Modeling the vibrational dynamics of solid benzene: Hexafluorobenzene. The anatomy of a phase transition

ChemicalPhysics North-Holland

172 (1993)

171-186

Modeling the vibrational dynamics of solid benzene : hexafluorobenzene. The anatomy of a phase transition Jeffrey H. Williams InstitutMax vonLaue-Paul Langevin, 156X. 38042 Grenoble,France Received

22 October

1992

We have studied the lowest temperature phase of the solid, C6Hs: C,F,. The molecular dynamics of this phase (IV) are seen to consist of thermally activated six-fold rotational reorientations of the molecules about their hexad axis together with vibrations of the molecular chains which constitute the solid. In phase III we have observed, in addition to the solid state rotations, the onset of molecular diffusion. We suggest that the transition from phase IV to phase III occurs as a consequence of increasing amounts of disorder arising from these large amplitude librations or rotations. Relatively simple molecular and electrostatic models are employed to rationalize the different types of experimental data.

1. Introduction The ability to predict the solid state packing of molecules and to comprehend the observed molecu: lar dynamics from a knowledge of the electrical properties of the isolated molecules and the measured solid state spectra is a goal much sought after but not easily realized. Although the strength of the various intermolecular interactions may be approximated the problem is not straightforward. We have investigated structure-property relationships in solid benzene : hexafluorobenzene. This is the simplest member of a very large class of layered organic compounds, sometimes referred to as charge transfer complexes. The charge distribution of the simple aromatic molecules benzene and hexafluorobenzene is of considerable interest. Their symmetry implies that all odd electric moments (dipole, octopole etc. ) vanish and the first non-vanishing electric moment is the molecular electric quadrupole moment, 8. Similarly, the molecular symmetry allows only one independent component of 8, S,, = - (S,+ S,). This quadrupole moment has been measured, for benzene and hexafluorobenzene, by electric-tieldgradient induced birefringence in the vapour phase 0301-0104/93/$06.00

0 1993 Elsevier Science Publishers

[ 11. In any scheme of molecular interactions, it is the first non-vanishing electrical moment which will dominate the electrostatic interaction of a pair of molecules. Thus it is with benzene and hexafluorobenzene the former has a large negative quadrupole moment ( - 29.0 x 1OP40 C m* ) and the latter, a large positive quadrupole moment (31.7 x 10e4’ C m’) [ 11. Simple mixing of these two liquids produces, at room temperature, a solid by virtue of the strong interaction between the two electrical moments. Gas phase investigations of the benzene: hexafluorobenzene dimer, with molecular beam electric resonance spectroscopy, revealed that the dimer is possessed of an induced dipole moment of 0.44 D [ 21. That is, almost + of an electron transferred over a typical intermolecular spacing of 3.7 A. With such a strong intermolecular polarization or charge transfer, the existence of a new solid, with physical properties distinct from those solids composed of the constituent molecules, was perhaps to be expected. We have investigated this solid, C6H6 : C6F6, with a variety of neutron scattering techniques, in an attempt to understand the origin of the instability of this material compared to that of solid benzene or solid hexafluorobenzene. The binary mixture melts at a temperature higher than solid benzene, 298 K as

B.V. All rights reserved.

172

J.H. Wdliams /Chemical Physics I72 (1993) 171-186

opposed to 278 K. Unlike solid pure benzene, however, it has a structure which exhibits instabilities: there are solid state phase transitions at 205,247 and 275 K [3].

2. Neutron scattering The details of neutron scattering theory are to be found in many standard texts, here we will only introduce a few important points. The observed intensity of neutrons scattered at a particular frequency, w, and into a particular scattered direction, i.e. the scattering law S( Q, w), from an incoherent scatterer may be approximated as [ 4 ]

S(Q,o)~:(uf)Q2exp(-2W,),

(1)

where Q represents the momentum transfer. We see clearly how the scattered intensity is a strong function of the momentum transfer and of the amplitude of oscillation of the scatterer, (u:). The DebyeWaller factor, exp ( - 2 W,), is the expectation value of the amplitude of motion of the scattering particle, i.e. the proton in our samples, and the scattering vector. Consider a lattice of particles whose position is nominally fixed but also contains a term, u(t), fluctuating in time. If each particle or molecule undergoes independent fluctuations the thermal average of the intensity scattered from a lattice will contain terms, exp( ( -m-Q) ). Expanding the exponential and using the average, (u-Q) = 0, for Q and (u) uncorrelated, we find that the powder average of the Debye-Waller factor is given by exp( -2W,)=exp(

- (uf)Q2/3).

(2)

The motion of the scatterer will arise from a number of sources. At low temperatures there will be the zero-point vibrational oscillations. As the temperature rises there may be sufficient thermal energy to excite low frequency molecular vibrations, together with intermolecular phonon modes and large amplitude angular librations or rotations. All will contribute to the measured ( u2), the mean squared amplitude of the proton oscillation.

2.1. Experimental details The experimental results discussed here were obtained on a variety of spectrometers at the Institut Max von Laue-Paul Langevin, Grenoble and on the time focusing crystal analyzer (TFXA) spectrometer found on the pulsed neutron source of the Rutherford Appleton Laboratory, England. TFXA is a high resolution inverse geometry spectrometer with a frequency range of 8 to 4000 cm-’ (1 cm-’ being 30 GHz) and a resolution on the order of z 2%. It is thus ideally suited for an investigation of molecular vibrational spectroscopy. Full details of the spectrometers of the ILL are to be found in the Yellow Book [ 51 which is available, upon request, from the scientific secretariat of the ILL. The solid samples, powdered in a cold mortar were placed into thin walled aluminium containers and cooled in the instrument cryostat The samples for the diffraction studies were mounted in vanadium containers. For the protonaceous material the sample thickness was of order 1 mm. With the deuterated analogues it was necessary, due to the smaller scattering cross sections, to use larger quantities of material. The data were analyzed and converted by standard procedure to the scatteringlaw, S(Q, 0). 2.2. Fixed window spectroscopy and quasielastic scattering It was known that solid C6H6 : C6F6 undergoes three solid state phase transitions below its melting point at 298 K [ 31; this was confirmed by the technique of neutron “fixed window” scattering (FWS). Here the scattering of the elastic line, in a high-resolution backscattering spectrometer, as a function of the sample temperature gives information on the localized dynamics of the scattering molecules which constitute the solid, in particular, a determination of the Debye-Waller factor [ 6 1. In such a FWS experiment one observes the spectral intensity at fro= 0. At low temperatures, the purely elastically scattered line and any quasielastic spectrum, with linewidth on the order of the instrument resolution function (2000 MHz), are contained within the energy window. The phonon spectrum will be at a much higher frequency, on the order of a few meV, and will not contribute to our measure-

