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Fictive temperature of GeO2 glass: Its determination by IR method and its effects on density and refractive index
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Journal of Non-Crystalline Solids 353 (2007) 4762–4766 www.elsevier.com/locate/jnoncrysol
Fictive temperature of GeO2 glass: Its determination by IR method and its effects on density and refractive index T.M. Gross, M. Tomozawa
*
Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3593, USA Received 19 December 2006 Available online 8 August 2007
Abstract A simple IR method of determining the fictive temperature of GeO2 glass, both surface and bulk, was developed using the same technique developed earlier for silica glass. Specifically, IR absorption and reflection peak wavenumbers of GeO2 structural bands were found to be correlated with the fictive temperature of the glass. Using this method structural relaxation kinetics can be investigated. Density and refractive index of GeO2 glass were also measured as a function of fictive temperature. 2007 Published by Elsevier B.V. PACS: 65.60.+a; 78.20.e; 78.30.j; 81.05.Kj Keywords: FTIR measurements; Infrared properties; Oxide glasses; Germania; Structural relaxation; Water in glass
1. Introduction A glass exhibits different structures and properties depending on the cooling rate from its melt. The cooling rate affects the temperature at which the supercooled liquid freezes to form the glassy state, the faster cooling rate shifting the temperature higher. The temperature at which the liquid structure freezes to turn into glass is known as the fictive temperature [1]. If a glass is held at a given temperature in the glass transition range, then the fictive temperature of the glass will approach the heat-treatment temperature over time. Many properties of glasses including density, refractive index, hardness, bulk modulus, and ionic diffusivity depend on fictive temperature. It has been shown that the peak wavenumber of infrared structural bands in various glasses including silica glasses are correlated with the fictive temperature and can be used
*
Corresponding author. Tel.: +1 518 276 6659; fax: +1 518 276 8554. E-mail address: [email protected] (M. Tomozawa).
0022-3093/$ - see front matter 2007 Published by Elsevier B.V. doi:10.1016/j.jnoncrysol.2007.06.057
as a simple measure of fictive temperature [2]. It is expected that the same technique is applicable to germanium dioxide glasses since these glasses exhibit similar structural bands to those of silica glass [3–6]. This possibility was explored. Glasses can be classified as either normal or anomalous depending on their fictive temperature–property relationship. In general, normal glasses exhibit increasing specific volume, decreasing density, decreasing refractive index, and decreasing hardness with increasing fictive temperature. Anomalous glasses show an opposite trend in these properties. Tetrahedrally coordinated glasses including germanium dioxide and silicon dioxide have been shown to exhibit anomalous behavior in their mechanical properties as shown by Kurkjian et al. [7]. Anomalies in the temperature and pressure coefficients of shear and bulk moduli are present in these glasses. SiO2 glasses are known to exhibit anomalous behavior in the fictive temperature dependence of density and refractive index. Fictive temperature dependence of density and refractive index of GeO2 glass was examined to see whether GeO2 glass behaves in a similar manner to silica glass.
T.M. Gross, M. Tomozawa / Journal of Non-Crystalline Solids 353 (2007) 4762–4766
3. Results Fig. 1 shows the IR absorption spectra for glass samples prepared with and without prior drying procedure, indicating that substantial reduction in the water content in the glass is achieved by the drying process of the powder [8]. Both glass samples had the same thickness of approximately 0.6 mm. The absorption peak at 3560 cm1 is due to the hydroxyl group [8]. The absorbance, A, is then directly related to the concentration of hydroxide by the equation A = ecd, where A is absorbance and e, c, and d are the extinction coefficient, concentration of absorbing species, and specimen thickness, respectively. All the subsequent work was performed using the dried samples. Fig. 2 shows the IR reflection spectrum of the glass, which exhibits the fundamental infrared structural band at 916 cm1. The overtone of this structural band can be observed at 1835 cm1 in IR absorption spectroscopy as shown for a 5 mm thick specimen in Fig. 3. This overtone has not 0.60
