- Email: [email protected]
Optical and physical properties of lanthanum gallogermanate glasses
Journal of Non-Crystalline Solids 231 (1998) 222±226
Optical and physical properties of lanthanum gallogermanate glasses Luu-Gen Hwa
a,* ,
Yi-Rui Chang a, Sung-Ping Szu
b
a b
Department of Physics, Fu-Jen Catholic University, Taipei 24205, Taiwan, ROC Department of Physics, National Chung-Hsing University, Taichung, Taiwan, ROC Received 16 December 1997; received in revised form 18 February 1998
Abstract Optical properties of lanthanum gallogermanate glasses were investigated by infrared (IR) transmission and IR re¯ectivity measurements. Several physical properties of these glasses, including density, index of refraction and ultrasonic velocities, were also measured. The experimental results are used to obtain elastic constants. These glasses are transparent over frequencies ranging from the near ultraviolet to the mid-IR (8 lm) and have ionic bond properties in their structure. Ó 1998 Elsevier Science B.V. All rights reserved. PACS: 61.43.Fs; 62.20.D; 78.30.L
1. Introduction Glasses containing heavy metal oxides are of interest for infrared (IR) transmission application due to their long IR cut-o wavelength in comparison with phosphate, borate and silicate glasses. Dumbaugh found that the addition of Ga2 O3 into PbO±Bi2 O3 and CdO±Bi2 O3 improved glass stability and these glasses are transparent to about 7 lm [1]. Kokubo et al. found that alkaliand alkaline-earth Ta2 O±Ga2 O3 or Nb2 O±Ga2 O3 glasses also have optical transmission to about 7 lm [2,3]. Glasses based on GeO2 make favorable ®ber core material because of their longer wavelength cut-o at which the GeO2 stretching vibration occurs. A recent study of barium gallo-
* Corresponding author. Tel.: +886-2 2903 1111 (ext 2436); fax: +886-2 2902 1038; e-mail: [email protected].
0022-3093/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 8 ) 0 0 4 5 5 - 4
germanate glasses demonstrated their potential for both IR optical waveguides and bulk optic components in the 3±5 lm region [4]. Lindquist and Shelby studied the properties of rare earth gallogermanate glasses [5]. The IR cut-o occurs at 6.05 lm. These glasses containing rare earth elements also have excellent chemical durability in water and very high Verdet constants due to the rare earth ion concentration. This second property makes these glasses suitable for use in Faraday rotation devices [5]. This paper reports on a segment of ongoing research program in which the optical and physical properties of the lanthanum gallogermanate glasses are investigated by measuring IR transmission, IR re¯ectivity, and ultrasonic pulseechos. The experimental results are used to obtain the elastic constants. The IR edge is discussed in the context of the intrinsic multiphonon absorption theory.
L.-G. Hwa et al. / Journal of Non-Crystalline Solids 231 (1998) 222±226
223
2. Experimental aspect Samples with formula: xLa2 O3 ±GeO2 ±y Ga2 O3 , mol% and where x La2 O3 mol%/GeO2 y Ga2 O3 mol%/GeO2 mol% were prepared by melting appropriate amounts of La2 O3 (Aldrich 99.9%), GeO2 (Aldrich 99.9%), Ga2 O3 (Aldrich 99.9%) in open atmosphere at temperatures between 1550 and 1650°C, for one to one hour and a half in a platinum crucible. The liquids were quenched by placing the bottom of the crucible in water. The glassy samples were identi®ed by X-ray diraction. To produce samples large enough for the experimental requirements, samples were batched to obtain 10 g. The glass-forming tendency will be discussed elsewhere [6]. The IR absorption spectra, including the transmission and re¯ectivity measurements, were carried out on a spectrometer (Perkin±Elmer FTIR2000) with an accessory of variable angle specular re¯ector. The resolution of the instrument is 0.7 cmÿ1 in the 300±4000 cmÿ1 region. Ultrasonic measurements were performed by a pulse-echo method with a pulser/receiver instrument (Panametrics model 5800) with quartz transducer. X-cut transducers were employed for longitudinal modes and Y-cut for shear modes. The pulse transit time was measured with a oscilloscope (Hewlett-Packard model 54502A). Several eects, such as multiple internal re¯ections within the transducer, sample thickness, and the acoustic impedance mismatch between glass sample and transducer, aect the accuracy of ultrasonic velocity measurements. The uncertainty is estimated about 1%. The density was determined by an Archimedes technique for which n-hexadecane was the working ¯uid. The accuracy of the measurement was 0.001 g/cm3 . The re¯ective indices of the sample were measured by Woolam's variable angle spectroscopic ellipsometer, and were accurate within 0.001.
