Effect of Pressure on Intermolecular Bonds in Solid Halogens

A bond charge model has been developed for the description 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 increasing 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 (D*) /1 / . ThB molecules are stacked in a planar arrangement as indi2 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 PHYSIQUE on C1, Br and I. Fig. 2 shows the usual zone centre symmetry coordinates for these four modes. In all of them, the atoms move within the plane of the molecules. The molecular stretching modes exhibit a frequency splitting, which is not yet understood in detail. The symmetric A -mode has a lower fre9 quency than the antisymmetric B -mode, while in various lattice 3 9 dynamical calculations the opposite sequence is obtained 151. We have developed a bond charge model for the description of the pressure dependence of the observed zone centre phonon frequencies. These calculations have been performed in two stages. For the description of the attractive part of the crystal potential, we have assumed Coulomb-interaction between positive ions and negative bond charges placed at the centres of the three types of bonds, the molecular bonds, the shortest, and second shortest intermolecular bonds. The repulsive part has been described by a spherically symmetric potential of Born-Mayer type: Urep = E exp(-KR). Static equilibrium conditions have been included to ensure, that the forces on an ion as well as the external stresses vanish. In this first stage, the five parameters ql, q2, 93, E and K have been fitted to the observed frequencies with the following results: For each pressure, one gets three values for the three different bond charges as indicated in fig. 4. Surprisingly, the bond charges depend linearly on their bond lengths within experimental error. Therefore, we can replace the three parameters ql, q p a n d q 3 by two new parameters q , and o: q ( ~ ) = q0 (1 R/u). On the other hand, we find, that also in this model the frequency of the symmetric molecular mode is higher than the frequency of the antisymmetric one. This discrepancy to the experimental results is removed by the use of a pressure dependend bond coupling parameter A / 6 / . Fig. 3 The positions o f the bond charges in this model. Fig. 4 The bond length dependence o f the bond charges. Within this model we find, that the parameters q, and E do not depend on pressure and are the same for the three halogens: q, = 2.62(6) e, E = 1.42(17) x lop9 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 4.30 The 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 and 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 compared 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 Chlor ine I I 0 10 20 30 40