♥♦7❝✐❞♦" ❡ ❉✲❛♠✐♥♦7❝✐❞♦"✳

❋✐❣✉&❛ ✷✳✷✿ ■❧✉#$%❛'(♦ ❞❛ ❈❧❛##✐✜❝❛'(♦ ❞♦# ❛♠✐♥♦1❝✐❞♦# #❡❣✉♥❞♦ ❛ ♣♦#✐'(♦ ❞❛ ❛♠✐♥❛✳

❋✐❣✉&❛ ✷✳✸✿ ❆♠✐♥♦1❝✐❞♦# ❊♥❛♥$✐8♠❡%♦#✿ ▲✲❆♠✐♥♦1❝✐❞♦✲❛♠✐♥♦1❝✐❞♦ ❧❡✈=❣✐%♦❀ ❉✲❆♠✐♥♦1❝✐❞♦✲ ❛♠✐♥♦1❝✐❞♦ ❞❡①$%=❣✐%♦✳

❆ ❛""✐♠❡5&✐❛ ❞♦ ❝❛&❜♦♥♦ α ( ♠✉✐5♦ ✐♠♣♦&5❛♥5❡ 5❛♠❜(♠✱ ❞❡✈✐❞♦ ❛♦ ❢❛5♦ ❞❡ ♣&♦♣✐❝✐❛& -✉❡ ❛ ♠♦❧(❝✉❧❛ ❞❡ ❛♠✐♥♦7❝✐❞♦ ❛""✉♠❛ ❝♦♥✜❣✉&❛<=♦ 5&✐❞✐♠❡♥"✐♦♥❛❧✱ ♣♦""✐❜✐❧✲ ✐5❛♥❞♦ ✈7&✐❛" ❢♦&♠❛" ❞❡ ❝♦♠❜✐♥❛<K❡" ❞♦" ❛♠✐♥♦7❝✐❞♦" ♣♦& ♠❡✐♦ ❞❡ ✉♠❛ ❧✐❣❛<=♦ ♣❡♣5?❞✐❝❛ ✭❋✐❣✉&❛ ✷✳✹✮✱ ❡♠ -✉❡ ✉♠❛ ❛♠✐♥❛ ❡ ✉♠❛ ❝❛&❜♦①✐❧❛ ❞❡ ❝❛❞❛ ❛♠✐♥♦7❝✐❞♦ "❡ ❧✐❣❛&=♦✱ ♣❛&❛

❢♦"♠❛" ✉♠ ❞✐♣❡♣*+❞❡♦✱ ♠❛✐- ♦✉*"♦- ❛♠✐♥♦/❝✐❞♦- -❡ ❧✐❣❛♠ ❛*3 ❢♦"♠❛" ✉♠❛ ❝❛❞❡✐❛ ♣♦❧✐♣❡♣✲ *+❞✐❝❛ 5✉❡ "❡-✉❧*❛"/ ❡♠ ✉♠❛ ♣"♦*❡+♥❛✱ -❡♥❞♦ 5✉❡ ♥6♦ ❛♣❡♥❛- ❛ -❡5✉7♥❝✐❛ ❞♦- ❛♠✐♥♦/❝✐❞♦-♥❛ ❝❛❞❡✐❛ ♣♦❧✐♣❡♣*+❞✐❝❛✱ ❝♦♠♦ *❛♠❜3♠ ❛ ❢♦"♠❛ 5✉❡ ❡❧❡- ❡-*6♦ ❞✐-♣♦-*♦- ❡-♣❛❝✐❛❧♠❡♥*❡✱ -6♦ ❡--❡♥❝✐❛✐- ♣❛"❛ ❞❡*❡"♠✐♥❛" ♦- *✐♣♦- ❞❡ ♣"♦*❡+♥❛- 5✉❡ -❡"6♦ ❢♦"♠❛❞❛-❬✷❪✱❬✽❪✱❬✾❪ ✳

❋✐❣✉"❛ ✷✳✹✿ ❘❡❛#$♦ ❡♥'(❡ ❞♦✐+ ♠♦♥♦♣❡♣'.❞❡♦+ ♣❛(❛ ❢♦(♠❛( ✉♠ ❞✐♣❡♣'.❞❡♦✳

❘❡-✉♠✐"❡♠♦- ❡♠ ✉♠❛ *❛❜❡❧❛ ✷✳✶✱ ❡♠ 5✉❛✐- ❝❛"❛❝*❡"+-*✐❝❛- -❡ ❡♥5✉❛❞"❛♠ ♦-20 ▲✲❆♠✐♥♦/❝✐❞♦-✱ 5✉❡ ❡-*6♦ ♣"❡-❡♥*❡- ♥♦- -❡"❡- ✈✐✈♦- ✿