0.40
Absorbance
Germanium dioxide glass was prepared from 99.98% purity germanium dioxide powder. A small quantity of water has a disproportionately large influence on glass properties and germanium dioxide glass has a strong affinity for water. In order to reduce the water content in the glass, the powder was dried in a platinum crucible in thin layers at 950 C for 0.5 h under dry air [8]. Additional layers of powder were added to the crucible and the heattreatment was repeated until approximately 40 g of dried powder was prepared. The dried powder was then melted at 1600 C in a platinum crucible and held at this temperature for 1 h. The crucible with the melt was quenched from 1600 C in cold water to form an annular crack in the glass in order to remove it from the crucible [8]. The glass sample was annealed at 550 C for 2 h and furnace cooled. The residual stress was confirmed to be absent using a polariscope. After annealing, samples were cut into the approximate size of 5 mm · 10 mm · 20 mm using a diamond saw. Cut samples were polished using a series of 240, 400, and 600 grit SiC polishing paper followed by final polishing with a 1 lm cerium oxide slurry to give an optical finish. The samples were heat-treated for various lengths of time at 475, 500, 525, and 550 C and the infrared spectra were obtained to measure IR peak wavenumber as a function of heat-treatment time until the peak position no longer changed at a constant temperature. At this point the structural relaxation of the germanium dioxide glass at the given temperature is complete and the heat-treatment temperature is considered equal to the fictive temperature of the glass. Once the peak position was determined at each of the four fictive temperatures studied, a curve relating IR peak wavenumber and fictive temperature was generated. The utility of this master curve is that the fictive temperature of a sample of germanium dioxide glass with unknown thermal history can be determined simply by taking an IR measurement of the glass in question. Both transmission and reflection modes of IR spectroscopy were used to generate master curves for bulk and surface fictive temperatures, respectively. The refractive index and density of the germanium dioxide glass samples at room temperature were measured as a function of fictive temperature using an Abbe refractometer and the Archimedes method, respectively. The refractive index at sodium D line, 589 nm, was measured using methylene chloride containing sulfur solution as a contact liquid in an Atago NAR-3T Abbe refractometer. The sample geometries for the refractive index samples were 20 mm · 8 mm · 3 mm parallelpipeds. Two adjacent sides with dimension 3 mm · 8 mm and 8 mm · 20 mm were polished to an optical finish as required for use with the instrument. The density was measured using the Archimedes method with a Mettler Toledo AG245 balance and density measurement kit. Ethanol, instead of water, was used as immersion liquid since GeO2 glass is easily corroded when
in contact with water. Sample masses were approximately 10 g in each case.
Not Dried Dried
0.20
0.00 4000
3800
3600
3400
3200
3000
Wavenumber (cm-1)
Fig. 1. IR absorption spectra for GeO2 glass samples prepared from dried and undried GeO2 powders. Thickness of samples was 0.6 mm. 100
916 cm-1
90 80
% Reflectance
2. Experimental procedure
4763
70 60 50 40 30 20 10 0 3650
3150
2650
2150
1650
1150
650
Wavenumber (cm-1)
Fig. 2. Infrared reflection spectrum for GeO2 glass. The peak at 916 cm1 is assigned to asymmetric stretching of Ge–O–Ge bridges.
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1835.1
500 C to 525 C
1835.0
5
550 C to 525 C
4
Wavenumber(cm-1)
Absorbance
1834.9
3
2 1835 cm
-1
1
0 4000
3600
3200
2800
2400
2000
1834.8 1834.7 1834.6 1834.5 1834.4 1834.3
1600
-1
Wavenumber (cm )
1834.2
Fig. 3. Infrared absorption spectrum for vitreous GeO2 glass. The peak at 1835 cm1 is an overtone to the fundamental structural band at 916 cm1 in reflection mode. Sample thickness was 5 mm.
1834.1 0
50
100
150
200
250
300
350
400
Time (minutes)
Fig. 5. Structural relaxation curves for GeO2 glasses in terms of an IR peak shift in absorption mode.
