INTERNAL AND EXTERNAL PHONONS IN MONOCLINIC TETRACYANOETHYLENE

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INTERNAL AND EXTERNAL PHONONS IN MONOCLINIC TETRACYANOETHYLENE

S. Chaplot, A. Mierzejewski, J. Lefebvre, G. Pawley, T. Luty

To cite this version:

S. Chaplot, A. Mierzejewski, J. Lefebvre, G. Pawley, T. Luty. INTERNAL AND EXTERNAL PHONONS IN MONOCLINIC TETRACYANOETHYLENE. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-584-C6-586. �10.1051/jphyscol:19816170�. �jpa-00221249�

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JOURNAL DE PHYSIQUE

CoZloque C6, suppze'ment au n O 1 2 , Tome 42, de'cembre 1981 page C6-584

INTERNAL AND EXTERNAL PHONONS I N MONOCLINIC TETRACYANOETHYLENE

* m JHC

S.L. Chaplot , A. Mierzejewski , J. ~ e f e b v r e * , G . S . pawley*and T. L U ~ Y * *

* Department of Physics, University of Edinburgh, Scotland

** I-4, Technical University of WrocZaw, Wroc-Zaw, PoZand

"ILL, GrenobZe, France

""Nuclear Physics Division, B M h a Atomic Research Center, Bombay, India

Abstract,- Dispersion curves of 1 2 e x t e r p a l and 10 Anternal phonon modes have been measured i n t h e a

,

^b* ^and^{c direc-}

t i o n s . The i n t e r n a l d i s p e r s i o n curves correspond t o t h e 5 low- frequency v i b r a t i o n s of t h e f r e e molecule and t h e y e x h i b i t a s i g n i f i c a n t proportion of l a t t i c e mode c h a r a c t e r involving both t r a n s l a t i o n a l and l i b r a t i o n a l motions. Recent l a t t i c e dynamical c a l c u l a t i o n s , i n which s e v e r a l i n t e r n a l modes a r e included, have y i e l d e d neutron s c a t t e r i n g cross-sections which have made p o s s i b l e t o a s s i g n t h e observed molecular v i b r a t i o n s .

1. Introduction.- Tetracyanoethylene flCNE/, one of t h e most corn- mon acceptors i n e l e c t r o n donor-acc ept o r /EDA/ complexes, f o m s two c r y s t a l l i n e phases, monoclinic (~2,,/n) s t a b l e above 292 K and cubic (Im3) s t a b l e below this temperature. Warming t h e cubic phase causes t h e t r a n s i t i o n t o t h e monoclinic s t r u c t u r e , but t h i s phase can be cooled down t o helium temperatures w i t h o u h r e v e r s e tran- s i t i o n , enabling i n e l a s t i c neutron s c a t t e r i n g experiments t o be made a t t h e most favourable temperature. The measurements of phonon d i s p e r s i o n curves a r e complete i n t h e low frequency range, 0-6 THz and a r e presented here. A s t h e IPCm molecule has many i n t e r n a l vi- b r a t i o n s a t low frequencies, it i s e s s e n t i a l t o include t h e vibra- t i o n s i n c a l c u l a t i o n s of one-phonon neutron s c a t t e r i n g cross-sections. Here, we r e p o r t s h o r t l y a model f o r t h e same.

2. Experimental.- The c r y s t a l of monoclinic TCNE of about 9 cm 3 was grown by t h e vapour d e p o s i t i o n technique and slowly cooled t o 5 K ( L 0.5 K) a t r a t e of 10 K/hour. The phonon d i s p e r s i o n curves have been measured a t t h e I n s t i t u t e Laue-Langevin on t h e t r i p l e axes spectromet e r

Im.

Focussing monochromators of p y r o l i t i c gra- p h i t e (002) and Cu (11'l) were used i n the low and high frequency region, along with p y r o l i t i c g r a p h i t e (002) analyser. Graphite (002) f i l t e r was used i n e i t h e s t h e i n c i d e n t o r s c a t t e r e d beam a s conve- nient. The W W i n a vanadium scan w a s 0.1 THz. The c r y s t a l was

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816170

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Figure 1. Ewerimerrbal phonon d i s p e r s i o n curves i n t h e monoclinic TCXX a t 5 X. Frequencies measured by Rman spectroscopy are i n d i c a t e d by t h e squme poin%s.

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C6-586 JOURNAL DE PHYSIQUE

W *

* *

3i

*

oriented i n a b

,

b c and c a planes i n d i f f e r e n t experiments.

Constant & scans were u s u a l l y employed with constant E scans i n a Pew cases.

R e s u l t s of t-he measvxements a r e shown on Figure 1. Most of t h e phonon frequencies a r e confirmed t o within 0.05 THz. A 1 1 t h e zone c e n t r e frequencies a r e well confirmed and assigned experimen- t a l l y using group t h e o r e t i c a l s e l e c t i o n r u l e s . The d i s p e r s i o n of t h e highest frequency branch i n a* d i r e c t i o n needed s p e c i a l atten- t i o n . This unusual d i s p e r s i o n has been confirmed i n both a?b* and a?c* o r i e n t a t i o n s ; however, i t s o r i g i n has t o be f u r t h e r i n v e s t i - gated.

3 . Theory.- The e x t e r n a l and lowest i n t e r n a l phonon d i s p e r s i o n re- l a t i o n s have been c a l c u l a t e d f o r a*, b* and c* d i r e c t i o n ~ , within an extended l a t t i c e dynamical model. The s e c u l a r equation,

D ( q )

g

^Cq) = ~ ~ ( q ) (q)

,

e

has been solved, The 26 ^X26 /with 7 ;free molecule v i b r a t i o n s included/ dynamical matrix has been constructed from t h e second deri- v a t i v e s of t-he c r y s t a l p o t e n t i a l , assumed t o be t h e sum of a n ex- t e r n a l and an i n t e r n a l p a r t . The i n t e r n a l p o t e n t i a l c o n t r i b u t e s t o t h e s e l f f o r c e constant only and i s r e l a t e d t o t h e f r e e molecule i n t e r n a l frequencies. The c o n t r i b u t i o n t o t h e f o r c e constants from t h e e x t e r n a l p o t e n t i a l can be e a s i l y obtained using nonbonded atomic p a i r p o t e n t i a l of "6-expS1 type. The mass matrix & has elements

where e ( i k )

-

e i s t h e atomic displacement p e r u n i t displacement of an atom i within t h e molecule k i n t h e 04-th degree of freedom.

;From t h e c a l c u l a t i o n s we note t h a t t h e phonons of frequencies below 5 THz cannot be l a b e l l e d a s purely exkernal o r i n t e r n a l . The phonon eigenvectors were used t o estimate t h e one-phonon neutron s c a t t e r i n g cross-sections. These were l a r g e l y c o n s i s t e n t with t h e experiments, t h u s supporting assignments of t h e phonon eigenvectors.

The agreement between t h e c a l c u l a t e d and experimental phonon frequencies was u s u a l l y about 10

-

^200k. ^{T h i s}leaves scope f o r an im- provement of t h e assumed e x t e r n a l p o t e n t i a l function. We f e e l , however, t h a t a molecular s h e l l model would be necessary f o r a c o r r e c t d e s c r i p t i o n o f t h e l a t t i c e dynanics.