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Quasi-elastic light scattering in glasses
Solid State Ionics 70/7 North-Holland
SOLID STATE IOWICS
1 ( 1994)375-379
Quasi-elastic light scattering in glasses P. Benassi, A. Fontana ’ Dipartimento di Fisica, Universita’di Trento, Povo. I-38050 Trento, Italy
E. Cazzanelli Dipartimento di Fisica, Universita’della Calabria, Arcavacata di Rende, I-87036 Cosenza, Italy
Some models and experimental results relative to light scattering from disordered solids are reviewed with particular attention to the low-frequency part of the spectrum. Measurements of the low-frequency Raman scattering of superionic glasses (AgI borate glasses and AgI phosphate glasses at several AgI concentrations) and non-superionic glasses (samarium phosphate glasses containing 5 or 25% of Sm203) are presented. By comparing spectra at different temperatures, a low-frequency extra-scattering (ES) has been separated from the usual disorder-induced scattering, which, at low frequencies, is due to acoustic modes. We found that the ES is approximately Lorentzian in shape and its intensity strongly increases with rising temperature. Because these spectral features are found in both classes of samples (i.e. superionic and non-superionic glasses), it indicates that the origin of quasielastic scattering is not related to high ionic conductivity of the superionic systems as has been suggested but seems to be a general characteristic of disordered structures.
1. Introduction For many years a great deal of theoretical and experimental work has been devoted to the study of light scattering spectra of disordered solids. Disordered-Induced Light Scattering (DILS) spectra, i.e. those spectral components that are absent in perfect crystals, become important in the spectra of all solids that show some kind of microscopic disorder. In fact, because of the disorder, the k-conservation rule breaks down and each mode of the system can couple with the radiation field, giving rise to a broad spectrum. In the harmonic approximation the intensity of the DILS component Zas( o) has been generally related to the overall density of states p( w ) and to the Bose population factor n (03, T) as follows [ 1 ] :
Lp(w,T) a
n(w,T)+l
w
’ To whom correspondence 0167-2738/94/$07.00
GB(~)P(~)
.
should be addressed.
0 1994 Elsevier Science B.V. All rights reserved.
Here, a frequency-dependent coupling coefficient Cas( w) has been introduced and the indexes cr and /3 (running over x, y and z) represent the polarization components of the scattered and incident electric fields. Eq. ( 1) can be formally compared with the expression of the one-phonon incoherent neutron scattering spectrum, Zi,,( O), which in a simple Bravais cubic lattice, reads [ 2 1:
Zinc ( 0, T) a
n(o,T)
w
+ 1 P(W).
In this expression the density of states is simply multiplied by the step-up factor n(o, T) + 1 and by the normalization of the harmonic propagator 1/w, while in the light scattering case (eq. ( 1) ) the same quantities are also multiplied by a frequency-dependent coupling coefficient C&o), which measures how much the modes with frequencies close to w are active in light scattering. Cas( o) strongly determines the DILS spectral shape and, in general, it may be a rather complicated function of o. In the past years much work has been devoted to
316
P. Benassi et al. /Quasi-elastic light scattermg in glasses
the theoretical determination of the coupling coefficient Cap(o) in a variety of disordered solids. The pioneering work on this subject by Whalley was concerned with orientationally disordered crystals [ 3 1. He showed that the randomly oriented molecules generate an “electrical” disorder that is responsible for the observed broad depolarized spectra. Assuming perfect lattice vibrations and no correlation between the anisotropic polarizabilities of different molecules, he derived an u2 behaviour for Cna( w) along the entire acoustic branch. Some years later Shuker and Gammon [4] assumed that the DILS spectrum in amorphous solids could originate from the mode localization produced by structural disorder. In their work the presence of “electrical disorder” was completely ignored and the DILS spectrum was described just as a coherent spectrum somewhat broadened because of the mode localization. In 1974 Martin and Brenig [ 5 ] developed a model for light scattering in amorphous films. They described this system in terms of fluctuating elastoptic coefficients and strain tensors, assuming that modes could be represented as distorted plane waves. They used an empirical gaussian ansatz for the spatial decay of the fluctuations correlation function, and, at low frequencies, the w2 dependence of C&o) they found agrees with the Whalley’s results. Due to the finite range 1/Fof the correlation function, at higher frequencies, two different cut-offs appear in the spectrum which are related to the longitudinal and transverse sound velocities cL and cT, respectively. This model [ 51 was used with some success in interpreting data of amorphous semiconductors and superionic glasses [ 6 1. In 1991 it was shown [ 71 that in electrically disordered solids (topologically ordered) with random polarizability distribution, the light scattering spectrum can be fully predicted once the average polarizability and its fluctuation are known. All of the quoted models predict a w2 dependence of the coupling coefficient at low o so that if harmonic dynamics are assumed, the reduced spectrum as Z(o,r)w/[n(w, T)+l] can be written =c(o)p(w)Zco4. However, deviations from the predicted o4 behaviour for the low-frequency light scattering intensity in amorphous materials have been found. The