been previously reported. In order to see clearly this absorbance peak, a finite specimen thickness is required as shown in Fig. 4. The structural relaxation study can be made following this IR peak wavenumber as shown in the next example. Pure germanium dioxide glass has a glass transition temperature of 476 C [9]. Germanium dioxide glass samples with initial fictive temperatures of 550 and 500 C were produced by holding the sample at these temperatures for 2 h and 5 h, respectively, and rapidly cooling. Then both samples were heat-treated at an intermediate temperature, 525 C, and their IR peak wavenumbers were recorded in absorbance mode as a function of heat-treatment time. As can be seen in Fig. 5 the time dependence of the IR peak wavenumber can be fitted with a simple exponential function, t tðtÞ tð1Þ UðtÞ ¼ ¼ exp ; tð0Þ tð1Þ s
where t(0), t(1), and t(t) are the initial peak position, the final equilibrium peak position, and the peak position at the heat-treatment time, t, respectively, of the germania glass structural band [10]. The relaxation time, s, for germania glass samples initially at a fictive temperature of 550 C was 17 min while that for germania glass samples with an initial fictive temperature of 500 C was 33 min. The relaxation curves in Fig. 5 show that IR structural band peak wavenumbers of the two samples with different initial fictive temperatures converge to the same value at the same heat-treatment temperature, indicating that the final wavenumber corresponds uniquely to the structure of the glass at the heat-treatment temperature. Thus, this wavenumber can be used as a measure of the fictive temperature corresponding to the heat-treatment temperature. Collecting these wavenumbers obtained at various temperatures, the master curve relating the IR peak position and 1835.6
1.40
1835.2 -1
Peak Position (cm )
1.20
1835.4
~5 mm thick ~2.5 mm thick ~0.5 mm thick
Absorbance
1.00
0.80
0.60
-1
1834.8 1834.6
0.40
1834.4
0.20
1834.2
0.00 2000
1800
1600
Wavenumber (cm-1)
Fig. 4. Absorption spectra for GeO2 glasses with various sample thicknesses, showing the effect of thickness on the 1835 cm1 peak.
o
ν(cm ) = - 0.0153 Tf ( C) + 1842.6
1835
1834 470
480
490
500
510
520
530
540
550
560
Fictive Temperature (oC)
Fig. 6. Master curve generated for IR absorption peak position vs. fictive temperature for GeO2 glass.
T.M. Gross, M. Tomozawa / Journal of Non-Crystalline Solids 353 (2007) 4762–4766 3.658 3.656 3.654
Density (g/cm3)
the fictive temperature can be generated as shown in Fig. 6. The final heat-treatment times at 475, 500, 525, and 550 C were approximately 30, 5, 3.5, and 2 h, respectively. The equation relating wavenumber to fictive temperature was determined to be m (cm1) = 0.0153Tf (C) + 1842.6. The error range is ±0.03 cm1 in wavenumbers, which corresponds to ±2 C in fictive temperature. This master curve can be used to determine the bulk fictive temperature of a germanium dioxide glass sample with unknown thermal history simply by measuring the peak position of the structural band in infrared absorption mode. The master curve generated from the reflection infrared spectrum for GeO2 glass is seen in Fig. 7. This master curve can be used to measure the surface fictive temperature of a germanium dioxide glass sample with unknown thermal history or to study the surface relaxation kinetics. The equation relating wavenumber to fictive temperature is m (cm1) = 0.0059Tf (C) + 919.83. The error range is ±0.025 cm1 in wavenumbers, which corresponds to ±4 oC. The refractive index and density are shown as a function of fictive temperature in Figs. 8 and 9, respectively. In both
4765
3.652 3.650 3.648 3.646 3.644 3.642 3.640 3.638 470
480
490
500
510
520
530
540
550
560
Temperature (oC)
Fig. 9. Density vs. fictive temperature for pure GeO2 glasses.
cases the values decreased with increasing fictive temperature. This shows that germanium dioxide behaves as a normal glass, similar to a soda-lime glass, in regards to properties such as density and refractive index. 4. Discussion
917.1000
ν (cm-1) = - 0.0059 Tf (oC) + 919.83
-1
Wavenumber (cm )
917.0000
916.9000
916.8000
916.7000
916.6000
916.5000 470
480
490
500
510
520
530
540
550
560
Fictive Temperature (oC)
Fig. 7. Master curve generated for IR reflection peak position vs. fictive temperature for GeO2 glass.
1.6090 1.6088 1.6086
Refractive Index
1.6084 1.6082 1.6080 1.6078 1.6076 1.6074 1.6072 1.6070 1.6068 470
480
490
500
510
520
530
Temperature (oC)
Fig. 8. Refractive index vs. fictive temperature for pure GeO2 glasses.