Fig. 1. IR transmission spectra of four lanthanum gallogermanate glasses.
glasses are transparent to 8 lm in the mid-IR region. The results indicate that if the ratio Ga2 O3 /GeO2 is constant, the IR cut-o wavelength becomes larger with increasing La2 O3 contents in the glass system. Fig. 2 gives the multiphonon edge absorption versus frequency for various lanthanum gallogermanate samples. The IR re¯ectivity spectra of lanthanum gallogermanate samples at near normal incidence are similar. One particular example of a 0.3La2 O3 ±GeO2 ± 0.25Ga2 O3 sample is given in Fig. 3. The density, q, index of refraction, n, longitudinal (VL ) sound velocities and transverse (VT ) sound velocities of seven lanthanum gallogermanate
3. Results IR transmission spectra of four lanthanum gallogermanate glasses are given in Fig. 1. These
Fig. 2. The multiphonon edge absorption versus frequency for four lanthanum gallogermanate glasses.
224
L.-G. Hwa et al. / Journal of Non-Crystalline Solids 231 (1998) 222±226
Fig. 3. The IR re¯ectivity spectra of a 0.3La2 O3 ±GeO2 ± 0.25Ga2 O3 glass at near normal incidence.
samples and SiO2 glass sample are given in Table 1. The density, index of refraction and longitudinal sound velocity increase as the La2 O3 content increases in a xLa2 O3 ±GeO2 ±0.25Ga2 O3 glass system. 4. Discussion The IR absorption edge, which limits transparency at longer wavelength, is due to the multiphonon interactions between electromagnetic wave and lattice vibrations (speci®cally, anharmonicity and nonlinear electric moments). The origins of the multiphonon absorption of the solids were discussed by Bendow [7]. The results in Fig. 2 show that the IR edge is smooth, and the multiphonon absorption coecients of these glasses decrease exponentially with increasing frequencies. These phenomena are typi-
cal of the intrinsic multiphonon absorption in most ionic materials [8±10]. One step further, the experiment on the frequency and temperature dependence of the multiphonon absorption may give a deeper insight of the exponential behavior of the intrinsic multiphonon edge absorption of the materials. In the IR re¯ectivity spectra of lanthanum gallogermanate glass, the principal features are a strong band at 760 cmÿ1 , two mid-frequency bands respectively at 510 and 370 cmÿ1 . Merzbacher carried out infrared re¯ectance spectroscopy study on a series of barium gallogermanate glasses [11], and concluded that the gallogermanate glasses are structurally analogous to the aluminosilicate glasses. By analogy with aluminosilicate, the band between 700 and 850 cmÿ1 is assigned to T±O stretching vibrations, where T represents a tetrahedrally coordinated cation [11]. Because of their similar masses and coordinations of Ge and Ga, we assign the band at 760 cmÿ1 to the combination of the T±O (T Ge or Ga) stretching vibration band in [GaOÿ 4 ] and [GeO4 ] tetrahedral network. The band at 510 cmÿ1 we attribute to a Ga±O± Ga bending vibration. This assignment agrees with previous observations on alkaline earth gallate glasses and lead gallosilicate glasses [12,13]. Not so many previous vibrational studies of the La-related structure have been performed. However, Yamaguchi et al. [14] and Takahashi and Ohtsuka [15] found the La±O related vibration mode in the 300±400 cmÿ1 range. Consequently, we assign the band at 370 cmÿ1 to La±O vibration mode in our samples.
