HAL Id: jpa-00224334
https://hal.archives-ouvertes.fr/jpa-00224334
Submitted on 1 Jan 1984
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.
EFFECT OF PRESSURE ON INTERMOLECULAR BONDS IN SOLID HALOGENS
P. Johannsen, W. Holzapfel
To cite this version:
P. Johannsen, W. Holzapfel. EFFECT OF PRESSURE ON INTERMOLECULAR BONDS IN SOLID HALOGENS. Journal de Physique Colloques, 1984, 45 (C8), pp.C8-191-C8-194.
�10.1051/jphyscol:1984834�. �jpa-00224334�
EFFECT OF PRESSURE ON INTERMOLECULAR BONDS IN SOLID HALOGENS P.G. Johannsen and W.B. Holzapfel
Paehber&ich Physikj Univers-Ltttt-GH-Paderbovn, D-4790 Paderbom, F.R.G.
.Résumé - Un modèle de charge liée a été développé pour décrire la variation avec la pression des phonons de centre de zone actifs sn Raman de Cl, 8r, et I. L'augmentation de la covalence des liaisons intermaléculaîres se traduit par une augmentation de la charge liée avec la pression.
Abstract - A bond charge model has been developed for the de- scription of the pressure dependence for the Raman-active zone centre phonon frequencies of CI, Br and I. The increase in covalency of the intermolecular bonds shows up in increa- sing values of the bond charges under pressure.
The halogens CI, Br and I form isomorphic molecular crystals. The structure is orthcrhombic with two molecules per primitive unit cell (D1*) /1 / . ThB molecules are stacked in a planar arrangement as indi-
2 h
cated in fig. 1. Although the crystal structure is quite simple, these materials cannot be considered as purely molecular crystals, in which the molecules are only bound by van-der-Waals-interaction, At ambient pressure, the shortest intermolecular bond is significantly shorter than van-der-Waals-diameter , and it is generally assumed, that this bond has markedly covalent character. It is uiell established by various high pressure measurements on iodine, that this covalency increases with pressure / 2 / .
Fig.1 - Crystal structure, Fig. 2 - Symmetry coordinates.
To complement the earlier high pressure data of iodine, lattice parameters of CI and 8r under pressure were studied recently/3/, and we have measured Raman-spectra of CI and Br up to 45 GPa M/.Generally, four Raman-active modes can be observed in high pressure measurements Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984834
C8-192 JOURNAL
DE
PHYSIQUEon C 1 , Br and
I.
Fig. 2 s h o w s the usual zone centre symmetry coor- dinates f o r these four modes. I n a l l o f them, the a t o m s move within the p l a n e of the molecules.The molecular stretching m o d e s exhibit a frequency s p l i t t i n g , which i s not yet understood i n detail. The symmetric A -mode has a lower f r e -
9
quency than the antisymmetric B - m o d e , while in various l a t t i c e 3 9
d y n a m i c a l c a l c u l a t i o n s the opposite sequence i s obtained 151.
W e have developed a bond c h a r g e model f o r the description o f the pressure dependence of the observed z o n e c e n t r e phonon frequencies.
These c a l c u l a t i o n s have been performed in two stages. F o r the d e - scription of t h e a t t r a c t i v e part of the c r y s t a l potential, w e have assumed Coulomb-interaction between positive i o n s and n e g a t i v e bond c h a r g e s placed a t the c e n t r e s o f t h e t h r e e t y p e s of bonds, the m o l e - cular bonds, the shortest, and second s h o r t e s t intermolecular bonds.
The repulsive part h a s been described by a spherically s y m m e t r i c potential of Born-Mayer type: U r e p = E exp(-KR). S t a t i c equilibrium c o n d i t i o n s have been included t o ensure, t h a t the f o r c e s on a n ion a s well a s the external s t r e s s e s vanish. I n t h i s f i r s t s t a g e , the f i v e p a r a m e t e r s ql, q 2 , 9 3 , E and K h a v e been fitted t o the observed f r e q u e n c i e s with t h e following results: F o r each pressure, o n e gets three values f o r the three different bond c h a r g e s a s indicated in fig. 4. S u r p r i s i n g l y , the bond c h a r g e s depend linearly on their bond lengths within experimental error. Therefore, we c a n replace the three parameters q l , q p a n d q 3 by t w o new parameters q , and o:
q ( ~ ) = q0 ( 1
-
R/u). O n t h e o t h e r h a n d , we f i n d , t h a t a l s o i n t h i s model the frequency o f the symmetric molecular mode i s higher than the frequency of t h e a n t i s y m m e t r i c one. T h i s discrepancy t o t h e experimen- tal r e s u l t s i s removed by the use o f a pressure dependend bond c o u p - ling parameter A / 6 / .Fig. 3 - T h e positions o f t h e bond charges in this model.