❚❛❜❡❧❛ ✷✳✶✿ ❚❛❜❡❧❛ ❞❡ ❝❧❛''✐✜❝❛*+♦ ❞♦' 20❛♠✐♥♦/❝✐❞♦' ♣1❡'❡♥2❡' ♥♦' '❡1❡' ✈✐✈♦'✿

❆♠✐♥♦/❝✐❞♦ ❙7♠❜♦❧♦ ❍✐❞1♦❢:❜✐❝♦ ❍✐❞1♦❢7❧✐❝♦ ❆❧✐❢/2✐❝♦ ❆1♦♠/2✐❝♦ ❊''❡♥❝✐❛❧ ◆+♦✲❊''❡♥❝✐❛❧

❆❧❛♥✐♥❛ ❆❧❛ ✭❆✮ ❳ ❳ ❳

❆1❣✐♥✐♥❛ ❆1❣ ✭❘✮ ❳ ❳ ❳

❆'♣❛12❛2♦ ❆'♣ ✭❇✮ ❳ ❳ ❳

❆'♣❛1❛❣✐♥❛ ❆'♥ ✭◆✮ ❳ ❳ ❳

❈✐'2❡7♥❛ ❈②' ✭❈✮ ❳ ❳ ❳

❋❡♥✐❧❛❧❛♥✐♥❛ G❤❡ ✭G✮ ❳ ❳ ❳

●❧✐❝✐♥❛ ●❧② ✭●✮ ❳ ❳ ❳

●❧✉2❛♠❛2♦ ●❧✉ ✭❩✮ ❳ ❳ ❳

●❧✉2❛♠✐♥❛ ●❧♥ ✭◗✮ ❳ ❳ ❳

❍✐'2✐❞✐♥❛ ❍✐' ✭❍✮ ❳ ❳ ❳

■'♦❧❡✉❝✐♥❛ ■❧❡ ✭■✮ ❳ ❳ ❳

▲❡✉❝✐♥❛ ▲❡✉ ✭▲✮ ❳ ❳

▲✐'✐♥❛ ▲②' ✭❑✮ ❳ ❳ ❳

▼❡2✐♦♥✐♥❛ ▼❡2 ✭▼✮ ❳ ❳ ❳

G1♦❧✐♥❛ G1♦ ✭G✮ ❳ ❳ ❳

❙❡1✐♥❛ ❙❡1 ✭▲✮ ❳ ❳ ❳

❚✐1♦'✐♥❛ ❚②1 ✭❨✮ ❳ ❳ ❳

❚1❡♦♥✐♥❛ ❚❤1 ✭❚✮ ❳ ❳ ❳

❚1✐♣♦❢❛♥♦ ❚1♣ ✭❲✮ ❳ ❳ ❳

❱❛❧✐♥❛ ❱❛❧ ✭❱✮ ❳ ❳ ❳

❈❛♣#$✉❧♦ ✸

❊*♣❡❝$-♦*❝♦♣✐❛ ❘❛♠❛♥

✸✳✶ ❋✉♥❞❛♠❡♥*♦, ❚❡./✐❝♦,

❆ ❡"♣❡❝%&♦"❝♦♣✐❛ ❘❛♠❛♥ - ✉♠❛ ❞❛" %-❝♥✐❝❛" 0♣%✐❝❛" ♠❛✐" ❞✐❢✉♥❞✐❞❛" ✉%✐❧✐③❛❞❛ ♥❛ ❝❛&❛❝%❡&✐③❛45♦ ❞❡ ♠❛%❡&✐❛✐"✳ ❊❧❛ ❝♦♥"✐"%❡ ❜❛"✐❝❛♠❡♥%❡ ❡♠ ✐♥❝✐❞✐& ✉♠ ❢❡✐①❡ ❞❡ ❧✉③ ♠♦♥♦❝&♦♠:%✐❝❛ ❣❡&❛❧♠❡♥%❡ ❝♦❡&❡♥%❡ ❡♠ ✉♠❛ ❛♠♦"%&❛ ❡ ❛♥❛❧✐"❛& ❛ ❧✉③ ❡"♣❛❧❤❛❞❛ ♣❡❧❛ ♠❡"♠❛✳