J.H. Williams /Chemical Physics I72 (1993) 171-186

ment. As the temperature increases the measured elastic line intensity falls due to the Debye-Waller factor. Here the molecules are fixed in the solid and are undergoing small amplitude oscillations and from eq. (2) we may estimate the magnitude of these motions by plotting In S( Q, ox 0) versus Q2. As the temperature increases the quasielastic spectrum will broaden due to the onset of additional molecular motions, for example, molecular rotations. These additional degrees of freedom will increase the total amplitude of oscillation and the broadened Lorentzian component of the quasielastic scattering may now fall outside the energy window of the spectrometer [ 61. In the case of benzene: hexafluorobenzene this is clearly seen to commence at Tx 150 K, see fig. 1. As the quasielastic spectrum broadens with increasing temperature the observed scattered intensity continues to fall. Eventually, the quasielastic spectrum is entirely outside the energy window and we are only left with the remainder of the elastic line, thus giving the observed step in the temperature dependence of the In S( Q, w z 0) curve, as seen in fig. 1. In this temperature region the characteristic frequency, v,, of any motion, the origin of the quasielastic scattering, is on the order of h/AE, where AE is the width of the energy window. If there are large-scale rearrangements of the solid phase

173

transitions, these are readily observed as a discontinuity in the observed scattering as a function of temperature above 200 K, see fig. 1. To understand these observations we make use of an analogy with NMR spectroscopy. In solid state NMR the narrowing of an observed resonance line with temperature is analyzed in terms of the Debye correlation time, r,. If we write rCx 1/v. which is the average rate of oscillation of the molecule containing the resonating or scattering atom we may write after the theory developed by Bloembergen, Purcell and Pound [7] (Av)‘=

(Avo)2~tan-1(aAv/vC)

,

where the linewidth (a frequency) is Av, Av,-, is the second moment of the rigid lattice which contains the scattering/resonating atom and represents the unnarrowed linewidth. The constant, (Y,accounts for the uncertainties in the integration limits in Bloembergen et al.‘s eq. (35 ), i.e. the derivation of the lattice second moment in terms of an integral over frequency space of the spectral function and from the uncertainties in the definition of Av with respect to the true lineshape. It is of order unity [ 6,7 1. Neutron scattering observes phenomena in w space whilst NMR probes directly in time. Thus the rigid lattice frequency limit in eq. (3) corresponds to slow dynamical processes which on a neutron scattering time scale would be indistinguishable from the instrument resolution function. From our experiment we may obtain, by fitting the data displayed in fig. 1 to an Arrhenius model (es. (4)), v= v0 exp( -EJRT)

Fig. 1. FWS plot of observed scattered intensity, that ts In S( Q, we 0) versus sample temperature for a polycrystalline sample of CsH6: CsF, measured at Q= 1.19 A-‘. The solid line is a lit to the data using the Arrhenius parameters given in the text. It is seen to be a good representation of the measured data up to the temperature where the phase transitions are seen to commence (205 K).

(4)

the activation barrier to motion in the solid. Here E, is taken to be the thermal barrier to rotational reorientation and v. to be the attempt frequency. The measured linewidth, A v in eq. ( 3 ), is a frequency and we assume r, = 1/v,. The model actually used to fully interpret the temperature dependence of the elastic scattering combines a vibrational function, the Debye-Waller factor determined at low temperatures, that is, at temperatures below which the thermally activated rotations or librations are not excited, together with, at higher temperatures, a rotational function to represent the thermally acti-

J.H. Wdliams /Chemical Physics 17.2 (1993) 171-186

174

vated molecular reorientations which give rise to the quasielastic scattering. Our data treatment has yielded the following parameters for C6Hs : C6Fs; the DebyeWaller factor was found to be

d dT

=2.46x

10-4A2K-1

(60
experiments it became apparent that one spectrometer would not allow us to completely characterize the molecular dynamics. On the high-resolution backscattering spectrometer, IN1 3, we were able to study the temperature dependence of the rotational motion of the scattering molecules, in our case the benzene partner, in the lowest temperature phase (IV) of this solid. However, to fully investigate the temperature dependence of the molecular diffusion, observed to be important in the higher temperature phases of this material, we were obliged to use the time-of-flight spectrometer, IN6, with its much larger available energy range but lower energy resolution. From both of these studies, i.e. low and high energy transfers, we were in a position to say what types of molecular motion, whether rotation, vibration or translation were present in which phase of the solid and what were the thermal energy barriers to the onset of motion. For example, it was observed that at the lowest temperatures studied, 5 < T(K) < 100, only vibrational motions were present; at about 150 K we observed the commencement of rotational motion; however, it was above the first phase transition, at 205 K, that translational motion, i.e. molecular diffusion was observed. Thereafter, as the sample temperature increases all three degrees of freedom are present [9] and the motions were observed to become more and more rapid with increasing temperature. Table 1 contains a summary of the Arrhenius modeling of our quasielastic neutron measurements of this material. We have assumed that the temperature dependence of both the rotational reorientation and the molecular diffusion follows the Arrhenius law. The temperature ranges of the various phases are given in the table. 2.3. Diffraction studies Fig. 2 is a thermodiffractogramme, measured on the low-resolution neutron diffractometer DlB, of C6D6: C6F6 between 100 and 290 K over a 26 range 1O-90 Owith a neutron wavelength of 2.5 1 A. It is seen that the Bragg patterns change significantly at the phase transitions. However, the three nuclei have much the same coherent scattering cross sections: 6.6 barn for C, 6.7 barn for D and 5.6 barn for F. It is therefore difftcult to distinguish, by neutron diffraction only, the two molecules which constitute the

J.H. Williams /Chemical Physics 172 (1993) 171-186

175

Table 1 Summary of quasielastic neutron scattering results; the rotational reorientational rates, v, are given m s-l and diffusion constants in m2 s-r. The exponential term for the rotational reorientation data is taken as a barrier to six-fold rotation and the associated pre-exponential term as the attempt frequency. Lowest temperature phase measurements together with the theory used to interpret the molecular motion in this solid may be found in ref. [ 111 v (s-1)

D, (m* s-‘)

phase II 247-272 K phase III 205-247 K

8.4(+0.3)x

lO’rexp[ -25300( f lOOO)/RT]

phase IV O-205 K

9.4(*0.5)X

lO”exp[-9400(

&500)/RT]

Fig. 2. Neutron diffraction pattern of CsDs: Ce,F, as a function of temperature between 289 and 100 K, observed between 20= lo”-89”.

solid. The necessary additional information was supplied by synchrotron scattering measurements at Daresbury, UK with an X-ray wavelength of 1.40302 A. Accurate atomic positions including deuterium were then obtained by Rietveld refinement of the neutron powder data. The structure of phase IV was found to be P2,la with a=9516 A, b=l.429 8, and ~~7.537 A;p=95.596” andZ=2 [lo]. Fig. 3 represents the results of this ab initio structure determination of the lowest temperature phase of C6H6 : C6F,. We look down the c axis and observe a benzene molecule on top of a hexafluorobenzene ring; the solid is composed of such dimers arranged

in infinite stacks. Note that the H atoms and the F atoms are neither fully eclipsed nor fully staggered and that there are many close approaches between molecules in neighbouring columns.