first experimental evidence was reported by Winterling [ 8 ] for amorphous silica. The anomaly consists of the presence of extra scattered intensity at low frequencies with respect to what is expected on the basis of DILS models; furthermore the extra scattering (ES) intensity increases with temperature more rapidly than does the Bose-Einstein population factor. Light scattering results together with low-temperature specific heat C,. and thermal conductivity measurements on a variety of glasses [ 91 indicate that low-energy excitations other than acoustic phonons exist in these systems, although modes of different nature may be necessary in order to explain the two kinds of phenomena. For example, Anderson et al. [ lo] and Phillips [ 111 assumed that, in glasses, atoms or groups of atoms may have more than one minimum potential energy configuration and that these configurations are separated by sufficiently low potential barriers that quantum tunneling may occur. The resulting tunneling splitting of the ground state is the low-energy extra mode that we have mentioned above. However, no microscopic description of such a “two-level-system” (TLS) was given. In any case, these modes can only account for the temperature dependence of CI,for Tless than z 1 K, and non-Debye-like behaviour is also observed in the range z lo-50 K indicating the presence of other excitations. These circumstances induced Karpov et al. [ 12 ] to extend the TLS model by considering more general potential shapes including wells with a single minimum. In this way good agreement was found with low-temperature experimental C,, data (see ref. [ 131 and references quoted therein). As regards the extra scattering, the same kind of structural defect model was used by Jackie et al. [ 141 who assumed a hopping mechanism from one minimum to the other to modulate the defect polarizability (“relaxation”); the mechanism predicts that the extra scattering is centered at zero frequency (quasi-elastic scattering) and that its width decreases with decreasing the temperature. Fleury et al. [ 151 found no evidence of the predicted narrow quasi-elastic component in amorphous silica at 4.2 K. Quantitative comparison has been made between the Jackie model and ultrasonic and Raman data in several kind of glasses [ 161. The results found indicate that models based on structural relaxation of
371
P. Benassi et al. /Quasi-elastic light scattering in glasses
intrinsic defects of the glass as a common origin for the ES and the low-temperature acoustic loss peaks fail in explaining the experimental data. The ES has been observed also in superionic systems, both glasses and disordered crystals, and several theoretical models [ 17,181 have been developed in order to describe the ES in terms of the high ionic mobility. In this paper we present light scattering data relative to several kinds of glasses which exhibit a strong ES. Measurements were performed over a wide range of temperature (4 K-C T-C 300 K) to obtain the temperature behaviour of the ES.
I
0 0
.’ 0
I
I
1
I
1
J
50
100
150 200
I
I
I
0
FREQUENCY
I
50
100
SHIFT
150 200
250
(cm-‘)
Fig. 2. Experimental low-frequency Raman spectra of ( Sm203),( P,OS), _-xat some different temperatures. On the left hand side: x=0.05, T=8 K (a), T= 160 K (b), T=293 K (c); ontherightx=0.25,T=15K(a),T=160K(b),T=300K(c).
2. Experimental Measurements were performed on superionic glasses ( AgI borate glasses and AgI phosphate glasses at several AgI concentrations) and non-superionic glasses (samarium phosphate glasses containing 5 and 25% of Sm,03 and gadolinium phosphate glasses containing 22% of Gd203). In figs. 1 and 2 we show the Raman spectra of some of the glasses at different temperatures. Beyond the obvious differences of the spectra arising from the molecular differences of the systems, a strong modification of the spectral shape is visible in all glasses at increasing temperature, which cannot be fully taken into account by the Bose population factor. As a matter of fact we found that spectra around 10 K
1
9l.lo-L-__A 6
10
2
FREQUENCY
SHIFT
100
200
(cm-‘)
Fig. 3. Log-log plot of the reduced Raman intensity in samarium phosphate glass with x=0.25 and T= 15 K. The slope of the strength line is 4.0 f 0. I. Table 1 Slopes of the low-frequency glasses at low temperature. Sample
reduced
X
Raman
T(K)
spectra
of some
slope of C(O)P(W)
(AgI)x(k#‘O~),-x (Sm20~)X(PzOS)I-, (GdzOs)x(PJ&),--x
50
0
FREQUENCY
Fig. 1. Experimental
low-frequency
3
100
50
SHIFT
Raman
(A~zOW&)O.~~ (left) and (AgI)&AgPO&.,, different temperatures.