The reflection peak for GeO2 glass at 916 cm1 in wavenumbers is known as the germania structural band from literature [3–6]. As can be seen in the paper by Venediktov et al., the vibrational spectrum for GeO2 glass and SiO2 glass exhibit similar spectra with peak wavenumbers shifted by the bond strength (k) and reduced mass (m) difqffiffiffiffiffiffiffi 1 k ference between Si–O and Ge–O bonds, t ¼ 2p . The m 1 1116 cm reflection band in SiO2 glass is known to be due to asymmetric stretching in the Si–O–Si bridges [11]. The reflection peak observed at 916 cm1 for GeO2 glass is analogous to this peak and can therefore also be assigned to asymmetric stretching. The force constant for Si–O, kSi–O, is 1.2 times higher than that of Ge–O [10] and the reduced mass, m, of Si–O is 0.78 times that of Ge–O. The experimental ratio of wavenumbers for SiO2 glass vs. tSiO2 GeO2 glass, tGeO ¼ 1:22, is in good agreement with the the2 oretical ratio, calculated to be 1.24. GeO2 glass has been shown to exhibit anomalous behavior in its vibrational dependence on fictive temperature, similar to SiO2 glass. That is, the IR peak wavenumbers decrease with increasing fictive temperature. As shown by Kurkjian, some thermal and mechanical properties of GeO2 glass also exhibit anomalous behavior [7]. The linear expansion coefficient and the temperature and pressure coefficients of shear and bulk moduli are anomalous. However, the fictive temperature dependence of the refractive index and density exhibit normal behavior, similar to those of soda-lime silicate glasses. These properties both decrease with increasing fictive temperature for GeO2 glass. This relationship is in contrast to the behavior of the structurally similar, SiO2 glass. Anomalous behavior in tetrahedrally coordinated glasses can be interpreted as an essentially random network of tetrahedra in which the oxy-
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gen angles (e.g. Si–O–Si or Ge–O–Ge) have a preference for two or more characteristic values. At any given temperature and pressure, a certain fraction of oxygen angles will be distributed around these characteristic values. Low oxygen angles will correspond to a higher density amorphous solid. Vukcevich [12] proposed a model for silica in which two characteristic oxygen angles, a and b, were preferred. The high density a form of silica had an oxygen angle of 138 and the low density b form had an oxygen angle of 145. The corresponding molar volumes were 26.00 cm3/ mol and 27.65 cm3/mol for a and b states, respectively. He concluded that the fraction of b was 100% at absolute zero and 75% at room temperature. The fraction of a increased with increasing temperature toward a limiting value of 50% at high temperature. At high temperature the thermal energy is comparable to the energy barriers between a and b states and an equal number of each of these states should be expected. At high temperature the tetrahedra can rotate between states with ease and the entropy of mixing will be maximized by having an equal number of tetrahedra in each state. With this model, the density, along with the refractive index, will increase with increasing temperature as is realized by silica glass. Kieffer and Haung [13,14] proposed recently, alternative models in which anomalies in density and refractive index will be apparent for GeO2 glasses in specific temperature and pressure ranges. However, in the fictive temperature range studied and under conditions of ambient pressure, GeO2 glasses are shown to exhibit normal behavior. 5. Conclusion It was shown that the fictive temperature of GeO2 glass can be determined by measuring the IR peak wavenumber
of the GeO2 glass structural band and using a pre-determined calibration curve. In spite of the anomalous behavior of the vibrational and some mechanical properties, refractive index and density exhibited the behavior of normal glasses.
Acknowledgement This research was supported by NSF Grant DMR0352773.
References [1] M. Tomozawa, in: H.S. Nalwa (Ed.), Silicon-Based Materials and Devices, vol. 1, Academic Press, San Diego, 2001, p. 127. [2] A. Agarwal, K.M. Davis, M. Tomozawa, J. Non-Cryst. Solids 185 (1995) 191. [3] A.A. Venedictov, V.N. Morozov, V.N. Polukhin, J. Appl. Spectrosc. 10 (1969) 656. [4] B.T.K. Chen, G.J. Su, J. Phys. Chem. Glasses 12 (1971) 33. [5] V.V. Obukhov-Denisov, N.N. Sobolev, V.P. Cheremisinov, Opt. Spectrosc. USSR 8 (1960) 505. [6] A. Margaryan, M.A. Pilliavin, in: Germanate Glasses: Structure, Spectroscopy, and Properties, Artech House Publishers, Massachusetts, 1993, p. 23. [7] C.R. Kurkjian, J.T. Krause, H.J. McSkimin, P. Andreatch, T.B. Bateman, in: Amorphous Materials, Wiley, New York, 1972, p. 463. [8] J.F. Cordaro, J.E. Kelly III, M. Tomozawa, Phys. Chem. Glasses 22 (1981) 90. [9] T.J. Kiczenski, C. Ma, E. Hammarsten, D. Wilkerson, M. Affatigato, S. Feller, J. Non-Cryst. Solids 272 (2000) 57. [10] O.V. Mazurin, J. Non-Cryst. Solids 25 (1977) 130. [11] R. Bruckner, J. Non-Cryst. Solids 5 (1970) 123. [12] M.R. Vukcevich, J. Non-Cryst. Solids 11 (1972) 25. [13] L. Huang, J. Kieffer, Phys. Rev. B 69 (2004) 224203-1. [14] L. Huang, J. Kieffer, Phys. Rev. B 69 (2004) 224204-1.