❆ ❧✉③ =✉❛♥❞♦ ❡♥%&❛ ❡♠ ❝♦♥%❛%♦ ❝♦♠ ✉♠ ❝❡&%♦ ♠❛%❡&✐❛❧ ✐♥%❡&❛❣✐&: ❝♦♠ ♦ ♠❡"♠♦✱ ♣&♦♠♦✈❡♥❞♦ ✉♠ ❡"♣❛❧❤❛♠❡♥%♦✱ =✉❡ ♣♦❞❡&: "❡& ❡❧:"%✐❝♦ =✉❛♥❞♦ ❛ ❢&❡=✉@♥❝✐❛ ❞❛ ❧✉③ ❡"♣❛❧❤❛❞❛ ❢♦& ✐❣✉❛❧ ❛ ❞❛ ❧✉③ ✐♥❝✐❞❡♥%❡ ✭νi =νe✮✱ ❞❡♥♦♠✐♥❛❞♦ ❡"♣❛❧❤❛♠❡♥%♦ ❘❛②❧❡✐❣❤✱ ✭♦ =✉❛❧ ❢♦✐ ❞❡"❝♦❜❡&%♦ ❡♠ 1871 ♣♦& ▲♦&❞ ❘❛②❧❡✐❣❤✮✱ ♦✉ ✉♠ ❡"♣❛❧❤❛♠❡♥%♦ ✐♥❡❧:"%✐❝♦✱ ❡♠ =✉❡ ❛ ❧✉③ ❡"♣❛❧❤❛❞❛ ❛♣&❡"❡♥%❛&: ✉♠❛ ❢&❡=✉@♥❝✐❛ ♠❡♥♦& ❞♦ =✉❡ ♦ ❞❛ ❧✉③ ✐♥❝✐❞❡♥%❡ ✭νe < νi✮✱ ❊"♣❛❧❤❛♠❡♥%♦ ❘❛♠❛♥ ❙%♦❦❡" ♦✉ ❢&❡=✉@♥❝✐❛ ♠❛✐♦& ❡♠ &❡❧❛45♦ ♦ ❞❛ ❧✉③ ✐♥❝✐❞❡♥%❡ ✭νe > νi✮✱ ❊"♣❛❧❤❛♠❡♥%♦ ❘❛♠❛♥ ❆♥%✐✲❙%♦❦❡"✳ ❊""❡ ❢❡♥H♠❡♥♦ ❢♦✐ ♣&❡❞✐%♦ ♣♦& ❙♠❡❦❛❧ ❡♠ 1923✱ ❡♠❜♦&❛ %❡♥❤❛ "✐❞♦ ❙✐& ❈✳ ❱✳ ❘❛♠❛♥ =✉❡♠ ♣&✐♠❡✐&❛♠❡♥%❡ ♦ ♦❜"❡&✈♦✉ ❡①♣❡&✐♠❡♥%❛❧♠❡♥%❡✳

❖" ❡"♣❛❧❤❛♠❡♥%♦" ♣♦❞❡♠ "❡& ❝❧❛""✐✜❝❛❞♦" =✉❛♥%♦ ❛ ❧✐♥❡❛&✐❞❛❞❡ ❞♦ ♣&♦❝❡""♦ ❡ ❛ ❝♦❡&@♥❝✐❛ ❞♦ ♠❡"♠♦✳ ❆ "❡❣✉✐& ❧✐"%❛&❡♠♦" ❛❧❣✉♥" %✐♣♦" ❞❡ ❡"♣❛❧❤❛♠❡♥%♦✿

• ❊"♣❛❧❤❛♠❡♥%♦ ❘❛♠❛♥ ❡ ❘❛②❧❡✐❣❤ ♥♦&♠❛✐"✿ "5♦ ♦" ❝✐%❛❞♦" ❛❝✐♠❛✱ "5♦ ❡"♣❛❧❤❛♠❡♥%♦" ✐♥❝♦❡&❡♥%❡" ❬✷✷❪✱ ❡♠❜♦&❛ ❡♠ ❛❧❣✉♥" ❝❛"♦" ❡"♣❡❝✐❛✐" ♦ ❡"♣❛❧❤❛♠❡♥%♦ ❘❛②❧❡✐❣❤ ♣♦""❛ "❡& ❝♦❡&❡♥%❡ ❡ ❛♠❜♦" "5♦ ♣&♦❝❡""♦" ❧✐♥❡❛&❡"✱ ♣♦✐" ❛ ✐♥%❡♥"✐❞❛❞❡ ❞♦ ❡"♣❛❧❤❛♠❡♥%♦