2.4. Vibrational or inelastic spectroscopy One of the traditional means of investigating the intermolecular potentials which exist in solids is via vibrational spectroscopy. Our inelastic studies of C6H, : C6F6 were undertaken on IN4, IN5 and IN6 at the ILL and on the crystal spectrometer, TFXA, at the Rutherford Appleton Laboratory, UK.

J.H. Wdliams /Chemical Physics I72 (1993) 171-186

176

Fig. 4 contains some of our vibrational data. This is an inelastic neutron spectrum measured in neutron energy gain, that is, the incoming energetic neutron has excited the molecules in the solid. The measurement was made on the spectrometer TFXA at 25 K, for a crystal spectrometer Q is not constant over the measured spectrum. The low frequency excitations seen in this figure are the intermolecular or phonon vibrations. The intramolecular vibrations, the vibrational distortions of the individual molecules, occur at higher frequencies (400-3200 cm-’ ); for a full description of these high frequency vibrations see ref.

1121.

r

In fig. 5 we see the substantial mode-softening which occurs in these phonon frequencies as the temperature increases towards the first phase transition at 205 K. Some of the data given in fig. 5, T-e 200 K, were measured on the crystal spectrometer TFXA, RAL, and some on IN6 at the ILL, see ref. [ 12 ] for details. Here, we present all our inelastic neutron measurements, 2.5 K> T> 280 K, and make some quantitative estimates of the magnitudes of the various intermolecular force constants. Above 205 K we are left with a much simpler inelastic spectrum, as is to be expected for a solid composed of infinite chains of dissimilar dimers with two dimers per unit cell [ 111. However, as the tempera-

0

(I

Fig. 3. The structure of phase IV of C4Hs: C6F6 viewed down the c axis. The alternating sequence of equidistant benzene and hexafluorobenzene molecules is clearly seen. The orientation of the molecules about the c axis is neither fully staggered nor eclipsed.

I

I

0

SO

100

150 TlQlpW~t”E

01 0

80 120 ENERGY TRANSFER (cm-i)

40

160

Fig. 4. Inelastic neutron scattering spectrum of a polycrystalline sample of C6H6: C6F6 measured at 25 K in Stokes excitation on the spectrometer TFXA, R4L (UK).

200

250

300

UC)

Fig. 5. Temperature dependence of the red-shift seen in the frequencies of the phonon lines of CsH6: C6F6 and the line corresponding to rotational excitation about the C4 axis in CsH6 (data denoted by + ). The position of the lowest temperature phase transition for C6H6 :C6F6 is indicated. Some of the data given in fig. 5 (Tc 200 K) were measured on the crystal spectrometer TFXA, KAL, and some on IN6 at the ILL, see ref. [ 121 for details. Here, we present all our inelastic neutron measurements, 2.5 K> T> 280 K.

J.H. Williams/Chemical

ture increases the intermolecular vibrational lines move to lower frequency and they also broaden. Consequently, following the change of frequency of all the lines seen in fig. 4 with temperature is not possible with the low resolution available to inelastic neutron scattering. Also given in fig. 5 is the red-shift of the most intense line seen in the neutron inelastic spectrum of pure solid benzene measured on TFXA and IN6. This inelastic study of C6H6:C6F6 is complementary to our quasielastic investigation. In the Arrhenius analysis of the temperature dependence of the linewidths, the exponential term is taken to be the activation barrier to the onset of motion and the pre-exponential term, yo= 1 /ro, is the attempt frequency. Absolute values for 1/r. are not to be taken as rigorously specifying a particular frequency, however, they can be taken as representing certain microscopic time scales, for example, given by phonon frequencies. From our quasielastic study we find that we are indeed able to compare our determined pre-exponential factors with the centre-of-gravity of the densityof-states measured by inelastic neutron scattering [ 6,111. For example, we derive from our quasielastic measurements of the temperature dependence of the rotation of the benzene partner in solid C6H6: C6F6, 7. = 454 x 1O-l5 s, which is equivalent to a frequency, ~~73 cm-‘. This frequency may be compared with the spectra displayed in fig. 4, the phonon density-ofstates for C6Hs : C6F6, where we see that agreement is good. A similar analysis of the quasielastic and inelastic dynamics of pure solid benzene also showed that it is possible to relate the pre-exponential term of the Arrhenius equation, 7,, determined from the temperature dependence of the FWS data to the centre-ofgravity of the density-of-states as measured by inelastic neutron scattering [ 6 1.

3. Molecular

interactions

Having measured lowest temperature hexafluorobenzene to whether or not it of the intermolecular erties, the observed

and modeling

the structure and dynamics of the phase of solid benzene: [ lo] it is of interest to inquire as is possible to rationalize, in terms distances and molecular propdynamical behaviour in terms of

Physics 172 (1993) 171-186

117

models using relatively simple electrostatic interactions. Consider a chain of alternating benzene and hexafluorobenzene molecules, the centres-of-mass lying on the chain axis. Let r be the distance between a benzene molecule and a neighbouring hexafluorobenzene molecule, with an associated vibrational force constant F, and r12 be the distance from this hexafluorobenzene molecule to the next benzene molecule with an associated vibrational force constant Flz. The change of polarity between the electric quadrupole moments of benzene and hexafluorobenzene determines the overall structure of the solid C6H, : C6F,. Similarly, we point to the electric quadrupole moment as the origin of the anisotropic intermolecular forces which determine the structure of pure solid benzene; these electrical moments being large. This particular model allows us to explain the columnar-like structure of alternating benzene and hexafluorobenzene molecules observed in experiment. What it does not allow us to predict so easily is the relative orientations of two neighbouring columns. That is, the nearest neighbour orientations. Molecules such as benzene and hexafluorobenzene have no permanent electric dipole moment. However, they do have, or rather they may be represented as having, bond dipole moments. That is, for the aromatic molecules, partial charged structures may be constructed to represent the positive and negative molecular quadrupole moments. Over very short intermolecular distances, it may well be that we are not justified in discussing the interaction of molecules, much larger than or of the same size as the dimensions over which we are interested in investigating, in terms of the molecular quadrupole moment. But we must instead consider the bond moments and their interactions. It is perhaps with such local models that we may be able to unravel the orientational behaviour and ordering of the columns of benzene and hexafluorobenzene molecules which constitute the binary complex. Previously, we were successful in analyzing the origin of the phonon-side bands seen in the low temperature inelastic neutron spectra of C6H6 : C6Fs [ 12 1. We considered the interaction of the vibrationally induced electric dipole moment of the benzene molecule and the electronically induced electric dipole moment of the hexafluorobenzene molecule.

