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Saw attenuation in C60 thin films at transition temperature
Physica B 263—264 (1999) 766—768
Saw attenuation in C
thin films at transition temperature
Tsuyoshi Takase*, Yong Sun, Tatsuro Miyasato Department of Computer Science and Electronics, Kyushu Institute of Technology, Iizuka, Fukuoka 820-8502, Japan
Abstract Surface acoustic wave (SAW) attenuation of microcrystalline C film prepared by vacuum evaporation is measured in the temperature range 150—300 K. A strong attenuation is observed near the temperature of the fcc—sc transition, at about 260 K. The attenuation may be related to a thermal activated relaxation mechanism having an activation energy of about 68 meV. No thermal hysteresis in the attenuation is observed in the temperature range. 1999 Elsevier Science B.V. All rights reserved. Keywords: C ; Phase transition; SAW attenuation; Relaxation
1. Introduction As the fullerene having the highest molecular symmetry, C , continues to be a material of great interest to both experimentalists and theoreticians. It is well known that at around 260 K there is a first order phase transition between face centred cubic (high temperature) and simple cubic (low temperature) structures, as has been verified for example by NMR [1], X-ray diffraction [2] and thermal calorimetry [3,4] measurements. At temperatures below the phase transition, the detailed behaviour of the molecules is not well understood, but it is believed they tunnel between a number of inequivalent orientationally ordered sites. This motion is known to be thermally activated and several techniques have been employed in order to
* Corresponding author. Tel.: #81-948-29-7681; fax: #81948-29-7681; e-mail: [email protected].
probe the motional dynamics. Two previous ultrasonic studies related to our own were by Shi et al. [5], and Saint-Paul et al. [6]. Shi et al. measured the acoustic velocity and the attenuation of solid C by means of a vibrating reed method. However their ultrasonic frequencies of 10—20 kHz were too low to investigate microscopic features of the attenuation process. On the other hand Saint-Paul et al. used surface acoustic wave (SAW) techniques with lithium niobate transducers at frequencies up to 550 MHz. At this frequency the peak in the SAW attenuation became broad and ill-defined at temperatures approaching the sc—fcc phase transition. Surface wave studies of thin films are necessary because bulk crystals of C are rare and fragile. In our own SAW experiments reported here, using quartz transducers at lower frequencies, we were able to obtain reproducible and well-defined peaks in acoustic attenuation which gave good results from which one could determine parameters of molecular motion.
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 2 8 4 - 8
T. Takase et al. / Physica B 263—264 (1999) 766—768
767
2. Experimental Our experimental technique follows closely that used by Nakagiri et al. [7] for SAW attenuation measurements of b-alumina thin films. The SAW devices were ST cut quartz with a 80 MHz fundamental frequency, with a size typically 10 mm;30 mm;1 mm. The C thin film was deposited by vacuum evaporation directly onto the surface of a SAW transducer, and had a thickness of approximately 1000 As . The C powder used as evaporation source had 99.9% purity, and the resulting C films were polycrystal with typical grain size about 400 As . A conventional pulse echo technique was used. The pulse generator was a MATEC model 7700/765 V, operating at SAW frequencies of 80, 160 and 240 MHz, although the first harmonic 160 MHz was generated only very weakly.
3. Results and discussion The experimental data are given in Fig. 1 which shows the temperature dependence of SAW attenuation at three different frequencies on the same sample, the 80 MHz fundamental frequency, and the first and second harmonics at 160 and 240 MHz. The attenuation is defined relative to the signal amplitude at a temperature of 150 K. We note that for each frequency there is a clear peak in attenuation which occurs at approximately the same temperature, 235 K, for all frequencies. In addition the peaks are quite asymmetric with a relatively rapid fall towards 260 K, the temperature of the phase transition. At 260 K the value of the attenuation is almost the same as it was at the low temperature end of the peak. This is quite different in behaviour from the data in Ref. [6], where the attenuation continues to increase towards 260 K essentially submerging the acoustic relaxation peak. Finally the attenuation at a given temperature increases rapidly with frequency, in fact following closely a square law dependence. No thermal hysteresis was obtained. Though it is not shown in Fig. 1, because the attenuation level is much lower, the same attenuation peak and transition temperatures were also obtained with samples grown on 40 MHz fundamental-frequency quartz substrates. All these
Fig. 1. The temperature dependence of SAW relative attenuation calibrated at 150 K; ‘;’ stands for the attenuation on 80 MHz, ‘#’ for 160 MHz and ‘*’ for 240 MHz.