❞✐"❡$❛♠❡♥$❡ ♣"♦♣♦"❝✐♦♥❛❧ , ✐""❛❞✐-♥❝✐❛ ❞❛ "❛❞✐❛./♦ ✐♥❝✐❞❡♥$❡✳

• ❊2♣❛❧❤❛♠❡♥$♦ ❍✐♣❡"✲❘❛♠❛♥ ❡ ❍✐♣❡"✲❘❛②❧❡✐❣❤✿ 2/♦ ♣"♦❝❡22♦2 ❡♠ :✉❡ ❛ "❛❞✐❛./♦ ♠♦♥♦❝"♦♠<$✐❝❛ ✐♥❝✐❞❡♥$❡ ♣♦22✉✐ ✉♠❛ ❛♠♣❧❛ ✐""❛❞✐-♥❝✐❛✱ ❡♠ :✉❡ ❛2 ❢"❡:✉?♥❝✐❛2 ❞❛2 "❛❞✐❛.@❡2 ❡2♣❛❧❤❛❞❛2 2❡"/♦ 2νi ♣❛"❛ ♦ ❡2♣❛❧❤❛♠❡♥$♦ ❍✐♣❡"✲❘❛②❧❡✐❣❤ ❡ 2νi −νm ❡ 2νi +νm ♣❛"❛ ♦2 ❡2♣❛❧❤❛♠❡♥$♦2 ❍✐♣❡"✲❘❛♠❛♥ ❙$♦❦❡2 ❡ ❍✐♣❡"✲❘❛♠❛♥ ❆♥$✐✲❙$♦❦❡2 "❡2♣❡❝$✐✈❛♠❡♥$❡✱ ♦♥❞❡2νiE ❛ ❢"❡:✉?♥❝✐❛ ❞❛ "❛❞✐❛./♦ ✐♥❝✐❞❡♥$❡ ❡ νmE ❛ ❢"❡:✉?♥❝✐❛ ❞❛ ♠♦❧E❝✉❧❛ ❬✷✷❪✱ 2❡♥❞♦ :✉❡ ❡22❡2 ❡2♣❛❧❤❛♠❡♥$♦2 2/♦ ✐♥❝♦❡"❡♥$❡2 ❡ ❛ "❛❞✐❛./♦ ❡2♣❛❧❤❛❞❛ E ♣"♦♣♦"❝✐♦♥❛❧ ❛♦ :✉❛❞"❛❞♦ ❞❛ ✐""❛❞✐-♥❝✐❛ ❞❛ ✐♥$❡♥2✐❞❛❞❡ ❞❛ "❛❞✐❛./♦ ✐♥❝✐❞❡♥$❡✱ $"❛$❛♥❞♦✲2❡ ❞❡22❛ ❢♦"♠❛ ❞❡ ✉♠ ♣"♦❝❡22♦ ♥/♦✲❧✐♥❡❛"✳

• ❊2♣❛❧❤❛♠❡♥$♦ ❞❡ 2❡❣✉♥❞❛ ♦"❞❡♠ ❍✐♣❡"✲❘❛♠❛♥ ❡ ❍✐♣❡"✲❘❛②❧❡✐❣❤✿ ❖ ♣"♦❝❡22♦ E 2❡♠❡❧❤❛♥$❡ ❛♦2 ❡2♣❡❧❤❛♠❡♥$♦2 ❍✐♣❡"✲❘❛♠❛♥ ❡ ❍✐♣❡"✲ ❘❛②❧❡✐❣❤✱ ♣♦"E♠ ❛ ✐""❛❞✐-♥❝✐❛ ❞❛ "❛❞✐❛./♦ ✐♥❝✐❞❡♥$❡ E3νi ♣❛"❛ ♦ ❡2♣❛❧❤❛♠❡♥$♦ ❍✐♣❡"✲❘❛②❧❡✐❣❤✱ ❧♦❣♦ ❛ ✐♥$❡♥2✐❞❛❞❡ ❞❛ "❛❞✐❛./♦ ❡2♣❛❧❤❛❞❛ 2❡"< ♣"♦♣♦"❝✐♦♥❛❧ ❛♦ ❝✉❜♦ ❞❛ "❛❞✐❛./♦ ✐♥❝✐❞❡♥$❡✳ K♦"$❛♥$♦✱ $❡"❡♠♦2 ✉♠ ♣"♦❝❡22♦ ♥/♦✲❧✐♥❡❛" ❡ $❛♠❜E♠ E ✐♥❝♦❡"❡♥$❡ ❝♦♠♦ ♦2 ❡2♣❛❧❤❛♠❡♥$♦2 ❝✐$❛❞♦2 ❛❝✐♠❛✳

