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Quantum precession of HCl molecule in hydroquinone clathrate
ELSEVIER
Physica B 202 (1994) 315-319
Quantum precession of HC1 molecule in hydroquinone clathrate S. T a k e d a a'*, H . K a t a o k a a, K . S h i b a t a b, S. I k e d a c, T. M a t s u o a, C.J. C a r l i l e d aDepartment of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan blnstitute for Material Research, Tohoku University, Sendai 980, Japan CNational Laboratory for High Energy Physics, Tsukuba 305, Japan dRutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OXl l OQX, UK
Abstract
The dynamical behaviour of HCI in the cage of 13-hydroquinone clathrate was investigated by neutron scattering with particular reference to the phase transition at 12.3 K. A quantum precessional transition of HC1 was observed at 4.3 meV as a broad peak, below the phase transition temperature for the stoichiometric compound. The peak width became much broader for the non-stoichiometric clathrate in which a fraction of cages are unoccupied. The peak disappeared for the deuterated compound. Quasielastic scattering appeared above the phase transition temperature (12.3 K).
1. Introduction
Polar molecules such as hydrogen chloride (HC1) do not behave as a quantum rotor in their pure state because of the strong intermolecular interactions unlike the cases of non-polar molecules and molecular groups such a s C H 4 and CH3 [1]. Their quasifree rotation, however, may be observed when they are incorporated as a guest molecule (G) in a host material such as in the hydroquinone clathrate compound, [C6H4(OH)2]3Gx. In this compound [2], the hydroxyl groups of the hydroquinone molecule, C r H 4 ( O H ) 2 , form hydrogen bonded rings as shown in Fig. 1 and construct an almost spherical cage with a free diameter of ca. 4.8 A situated 5.5 A apart in the vertical direction in this figure. The wall of the cage is constructed by the six benzene rings of the hydroquinone molecu* Corresponding author.
les and is shared by neighbouring cages 9.8/~ apart approximately in the horizontal direction in Fig. 1. A guest molecule is confined in each cage and direct interactions between the guest molecules are diminished. The space group of the crystal of hydroquinone clathrate of hydrogen chloride, [C6H4(OH)2]3(HCI)x with x ~ l , is R3 at room temperature [3]. The C1 atom of HC1 locates on the threefold symmetry axis of the crystal. The position of the H atom of HC1 has been determined by neutron diffraction experiments to be on the threefold symmetry axis with a large thermal vibration parameter [3]. The distance, 1.06/~, between H and C1 atoms is smaller than the bond length of the HC1 molecule in the gas phase (1.275 ,~). The HC1 molecule, therefore, may precess around the threefold symmetry axis of the crystal. A phase transition was observed at 12.3 K for the hydrogen compound, [C6H4(OH)2"]3(HCI)o.99,
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S. Takeda et al./Physica B 202 (1994) 315-319
Fig. 1. The host cage of 13-hydroquinone clathrate in which the HC1 molecule is confined. The heavy lines represent the hydrogen bonds between neighbouring oxygen atoms of hydroquinone molecules and the hexagons stand for the benzene rings.
ratio of the benzene ring was determined to be 91% by the same method as above. The clathrate, [C6D4(OH)2]a(HC1)I, was precipitated out from ethyl ether saturated with HCI when an ethyl ether solution of C6D4(OH)2 was added dropwise at - 30°C. This careful preparation was necessary to obtain a clathrate compound with the stoichiometric composition, [C6D4(OH)2]3(HCI)I.o. A non-stoichiometric compound, [C6D4(OH)E]a(HCI)0.75, was also prepared. The deuterated compound, [C604(OD)E]a(DCl)o.89, was obtained by a similar method by using C 6 D 4 ( O D ) 2 and DC1 instead of C6D4(OH)2 and HC1. The compositions of the compounds were determined by elemental analysis.
3. Results and discussion and at 14K for the deuterated compound, ECtD4(OD)233(DC1)o.98 [43, while the hydroquinone clathrates of argon and krypton do not undergo any phase transition [5]. Therefore the phase transition may be related to a change of the precessional or orientational state of the HCI molecule in the cage. The purpose of the present study is to investigate the dynamical behaviour of the HC1 molecule in the hydroquinone clathrate both in the high and in the low temperature phases. We found from the neutron scattering experiments that the HC1 molecule precesses quantum mechanically even in the low temperature phase and that the neutron scattering peak for the precessional excitation was broader for the non-stoichiometric clathrate where some of the cages are vacant.
