HAL Id: jpa-00221258
https://hal.archives-ouvertes.fr/jpa-00221258
Submitted on 1 Jan 1981
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
PHONON DISPERSION CURVES IN THE
MOLECULAR CRYSTALS NAPHTHALENE AND
ANTHRACENE MEASURED BY INELASTIC
NEUTRON SCATTERING
B. Dorner, E. Bokhenkov, E. Sheka, S. Chaplot, G. Pawley, J. Kalus, U.
Schmelzer, I. Natkaniec
To cite this version:
JOURNAL DE P H Y S I Q U E
CoZZoque C6, suppZdment au n012, Tome 4 2 , de'cembre 1981 page C6-602
PHONON DISPERSION CURVES I N THE MOLECULAR CRYSTALS NAPHTHALENE AND ANTHRACENE MEASURED BY I N E L A S T I C NEUTRON SCATTERING
**
**
B . Dorner, E.L. ~okhenkov*, E . F . Sheka*, S.L. Chaplot
,
G . S . Pawley,
J . ~alus***, U . Schmelzer*** and I . ~atkaniec**** ILL Grenob Ze, France
" ~ n s t
.
Sol. S t a t . Physics, ChernogoZovka, USSR **physics Dept. Univ. Edinburgh, U. K.***
Physics Dept. Uniu. Bayreuth, F. R. G.****
I n s t . NucZ. Phys. Krakow, PolandA b s t r a c t .
-
Wedetermined t h e 12 e x t e r n a l and t h e 4 l o w e s t i n t e r n a l d i s p e r s i o n b r a n c h e s f o r s e v e r a l symmetry d i r e c t i o n s i n n a p h t h a l e n e a t 6 K and a n t h r a c e n e a t 12 K . The zone c e n t r e modes have been a s - s i g n e d unambiguously. The t e m p e r a t u r e dependence w a s s t u d i e d f o r b o t h c r y s t a l s , w h i l e t h e p r e s s u r e dependence o n l y f o r n a p h t h a l e n e . A t c o n s t a n t volume t h e f r e q u e n c i e s o f n a p h t h a l e n e would i n c r e a s e much more w i t h t e m p e r a t u r e t h a n t h o s e o f a n t h r a c e n e .By i n e l a s t i c n e u t r o n s c a t t e r i n g we d e t e r m i n e d t h e 16 l o w e s t phonon d i s - p e r s i o n b r a n c h e s f o r s e v e r a l symmetry d i r e c t i o n s f o r d e u t e r a t e d naph- t h a l e n e a t 6 K and f o r d e u t e r a t e d a n t h r a c e n e a t 12 K . These two mole- c u l e s c r y s t a l l i z e i n t h e same m o n o c l i n i c s t r u c t u r e P 2 1 / a w i t h two mole- c u l e s p e r u n i t c e l l . Unter t h e assumption o f r i g i d molecules one ex- p e c t s 12 e x t e r n a l modes. T h i s assumption i s a c c e p t a b l y w e l l f u l f i l l e d f o r n a p h t h a l e n e , where a n e n e r g y gap o f a b o u t 1 THz was o b s e r v e d be- tween t h e e x t e r n a l and t h e l o w e s t i n t e r n a l modes w h i l e i n t h e c a s e o f a n t h r a c e n e t h e f o u r l o w e s t i n t e r n a l modes a r e i n t h e r e g i o n o f t h e ex- t e r n a l modes and a s t r o n g i n t e r a c t i o n i s o b s e r v e d , s e e F i g . 1 F i g . 1: The 16 l o w e s t phonon . . ! , d i s p e r s i o n b r a n c h e s i n Anthra- , c e n e a t 12 K . The d o t t e d l i n e s v i s u a l i z e e x p e r i m e n t a l l y de- lZ0 t e r m i n e d a n t i c r o s , s i n g s and e i g e n v e c t o r e x c h a n g e s . Sound v e l o c i t i e s a t 300 K a r e i n - d i c a t e d by s t r a i g h t l i n e s . r z r Y r Y c A r A
ANTISYM SYM SYM ANTlSYM ANTISYM SYM
PHONON WAVEVECTOR
To perform the experiment it was crucial to have a lattice dyna- mics model calculation beforehand. The model is based on atom-atom potentials between different molecules /1,2/.
