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Relaxation kinetics of the sine-Gordon breather mode in 4-methyl-pyridine crystal at low temperature
PHYSICA ELSEVIER
Physica B 213&214 (1995) 646 648
Relaxation kinetics of the sine-Gordon breather mode in 4-methyl-pyridine crystal at low temperature F. Fillaux a' *, C.J. Carlile b, J.C. Cook e, A. Heidemann c, G.J. Kearley c, S. Ikeda a, A. Inaba e a Laboratoire de Spectrochimie Infrarouge et Raman, CNRS. 2 rue Henry Dunant, 94320 Thiais, France h Rutherford Appleton Laboratoo', Chilton, Didcot, Oxon, OXI 10QX, UK e lnstitut Laue-Langevin. BP 156)(, 38042 Grenoble Cedex, France a BSF, Laboratoo'for High Ener~' Physics (KEKL Oho 1-1, Tsukuba, lbaraki 305, Japan ¢ Department of Chemistry. Facul~ of Science, Osaka UnirersiO,, Toyonaka, Osaka 560, Japan
Abstract
INS spectra of 4-methyl-pyridine at 2 K with a resolution of 1.2 ~teV (IN 10 spectrometer at ILL) reveal that the bands previously observed at 510 and 468 ~teV show partially resolved components (516.3 512.4 laeV and 469.6-465.2 geV, respectively). After ~ 70 h, the intensity of the weakest component at 512.4 ~teV has almost vanished whilst that of the other component increases by a factor ~3. Neutron energy-gain and energy-loss peak intensities were measured simultaneously, as a function of time, with the LAM-80ET spectrometer at KEK. For both experiments, the kinetics are very similar.
1. Introduction
The rotational dynamics of the methyl groups in solid 4-methyl-pyridine (4MP or y-picoline) have been thoroughly investigated with inelastic neutron-scattering (INS) spectroscopy. The first measurement ever reported [1] of the tunnelling transition showed a single band at 5201aeV. However, the resolution was quite limited (~2001aeV). With better resolution on the IRIS spectrometer ( ~ 15 rteV), this band was found to be split into several components [2]. As well as the main band at 510 laeV, weaker bands at 468 and 535 geV were partially resolved. Further analysis of the main band at 510 laeV revealed that it could be decomposed into two unresolved components. However, the best resolution ever
*Corresponding author.
obtained so far on an INS spectrometer ( ~ 9 ~teV) [3] did not confirm the fourth component. Further measurements on isotopic mixtures of 4MP [4] and on the partially deuterated analogue [5] have shown that the methyl dynamics are well represented by the quantum sine-Gordon model which describes infinite chains of coupled rotors. The two side-bands were assigned to the in-phase (468 geV) and out-of plane (535 ~teV) collective tunnelling transitions of the chain. The most intense band at 510 laeV, on the other hand, was attributed to the quantized travelling mode of a pseudo-particle or soliton: the breather mode or doublet. Neither this approach nor any other proposed so far, provide any explanation for the fourth component in the tunnelling frequency-range. Therefore, new spectra with the best resolution ever obtained ( ~ 1 geV) have been recorded in order to gain information on the exact number of components, In the course of these studies, it
0921-4526/95/$09.50 ,~ 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 i 0 0 2 3 8 - 3
647
F Fillattr et al. / Physica B 213&214 (1995) 646 648
appeared that the band change with time.
intensities and
frequencies
2. Experimental The commercial sample, purchased from Aldrich, was distilled three times and kept under a controlled atmosphere. A flat aluminium container (0.5 mm thick) filled with 4 M P was loaded into either a liquid helium cryostat (IN10) or a sorption cryostat (LAM-80ET). Detailed descriptions of the IN10 and L A M - 8 0 E T spectrometers can be found in Refs. [6, 7], respectively.
Table 1 Band decomposition into Gaussian components for the INS spectra of 4-methyl-pyridine at 2 K Time (h)
Freq. (~eV)
Width (~eV)
Area (a.u.)
Freq. Width (I.teV) (laeV)
Area (a.u.)
