NEUTRON SPECTROSCOPY OF INTERNAL PHONONS OF NAPHTHALENE AND ANTHRACENE CRYSTALS

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NEUTRON SPECTROSCOPY OF INTERNAL

PHONONS OF NAPHTHALENE AND

ANTHRACENE CRYSTALS

E. Bokhenkov, A. Kolesnikov, T. Krivenko, E. Shek, V. Dementjev, I.

Natkaniec

To cite this version:

JOURNAL DE PHYSIQUE

CoZZoque C6, suppliment au n032, Tome 42, diceinbre 1981 page C6-605

NEUTRON SPECTROSCOPY OF INTERNAL PHONONS OF NAPHTHALENE AND ANTHRACENE CRYSTALS

*

E.L. Bokhenkov, A.I. Kolesnikov, T.A. Krivenko, E.F. Sheka, V.A. Dementjev and I. ~atkaniec*"

I n s t i t u t e o f Solid S t a t e Physics, Acadeng o f Sciences o f t h e USSR, ChemogoZovka, USSR

nu he

Timiryazev Academy o f Agriculture, Moscow, USSR

**

_{Joint I n s t i t u t e for Nuclear Research, Dubna, USSR}

Abstract.- I n e l a s t i c incoherent neutron s c a t t e r i n g (IINS) spec- t r a from anthracene and naphthalene c r y f t a l s were measured a t T=4.7K i n the energy range 200-1500 cm

.

~ x p e r i m e n a l d a t a a r e w e l l described by the c a l c u l a t e d s p e c t r a of one-phonon s c a t t e r -

ing.

The IINS s p e c t r a from anthracene-do and naphthalene-&, polycry- s t a l l i n e specimens were obtained a t 4.7K using t h e KDSOG i n v e r t e d geometry time-of-flight spectrometer a t the IBR pulsed r e a c t o r of t h e JINR Dubna (I), The s p e c t r a measured r e s u l t from a three-dimensional convolution i n the form

N(to) = ~ t ~ \ \ \ d E ~ m d t F ( E ~ , E , ~ ~ , ~ ) ~ ( E ~ , B ,

0

,TI where F i s t h e apparatus f u n c t i o n of the spectrometer and

6

i s t h e cross-section of neutron s c a t t e r i n g . A d e t a i l e d d e s c r i p t i o n of a l l t h e q u a n t i t i e s t h a t appear i n Eq. i s given i n Ref.2.

Proceeding from t h e s o l u t i o n of t h e harmonic dynamics of a poly- atomic c r y s t a l ( 3, we c a l c u l a t e d t h e cross-section of one-phonon IINS computing previously t h e weighted density of s t a t e s .

I n t h e t o p of FLg.1 the f u n c t i o n g(4 ) i s t h e d e n s i t y of s t a t e s of t h e 144-mode phonon spectrum of a n t d a c e n e c r y s t a l ; i n t h e mid- p a r t G ( S ) d e p i c t s the weighted density i n t e g r a t e d over a l l hydroge- ne atoms. The cross-section of one-phonon IINS i s shown i n t h e bot- tom of Fig.1.

Experimental spectrum of IINS from anthracene c r y s t a l i s shown i n Fig.2a. Fig.2b demonstrates the c a l c u l a t e d spectrum of t h e one- phonon IINS i n the range of the i n t e r n a l phonon modes which i s the r e s u l t of t h e convolution of t h e s c a t t e r i n g cross-section (Fig.1, bottom) with t h e apparatus f u n c t i o n of the instrument. As-seen from Fig.2 t h i s spectrum f i t s t h e experimental one r a t h e r well. It should be noted t h a t though t h e energy r e s o l u t i o n of the instrument i s not high and amounts t o an average of

VO,

n e g l e c t of t h e phonon disper- s i o n and replacement of G(4 ) by a s e t of -function lead t o a con- s i d e r a b l e d e v i a t i o n of t h e computation from the experiment.

C6-606 JOURNAL DE PHYSIQUE

P i

X

: Calculated

g(d

) t o p ;

G(3

) (midpart);

*

one-phonon cross-section (bottom) f o r t h e 144-

mode phonon spectrum of anthracene-do c r y s t a l

Pig.2 : IINS TOF spec- t r a from anthracene-do c r y s t a l i n t h e ener r e g i o n 200-1500 cm-e a. Experiment, T=4.7K; b. Calculated spectrum of one-phonon IINS

TOF channel number

Experimental spectrum of I I N S from naphthalene c r y s t a l i s shown i n F i g . 3 ~ . Spectrum i n Fig.3b i s c a l c u l a t e d i n t h e same way a s it

was made above f o r anthracene c r y s t a l . Spectrum i n Pig.3a i s c a l c u l a t - ed approximating t h e i n t e r n a l phonon d e n s i t y of s t a t e s by a s e t of

able t o o r l e s s than t h e instrument resolution. But i n t h e range 200 cm-I and lower only the i n c l u s i o n of phonon d i s p e r s i o n enables t h e experimental spectrum t o be properly described.

Energy Transfer (cm-'1

Fig.3 : IINS TOF s p e c t r a from naphthalene -d crys4.p i n t h e energy region 170- -1500 cm ;

a. C culated one-phonon IINS spectrum i n

P

t h e -approximat i o n f o r non-int e r a c t i n g molecules;

b. Calculated spectrum on t h e b a s i s of s o l u t i o n of t h e dynamical problem f o r I08 c r y e t a l phonon modes;

c. Experimental spectrum, T=4.7$

IS001

lo5

01

7

I9O'-

*

_{f # 5 :}

TOF s h a r d number (C-Y~JIS) E L---

Fig.4 :Calculated and measured dis-

2

persion of t h e lowest i n t e r n a l mo-

d e s (B -lower, pper) of naph- t h a l e n a ~ g cry st$?-u

I l l 1 I I I I

0.5

-

0

-

0.5

Reduced wavevector

Fig.4 i l l u s t r a t e s t h e comparison between the measured d i s p e r s i o n of t h e two low-f r e quency i n t e r n a l modes of naphthalene-dg c r y s t a l ( 4 ) and c a l c u l a t i o n s ( s o l i d and dashed l i n e s ) . The c a l c u l a t i o n s perform- ed by the method described i n Ref.3 f i t t h e experiment very well. References

I, I;M,Frank, Sov. J,Part.Nucl. ,2,805 (1973)

2. E.L.Bokhenkov, 1.Natkaniec and E.F.Sheka, Sov.Phys.-JETP 43,536 ( 1976)

3. ~ . ~ . ~ o k h e n k o v , A.I.Kolesnikov, T.A.Krivenko, E.F.Sheka and V,A.Dementjev, these Proceedings, F.