- Email: [email protected]
Independently relaxing nanoscale inhomogeneities as a model for structural relaxation: light scattering around the glass transition region
JOURNAL
ELSEVIER
O l~
Journal of Non-Crystalline Solids 203 (1996) 186-191
Independently relaxing nanoscale inhomogeneities as a model for structural relaxation: light scattering around the glass transition region J. Schroeder a,*, M. Lee a, S.K. Saha a, J.H Whang
b, C.T.
Moynihan b
a Department of Physics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA b Department of Materials Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
Abstract
Recent observations of anomalous light scattering (Rayleigh, Brillouin and Raman) and small angle X-ray scattering in the glass transition region indicate that the apparent distribution of structural relaxation times corresponds to a physical distribution of nanoscale inhomogeneities (density fluctuations) with varying properties. A modified version of the Tool-Narayanaswamy model, in agreement with this feature, has been developed. Examples from halide glasses will be discussed. The measurement of the boson peaks in glasses and their interpretation with respect to density fluctuations is presented. The range and degree of disorder in a glass is obtained in a quantitative fashion from the behavior of the spectral form of the boson peaks with temperature.
1. Introduction
The process of establishing equilibrium in a system is known as a relaxation process. A sudden change in temperature or pressure upsets the equilibrium values of certain properties of a liquid such as specific volume, viscosity, enthalpy and index of refraction. This causes a rapid change in the properties of a liquid, followed by a slower approach to new equilibrium values. Structural relaxation is the kinetically impeded rearrangement of the structure of a liquid in response to changes in external variables
* Corresponding author. Tel.: + 1-518 276 8408; fax: + 1-518 276 6680; e-mail: [email protected].
such as temperature or pressure [1], and is commonly associated with the glass transition. A plot of a property such as the specific volume, enthalpy or refractive index (v, H, or n, respectively) versus temperature for heating and cooling reveals a hysteresis in the glass transition region. This broken reversibility is the absence of a reversible transition between non-equilibrium and equilibrium states [2]. It is the aim of this paper to achieve a better understanding of the glassy state and structural relaxation by applying Rayleigh scattering, Brillouin scattering and Raman scattering techniques to several glasses as they are heated and cooled through the glass transition region. The Rayleigh and Brillouin scattering spectrum of a glass provides information
0022-3093/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 ( 9 6 ) 0 0 5 0 0 - 5
J. Schroeder et at/Journal of Non-Crystalline Solids 203 (1996) 186-191
on the non-propagating diffusive fluctuations and propagating fluctuations, respectively. Fluctuations in density (entropy) or composition (mass) for a multicomponent system belong to the first category, whereas the second category, namely, the propagating fluctuations, are pressure variations that manifest themselves as acoustic waves. The principal measurement which characterizes the microinhomogeneity of a medium is the Landau-Placzek (LP) ratio defined by RLp = I R / 2 I B : I R is Rayleigh scattering intensity at the frequency of incident light, and I B is the frequency shifted Brillouin scattering peak due to acoustic phonons. Any local deviation from lattice periodicity leads to the localization of vibrations. Disorder in the glassy network manifests itself in the boson peak low frequency region of the Raman scattering spectrum, which is a salient feature of the amorphous or vitreous states [3]. Duvai et al. [4] have suggested a model for the boson peak in which they assume a non-continuous structure in the glass. The change in the density of vibrational states, which causes the Raman scattering in the vicinity of the boson peak, originates from the vibration of what Duval et al. call 'blobs'. Duval and co-workers [4-6] have interpreted inelastic neutron scattering and Raman scattering boson peak results for inorganic glasses and polymers as indicating discontinuities in the glass structure corresponding to regions (blobs) 2-5 nm in size. Malinovsky and Sokolov [7] attribute the boson peak to the fluctuations of these microregions. Malinovsky and Sokolov [7] and Sokolov et al. [8] have estimated sizes in the range 1.5-3.0 nm for structural density fluctuations responsible for the low frequency boson peak in the Raman spectra of polymers and various oxide glasses, including B203. The detection of a low frequency boson peak in the Raman scattering in glasses may correlate with the anomalous behavior found in the Rayleigh and Brillouin light scattering measurements of certain glasses in the glass transition region.
