- Email: [email protected]
Brillouin scattering study of the orientationally disordered phase of cyclohexanol
Volume 78A, number 2
PHYSICS LETTERS
21 July 1980
BRILLOUIN SCATTERING STUDY OF THE ORIENTATIONALLY DISORDERED PHASE OF CYCLOHEXANOL
J. PELOUS, R. VACHER and J.P. BONNET Laboratoire de Spectromttrie Rayleigh Brillouin, UniversitC des Sciences et Techniques du Languedoc, 34060 Montpellier Ckdex, France
and J.L. RIBET Groupe de Dynamique des Phases Condenkes, 34060 Montpellier Ckdex, France
Universitk des Sciences et Techniques du Languedoc,
Received 13 May 1980
Brillouin scattering was used to measure the velocity and attenuation of longitudinal hypersonic waves ln the orientationally disordered (OD) phase of a cyclohexanol single crystal and at the OD-liquid transition..‘Our results show that the coupling with a high-frequency relaxation mechanism, which dominates the behaviour of the hypersonic waves in the liquid, is still efficient in the OD phase.
The liquid and solid phases of cyclohexanol have been extensively studied by several techniques [l-3]. In particular, acoustical measurements by ultrasonic techniques and Brillouin scattering have shown the existence of a high-frequency mechanical relaxation [4] in the liquid. Several processes have been put forward for explaining this relaxation, but the most likely is a perturbation related to a monomer-dimer equilibrium. Below 25“C, cyclohexanol undergoes a transition to a plasticcrystal phase. In this phase, the centers of mass of the molecules are ordered in a cubic lattice, but molecular motions are still possible, leading to a dynamical orientational disorder. Ultrasonic measurements have been performed by Green and Scheie [5] in this phase of cyclohexanol on polycrystalline samples. The average longitudinal sound velocity was found very similar to that in the liquid; the acoustic attenuation was not measured. In this letter we report the results of a Brillouin scattering measurement in the orientationally disordered (OD) phase of a cyclohexanol, single crystal, with the purpose of obtaining information on the high-frequency molecular relaxation in this phase. In order to obtain single crystals of good optical
quality, the commercial liquid cyclohexanol was distilled several times to remove water. After this purification, the melting point was found to be 25”C, indicating a high degree of purity (a small water content can lower the melting point down to 23°C). Single crystals were grown by the Bridgman method in sealed glass cells. The orientation of the sample was unknown in our experiments. The spectrometer used for this study has been described previously [6]. It consists of a tandem arrangement of a double-pass plane and a confocal FabryPerot interferometer leading to a contrast of lo7 and a resolving power of 2 X lo7 (30 MHz) which allows precise measurements of the linewidth. The experiments were performed in a backscattering configuration. The accuracy of the measurements is of about 1% for the frequency shift and 10% for the linewidth. The index of refraction n was calculated using the Lorenz-Lorentz relation, starting from the value measured in the supercooled liquid (n = 1.4698 at 22.6”C and A = 5 145 A) [7] and from the temperature dependence of the density (~(~~~~-3) = 0.9721 - 6.89 X 10m4 t in the OD phase and pccm-3) = 0.9627 - 7.6 X 1O-4 t in the liquid phase) [5] . 195
It_
-+-+.+,+
*loo, _ ‘;
2000. VI
Yy+*,
, ,
0 D
CRYSTAL
--
---
if
+;;i
+ +b.
i I
E _=I900 tu s 9
21 July 1980
PHYSICS LETTERS
Volume 78A, number 2
*CID
1800
CRYSTAL-------r
I
:y+ 1700 -10
“1,. 0
10
20 30 TEMPERATURE
J :0 .o‘ (C )
0
10
20 TEMPERATURE
30
4
(2)
Fig. 1. Variation of the velocity of longitudinal hypersounds versus temperature in cyclohexanol.
Fig. 2. Variation of the inverse mean free path of longitudinal hypersounds versus temperature in cyclohexanol.
