Journal of Physics and Chemistry of Solids 61 (2000) 1973±1978
www.elsevier.nl/locate/jpcs
Photoluminescence and Raman investigations of structural transformation of fullerenes into carbon nanotubes in vacuum annealed C60/C70 1 Ni ®lms E. Czerwosz a,b,*, B. Surma c, A. Wnuk c b
a Institute of Experimental Physics, Warsaw University, Warsaw, Poland Institute of Vacuum Technology, ul. Dluga 44/50, 00-241 Warsaw, Poland c Institute of Electronic Materials Technology, Warsaw, Poland
Received 4 May 2000; accepted 17 May 2000
Abstract In this paper the luminescence and Raman investigations of structural changes undergoing in C60/C70 1 Ni ®lms annealed at vacuum are presented. Because of the annealing process of these ®lms, multishell carbon nanotubes were obtained. The structural changes occurring in the ®lms in various thermal conditions were observed by photoluminescence (PL) and Raman spectra. In room temperature Raman spectrum of air exposed ªas grownº C60/C70 1 Ni ®lms only C60 and C70 vibrational bands were found. The bands connected to graphite (,1340, 1580 and 1620 cm 21) and nanotubes (1565 cm 21) vibrations were observed in Raman spectra of annealed ®lms. In the PL spectrum of ªas grownº C60/C70 1 Ni ®lms three PL peaks were observed. In PL spectra of annealed layers (at 620 and 770 K containing nanotubes) an additional PL peak at 11,940 cm 21 was found. This peak could be attributed to a transition between vibronic states of carbon. In the PL spectra of annealed ®lms, no shift of PL peaks was observed with increasing measurement's temperature (from 6 to 300 K). q 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Fullerenes; A. Nanostructures; B. Vapour deposition; C. Raman spectroscopy; D. Luminescence
1. Introduction Photoluminescence and Raman spectroscopy are used as powerful instruments for the investigation of structural changes in many species of solid phase. Raman and luminescence spectra of C60 and C70 fullerenes in solutions and as solid samples were investigated at various temperatures by many authors. The photoluminescence (PL) spectra of C60 in solid state is attributed to electronic transition from the lowest unoccupied molecular orbital (T1u) to the highest occupied molecular orbital (Hu) and to excitons formed in periodic crystalline structure. Such electronic transition for single C60 is dipole forbidden but the luminescence in solid C60 could occur because of the Herzberg±Teller effect, * Corresponding author. Institute of Vacuum Technology, ul. Dluga 44/50, 00-241 Warsaw, Poland. Tel.: 148-22-6283031. E-mail address:
[email protected] (E. Czerwosz).
which causes vibronic mixing with higher orbitals [1±5]. In the PL spectra, phonon replicas of some vibrational modes of fullerene C60 molecules (observed in solutions as well as in solid samples) [3,4] and excitons related to impurities and defects introduced to crystal lattice [1] accompany the main PL peak. PL spectra obtained by different groups are various due to structural differences of the investigated samples. The main PL peak attributed to (T1u) ! (Hu) transition is observed at different values depending on the crystalline order in investigated samples. The energy of electronic transition attributed to this peak is of ,1.69 eV for polycrystalline C60, 1.698 eV for C60 thin ®lms and 1.65 eV for C60 polymer [1±4,6]. The broadening of PL peaks observed in PL spectra of C60 ®lms results from localisation of C60 molecule in statistically varying environment. The width of the PL peak diminishes with increasing crystalline order. The Raman spectra of C60 molecules in solid state show
0022-3697/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(00)00185-2
1974
E. Czerwosz et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1973±1978
Fig. 1. TEM image obtained by moving the C60/C70 1 Ni ®lm onto microscope mesh [10]. The image presents the multiphase structure composed of carbon nanotubes, fullerenes grains and carbon deposit around the carbon nanotubes.