(cm-‘)
spectra
of (AgI),,,,
(right)
atsome
well approximate cies, as expected table 1). On the w4 behaviour is tensity increases
0.55 0.05 0.25 0.22
12 8 15 9
4.0* 0.2 3.8kO.l 4.OkO.l 3.8+0.1
the o4 behaviour at low frequenfrom DILS models (see fig. 3 and contrary, at higher temperature, the lost and low-frequency spectral inmore rapidly than the Bose popu-
378
P. Benassi et al. /Quasi-elastic light scattering in glasses
lation factor. This anomalous temperature behaviour is referred to as ES [ 16,191. In order to extract the spectral shape and temperature dependence of the ES we have assumed it to be negligible at T'z 10 K, so that its shape and intensity may be obtained by comparing the reduced spectra at any given temperature T with that at T'z 10 K. In fact it is observed that above 50-60 cm-’ frequency shift the only temperature dependence of the Raman intensity derives from the Bose population factor n( o, T); so it is easy to normalize the reduced spectra measured at several temperatures in the frequency range above 50-60 cm-‘. The lower-temperature measured spectra was then subtracted from the highertemperature one and the ES spectrum at given temperature can be written as
Z(o, T)
ZES(q T)=
n(o,
x[n(w,T)+ll
Z(w, T’) T')+ 1>
T)+l-a
n(o,
>
(3)
where a is the normalization factor in the frequency range 50-60 cm-’ and T' is the lowest measured temperature. obtained for the The data (AgI),( AgP03 ) , _-x glass at two different temperatures are shown, as an example, in fig. 4. For all the systems we have examined, the results we have obtained can be summarized as follows: ( 1) The ES has a Lorentzian-like line-shape centered at zero frequency. (2) The spectral shape of the ES does not change significantly, within our experimental uncertainty,
_
-T=290K ++++TzeO
x= 0.55 K
-
15 frequency
0 shift
i
15 (cm-‘)
Fig. 4. line-shape as in (AgI)0.5,(AgP03)0.45 at different temperatures by a factor of 16 order to show the shape is same.
Table 2 FWHM of obtained in
Lorentzian-like
line-shape
of
(see text) as
_xglasses for
X
r,(cm-‘)
0.0
25+10
0.1 0.2 0.3 0.4 0.55
19*4 19t4 14+2 12.5+ I.5 11.011.2
in the temperature range we have examined. ( 3 ) The temperature dependence of the ES intensity increases more rapidly than the Bose population factor. (4) In the AgI-based glasses, the width T’, of the ES, measured at several AgI content, decreases at increasing AgI content and tends almost linearly to that measured in a-AgI. The ES spectral widths versus AgI content, are reported in table 2.
3. Discussion As far as the physical origin of the ES is concerned, in superionic systems, it could be natural to assign the ES to the polarizability modulation due to the ionic diffusion. Several theoretical models have been developed to relate the light scattering spectral shape to the fast-ion motion [ 171. However, a theoretical prediction of the scattering contributions due to the ionic diffusion is still an open problem both for crystals and for glasses; in the latter case there does not exist, to our knowledge, any realistic approach to treat the ionic diffusion in a glass. In any case, the observed temperature dependence of the spectral shape of the ES can be used in our opinion to exclude any direct scattering contribution due to the polarizability modulation of travelling ions, at least in the frequency range we have measured in our experiments (above a few wavenumbers). Indeed, within the models connecting the light scattering with the ionic motion, the spectral width of such a contribution should be expected to be strongly temperasince the diffusion coefficient ture-dependent, strongly increases with temperature. Furthermore,
P. Benassi et al. /Quasi-elastic light scattering in glasses
in the case of AgI-containing superionic glasses, a spectral broadening should be expected at increasing AgI content, which is known to induce an enhancement of the ion mobility (see ref. [ 161 and references quoted therein). Both predictions on the temperature and AgI concentration dependence are in contrast with the experimental observation, so that we are forced to rule out the hypothesis that a tight correlation between ES and ion motion exists. Finally we have to pay attention to the fact that the ES has been found also in non-superionic systems with very similar shapes and temperature dependences. This fact suggest that the origin of the ES is common to a class of disordered systems, either superionic or non-superionic. A possible explanation of the ES could be that it is related to some characteristic low-frequency excitations which would be the cause of the anomalies in the specific heat and thermal conductivity. The discussion on this argument is at present very large [ 201. Our experimental work is in progress to try to understand whether these models agree with experimental results.
