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Inelastic light scattering in halide glasses at high temperatures: boson peaks and the degree of disorder
J O U R N A L OF
Journal of Non-Crystalline Solids 161 (1993)173-176 North-Holland
~
'
C
~
L~I~
Inelastic light scattering in halide glasses at high temperatures: boson peaks and the degree of disorder J o h n Schroeder, Susanta K. Saha, Markus R. Silvestri, Mierie Lee and Cornelius T. M o y n i h a n Department of Physics and Materials Engineering and Center for Glass Science and Technology, Rensselaer Polytechnic Institute, Troy, N Y 12180-3590, USA
Inelastic light scattering measurements as a function of temperature were carried out for three ZrF4- or HfF4-based fluoride glass samples. The frequency regime probed is from close to the exciting line to 300 c m - 1, with a temperature range extended from ambient to above the glass transition region. The low frequency Raman scattering containing a dominant spectral line (the boson peak) is interpreted in terms of the amplitude and magnitude of the density fluctuations in the glass. The degree and range of disorder in a glass is obtained in a quantitative sense from the behaviour of the spectral form of the boson peak with temperature.
1. Introduction
In recent years inelastic light scattering experiments have contributed to our understanding of the macroscopic and microscopic physical properties of amorphous solids or glasses. Much effort has been devoted to determining the intermediate range order which can differentiate a variety of amorphous solids with similar short range order. The most important aspect of the experimental Raman spectra of glasses is the breakdown of the wave-vector selection rule for Raman scattering in crystals. This leads to a continuous and broad Raman spectrum for glasses, instead of a discrete and narrow spectrum in crystals. Shuker and Gammon [1] showed that for glasses the Stokes Raman intensity, I~v~(o3, T), at frequency, o3,
Correspondence to: Dr J. Schroeder, Departments of Physics and Center for Glass Science and Technology, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA. Tel: + 1-518 276 8408. Telefax: + 1-518 276 6680.
and at equilibrium or phonon temperature, T, is given by n(o3, T) + 1 I,~-
o5
y" b
-
b
where gb(o3) is the density of vibrational states in band b, n(o3, T) is the boson thermal occupation number, C,,t~(o~) b - is the Raman coupling constant of band b to the optical radiation field and subscripts ot[3(7~) index the incident (scattered) light polarization. Disorder in the glass network manifests itself in low frequency Raman scattering, which is a salient feature of the amorphous and vitreous states [2]. This low frequency Raman scattering peak is located in the spectral range from 20 to 80 cm -~. Due to its dependence on the Bose distribution function, this low frequency peak is often referred to as the boson peak. This boson peak is also observed in numerous liquids [3]. The spectral shape of the boson peak is the same for different glasses and does not depend markedly on their respective chemical compositions [4]. Although the boson peak is a universal characteristic of glasses, its origin is not well under-
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
174
J. Schroeder et al. / Inelastic light scattering in halide glasses at high temperatures
stood. Nemanich [5] has fitted experimental resuits to the Martin and Brenig model [6], in which the boson peak frequency depends on the maxim u m in cb(o3). Although this model describes the low frequency part of the boson p e a k very well, it fails at the high frequency end ( ~ > 03m~,). The interpretation of the boson peak in terms of the maximum in cb(~) also fails to explain the recent results of inelastic neutron scattering and heat capacity m e a s u r e m e n t s in glasses [4,7]. Duval et al. [8] have suggested a model for the boson p e a k in which they assume a non-continuous structure in the glass. The change in the density of vibrational states (DVS), which causes the R a m a n scattering in the vicinity of the boson peak, originates from the vibration of what Duval et al. call 'blobs'. According to this model, the atoms are more strongly bonded within a 'blob' than in the region separating two 'blobs'. In this sense, the 'blobs' are somewhat analogous to microcrystallites except that the 'blobs' are amorphous. In glasses, periodic atomic arrangement is violated strongly after several coordination spheres. Malinovsky and Sokolov [4] attribute the boson p e a k to the fluctuations of these micro-regions. In this paper, we present a study of the boson p e a k and other features of the R a m a n spectra of three heavy metal fluoride glasses as a function of temperature.
Boson Peak
'~
ZBIA ~
-..~
@ ~mt
N !