Journal of Non-Crystalline Solids 353 (2007) 4762–4766 www.elsevier.com/locate/jnoncrysol
Fictive temperature of GeO2 glass: Its determination by IR method and its effects on density and refractive index T.M. Gross, M. Tomozawa
*
Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3593, USA Received 19 December 2006 Available online 8 August 2007
Abstract A simple IR method of determining the fictive temperature of GeO2 glass, both surface and bulk, was developed using the same technique developed earlier for silica glass. Specifically, IR absorption and reflection peak wavenumbers of GeO2 structural bands were found to be correlated with the fictive temperature of the glass. Using this method structural relaxation kinetics can be investigated. Density and refractive index of GeO2 glass were also measured as a function of fictive temperature. 2007 Published by Elsevier B.V. PACS: 65.60.+a; 78.20.e; 78.30.j; 81.05.Kj Keywords: FTIR measurements; Infrared properties; Oxide glasses; Germania; Structural relaxation; Water in glass
1. Introduction A glass exhibits different structures and properties depending on the cooling rate from its melt. The cooling rate affects the temperature at which the supercooled liquid freezes to form the glassy state, the faster cooling rate shifting the temperature higher. The temperature at which the liquid structure freezes to turn into glass is known as the fictive temperature [1]. If a glass is held at a given temperature in the glass transition range, then the fictive temperature of the glass will approach the heat-treatment temperature over time. Many properties of glasses including density, refractive index, hardness, bulk modulus, and ionic diffusivity depend on fictive temperature. It has been shown that the peak wavenumber of infrared structural bands in various glasses including silica glasses are correlated with the fictive temperature and can be used
*
Corresponding author. Tel.: +1 518 276 6659; fax: +1 518 276 8554. E-mail address: [email protected] (M. Tomozawa).
0022-3093/$ - see front matter 2007 Published by Elsevier B.V. doi:10.1016/j.jnoncrysol.2007.06.057
as a simple measure of fictive temperature [2]. It is expected that the same technique is applicable to germanium dioxide glasses since these glasses exhibit similar structural bands to those of silica glass [3–6]. This possibility was explored. Glasses can be classified as either normal or anomalous depending on their fictive temperature–property relationship. In general, normal glasses exhibit increasing specific volume, decreasing density, decreasing refractive index, and decreasing hardness with increasing fictive temperature. Anomalous glasses show an opposite trend in these properties. Tetrahedrally coordinated glasses including germanium dioxide and silicon dioxide have been shown to exhibit anomalous behavior in their mechanical properties as shown by Kurkjian et al. [7]. Anomalies in the temperature and pressure coefficients of shear and bulk moduli are present in these glasses. SiO2 glasses are known to exhibit anomalous behavior in the fictive temperature dependence of density and refractive index. Fictive temperature dependence of density and refractive index of GeO2 glass was examined to see whether GeO2 glass behaves in a similar manner to silica glass.