their internal and external vibrational modes. The torsional motions of molecules about their axes on the lattice site and restricted translational displacements within the lattice could cause the changes in internal modes. Additionally imperfections of lattice or doping bring out to differences in spectra. For example, the frequency of Raman modes depends on the ambient atmosphere, i.e. vacuum or air atmosphere [7±9]. Oxygen can induce modi®cation of C60 crystalline structure that in¯uences the Raman spectrum, particularly C60 Ag mode (1469 cm 21) [7]. We found that Ni addition to the C60/C70 ®lm connected with vacuum annealing lead to the formation of multiphase structure with the mesoscopic phase of multishell carbon nanotubes as one of the products [10,11]. As we know this method of obtaining carbon nanotubes is a new one and the observation of structural changes during this vacuum annealing process could give the answer to the question of nanotubes formation mechanism by transformation of fullerenes. In this paper, we present results of PL and Raman spectroscopy investigations of structural changes undergoing in vacuum annealed C60/C70 1 Ni ®lms. Photoluminescence and Raman spectra show that phase transition changes of ®lm cause the appearance of new PL and Raman bands connected to structural transformation.
2. Experimental The fullerenes used in our technology were obtained by the arc method [12]. They were conditioned at the temperature of 473 K to remove the solvent's deposits. The C60/C70 mixture (8:2 weight ratio) and Ni compound were placed into separated Ta boats. They were heated (up to 573 K) and evacuated to 10 25 Torr for 2 h before the deposition process. The Mo substrate was degreased before introducing it into the vacuum chamber. The evaporation process was carried
out under the pressure of 10 25 Torr and at the temperature of 550±580 K (measured on the surface of the substrate). The deposition rate was 0.3±0.4 nm/s. After the deposition process the layers were annealed at the temperature of 620 and 770 K under the pressure of 10 25 Torr for 1.5 h. As we have shown in our previous papers [10,11] ªas grownº C60/C70 1 Ni ®lm was composed of grains of crystalline C60 (amorphous or fcc type), Ni nano- and microcrystals and loosely connected graphite planes. The structure of the ®lm annealed at temperature of 770 K contained polycrystalline fullerenes, graphite and multishell carbon nanotubes. The contents of Ni in the ®lm annealed at the temperature of 770 K were approximately 0.2 wt.%. The TEM image of the investigated ®lm annealed at the temperature of 770 K is presented in Fig. 1. The PL spectra of ®lms were measured at temperatures 6, 150 and 300 K using 488 nm line of Ar 1 laser as an excitation source, Jobin±Yvon HR460 monochromator and photomultiplier with S20 type of cathode. All spectra were measured at the same experimental conditions, i.e. the same width of slit, laser power density, photomultiplier supply and they were ®xed on the same ªcold ®ngerº stage during the one cycle of measurements. Higher sensitivity of LOCK-IN ampli®er and broader slit of monochromator was applied only to spectrum of ªas grownº ®lms. The spectra were recorded in several places within the ®lm surface to con®rm the homogeneity of the ®lms. Room temperature Raman measurements (in air atmosphere) were carried out with a triple-grating monochromator, Ar 1 laser operating at 514.5 nm line with the power density of 4 W/cm 2. The scattering geometry was 908. The analysis of PL and Raman spectra was performed with Gaussian line shape analysis of the measured spectra.
3. Results and discussion 3.1. Raman spectra In Raman spectrum of C60/C70 and of ªas grownº C60/ C70 1 Ni ®lms the vibrational frequencies characteristic for air exposed C60 and C70 ®lms were observed. We observe C60-vibrational frequencies at 270, 492, 1427, 1468, 1480 and 1575 cm 21 and some very weak C70 vibrational frequencies at 1062, 1183, 1226, 1448 and 1570 cm 21 (Fig. 2a), which frequencies are in good agreement with results obtained in Ref. [13]. Our measurements were performed in air atmosphere, so the presented spectrum is typical for the C60/C70 layer exposed to the air. Observed frequencies are different compared to the vibrational frequencies of these molecules in species placed in vacuum chamber what could be interpreted as the result of oxygen adsorption on the ®lms surface. Full width at half maximum (FWHM) and energy of Raman modes observed for C60/C70 ®lm prove that this ®lm contains mostly C60 crystalline grains with fcc type structure. The FWHM of Raman bands observed for
E. Czerwosz et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1973±1978
Fig. 2. Raman spectra of air exposed C60/C70 1 Ni ®lms deposited on Mo substrate in form of: (a) ªas grownº ®lm and ®lms annealed at temperature of (b) 620 K (c) 770 K. In the inset Gaussian line shape analysis results for Raman bands placed in 1500±1700 cm 21 spectral range are presented (wide solid line Ð experimental spectrum, thin solid line Ð ®tted line shape, dotted lines Ð Gaussian constituents of ®tted spectrum).