With help of the calculated eigenvectors the phonon intensities in different Brillouin zones have been predicted and nicely confirmed
by the experiment ( 3 , 4 ) for the centres of the Brillouin zones. For
finite phonon wavevectors many anticrossings of modes and eigenvector exchanges have been observed and analysed experimentally. For these two molecular crystals we obtained a complete set of experimentally de- termined dispersion curves. All zone centre modes have been assiged un- ambiguously to their groupe theoretical representations. The agreement between measured and calculated /5/ frequencies was qualitatively good but differed by up to 20%. The inclusion of a quadrupol moment /6/ im- proved the agreement very much.
In the case of anthracene we analysed the lowest internal modes
further by an eigenvector determination / 7 / . The four lowest internal
modes correspond to the BjU (Butterfly) and the AU (twist around the long axis) modes of the free molecule.
The temperature dependence at normal pressure has been investi-
gated as well /8,9/. All phonon frequencies decrease with increasing
temperature and the signals broaden such that many branches become un- observable at room temperature. We tried to include anharmonic effects by calculating the third and fourth order terms of the potential experi- enced by a particular mode with its proper eingenvector /lo/. The am-
plitudes of a11 other modes were kept zero. The calculculated anharmo- nic contributions had the right tendency but were much smaller than the observed ones.
The pressure dependence is so far studied only for naphthalene at
100 K and a hydrostatic pressure of 3 K bar /11/. We found very good
agreement between measured mode-Gruneinsenparameters and calculated Fig. 2: Temperature depen- dence of librational fre- quency (2.52 THz at 6 K ) versus temperature dependent
-0.3 - volume. Measured(--- ) and
calculated ( .
....
) Griineisen-parameters give frequency
-a2 - dependence at const. T.
C6-604 JOURNAL DE PHYSIQUE
ones /12/. This good agreement sollicitated a calculation for negative pressure, this means for an increased volume. The decrease of the li- bration frequency at normal pressure with increasing temperature is plotted in Fig. 2 versus the temperature dependent volume change to- gether with the calculated ones for the expanded volume at const. tem- perature. Apparently the experimental frequency decreases less than pre-
dicted from the Griineisenparameters. Thus we conclude that in naphtha-
lene frequencies at constant volume would increase with increasing tem- perature. This observation agrees with results from pressure dependent Raman scattering /13/. Encouraged by the good areement between measured and calculated Griineisenparameters for naphthalene we calculated them
for anthracene /9/, and made a comparison like the one in Fig. 2. We
found that in anthracene the frequency shift at const. volume would be smaller than in naphthalene, again in agreement with /13/. Nevertheless we plan to measure the pressure dependence in anthracene as well.
/I/ A.I. Kitaigorodsky; J. Chim. Phys.
63,
9 (1966)/2/ D.E. Williams; J. Chem. Phys.
45,
3770 (1966),47,
4680 (1967)/3/ I. Natkaniec, E.L. Bokhenkov, B. Dorner, J. Kalus, G.A. Mackenzie,
G.3. Pawley, U. Schmelzer and E.F. Sheka; J. Phys. C.
12,
4265(1980)
/4/ B. Dorner, E.L. Bokhenkov, S.L. Chaplot, J. Kalus, I. Natkaniec,
G.S. Pawley, N. Schmelzer and E.F. Sheka; J. Phys. C submitted
/5/ G.S. Pawley; Phys. Stat. Sol. 20, 347 (1967)
/6/ R. Righini, S. Califano and S.H. Walmsley; Chem. Rphys.
50,
113(1980)
/7/ S.L. Chaplot, G.S. Pawley, E.L. Bokhenkov, B. Dorner, V.K. Jindal,
J. Kalus, I Natkaniec and E.F. Sheka; Chem. Phys.
57,
407 (1981)/8/ E.F. Sheka, E.L. Bokhenkov, B. Dorner, J. Kalus, G.A. Mackenzie,
I. Natkaniec, G.S. Pawley and U. Schmelzer; to be published
/9/ V.K. Jindal, J. Kalus, E.L. Bokhenkov, S.L. Chaplot, B. Dorner,
I. Natkaniec, G.S. Pawley and E.F. Sheka; J. Phys. C submitted
/lo/ J. Kalus, B. Dorner, V.K. Jindal, N. Karl, I. Natkaniec, G.S.
Pawley, W. Press and E.F. Sheka; J. Phys. C submitted
/11/ U. Schmelzer, E.L. Bokhenkov, B. Dorner, J. Kalus, G.A. Mackenzie,
I. Natkaniec, G.S. Pawley and E.F. Sheka; J. Phys. C
14,
1025 (1(1981)
/12/ G. S.Pawley and K. Mika; Phys. Stat. So1.b