2. Experimental aspects The heavy metal fluoride glasses ZBLA, ZBLAN20 and HBLAN20 used in this study were prepared in our laboratory and at Galileo Electro-
187
Landau-Placzek Ratio 25 ¸ ZBLA
24"
I
O Heating
~
•
Cooling
23
._1
22
/ 2.1
20 501
:
5i0
6;0
650
Temp(K) Fig. 1. Comparison of Landau-Placzek ratio curves for heating and coolingof ZBLA. Optics as described in Ref. [9]. The glass transition temperatures of ZBLA, ZBLAN20 and HBLAN20 are, respectively, 306°C, 260°C and 269°C. Their compositions are given in Refs. [10,11]. The Landau-Placzek ratio, RLp, was measured during heating and cooling of ZBLA and ZBLAN20 glasses through the transition region. To achieve a small line width of about 20 MHz in the incident light beam, an etalon was placed into the argon-ion laser, which was operating at 488 nm. The scattered light was collected at 90 ° and analyzed with a threepass Fabry-Perot interferometer housed in a thermally stabilized box. The light then, after passing a spatial and spike filter, was detected by a cooled ( - 20°C) photomultiplier tube (PMT) (ITT FW-130) with a dark count of approximately 0.5 counts/s. A Burleigh DAS-1 system drove the Fabry-Perot and collected the signals from the PMT, which were later transferred to an MS-DOS computer system for further analysis. Low-frequency Raman and Raman scattering were also measured during heating and cooling of a HBLAN20 glass through the transition region. An argon-ion laser (at 488 nm) and 0.85 m double grating monochromater (SPEX 1403) with photon
J. Schroeder et al. / Journal of Non-Crystalline Solids 203 (1996) 186-191
188
Landau.Placzek
Ratio
peak and subsequent decrease followed by a gradual increase in the LP ratio which may be a universal feature of glass-forming liquids. The cooling curve
ZBLAN20 90"
Longitudinal 18.0"
C,
(a)
Shift
ZBLA
70' 17.5
50 17.0 T
30 300
g.~ 500
400
•
16.5
600
\
Temp(K) Fig. 2. Landau-Placzek ratio, RLp, versus temperature during heating of ZBLAN20 glass through the transition region.
16.0 200
Fig. 1 compares the LP ratio curves for heating and cooling of ZBLA samples. During heating of the ZBLA glass the LP ratio decreases with increasing temperature up to the glass transition temperature at which the LP ratio appears to be a minimum. The LP ratio then increases with a local maximum in the glass transition region. Similar anomalous behavior has been observed in Bokov and Andreev's study [12] and in Golubkov's small angle X-ray scattering experiments on B203 glass [13]. It appears that anomalous scattering in the transition region has a
400
500
600
700
Temp(K)
counting electronics (resolution approximately 2 cm -1 ) were employed at a 90 ° scattering angle. For all measurements above the ambient temperature, the samples were placed on a glass plate and positioned in a temperature controlled molybdenum furnace with temperature stability of about _ I°C. The furnace had three optical windows, which made it possible to collect 90 ° scattered light. The temperature inside the furnace was monitored with a chromel-alumel thermocouple positioned just beneath the sample holder.
3. Results
300
Longitudinal
19
(b)
Shift
ZBLAN20
18 ¸
r~
17' T8
200
3~0
4~0
500
600
Temp(K) Fig. 3. (a) Longitudinal Brillouin shift of ZBLA as function of temperature during heating. The line is drawn as a guide for the eye. (b) Longitudinal Brillouin shift of ZBLAN20 as function of temperature during heating. The line is drawn as a guide for the eye.