I
250 500 750 Raman Shift(1/cm) Fig. 1. 'Boson peaks' around 45 l/cm for ZBLAN20. ZBLA, and HBLAN20 at room temperature. An argon-ion laser (at 488 nm) and a SPEX 1403 0.85 m double grating monochromator with photon counting electronics (resolution approximately 2 c m - 1 ) were employed to collect the low frequency R a m a n spectra at a 90 ° scattering angle. For measurements above the ambient temperature, the samples were placed on a glass plate and positioned in a temperature-controlled molybdenum furnace with a t e m p e r a t u r e stability of about + I°C. The furnace had three optical windows, which made it possible to collect 90 ° scattered light. The t e m p e r a t u r e inside the furnace was monitored with a c h r o m e l - a l u m e l thermocouple positioned just beneath the sample holder.
2. Experimental aspects The heavy metal fluoride glasses ZBLA, Z B L A N 2 0 and H B L A N 2 0 used in this study were p r e p a r e d at Galileo Electro-Optics Corporation, as described in ref. [9]. The compositions and the glass transition temperatures, Tg, are given in table 1.
3. Results For all three heavy metal fluoride glass sampies, a boson peak at around 45 cm -1 was observed in the R a m a n spectrum at room temperature, as shown in fig. 1. In fig. 2, the R a m a n
Table 1 Composition (mol%) and glass transition temperature, Tg (°C), of the samples Sample name ZBLA ZBLAN20 HBLAN20
ZrF4 57 53 0
HfF4 0 0 53
BaF2 36 20 20
LaF3 3 4 4
AIF3
4 3 3
NaF 0 20 20
Tg (DSC) 306 260 269
Tg (1013p)
303 251 265
J. Schroeder et al. / Inelastic light scattering in halide glasses at high temperatures
1.0 --
~1
' '
ZBLAN20
I " " I '
'
~
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[
'
/II\ I
[ / 0.0
,:10_0
t
al
200
400
600
800
Raman Shift (l/cm)
Lo[
~ 0
*-
0
ZBLAN20
O
~t
I" I I O.D"
-~o~
o
20.0/
,
0
Fig. 2. The effect of increase in temperature on 'boson peaks'.
175
.
l'r .
'
loo
I
,
200
I
300
250C '
v
IOO
I
,
I
,
lOO
200
,
,
I 200
I
300
i 3OO
Ramn Shift [1/cm] Fig. 4. Temperature dependence of depolarization ratio.
spectra of ZBLAN20 glass are shown as a function of temperature. As the temperature increases, the low frequency Raman intensity in the vicinity of the exciting line also increases. The boson peak is highly depolarized. The depolarization ratio, IHv/Iw, in the low frequency range 20-70 cm -1 is found to be around 0.21 for HBLAN20, 0.24 for ZBLAN20 and 0.40 for ZBLA at room temperature, as shown in the plot depolarization ratio versus Raman shift in fig. 3. As temperature is increased, the depolarization ratio does not change significantly, as shown in fig. 4 for ZBLAN20 glass. For all three glasses, the most prominent vibrational Raman peak occurs at around 575 cm -1. This line is assigned with the Z r - F vibration in a six coordinated Zr 4+ [10,11].
0
'~ eg 0.6 ee
@
0.4
. i
N t_
.m
0.2
m
0
0.0 0
250 Raman
500 Shift
750
(1/cm)
Fig. 3. Depolarization ratio at room temperature.
4. Discussion
The boson peak intensity in fig. 1 is much less for the ZBLA glass than for the other two glasses, which contain NaF. As shown in fig. 2, as temperature increases, the low frequency (~b <03bo.~on peak) Raman intensity also increases. Near and slightly above the glass transition temperature, the 'light scattering excess' becomes very high by comparison with the boson peak and overlaps with the boson peak, making the peak difficult to resolve. This type of 'light scattering excess' has also been seen in other glass systems and may be explained by tunneling of structural defect states in the glass [12]. The depolarization ratio of HBLAN20 (0.24) is consistent with the theoretically calculated value of the depolarization ratio (~ 0.28) by Winterling [12] using the Martin and Brenig model [6] for the low frequency regime. It is interesting to note that the depolarization ratio of ZBLA glass (0.40) is much higher than both the theoretical prediction by Winterling [12] and the observed value for the other glasses containing NaF. As we increase the temperature from room temperature to beyond the glass transition region, the depolarization ratio does not change significantly which means that the anisotropy effects are still negligible. The vibrational Raman peaks neither change their peak position nor linewidths with increasing temperature. As the temperature increases, the effect of the very high background counts along with the 'light scattering
176
J. Schroeder et al. / Inelastic light scattering in halide glasses at high temperatures
excess' in the low frequency Raman spectra makes it difficult to do any conclusive analysis of the peak position and linewidth of the boson peak.