Table 1 The density, q, index of refraction, n, longitudinal (VL ) and transverse (VT ) sound velocities of seven lanthanum gallogermanate samples and the SiO2 glass sample Sample
q (g/cm3 )
n (514.5 nm)
VL (m/s)
VT (m/s)
0.20La2 O3 ±GeO2 ±0.25Ga2 O3 0.25La2 O3 ±GeO2 ±0.25Ga2 O3 0.33La2 O3 ±GeO2 ±0.25Ga2 O3 0.50La2 O3 ±GeO2 ±0.25Ga2 O3 0.25La2 O3 ±GeO2 ±0.20Ga2 O3 0.25La2 O3 ±GeO2 ±0.33Ga2 O3 0.25La2 O3 ±GeO2 ±0.50Ga2 O3 SiO2
5.137 5.332 5.375 5.438 5.271 5.226 5.246 2.203
1.842 1.866 1.865 1.897 1.852 1.856 1.790 1.462
5203.2 5224.4 5242.3 5272.5 5280.2 5280.2 5340.8 5944.2
2717.8 2678.4 2659.0 2699.5 2693.2 2735.9 2764.3 3748.7
L.-G. Hwa et al. / Journal of Non-Crystalline Solids 231 (1998) 222±226
225
For pure longitudinal waves C11 qV2L , and for pure transverse waves C44 qV2T , where VL and VT respectively are the longitudinal and transverse velocities. The sound velocities also allow the determination of Young's modulus E, bulk modulus B, and Poisson's ratio r, by the following equations: 3V 2 ÿ 4VT2 ; 1 E qVT2 L2 VL ÿ VT2 Bq
3VL2 ÿ 4VT2 ; 3
2
VL2 ÿ 2VT2 : 3 2 VL2 ÿ VT2 Table 2 gives the calculated elastic constants (C11 , C44 and C12 ), the C44 /C12 ratio, Young's modulus, bulk modulus and Poisson's ratio for seven lanthanum gallogermanate samples and the SiO2 sample. The overall uncertainty for these calculated quantities is estimated to be 2%. The calculated elastic constants, C11 , of lanthanum gallogermanate samples are about two times larger than that of the SiO2 sample. This dierence implies that lanthanum gallogermanate samples possess a rigid lattice structure. The C44 /C12 ratio is less than unity for our samples. This C44 /C12 ratio is an indicator of the force ®eld: central forces if C44 /C12 1 and non-central forces if C44 /C12 ¹ 1. As the ratio of C44 /C12 approaches unity, the central force ®eld may reduce fraction of broken bonds in the glass structure. Poisson's ratio of the lanthanum gallogermanate samples is in the range of 0.31±0.33, whereas in SiO2 glass this ratio is 0.17. The larger Poisson's ratio may be due to ionic bonds, in comparison with SiO2 , which is predominantly covalent [16±18]. r
Fig. 4. The logarithm of absorption coecient versus frequency for a 0.2La2 O3 ±GeO2 ±0.25Ga2 O3 glass.
To understand the relation between the fundamental absorption (deduced from re¯ectivity measurements) and the multiphonon edge absorption, we plot the logarithm of absorption coecient versus frequency for a 0.2La2 O3 ±GeO2 ±0.33Ga2 O3 sample, as indicated in Fig. 4. The results show that this sample has two-to-three phonon absorption behavior. In a glass the elastic strain produced by a stress can be described by two independent elastic constants, C11 and C44 . The Cauchy relation 2C44 C11 ) C12 allows one to determine C12 .
Table 2 The calculated elastic constants (C11 , C44 and C12 ), the C44 /C12 ratio, Young's modulus, E, bulk modulus, B, and Poisson's ratio, r, for lanthanum gallogermanate samples and a SiO2 glass sample Sample
C11 (GPa)
C44 (GPa)
C12 (GPa)
C44 /C12
E (GPa)
B (GPa)
r (GPa)
0.20La2 O3 ±GeO2 ±0.25Ga2 O3 0.25La2 O3 ±GeO2 ±0.25Ga2 O3 0.33La2 O3 ±GeO2 ±0.25Ga2 O3 0.50La2 O3 ±GeO2 ±0.25Ga2 O3 0.25La2 O3 ±GeO2 ±0.20Ga2 O3 0.25La2 O3 ±GeO2 ±0.33Ga2 O3 0.25La2 O3 ±GeO2 ±0.50Ga2 O3 SiO2
139.1 145.5 147.7 151.2 139.7 145.7 149.6 79.0
37.9 38.3 37.9 38.8 38.2 39.1 40.1 31.0
63.3 68.9 71.9 73.6 63.3 67.5 69.4 17.0
0.60 0.56 0.53 0.53 0.60 0.58 0.58 1.82
99.6 101.1 100.8 104.8 100.3 103.0 105.6 72.4
88.5 94.5 97.0 98.3 88.7 93.5 96.2 36.6
0.31 0.32 0.33 0.32 0.31 0.32 0.32 0.17
226
L.-G. Hwa et al. / Journal of Non-Crystalline Solids 231 (1998) 222±226
5. Conclusion We conclude that bonding in our lanthanum gallogermanate samples is mostly ionic. Both multiphonon edge absorption and elastic constant results are consistent with ionic bond eects in the glass structure. Acknowledgements The authors thank Ms S.Y. Lay of the department of physics, Fu-Jen Catholic University, for helping with the ultrasonic measurements, and Mr C.P. Shu of the department of physics, National Chung-Hsin University, for preparing glass samples used in this study. This work was supported in part by the National Science Council of R.O.C. under grant number NSC-86-2112-M-005-010. References [1] W.H. Dumbaugh, Phys. Chem. Glasses 27 (1986) 119. [2] T. Kokubo, Y. Inaka, S. Sakka, J. Non-Cryst. Solids 80 (1986) 518.
