- Email: [email protected]
Saturation of multiphonon relaxation rates of rare-earth ions in glasses and phonon localization in disordered structures
Journal of Luminescence 87}89 (2000) 598}600
Saturation of multiphonon relaxation rates of rare-earth ions in glasses and phonon localization in disordered structures F. PelleH *, F. Auzel Groupe d'Optique des Terres Rares, LPCM (UPR 211) CNRS, 1, Place Aristide Briand, 92195 Meudon Cedex, France
Abstract The e!ect of temperature on the saturation of the multiphonon relaxation rate is investigated. The relaxation rate is deduced from the decay time of the H multiplet of Tm> ions, measured from 10 K up to 550 K for di!erent excitation powers in a tellurite glass. Increasing the temperature, at "xed excitation power, the multiphonon-relaxation rate (= ) increases as usual. However, an hysteresis is observed, a discontinuity appears at 350 K due to an irreversible compositional change of the glass as con"rmed by thermal analysis. Two domains shall be considered: before (phase I) and after (phase II) the glass modi"cation. In each of these domains, at "xed excitation density, the non-radiative decay rate follows the classical law, the mediating phonon frequency remains unchanged whatever the excited state density. Applying our modi"ed model for the = dependence with the excited state density, at "xed temperature, allows to deduce the phonon di!usion length. We "nd that this critical distance is in good agreement with the glass cohesive length deduced from the boson peak recorded by Raman scattering. The results are discussed in the frame of phonon localization in disordered structures. 2000 Elsevier Science B.V. All rights reserved. Keywords: Non-radiative relaxation; Amorphous materials
1. Introduction Recently, a saturation e!ect of the multiphonon relaxation rate has been demonstrated for rare-earth (RE) ions in glasses. A model was proposed based on the simultaneous "lling of the accepting modes by excited ions lying in a common phonon bath [1}3]. Since this e!ect is not observed in crystals, the saturation of multiphonon process seems closely related to the structure of glasses where, due to the disorder, the energetic vibrations stay localized in a small volume. Here, we correlate the phonon di!usion length determined by radiationless decays with the short-range order distances estimated from the boson peak recorded in the low-frequency range by Raman scattering experiments [4]. Glasses also di!er from crystals by the thermal behavior of their thermal conductivity and phonon mean free path is shown to decrease with increasing the temperature [5]. To
* Corresponding author. Fax: 33-1-45-07-51-07-1. E-mail address: [email protected] (F. PelleH )
complete the links between our model and phonon propagation in glassy systems, we report the e!ect of excited state density on multiphonon relaxation rate as a function of temperature from 10 up to 550 K. We focus our interest on the H multiplet of Tm> ion in a tellu rite glass with an increase of the excitation density [2]. The phonon di!usion length is observed to decrease with the temperature increase in agreement with the temperature behavior of the phonon mean free path in glasses. The good agreement between both type of results supports our previous model.
2. Results and discussion 2.1. Experimental The experimental setup for decay measurements themselves are described elsewhere [2]. For this temperature study, a closed-cycle cooling device (CTI Cryogenics) is used for low temperature experiments and a Polystat 5N (Bioblock) for high temperatures. Raman spectra were
0022-2313/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 3 0 7 - 5
F. Pelle& , F. Auzel / Journal of Luminescence 87}89 (2000) 598}600
excited by Ar> ion laser emission. The scattered light was collected, at right angle, by lenses and dispersed by a triple monochromator (T800 Coderg). DTA measurements were performed with a double symmetric analyser (TAG24 Setaram) allowing simultaneous thermal and gravimetric studies. All experiments were done with a low concentrated Tm> (0.2 at%) tellurite glass (80 TeO }20Li O) to avoid contributions of energy transfer to the decay rate. The H (Tm>) multiplet is resonantly excited in order to determine exactly the excited state population (N ), taking into account the Tm> concen tration, the absorption cross section, and the power of the excitation measured at the entrance face of the sample. The decay times were measured monitoring the H PF transition to avoid any pollution of the signal by the laser radiation. The multiphonon relaxation rate (= ) is obtained, as usual, after subtracting the radiative rate, deduced by a Judd}Ofelt analysis, from the experimental decay rate.