178

J.H. Williams /Chemical Physics 172 (1993) 171-186

For an electrostatic interaction, the interaction energy between dipole moments 1 and 2, U(r), is given by [I31

+sin 8, sin 0, cos@) ,

(5)

where r is the bond dipole separation and the angles arise from the relative orientation (the tilt) of the dipoles to the line joining the centres-of-mass of the bond dipoles and @is a rotational orientation about the molecular C6 axis [ 13 1. The bond dipole moments of the benzene molecule have been determined from the intensity of infrared vibrational transitions [ 141. It is found that the electric dipole moment of the C--H bond in the benzene molecule is P(,-~)= -0.25 D= -833x 1O-33 C m [ 141, the polarity being C (a- )--H (6+ ). Sverdlov et al. [ 141 give the C--F bond dipole moment in CzF6 as &or) = 2.4 D= 8.0 X 10w3’ C m, the polarity being C (6+ )--F( 6- ). In hexafluorobenzene it is likely, due to the aromatic character of the molecule, that the C--F bond dipole moments will be larger than those seen in the alkyl halide C2F6. Using eq. (5) with these values for the bond dipole moments together with the crystallographic distances and angles we may estimate the attractive and repulsive contributions to interactions perpendicular to the chain axis. Due to the particularly small distances between H atoms on a benzene ring and F atoms on neighbouring hexafluorobenzene rings (2.52-2.7 8, [ lo] ) we find a total interaction energy of 33.1 x 1O-2* J or 19.92 kJ mol-’ for the bond dipole-bond dipole interaction between a benzene molecule and its four nearest hexafluorobenzene neighbours which are situated in the molecular planes above and below it. Interactions of opposite phase, due to the polarity change between &cn) and ,+r), will arise through bond dipole-bond dipole interactions of nearest neighbour benzene (2.75-2.92 8, [ lo] ) molecules in the same plane. With the known bond lengths and angles these oppositely phased contributions may be estimated as - 2 x 1Om2’ J. Thus, our estimate for the total interaction energy, for a benzene molecule with its neighbours, is 3 1.1 x 1OM2i J or 18.7 kJ mol-‘, this being a measure of the barrier to six-fold rotation. We note that measurements of

the six-fold barrier to rotation, seen by the benzene partner in the binary complex, are 9.5 [ 91 and 12 kJ mol-’ [ 6 ] as determined by quasielastic neutron scattering and 14.2 kJ mol-’ as found by NMR [ 31. The interactions between C6F6 molecules is particularly large because of the large electric moment of the C--F bonds. We find the C6F6---C6F6 bond dipole-bond dipole interaction energy to be 70.7~ 10m2’ J (the F---F distances are 2.82-2.9 A [ lo] ); this will be out of phase with the C6Hs---C6F6 bond dipole-bond dipole interaction energy of -33.1 x 10e2’ J. The difference, 37.6~ 10M2’ J or 22.6 kJ mol-’ is a measure of the barrier to reorientation or activation energy for the six-fold rotation of the hexafluorobenzene molecules. Ripmeester et al. [ 31 have determined this activation barrier with NMR techniques and they find E,= 29.3 kJ mol- ’ for motion of the hexafluorobenzene molecule in this phase. We note that this simple electrostatic model has not predicted the absolute values of these barriers but has given the correct ordering and order of magnitudes. A consideration of the high-resolution laser Raman measurements of Laposa et al. [ 151 on C6H6:CsF6 and C6D6: C6F6 clearly shows that there are only three resonances, centred around 45 cm-’ at 25 K (see fig. 4), which show no frequency shift upon deuteration. We therefore assign these low frequency modes as acoustic phonons as they reflect mainly the motion of the heavier C6F6 molecule. Conversely, the highest frequency phonon lines, centered around 100 cm-’ (see fig. 4), show a systematic frequency shift ( x 2 cm- ’ ) upon deuteration and can be assigned as optical phonons as they reflect mainly the motion of the lighter benzene molecule. For the symmetric vibration, the acoustic phonon of the molecular chain, we may write the vibrational frequency as [ 111

(6) where the force constant F represents mainly the motion of the heavier hexafluorobenzene molecule within an isolated C6H6: C6F6 pair and m is the reduced mass of the molecular pair, m = 9 1.77 X 10V2’ kg. For the higher frequency, antisymmetric vibration or optic phonon, which reflects mainly the mo-

119

J.H. Williams /Chemical Physics 172 (1993) 171-186

tion of the lighter benzene

molecule,

we may write

[ill 1 w opt -zz

F+ ___ 2F,* m ’ J--

(7)

fluorobenzene molecules, along the chain direction, tive interaction potential Thus, from [ 61 we have V(r) =

where F12represents the coupling of an individual molecular pair, benzene : hexafluorobenzene, to the next neighbour in the molecular chains which make up the solid. In fig. 5 we show the temperature dependence of these solid state vibrational frequencies. We have taken the lowest frequency vibration, occurring at 27.5 cm-’ at 10 K, to represent an acoustical phonon and the vibration observed at 67 cm-’ at 10 K to represent the optical phonon. We display in fig. 6 the temperature dependence of the derived force constants, F for the acoustic mode and F12for the optic mode. Also shown are the positions of the solid state phase transitions of this material and it is seen that the changes in the force constants, particularly F, correlate with the positions of these phase transitions. We wish to estimate the magnitude of the intermolecular vibrations using a simple electrostatic model to represent the intermolecular forces. For an isolated C6H6--C6F6 molecular pair, we assume that the electrostatic interaction, V(r), between the electric quadrupole moments of the benzene and hexa-

0

50

100

200

150 TIlnpWlt”rl

250

300

CKI

Fig. 6. Temperature dependence of the force constants derived from the data in fig. 5. F represents the acoustic force constant and FIz the force constant associated with the optic mode. The data represented by the diamonds is a symmetric force constant calculated for an isolated dimer with the known intermolecular spacings (along the c axis). It can be seen that this is a reasonable representation of the experimental acoustic phonon frequency in all the solid state phases of this material.

separated by a distance r represents well the attracparallel to the chain axis.

3@c,n, @c,,, 4(4ne&5 ’

(8)

where we may relate this intermolecular potential to an intermolecular vibrational force constant, F, via V(r) = iF(x*)

.

Differentiating twice with respect to intermolecular distance gives the force constant -aV(r)

ax*

=F=

9y;;;o$F6.