2. Experimental methods Fully deuterated hydroquinone, C 6 D 4 ( O D ) 2 , was prepared by the method reported by Yao and Heller [6]. The deuteration ratio was determined to be 94% by high resolution 1H-NMR measurements on the sample dissolved in deuterated acetone. A partially deuterated compound, C6D4(OH)2, was obtained by recrystallization of C6D4(OD)2 from H 20 solution. The deuteration
The neutron scattering spectra of the protonated compound, [C6D4(OH)2]3(HClh.o, were recorded around the phase transition temperature (12.3 K). The spectra were measured using the inverse geometry time-of-flight (TOF) crystal analyzer spectrometer, LAM-40, at the KENS spallation neutron source at National Laboratory for High Energy Physics, Japan [71. Pyrolytic graphite was used as the crystal analyzer ((0 0 2) reflection). Seven spectra with different momentum transfer values between 0.41 and 2.47 A- 1 at the elastic peak position were accumulated simultaneously and summed to improve the statistics. The spectra were collected in runs spanning 6-16 h. The background signal was low and flat in the energy transfer region of interest. The observed spectrum was normalized to the incident neutron spectrum and the scattering function, S(Q, o~), was obtained after correction for the detector efficiencies. The scattering function, S(Q, o~), of the neutron energy loss region at different temperatures is shown in Fig. 2. The temperature of the sample was controlled to + 0.5 K of the set point in a variable temperature liquid helium cryostat. Below the phase transition temperature (12.3 K), a broad peak was clearly observed at 4.3 meV with a small shoulder at 6meV. The peak at 4.3 meV disappeared for the deuterated compound, [ C 6 D 4 ( O D ) 2 ] 3 ( D C I ) o . s 9 , while the other feature at
317
S. Takeda et al./Physica B 202 (1994) 315-319
0.10.
,, ....
, ....
0.03
, ....
I '''J .... ' .... Q3(HCI)o.75
Q3(HCI)I.0 0 . 0 8
-
,--., 0.02 3
o.o6t
~ I ~
[~~1~
3 d
0.01 0.04
-
Q3(HCI)I.0 4.2K t
0.02
0.00
-
iI
0.00
[ ....
l i l i l l
. . . .
I
0 5 10 Energy Transfer / meV '
Fig. 2. Inelastic neutron scattering spectra of [CrD4(OH)2]3(HCIh. o around the phase transition temperature (12.3K). The Q in Q3(HC1)I.o stands for C6DJOH)2. Each spectrum is shifted along the ordinate by 0.01 to avoid overlapping.
6 meV remained. This behaviour was also observed on the TFXA spectrometer on ISIS (Rutherford Appleton Laboratory, UK). The line shape of the 4.3meV peak depended on the concentration of HC1 in the clathrate as shown in Fig. 3. What appears as a clear peak at 4.3 meV in the case of the stoichiometric clathrate compound became significantly diffuse when the vacant cages in the clathrate were increased to 25%. This peak is assigned to the excitation between the precessional levels of the HC1 molecule in the cage. This assignment is consistent with the spin-lattice relaxation rate, Ti-~, of the proton as measured by NMR at 35.5MHz for the fully protonated compound, I-C6H4(OH)213(HCI)o.99 I-8]. The Ti-1 showed a maximum at 5 K due to the transition between
0 5 10 15 Energy Transfer / meV ,
I
. . . .
J
. . . .
i
. . . .