T.M. Gross, M. Tomozawa / Journal of Non-Crystalline Solids 353 (2007) 4762–4766
3. Results Fig. 1 shows the IR absorption spectra for glass samples prepared with and without prior drying procedure, indicating that substantial reduction in the water content in the glass is achieved by the drying process of the powder [8]. Both glass samples had the same thickness of approximately 0.6 mm. The absorption peak at 3560 cm1 is due to the hydroxyl group [8]. The absorbance, A, is then directly related to the concentration of hydroxide by the equation A = ecd, where A is absorbance and e, c, and d are the extinction coefficient, concentration of absorbing species, and specimen thickness, respectively. All the subsequent work was performed using the dried samples. Fig. 2 shows the IR reflection spectrum of the glass, which exhibits the fundamental infrared structural band at 916 cm1. The overtone of this structural band can be observed at 1835 cm1 in IR absorption spectroscopy as shown for a 5 mm thick specimen in Fig. 3. This overtone has not 0.60
0.40
Absorbance
Germanium dioxide glass was prepared from 99.98% purity germanium dioxide powder. A small quantity of water has a disproportionately large influence on glass properties and germanium dioxide glass has a strong affinity for water. In order to reduce the water content in the glass, the powder was dried in a platinum crucible in thin layers at 950 C for 0.5 h under dry air [8]. Additional layers of powder were added to the crucible and the heattreatment was repeated until approximately 40 g of dried powder was prepared. The dried powder was then melted at 1600 C in a platinum crucible and held at this temperature for 1 h. The crucible with the melt was quenched from 1600 C in cold water to form an annular crack in the glass in order to remove it from the crucible [8]. The glass sample was annealed at 550 C for 2 h and furnace cooled. The residual stress was confirmed to be absent using a polariscope. After annealing, samples were cut into the approximate size of 5 mm · 10 mm · 20 mm using a diamond saw. Cut samples were polished using a series of 240, 400, and 600 grit SiC polishing paper followed by final polishing with a 1 lm cerium oxide slurry to give an optical finish. The samples were heat-treated for various lengths of time at 475, 500, 525, and 550 C and the infrared spectra were obtained to measure IR peak wavenumber as a function of heat-treatment time until the peak position no longer changed at a constant temperature. At this point the structural relaxation of the germanium dioxide glass at the given temperature is complete and the heat-treatment temperature is considered equal to the fictive temperature of the glass. Once the peak position was determined at each of the four fictive temperatures studied, a curve relating IR peak wavenumber and fictive temperature was generated. The utility of this master curve is that the fictive temperature of a sample of germanium dioxide glass with unknown thermal history can be determined simply by taking an IR measurement of the glass in question. Both transmission and reflection modes of IR spectroscopy were used to generate master curves for bulk and surface fictive temperatures, respectively. The refractive index and density of the germanium dioxide glass samples at room temperature were measured as a function of fictive temperature using an Abbe refractometer and the Archimedes method, respectively. The refractive index at sodium D line, 589 nm, was measured using methylene chloride containing sulfur solution as a contact liquid in an Atago NAR-3T Abbe refractometer. The sample geometries for the refractive index samples were 20 mm · 8 mm · 3 mm parallelpipeds. Two adjacent sides with dimension 3 mm · 8 mm and 8 mm · 20 mm were polished to an optical finish as required for use with the instrument. The density was measured using the Archimedes method with a Mettler Toledo AG245 balance and density measurement kit. Ethanol, instead of water, was used as immersion liquid since GeO2 glass is easily corroded when
in contact with water. Sample masses were approximately 10 g in each case.
Not Dried Dried
0.20
0.00 4000
3800
3600
3400
3200
3000
Wavenumber (cm-1)
Fig. 1. IR absorption spectra for GeO2 glass samples prepared from dried and undried GeO2 powders. Thickness of samples was 0.6 mm. 100
916 cm-1
90 80
% Reflectance
2. Experimental procedure
4763
70 60 50 40 30 20 10 0 3650
3150
2650
2150
1650
1150
650
Wavenumber (cm-1)
Fig. 2. Infrared reflection spectrum for GeO2 glass. The peak at 916 cm1 is assigned to asymmetric stretching of Ge–O–Ge bridges.
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T.M. Gross, M. Tomozawa / Journal of Non-Crystalline Solids 353 (2007) 4762–4766 6
1835.1
500 C to 525 C
1835.0
5
550 C to 525 C
4
Wavenumber(cm-1)
Absorbance
1834.9
3
2 1835 cm
-1
1
0 4000
3600
3200
2800
2400
2000
1834.8 1834.7 1834.6 1834.5 1834.4 1834.3
1600
-1
Wavenumber (cm )
1834.2
Fig. 3. Infrared absorption spectrum for vitreous GeO2 glass. The peak at 1835 cm1 is an overtone to the fundamental structural band at 916 cm1 in reflection mode. Sample thickness was 5 mm.