J. Schroeder et al. / Journal of Non-C~stalline Solids 203 (1996) 186-191 Brillouin
Linewidth
200
189
(a)
ZBLA o
Heating
•
Cooling
= k
.
r-
A~ k.
rg
2
5o0
5;0
\
=
100
200
65o Raman Shift (lJcm)
Temp(K) Fig. 4. Comparision of total Brillouin linewidth curves for heating and cooling of ZBLA.
does not strictly follow the heating curve but it displays a hysteresis effect. The cooling curve has two peaks of much smaller intensities than the heating peak in the glass transition region and follows the heating curve below Tg. Anomalous behavior of the LP ratio in the glass transition region of ZBLAN20 is also seen in Fig. 2. Again the LP ratio decreases up to the glass transition region temperature and then increases with an anomalous peak in the glass transition region. Fig. 3(a) and (b) show the longitudinal Brillouin shift of ZBLA and ZBLAN20, respectively, as a function of temperature during heating in which we observe a marked change in slope near Tg. The shifts at room temperature are approximately 17.4 GHz for ZBLA and 18.2 GHz for ZBLAN20 and decrease, monotonically, with increasing temperature, whereas in the glass transition region the shifts decrease more rapidly for both samples. The measurement of the Brillouin shifts allows the calculation of Che sound velocity, provided the refractive index of the material is known [t4]. Fig. 4 compares Brillouin linewidth curves for heating and cooling of ZBLA. This graph shows
(bi
28oo
. . . . . . . . . .
il o
,
0
,
i
200
,
,
i
,
400
,
i
600
,
,
800
Raman Shift (1/cm) Fig. 5. (a) Raman spectra showing boson peaks during heating of HBLAN20 glass through the glass transition region with uppermost trace at 550.5 K, the next at 533 K, then 450 K and the lowest at 301 K, Tg = 542 K. (b) Raman spectra during cooling of HBLAN20 with uppermost trace at 550 K, the intermediate trace at 483 K and the lowest trace at 301 K, Tg = 542 K.
small fluctuations of the Brillouin linewidth in the glass transition region. These fluctuations are within the accuracy of the measurement,
190
Z Schroeder et al. / Journal of Non-Crystalline Solids 203 (1996) 186-191
In Fig. 5(a) and (b) the Raman spectra of HBLAN20 glass during heating and cooling are shown, respectively, as a function of temperature. The low frequency boson peak and the most prominent vibrational Raman peak are observed around 45 cm -1 and 575 cm -~, respectively. No hysteresis effect is observed for heating and cooling in the low frequency Raman scattering. It has been found that the broad spectral feature of the boson peak is the same for different glasses and is independent of their chemical composition. The size of ordered microregions, or the structural correlation range, can be estimated from the position of the low frequency boson peak and the sound velocity determined by the Brillouin shift [7,8,15,16].
4. Discussion
In the previous paper [11] we reported the depolarization ratios (the ratios of the intensities of depolarized to polarized light scattering spectra), IHv/Ivv, for ZBLA, ZBLAN20, and HBLAN20 from the Raman scattering measurements. The depolarization ratio of ZBLA glass ( ~ 0.40 in the low frequency range 20-70 cm- 1) was much higher than both the theoretical prediction by Winterling [17] using the Martin and Brenig (MB) model [18] and the observed value for the other glasses containing NaF. In Ref. [19] the authors presented a comparison of the MB predictions with their experimental results of the low-frequency Raman scattering study. The observed depolarization ratios for some fragile glass formers were ~ 3 / 4 , while the MB predictions for to ~ 0 were 0.14-0.27, consistently too small. Only quartz glass gave reasonable agreement, however, the MB model predicts a fairly strong frequency dependence for all these materials including quartz, which they did not observe. A similar disagreement was noted by Nemanich [20] for several chalcogenide glasses. It seems that good glass formers show reasonable agreement with the MB predictions for the depolarization ratio for to ~ O, however, fragile glass formers show poor agreement. The behavior of the Landau-Placzek ratio above and below Tg is explained by variations in density (entropy) fluctuations or specific volume fluctuations. It is evident that the actual magnitude of the