References [l]F.L.GaleenerandP.N. Sen,Phys.Rev.B 17 (1978) 1928. [2] S.W. Lovesey, Theory of Neutron Scattering from Condensed Matter (Clarendon Press, Oxford, 1984). [3] E. Whalleyand J.E. Bertie, J. Chem. Phys. 64 (1967) 1264. [4] R. Shuker and R.W. Gamon, Phys. Rev. Lett. 25 (1970) 222.
319
[S] A.J. Martin and W. Brenig, Phys. Status Solidi (b) 64 (1974) 163. [6] R.J. Nemanich, Phys. Rev. B 16 (1977) 1655; G. Carini, M. Cutroni, A. Fontana, G. Mariotto and F. Rocca, Phys. Rev. B 29 (1984) 3567. [l] P. Benassi, 0. Pilla, V. Mazzacurati, M. Montagna, G. Ruocco and G. Signorelli, Phys. Rev. B 44 ( 1991) 11734. [ 81 G. Winterling, Phys. Rev. B 12 ( 1975) 2432. [ 9 ] R.C. Zeller and R.O. Pohl, Phys. Rev. B 4 ( 197 1) 2029. [IO] P.W. Anderson, B.I. Halperin and C. Varma, Philos. Mag. 25 (1972) 1. [ 111 W.A. Phillips, J. Low Temp. Phys. 7 ( 1972) 35 1. [ 12 ] V.G. Karpov, M.I. Khnger and F.N. Ignatiev, Sov. Phys. JEPT 57 (1983) 439. [ 131 U. Buchenau, Yu.M. Galperin, V.L. Gurevich and H.R. Schober, Phys. Rev. B 43 ( 1991) 5039. [ 14 ] N. Theodorakopoulos and J. JlckJe, Phys. Rev. B 14 ( 1976) 2637. [ 15 ] K_B. Lyons, P.A. Fieury, R.H. Stolen and M.A. Bosch, Phys. Rev. B 26 (1982) 7123. [ 161 P.A.M. Rodrigues, P. Benassi and A. Fontana, J. Non-Cryst. Solids 143 (1992) 274; G. Carini, M. Federico, A. Fontana and G.A. Sanders, Phys. Rev. B 47 (1993) 3005. [ 171 T. Geisel, in: Physics of Superionic Conductors, Topics in Current Physics, Vol. 15, ed. M.B. Salomon (Springer, Berlin, 1979) p. 201; W. Dieterich, T. Geisel and I. Peschel, Z. Phys. B 29 (1978) 5. [ 18 ] E. Cazzanelli, A. Fontana, G. Mariotto, V. Mazzacurati, G. Ruocco and G. Signorelli, Phys. Rev. B 28 ( 1983) 7269. [ 191 A. Fontana, G. Mariotto and F. Rocca, Phys. Status Solidi (b)129 (1985)489. [20] L. Gil, M.A. Ramos, A. Bringer and U. Buchenau, Phys. Rev. Lett. 70 ( 1993) 182; U. Buchenau, Yu.M. Galperin, V.L. Gurevich, D.A. Parshin, M.A. Ramos and H.R. Shober, Phys. Rev. B 46 (1992) 2798; D.A. Parshin, NATO Adv. Research Workshop, Les Houches, France, 16-25 Feb. 1993.