J
Fig. 3. Dependence of the line shape of the 4.3 meV peak on the concentration of HCI in the clathrate. The Q in Q3(HCI)x denotes C6D4(OH)2. The poor statistics for Q3(HCI)0.75 is caused by a shorter measuring time (3 h) compared with 13 h for Q3(HCI)I.o.
the precessional levels. The energy splitting of the levels estimated from the slope of Ti-1 agrees well with the peak energy at 4.3 meV of the present inelastic neutron scattering spectra, if a distribution of the precessional excitation energy is assumed to account for the large width of the peak. The halfwidth at half-maximum of the peak at 4.3 meV is 2 meV, which is much wider than the resolution of the LAM-40 spectrometer (0.3 meV). The width did not change on cooling the sample from 4.2 K down to 2.3 K, which suggests that the width of the precessional energy level is intrinsically broad, probably reflecting an interaction between HC1 molecules in different cages. Strong coupling with other motional modes will also broaden the peak. For example the translational vibration or rattling of the HC1 molecule in the cage will cause the precessional angle to fluctuate. In order to estimate the magnitude of the potential barrier hindering the precession of the HC1
318
s. Takeda et al./Physica B 202 (1994) 315-319
molecule in the cage, it is useful to calculate the precessional energy level scheme for the case of no potential barrier, i.e. for free precession. The precessional energy scheme as well as the m o m e n t of inertia depend on the precessional angle, 0, in Fig. 1. The calculated energy differences between the two lowest precessional levels are listed in Table 1 for three different precessional angles. The separation of the two lowest levels for free precession corresponds to the tunnelling splitting for the high barrier case and is sensitive to the barrier height. The observed energy of 4.3 meV is not so low compared with the calculated values for free precession given in Table 1. The hindering barrier for precession of the HCI molecule in a cage, thus, appears to be quite small, even in the low temperature phase. Above the phase transition temperature (12.3 K), quasielastic scattering appears as shown in Fig. 2. The quasielastic contribution was separated from the elastic and neighbouring inelastic peaks by subtracting the lowest temperature spectrum observed at 2.3 K from the high temperature spectrum. The result for 22.0 K is shown in Fig. 4 as an example. It shows a significant dip around 4 or 5 meV which suggests that the intensity of the 4.3 meV peak falls when the temperature was increased from 2.3 to 22.0 K. A broad infrared absorption around 3 meV has been reported as a rotational excitation of HCI at 18 K in the clathrate with 73.5% HC1 [9]. The quasielastic peak was fitted by the following Lorentzian function [10]: S(Q, co) = A l ( Q ) ( 1 / ~ ) ( 3 z / ( 9 +
0)2Z'2)),
Q showed a m a x i m u m at 1.8 ~ - 1 , indicating that the separation between the equilibrium positions of the proton in HCI is 1.5 ~ in the case of the threesite model and therefore the precessional angle shown in Fig. 1 is 45 ° at 22.0 K. The derived angle seems consistent with 34 ° estimated from the structure analysis at room temperature [3]. We also examined a rotational diffusion model for the precession of the proton in the HCI molecule. The rotational diffusion can be approximated by the j u m p model with a large number of equilibrium positions. N (/> 12), of the proton on the circle [10]. Calculation of the Q-dependence of the quasielastic structure factor for N = 12 showed a m a x i m u m at 4 / ~ - 1 in the case of 34 ° of the precessional angle and at 2.2/~-1 even in the case that m a x i m u m precessional angle was assumed,
Table 1 Precessional angle O, moment of inertia I and energy separation between the two lowest precessional levels of HCI O (deg)
I (kgm 2)
Eol (meV)
30 20 10
6.5 x 10-48 3.1 x 10-48 7.9 x 10 49
5.3 11 44
.
.~
.
.
.
I
.
.
.
.
]
.
.
.
.
I
.
.
.
.
I
.
.
.
.
0.04
(1)
where
A,(Q)
= ~-(1-
0.02
sin(Qrx/~ )/(Qr~J3)),
assuming three equivalent disordered sites for the proton in the HCI molecule which are equally spaced by a distance r on a circle similar to a methyl group. This assumption is based on the structure in which a crystallographic threefold symmetry axis runs through the chlorine a t o m in the high temperature phase as shown in Fig. 1. The three-site model is also suggested by Q-dependence of the quasielastic structure factor. The observed quasielastic structure factor as a function of
g
o
r~ o ,
-I0
,
i
~
I
~
,
,
f
I
~
,
,
,
0
10
Energy transfer / m e V Fig. 4. Lorentzian fitting of the quasielastic scattering from [CrD4(OH)2]3(HClh.o at 22.0K.