2.2. Temperature dependence of the multiphonon relaxation rate (at xxed excited state densities) The H #uorescence decay has been recorded from 10 up to 550 K for di!erent excitation powers. For a "xed excitation power, = increases, as usual, with increasing temperature. However, the value measured at 375 K is less than the decay rate measured at 300 K. Then, increasing the temperature up to 550 K, = increases again as usual. Cooling back to 300 K, the measured value is found less than before heating the sample as shown in Fig. 1. Thermal analysis (DTA and gravimetric curves), performed from 300 up to 600 K, shows a weight loss of the glass between 320 and 360 K which explains the observed hysteresis in the temperature dependence of the decay rates due to a modi"cation of the local environment after the heating cycle. Then, two domains will be considered: below (phase I) and above (phase II) the glass modi"cation. In each of these domains, = follows the classical law (n#1), [6] with N the phonon occupation number and N the process order. The "t of experimental
Fig. 2. Multiphonon relaxation rate of H (Tm>) multiplet as a function of excited state density (䊏T"85 K; 䉬T"230 K; 䢇T"300 K; continuous lines: theoretical curves obtained using Eq. (1)).
data (continuous lines in Fig. 1) to the classical law is obtained for a mediating frequency equal respectively to 720 and 880 cm\ for phase I and phase II whatever the excitation power. 2.3. Excited state density dependence of the multiphonon relaxation rate (at xxed temperatures) The = dependence with excited state density is inves tigated from 85 up to 550 K since, below 85 K, the non-radiative process is negligible. = decreases when increasing N as shown in Fig. 2 for several temper atures. We had proposed a process to explain this behavior [1}3]. We will recall the streamlines of our approach for sake of completeness. = decreases exponentially with the energy gap for a "xed value of N . Increasing the excited state density yields, on a semi-logarithmic plot, in a set of lines of ascending slope [2]. A change of the coupled frequency could explain such a trend but the = thermal dependence (Section 2.2) does not support this assumption. We had been led by previous investigations [1}3] to the conclusion that in multiphonon nonradiative decay, the initial step, i.e. the enhancement of the non-radiative transition by the promoting modes, is insensitive to the excited state density whereas the accepting modes start being saturated. De"ning a spherical volume of radius l for phonon di!usion common at least to two nearby excited ions and assuming a RE random distribution, an average of x excited ions is found to lie within this phonon di!usion volume around one excited ion. With x "N l [1!exp(!N l )], the formula J J for non-radiative decay was shown to become [1] = "= exp[!S (2n #1)](n #1)>V , S>V , N . ; (1) [(1#x )N]! S The least-squares "t of the multiphonon decay rate as a function of N (¹ being "xed) has been performed using Eq. (1) with l (through x ) as the only free para meter (continuous lines in Fig. 2). The calculated phonon
Fig. 1. Multiphonon relaxation rate of H (Tm>) multiplet as a function of temperature (䢇 experimental data, continuous lines: theoretical curves).
599
600
F. Pelle& , F. Auzel / Journal of Luminescence 87}89 (2000) 598}600
domains using v determined at 300 K [2], equals respec tively to 11 and 14 As and for s"0.65 (mean value between linear and spherical shapes) and for s"0.8 for spherical domains. Such values are within the range of our l . 3. Conclusion Fig. 3. Phonon di!usion length derived from Eq. (1) as a function of temperature.