distribution of relaxation times depends strongly on the size of the independently relaxing regions as noted by Moynihan and Schroeder [1] and Donth [21]. The experimental values of the distribution of relaxation times demand regions which are typically a few nm across [4-8,13]. At temperatures in the glass transition, a growth in the magnitude of the density fluctuations is caused by structural relaxations of these nanoscale inhomogeneities whereas in the glassy state, below Tg, the nanoscale inhomogeneities are frozen-in and rearrangements are impossible. These regions behave as the disordered lattice at a higher temperature [13]. Therefore, the regions are causing an additional increase in the Rayleigh intensity which produces the anomalous peak in the Landau-Placzek ratio curves. This additional intensity decreases with further increase in the temperature as the transition from the glassy state to the liquid state reaches equilibrium values. In addition, at high temperatures there is an uncoupling of propagating and non-propagating modes. The changing structure may decrease the coordination number of the Zr 4+ complexes, affecting the sound velocity such that both the isothermal and adiabatic compressibilities are affected. From Fig. 3(a) and (b) it is evident that this effect manifests itself in a decrease of the Brillouin shift as Tg is traversed. 5. Conclusions
Rayleigh and Brillouin scattering techniques have been applied to two fluoride glasses, ZBLA and ZBLAN20, and Raman scattering technique has been applied to HBLAN20 glass during heating and cooling through the glass transition region. Anomalous behavior is observed in the glass transition region for the Landau-Placzek ratio and a hysteresis effect is also observed for heating versus cooling. The interpretation of these results offer some solid evidence as to the physical origin of the non-exponential character of structural relaxation kinetics in terms of independently relaxing nanoscale inhomogeneities. We feel that the arguments discussed here are of sufficient validity to account qualitatively for the anomalous light scattering. The low frequency broad peak of the Raman spectra, the so-called boson peak, is observed for
J. Schroeder et aL / Journal of Non-Crystalline Solids 203 (1996) 186-191
H B L A N 2 0 glass during heating and cooling. The hysteresis effect w h i c h is o b s e r v e d in the R a y l e i g h scattering (diffusive m o d e ) is not f o u n d in the l o w f r e q u e n c y R a m a n scattering (vibrational m o d e ) for heating and cooling. The b o s o n p e a k in R a m a n scattering permits to d e t e r m i n e the structural correlation length and is c o n s i d e r e d a typical sign o f interm e d i a t e - r a n g e order in glasses.
Acknowledgements The authors gratefully a c k n o w l e d g e the partial support o f this w o r k by the National S c i e n c e Foundation under Grant No. D M R - 8 8 - 0 1 0 0 4 .
References [1] C.T. Moynihan and J. Schroeder, J. Non-Cryst. Solids 160 (1993) 52. [2] S.V. Nemilov, Sov. J. Glass Phys. Chem. 15 (1989) 305. [3] G.O. Karapetyan, L.V. Maksimov and O.V. Yanush, Soy. J. Glass Phys. Chem. 18 (1992) 412. [4] E. Duval, A. Boukenter and T. Achibat, J. Phys. Condens. Matter 2 (1990) 10227. [5] T. Achibat, A. Boukenter, E. Duval, G, Lorentz and S. Etienne, J. Chem. Phys. 95 (1991) 2949.