C60/C70 1 Ni ªas grownº ®lms are broader than for C60/C70 ®lms but they are not shifted and that could be interpreted as a result of higher disorder in the neighbourhood of C60 molecules. C60 vibrational bands dominate in Raman spectrum of the C60/C70 1 Ni ®lm annealed at the temperature of 620 K (Fig. 2). The frequencies of C60 and C70 vibrational modes remain unchanged. Their FWHM is almost unchanged. The broadening of a group of bands in the spectral region 1500± 1700 cm 21 in comparison to the spectrum of ªas grownº layer could be noticed. The very weak changes in the spectral region 1500±1700 cm 21 could be connected to the formation of vibrational bands placed at 1565 cm 21. Recently it was found for single wall fullerene like nanotube that one of Raman modes for this structure is 1567 cm 21 [14] that result could be compared with our observation.
1975
Three additional Raman bands appear in Raman spectra of the C60/C70 1 Ni ®lm annealed at the temperatures of 770 K (Fig. 2d). In the inset of Fig. 2, the Gaussian line shape ®t to the spectral region 1500±1700 cm 21 of Raman spectrum for this ®lm is presented. The results of this ®t are gathered in Table 1. Two of three ®tted Gaussian constituents (1580 and 1618 cm 21) could be attributed to glassy or amorphous carbon. Their frequencies and FWHM are consistent with the frequencies and FWHM of graphite derived bands observed for carbon materials [15±17]. As it was shown in Refs. [15±17] the FWHM of the 1580 cm 21 band becomes larger when the graphite grains becomes smaller or the disorder in the graphite structure increases. The band at 1618 cm 21 is connected the disorder induced within the graphite planar crystal structure and its frequency could be correlated to the graphite crystal planar domain size [17]. The Raman band placed at 1350 cm 21 observed in this spectrum is also connected to graphite vibrations. Usually the intensity of this band is weak and its shape is asymmetric. Its origin is similar to this of the disorder induced 1618 cm 21 band [18]. In our case, it is dif®cult to describe in detail the shape and determine the exact energy of this mode because of the existence of stronger overlapping Raman bands in this spectral range. The narrow band placed at 1565 cm 21 could be attributed to the vibrations of nanotubes. The vibrational bands for multishell and single wall carbon nanotubes were observed at 1566 and 1592 cm 21 by Holden et al. [18], by Hiura et al. [19] at 1574 cm 21 and by Rao [14] at 1567 cm 21. Differences in the measured frequencies of Raman modes of nanotubes vibrations could result from different structure of nanotubes. Nowadays it is known that frequencies of vibrational modes of single wall nanotube are dependent on the symmetry of nanotubes [14]. Generally, the symmetry of the nanotube could depend on its radius, helix angle and construction of nanotube based on hexagons only or on hexagons connected with heptagons included as a lattice imperfection. Recently the model of nanotube constructed of hexagons and heptagones and calculation of Raman frequencies for such structure was presented by Prilutski et al. [20]. In our Raman spectra of C60/C70 1 Ni vacuum annealed layers we could also expect different frequencies of bands connected to vibrations of multishell nanotubes. However as we presented in Refs. [10,11] the nanotube obtained by us by catalytic transformation of fullerenes
Table 1 Table1 Result of Gaussian line shape analysis of spectral region 1500±1700 cm 21 for C60/C70 1 Ni layer annealed at various temperatures (Dn max Ð Raman shift value in maximum of ®tted Gaussian line, G Ð FWHM of ®tted Gaussian line) Annealing temperature (K)
770
Frequencies n and G Ð FWHM for Gaussian constituents of Raman bands Dn max (cm 21)
G (cm 21)
Dn max (cm 21)
G (cm 21)
Dn max (cm 21)
G (cm 21)
1565
20
1586
56
1618
76
1976
E. Czerwosz et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1973±1978
Fig. 3. Temperature dependent PL spectra of C60/C70 1 Ni ®lm annealed at temperature of 770 K at measurement temperature: (a) 6 K; (b) 150 K; (c)300 K.