s. Takeda et al./Physica B 202 (1994) 315-319
i.e. 0 = 90 °. The result of the calculation is inconsistent with the observations. Thus we adopted the three-site model for the analysis of the quasielastic peak between 13.5 and 22.0 K. A t ( Q ) in Eq. (1)was summed over seven different values of m o m e n t u m transfer. Q, since the width of the quasielastic peak was independent of Q between 0.41 and 2.47 ~ - 1 . The correlation time, z, was determined by a fitting process as z = 1 . 5 x 1 0 - 1 2 s at 13.5K, z = 1 . 6 x l 0 -12 s at 15.3K and r = 1.7x10 -12 s at 22.0 K. The temperature dependence of z is not significant in this region.
4. Conclusions The HC1 molecules contained within the clathrate precess quantum mechanically in the low temperature phase and the phase transition seems to be accompanied primarily by a change of the precessional state of the HCI molecule in the cage. High resolution neutron powder diffraction measurements o n [C6H4(OH)2]3(HC1)0.9 9 showed that the transition from the high to the low temperature phase is accompanied by only a small distortion of the unit cell and a lowering of its symmetry. The cell, however, remains essentially the same size [11]. N o significant difference was observed between 4 and 20 K in the neutron inelastic scattering spectra (TFXA) in the energy transfer region from 10 to 250 meV. This is also consistent with only a small difference in the host lattice between the high and the low temperature phases. In the high temperature phase, there is a threefold symmetry axis of the crystal (Fig. 1) and the hindering potential for the precession has also threefold symmetry in this phase. This feature resembles the internal rotation of a methyl group. The precessional ground state is a non-degenerate A-symmetry state and the precessional first excited state is a doubly degenerate E-symmetry of the C3-symmetry representation. The threefold symmetry of the hindering potential, however, m a y be destroyed when the crystal undergoes a phase transition to the low temperature phase, a situation different from that of the methyl group. This occurs
319
because the HC1 molecule does not possess intrinsic threefold symmetry itself. In this reduced symmetry the first precessional excited state splits into two non-degenerate sublevels within the picture of isolated single particle precession. Interaction between HCI molecules in the different cages probably makes the energy scheme more complicated. The broadening of the precessional excitation in HCI due to the increase in the number of vacant cages in the clathrate (Fig. 3) m a y be related to the observed shift of the phase transition toward low temperature [12]. Detailed analysis of the precessional geometry of the hydrogen chloride molecule in the high and in the low temperature phases, which can be derived from the dependence of the neutron scattering intensity on the m o m e n t u m transfer, will be presented in a separate paper together with a full description and analysis of the spinlattice relaxation rate of the proton and the deuteron for [C6H4(OH)2]3(HC1)0.99 and [C6D4(OD)213(DCI)o.98, respectively, by nuclear magnetic resonance [8].
References [1] M. Prager, Physica B 174 (1991) 218; and the references cited therein. I-2] H.M. Powell, Non Stoichiometric Compounds, ed. L. Mandelcorn (Academic Press, New York, 1964) ch. 7. [3] J.C.A. Boeyens and J.A. Pretorius, Acta Crystallogr. B 33 (1977) 2120. 1-4] H. Ukegawa, Dissertation, Osaka University (1988). 1-5] J.C. Burgiel, H. Meyer and R.C. Richards, J. Chem. Phys. 43 (1965) 4291. [6] H.C. Yao and H.C. Heller, Anal. Chem. 41 (1969) 1540. 1-7] K. lnoue, Y. Ishikawa,N. Watanabe, K. Kaji, Y. Kiyanagi, H. Iwasa and M. Kohgi, Nucl. Instr. Meth. Phys. Res. A 238 (1985) 401. [81 S. Takeda et al., manuscript in preparation for publication. [9"1 C. Barthel, X. Gerbaux and A. Hadni, Spectrochim. Acta 26A (1979) 1183. [10"1 M. Bee, Quasielastic Neutron Scattering (Adam Hilger, Bristol, 1988) ch. 6. [11"1 T. Matsuo, W.I.F. David, A.J. Leadbetter and H. Suga, ISIS Annual Report (1988) A27. [12] H. Ukegawa, T. Matsuo and H. Suga, Solid State Commun. 76 (1990) 221.