di!usion length (Fig. 3) decreases when increasing the temperature as expected from a thermal approach [5]. A discontinuity is again observed at 375 K in the variation of l with temperature in agreement with the glass compositional change. Our model is based on the particular phonon propagation in glasses. Because light scattering in glasses is strongly correlated at lower frequency, to the speci"c propagation of vibrations in the disordered structure, we have investigated low-frequency Raman scattering to get another independently derived link with our l . 2.4. Raman scattering Light scattering at low frequency (below 80 cm\) observed in glassy systems (boson peak) results from an excess of the vibrational density of states with respect to the Debye density of states. To interpret this excess, Duval [4] considers an inhomogeneous medium made up of cohesive domain regions separated by weakly bonded regions, then the boson vibrational frequency u is proportional to sv /¸ with s a shape factor (0.5 for Q linear domains and 0.8 for spherical ones), v the sound velocity in the host, ¸ the size of the domain [4,7]. The boson peak was recorded on Raman spectra at 47 cm\ at room temperature. The derived sizes of the cohesive
The e!ect of the temperature on the saturation of multiphonon relaxation rate of H (Tm>) multiplet in a tellurite glass has been studied between 85 up to 550 K. It is demonstrated that the phonon di!usion length is strongly correlated to the degree of order of the RE environment. This supports our "rst assumption, i.e. the bottleneck e!ect is linked to the phonon mean free path which limits the energy dissipation in disordered structures; high energetic vibrations resulting from non-radiative relaxation stay localized in small volumes.
Acknowledgements The work is partially supported by INTAS grant No. 96-0232. The authors thank Monique Genotelle for melting the samples and measuring their thermal properties, Nicole Gardant for Raman experiments and Michel Mortier for fruitful discussions.
References [1] [2] [3] [4]
F. Auzel, F. PelleH , Phys. Rev. B 55 (1997) 11 006. F. PelleH , F. Auzel, J. Opt. Soc. Am. B 15 (1998) 667. F. Auzel, F. PelleH , J. Lumin. 69 (1996) 249. E. Duval, A. Boukenter, B. Champagnon, Phys. Rev. Lett. 56 (1986) 2052. [5] R.C. Zeller, R.O. Pohl, Phy. Rev. B 35 (1987) 4067. [6] L.A. Riseberg, H.M. Moos, Phy. Rev. 174 (1968) 429. [7] E. Duval, A. Boukenter, T. Achibat, J. Phys.: Condens. Matter 2 (1990) 10 227.
Saturation of multiphonon relaxation rates of rare-earth ions in glasses and phonon localization in disordered structures F. PelleH *, F. Auzel Groupe d'Optique des Terres Rares, LPCM (UPR 211) CNRS, 1, Place Aristide Briand, 92195 Meudon Cedex, France
Abstract The e!ect of temperature on the saturation of the multiphonon relaxation rate is investigated. The relaxation rate is deduced from the decay time of the H multiplet of Tm> ions, measured from 10 K up to 550 K for di!erent excitation powers in a tellurite glass. Increasing the temperature, at "xed excitation power, the multiphonon-relaxation rate (= ) increases as usual. However, an hysteresis is observed, a discontinuity appears at 350 K due to an irreversible compositional change of the glass as con"rmed by thermal analysis. Two domains shall be considered: before (phase I) and after (phase II) the glass modi"cation. In each of these domains, at "xed excitation density, the non-radiative decay rate follows the classical law, the mediating phonon frequency remains unchanged whatever the excited state density. Applying our modi"ed model for the = dependence with the excited state density, at "xed temperature, allows to deduce the phonon di!usion length. We "nd that this critical distance is in good agreement with the glass cohesive length deduced from the boson peak recorded by Raman scattering. The results are discussed in the frame of phonon localization in disordered structures. 2000 Elsevier Science B.V. All rights reserved. Keywords: Non-radiative relaxation; Amorphous materials
1. Introduction Recently, a saturation e!ect of the multiphonon relaxation rate has been demonstrated for rare-earth (RE) ions in glasses. A model was proposed based on the simultaneous "lling of the accepting modes by excited ions lying in a common phonon bath [1}3]. Since this e!ect is not observed in crystals, the saturation of multiphonon process seems closely related to the structure of glasses where, due to the disorder, the energetic vibrations stay localized in a small volume. Here, we correlate the phonon di!usion length determined by radiationless decays with the short-range order distances estimated from the boson peak recorded in the low-frequency range by Raman scattering experiments [4]. Glasses also di!er from crystals by the thermal behavior of their thermal conductivity and phonon mean free path is shown to decrease with increasing the temperature [5]. To
* Corresponding author. Fax: 33-1-45-07-51-07-1. E-mail address: [email protected] (F. PelleH )
complete the links between our model and phonon propagation in glassy systems, we report the e!ect of excited state density on multiphonon relaxation rate as a function of temperature from 10 up to 550 K. We focus our interest on the H multiplet of Tm> ion in a tellu rite glass with an increase of the excitation density [2]. The phonon di!usion length is observed to decrease with the temperature increase in agreement with the temperature behavior of the phonon mean free path in glasses. The good agreement between both type of results supports our previous model.