191
[6] E. Duval, A. Boukenter, T. Achibat and B. Champagnon, in: The Physics of Non-Crystalline Solids, ed. L. D. Pye, W.C. LaCourse and H.J. Stevens (Taylor and Francis, Washington, DC, 1992) p. 82. [7] V.K. Malinovsky and A.P. Sokolov, Solid State Commun. 57 (1986) 757. [8] A.P.Sokolov, A. Kisliuk, M. Soltwisch and D. Quitmann, Phys. Rev. Lett. 69 (1992) 1540. [9] Y. Nakao and C.T. Moynihan, Mater. Sci. Forum 67&68 (1991) 187. [10] J. Schroeder, L.G. Hwa, X. S. Zhao, L. Busse and I. Aggarwal, in: Proc. 6th Int. Halide Glass Conference, Clausthal, Germany, Oct. 1989; L.-G. Hwa, PhD thesis, Rensselaer Polytechnic Institute (1989). [11] J. Schroeder, S.K. Saha, M.R. Silvestri, M. Lee and C.T. Moynihan, J. Non-Cryst. Solids 161 (1993) 173. [12] N.A. Bokov and N.S. Andreev, Soy. J. Glass Phys. Chem. 15 (1989) 243. [13] V.V. Golukov, Soy. J. Glass Phys. Chem. 15 (1989) 280. [14] L. Brillouin, Ann. Phys. (Paris) 17 (1922) 88. [15] E. Duval, A. Boukenter and B. Champagnon, Phys. Rev. Lett. 56 (1986) 2052. [16] V.K. Malinovsky, V.N. Novikov, A.P. Sokolov and V.G. Dodonov, Solid State Commun. 65 (1988) 681. [17] G. Wintering, Phys. Rev. B12 (1975) 2432. [18] A.J. Martin and R.W. Brenig, Phys. Status Solidi B64 (1974) 163. [19] N.J. Tao, G. Li, X. Chen, W.M. Du and H.Z. Cummins, Phys. Rev. A44 (1991) 6665. [20] R.J. Nemanich, Phys. Rev. B16 (1977) 1655. [21] E. Donth, J. Non-Cryst. Solids 53 (1982) 325.
ELSEVIER
O l~
Journal of Non-Crystalline Solids 203 (1996) 186-191
Independently relaxing nanoscale inhomogeneities as a model for structural relaxation: light scattering around the glass transition region J. Schroeder a,*, M. Lee a, S.K. Saha a, J.H Whang
b, C.T.
Moynihan b
a Department of Physics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA b Department of Materials Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
Abstract
Recent observations of anomalous light scattering (Rayleigh, Brillouin and Raman) and small angle X-ray scattering in the glass transition region indicate that the apparent distribution of structural relaxation times corresponds to a physical distribution of nanoscale inhomogeneities (density fluctuations) with varying properties. A modified version of the Tool-Narayanaswamy model, in agreement with this feature, has been developed. Examples from halide glasses will be discussed. The measurement of the boson peaks in glasses and their interpretation with respect to density fluctuations is presented. The range and degree of disorder in a glass is obtained in a quantitative fashion from the behavior of the spectral form of the boson peaks with temperature.
1. Introduction
The process of establishing equilibrium in a system is known as a relaxation process. A sudden change in temperature or pressure upsets the equilibrium values of certain properties of a liquid such as specific volume, viscosity, enthalpy and index of refraction. This causes a rapid change in the properties of a liquid, followed by a slower approach to new equilibrium values. Structural relaxation is the kinetically impeded rearrangement of the structure of a liquid in response to changes in external variables
* Corresponding author. Tel.: + 1-518 276 8408; fax: + 1-518 276 6680; e-mail: [email protected].