(9)

With experimental values for the molecular quadrupole moments, benzene - 29.0~ 10m4’ C m* [ 11, hexafluorobenzene 3 1.7 x 10m40 C m* [ 1] and the known low temperature intermolecular stacking along the c direction, 3.77 8, [ lo], that is r, we find F= 1.68 mass of the dimer is kg s-*. The reduced 9 1.77 x 1O-*’ kg and we calculate that the fundamental vibration would appear at 23 cm-‘. A consideration of the spectrum given in fig. 4 and the data given in fig. 5 shows that this is a reasonable estimate. The lowest frequency line, an acoustic phonon, observed is at 27.5 cm-‘. To represent the inter-dimer force constant, Fi2, we will consider the influence of the electric field gradient, E' , of a neighbouring aromatic molecule, which arises from its charge distribution, on the quadrupole polarizability of the benzene partner in the dimer under investigation. Our system of three molecules, either a benzene sandwiched between two hexafluorobenzene molecules or a sandwiched hexafluorobenzene ring, is on the time scale of the diffraction experiment centro-symmetric. With no evidence from our diffraction results of this solid phase, for molecular dimerization quadrupole-induced electric dipoles cannot contribute significantly in this electrostatic model. We will return to this point a little later. Indeed, on the time scale of the diffraction experiment ( < lo-i4 s) the benzene and hexafluorobenzene molecules appear equi-spaced along the c axis. Thus there is only one force constant needed to describe the vibrational dynamics along this direction. However, on the vibrational time scale ( 1O-l*- 1O- I3

180

J.H. Williams /Chemical Physics I72 (1993) 171-186

s), the chains of molecules will become unstable to vibrational motions; a Peierls distortion, and an apparent dimerization will arise requiring two force constants, F and F12,for its interpretation. For the origin of F it is only necessary to consider the intermolecular interactions of an isolated dimer. However, as it is only possible to observe an antisymmetric stretch, i.e. the optic phonon, because of the presence of a third molecule we think this is a reasonable model. The electric field gradient of this neighbouring third molecule modifies the pair potential, eq. (8 ), by inducing an electric quadrupole moment through the quadrupole polarizability, C, of the target molecules. We may write for the total quadrupole moment of a molecule in a field gradient [ 13 ] @ae= 6% + Cap&s

>

(10)

where 8’ represents the permanent quadrupole moment given above and the second term is that induced by the field gradient of the neighbouring molecular charge distribution. There is no contribution to the total quadrupole moment from the field of the neighbouring charge distribution as the dipole: quadrupole polarizability, A, is zero for a centro-symmetric system [ 131. The distorting field gradient, arising from the molecular quadrupole moment of the neighbouring molecule, may be found from

Ta8;rs= (4xto)-‘V,VBVxVsr-‘=

24 (4mo)r5

(11)

for our linear, chain-like molecular system. With an r-’ dependence on intermolecular distance it will only be the nearest neighbours which give rise to such interactions. If we consider the molecule in the applied field gradient as a sphere of radius CJ,then we may approximate C as C= ( 41ceo)a5. The electric polarizability, cy, for a benzene molecule in the visible region is 11.56~10-~~ C2 mz J-‘=10.39~10-~~ cm3 [l] which may be approximated as (4%~~)g3. We take the cubed root of this electric polarizability as a measure of U. The induced quadrupole moment is therefore given by

@total

=

80

+

(4%) fJ%@ (47cto)rs

’

(12)

For example, with I? = 494 x 1Oe51 F m4 for the benzene molecule, r= 3.77 A and the known quadrupole moment of the hexafluorobenzene molecule we obtain an induced quadrupole moment for benzene of 49.35 x lo-““ C m2. Similarly, the induced quadrupole moment for hexafluorobenzene will be, with c$C6Fgj=501x 10e5’ Fm4, 45.78x 10-40C m’. Thus, @‘Otal @total and hexafluoroknzene benzene= 2.78:,,,,, These induced quadrupole = 2.4480hexanuorobenzene. moments are large; however, the permanent quadrupole moments which give rise to the distorting field gradient are also, for typical molecular quadrupole moments, large. The new total quadrupole moments will be larger by factors 2.7 and 2.44 for benzene and hexafluorobenzene, respectively, giving an enhancement of the intermolecular interaction potential (see eq. (S)), V(r),of2.44x2.7=6.59. This large increase in V(r) will result in a larger force constant for the asymmetric stretch which involves the lighter benzene partner and occurs at higher frequency than for the symmetric stretch of the CsH6-C6F6 intermolecular bond. With our estimate of the acoustic force constant F= 1.68kg sm2 and taking our experimental value for the optic force constant, F+2F,2=11.07kgs-2wefindF,2=4.7kgs-2.Then, from eq. (7) we calculate w,,,=58.3 cm-‘, which from fig. 4 is seen to be in some agreement with the lowest frequency optical mode seen at 67 cm-’ at 25 K. We see from these figures how our simple vibrational model readily explains the magnitude of the acoustic vibrational mode. For example, we estimate from our model F= 1.68 kg se2 at low temperatures and we measure at the lowest temperature studied F=2.35 kg sw2. This measured value falls over the temperature range of phase IV to 1.52 kg sm2 at 200 K. Our model of the field gradient induced electric quadrupole moments estimates F12=4.7 kg se2; however, we observe from the measured optic phonon F ,2=6.22 kg se2 at the lowest temperature studied, 10 K. This value was also observed to fall, a softening of the optic phonon frequency as the temperature mounted towards the first phase transition observed in this solid, giving F12= 3.7 kg s-2 at 200 K when the optic phonon frequency is 50 cm-‘.

J.H. William /Chemical Physics 172 (1993) 171-186

We believe that it is possible to account for this trend in the temperature dependence of the magnitude of F,*. At the lowest temperatures our theoretical estimate for Flz is too small when compared to the experimental value. However, at 200 K, near the phase transition from phase IV to phase III, our estimate for F12 is in better agreement with the experimental value. It is seen from fig. 6 that the value of Flz falls over this temperature range. We must ask, therefore, which intermolecular interaction is seen to disappear over this temperature range, which we have not accounted for by our field gradient induced quadrupole model of the molecular interactions? Our model does not include intermolecular interactions perpendicular to the main chain axis; that is, the interactions which give rise to the relative orientation of the benzene and hexafluorobenzene molecules in neighbouring chains. We know from our quasielastic neutron measurements that over this temperature range we are observing the onset of molecular rotation [ 91. There is a thermally activated six-fold rotation of both the benzene and hexafluorobenzene molecules in this lowest temperature phase. We have estimated the barrier to this rotation for the benzene molecule, V( Rot.), to be 9.5 [ 91 and 12 kJ mol- ’ [ 61 and it is found from NMR to be 14.4 kJ mol-’ [3]. Similarly, our crystallographic study has shown us how short some of the C--H...F-IC perpendicular intermolecular bond distances, rperp, are, typically 2.52-2.7 A [lo]. Estimating a perpendicular force constant as V(Rot.)/r&,,, we find the perpendicular contribution to Fi2, Fi2(perp) to be x0.25 kg s-* giving a value between 1.5 and 3.0 kg s-* as the total perpendicular contribution if we assume, from our crystallographic study, that there is at least one weak bond per H atom per molecule (a factor between 6 and 12). Thus we now estimate FL2=FL2(perp) +F,,(parallel)=2.35+4.7=7.05 kgs-*,whichisin better agreement with experiment, i.e. 6.22 kg s-*. As the temperature mounts the perpendicular force constants decrease. These perpendicular interactions weaken and in figs. 5 and 6 we observe the loss of the perpendicular contribution to the optic phonon mode, leaving at temperatures above which six-fold rotations about the C6 chain axis are observed only the parallel contribution to F,,. Indeed, at the highest temperatures investigated, near the melting point of