Physica B 202 (1994) 315-319
Quantum precession of HC1 molecule in hydroquinone clathrate S. T a k e d a a'*, H . K a t a o k a a, K . S h i b a t a b, S. I k e d a c, T. M a t s u o a, C.J. C a r l i l e d aDepartment of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan blnstitute for Material Research, Tohoku University, Sendai 980, Japan CNational Laboratory for High Energy Physics, Tsukuba 305, Japan dRutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OXl l OQX, UK
Abstract
The dynamical behaviour of HCI in the cage of 13-hydroquinone clathrate was investigated by neutron scattering with particular reference to the phase transition at 12.3 K. A quantum precessional transition of HC1 was observed at 4.3 meV as a broad peak, below the phase transition temperature for the stoichiometric compound. The peak width became much broader for the non-stoichiometric clathrate in which a fraction of cages are unoccupied. The peak disappeared for the deuterated compound. Quasielastic scattering appeared above the phase transition temperature (12.3 K).
1. Introduction
Polar molecules such as hydrogen chloride (HC1) do not behave as a quantum rotor in their pure state because of the strong intermolecular interactions unlike the cases of non-polar molecules and molecular groups such a s C H 4 and CH3 [1]. Their quasifree rotation, however, may be observed when they are incorporated as a guest molecule (G) in a host material such as in the hydroquinone clathrate compound, [C6H4(OH)2]3Gx. In this compound [2], the hydroxyl groups of the hydroquinone molecule, C r H 4 ( O H ) 2 , form hydrogen bonded rings as shown in Fig. 1 and construct an almost spherical cage with a free diameter of ca. 4.8 A situated 5.5 A apart in the vertical direction in this figure. The wall of the cage is constructed by the six benzene rings of the hydroquinone molecu* Corresponding author.
les and is shared by neighbouring cages 9.8/~ apart approximately in the horizontal direction in Fig. 1. A guest molecule is confined in each cage and direct interactions between the guest molecules are diminished. The space group of the crystal of hydroquinone clathrate of hydrogen chloride, [C6H4(OH)2]3(HCI)x with x ~ l , is R3 at room temperature [3]. The C1 atom of HC1 locates on the threefold symmetry axis of the crystal. The position of the H atom of HC1 has been determined by neutron diffraction experiments to be on the threefold symmetry axis with a large thermal vibration parameter [3]. The distance, 1.06/~, between H and C1 atoms is smaller than the bond length of the HC1 molecule in the gas phase (1.275 ,~). The HC1 molecule, therefore, may precess around the threefold symmetry axis of the crystal. A phase transition was observed at 12.3 K for the hydrogen compound, [C6H4(OH)2"]3(HCI)o.99,
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S. Takeda et al./Physica B 202 (1994) 315-319
Fig. 1. The host cage of 13-hydroquinone clathrate in which the HC1 molecule is confined. The heavy lines represent the hydrogen bonds between neighbouring oxygen atoms of hydroquinone molecules and the hexagons stand for the benzene rings.
ratio of the benzene ring was determined to be 91% by the same method as above. The clathrate, [C6D4(OH)2]a(HC1)I, was precipitated out from ethyl ether saturated with HCI when an ethyl ether solution of C6D4(OH)2 was added dropwise at - 30°C. This careful preparation was necessary to obtain a clathrate compound with the stoichiometric composition, [C6D4(OH)2]3(HCI)I.o. A non-stoichiometric compound, [C6D4(OH)E]a(HCI)0.75, was also prepared. The deuterated compound, [C604(OD)E]a(DCl)o.89, was obtained by a similar method by using C 6 D 4 ( O D ) 2 and DC1 instead of C6D4(OH)2 and HC1. The compositions of the compounds were determined by elemental analysis.
3. Results and discussion and at 14K for the deuterated compound, ECtD4(OD)233(DC1)o.98 [43, while the hydroquinone clathrates of argon and krypton do not undergo any phase transition [5]. Therefore the phase transition may be related to a change of the precessional or orientational state of the HCI molecule in the cage. The purpose of the present study is to investigate the dynamical behaviour of the HC1 molecule in the hydroquinone clathrate both in the high and in the low temperature phases. We found from the neutron scattering experiments that the HC1 molecule precesses quantum mechanically even in the low temperature phase and that the neutron scattering peak for the precessional excitation was broader for the non-stoichiometric clathrate where some of the cages are vacant.