such as temperature or pressure [1], and is commonly associated with the glass transition. A plot of a property such as the specific volume, enthalpy or refractive index (v, H, or n, respectively) versus temperature for heating and cooling reveals a hysteresis in the glass transition region. This broken reversibility is the absence of a reversible transition between non-equilibrium and equilibrium states [2]. It is the aim of this paper to achieve a better understanding of the glassy state and structural relaxation by applying Rayleigh scattering, Brillouin scattering and Raman scattering techniques to several glasses as they are heated and cooled through the glass transition region. The Rayleigh and Brillouin scattering spectrum of a glass provides information
0022-3093/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 ( 9 6 ) 0 0 5 0 0 - 5
J. Schroeder et at/Journal of Non-Crystalline Solids 203 (1996) 186-191
on the non-propagating diffusive fluctuations and propagating fluctuations, respectively. Fluctuations in density (entropy) or composition (mass) for a multicomponent system belong to the first category, whereas the second category, namely, the propagating fluctuations, are pressure variations that manifest themselves as acoustic waves. The principal measurement which characterizes the microinhomogeneity of a medium is the Landau-Placzek (LP) ratio defined by RLp = I R / 2 I B : I R is Rayleigh scattering intensity at the frequency of incident light, and I B is the frequency shifted Brillouin scattering peak due to acoustic phonons. Any local deviation from lattice periodicity leads to the localization of vibrations. Disorder in the glassy network manifests itself in the boson peak low frequency region of the Raman scattering spectrum, which is a salient feature of the amorphous or vitreous states [3]. Duvai et al. [4] have suggested a model for the boson peak in which they assume a non-continuous structure in the glass. The change in the density of vibrational states, which causes the Raman scattering in the vicinity of the boson peak, originates from the vibration of what Duval et al. call 'blobs'. Duval and co-workers [4-6] have interpreted inelastic neutron scattering and Raman scattering boson peak results for inorganic glasses and polymers as indicating discontinuities in the glass structure corresponding to regions (blobs) 2-5 nm in size. Malinovsky and Sokolov [7] attribute the boson peak to the fluctuations of these microregions. Malinovsky and Sokolov [7] and Sokolov et al. [8] have estimated sizes in the range 1.5-3.0 nm for structural density fluctuations responsible for the low frequency boson peak in the Raman spectra of polymers and various oxide glasses, including B203. The detection of a low frequency boson peak in the Raman scattering in glasses may correlate with the anomalous behavior found in the Rayleigh and Brillouin light scattering measurements of certain glasses in the glass transition region.
2. Experimental aspects The heavy metal fluoride glasses ZBLA, ZBLAN20 and HBLAN20 used in this study were prepared in our laboratory and at Galileo Electro-
187
Landau-Placzek Ratio 25 ¸ ZBLA
24"
I
O Heating
~
•
Cooling
23
._1
22
/ 2.1
20 501
:
5i0
6;0
650
Temp(K) Fig. 1. Comparison of Landau-Placzek ratio curves for heating and coolingof ZBLA. Optics as described in Ref. [9]. The glass transition temperatures of ZBLA, ZBLAN20 and HBLAN20 are, respectively, 306°C, 260°C and 269°C. Their compositions are given in Refs. [10,11]. The Landau-Placzek ratio, RLp, was measured during heating and cooling of ZBLA and ZBLAN20 glasses through the transition region. To achieve a small line width of about 20 MHz in the incident light beam, an etalon was placed into the argon-ion laser, which was operating at 488 nm. The scattered light was collected at 90 ° and analyzed with a threepass Fabry-Perot interferometer housed in a thermally stabilized box. The light then, after passing a spatial and spike filter, was detected by a cooled ( - 20°C) photomultiplier tube (PMT) (ITT FW-130) with a dark count of approximately 0.5 counts/s. A Burleigh DAS-1 system drove the Fabry-Perot and collected the signals from the PMT, which were later transferred to an MS-DOS computer system for further analysis. Low-frequency Raman and Raman scattering were also measured during heating and cooling of a HBLAN20 glass through the transition region. An argon-ion laser (at 488 nm) and 0.85 m double grating monochromater (SPEX 1403) with photon
J. Schroeder et al. / Journal of Non-Crystalline Solids 203 (1996) 186-191
188
Landau.Placzek
Ratio
peak and subsequent decrease followed by a gradual increase in the LP ratio which may be a universal feature of glass-forming liquids. The cooling curve
ZBLAN20 90"
Longitudinal 18.0"
C,
(a)
Shift
ZBLA
70' 17.5
50 17.0 T
30 300
g.~ 500
400
•
16.5
600
\
Temp(K) Fig. 2. Landau-Placzek ratio, RLp, versus temperature during heating of ZBLAN20 glass through the transition region.