SOLID STATE IOWICS
1 ( 1994)375-379
Quasi-elastic light scattering in glasses P. Benassi, A. Fontana ’ Dipartimento di Fisica, Universita’di Trento, Povo. I-38050 Trento, Italy
E. Cazzanelli Dipartimento di Fisica, Universita’della Calabria, Arcavacata di Rende, I-87036 Cosenza, Italy
Some models and experimental results relative to light scattering from disordered solids are reviewed with particular attention to the low-frequency part of the spectrum. Measurements of the low-frequency Raman scattering of superionic glasses (AgI borate glasses and AgI phosphate glasses at several AgI concentrations) and non-superionic glasses (samarium phosphate glasses containing 5 or 25% of Sm203) are presented. By comparing spectra at different temperatures, a low-frequency extra-scattering (ES) has been separated from the usual disorder-induced scattering, which, at low frequencies, is due to acoustic modes. We found that the ES is approximately Lorentzian in shape and its intensity strongly increases with rising temperature. Because these spectral features are found in both classes of samples (i.e. superionic and non-superionic glasses), it indicates that the origin of quasielastic scattering is not related to high ionic conductivity of the superionic systems as has been suggested but seems to be a general characteristic of disordered structures.
1. Introduction For many years a great deal of theoretical and experimental work has been devoted to the study of light scattering spectra of disordered solids. Disordered-Induced Light Scattering (DILS) spectra, i.e. those spectral components that are absent in perfect crystals, become important in the spectra of all solids that show some kind of microscopic disorder. In fact, because of the disorder, the k-conservation rule breaks down and each mode of the system can couple with the radiation field, giving rise to a broad spectrum. In the harmonic approximation the intensity of the DILS component Zas( o) has been generally related to the overall density of states p( w ) and to the Bose population factor n (03, T) as follows [ 1 ] :
Lp(w,T) a
n(w,T)+l
w
’ To whom correspondence 0167-2738/94/$07.00
GB(~)P(~)
.
should be addressed.
0 1994 Elsevier Science B.V. All rights reserved.
Here, a frequency-dependent coupling coefficient Cas( w) has been introduced and the indexes cr and /3 (running over x, y and z) represent the polarization components of the scattered and incident electric fields. Eq. ( 1) can be formally compared with the expression of the one-phonon incoherent neutron scattering spectrum, Zi,,( O), which in a simple Bravais cubic lattice, reads [ 2 1:
Zinc ( 0, T) a
n(o,T)
w
+ 1 P(W).
In this expression the density of states is simply multiplied by the step-up factor n(o, T) + 1 and by the normalization of the harmonic propagator 1/w, while in the light scattering case (eq. ( 1) ) the same quantities are also multiplied by a frequency-dependent coupling coefficient C&o), which measures how much the modes with frequencies close to w are active in light scattering. Cas( o) strongly determines the DILS spectral shape and, in general, it may be a rather complicated function of o. In the past years much work has been devoted to
316
P. Benassi et al. /Quasi-elastic light scattermg in glasses
the theoretical determination of the coupling coefficient Cap(o) in a variety of disordered solids. The pioneering work on this subject by Whalley was concerned with orientationally disordered crystals [ 3 1. He showed that the randomly oriented molecules generate an “electrical” disorder that is responsible for the observed broad depolarized spectra. Assuming perfect lattice vibrations and no correlation between the anisotropic polarizabilities of different molecules, he derived an u2 behaviour for Cna( w) along the entire acoustic branch. Some years later Shuker and Gammon [4] assumed that the DILS spectrum in amorphous solids could originate from the mode localization produced by structural disorder. In their work the presence of “electrical disorder” was completely ignored and the DILS spectrum was described just as a coherent spectrum somewhat broadened because of the mode localization. In 1974 Martin and Brenig [ 5 ] developed a model for light scattering in amorphous films. They described this system in terms of fluctuating elastoptic coefficients and strain tensors, assuming that modes could be represented as distorted plane waves. They used an empirical gaussian ansatz for the spatial decay of the fluctuations correlation function, and, at low frequencies, the w2 dependence of C&o) they found agrees with the Whalley’s results. Due to the finite range 1/Fof the correlation function, at higher frequencies, two different cut-offs appear in the spectrum which are related to the longitudinal and transverse sound velocities cL and cT, respectively. This model [ 51 was used with some success in interpreting data of amorphous semiconductors and superionic glasses [ 6 1. In 1991 it was shown [ 71 that in electrically disordered solids (topologically ordered) with random polarizability distribution, the light scattering spectrum can be fully predicted once the average polarizability and its fluctuation are known. All of the quoted models predict a w2 dependence of the coupling coefficient at low o so that if harmonic dynamics are assumed, the reduced spectrum as Z(o,r)w/[n(w, T)+l] can be written =c(o)p(w)Zco4. However, deviations from the predicted o4 behaviour for the low-frequency light scattering intensity in amorphous materials have been found. The