features of attenuation below 240 K are suggestive of Debye type relaxation which may be generally described by the following: uq , aJ 1#uq
(1)
where a is coefficient of attenuation, u is angular frequency of the SAW and q is relaxation time. When temperature is significantly lower than the relaxation peak temperature (i.e., uq'1), then Eq. (1) becomes approximately 1 aJ . q
(2)
The relaxation time q depends on sample temperature ¹, and if it is determined by an activation process q may be written as
E 1 "u exp ! , q k ¹
(3)
where u is the attempt frequency, E is activation energy and k is Boltzmann constant. If Eq. (3) replaces Eq. (2) well below the relaxation peak, then a is given by following,
E a "C exp ! , k ¹
(4)
where a , which is proportional to a, is the rela tive attenuation and C is a constant. Eq. (4) con tains the temperature dependence of the relative
768
T. Takase et al. / Physica B 263—264 (1999) 766—768
higher frequencies, in the expected manner. The answer lies in the fact that at temperatures above the phase transition the operative mechanism must totally disappear since the molecular motion is no longer orientationally frozen. The rapid decline of attenuation from the peak presumably reflects the precursor dynamics of this effect, and future SAW work with carefully selected, high quality, samples and appropriate frequencies should give much information on these effects. Fig. 2. The temperature dependence of ln (a )"ln (C )! E /k ¹ below 240 K. E "68 meV is obtained by line fitting to data for each attempt frequency.
attenuation, whilst its frequency dependence is represented by coefficient C . Fig. 2 shows the attenu ation data between 150 and 220 K on Fig. 1 fitted to Eq. (4). It is clear that data for all three frequencies are broadly consistent with the Debye model based on a single value of activation energy E ; the average of all data sets is 68 meV. This value is in good agreement with the figure of 70 meV obtained by Saint-Paul et al., but is three times smaller than that given by Shi et al. Saint-Paul et al. speculated that this discrepancy was the result of the impurities in their own sample. However, our samples which are of much higher purity than Saint Paul et al. give a similar value. It is possible however that their impurities may have given rise to the smearing effects they observed at temperatures approaching the phase transition [6]. Another experimental difference is their use of lithium niobate transducers, which has much larger dielectric and piezoelectric coupling constants, so that the large SAW amplitude might conceivably modify the C relaxation process itself. We note that the value of 68 meV is close to that calculated by La Rocca [8] who showed that the C molecule has two favoured orienta tions energetically separated by 65 meV. The frequency dependence of the attenuation prefactor is also given by Fig. 2, and found to fit well to u, thus providing further support for the Debye model, as seen from Eq. (1). Since in most respects the behaviour of the C films can be described as Debye relaxation, we need to ask why the peak temperature of the ultrasonic attenuation does not move to higher values at
4. Conclusions Using SAW techniques we have studied the ultrasonic attenuation arising from molecular motions of C in the sc, low temperature phase. We find strong Debye-type relaxation, with an activation energy of 68 meV. We also find evidence for the precursor dynamics of the structural phase transition itself into the orientationally freed regime.
Acknowledgement We acknowledge our thanks to F. Hoyose and the Center for Microelectronic Systems, KIT, for the preparation of SAW transducers, and helpful discussions with J.K. Wigmore.
References [1] R. Tycko, G. Dabbagh, R.M. Fleming, R.C. Haddon, A.V. Makhija, S.M. Zahurak, Phys. Rev. Lett. 67 (1991) 1886. [2] P.A. Heiny, J.E. Fischer, A.R. McGhie, W.J. Romanow, A.M. Denenstein, J.P. McCauley Jr., A.B. Smith, III, Phys. Rev. Lett. 66 (1991) 2911. [3] J.E. Fischer, A.R. McGhie, J.K. Estrada, M. Halus\ ka, H. Kuzmany, H.-U. ter Meer, Phys. Rev. B 53 (1996) 11 418. [4] G. Pitsi, J. Caerels, J. Thoen, Phys. Rev. B 55 (1997) 915. [5] X.D. Shi, A.R. Kortan, J.M. Williams, A.M. Kini, B.M. Savall, P.M. Chaikin, Phys. Rev. Lett. 68 (1992) 827. [6] M. Saint-Paul, M. Nu´n ez-Regueiro, R. Britel, B. Pannetier, P. Monceau, Solid State Commun. 83 (1992) 799. [7] Y. Nakagiri, K. Nobugai, F. Kanamaru, T. Miyasato, Phys. Rev. B 45 (1992) 6148. [8] G.C. La Rocca, Europhys. Lett. 25 (1994) 5.