16.0 200
Fig. 1 compares the LP ratio curves for heating and cooling of ZBLA samples. During heating of the ZBLA glass the LP ratio decreases with increasing temperature up to the glass transition temperature at which the LP ratio appears to be a minimum. The LP ratio then increases with a local maximum in the glass transition region. Similar anomalous behavior has been observed in Bokov and Andreev's study [12] and in Golubkov's small angle X-ray scattering experiments on B203 glass [13]. It appears that anomalous scattering in the transition region has a
400
500
600
700
Temp(K)
counting electronics (resolution approximately 2 cm -1 ) were employed at a 90 ° scattering angle. For all measurements above the ambient temperature, the samples were placed on a glass plate and positioned in a temperature controlled molybdenum furnace with temperature stability of about _ I°C. The furnace had three optical windows, which made it possible to collect 90 ° scattered light. The temperature inside the furnace was monitored with a chromel-alumel thermocouple positioned just beneath the sample holder.
3. Results
300
Longitudinal
19
(b)
Shift
ZBLAN20
18 ¸
r~
17' T8
200
3~0
4~0
500
600
Temp(K) Fig. 3. (a) Longitudinal Brillouin shift of ZBLA as function of temperature during heating. The line is drawn as a guide for the eye. (b) Longitudinal Brillouin shift of ZBLAN20 as function of temperature during heating. The line is drawn as a guide for the eye.
J. Schroeder et al. / Journal of Non-C~stalline Solids 203 (1996) 186-191 Brillouin
Linewidth
200
189
(a)
ZBLA o
Heating
•
Cooling
= k
.
r-
A~ k.
rg
2
5o0
5;0
\
=
100
200
65o Raman Shift (lJcm)
Temp(K) Fig. 4. Comparision of total Brillouin linewidth curves for heating and cooling of ZBLA.
does not strictly follow the heating curve but it displays a hysteresis effect. The cooling curve has two peaks of much smaller intensities than the heating peak in the glass transition region and follows the heating curve below Tg. Anomalous behavior of the LP ratio in the glass transition region of ZBLAN20 is also seen in Fig. 2. Again the LP ratio decreases up to the glass transition region temperature and then increases with an anomalous peak in the glass transition region. Fig. 3(a) and (b) show the longitudinal Brillouin shift of ZBLA and ZBLAN20, respectively, as a function of temperature during heating in which we observe a marked change in slope near Tg. The shifts at room temperature are approximately 17.4 GHz for ZBLA and 18.2 GHz for ZBLAN20 and decrease, monotonically, with increasing temperature, whereas in the glass transition region the shifts decrease more rapidly for both samples. The measurement of the Brillouin shifts allows the calculation of Che sound velocity, provided the refractive index of the material is known [t4]. Fig. 4 compares Brillouin linewidth curves for heating and cooling of ZBLA. This graph shows
(bi
28oo
. . . . . . . . . .
il o
,
0
,
i
200
,
,
i
,
400
,
i
600
,
,
800
Raman Shift (1/cm) Fig. 5. (a) Raman spectra showing boson peaks during heating of HBLAN20 glass through the glass transition region with uppermost trace at 550.5 K, the next at 533 K, then 450 K and the lowest at 301 K, Tg = 542 K. (b) Raman spectra during cooling of HBLAN20 with uppermost trace at 550 K, the intermediate trace at 483 K and the lowest trace at 301 K, Tg = 542 K.
small fluctuations of the Brillouin linewidth in the glass transition region. These fluctuations are within the accuracy of the measurement,
190
Z Schroeder et al. / Journal of Non-Crystalline Solids 203 (1996) 186-191
In Fig. 5(a) and (b) the Raman spectra of HBLAN20 glass during heating and cooling are shown, respectively, as a function of temperature. The low frequency boson peak and the most prominent vibrational Raman peak are observed around 45 cm -1 and 575 cm -~, respectively. No hysteresis effect is observed for heating and cooling in the low frequency Raman scattering. It has been found that the broad spectral feature of the boson peak is the same for different glasses and is independent of their chemical composition. The size of ordered microregions, or the structural correlation range, can be estimated from the position of the low frequency boson peak and the sound velocity determined by the Brillouin shift [7,8,15,16].