first experimental evidence was reported by Winterling [ 8 ] for amorphous silica. The anomaly consists of the presence of extra scattered intensity at low frequencies with respect to what is expected on the basis of DILS models; furthermore the extra scattering (ES) intensity increases with temperature more rapidly than does the Bose-Einstein population factor. Light scattering results together with low-temperature specific heat C,. and thermal conductivity measurements on a variety of glasses [ 91 indicate that low-energy excitations other than acoustic phonons exist in these systems, although modes of different nature may be necessary in order to explain the two kinds of phenomena. For example, Anderson et al. [ lo] and Phillips [ 111 assumed that, in glasses, atoms or groups of atoms may have more than one minimum potential energy configuration and that these configurations are separated by sufficiently low potential barriers that quantum tunneling may occur. The resulting tunneling splitting of the ground state is the low-energy extra mode that we have mentioned above. However, no microscopic description of such a “two-level-system” (TLS) was given. In any case, these modes can only account for the temperature dependence of CI,for Tless than z 1 K, and non-Debye-like behaviour is also observed in the range z lo-50 K indicating the presence of other excitations. These circumstances induced Karpov et al. [ 12 ] to extend the TLS model by considering more general potential shapes including wells with a single minimum. In this way good agreement was found with low-temperature experimental C,, data (see ref. [ 131 and references quoted therein). As regards the extra scattering, the same kind of structural defect model was used by Jackie et al. [ 141 who assumed a hopping mechanism from one minimum to the other to modulate the defect polarizability (“relaxation”); the mechanism predicts that the extra scattering is centered at zero frequency (quasi-elastic scattering) and that its width decreases with decreasing the temperature. Fleury et al. [ 151 found no evidence of the predicted narrow quasi-elastic component in amorphous silica at 4.2 K. Quantitative comparison has been made between the Jackie model and ultrasonic and Raman data in several kind of glasses [ 161. The results found indicate that models based on structural relaxation of
371
P. Benassi et al. /Quasi-elastic light scattering in glasses
intrinsic defects of the glass as a common origin for the ES and the low-temperature acoustic loss peaks fail in explaining the experimental data. The ES has been observed also in superionic systems, both glasses and disordered crystals, and several theoretical models [ 17,181 have been developed in order to describe the ES in terms of the high ionic mobility. In this paper we present light scattering data relative to several kinds of glasses which exhibit a strong ES. Measurements were performed over a wide range of temperature (4 K-C T-C 300 K) to obtain the temperature behaviour of the ES.
I
0 0
.’ 0
I
I
1
I
1
J
50
100
150 200
I
I
I
0
FREQUENCY
I
50
100
SHIFT
150 200
250
(cm-‘)
Fig. 2. Experimental low-frequency Raman spectra of ( Sm203),( P,OS), _-xat some different temperatures. On the left hand side: x=0.05, T=8 K (a), T= 160 K (b), T=293 K (c); ontherightx=0.25,T=15K(a),T=160K(b),T=300K(c).
2. Experimental Measurements were performed on superionic glasses ( AgI borate glasses and AgI phosphate glasses at several AgI concentrations) and non-superionic glasses (samarium phosphate glasses containing 5 and 25% of Sm,03 and gadolinium phosphate glasses containing 22% of Gd203). In figs. 1 and 2 we show the Raman spectra of some of the glasses at different temperatures. Beyond the obvious differences of the spectra arising from the molecular differences of the systems, a strong modification of the spectral shape is visible in all glasses at increasing temperature, which cannot be fully taken into account by the Bose population factor. As a matter of fact we found that spectra around 10 K
1
9l.lo-L-__A 6
10
2
FREQUENCY
SHIFT
100
200
(cm-‘)
Fig. 3. Log-log plot of the reduced Raman intensity in samarium phosphate glass with x=0.25 and T= 15 K. The slope of the strength line is 4.0 f 0. I. Table 1 Slopes of the low-frequency glasses at low temperature. Sample
reduced
X
Raman
T(K)
spectra
of some
slope of C(O)P(W)
(AgI)x(k#‘O~),-x (Sm20~)X(PzOS)I-, (GdzOs)x(PJ&),--x
50
0
FREQUENCY
Fig. 1. Experimental
low-frequency
3
100
50
SHIFT
Raman
(A~zOW&)O.~~ (left) and (AgI)&AgPO&.,, different temperatures.