into nanotubes have almost the same helix angle what could be connected with their similar symmetry. Time-dependent Raman spectra were also measured for all samples. The ªas grownº and annealed C60/C70 1 Ni ®lms were exposed to 514, 5 nm laser beam with laser beam power density of 10 W/cm 2 for 60 min. No changes of Raman spectrum were observed during this time what suggests that no polymerisation effect occur as it was noticed for C60 ®lms in Ref. [21]. Also no polymerisation effect could be deduced from the Raman spectra of annealed ®lm for temperature range 300±620 K. Raman spectra obtained for this temperature range do not contain any signi®cant difference in Raman modes energy or FWHM. 3.2. Photoluminescence spectra PL spectra of annealed C60/C70 1 Ni ®lms at different measurement temperature (6, 150 and 300 K) do not exhibit any shifts of PL peak. The increase of PL intensity with decreasing measurement temperature results from diminishing population of temperature excited electrons in higher states. In Fig. 3 the PL spectra for C60/C70 1 Ni ®lm annealed at 770 K are presented. Temperature dependence (in the temperature range 10±150 K) of C60 ®lm was investigated by Averitt et al. [4] and the changes in PL spectra were interpreted by them as a results of phase transition occurring at the temperature of 150 K. In our case it should be noticed that no phase transition in annealed ®lms occurred due to measurement temperature changes. The 6 K PL spectra of ªas grownº and annealed (at 620 and 770 K) C60/C70 1 Ni ®lms are shown in Fig. 4. Additionally, the spectrum of C60/C70 ®lm (on Mo substrate) is
Fig. 4. 6 K PL spectra of C60/C70 1 Ni ®lms (a) ªªas grownº, annealed at the temperature of (b) 620 K (c) 770 K and d) C60/C70 ®lm.
shown in this ®gure (Fig. 4d). The intensity of PL spectra of investigated ®lms could not be compared because of various thickness of ®lms and their different phase composition. The results of Gaussian line shape analysis of these spectra are presented in Fig. 5. Numerical data concerning n (wavenumber of maximum of ®tted Gaussian line), l (wavelength of maximum for ®tted Gaussian line) and G 1/2 (FWHM of ®tted Gaussian constituents) for C60/C70 and C60/C70 1 Ni ®lms are gathered in Table 2. The Gaussian line shape analysis for PL spectrum of ªas grownº C60/C70 1 Ni ®lm is not unmistakable because of the broadening of PL peaks. Table 2 contains only approximated results obtained for this spectrum. In the PL spectra of ªas grownº and annealed C60/ C70 1 Ni ®lms the strongest PL peak shifts from ,13,600 to 13,649 cm 21 with increasing annealing temperature. For
E. Czerwosz et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1973±1978
1977
connection with the existence of mentioned traps in disordered network of C60 is more probable than their vibronic origin. It is also very probable that intensity and broadening of these PL peaks do not allow for observation of weaker effects connected to vibronic transitions in this spectral range. The P3 peak at 11,940 cm 21 is observed in the PL spectra of both annealed ®lms. The energy of this transition is the same for both annealed samples. This energy does not coincidence with any C60 vibrational mode. Such transition was not observed for any C60 crystalline type (i.e. crystal, polycrystalline, polymer or ®lms) and we suppose that this transition could be attributed to vibrations of carbon nanotubes or graphite. Taking into account the FWHM of this peak, we could suppose the vibrational origin of this peak. The band marked X is found in the PL spectra of all investigated C60/C70 1 Ni ®lms. The wavenumber, intensity and FWHM for this band are different for all ®lms (see Table 2). Such a band was also observed in the PL spectra of C60 in the form of polycrystalline ®lm or polycrystal [1,3,4]. Its origin could be connected to the surface-related exciton state in the fullerenes as it was suggested for crystalline anthracene in Refs. [23,24]. This low energetic peak is due to chemical impurities such as residual solvents, residual C70 or C60O2. On other hand this PL peak is observed for all ®lms investigated by us and its intensity decreases comparatively to the intensity of the 0±0 transition band when the annealing temperature arises. The annealing process could remove the surface adsorbed oxygen what is manifested as the decrease of the intensity of this peak (see Table 2). This observation is consistent with the conclusion about the presence of oxygen in investigated ®lms obtained from the Raman spectra.