5. Conclusions
The low frequency boson peak is observed around 45 cm -1 in all the heavy metal fluoride glasses. As the temperature increases to close to or beyond the glass transition region, the 'light scattering excess' dominates the low frequency Raman spectrum. The boson peak is highly depolarized. The depolarization ratio of ZBLA glass (~ 0.40) is much higher than the other two glasses (~ 0.24) containing Na. As the temperature increases to the glass transition region, the vibrational Raman peak position does not change. This research was supported in part by the National Science Foundation (NSF)-USA under Grant No. MRG-DMR-88-01004.
References [1] R. Shuker and R.W. Gammon, Phys. Rev. Lett. 25 (1970) 222. [2] G.O. Karapetyan, L.V. Maksimov and O.V. Yanush, Sov. J. Glass Phys. Chem. 18 (1992) 412. [3] N.J. Tao, X.L. Chen, W.M. Du and H.Z. Cummins, Phys. Rev. A44 (1991) 6665. [4] V.K. Malinovsky and R.A.P. Sokolov, Solid State Commun. 57 (1986) 757. [5] R.J. Nemanich, Phys. Rev. B16 (1977) 1655. [6] A.J. Martin and R.W. Brenig, Phys. Status Solidi B64 (1974) 163. [7] U. Buchenau, M. Prager, N. Nucker, A.J. Dianoux, N. Ahmed and W.A. Phillips, Phys. Rev. B34 (1986) 5665. [8] E. Duval, A. Boukenter and T. Achibat, J. Phys. Cond. Matter. 2 (1990) 10227. [9] Y. Nakao and C.T. Moynihan, Mater. Sci. Forum 67&68 (1991) 187. [10] Y. Kawamoto, Phys. Chem. Glasses 25 (1984) 88. [11] G.E. Walrafen, M.S. Kokmabadi, S. Guha, P.N. Krishnam and D.C. Tran, J. Chem. Phys. 83 (1985) 4427. [12] G. Winterling, Phys. Rev. B12 (1975) 2432.
Journal of Non-Crystalline Solids 161 (1993)173-176 North-Holland
~
'
C
~
L~I~
Inelastic light scattering in halide glasses at high temperatures: boson peaks and the degree of disorder J o h n Schroeder, Susanta K. Saha, Markus R. Silvestri, Mierie Lee and Cornelius T. M o y n i h a n Department of Physics and Materials Engineering and Center for Glass Science and Technology, Rensselaer Polytechnic Institute, Troy, N Y 12180-3590, USA
Inelastic light scattering measurements as a function of temperature were carried out for three ZrF4- or HfF4-based fluoride glass samples. The frequency regime probed is from close to the exciting line to 300 c m - 1, with a temperature range extended from ambient to above the glass transition region. The low frequency Raman scattering containing a dominant spectral line (the boson peak) is interpreted in terms of the amplitude and magnitude of the density fluctuations in the glass. The degree and range of disorder in a glass is obtained in a quantitative sense from the behaviour of the spectral form of the boson peak with temperature.
1. Introduction
In recent years inelastic light scattering experiments have contributed to our understanding of the macroscopic and microscopic physical properties of amorphous solids or glasses. Much effort has been devoted to determining the intermediate range order which can differentiate a variety of amorphous solids with similar short range order. The most important aspect of the experimental Raman spectra of glasses is the breakdown of the wave-vector selection rule for Raman scattering in crystals. This leads to a continuous and broad Raman spectrum for glasses, instead of a discrete and narrow spectrum in crystals. Shuker and Gammon [1] showed that for glasses the Stokes Raman intensity, I~v~(o3, T), at frequency, o3,
Correspondence to: Dr J. Schroeder, Departments of Physics and Center for Glass Science and Technology, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA. Tel: + 1-518 276 8408. Telefax: + 1-518 276 6680.