Saw attenuation in C
thin films at transition temperature
Tsuyoshi Takase*, Yong Sun, Tatsuro Miyasato Department of Computer Science and Electronics, Kyushu Institute of Technology, Iizuka, Fukuoka 820-8502, Japan
Abstract Surface acoustic wave (SAW) attenuation of microcrystalline C film prepared by vacuum evaporation is measured in the temperature range 150—300 K. A strong attenuation is observed near the temperature of the fcc—sc transition, at about 260 K. The attenuation may be related to a thermal activated relaxation mechanism having an activation energy of about 68 meV. No thermal hysteresis in the attenuation is observed in the temperature range. 1999 Elsevier Science B.V. All rights reserved. Keywords: C ; Phase transition; SAW attenuation; Relaxation
1. Introduction As the fullerene having the highest molecular symmetry, C , continues to be a material of great interest to both experimentalists and theoreticians. It is well known that at around 260 K there is a first order phase transition between face centred cubic (high temperature) and simple cubic (low temperature) structures, as has been verified for example by NMR [1], X-ray diffraction [2] and thermal calorimetry [3,4] measurements. At temperatures below the phase transition, the detailed behaviour of the molecules is not well understood, but it is believed they tunnel between a number of inequivalent orientationally ordered sites. This motion is known to be thermally activated and several techniques have been employed in order to
* Corresponding author. Tel.: #81-948-29-7681; fax: #81948-29-7681; e-mail: [email protected].
probe the motional dynamics. Two previous ultrasonic studies related to our own were by Shi et al. [5], and Saint-Paul et al. [6]. Shi et al. measured the acoustic velocity and the attenuation of solid C by means of a vibrating reed method. However their ultrasonic frequencies of 10—20 kHz were too low to investigate microscopic features of the attenuation process. On the other hand Saint-Paul et al. used surface acoustic wave (SAW) techniques with lithium niobate transducers at frequencies up to 550 MHz. At this frequency the peak in the SAW attenuation became broad and ill-defined at temperatures approaching the sc—fcc phase transition. Surface wave studies of thin films are necessary because bulk crystals of C are rare and fragile. In our own SAW experiments reported here, using quartz transducers at lower frequencies, we were able to obtain reproducible and well-defined peaks in acoustic attenuation which gave good results from which one could determine parameters of molecular motion.
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 2 8 4 - 8
T. Takase et al. / Physica B 263—264 (1999) 766—768
767
2. Experimental Our experimental technique follows closely that used by Nakagiri et al. [7] for SAW attenuation measurements of b-alumina thin films. The SAW devices were ST cut quartz with a 80 MHz fundamental frequency, with a size typically 10 mm;30 mm;1 mm. The C thin film was deposited by vacuum evaporation directly onto the surface of a SAW transducer, and had a thickness of approximately 1000 As . The C powder used as evaporation source had 99.9% purity, and the resulting C films were polycrystal with typical grain size about 400 As . A conventional pulse echo technique was used. The pulse generator was a MATEC model 7700/765 V, operating at SAW frequencies of 80, 160 and 240 MHz, although the first harmonic 160 MHz was generated only very weakly.
3. Results and discussion The experimental data are given in Fig. 1 which shows the temperature dependence of SAW attenuation at three different frequencies on the same sample, the 80 MHz fundamental frequency, and the first and second harmonics at 160 and 240 MHz. The attenuation is defined relative to the signal amplitude at a temperature of 150 K. We note that for each frequency there is a clear peak in attenuation which occurs at approximately the same temperature, 235 K, for all frequencies. In addition the peaks are quite asymmetric with a relatively rapid fall towards 260 K, the temperature of the phase transition. At 260 K the value of the attenuation is almost the same as it was at the low temperature end of the peak. This is quite different in behaviour from the data in Ref. [6], where the attenuation continues to increase towards 260 K essentially submerging the acoustic relaxation peak. Finally the attenuation at a given temperature increases rapidly with frequency, in fact following closely a square law dependence. No thermal hysteresis was obtained. Though it is not shown in Fig. 1, because the attenuation level is much lower, the same attenuation peak and transition temperatures were also obtained with samples grown on 40 MHz fundamental-frequency quartz substrates. All these
Fig. 1. The temperature dependence of SAW relative attenuation calibrated at 150 K; ‘;’ stands for the attenuation on 80 MHz, ‘#’ for 160 MHz and ‘*’ for 240 MHz.