Fig. 5. Gaussian line shape analysis results for 6 K P L spectra of (a) C60/C70 ®lm and for C60/C70 1 Ni ®lms annealed at the temperature of (b) 620 K (c) 770 K (wide solid lines Ð experimental PL spectra, thin solid lines Ð ®tted line shapes, dotted lines Ð Gaussian constituents of ®tted spectra).
C60/C70 layer relative PL peak is placed at 13,649 cm 21. This PL peak was observed for C60 polycrystalline as well as for C60 thin ®lms [1,2] and was connected with 0±0 electronic transition between molecular orbitals T1u and Hu. The FWHM of this peak remain practically identical for all investigated ®lms. This peak shifts toward higher energy for C60/C70 1 Ni ®lms annealed at the temperature of 770 K (comparatively to the relative PL peak observed for ªas grownº ®lm) and this shift could be the result of ordering of C60 grain's structure. This ordering could be connected to transformation of amorphous C60 structure to fcc type C60 structure. This effect is manifested as a shift of PL peak to the energy 13,649 cm 21 which energy was observed for C60/ C70 ®lm with fcc type structure grains. The other two peaks are described as P1 and P2 and placed in the red wing of PL spectra of annealed ®lms (see Table 2). Similar peaks were found by several authors for C60 thin ®lms and were attributed to the vibronic transition in the C60 molecule [2,3,6,22] or to C60X traps (dislocations, vacancies or impurities) [1]. The energy of these transitions for the C60/C70 ®lm is very close to the energy of relative transition in ®lms annealed at 620 K C60/ C70 1 Ni. The P1 and P2 bands in the spectrum of C60/ C70 1 Ni layer annealed at 770 K are blue shifted. In PL spectrum of ªas grownº ®lm only P1 band is found. Obtained energies of P1, P2 peaks do not coincidence with any vibrational transition in C60 molecule. Their
4. Summary The following conclusions should be taken into account: 1. The changes in Raman spectra of ªas grownº and annealed C60/C70 1 Ni ®lm show the structural transition from fullerenes to graphite and carbon nanotubes. 2. No polymerisation effect of C60 molecules was found by Raman spectroscopy.
Table 2 Result of Gaussian line shape analysis of 6 K PL spectrum of C60/C70, ªas grownº and annealed C60/C70 1 Ni layers (n Ð wavenumber of maximum of ®tted Gaussian line, G 1/2 Ð FWHM of ®tted Gaussian line) C60/C70
X1 0±0 P1 P2 P3
C60/C70 1 Ni ªas grownº
C60/C70 1 Ni annealed at 620 K
C60/C70 1 Ni annealed at 770 K
n (cm 21)
l /G 1/2 (nm)
n (cm 21)
l (nm)
n (cm 21)
l /G 1/2 (nm)
n (cm 21)
l /G 1/2 (nm)
14,297 13,649 13,033 12,364
699.45/ 18.5 732.64/ 25 767.25/30.7 808.76/44.6
14,313 13,601 13,017
698.6 735.21 768.19
14,312 13,601 13,017 12,364 11,940
698.67/ 54.7 735.21/ 24.3 768.19/30.5 808.76/30.4 837.53/33.1
14,185 13,649 13,108 12,474 11,940
704.95/ 49.8 732.64/ 25.0 762.9/31.8 801.54/32.3 837.53/33.1
1978
E. Czerwosz et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1973±1978
3. Nanosized graphite grains existence have been proved by the Raman spectra of annealed ®lms. 4. The 6 K PL spectra of all C60/C70 1 Ni and C60/C70 ®lms indicate that the 0±0 radiative transition in C60 molecules plays a dominant role in all investigated ®lms the. Despite occurring structural changes, the PL peaks attributed to other phases could not be observed. We can deduce that quantum the yield of electron transitions in C60 molecule is much higher than other vibronic transitions. 5. The X PL feature is observed in the spectra of all investigated layers and could be connected with surface adsorbed oxygen traps in polycrystalline ®lm. The annealing process removes the oxygen (because of structural changes of ®lm). This is manifested as the decrease of the intensity of this peak. Then we could suggest that the formation of nanotubes in our technology could be based on the transformation of C60 molecules through nanosized graphite to carbon nanotubes via Ni catalytic affection with carbon.