4. Discussion
In the previous paper [11] we reported the depolarization ratios (the ratios of the intensities of depolarized to polarized light scattering spectra), IHv/Ivv, for ZBLA, ZBLAN20, and HBLAN20 from the Raman scattering measurements. The depolarization ratio of ZBLA glass ( ~ 0.40 in the low frequency range 20-70 cm- 1) was much higher than both the theoretical prediction by Winterling [17] using the Martin and Brenig (MB) model [18] and the observed value for the other glasses containing NaF. In Ref. [19] the authors presented a comparison of the MB predictions with their experimental results of the low-frequency Raman scattering study. The observed depolarization ratios for some fragile glass formers were ~ 3 / 4 , while the MB predictions for to ~ 0 were 0.14-0.27, consistently too small. Only quartz glass gave reasonable agreement, however, the MB model predicts a fairly strong frequency dependence for all these materials including quartz, which they did not observe. A similar disagreement was noted by Nemanich [20] for several chalcogenide glasses. It seems that good glass formers show reasonable agreement with the MB predictions for the depolarization ratio for to ~ O, however, fragile glass formers show poor agreement. The behavior of the Landau-Placzek ratio above and below Tg is explained by variations in density (entropy) fluctuations or specific volume fluctuations. It is evident that the actual magnitude of the
distribution of relaxation times depends strongly on the size of the independently relaxing regions as noted by Moynihan and Schroeder [1] and Donth [21]. The experimental values of the distribution of relaxation times demand regions which are typically a few nm across [4-8,13]. At temperatures in the glass transition, a growth in the magnitude of the density fluctuations is caused by structural relaxations of these nanoscale inhomogeneities whereas in the glassy state, below Tg, the nanoscale inhomogeneities are frozen-in and rearrangements are impossible. These regions behave as the disordered lattice at a higher temperature [13]. Therefore, the regions are causing an additional increase in the Rayleigh intensity which produces the anomalous peak in the Landau-Placzek ratio curves. This additional intensity decreases with further increase in the temperature as the transition from the glassy state to the liquid state reaches equilibrium values. In addition, at high temperatures there is an uncoupling of propagating and non-propagating modes. The changing structure may decrease the coordination number of the Zr 4+ complexes, affecting the sound velocity such that both the isothermal and adiabatic compressibilities are affected. From Fig. 3(a) and (b) it is evident that this effect manifests itself in a decrease of the Brillouin shift as Tg is traversed. 5. Conclusions
Rayleigh and Brillouin scattering techniques have been applied to two fluoride glasses, ZBLA and ZBLAN20, and Raman scattering technique has been applied to HBLAN20 glass during heating and cooling through the glass transition region. Anomalous behavior is observed in the glass transition region for the Landau-Placzek ratio and a hysteresis effect is also observed for heating versus cooling. The interpretation of these results offer some solid evidence as to the physical origin of the non-exponential character of structural relaxation kinetics in terms of independently relaxing nanoscale inhomogeneities. We feel that the arguments discussed here are of sufficient validity to account qualitatively for the anomalous light scattering. The low frequency broad peak of the Raman spectra, the so-called boson peak, is observed for
J. Schroeder et aL / Journal of Non-Crystalline Solids 203 (1996) 186-191
H B L A N 2 0 glass during heating and cooling. The hysteresis effect w h i c h is o b s e r v e d in the R a y l e i g h scattering (diffusive m o d e ) is not f o u n d in the l o w f r e q u e n c y R a m a n scattering (vibrational m o d e ) for heating and cooling. The b o s o n p e a k in R a m a n scattering permits to d e t e r m i n e the structural correlation length and is c o n s i d e r e d a typical sign o f interm e d i a t e - r a n g e order in glasses.
Acknowledgements The authors gratefully a c k n o w l e d g e the partial support o f this w o r k by the National S c i e n c e Foundation under Grant No. D M R - 8 8 - 0 1 0 0 4 .
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