181

the solid, the molecular interactions, parallel and perpendicular to the c axis, become more isotropic. As a comparison we have calculated the acoustic mode frequency arising from the vibrations of the benzene-hexafluorobenzene dimer using the intermolecular spacings occurring in the different phases of this material. We have found [lo] that at 30 K (phase IV) the intermolecular spacing (benzene: hexafluorobenzene) along the c axis is 3.77 A, in phase III at 2 15 K this distance is 3.647 A, in phase II at 260 K it is 3.651 A and at 279 K, in phase I, the spacing has become 3.6 14 8, [ lo]. Using eq. (6 ) and these distances we calculated force constants: 1.69 kg s-*at30K,2.14kgs-*at215K,2.12kgs-*at260 K and 2.28 kg s-* at 279 K. These force constants correspond to the frequencies 22.8 cm-’ (30 K), 25.6 cm-’ (215 K), 25.5 cm-’ (260 K) and 26.4 cm-’ (279 K). These force constants have been plotted in fig. 6 and it is seen that these estimates closely follow the experimental values through the various solid state phases up to the melting point of the solid. However, we note that they increase with increasing temperature whereas our measurements show that there is a softening or weakening of these vibrations with increasing temperature. There must, therefore, be other intermolecular interactions involving the C6F6 molecule which are a function of temperature and which are not included in our model. We note, that with V(Rot.) for C6Fs of 29.3 kJ mol-’ [ 31 and r,,=2.82-2.9 8, [lo] the perpendicular force constant for a pair of hexafluorobenzene molecules interacting in adjacent chains, Fcperpj, would be 0.58 kg s-*. It could again be the loss of this perpendicular interaction that we observe in the temperature dependence of F. Having considered the possible origins of the intermolecular dynamics of C6H6: C6Fs in terms of the component static molecular properties, i.e. quadrupole moments and their polarizabilities, it is of interest to consider briefly the possible contribution of vibrational or dynamic properties. Our model of a benzene molecule equidistant between two hexafluorobenzene molecules has no static quadrupole-induced dipole moment. If we let R+ and R_ be the two intermolecular distances on either side of the benzene ring, we may write for the total static quadrupole-induced dipole moment on the benzene molecule, pknsene,

[ 111

182

&$_

J.H. Wdliams /Chemical Physm 172 (1993) 171-186

= (YbenzeneEhexafluorobenzene

,

(13)

where CY,,=,,=~,,= is the static polarizability of the benzene molecule and the intermolecular electric field arises from the quadrupole moment of the hexafluorobenzene molecules, @c6r6.Thus, [ 111 Eh+exafluorobe-e= _ @j&R

;4(

4ne0) - 1 ,

and

+K&N$W ;

k,(w) =a+(w)Ep(t)

7

where the field and its time derivative, & act on the symmetric and antisymmetric parts of the dynamic polarizability, respectively [ 13 1. For the time derivative of the field we may write

l?,(1)

d =a,.

Eh_exseuombenzene = 6,9c6rSR14 ( 47Ct,,)- 1 , and the total induced static dipole moment is zero, as expected for a centro-symmetric molecular trio. We have observed from our diffraction measurements of the solid structure [lo] that this is indeed the arrangement on an essentially static time scale. However, at vibrational frequencies the distorting electric fields become functions of time and we may write

The symmetric dynamic polarizability written as [ 13 ] a(w)=

=zl

and

47t ~,o~OlPl~)<~lPlO) 5 c 2 2 I

W,o-W

4~%<0IPI1)<1IPl~0) w&-w’

.

(15)

The antisymmetric part of the dynamic polarizabilityis [ 131

a,(o)=

= -6@c6F6R;4(4rce,,)-1 COSO,~,~,

may be

F 1 wcwy.yo) I

R---4niw(01~11)(11~10) h

w:o-w2

9

(16)

where ooPt and w,, represent the vibrational frequencies of the two hexafluorobenzene molecules. Here we take mop,to be the optic frequency and o,, to be the acoustic frequency. Then,

where we have approximated the sum over vibrational states to the lowest frequency fundamental vibration of the molecule of interest. Therefore the total induced oscillating dipole moment, symmetric and antisymmetric parts, will be

E’“*(t)=-

P toti=a(w)E(t)--(Y’(w)E(t).

68aF6

R4(4xeo)

(cosw,,,t-cosw,,t),

and for t= w,‘, the time of the slowest vibrational period, we may write E’0’81(t)=

.

(14)

For example, with wzQt~4.28~ 1O24 sd2 and w~~~0.656x1024 sm2, we find Eto”‘(t)x6(5.5)x @06P6R-4(4neo)-1. We find, therefore, that there is now a finite dynamic electric field at the central benzene molecule. To estimate the oscillating electric dipole moment induced by this time-dependent electric field we have to use a vibrational polarizability, a(w). The induced oscillating dipole moment is given by

(17)

In our approximation, the sum over states may be represented as the lowest frequency fundamental vibration of the benzene molecule. We find that the symmetric polarizability varies in magnitude, 8.8 x 10P41 C2 m2 J-l (at an optic phonon frequency 0~70 cm-‘) to 8.1~10-~’ C2 m2 J-l (at w=30 cm-- ’ ); whilst the antisymmetric part of the dynamic polarizability varies over 1.5 x 1Om4’C2 m2 J- ’ (at W 0Q,=70cm-L)to0.8X10-41C2m2J-1 (atwo,,= cm- ’ ) . These are modest polarizabilities, being more than a factor 10 smaller than the optical polarizability of the benzene molecule. However, there is a tinite oscillating dipole moment in this material, provided woQ,is a long way from the frequency of the acoustic phonons, a(w)xcu’(w) when (w&-w2)

J.H. Wdliams/Chemical PhysicsI72 (1993) 171-186

-+O. With such a dynamic polarizability the induced oscillating dipole will be, over the range of observed w,,,, p(o) =a(o)E(t) x0.5-2.5 D, depending upon the particular values of a(o) and E(t). To estimate the oscillator strength matrix element, (0 Ip Ii) ( i Ip IO), we have calculated the magnitude of the vibrational amplitude, (u), for this fundamental vibration and multiplied this amplitude by the electronic charge to obtain the “transition dipole” which we have then squared. Consider ( u2) = 3kT/ 4n2mwf,, where m is the mass of the benzene molecule. With T= 100 K, m = 130x lo-” kg and 0,~=400 cm-’ we find (u) 20.025 A, giving (Olpll)=e (~)=40OxlO-~~C mzO.1 D. Thus, (Ol~ll)(ll~~O)x160x10-63C2m2. Of particular interest is the way in which these oscillating dipole moments interact along the molecular chain (c direction). We assume that the point dipole-dipole electrostatic interaction energy, V( r, 1), is the main contribution to the cohesive intermolecular force of the chain. Thus,

(18) We display in fig. 7 the magnitude of this dynamic dipole-dipole interaction energy as a function of the

-10

3 2% *

1 30

1 40 Optic

50

60

Phonon Frequency

70

80

(cm.‘)

Fig. 7. Representation of the optic phonon frequency dependence of the calculated oscillating dipole-dipole interaction energy, I’( r, t), along a single molecular chain. This interaction energy is calculated for two limiting values of the acoustic phonon frequency, 26 cm-i (low temperaturelimit) and 21 cm-’ (value at the temperature of the first phase transition). As the optic phonon frequency is continually red-shifted with temperature in phase IV we can see how V( r, t) falls rapidly with increasing temperature. We have included some specific temperatures at the ap propriate optic phonon frequencies.