5 31 47 70
516.6 517.4 517.6 517.4
1.64 1.31 1.25 1.21
0.19 0.37 0.41 0.42
512.9 513.8 514.1 514.3
0.22 0.14 0.11 0.08
2.58 2.17 2.24 1.97
3. Results and discussion The first INS spectrum from I N l 0 of 4 M P at 2 K (Fig. la) reveals that the main band is asymmetric with a maximum of intensity at 516.3 ~teV and a shoulder at 512.4 laeV. The weaker band at 469.6 laeV is also asymmetric with a shoulder at 465 ~eV. The band at 535 laeV was not accessible. After ~ 70 h the main component has shifted to 517.4 peV and its intensity has increased by a factor ~ 3 (Fig. lb). The band remains asymmetric with a relatively weak shoulder at 513.7 taeV. At the same time, the band at ~ 4 7 0 laeV has almost disappeared. Its intensity has reduced by a factor ~ 3. Band decomposition into Gaussians (Table 1) reveals that the component at ~ 517 laeV increases in intensity more rapidly than the component at ~ 513 i,teV and the total intensity between 500 and 525 I.teV increases significantly during the first 30 h. The intensity ratio (15~3,/15~) follows approximately an exponential decay with a decay time of roughly
J
.~ 0.6
,~ 0.4 0.2 0 0
10
20
30 40 SO time (hour)
60
70
80
Fig. 2. Intensity ratio 1513/I517 for the bands at 513 and 517 ~teV, respectively. Filled circles: measured; solid line: exponential fit: y = 1.1 l exp( - 0.028x).
36 h (Fig. 2). After 70 h, the component at 517.4 peV is very narrow. The width being limited by the resolution function. With the L A M - 8 0 E T spectrometer, we have measured the intensity ratio of I o , 1,/11 ~o for the 0 ~ 1 and 1 ~ 0 transitions observed with the 004 and 006 reflections, respectively, of the mica analyser (Fig. 3). The decay is also approximately exponential with time constant of roughly 38 h (Fig. 4).
2 b
i
-0.520
i
"1
-0.500 -0.480 Energy Transfer (meV)
-0.460
Fig. 1. INS spectra of 4-methyl-pyridine at 1.6 K obtained with the INI0 spectrometer. (a): after ~ 5 h: (bt: after ~ 70 h.
4. Conclusion The time dependence of the INS spectral profile of 4 M P provides a straightforward way to reconcile all previous experiments. The IRIS spectrum had been obtained very rapidly after quenching the sample in liquid helium [2] and the suggested fourth component was, in retrospect, probably real. The IN5 spectrum, on the other hand, was obtained at 0.5 K after the sample had been cold for a few days [3]. The crystal was, therefore, com-
648
F. Fillaux et al. /Physica B 213&214 (1995) 646 648
Energy transfer mica 006 (meV) 0.7 0.65 0.6 0.55 0.5 0.45 I
J
0-->
i
I
I
]
I
.o
I
E
i
--> 0
i
! 0
t
o
"3
•
20
40
60 80 time (hour)
100
120
Fig. 4. Intensity ratio I~o/'1o~1 for the 1 ~ 0 and 0 ~ 1 transitions, respectively. Filled circles: measured; solid line: exponential fit: ) = 2.80 exp( - 0.034x).
_=
I
I
I
!
I
0.4 0.45 0.5 0.55 0.6 0.65 0.7 Energy transfer mica 004 (meV) Fig. 3. INS spectra of 4-methyl-pyridine at 0.3 K obtained with the LAM-ET80 spectrometer. This speclrometer collects neutron energy loss spectrum from the 004 planes of the mica analyzer (lower scale) overlapped with the neutron energy gain spectrum from the 006 planes (upper scalet. The 1 -~ 0 transition, which vanishes, is due to the 006 reflection.