• ❊2♣❛❧❤❛♠❡♥$♦ ❘❛♠❛♥ ❆♥$✐✲❙$♦❦❡2 ❈♦❡"❡♥$❡ ✭❈❆❘❙✮ ❡ ❊2♣❛❧❤❛♠❡♥$♦ ❙$♦❦❡2 ❈♦❡"✲ ❡♥$❡ ✭❈❙❘❙✮✿ ❛2 2✐❣❧❛2 ❞❡22❡ ❡2♣❛❧❤❛♠❡♥$♦2 2/♦ ♣"♦✈❡♥✐❡♥$❡2 ❞❛ ♥♦♠❡♥❝❧❛$✉"❛ ❞♦2 ♣"♦❝❡22♦2 ❡♠ ✐♥❣❧?2✳ ❆♣❡2❛" ❞❡ $❛♠❜E♠ 2❡ $"❛$❛"❡♠ ❞❡ ♣"♦❝❡22♦2 ♥/♦✲❧✐♥❡❛"❡2 ✭❛ ❢"❡:✉?♥❝✐❛ ❡2♣❛❧❤❛❞❛ ♥♦2 ❞♦✐2 ❝❛2♦2 E ♣"♦♣♦"❝✐♦♥❛❧ ❛♦ :✉❛❞"❛❞♦ ❞❛ ✐""❛❞✐-♥❝✐❛ ❞❛ "❛❞✐❛./♦ ✐♥❝✐❞❡♥$❡✮✱ ❡22❡2 ♣♦22✉❡♠ ✉♠ ❞✐❢❡"❡♥❝✐❛❧ ❡♠ "❡❧❛./♦ ❛♦ ❞❡♠❛✐2 ♣"♦❝❡22♦2✱ ♣❡❧♦ ❢❛$♦ ❞❛ ❝♦❡"?♥❝✐❛ :✉❡ ♣"♦♣✐❝✐❛ ✉♠❛ ✐♥$❡♥2✐❞❛❞❡ ❜❡♠ ♠❛✐♦" ❞❛ "❛❞✐❛./♦ ❡2♣❛❧✲ ❤❛❞❛ ❝❡"❝❛ ❞❡ ✺ ❛ ✶✵ ✈❡③❡2 ♦"❞❡♠ ❞❡ ♠❛✐♦" ❞♦ :✉❡ ❛ ❞♦ ❘❛♠❛♥ ◆♦"♠❛❧ ❬✷✶❪✱ ❞❡✈✐❞♦ ❛ ❜❛✐①❛ ❞✐2♣❡"2/♦ ❞❛ ♠❡2♠❛✳ ◆♦2 ❞♦✐2 ♣"♦❝❡22♦2 ✉$✐❧✐③❛♠✲2❡ ❞♦2 ❢❡✐①❡2 ♠♦♥♦❝"♦♠<$✐✲ ❝♦2 ❝♦❤❡"❡♥$❡2 ❝♦♠ ❢"❡:✉?♥❝✐❛2 ν1 ❡ ν2✱ ❡♠ :✉❡ ν1 > ν2✱ ❛2 :✉❛✐2 ❛♦ ❝♦✐♥❝✐❞✐"❡♠

❡2♣❛❝✐❛❧♠❡♥$❡ ❡ $❡♠♣♦"❛❧♠❡♥$❡ ❣❡"❛"/♦ ❢"❡:✉?♥❝✐❛2 ❡2♣❛❧❤❛❞❛2 ❞♦ $✐♣♦ ν1 +νm ✭❈❆❘❙✮ ❡ ν1−νm ✭❈❙❘❙✮✱ ❡♠ :✉❡ 2❡ ♠❛♥$?♠ ❛ ❢"❡:✉?♥❝✐❛ ν1 ❝♦♥2$❛♥$❡ ❡ 2❡ ✈❛"✐❛

ν2✱ ❝♦♠ ♦ ♦❜❥❡$✐✈♦ ❞❡ ν1−ν2 =νm✳ ❊22❛ ❞✐❢❡"❡♥.❛ ❡♥$"❡ ❛2 ❞✉❛2 ❢"❡:✉?♥❝✐❛2 2❡"<

✐❣✉❛❧ ❛ ❞❛ ❢"❡:✉?♥❝✐❛ ♠♦❧❡❝✉❧❛"✱ ♣♦"$❛♥$♦✱ νea=ν1+νm =ν1+ (ν1−ν2) = 2ν1−ν2✱

❢"❡:✉?♥❝✐❛ ❡2♣❛❧❤❛❞❛ ♣❛"❛ ♦ ❈❆❘❙ ❡ νes = ν1−νm = ν1 −(ν1−ν2) = 2ν2 −ν1✱