183

value of the optic phonon frequency. We have made the calculation for two values of the acoustic phonon frequency. As seen in fig. 5, both the acoustic and optic phonon frequencies are red-shifted with temperature. The two values of the acoustic frequency used in calculating the results displayed in fig. 7 correspond to the lowest temperature acoustic frequency, 26 cm-‘, and the value of the acoustic frequency at the temperature of the lowest temperature phase transition seen in this material, 21 cm-‘. The lower acoustic frequency allows a much larger dynamic electric field, see eq. ( 14), to interact with the dynamic polarizability of the benzene molecule, giving a larger p(o), which in turn gives a much larger I’( r, t), see eq. (18). We are interested in investigating how the magnitude of this cohesive dipole-dipole interaction, between the molecules of the chain, varies near the position of the phase transition. It is seen in fig. 7 that it falls significantly. The range of optic frequencies investigated corresponds to the range of frequencies observed experimentally in the lowest temperature phase. The frequency of the continually red-shifted, optic phonon line at the temperature of the phase transition (205 K) is marked. It is clearly seen that V( r, t) has fallen substantially over the temperature range of the lowest temperature phase of C6H6 : CbF6. When the intermolecular cohesive energy of the molecules in the chains falls, relative to kT, the chains will become unstable to thermal fluctuations. As mop, approaches o,,, that is as the frequency of the optic phonon approaches that of the acoustic phonon (see fig. 6)) we see from eq. ( 14) how the dynamic electric field disappears. Then, for fairly constant values of the dynamic polarizability the induced oscillating dipole moment also falls and the cohesive frequency dependent dipole-dipole interaction falls rapidly, see eq. ( 18 ) . It is seen from fig. 7 that this approach of the two frequencies occurs as the temperature of the solid mounts towards the various phase transitions seen in this material, i.e. 205, 247 and 275 K. The solid is evidently unstable to thermal fluctuations at these temperatures as predicted by our dynamic model. It is therefore possible to explain the dynamic behaviour of this solid using either a dynamical model involving time dependent (low frequency) electric

184

J.H. Wdliams /Chemical Physics 172 (1993) 171-186

fields or a static model involving interacting molecular quadrupole moments. As to the more appropriate molecular model, we point to the magnitudes of the two types of interactions, static and dynamic. In fig. 7 we see that the dynamic dipole-dipole interaction energy is calculated to be in the order of a few terms of milli-electron volts, whilst the static quadrupole interaction energy is calculated to be a few hundreds of millielectron volts. If the dynamic model makes a significant contribution to the properties of the solid it is likely to be at low temperatures where we see from fig. 7 that V(r, t) is largest.

4. Discussion One of the outcomes of this experimental study of phase III and phase IV of solid benzene: hexafluorobenzene is the ability to describe in some detail the mechanism of the phase transition which occurs at 205 K. The stoichiometric formula tells us that this solid is 50% benzene and 50% hexafluorobenzene. Our crystallographic experiments allowed us to localize in the solid the relative positions of these two types of molecules. In fig. 3 we see that the solid may be described as being composed of alternating layers of benzene and hexafluorobenzene molecules, this being the most stable configuration for the electrostatic interaction of electric quadrupole moments of opposite sign. What is also readily observed, particularly in fig. 3, is the interpenetration of the C-H and C-F bonds of molecules in neighbouring columns. That is, at low temperatures the bonds on one type of molecule closely approach neighbouring aromatics, indeed, aromatics of the other type. Thus C-H bonds on a benzene molecule are directed towards and come very close to F atoms of the C-F bonds of a hexafluorobenzene molecule, a hexafluorobenzene molecule in the layers above and below. It is possible, therefore, to envisage a network of weakly polarized hydrogen bonds as the means of stabilizing the lattice. The same model may be invoked for solid benzene, where a consideration of the crystal structure [ 16,17 ] shows that the solid is made up of slipped parallel and Tshaped pair-wise orientations of aromatic rings. In solid benzene these weakly polarized intermolecular

bonds arise because the C-H bond, the positive end of the electric quadrupole moment, points into the rt cloud of a neighbouring molecule, the negative end of the electric quadrupole moment. Of interest to this structure and its stability is the observation, made from quasielastic neutron scattering, that at temperatures above about 150 K the benzene molecules have sufficient energy to undergo sixfold reorientations. That the first phase transition occurs at a temperature substantially higher than this onset of thermally activated rotation tells us that a certain amplitude of rotational motion is required before the lattice becomes unstable. The presence of some hysteresis in the temperature of this first phase transition [ 3,9] can be rationalized with this necessity for a certain magnitude of rotational excitation before the solid lattice becomes sufftciently unstable to thermal fluctuations as to change. Within the solid the molecules occupy energy minima which contain quantized levels (rovibrational or librational); excitations within these minima are seen in the spectra displayed in fig. 4. Before the molecule “jumps” from one site to another, i.e. undergoes a six-fold reorientation, it occupies one of the quantized levels in the potential well. These wells are quite deep, in C6H6 : C6F6 the height of the barrier to rotation is about 9.5 kJ mol- ‘, z 100 meV, as determined from the temperature dependence of S( Q, o) [ 91 and 12 kJ mol- ’ from the temperature dependence of S( Q, wz 0) [ 61. In solid benzene, the height of the barrier between equivalent minima is 17.6 kJ mol-’ as measured from the temperature dependence of NMR linewidths [ 18 ] and 15 kJ mol- ’ as determined from FWS measurements [ 61. When the molecule “jumps” it goes from one level in one potential well to another level in another potential well. These two levels have a small or a zero energy difference. Such a model of bound librational states being connected to a continuum of free rotor levels which exist above the six-fold barrier implies that the rotational motion of the benzene ring becomes free. However, this is likely to be an extreme situation. In fig. 4 we see that not one of the phonon lines has a frequency which goes to zero as we approach the phase transition at 205 K. Also, in the quasielastic neutron scattering study of the organic complex, naphthalene-tetracyanobenzene, which can be considered as another