pletely relaxed and the fourth component had already disappeared and could not be observed. The accuracy of the exponents was limited by the time required for the acquisition of spectra with satisfactory statistical errors, which was about 12 h for both experiments. Under such conditions, we estimate that the kinetics observed in both experiments are not significantly different. We conclude that the multi-component nature of the INS spectrum between 510 and 520 geV is likely to be related to the population of the first excited state. Within the quantum sine-Gordon theory, the n = 1 state is the first travelling state of the breather mode. In principle, for an ideal continuous chain, there is no relaxation channel for the travelling breathers. The lifetime of the travelling states should be infinity. Although not infinity in 4MP, the lifetime remains, however, of the
order of several days. (Compare to the time scale of the breather internal oscillation ~ 10-12 s). The band at 517 laeV is assigned to the "unperturbed" travelling state. The band at 513- 514 I,teV, on the other hand, is attributed to the 0 ~ 1 transition of breathers interacting with other breathers already in the n = 1 travelling state. In the quantum sine-Gordon theory, there is no breather-breather interaction and the 0 ~ 1 frequency should not depend on the population of the excited state. Therefore, the observed time dependence is due to slight deviations of the actual methyl group dynamics from the ideal sine-Gordon system. The decay of the in-phase tunnelling transition also suggests that there is some interaction with the travelling breathers. Further experiments with improved resolution should shed new light on this fascinating system.
References [1] B. Alefeld, A. Kollmar and B.A. Dasannacharya, J. Chem. Phys. 63 (1975) 4415. [2] C.J. Carlile, S. Clough, A.J. Horsewill and A. Smith, Chem. Phys. 134 (1989) 437. [3] F. Fillaux, C.J. Carlile and G.J. Kearley, ILL annual Report [1989). [4] F. Fillaux and C.J. Carlile, Phys. Rev. B 42 (1990) 5990. [5] F. Fillaux, C.J. Carlile and G.J. Kearley, Phys. Rev. B 44 (1991) 12280. [6] J.C. Cook, W. Petry, A. Heidemann and J.F. Barthelemy, Nucl. Instr. and Meth. A 312 (1992) 553. [7] K. Inoue, T. Kawaya, Y. Kiyanagi, S. Ikeda, K. Shibata, H. lwasa. T. Kawiyama, N. Watanabe and Y. Izumi, Nucl. Instr. and Meth. A 309 (1991) 294.
Physica B 213&214 (1995) 646 648
Relaxation kinetics of the sine-Gordon breather mode in 4-methyl-pyridine crystal at low temperature F. Fillaux a' *, C.J. Carlile b, J.C. Cook e, A. Heidemann c, G.J. Kearley c, S. Ikeda a, A. Inaba e a Laboratoire de Spectrochimie Infrarouge et Raman, CNRS. 2 rue Henry Dunant, 94320 Thiais, France h Rutherford Appleton Laboratoo', Chilton, Didcot, Oxon, OXI 10QX, UK e lnstitut Laue-Langevin. BP 156)(, 38042 Grenoble Cedex, France a BSF, Laboratoo'for High Ener~' Physics (KEKL Oho 1-1, Tsukuba, lbaraki 305, Japan ¢ Department of Chemistry. Facul~ of Science, Osaka UnirersiO,, Toyonaka, Osaka 560, Japan
Abstract
INS spectra of 4-methyl-pyridine at 2 K with a resolution of 1.2 ~teV (IN 10 spectrometer at ILL) reveal that the bands previously observed at 510 and 468 ~teV show partially resolved components (516.3 512.4 laeV and 469.6-465.2 geV, respectively). After ~ 70 h, the intensity of the weakest component at 512.4 ~teV has almost vanished whilst that of the other component increases by a factor ~3. Neutron energy-gain and energy-loss peak intensities were measured simultaneously, as a function of time, with the LAM-80ET spectrometer at KEK. For both experiments, the kinetics are very similar.