2. Results and discussion 2.1. Experimental The experimental setup for decay measurements themselves are described elsewhere [2]. For this temperature study, a closed-cycle cooling device (CTI Cryogenics) is used for low temperature experiments and a Polystat 5N (Bioblock) for high temperatures. Raman spectra were
0022-2313/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 3 0 7 - 5
F. Pelle& , F. Auzel / Journal of Luminescence 87}89 (2000) 598}600
excited by Ar> ion laser emission. The scattered light was collected, at right angle, by lenses and dispersed by a triple monochromator (T800 Coderg). DTA measurements were performed with a double symmetric analyser (TAG24 Setaram) allowing simultaneous thermal and gravimetric studies. All experiments were done with a low concentrated Tm> (0.2 at%) tellurite glass (80 TeO }20Li O) to avoid contributions of energy transfer to the decay rate. The H (Tm>) multiplet is resonantly excited in order to determine exactly the excited state population (N ), taking into account the Tm> concen tration, the absorption cross section, and the power of the excitation measured at the entrance face of the sample. The decay times were measured monitoring the H PF transition to avoid any pollution of the signal by the laser radiation. The multiphonon relaxation rate (= ) is obtained, as usual, after subtracting the radiative rate, deduced by a Judd}Ofelt analysis, from the experimental decay rate.
2.2. Temperature dependence of the multiphonon relaxation rate (at xxed excited state densities) The H #uorescence decay has been recorded from 10 up to 550 K for di!erent excitation powers. For a "xed excitation power, = increases, as usual, with increasing temperature. However, the value measured at 375 K is less than the decay rate measured at 300 K. Then, increasing the temperature up to 550 K, = increases again as usual. Cooling back to 300 K, the measured value is found less than before heating the sample as shown in Fig. 1. Thermal analysis (DTA and gravimetric curves), performed from 300 up to 600 K, shows a weight loss of the glass between 320 and 360 K which explains the observed hysteresis in the temperature dependence of the decay rates due to a modi"cation of the local environment after the heating cycle. Then, two domains will be considered: below (phase I) and above (phase II) the glass modi"cation. In each of these domains, = follows the classical law (n#1), [6] with N the phonon occupation number and N the process order. The "t of experimental
Fig. 2. Multiphonon relaxation rate of H (Tm>) multiplet as a function of excited state density (䊏T"85 K; 䉬T"230 K; 䢇T"300 K; continuous lines: theoretical curves obtained using Eq. (1)).
