Harmonic Dynamics of Anthracene Crystal

Abstract

A method is suggested for the calculation of the complete phonon spectrum of a polyatomic molecular crystal in the entire Brillouin zone. The spectrum includes both external and internal phonons and the method involves breaking up the high order dynamical matrix into several blocks covering large groups of phonons revealing marked intermode mixing inside a group and neghgible mixing among the modes of the neighbouring groups. The phonon mode structure is assigned through the analysis of the eigenvector matrix. The calculations using the suggested method are controlled by the calculation of all 144 frequencies at the point q = 0. The dispersion curves and the density of states of the entire 144-mode phonon spectrum of anthracene-do crystal are presented.

Spectroscopy of amorphous substances with molecular structure

“…Ïðè âçàèìîäåéñòâèè ñî ñâåòîì ïåðåñòàåò âûïîëíÿòüñÿ ïðàâèëî îòáîðà äëÿ îäíîôîíîííûõ ïåðåõîäîâ 0, = ≈ G 3 è îäíîôîíîííûé ñïåêòð ÊÐÑ àìîðôèêà ôîðìèðóåòñÿ ïîëíîé ïëîòíîñòüþ ôîíîííûõ ñîñòîÿíèé â îòëè-÷èå îò ñïåêòðà 0, = G ìîä êðèñòàëëà. Ïëîòíîñòü êîëåáàòåëüíûõ ñîñòîÿíèé ìîëåêóëÿðíûõ òâåðäûõ òåë â íèçêî÷àñòîòíîé îáëàñòè (îò íóëÿ äî 150 200 ñì 1 ) ÿâëÿåòñÿ íåïðåðûâíîé ôóíêöèåé ÷àñòîòû [30]. Âñëåäñòâèå ýòî-ãî âìåñòî õàðàêòåðíîãî óçêîïîëîñíîãî ñïåêòðà ÊÐÑ ìîëåêóëÿðíîãî êðè-ñòàëëà ñïåêòð àìîðôèêà â ýòîé îáëàñòè äîëaeåí èìåòü âèä íåïðåðûâíîãî ðàñïðåäåëåíèÿ èíòåíñèâíîñòè â çàâèñèìîñòè îò ÷àñòîòû.…”

“…Òàê, â îáëàñòè äî 100 ñì 1 ðàñïîëàãàþòñÿ 9 êîëåáàíèé, íàèìåíü-øàÿ ÷àñòîòà êîòîðûõ ñîñòàâëÿåò âñåãî 9 ñì 1 . Èç ôèçèêè ôîíîíîâ ìî-ëåêóëÿðíûõ êðèñòàëëîâ èçâåñòíî [30], ÷òî êîðîòêîäåéñòâóþùèé àòîì-àòîìíûé ïîòåíöèàë ìåaeìîëåêóëÿðíîãî âçàèìîäåéñòâèÿ ïðèâîäèò ê êî-ëåáàòåëüíûì ñîñòîÿíèÿì, îáóñëîâëåííûì âíåøíèìè ñòåïåíÿìè ñâîáîäû ìîëåêóëû, îïèñûâàþùèìè ïî ñòóïàòåëüíîå è âðàùàòåëüíîå äâèaeåíèÿ åå Ðèñ. 13.…”

“…Ýòè êîëåáàíèÿ õàðàêòåðèçóþòñÿ çàìåòíîé äèñïåðñèåé, ïðèâîäÿùåé ê íåïðå-ðûâíîé ïëîòíîñòè êîëåáàòåëüíûõ ñîñòîÿíèé (ñì., íàïðèìåð, ñïåêòð êðè-ñòàëëà íàôòàëèíà [52]).  ñëó÷àå ïåðåêðûòèÿ ñïåêòðà âíåøíèõ êîëåáà-íèé ñî ñïåêòðîì âíóòðåííèõ, âíóòðèìîëåêóëÿðíûõ êîëåáàíèé êàðòèíà êîëåáàòåëüíîãî ñïåêòðà ñóùåñòâåííî óñëîaeíÿåòñÿ (ñì., íàïðèìåð, ñïåêòð êðèñòàëëà àíòðàöåíà [30]). Äëÿ ÌÁÁÀ èç-çà áîëüøîãî ÷èñëà âíó-òðåííèõ êîëåáàíèé, ïîïàäàþùèõ â îáëàñòü âíåøíèõ, êàðòèíà ñïåêòðà ÷ðåçâû÷àéíî ñëîaeíà.…”