2. Experimental methods Fully deuterated hydroquinone, C 6 D 4 ( O D ) 2 , was prepared by the method reported by Yao and Heller [6]. The deuteration ratio was determined to be 94% by high resolution 1H-NMR measurements on the sample dissolved in deuterated acetone. A partially deuterated compound, C6D4(OH)2, was obtained by recrystallization of C6D4(OD)2 from H 20 solution. The deuteration
The neutron scattering spectra of the protonated compound, [C6D4(OH)2]3(HClh.o, were recorded around the phase transition temperature (12.3 K). The spectra were measured using the inverse geometry time-of-flight (TOF) crystal analyzer spectrometer, LAM-40, at the KENS spallation neutron source at National Laboratory for High Energy Physics, Japan [71. Pyrolytic graphite was used as the crystal analyzer ((0 0 2) reflection). Seven spectra with different momentum transfer values between 0.41 and 2.47 A- 1 at the elastic peak position were accumulated simultaneously and summed to improve the statistics. The spectra were collected in runs spanning 6-16 h. The background signal was low and flat in the energy transfer region of interest. The observed spectrum was normalized to the incident neutron spectrum and the scattering function, S(Q, o~), was obtained after correction for the detector efficiencies. The scattering function, S(Q, o~), of the neutron energy loss region at different temperatures is shown in Fig. 2. The temperature of the sample was controlled to + 0.5 K of the set point in a variable temperature liquid helium cryostat. Below the phase transition temperature (12.3 K), a broad peak was clearly observed at 4.3 meV with a small shoulder at 6meV. The peak at 4.3 meV disappeared for the deuterated compound, [ C 6 D 4 ( O D ) 2 ] 3 ( D C I ) o . s 9 , while the other feature at
317
S. Takeda et al./Physica B 202 (1994) 315-319
0.10.
,, ....
, ....
0.03
, ....
I '''J .... ' .... Q3(HCI)o.75
Q3(HCI)I.0 0 . 0 8
-
,--., 0.02 3
o.o6t
~ I ~
[~~1~
3 d
0.01 0.04
-
Q3(HCI)I.0 4.2K t
0.02
0.00
-
iI
0.00
[ ....
l i l i l l
. . . .
I
0 5 10 Energy Transfer / meV '
Fig. 2. Inelastic neutron scattering spectra of [CrD4(OH)2]3(HCIh. o around the phase transition temperature (12.3K). The Q in Q3(HC1)I.o stands for C6DJOH)2. Each spectrum is shifted along the ordinate by 0.01 to avoid overlapping.
6 meV remained. This behaviour was also observed on the TFXA spectrometer on ISIS (Rutherford Appleton Laboratory, UK). The line shape of the 4.3meV peak depended on the concentration of HC1 in the clathrate as shown in Fig. 3. What appears as a clear peak at 4.3 meV in the case of the stoichiometric clathrate compound became significantly diffuse when the vacant cages in the clathrate were increased to 25%. This peak is assigned to the excitation between the precessional levels of the HC1 molecule in the cage. This assignment is consistent with the spin-lattice relaxation rate, Ti-~, of the proton as measured by NMR at 35.5MHz for the fully protonated compound, I-C6H4(OH)213(HCI)o.99 I-8]. The Ti-1 showed a maximum at 5 K due to the transition between
0 5 10 15 Energy Transfer / meV ,
I
. . . .
J
. . . .
i
. . . .