1834.1 0
50
100
150
200
250
300
350
400
Time (minutes)
Fig. 5. Structural relaxation curves for GeO2 glasses in terms of an IR peak shift in absorption mode.
been previously reported. In order to see clearly this absorbance peak, a finite specimen thickness is required as shown in Fig. 4. The structural relaxation study can be made following this IR peak wavenumber as shown in the next example. Pure germanium dioxide glass has a glass transition temperature of 476 C [9]. Germanium dioxide glass samples with initial fictive temperatures of 550 and 500 C were produced by holding the sample at these temperatures for 2 h and 5 h, respectively, and rapidly cooling. Then both samples were heat-treated at an intermediate temperature, 525 C, and their IR peak wavenumbers were recorded in absorbance mode as a function of heat-treatment time. As can be seen in Fig. 5 the time dependence of the IR peak wavenumber can be fitted with a simple exponential function, t tðtÞ tð1Þ UðtÞ ¼ ¼ exp ; tð0Þ tð1Þ s
where t(0), t(1), and t(t) are the initial peak position, the final equilibrium peak position, and the peak position at the heat-treatment time, t, respectively, of the germania glass structural band [10]. The relaxation time, s, for germania glass samples initially at a fictive temperature of 550 C was 17 min while that for germania glass samples with an initial fictive temperature of 500 C was 33 min. The relaxation curves in Fig. 5 show that IR structural band peak wavenumbers of the two samples with different initial fictive temperatures converge to the same value at the same heat-treatment temperature, indicating that the final wavenumber corresponds uniquely to the structure of the glass at the heat-treatment temperature. Thus, this wavenumber can be used as a measure of the fictive temperature corresponding to the heat-treatment temperature. Collecting these wavenumbers obtained at various temperatures, the master curve relating the IR peak position and 1835.6
1.40
1835.2 -1
Peak Position (cm )
1.20
1835.4
~5 mm thick ~2.5 mm thick ~0.5 mm thick
Absorbance
1.00
0.80
0.60
-1
1834.8 1834.6
0.40
1834.4
0.20
1834.2
0.00 2000
1800
1600
Wavenumber (cm-1)
Fig. 4. Absorption spectra for GeO2 glasses with various sample thicknesses, showing the effect of thickness on the 1835 cm1 peak.
o
ν(cm ) = - 0.0153 Tf ( C) + 1842.6
1835
1834 470
480
490
500
510
520
530
540
550
560
Fictive Temperature (oC)
Fig. 6. Master curve generated for IR absorption peak position vs. fictive temperature for GeO2 glass.
T.M. Gross, M. Tomozawa / Journal of Non-Crystalline Solids 353 (2007) 4762–4766 3.658 3.656 3.654
Density (g/cm3)
the fictive temperature can be generated as shown in Fig. 6. The final heat-treatment times at 475, 500, 525, and 550 C were approximately 30, 5, 3.5, and 2 h, respectively. The equation relating wavenumber to fictive temperature was determined to be m (cm1) = 0.0153Tf (C) + 1842.6. The error range is ±0.03 cm1 in wavenumbers, which corresponds to ±2 C in fictive temperature. This master curve can be used to determine the bulk fictive temperature of a germanium dioxide glass sample with unknown thermal history simply by measuring the peak position of the structural band in infrared absorption mode. The master curve generated from the reflection infrared spectrum for GeO2 glass is seen in Fig. 7. This master curve can be used to measure the surface fictive temperature of a germanium dioxide glass sample with unknown thermal history or to study the surface relaxation kinetics. The equation relating wavenumber to fictive temperature is m (cm1) = 0.0059Tf (C) + 919.83. The error range is ±0.025 cm1 in wavenumbers, which corresponds to ±4 oC. The refractive index and density are shown as a function of fictive temperature in Figs. 8 and 9, respectively. In both
4765
3.652 3.650 3.648 3.646 3.644 3.642 3.640 3.638 470
480
490
500
510
520
530
540
550
560
Temperature (oC)
Fig. 9. Density vs. fictive temperature for pure GeO2 glasses.
cases the values decreased with increasing fictive temperature. This shows that germanium dioxide behaves as a normal glass, similar to a soda-lime glass, in regards to properties such as density and refractive index. 4. Discussion
917.1000
ν (cm-1) = - 0.0059 Tf (oC) + 919.83
-1
Wavenumber (cm )
917.0000
916.9000
916.8000
916.7000
916.6000
916.5000 470
480
490
500
510
520
530
540
550
560
Fictive Temperature (oC)
Fig. 7. Master curve generated for IR reflection peak position vs. fictive temperature for GeO2 glass.