and at equilibrium or phonon temperature, T, is given by n(o3, T) + 1 I,~-
o5
y" b
-
b
where gb(o3) is the density of vibrational states in band b, n(o3, T) is the boson thermal occupation number, C,,t~(o~) b - is the Raman coupling constant of band b to the optical radiation field and subscripts ot[3(7~) index the incident (scattered) light polarization. Disorder in the glass network manifests itself in low frequency Raman scattering, which is a salient feature of the amorphous and vitreous states [2]. This low frequency Raman scattering peak is located in the spectral range from 20 to 80 cm -~. Due to its dependence on the Bose distribution function, this low frequency peak is often referred to as the boson peak. This boson peak is also observed in numerous liquids [3]. The spectral shape of the boson peak is the same for different glasses and does not depend markedly on their respective chemical compositions [4]. Although the boson peak is a universal characteristic of glasses, its origin is not well under-
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
174
J. Schroeder et al. / Inelastic light scattering in halide glasses at high temperatures
stood. Nemanich [5] has fitted experimental resuits to the Martin and Brenig model [6], in which the boson peak frequency depends on the maxim u m in cb(o3). Although this model describes the low frequency part of the boson p e a k very well, it fails at the high frequency end ( ~ > 03m~,). The interpretation of the boson peak in terms of the maximum in cb(~) also fails to explain the recent results of inelastic neutron scattering and heat capacity m e a s u r e m e n t s in glasses [4,7]. Duval et al. [8] have suggested a model for the boson p e a k in which they assume a non-continuous structure in the glass. The change in the density of vibrational states (DVS), which causes the R a m a n scattering in the vicinity of the boson peak, originates from the vibration of what Duval et al. call 'blobs'. According to this model, the atoms are more strongly bonded within a 'blob' than in the region separating two 'blobs'. In this sense, the 'blobs' are somewhat analogous to microcrystallites except that the 'blobs' are amorphous. In glasses, periodic atomic arrangement is violated strongly after several coordination spheres. Malinovsky and Sokolov [4] attribute the boson p e a k to the fluctuations of these micro-regions. In this paper, we present a study of the boson p e a k and other features of the R a m a n spectra of three heavy metal fluoride glasses as a function of temperature.
Boson Peak
'~
ZBIA ~
-..~
@ ~mt
N !
I
250 500 750 Raman Shift(1/cm) Fig. 1. 'Boson peaks' around 45 l/cm for ZBLAN20. ZBLA, and HBLAN20 at room temperature. An argon-ion laser (at 488 nm) and a SPEX 1403 0.85 m double grating monochromator with photon counting electronics (resolution approximately 2 c m - 1 ) were employed to collect the low frequency R a m a n spectra at a 90 ° scattering angle. For measurements above the ambient temperature, the samples were placed on a glass plate and positioned in a temperature-controlled molybdenum furnace with a t e m p e r a t u r e stability of about + I°C. The furnace had three optical windows, which made it possible to collect 90 ° scattered light. The t e m p e r a t u r e inside the furnace was monitored with a c h r o m e l - a l u m e l thermocouple positioned just beneath the sample holder.
2. Experimental aspects The heavy metal fluoride glasses ZBLA, Z B L A N 2 0 and H B L A N 2 0 used in this study were p r e p a r e d at Galileo Electro-Optics Corporation, as described in ref. [9]. The compositions and the glass transition temperatures, Tg, are given in table 1.
3. Results For all three heavy metal fluoride glass sampies, a boson peak at around 45 cm -1 was observed in the R a m a n spectrum at room temperature, as shown in fig. 1. In fig. 2, the R a m a n
Table 1 Composition (mol%) and glass transition temperature, Tg (°C), of the samples Sample name ZBLA ZBLAN20 HBLAN20
ZrF4 57 53 0
HfF4 0 0 53
BaF2 36 20 20
LaF3 3 4 4
AIF3
4 3 3
NaF 0 20 20
Tg (DSC) 306 260 269
Tg (1013p)
303 251 265
J. Schroeder et al. / Inelastic light scattering in halide glasses at high temperatures
1.0 --
~1
' '
ZBLAN20
I " " I '
'
~
! '
[
'
/II\ I
[ / 0.0
,:10_0
t
al
200
400
600
800
Raman Shift (l/cm)
Lo[
~ 0
*-
0
ZBLAN20
O
~t
I" I I O.D"
-~o~
o
20.0/
,
0
Fig. 2. The effect of increase in temperature on 'boson peaks'.
175
.
l'r .