1. Introduction
The rotational dynamics of the methyl groups in solid 4-methyl-pyridine (4MP or y-picoline) have been thoroughly investigated with inelastic neutron-scattering (INS) spectroscopy. The first measurement ever reported [1] of the tunnelling transition showed a single band at 5201aeV. However, the resolution was quite limited (~2001aeV). With better resolution on the IRIS spectrometer ( ~ 15 rteV), this band was found to be split into several components [2]. As well as the main band at 510 laeV, weaker bands at 468 and 535 geV were partially resolved. Further analysis of the main band at 510 laeV revealed that it could be decomposed into two unresolved components. However, the best resolution ever
*Corresponding author.
obtained so far on an INS spectrometer ( ~ 9 ~teV) [3] did not confirm the fourth component. Further measurements on isotopic mixtures of 4MP [4] and on the partially deuterated analogue [5] have shown that the methyl dynamics are well represented by the quantum sine-Gordon model which describes infinite chains of coupled rotors. The two side-bands were assigned to the in-phase (468 geV) and out-of plane (535 ~teV) collective tunnelling transitions of the chain. The most intense band at 510 laeV, on the other hand, was attributed to the quantized travelling mode of a pseudo-particle or soliton: the breather mode or doublet. Neither this approach nor any other proposed so far, provide any explanation for the fourth component in the tunnelling frequency-range. Therefore, new spectra with the best resolution ever obtained ( ~ 1 geV) have been recorded in order to gain information on the exact number of components, In the course of these studies, it
0921-4526/95/$09.50 ,~ 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 i 0 0 2 3 8 - 3
647
F Fillattr et al. / Physica B 213&214 (1995) 646 648
appeared that the band change with time.
intensities and
frequencies
2. Experimental The commercial sample, purchased from Aldrich, was distilled three times and kept under a controlled atmosphere. A flat aluminium container (0.5 mm thick) filled with 4 M P was loaded into either a liquid helium cryostat (IN10) or a sorption cryostat (LAM-80ET). Detailed descriptions of the IN10 and L A M - 8 0 E T spectrometers can be found in Refs. [6, 7], respectively.
Table 1 Band decomposition into Gaussian components for the INS spectra of 4-methyl-pyridine at 2 K Time (h)
Freq. (~eV)
Width (~eV)
Area (a.u.)
Freq. Width (I.teV) (laeV)
Area (a.u.)
5 31 47 70
516.6 517.4 517.6 517.4
1.64 1.31 1.25 1.21
0.19 0.37 0.41 0.42
512.9 513.8 514.1 514.3
0.22 0.14 0.11 0.08
2.58 2.17 2.24 1.97
3. Results and discussion The first INS spectrum from I N l 0 of 4 M P at 2 K (Fig. la) reveals that the main band is asymmetric with a maximum of intensity at 516.3 ~teV and a shoulder at 512.4 laeV. The weaker band at 469.6 laeV is also asymmetric with a shoulder at 465 ~eV. The band at 535 laeV was not accessible. After ~ 70 h the main component has shifted to 517.4 peV and its intensity has increased by a factor ~ 3 (Fig. lb). The band remains asymmetric with a relatively weak shoulder at 513.7 taeV. At the same time, the band at ~ 4 7 0 laeV has almost disappeared. Its intensity has reduced by a factor ~ 3. Band decomposition into Gaussians (Table 1) reveals that the component at ~ 517 laeV increases in intensity more rapidly than the component at ~ 513 i,teV and the total intensity between 500 and 525 I.teV increases significantly during the first 30 h. The intensity ratio (15~3,/15~) follows approximately an exponential decay with a decay time of roughly
J
.~ 0.6
,~ 0.4 0.2 0 0
10
20
30 40 SO time (hour)
60
70
80
Fig. 2. Intensity ratio 1513/I517 for the bands at 513 and 517 ~teV, respectively. Filled circles: measured; solid line: exponential fit: y = 1.1 l exp( - 0.028x).
36 h (Fig. 2). After 70 h, the component at 517.4 peV is very narrow. The width being limited by the resolution function. With the L A M - 8 0 E T spectrometer, we have measured the intensity ratio of I o , 1,/11 ~o for the 0 ~ 1 and 1 ~ 0 transitions observed with the 004 and 006 reflections, respectively, of the mica analyser (Fig. 3). The decay is also approximately exponential with time constant of roughly 38 h (Fig. 4).