[3] T. Kokubo, Y. Inaka, S. Sakka, J. Non-Cryst. Solids 81 (1987) 337. [4] P.L. Higby, I.D. Aggarwal, J. Non-Cryst. Solids 163 (1993) 303. [5] B.H. Lindquist, J.E. Shelby, Phys. Chem. Glasses 35 (1994) 1. [6] S.P. Szu, C.P. Shu, L.G. Hwa, submitted to J. Non-Cryst. Solids, 1997. [7] B. Bendow, in: H. Ehrenreich, F. Seitz, D. Turnbull (Eds.), Solid State Physics, vol. 3, 1978, p. 249. [8] B. Bendow, M.G. Drexhage, H.G. Lipston, J. Appl. Phys. 52 (1981) 1460. [9] S.Y. Ko, L.G. Hwa, Chin. J. Mater. Sci. 27 (1995) 67. [10] L.G. Hwa, C.C. Chen, S.L. Hwang, Chin. J. Phys. 35 (1997) 78. [11] C.I. Merzbacher, Phys. Chem. Glasses 33 (1992) 233. [12] K. Fukumi, S. Sakka, J. Non-Cryst. Solids 94 (1987) 251. [13] J.A. Ruller, J.M. Jewell, J. Non-Cryst. Solids 175 (1994) 91. [14] O. Yamaguchi, H. Kawabata, H. Hashimoto, K. Shimizu, J. Am. Ceram. Soc. 70 (1987) C131. [15] J. Takahashi, T. Ohtsuka, J. Am. Ceram. Soc. 72 (1989) 426. [16] M.P. Brassington, T. Halling, A.J. Miller, G.A. Saunders, Mater. Res. Bull. 16 (1981) 613. [17] R. Ota, N. Soga, J. Non-Cryst. Solids 56 (1983) 105. [18] A.N. Streeram, A.K. Varshneya, D.R. Swiler, J. NonCryst. Solids 128 (1991) 294.
Optical and physical properties of lanthanum gallogermanate glasses Luu-Gen Hwa
a,* ,
Yi-Rui Chang a, Sung-Ping Szu
b
a b
Department of Physics, Fu-Jen Catholic University, Taipei 24205, Taiwan, ROC Department of Physics, National Chung-Hsing University, Taichung, Taiwan, ROC Received 16 December 1997; received in revised form 18 February 1998
Abstract Optical properties of lanthanum gallogermanate glasses were investigated by infrared (IR) transmission and IR re¯ectivity measurements. Several physical properties of these glasses, including density, index of refraction and ultrasonic velocities, were also measured. The experimental results are used to obtain elastic constants. These glasses are transparent over frequencies ranging from the near ultraviolet to the mid-IR (8 lm) and have ionic bond properties in their structure. Ó 1998 Elsevier Science B.V. All rights reserved. PACS: 61.43.Fs; 62.20.D; 78.30.L
1. Introduction Glasses containing heavy metal oxides are of interest for infrared (IR) transmission application due to their long IR cut-o wavelength in comparison with phosphate, borate and silicate glasses. Dumbaugh found that the addition of Ga2 O3 into PbO±Bi2 O3 and CdO±Bi2 O3 improved glass stability and these glasses are transparent to about 7 lm [1]. Kokubo et al. found that alkaliand alkaline-earth Ta2 O±Ga2 O3 or Nb2 O±Ga2 O3 glasses also have optical transmission to about 7 lm [2,3]. Glasses based on GeO2 make favorable ®ber core material because of their longer wavelength cut-o at which the GeO2 stretching vibration occurs. A recent study of barium gallo-
* Corresponding author. Tel.: +886-2 2903 1111 (ext 2436); fax: +886-2 2902 1038; e-mail: [email protected].
0022-3093/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 8 ) 0 0 4 5 5 - 4
germanate glasses demonstrated their potential for both IR optical waveguides and bulk optic components in the 3±5 lm region [4]. Lindquist and Shelby studied the properties of rare earth gallogermanate glasses [5]. The IR cut-o occurs at 6.05 lm. These glasses containing rare earth elements also have excellent chemical durability in water and very high Verdet constants due to the rare earth ion concentration. This second property makes these glasses suitable for use in Faraday rotation devices [5]. This paper reports on a segment of ongoing research program in which the optical and physical properties of the lanthanum gallogermanate glasses are investigated by measuring IR transmission, IR re¯ectivity, and ultrasonic pulseechos. The experimental results are used to obtain the elastic constants. The IR edge is discussed in the context of the intrinsic multiphonon absorption theory.