Our measurements were performed in the OD phase between -7°C and 25°C and in the liquid up to 4O’C. The velocity u of hypersonic waves is related to the Brillouin frequency shift vg by the expression vg = 2n(u/hO)sin(0/2), where & is the wavelength of the ‘incident light and 0 the scattering angle. The temperature variation of the velocity of longitudinal hypersound is shown in fig. 1. In contrast to the results of Green and Scheie [5], the velocity exhibits a discontinuity at the OD-liquid transition, as already observed in other materials at this transition. The ratio of the velocity in the OD and liquid phases is equal to 1.16 in cyclohexanol. This can be compared to the values 1.38 in succinonitrile [8], 1.35 in CC& [9], 1.46 in CBr, [lo], 1.35 in cyclohexanol [ 111, 1.49 in Li2S04 [12] (taking into account the 1% change in density at the phase transition, the discontinuity is of about 33% for the elastic modulus). This shows that the elastic properties are sensitive to the order modifications associated with the transition even if the amplitude of the discontinuity is small because of the liquid-like properties of the OD phase. The inverse mean free path 1-l (power acoustic attenuation) can be deduced from the half-width at half-height r of the Brillouin line from the expression ‘r-l = 4nF’/u. The results are plotted in fig. 2 for the same temperature range. An interesting feature is that when cooling from the liquid to the OD phase, the attenuation decreases and shows no appreciable discontinuity at the transition. This behaviour has already
been observed in succinotrile [8] and presumably (no quantitative measurements made) in CBr, [lo]. On the contrary measurements in Ccl, [9] show a discontinuity of the attenuation; neopentane in its liquid phase exhibits a similar feature [ 131. In cyclohexanol the attenuation below 10°C tends to be constant down to -7”C, even when going close to the solid-OD transition which takes place at -8’C. This indicates that the coupling of 12 GHz hypersounds with the relaxation mechanism is less efficient as the regime WT s 1 is reached (here o is the angular frequency of phonons and T the relaxation time). In the liquid phase, our measurement of the velocity (1756 m s-1 at 25°C and 10 GHz) is in agreement with the value given by Choi et al. [4] (1715 m s-l at 25°C and 7 GHz) within experimental uncertainties. When compared to the average of three ultrasonic results (a 1460 m s-l at 25°C) [4,5,14], our measurement confirms the existence of a strong dispersion related to a high-frequency relaxation mechanism. Also related to this dispersion, we observe a large temperature coefficient of the velocity: Au/Ar = -7.6 m s-l K-l. In the OD phase we find u = 2010 m s-l for t = 24°C and a frequency of 11.5 GHz. The average temperature coefficient is equal to -3.8 m s-l K-l. Lacking from measurements at lower frequencies, in the single crystal, it is not possible to separate the part of this temperature coefficient which is due to relaxation from that related to dilatation effects. However, the observation that the attenuation is nearly insensitive to the liquid-OD tran-
196
Volume 78A, number 2
PHYSICS LETTERS
sition leads us to the conclusion that the coupling of phonons with a high-frequency molecular relaxation is still effective in the high temperature range of the OD phase. Therefore, at least one part of the temperature coefficient of the velocity must be due to the dispersion related to this coupling. Finally it must be noted that no pretransitional effect was observed near the OD-liquid transition, a feature which is also true for succinonitrile, CBr,Li,SO, . This is in contrast with the softening of the longitudinal velocity observed in Ccl,. So, in our opinion, it remains to elucidate how the softening (or non-softening) of the longitudinal modes and the behaviour of the attenuation can be related to the OD-liquid transition. References [l] K. Adachi, M. Suga and S. Seki, BuIl. Chem. Sot. Japan 41 (1968) 1073.
21 July 1980
[2] K. Adachi et aL, Mol. Cryst. Liq. Cryst. 18 (1972) 345. [3] T. Eguchi, G. Soda and H. Chihara, J. Non Cryst. Solids 21 (1974) 143. [4] P.K. Choi, K. Takagi and K. Negishi, Japan J. AppL Phys. 17 (1978) 97. [5] J.R. Green and C.E. Scheie, J. Phys. Chem. Solids 28 (1967) 383. [6] R. Vacher and J. Pelous, Phys. Rev. B14 (1976) 823. [7] Landolt and Bornstein, Vol. 4 (Springer, Berlin) 6th Ed. [ 81 L. Boyer, R. Vacher, M. Adam and L. Cecchi, Proc. 2nd Intern. Conf. on Light scattering in solids, ed. M. Balkanski (Paris, 1971) p. 498. [9] C. Levy-Mannheim, M. Djabourov, J. Leblond and P.H.E. Meijer, Phys. Lett. 50A (1974) 75. [lo] V.J. Tekippe and L.L. Abels, Phys. Lett. 60A (1977) 129. [ 111 SF. Ahmad, H. Kiefte and M.J. Clouter, J. Chem. Phys. 69 (1978) 5468. [ 121 R. Aronsson, H.E.G. Knape and L.M. Torell, Phys. Lett. 73A (1979) 210. [ 131 A. Wergin, W. Krasser and J.P. Boon, MoL Phys. 34 (1977) 1637. [14] W. Schaaffs, Z. Phys. Chem. 194 (1944) 28.