J
Fig. 3. Dependence of the line shape of the 4.3 meV peak on the concentration of HCI in the clathrate. The Q in Q3(HCI)x denotes C6D4(OH)2. The poor statistics for Q3(HCI)0.75 is caused by a shorter measuring time (3 h) compared with 13 h for Q3(HCI)I.o.
the precessional levels. The energy splitting of the levels estimated from the slope of Ti-1 agrees well with the peak energy at 4.3 meV of the present inelastic neutron scattering spectra, if a distribution of the precessional excitation energy is assumed to account for the large width of the peak. The halfwidth at half-maximum of the peak at 4.3 meV is 2 meV, which is much wider than the resolution of the LAM-40 spectrometer (0.3 meV). The width did not change on cooling the sample from 4.2 K down to 2.3 K, which suggests that the width of the precessional energy level is intrinsically broad, probably reflecting an interaction between HC1 molecules in different cages. Strong coupling with other motional modes will also broaden the peak. For example the translational vibration or rattling of the HC1 molecule in the cage will cause the precessional angle to fluctuate. In order to estimate the magnitude of the potential barrier hindering the precession of the HC1
318
s. Takeda et al./Physica B 202 (1994) 315-319
molecule in the cage, it is useful to calculate the precessional energy level scheme for the case of no potential barrier, i.e. for free precession. The precessional energy scheme as well as the m o m e n t of inertia depend on the precessional angle, 0, in Fig. 1. The calculated energy differences between the two lowest precessional levels are listed in Table 1 for three different precessional angles. The separation of the two lowest levels for free precession corresponds to the tunnelling splitting for the high barrier case and is sensitive to the barrier height. The observed energy of 4.3 meV is not so low compared with the calculated values for free precession given in Table 1. The hindering barrier for precession of the HCI molecule in a cage, thus, appears to be quite small, even in the low temperature phase. Above the phase transition temperature (12.3 K), quasielastic scattering appears as shown in Fig. 2. The quasielastic contribution was separated from the elastic and neighbouring inelastic peaks by subtracting the lowest temperature spectrum observed at 2.3 K from the high temperature spectrum. The result for 22.0 K is shown in Fig. 4 as an example. It shows a significant dip around 4 or 5 meV which suggests that the intensity of the 4.3 meV peak falls when the temperature was increased from 2.3 to 22.0 K. A broad infrared absorption around 3 meV has been reported as a rotational excitation of HCI at 18 K in the clathrate with 73.5% HC1 [9]. The quasielastic peak was fitted by the following Lorentzian function [10]: S(Q, co) = A l ( Q ) ( 1 / ~ ) ( 3 z / ( 9 +
0)2Z'2)),
Q showed a m a x i m u m at 1.8 ~ - 1 , indicating that the separation between the equilibrium positions of the proton in HCI is 1.5 ~ in the case of the threesite model and therefore the precessional angle shown in Fig. 1 is 45 ° at 22.0 K. The derived angle seems consistent with 34 ° estimated from the structure analysis at room temperature [3]. We also examined a rotational diffusion model for the precession of the proton in the HCI molecule. The rotational diffusion can be approximated by the j u m p model with a large number of equilibrium positions. N (/> 12), of the proton on the circle [10]. Calculation of the Q-dependence of the quasielastic structure factor for N = 12 showed a m a x i m u m at 4 / ~ - 1 in the case of 34 ° of the precessional angle and at 2.2/~-1 even in the case that m a x i m u m precessional angle was assumed,
Table 1 Precessional angle O, moment of inertia I and energy separation between the two lowest precessional levels of HCI O (deg)
I (kgm 2)
Eol (meV)
30 20 10
6.5 x 10-48 3.1 x 10-48 7.9 x 10 49
5.3 11 44
.
.~
.
.
.
I
.
.
.
.
]
.
.
.
.
I
.
.
.
.
I
.
.
.
.
0.04
(1)
where
A,(Q)
= ~-(1-
0.02
sin(Qrx/~ )/(Qr~J3)),
assuming three equivalent disordered sites for the proton in the HCI molecule which are equally spaced by a distance r on a circle similar to a methyl group. This assumption is based on the structure in which a crystallographic threefold symmetry axis runs through the chlorine a t o m in the high temperature phase as shown in Fig. 1. The three-site model is also suggested by Q-dependence of the quasielastic structure factor. The observed quasielastic structure factor as a function of
g
o
r~ o ,
-I0
,
i
~
I
~
,
,
f
I
~
,
,
,
0
10
Energy transfer / m e V Fig. 4. Lorentzian fitting of the quasielastic scattering from [CrD4(OH)2]3(HClh.o at 22.0K.