2 b
i
-0.520
i
"1
-0.500 -0.480 Energy Transfer (meV)
-0.460
Fig. 1. INS spectra of 4-methyl-pyridine at 1.6 K obtained with the INI0 spectrometer. (a): after ~ 5 h: (bt: after ~ 70 h.
4. Conclusion The time dependence of the INS spectral profile of 4 M P provides a straightforward way to reconcile all previous experiments. The IRIS spectrum had been obtained very rapidly after quenching the sample in liquid helium [2] and the suggested fourth component was, in retrospect, probably real. The IN5 spectrum, on the other hand, was obtained at 0.5 K after the sample had been cold for a few days [3]. The crystal was, therefore, com-
648
F. Fillaux et al. /Physica B 213&214 (1995) 646 648
Energy transfer mica 006 (meV) 0.7 0.65 0.6 0.55 0.5 0.45 I
J
0-->
i
I
I
]
I
.o
I
E
i
--> 0
i
! 0
t
o
"3
•
20
40
60 80 time (hour)
100
120
Fig. 4. Intensity ratio I~o/'1o~1 for the 1 ~ 0 and 0 ~ 1 transitions, respectively. Filled circles: measured; solid line: exponential fit: ) = 2.80 exp( - 0.034x).
_=
I
I
I
!
I
0.4 0.45 0.5 0.55 0.6 0.65 0.7 Energy transfer mica 004 (meV) Fig. 3. INS spectra of 4-methyl-pyridine at 0.3 K obtained with the LAM-ET80 spectrometer. This speclrometer collects neutron energy loss spectrum from the 004 planes of the mica analyzer (lower scale) overlapped with the neutron energy gain spectrum from the 006 planes (upper scalet. The 1 -~ 0 transition, which vanishes, is due to the 006 reflection.
pletely relaxed and the fourth component had already disappeared and could not be observed. The accuracy of the exponents was limited by the time required for the acquisition of spectra with satisfactory statistical errors, which was about 12 h for both experiments. Under such conditions, we estimate that the kinetics observed in both experiments are not significantly different. We conclude that the multi-component nature of the INS spectrum between 510 and 520 geV is likely to be related to the population of the first excited state. Within the quantum sine-Gordon theory, the n = 1 state is the first travelling state of the breather mode. In principle, for an ideal continuous chain, there is no relaxation channel for the travelling breathers. The lifetime of the travelling states should be infinity. Although not infinity in 4MP, the lifetime remains, however, of the
order of several days. (Compare to the time scale of the breather internal oscillation ~ 10-12 s). The band at 517 laeV is assigned to the "unperturbed" travelling state. The band at 513- 514 I,teV, on the other hand, is attributed to the 0 ~ 1 transition of breathers interacting with other breathers already in the n = 1 travelling state. In the quantum sine-Gordon theory, there is no breather-breather interaction and the 0 ~ 1 frequency should not depend on the population of the excited state. Therefore, the observed time dependence is due to slight deviations of the actual methyl group dynamics from the ideal sine-Gordon system. The decay of the in-phase tunnelling transition also suggests that there is some interaction with the travelling breathers. Further experiments with improved resolution should shed new light on this fascinating system.
References [1] B. Alefeld, A. Kollmar and B.A. Dasannacharya, J. Chem. Phys. 63 (1975) 4415. [2] C.J. Carlile, S. Clough, A.J. Horsewill and A. Smith, Chem. Phys. 134 (1989) 437. [3] F. Fillaux, C.J. Carlile and G.J. Kearley, ILL annual Report [1989). [4] F. Fillaux and C.J. Carlile, Phys. Rev. B 42 (1990) 5990. [5] F. Fillaux, C.J. Carlile and G.J. Kearley, Phys. Rev. B 44 (1991) 12280. [6] J.C. Cook, W. Petry, A. Heidemann and J.F. Barthelemy, Nucl. Instr. and Meth. A 312 (1992) 553. [7] K. Inoue, T. Kawaya, Y. Kiyanagi, S. Ikeda, K. Shibata, H. lwasa. T. Kawiyama, N. Watanabe and Y. Izumi, Nucl. Instr. and Meth. A 309 (1991) 294.