F i g . 4 - T h e bond length d e p e n d e n c e
o f the bond charges.
q, = 2.62(6) e, E = 1.42(17) x
l o p 9
erg.The parameter K shows a characteristic value for each of the three halogens with a systematic variation from C1 to Br and I:
C 1 B r I
(
2.60(8) 2.33(10) 2.19(4)The most interesting parameter is 0 , the characteristic bond length, at which the respective bond charges would become zero. If bond charges are reasonable parameters for the covalency of a bond, a should be of the order of van-der-Waals-diameter. Within this model,
0 shows a slight variation with pressure. Its value a, at low pressures is in fact very similar to van-der-Waals-diameter:
ovdW(!)
3.62 3.90 4.30The bond coupling parameter A , shows a strong increase with pressure (%10%/GPa). Its contribution to the force constants, however, does not exceed 2%, even at the highest pressures.
Fig. 5 shows the variation of the bond charges with pressure. It should be noted, that the changes in the bond strengths are reproduced in our model b y the changes of the respective bond charges.
Fig. 5 - Effect of pressure on the bond charges in this model.
C8-194 JOURNAL DE PHYSIQUE
The e x p e r i m e n t a l a n d c , a l c u l a t e d f r e q u e n c i e s o f c h l o r i n e a n d b r o m i n e a r e c o m p a r e d i n f i g . 6, w h i c h shows, t h a t t h e p r e s e n t m o d e l g i v e s a r e a s o n a b l e d e s c r i p t i o n o f t h e l a t t i c e d y n a m i c s i n t h e s o l i d h a l o g e n s . The l i m i t a t i o n s o f a r i g i d b o n d c h a r g e m o d e l a r e i n d i c a t e d b y t h e a d d i t i o n a l " b o n d c o u p l i n g u p a r a m e t e r .
A 9
Bromine
1 I I
0
I C h l o r i n e
I I
0 1 0 20 30 40
P ( G P ~ )
F i g . 6
-
E x p e r i m e n t a l a n d c a l c u l a t e d ( c o n t i n u o s l i n e s ) f r e q u e n c i e s o f c h l o r i n e a n d b r o m i n e .R e f e r e n c e s :
/'I/ COLLIN R.L., A c t a C r y s t a l l o g r . 9, ( 1 9 5 6 ) ~ 5 3 7
DONOHUE J . a n d GOODMAN S.H., A c t a C r y s t a l l o g r .
18,
( 1 9 6 5 ) ~ 5 6 8 VDNNEGUT B. a n d WARREN B.E., J . Am. Chem. S o c . 5 8 , ( 1 9 3 7 ) ~ 2 4 5 9 /2/ TAKEMURA K.. MINOMURA S., SHIMOMURA O . , F U J I 1rand
AXE J.o.,
P h y s . R e v . 8 2 6 , ( 1 9 8 2 ) ~ 9 9 8
SHIMONURA O ~ T A K E N U R A K . a n d AOKI K., " H i g h P r e s s u r e i n R e s e a r c h a n d I n d u s t r y " , ed. BACKMAN C.M., JOHANNISSON T. a n d TEGNER L.9 P r o c . 8 t h AIRAPT a n d 1 9 t h EHPRG C o n f . ( ~ p p s a l a ) 1 9 8 2
/ 3 / DOSING E.F., GROSSHANS W . a n d HOLZAPFEL W.B., t h i s c o n f e r e n c e / 4 / JOHANNSEN P.G. a n d HOLZAPFEL W.B., J . P h y s .
u,
( 1 9 8 3 ) ~ 1 9 6 1 JOHANNSEN P.G. a n d HOLZAPFEL W.B., J. P h y s .E,
( 1 9 8 3 ) ~ L 1 1 7 7 / 5 / PASTERNAK A., ANDERSON A . a n d LEECH J.W., J. P h y s .Q,
( 1 9 7 7 1 , 3 2 6 1PASTERNAK A., ANDERSON A . a n d LEECH J.W., J. P h y s . C11, ( 1 9 7 8 ) , 1 5 6 3 / 6 / KOBASHI K. a n d ETTERS D., J . Chem. P h y s .