197
PHYSICS LETTERS
21 July 1980
BRILLOUIN SCATTERING STUDY OF THE ORIENTATIONALLY DISORDERED PHASE OF CYCLOHEXANOL
J. PELOUS, R. VACHER and J.P. BONNET Laboratoire de Spectromttrie Rayleigh Brillouin, UniversitC des Sciences et Techniques du Languedoc, 34060 Montpellier Ckdex, France
and J.L. RIBET Groupe de Dynamique des Phases Condenkes, 34060 Montpellier Ckdex, France
Universitk des Sciences et Techniques du Languedoc,
Received 13 May 1980
Brillouin scattering was used to measure the velocity and attenuation of longitudinal hypersonic waves ln the orientationally disordered (OD) phase of a cyclohexanol single crystal and at the OD-liquid transition..‘Our results show that the coupling with a high-frequency relaxation mechanism, which dominates the behaviour of the hypersonic waves in the liquid, is still efficient in the OD phase.
The liquid and solid phases of cyclohexanol have been extensively studied by several techniques [l-3]. In particular, acoustical measurements by ultrasonic techniques and Brillouin scattering have shown the existence of a high-frequency mechanical relaxation [4] in the liquid. Several processes have been put forward for explaining this relaxation, but the most likely is a perturbation related to a monomer-dimer equilibrium. Below 25“C, cyclohexanol undergoes a transition to a plasticcrystal phase. In this phase, the centers of mass of the molecules are ordered in a cubic lattice, but molecular motions are still possible, leading to a dynamical orientational disorder. Ultrasonic measurements have been performed by Green and Scheie [5] in this phase of cyclohexanol on polycrystalline samples. The average longitudinal sound velocity was found very similar to that in the liquid; the acoustic attenuation was not measured. In this letter we report the results of a Brillouin scattering measurement in the orientationally disordered (OD) phase of a cyclohexanol, single crystal, with the purpose of obtaining information on the high-frequency molecular relaxation in this phase. In order to obtain single crystals of good optical
quality, the commercial liquid cyclohexanol was distilled several times to remove water. After this purification, the melting point was found to be 25”C, indicating a high degree of purity (a small water content can lower the melting point down to 23°C). Single crystals were grown by the Bridgman method in sealed glass cells. The orientation of the sample was unknown in our experiments. The spectrometer used for this study has been described previously [6]. It consists of a tandem arrangement of a double-pass plane and a confocal FabryPerot interferometer leading to a contrast of lo7 and a resolving power of 2 X lo7 (30 MHz) which allows precise measurements of the linewidth. The experiments were performed in a backscattering configuration. The accuracy of the measurements is of about 1% for the frequency shift and 10% for the linewidth. The index of refraction n was calculated using the Lorenz-Lorentz relation, starting from the value measured in the supercooled liquid (n = 1.4698 at 22.6”C and A = 5 145 A) [7] and from the temperature dependence of the density (~(~~~~-3) = 0.9721 - 6.89 X 10m4 t in the OD phase and pccm-3) = 0.9627 - 7.6 X 1O-4 t in the liquid phase) [5] . 195
It_
-+-+.+,+
*loo, _ ‘;
2000. VI
Yy+*,
, ,
0 D
CRYSTAL
--
---
if
+;;i
+ +b.
i I
E _=I900 tu s 9
21 July 1980
PHYSICS LETTERS
Volume 78A, number 2
*CID
1800
CRYSTAL-------r
I
:y+ 1700 -10
“1,. 0
10
20 30 TEMPERATURE
J :0 .o‘ (C )
0
10
20 TEMPERATURE
30
4
(2)
Fig. 1. Variation of the velocity of longitudinal hypersounds versus temperature in cyclohexanol.
Fig. 2. Variation of the inverse mean free path of longitudinal hypersounds versus temperature in cyclohexanol.