s. Takeda et al./Physica B 202 (1994) 315-319
i.e. 0 = 90 °. The result of the calculation is inconsistent with the observations. Thus we adopted the three-site model for the analysis of the quasielastic peak between 13.5 and 22.0 K. A t ( Q ) in Eq. (1)was summed over seven different values of m o m e n t u m transfer. Q, since the width of the quasielastic peak was independent of Q between 0.41 and 2.47 ~ - 1 . The correlation time, z, was determined by a fitting process as z = 1 . 5 x 1 0 - 1 2 s at 13.5K, z = 1 . 6 x l 0 -12 s at 15.3K and r = 1.7x10 -12 s at 22.0 K. The temperature dependence of z is not significant in this region.
4. Conclusions The HC1 molecules contained within the clathrate precess quantum mechanically in the low temperature phase and the phase transition seems to be accompanied primarily by a change of the precessional state of the HCI molecule in the cage. High resolution neutron powder diffraction measurements o n [C6H4(OH)2]3(HC1)0.9 9 showed that the transition from the high to the low temperature phase is accompanied by only a small distortion of the unit cell and a lowering of its symmetry. The cell, however, remains essentially the same size [11]. N o significant difference was observed between 4 and 20 K in the neutron inelastic scattering spectra (TFXA) in the energy transfer region from 10 to 250 meV. This is also consistent with only a small difference in the host lattice between the high and the low temperature phases. In the high temperature phase, there is a threefold symmetry axis of the crystal (Fig. 1) and the hindering potential for the precession has also threefold symmetry in this phase. This feature resembles the internal rotation of a methyl group. The precessional ground state is a non-degenerate A-symmetry state and the precessional first excited state is a doubly degenerate E-symmetry of the C3-symmetry representation. The threefold symmetry of the hindering potential, however, m a y be destroyed when the crystal undergoes a phase transition to the low temperature phase, a situation different from that of the methyl group. This occurs
319
because the HC1 molecule does not possess intrinsic threefold symmetry itself. In this reduced symmetry the first precessional excited state splits into two non-degenerate sublevels within the picture of isolated single particle precession. Interaction between HCI molecules in the different cages probably makes the energy scheme more complicated. The broadening of the precessional excitation in HCI due to the increase in the number of vacant cages in the clathrate (Fig. 3) m a y be related to the observed shift of the phase transition toward low temperature [12]. Detailed analysis of the precessional geometry of the hydrogen chloride molecule in the high and in the low temperature phases, which can be derived from the dependence of the neutron scattering intensity on the m o m e n t u m transfer, will be presented in a separate paper together with a full description and analysis of the spinlattice relaxation rate of the proton and the deuteron for [C6H4(OH)2]3(HC1)0.99 and [C6D4(OD)213(DCI)o.98, respectively, by nuclear magnetic resonance [8].
References [1] M. Prager, Physica B 174 (1991) 218; and the references cited therein. I-2] H.M. Powell, Non Stoichiometric Compounds, ed. L. Mandelcorn (Academic Press, New York, 1964) ch. 7. [3] J.C.A. Boeyens and J.A. Pretorius, Acta Crystallogr. B 33 (1977) 2120. 1-4] H. Ukegawa, Dissertation, Osaka University (1988). 1-5] J.C. Burgiel, H. Meyer and R.C. Richards, J. Chem. Phys. 43 (1965) 4291. [6] H.C. Yao and H.C. Heller, Anal. Chem. 41 (1969) 1540. 1-7] K. lnoue, Y. Ishikawa,N. Watanabe, K. Kaji, Y. Kiyanagi, H. Iwasa and M. Kohgi, Nucl. Instr. Meth. Phys. Res. A 238 (1985) 401. [81 S. Takeda et al., manuscript in preparation for publication. [9"1 C. Barthel, X. Gerbaux and A. Hadni, Spectrochim. Acta 26A (1979) 1183. [10"1 M. Bee, Quasielastic Neutron Scattering (Adam Hilger, Bristol, 1988) ch. 6. [11"1 T. Matsuo, W.I.F. David, A.J. Leadbetter and H. Suga, ISIS Annual Report (1988) A27. [12] H. Ukegawa, T. Matsuo and H. Suga, Solid State Commun. 76 (1990) 221.