[5] [6] [7] [8] [9] [10] [11] [12] [13]
[14]
Acknowledgements We thank P. Dl¤uzÇewski for the TEM image of the C60/ C70 1 Ni ®lm containing carbon nanotube and E. Starnawska for Ni contents analysis. This work was supported by a grant from the Polish Committee of Scienti®c Research (grant number 1535/T08/97/12). References
[15] [16] [17] [18]
[19] [20]
[1] W. Guss, J. Feldmann, E.O. GoÈbel, H. Mohn, W. MuÈller, P. HaÈussler, H.-U. Meer, Phys. Rev. Lett. 72 (1994) 2644. [2] Y. Wang, J.M. Holden, A.M. Rao, P.C. Ecklund, U.D. Venkateswaren, D. Eastwood, R. Lidberg, G. Dresselhaus, M.S. Drresselhaus, Phys. Rev. B 51 (1995) 4547. [3] E. Shin, J. Park, M. Lee, D. Kim, Y.D. Suh, S.I. Yang, S.M. Jin, S.K. Kim, Chem. Phys. Lett. 209 (1993) 427. [4] R.D. Averrit, P.M. Pippenger, V.O. Papanyan, J.A. Dura,
[21] [22] [23] [24]
P. Nordlander, N.J. Halas, Chem. Phys. Lett. 242 (1995) 592. F. Negri, G. Orlandi, F. Zerbetto, J. Chem. Phys. 97 (1992) 6496. C. Wen, T. Aida, I. Honma, H. Komiyama, K. Yamada, J. Phys.: Condens. Matter 6 (1994) 160. S.J. Duclos, R.C. Haddon, S.H. Glarum, A.F. Hebard, K.B. Lyons, Solid State Commun. 80 (1991) 481. M. Matus, H. Kuzmany, E. Sohme, Phys. Rev. Lett. 68 (1992) 2822. K. Matsuishi, K. Tada, S. Onari, T. Arai, R.L. Meng, C.W. Chu, Philos. Mag. B 70 (1994) 795. E. Czerwosz, P. Dl¤uzÇewski, G. Dmowska, R. Nowakowski, E. Starnawska, H. Wronka, Appl. Surf. Sci. 141 (1999) 350. E. Czerwosz, P. Dl¤uzÇewski, R. Nowakowski, Vacuum 54 (1999) 57. W. Kratschmer, L.D. Lamb, K. Fostiropoulos, D.R. Huffman, Nature 347 (1990) 354. D.S. Bethune, G. Meijer, W.C. Tang, H.J. Rosen, W.G. Golden, H. Seki, C.A. Brown, M.S. de Vries, Chem. Phys. Lett. 179 (1991) 181. A.M. Rao, E. Richter, Sh. Bandow, B. Chase, P.C. Eklund, K.A. Williams, S. Fang, K.R. Subbaswamy, M. Menon, A. Thess, R.E. Smalley, G. Dresselhaus, M.S. Dresselhaus, Science 275 (1997) 187. R.J. Nemanich, S.A. Solin, Phys. Rev. B 20 (1979) 392. T.C. Chieu, M.S. Dresselhaus, M. Endo, Phys. Rev. B 26 (1982) 5867. L. Nikiel, P. Jagodzinski, Carbon 31 (1993) 1313. J.M. Holden, P. Zhou, X.-X. Bi, P.C. Eklund, Sh. Bandow, R.A. Jishi, K. Das Chowdhury, G. Dresselhaus, M.S. Dresselhaus, Chem. Phys. Lett. 220 (1994) 186. H. Hiura, T.W. Ebbesen, K. Tanigaki, H. Takahashi, Phys. Chem. Lett. 202 (1993) 509. Yu.I. Prilutski, S.S. Durov, A.V. Nazarenko, Phys. Status Solidi (b) 211 (1999) 213. Y. Wang, J.M. Holden, Z.-H. Dong, X.-X. Bi, P.C. Eklund, Chem. Phys. Lett. 211 (1993 ) 341. T. Ohno, K. Matsuishi, S. Onari, Solid State Commun. 101 (1996) 789. M.S. Brodin, M.A. Dudinskii, S.V. Marisova, Opt. Spectrosc. (1973) 34,651. M.R. Philpott, J.M. Turlet, J. Chem. Phys. 64 (1976) 2852.