'
loo
I
,
200
I
300
250C '
v
IOO
I
,
I
,
lOO
200
,
,
I 200
I
300
i 3OO
Ramn Shift [1/cm] Fig. 4. Temperature dependence of depolarization ratio.
spectra of ZBLAN20 glass are shown as a function of temperature. As the temperature increases, the low frequency Raman intensity in the vicinity of the exciting line also increases. The boson peak is highly depolarized. The depolarization ratio, IHv/Iw, in the low frequency range 20-70 cm -1 is found to be around 0.21 for HBLAN20, 0.24 for ZBLAN20 and 0.40 for ZBLA at room temperature, as shown in the plot depolarization ratio versus Raman shift in fig. 3. As temperature is increased, the depolarization ratio does not change significantly, as shown in fig. 4 for ZBLAN20 glass. For all three glasses, the most prominent vibrational Raman peak occurs at around 575 cm -1. This line is assigned with the Z r - F vibration in a six coordinated Zr 4+ [10,11].
0
'~ eg 0.6 ee
@
0.4
. i
N t_
.m
0.2
m
0
0.0 0
250 Raman
500 Shift
750
(1/cm)
Fig. 3. Depolarization ratio at room temperature.
4. Discussion
The boson peak intensity in fig. 1 is much less for the ZBLA glass than for the other two glasses, which contain NaF. As shown in fig. 2, as temperature increases, the low frequency (~b <03bo.~on peak) Raman intensity also increases. Near and slightly above the glass transition temperature, the 'light scattering excess' becomes very high by comparison with the boson peak and overlaps with the boson peak, making the peak difficult to resolve. This type of 'light scattering excess' has also been seen in other glass systems and may be explained by tunneling of structural defect states in the glass [12]. The depolarization ratio of HBLAN20 (0.24) is consistent with the theoretically calculated value of the depolarization ratio (~ 0.28) by Winterling [12] using the Martin and Brenig model [6] for the low frequency regime. It is interesting to note that the depolarization ratio of ZBLA glass (0.40) is much higher than both the theoretical prediction by Winterling [12] and the observed value for the other glasses containing NaF. As we increase the temperature from room temperature to beyond the glass transition region, the depolarization ratio does not change significantly which means that the anisotropy effects are still negligible. The vibrational Raman peaks neither change their peak position nor linewidths with increasing temperature. As the temperature increases, the effect of the very high background counts along with the 'light scattering
176
J. Schroeder et al. / Inelastic light scattering in halide glasses at high temperatures
excess' in the low frequency Raman spectra makes it difficult to do any conclusive analysis of the peak position and linewidth of the boson peak.
5. Conclusions
The low frequency boson peak is observed around 45 cm -1 in all the heavy metal fluoride glasses. As the temperature increases to close to or beyond the glass transition region, the 'light scattering excess' dominates the low frequency Raman spectrum. The boson peak is highly depolarized. The depolarization ratio of ZBLA glass (~ 0.40) is much higher than the other two glasses (~ 0.24) containing Na. As the temperature increases to the glass transition region, the vibrational Raman peak position does not change. This research was supported in part by the National Science Foundation (NSF)-USA under Grant No. MRG-DMR-88-01004.
References [1] R. Shuker and R.W. Gammon, Phys. Rev. Lett. 25 (1970) 222. [2] G.O. Karapetyan, L.V. Maksimov and O.V. Yanush, Sov. J. Glass Phys. Chem. 18 (1992) 412. [3] N.J. Tao, X.L. Chen, W.M. Du and H.Z. Cummins, Phys. Rev. A44 (1991) 6665. [4] V.K. Malinovsky and R.A.P. Sokolov, Solid State Commun. 57 (1986) 757. [5] R.J. Nemanich, Phys. Rev. B16 (1977) 1655. [6] A.J. Martin and R.W. Brenig, Phys. Status Solidi B64 (1974) 163. [7] U. Buchenau, M. Prager, N. Nucker, A.J. Dianoux, N. Ahmed and W.A. Phillips, Phys. Rev. B34 (1986) 5665. [8] E. Duval, A. Boukenter and T. Achibat, J. Phys. Cond. Matter. 2 (1990) 10227. [9] Y. Nakao and C.T. Moynihan, Mater. Sci. Forum 67&68 (1991) 187. [10] Y. Kawamoto, Phys. Chem. Glasses 25 (1984) 88. [11] G.E. Walrafen, M.S. Kokmabadi, S. Guha, P.N. Krishnam and D.C. Tran, J. Chem. Phys. 83 (1985) 4427. [12] G. Winterling, Phys. Rev. B12 (1975) 2432.