LATTICE DYNAMICS CALCULATIONS FOR SOLID BIPHENYL IN THE HIGH TEMPERATURE PHASE

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LATTICE DYNAMICS CALCULATIONS FOR SOLID BIPHENYL IN THE HIGH TEMPERATURE PHASE

T. Wasiutynski, I. Natkaniec, A. Belushkin

To cite this version:

T. Wasiutynski, I. Natkaniec, A. Belushkin. LATTICE DYNAMICS CALCULATIONS FOR SOLID BIPHENYL IN THE HIGH TEMPERATURE PHASE. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-599-C6-601. �10.1051/jphyscol:19816175�. �jpa-00221257�

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JOURNAL DE PHYSIQUE

Colloque C6, suppldment au n012, Tome 42, de'cembre 1981

LATTICE DYNAMICS CALCULATIONS FOR SOLID BIPHENYL IN THE HIGH TEMPERATURE PHASE

T. Wasiutynski, I. Natkaniec and A.I. ~elushkin*

I n s t i t u t e o f Nuclear Physics, Krakow, Poland

-n Joint I n s t i t u t e o f Nuclear Research, Dubna, USSR

Abstract. The l a t t i c e dynamics model with e x p l i c i t l y imcluded l n t e r p h e n y l modes wae formulated. The i n t e m o l e c u l a r poten- tial of t h e *6-expn form with W i l l i a m s parameters was ased.

The phase t r a n s i t i o n t o t h e incommensurate phase was i n t e r - p r e t e d a s a phonon i n s t a b i l i t y f o r t h e wave v e c t o r i n s i d e t h e B r i l l o n i n zone q m (0, 0.4, 0).

i. Model.

-

The p o t e n t i a l energy of t h e c r y s t a l under study is ex- pressed i n t h e forms

V = ?- ECKI 19; + K 2 * K 3 lim - ro12 + K L sin2 IPm + z V m n ]

2 rn ( 1 )

The f i r s t term i n ( I ) d e s c r i b e s in-plane deformation of t h e C-C bond, t h e second term d e s c r i b e s out-of-plane deformation, t h e t h i r d term s t r e t c h i n g , t h e f o u r t h t o r s i o n , The last t e r n d e s c r i b e s i n t e r a c t i o n be tween chemically nonbonded at oms and has t h e well known w6-expn f ormt

Vmn = TEA.. exp (-8.. r . . ) -C.. r.: 6 1

IJ '1 I J I J 11 IJ

The empirical parameters A, B and C were taken from W i l l i a m s /i/.

The remaining parameters i n ( 1 ) were adjusted i n o r d e r t o o b t a i n t h e b e s t agreement with t h e experiment. The f i n a l values i n u n i t s of kcal/mole and A a r e t

Ki o $25 K2 r 45 K3 ⁿ97.8 K4 ^P52.5 ro r 1.2937

2. Results.

-

The l a t t i c e dynamics c a l c u l a t i o n s have t o be p e r f o w e d a t t h e minimum of t h e l a t t i c e energy, This i s t h e c o n d i t i o n f o r t h e l a t t i c e s t a b i l i t y . A s t h e f i r s t s t e p t h e l a t t i a e energy was mini- mised with r e s p e c t t o all s t r u c t u r a l paraaieters. The r e s u l t s a r e presented i n t a b l e i.

Table i

The comparison of c a l c u l a t e d and experimental c r y s t a l s t r u c t u r e of s o l i d biphenyl at high temperature phase

a a l o u l a t e d experimental /2/

W 3 60.1 59.0 a

7.797 7.82

c 9.518 9.44 b

5.490 6.58

P 88.6 94.6

W1 99.4 99.2

W2 106.4 103.7

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816175

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C6-600 JOURNAL DE PHYSIQUE

where 8, b, C and p a r e u n i t o e l l parameters _o,, w 2 , w3 a r e Euler angles of the molecule. With the help of the intermolecular p o t e n t i a l of the form ( 1) the phonon d i s p e r s i o n curves i n harmonio approximation were caloulated. Figure i presents 16 low lying phonon branches.

cm-' q = lO.f.0) _cm-'

350

1

ANTISYMMETRIC I ^SYMMETRIC

4

³⁵⁰

320 stretching

280 out oi olane 270 in plane 260

out of plane

torsion

Fig. 1 t Phonon d i s p e r s i o n curves i n biphenyl f o r the

( 0 i 0 ) direction.

A s o m be seen from the f i g u r e t h e r e i s s t r o n g nixing between exter- n a l modes of the biphenyl molecule and the two i n t e r n a l modest out- -of-plane deformation and torsion. A l l the modes show l a r g e disper-

@on. The olose inspection of the eigenvectors of the lowest branch gives us information about t h e oharaoter o f the motion. For small q v a l a e s the character of the motion i s t r a n s l a t i o n a l . For l a r g e r q values t h e oharaater of t h e aarve changes t o the t o r s i o n a l one. For the j u 0.4 where t h e r e i s a deep minimum i n the curve i t i s pre- dominantly of the t o r s i o n a l type. The p o s i t i o n of the minimum i s

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very s e n s i t i v e t o the value of K4. It i s connected with the ineta- b i l i t y of the t o r s i o n a l mode. This f a c t was confirmed experimental- l y by coherent neutron s c a t t e r i n g by Ca%lleau e t ale /3/. They found s o f t mode l i k e behaviour of the pbonon a t 5 = 0.47 which is i n q u i t e good agreement with t h e present caloulations.

References

/I/ D.E. Williams, J.Chem.Phys. 47, 4680 (1967)

/2/ G.P. Charboneau, Y. Delugeard, Acta Crystallogr. u, 1420(1976) /3/ H. Cailleau, F. Moussa, J, Mons, Solid S t a t e ComBun. 31, 521

( 1979).