(cm-‘)
spectra
of (AgI),,,,
(right)
atsome
well approximate cies, as expected table 1). On the w4 behaviour is tensity increases
0.55 0.05 0.25 0.22
12 8 15 9
4.0* 0.2 3.8kO.l 4.OkO.l 3.8+0.1
the o4 behaviour at low frequenfrom DILS models (see fig. 3 and contrary, at higher temperature, the lost and low-frequency spectral inmore rapidly than the Bose popu-
378
P. Benassi et al. /Quasi-elastic light scattering in glasses
lation factor. This anomalous temperature behaviour is referred to as ES [ 16,191. In order to extract the spectral shape and temperature dependence of the ES we have assumed it to be negligible at T'z 10 K, so that its shape and intensity may be obtained by comparing the reduced spectra at any given temperature T with that at T'z 10 K. In fact it is observed that above 50-60 cm-’ frequency shift the only temperature dependence of the Raman intensity derives from the Bose population factor n( o, T); so it is easy to normalize the reduced spectra measured at several temperatures in the frequency range above 50-60 cm-‘. The lower-temperature measured spectra was then subtracted from the highertemperature one and the ES spectrum at given temperature can be written as
Z(o, T)
ZES(q T)=
n(o,
x[n(w,T)+ll
Z(w, T’) T')+ 1>
T)+l-a
n(o,
>
(3)
where a is the normalization factor in the frequency range 50-60 cm-’ and T' is the lowest measured temperature. obtained for the The data (AgI),( AgP03 ) , _-x glass at two different temperatures are shown, as an example, in fig. 4. For all the systems we have examined, the results we have obtained can be summarized as follows: ( 1) The ES has a Lorentzian-like line-shape centered at zero frequency. (2) The spectral shape of the ES does not change significantly, within our experimental uncertainty,
_
-T=290K ++++TzeO
x= 0.55 K
-
15 frequency
0 shift
i
15 (cm-‘)
Fig. 4. line-shape as in (AgI)0.5,(AgP03)0.45 at different temperatures by a factor of 16 order to show the shape is same.
Table 2 FWHM of obtained in
Lorentzian-like
line-shape
of
(see text) as
_xglasses for
X
r,(cm-‘)
0.0
25+10
0.1 0.2 0.3 0.4 0.55
19*4 19t4 14+2 12.5+ I.5 11.011.2
in the temperature range we have examined. ( 3 ) The temperature dependence of the ES intensity increases more rapidly than the Bose population factor. (4) In the AgI-based glasses, the width T’, of the ES, measured at several AgI content, decreases at increasing AgI content and tends almost linearly to that measured in a-AgI. The ES spectral widths versus AgI content, are reported in table 2.
3. Discussion As far as the physical origin of the ES is concerned, in superionic systems, it could be natural to assign the ES to the polarizability modulation due to the ionic diffusion. Several theoretical models have been developed to relate the light scattering spectral shape to the fast-ion motion [ 171. However, a theoretical prediction of the scattering contributions due to the ionic diffusion is still an open problem both for crystals and for glasses; in the latter case there does not exist, to our knowledge, any realistic approach to treat the ionic diffusion in a glass. In any case, the observed temperature dependence of the spectral shape of the ES can be used in our opinion to exclude any direct scattering contribution due to the polarizability modulation of travelling ions, at least in the frequency range we have measured in our experiments (above a few wavenumbers). Indeed, within the models connecting the light scattering with the ionic motion, the spectral width of such a contribution should be expected to be strongly temperasince the diffusion coefficient ture-dependent, strongly increases with temperature. Furthermore,
P. Benassi et al. /Quasi-elastic light scattering in glasses
in the case of AgI-containing superionic glasses, a spectral broadening should be expected at increasing AgI content, which is known to induce an enhancement of the ion mobility (see ref. [ 161 and references quoted therein). Both predictions on the temperature and AgI concentration dependence are in contrast with the experimental observation, so that we are forced to rule out the hypothesis that a tight correlation between ES and ion motion exists. Finally we have to pay attention to the fact that the ES has been found also in non-superionic systems with very similar shapes and temperature dependences. This fact suggest that the origin of the ES is common to a class of disordered systems, either superionic or non-superionic. A possible explanation of the ES could be that it is related to some characteristic low-frequency excitations which would be the cause of the anomalies in the specific heat and thermal conductivity. The discussion on this argument is at present very large [ 201. Our experimental work is in progress to try to understand whether these models agree with experimental results.
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