Our measurements were performed in the OD phase between -7°C and 25°C and in the liquid up to 4O’C. The velocity u of hypersonic waves is related to the Brillouin frequency shift vg by the expression vg = 2n(u/hO)sin(0/2), where & is the wavelength of the ‘incident light and 0 the scattering angle. The temperature variation of the velocity of longitudinal hypersound is shown in fig. 1. In contrast to the results of Green and Scheie [5], the velocity exhibits a discontinuity at the OD-liquid transition, as already observed in other materials at this transition. The ratio of the velocity in the OD and liquid phases is equal to 1.16 in cyclohexanol. This can be compared to the values 1.38 in succinonitrile [8], 1.35 in CC& [9], 1.46 in CBr, [lo], 1.35 in cyclohexanol [ 111, 1.49 in Li2S04 [12] (taking into account the 1% change in density at the phase transition, the discontinuity is of about 33% for the elastic modulus). This shows that the elastic properties are sensitive to the order modifications associated with the transition even if the amplitude of the discontinuity is small because of the liquid-like properties of the OD phase. The inverse mean free path 1-l (power acoustic attenuation) can be deduced from the half-width at half-height r of the Brillouin line from the expression ‘r-l = 4nF’/u. The results are plotted in fig. 2 for the same temperature range. An interesting feature is that when cooling from the liquid to the OD phase, the attenuation decreases and shows no appreciable discontinuity at the transition. This behaviour has already
been observed in succinotrile [8] and presumably (no quantitative measurements made) in CBr, [lo]. On the contrary measurements in Ccl, [9] show a discontinuity of the attenuation; neopentane in its liquid phase exhibits a similar feature [ 131. In cyclohexanol the attenuation below 10°C tends to be constant down to -7”C, even when going close to the solid-OD transition which takes place at -8’C. This indicates that the coupling of 12 GHz hypersounds with the relaxation mechanism is less efficient as the regime WT s 1 is reached (here o is the angular frequency of phonons and T the relaxation time). In the liquid phase, our measurement of the velocity (1756 m s-1 at 25°C and 10 GHz) is in agreement with the value given by Choi et al. [4] (1715 m s-l at 25°C and 7 GHz) within experimental uncertainties. When compared to the average of three ultrasonic results (a 1460 m s-l at 25°C) [4,5,14], our measurement confirms the existence of a strong dispersion related to a high-frequency relaxation mechanism. Also related to this dispersion, we observe a large temperature coefficient of the velocity: Au/Ar = -7.6 m s-l K-l. In the OD phase we find u = 2010 m s-l for t = 24°C and a frequency of 11.5 GHz. The average temperature coefficient is equal to -3.8 m s-l K-l. Lacking from measurements at lower frequencies, in the single crystal, it is not possible to separate the part of this temperature coefficient which is due to relaxation from that related to dilatation effects. However, the observation that the attenuation is nearly insensitive to the liquid-OD tran-
196
Volume 78A, number 2
PHYSICS LETTERS
sition leads us to the conclusion that the coupling of phonons with a high-frequency molecular relaxation is still effective in the high temperature range of the OD phase. Therefore, at least one part of the temperature coefficient of the velocity must be due to the dispersion related to this coupling. Finally it must be noted that no pretransitional effect was observed near the OD-liquid transition, a feature which is also true for succinonitrile, CBr,Li,SO, . This is in contrast with the softening of the longitudinal velocity observed in Ccl,. So, in our opinion, it remains to elucidate how the softening (or non-softening) of the longitudinal modes and the behaviour of the attenuation can be related to the OD-liquid transition. References [l] K. Adachi, M. Suga and S. Seki, BuIl. Chem. Sot. Japan 41 (1968) 1073.
21 July 1980
[2] K. Adachi et aL, Mol. Cryst. Liq. Cryst. 18 (1972) 345. [3] T. Eguchi, G. Soda and H. Chihara, J. Non Cryst. Solids 21 (1974) 143. [4] P.K. Choi, K. Takagi and K. Negishi, Japan J. AppL Phys. 17 (1978) 97. [5] J.R. Green and C.E. Scheie, J. Phys. Chem. Solids 28 (1967) 383. [6] R. Vacher and J. Pelous, Phys. Rev. B14 (1976) 823. [7] Landolt and Bornstein, Vol. 4 (Springer, Berlin) 6th Ed. [ 81 L. Boyer, R. Vacher, M. Adam and L. Cecchi, Proc. 2nd Intern. Conf. on Light scattering in solids, ed. M. Balkanski (Paris, 1971) p. 498. [9] C. Levy-Mannheim, M. Djabourov, J. Leblond and P.H.E. Meijer, Phys. Lett. 50A (1974) 75. [lo] V.J. Tekippe and L.L. Abels, Phys. Lett. 60A (1977) 129. [ 111 SF. Ahmad, H. Kiefte and M.J. Clouter, J. Chem. Phys. 69 (1978) 5468. [ 121 R. Aronsson, H.E.G. Knape and L.M. Torell, Phys. Lett. 73A (1979) 210. [ 131 A. Wergin, W. Krasser and J.P. Boon, MoL Phys. 34 (1977) 1637. [14] W. Schaaffs, Z. Phys. Chem. 194 (1944) 28.
197