data (continuous lines in Fig. 1) to the classical law is obtained for a mediating frequency equal respectively to 720 and 880 cm\ for phase I and phase II whatever the excitation power. 2.3. Excited state density dependence of the multiphonon relaxation rate (at xxed temperatures) The = dependence with excited state density is inves tigated from 85 up to 550 K since, below 85 K, the non-radiative process is negligible. = decreases when increasing N as shown in Fig. 2 for several temper atures. We had proposed a process to explain this behavior [1}3]. We will recall the streamlines of our approach for sake of completeness. = decreases exponentially with the energy gap for a "xed value of N . Increasing the excited state density yields, on a semi-logarithmic plot, in a set of lines of ascending slope [2]. A change of the coupled frequency could explain such a trend but the = thermal dependence (Section 2.2) does not support this assumption. We had been led by previous investigations [1}3] to the conclusion that in multiphonon nonradiative decay, the initial step, i.e. the enhancement of the non-radiative transition by the promoting modes, is insensitive to the excited state density whereas the accepting modes start being saturated. De"ning a spherical volume of radius l for phonon di!usion common at least to two nearby excited ions and assuming a RE random distribution, an average of x excited ions is found to lie within this phonon di!usion volume around one excited ion. With x "N l [1!exp(!N l )], the formula J J for non-radiative decay was shown to become [1] = "= exp[!S (2n #1)](n #1)>V , S>V , N . ; (1) [(1#x )N]! S The least-squares "t of the multiphonon decay rate as a function of N (¹ being "xed) has been performed using Eq. (1) with l (through x ) as the only free para meter (continuous lines in Fig. 2). The calculated phonon
Fig. 1. Multiphonon relaxation rate of H (Tm>) multiplet as a function of temperature (䢇 experimental data, continuous lines: theoretical curves).
599
600
F. Pelle& , F. Auzel / Journal of Luminescence 87}89 (2000) 598}600
domains using v determined at 300 K [2], equals respec tively to 11 and 14 As and for s"0.65 (mean value between linear and spherical shapes) and for s"0.8 for spherical domains. Such values are within the range of our l . 3. Conclusion Fig. 3. Phonon di!usion length derived from Eq. (1) as a function of temperature.
di!usion length (Fig. 3) decreases when increasing the temperature as expected from a thermal approach [5]. A discontinuity is again observed at 375 K in the variation of l with temperature in agreement with the glass compositional change. Our model is based on the particular phonon propagation in glasses. Because light scattering in glasses is strongly correlated at lower frequency, to the speci"c propagation of vibrations in the disordered structure, we have investigated low-frequency Raman scattering to get another independently derived link with our l . 2.4. Raman scattering Light scattering at low frequency (below 80 cm\) observed in glassy systems (boson peak) results from an excess of the vibrational density of states with respect to the Debye density of states. To interpret this excess, Duval [4] considers an inhomogeneous medium made up of cohesive domain regions separated by weakly bonded regions, then the boson vibrational frequency u is proportional to sv /¸ with s a shape factor (0.5 for Q linear domains and 0.8 for spherical ones), v the sound velocity in the host, ¸ the size of the domain [4,7]. The boson peak was recorded on Raman spectra at 47 cm\ at room temperature. The derived sizes of the cohesive
The e!ect of the temperature on the saturation of multiphonon relaxation rate of H (Tm>) multiplet in a tellurite glass has been studied between 85 up to 550 K. It is demonstrated that the phonon di!usion length is strongly correlated to the degree of order of the RE environment. This supports our "rst assumption, i.e. the bottleneck e!ect is linked to the phonon mean free path which limits the energy dissipation in disordered structures; high energetic vibrations resulting from non-radiative relaxation stay localized in small volumes.
Acknowledgements The work is partially supported by INTAS grant No. 96-0232. The authors thank Monique Genotelle for melting the samples and measuring their thermal properties, Nicole Gardant for Raman experiments and Michel Mortier for fruitful discussions.
References [1] [2] [3] [4]
F. Auzel, F. PelleH , Phys. Rev. B 55 (1997) 11 006. F. PelleH , F. Auzel, J. Opt. Soc. Am. B 15 (1998) 667. F. Auzel, F. PelleH , J. Lumin. 69 (1996) 249. E. Duval, A. Boukenter, B. Champagnon, Phys. Rev. Lett. 56 (1986) 2052. [5] R.C. Zeller, R.O. Pohl, Phy. Rev. B 35 (1987) 4067. [6] L.A. Riseberg, H.M. Moos, Phy. Rev. 174 (1968) 429. [7] E. Duval, A. Boukenter, T. Achibat, J. Phys.: Condens. Matter 2 (1990) 10 227.