J.H. Williams /Chemical Physics 172 (1993) 171-186

185

member of the class of charge transfer complexes of which benzene: hexafluorobenzene is the simplest member, Czamiecka et al. [ 19 ] observed a low temperature phase transition. Above this phase transition the naphthalene molecule is seen to execute thermally activated reorientations of 36’. In this complex, because of the Dzh symmetry of the naphthalene molecule, large amplitude rotations as we have assumed for benzene are not possible. Perhaps, it is only necessary to invoke large amplitude motions of the molecules in the benzene complex and not necessarily the 60” rotations we have assumed to trigger the lattice dynamics. We know [ 6 ] that the most intense line seen in the density-of-states in fig. 4, 67 cm-‘, corresponds to excitations about the C6 axis and we clearly see that this line, although strongly red-shifted as we approach the phase transition, remains finite. That is, as far as our experimental resolution is concerned, the lines broaden as they red-shift and inelastic neutron scattering is not a high resolution spectroscopic technique. The temperature dependence of this excitation about the C6 axis in the spectrum of C6H6: C6F6 is seen from fig. 4 to be the same as that for this excitation in solid pure benzene over the same temperature range, although the frequencies are different

1201. Similarly, we see from the volume changes in the unit cell that the molecules in one column, parallel to the c axis, disengage themselves from those in neighbouring columns, as would be required for the onset of rotational freedom about the Cs axis, that is near this phase transition the expansion of the unit cell is highly anisotropic and may be interpreted as a separation of the columns. At 30 K, we find the unit cell volume to be 530 A3 with a cross section, ab, of 70.69 A* and at 2 15 K, in phase III, the unit cell volume has become 568 A’ and the cross section 96.43 A*

161.

[lOI.

Due to these excitations, which introduce disorder into the solid, the weak hydrogen bonds holding any one molecule to the molecules in the layers above and below it will be disrupted. When this occurs, and we may think of this happening as a molecule loses its hexagonal character, gaining rotational or librational excitation and becoming more disc-like, then the lattice will become susceptible to perturbations. The lattice will have lost the stabilization arising from the weak, inter-stack hydrogen bonds and the long columns of rotating discs will only interact weakly between themselves. Previously, we gave the results of our FWS on pure solid benzene and C6H6 : C6F6 and it was observed that the Arrhenius parameters, which govern the rotational motion of the benzene molecules in both solids, were very similar. Consequently, at the temperature of the phase transition seen in C6H6:C6F6 the benzene molecules in solid benzene will have the same level of angular or librational excitation. Another source of information on the intermolec-

In conclusion, whereas in pure benzene, where quadrupole moments of like polarity interact to give a solid composed of slipped parallel and T-ordered pairs of molecules, i.e. 11and t-, in C6H,:C6F6, the opposite polarity of the quadrupole-quadrupole interaction produces stacked chains of alternating, parallel benzene and hexafluorobenzene molecules; the one structure being more stable to thermal excitations, particularly, excitations transverse to the main chain direction than the other. Just as bricks stacked one on top of another in parallel columns is not a sound technique for constructing buildings it also fails to give stable extended molecular structures because of its susceptibility to vibrations perpendicular to the column axis. Solid benzene, on the other hand, having a more complex structure of overlapping and interpenetrating layers of molecules has greater stability, even with the same level of individual molecular librational excitation. It is not so susceptible to lattice distortions, and has no phase transitions below its melting point.

ular potentials present in this solid comes from modeling the temperature dependence of the measured diffraction lines, for example, those measured at low resolution on D 1B (see fig. 1). The temperature dependence of any particular line can be related to thermal expansion along particular, well characterized, crystallographic directions. For C6H6: C6F, this thermal expansion is seen to be approximately equal for directions parallel and perpendicular to the c axis below 150 K and becomes increasingly anisotropic as a precursor to the phase transition at 205 K [ 201. The nature of this anisotropy suggests that the phase transition is associated with the onset of rotational motion, as indicated by the quasielastic measurements

J.H. Williams /Chemical Physics I72 (1993) 171-186

186

Our investigations of this solid have persuaded us that it is possible to interpret the structure and the dynamics of C6H6: C6F6 in terms of the electrostatic interactions of the constituent molecules. The ability to understand the origin of the lattice instabilities in C6Hs: C6F6 allows us to make predictions about other aromatic layered compounds. A survey of the literature shows that most of the organic, “donor-acceptor” or charge transfer complexes have at least one solid state phase transition in the same temperature range as C6H6 : C6F6. Such insights into the organization and behaviour of polyatomic molecules in crystal structures have profound implications for our ability to design and produce new materials with unique mechanical, optical or electronic properties.

Acknowledgement The author gratefully acknowledges the allocation committees of the various research facilities, where the experiments described in this paper were performed, for the availability of beam time. He also wishes to express his gratitude to Drs. Jeremy Cockcroft, Andy Fitch, Ross White and Bernhard Frick.

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and J.H. Williams, Chem.

[2] J.M. Steed, T.A. Dixon and W. Klemperer, J. Chem. Phys. 70 ( 1979) 4940. [3] J.A. Ripmeester, D.A. Wright, C.A. Fyfe and R.K. Boyd, J. Chem. Sot. Faraday Trans. II 74 (1978) 1164. [4] G.E. Bacon, Neutron scattering (Oxford Univ. Press, Oxford, 1955). [ 51 B. Maier and H. Blank, eds., Neutron research facilities at the Institut Laue-Langevin (Institut Laue-Iangevin, Grenoble, 1988). [6] J.H. Williams and B. Frick, Chem. Phys. 166 (1992) 425. [ 71 N.B. Bloembergen, E.M. Purcell and R.V. Pound, Phys. Rev. 73 (1948) 679. [8] A.J. Leadbetter and R.E. Lechner, in: The plastically crystalline state, ed. J.N. Sherwood (Wiley, New York, 1979). [9] J.H. Williams, Mol. Phys. 73 (1991) 113. [ lo] J.H. Williams, J.K. Cockcroft and A.N. Fitch, Angew. Chem. 31 (1992) 1655. [ 111 J.H. Williams, Mol. Phys. 73 ( 1991) 99. [ 121 J.H. Williams, Chem. Phys. 167 (1992) 215. [ 131 A.D. Buckingham, Advan. Chem. Phys. 12 (1967) 127. [ 141 L.M. Sverdlov, M.A. Kovner and E.P. Krainov, Vibrational spectra of polyatomic molecules (Wiley, New York, 1974). [ 151 J.D. Laposa, M.J. McGlinchey and C. Montgomery, Spectrochim. Acta 39A (1983) 863. [ 16 ] E.G. Cox, D. W.J. Cruickshank and J.A.S. Smith, Proc. Roy. Soc.A247 (1958) 1. [ 171 G.E. Bacon, N.A. Curry and S.A. Wilson, Proc. Roy. Sot. A 279 (1964) 98. [ 181 E.R. Andrew and R.G. Eades, Proc. Roy. Sot. A 218 (1953) 537. [ 191 K. Czarniecka, J.M. Janik, J.A. Janik, J. Krawczyk, I. Natkaniec, J. Wasicki, R. Kowal, K. Pigon and K. Otnes, J. Chem. Phys. 85 (1986) 7289. [ 20 ] S.T. Bramwell and J.H. Williams, J. Chem. Sot. Faraday Trans. 88 (1992) 2721.