1.6090 1.6088 1.6086
Refractive Index
1.6084 1.6082 1.6080 1.6078 1.6076 1.6074 1.6072 1.6070 1.6068 470
480
490
500
510
520
530
Temperature (oC)
Fig. 8. Refractive index vs. fictive temperature for pure GeO2 glasses.
The reflection peak for GeO2 glass at 916 cm1 in wavenumbers is known as the germania structural band from literature [3–6]. As can be seen in the paper by Venediktov et al., the vibrational spectrum for GeO2 glass and SiO2 glass exhibit similar spectra with peak wavenumbers shifted by the bond strength (k) and reduced mass (m) difqffiffiffiffiffiffiffi 1 k ference between Si–O and Ge–O bonds, t ¼ 2p . The m 1 1116 cm reflection band in SiO2 glass is known to be due to asymmetric stretching in the Si–O–Si bridges [11]. The reflection peak observed at 916 cm1 for GeO2 glass is analogous to this peak and can therefore also be assigned to asymmetric stretching. The force constant for Si–O, kSi–O, is 1.2 times higher than that of Ge–O [10] and the reduced mass, m, of Si–O is 0.78 times that of Ge–O. The experimental ratio of wavenumbers for SiO2 glass vs. tSiO2 GeO2 glass, tGeO ¼ 1:22, is in good agreement with the the2 oretical ratio, calculated to be 1.24. GeO2 glass has been shown to exhibit anomalous behavior in its vibrational dependence on fictive temperature, similar to SiO2 glass. That is, the IR peak wavenumbers decrease with increasing fictive temperature. As shown by Kurkjian, some thermal and mechanical properties of GeO2 glass also exhibit anomalous behavior [7]. The linear expansion coefficient and the temperature and pressure coefficients of shear and bulk moduli are anomalous. However, the fictive temperature dependence of the refractive index and density exhibit normal behavior, similar to those of soda-lime silicate glasses. These properties both decrease with increasing fictive temperature for GeO2 glass. This relationship is in contrast to the behavior of the structurally similar, SiO2 glass. Anomalous behavior in tetrahedrally coordinated glasses can be interpreted as an essentially random network of tetrahedra in which the oxy-
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gen angles (e.g. Si–O–Si or Ge–O–Ge) have a preference for two or more characteristic values. At any given temperature and pressure, a certain fraction of oxygen angles will be distributed around these characteristic values. Low oxygen angles will correspond to a higher density amorphous solid. Vukcevich [12] proposed a model for silica in which two characteristic oxygen angles, a and b, were preferred. The high density a form of silica had an oxygen angle of 138 and the low density b form had an oxygen angle of 145. The corresponding molar volumes were 26.00 cm3/ mol and 27.65 cm3/mol for a and b states, respectively. He concluded that the fraction of b was 100% at absolute zero and 75% at room temperature. The fraction of a increased with increasing temperature toward a limiting value of 50% at high temperature. At high temperature the thermal energy is comparable to the energy barriers between a and b states and an equal number of each of these states should be expected. At high temperature the tetrahedra can rotate between states with ease and the entropy of mixing will be maximized by having an equal number of tetrahedra in each state. With this model, the density, along with the refractive index, will increase with increasing temperature as is realized by silica glass. Kieffer and Haung [13,14] proposed recently, alternative models in which anomalies in density and refractive index will be apparent for GeO2 glasses in specific temperature and pressure ranges. However, in the fictive temperature range studied and under conditions of ambient pressure, GeO2 glasses are shown to exhibit normal behavior. 5. Conclusion It was shown that the fictive temperature of GeO2 glass can be determined by measuring the IR peak wavenumber
of the GeO2 glass structural band and using a pre-determined calibration curve. In spite of the anomalous behavior of the vibrational and some mechanical properties, refractive index and density exhibited the behavior of normal glasses.
Acknowledgement This research was supported by NSF Grant DMR0352773.
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