features of attenuation below 240 K are suggestive of Debye type relaxation which may be generally described by the following: uq , aJ 1#uq
(1)
where a is coefficient of attenuation, u is angular frequency of the SAW and q is relaxation time. When temperature is significantly lower than the relaxation peak temperature (i.e., uq'1), then Eq. (1) becomes approximately 1 aJ . q
(2)
The relaxation time q depends on sample temperature ¹, and if it is determined by an activation process q may be written as
E 1 "u exp ! , q k ¹
(3)
where u is the attempt frequency, E is activation energy and k is Boltzmann constant. If Eq. (3) replaces Eq. (2) well below the relaxation peak, then a is given by following,
E a "C exp ! , k ¹
(4)
where a , which is proportional to a, is the rela tive attenuation and C is a constant. Eq. (4) con tains the temperature dependence of the relative
768
T. Takase et al. / Physica B 263—264 (1999) 766—768
higher frequencies, in the expected manner. The answer lies in the fact that at temperatures above the phase transition the operative mechanism must totally disappear since the molecular motion is no longer orientationally frozen. The rapid decline of attenuation from the peak presumably reflects the precursor dynamics of this effect, and future SAW work with carefully selected, high quality, samples and appropriate frequencies should give much information on these effects. Fig. 2. The temperature dependence of ln (a )"ln (C )! E /k ¹ below 240 K. E "68 meV is obtained by line fitting to data for each attempt frequency.
attenuation, whilst its frequency dependence is represented by coefficient C . Fig. 2 shows the attenu ation data between 150 and 220 K on Fig. 1 fitted to Eq. (4). It is clear that data for all three frequencies are broadly consistent with the Debye model based on a single value of activation energy E ; the average of all data sets is 68 meV. This value is in good agreement with the figure of 70 meV obtained by Saint-Paul et al., but is three times smaller than that given by Shi et al. Saint-Paul et al. speculated that this discrepancy was the result of the impurities in their own sample. However, our samples which are of much higher purity than Saint Paul et al. give a similar value. It is possible however that their impurities may have given rise to the smearing effects they observed at temperatures approaching the phase transition [6]. Another experimental difference is their use of lithium niobate transducers, which has much larger dielectric and piezoelectric coupling constants, so that the large SAW amplitude might conceivably modify the C relaxation process itself. We note that the value of 68 meV is close to that calculated by La Rocca [8] who showed that the C molecule has two favoured orienta tions energetically separated by 65 meV. The frequency dependence of the attenuation prefactor is also given by Fig. 2, and found to fit well to u, thus providing further support for the Debye model, as seen from Eq. (1). Since in most respects the behaviour of the C films can be described as Debye relaxation, we need to ask why the peak temperature of the ultrasonic attenuation does not move to higher values at
4. Conclusions Using SAW techniques we have studied the ultrasonic attenuation arising from molecular motions of C in the sc, low temperature phase. We find strong Debye-type relaxation, with an activation energy of 68 meV. We also find evidence for the precursor dynamics of the structural phase transition itself into the orientationally freed regime.
Acknowledgement We acknowledge our thanks to F. Hoyose and the Center for Microelectronic Systems, KIT, for the preparation of SAW transducers, and helpful discussions with J.K. Wigmore.
References [1] R. Tycko, G. Dabbagh, R.M. Fleming, R.C. Haddon, A.V. Makhija, S.M. Zahurak, Phys. Rev. Lett. 67 (1991) 1886. [2] P.A. Heiny, J.E. Fischer, A.R. McGhie, W.J. Romanow, A.M. Denenstein, J.P. McCauley Jr., A.B. Smith, III, Phys. Rev. Lett. 66 (1991) 2911. [3] J.E. Fischer, A.R. McGhie, J.K. Estrada, M. Halus\ ka, H. Kuzmany, H.-U. ter Meer, Phys. Rev. B 53 (1996) 11 418. [4] G. Pitsi, J. Caerels, J. Thoen, Phys. Rev. B 55 (1997) 915. [5] X.D. Shi, A.R. Kortan, J.M. Williams, A.M. Kini, B.M. Savall, P.M. Chaikin, Phys. Rev. Lett. 68 (1992) 827. [6] M. Saint-Paul, M. Nu´n ez-Regueiro, R. Britel, B. Pannetier, P. Monceau, Solid State Commun. 83 (1992) 799. [7] Y. Nakagiri, K. Nobugai, F. Kanamaru, T. Miyasato, Phys. Rev. B 45 (1992) 6148. [8] G.C. La Rocca, Europhys. Lett. 25 (1994) 5.