L.-G. Hwa et al. / Journal of Non-Crystalline Solids 231 (1998) 222±226
223
2. Experimental aspect Samples with formula: xLa2 O3 ±GeO2 ±y Ga2 O3 , mol% and where x La2 O3 mol%/GeO2 y Ga2 O3 mol%/GeO2 mol% were prepared by melting appropriate amounts of La2 O3 (Aldrich 99.9%), GeO2 (Aldrich 99.9%), Ga2 O3 (Aldrich 99.9%) in open atmosphere at temperatures between 1550 and 1650°C, for one to one hour and a half in a platinum crucible. The liquids were quenched by placing the bottom of the crucible in water. The glassy samples were identi®ed by X-ray diraction. To produce samples large enough for the experimental requirements, samples were batched to obtain 10 g. The glass-forming tendency will be discussed elsewhere [6]. The IR absorption spectra, including the transmission and re¯ectivity measurements, were carried out on a spectrometer (Perkin±Elmer FTIR2000) with an accessory of variable angle specular re¯ector. The resolution of the instrument is 0.7 cmÿ1 in the 300±4000 cmÿ1 region. Ultrasonic measurements were performed by a pulse-echo method with a pulser/receiver instrument (Panametrics model 5800) with quartz transducer. X-cut transducers were employed for longitudinal modes and Y-cut for shear modes. The pulse transit time was measured with a oscilloscope (Hewlett-Packard model 54502A). Several eects, such as multiple internal re¯ections within the transducer, sample thickness, and the acoustic impedance mismatch between glass sample and transducer, aect the accuracy of ultrasonic velocity measurements. The uncertainty is estimated about 1%. The density was determined by an Archimedes technique for which n-hexadecane was the working ¯uid. The accuracy of the measurement was 0.001 g/cm3 . The re¯ective indices of the sample were measured by Woolam's variable angle spectroscopic ellipsometer, and were accurate within 0.001.
Fig. 1. IR transmission spectra of four lanthanum gallogermanate glasses.
glasses are transparent to 8 lm in the mid-IR region. The results indicate that if the ratio Ga2 O3 /GeO2 is constant, the IR cut-o wavelength becomes larger with increasing La2 O3 contents in the glass system. Fig. 2 gives the multiphonon edge absorption versus frequency for various lanthanum gallogermanate samples. The IR re¯ectivity spectra of lanthanum gallogermanate samples at near normal incidence are similar. One particular example of a 0.3La2 O3 ±GeO2 ± 0.25Ga2 O3 sample is given in Fig. 3. The density, q, index of refraction, n, longitudinal (VL ) sound velocities and transverse (VT ) sound velocities of seven lanthanum gallogermanate
3. Results IR transmission spectra of four lanthanum gallogermanate glasses are given in Fig. 1. These
Fig. 2. The multiphonon edge absorption versus frequency for four lanthanum gallogermanate glasses.
224
L.-G. Hwa et al. / Journal of Non-Crystalline Solids 231 (1998) 222±226
Fig. 3. The IR re¯ectivity spectra of a 0.3La2 O3 ±GeO2 ± 0.25Ga2 O3 glass at near normal incidence.
samples and SiO2 glass sample are given in Table 1. The density, index of refraction and longitudinal sound velocity increase as the La2 O3 content increases in a xLa2 O3 ±GeO2 ±0.25Ga2 O3 glass system. 4. Discussion The IR absorption edge, which limits transparency at longer wavelength, is due to the multiphonon interactions between electromagnetic wave and lattice vibrations (speci®cally, anharmonicity and nonlinear electric moments). The origins of the multiphonon absorption of the solids were discussed by Bendow [7]. The results in Fig. 2 show that the IR edge is smooth, and the multiphonon absorption coecients of these glasses decrease exponentially with increasing frequencies. These phenomena are typi-
cal of the intrinsic multiphonon absorption in most ionic materials [8±10]. One step further, the experiment on the frequency and temperature dependence of the multiphonon absorption may give a deeper insight of the exponential behavior of the intrinsic multiphonon edge absorption of the materials. In the IR re¯ectivity spectra of lanthanum gallogermanate glass, the principal features are a strong band at 760 cmÿ1 , two mid-frequency bands respectively at 510 and 370 cmÿ1 . Merzbacher carried out infrared re¯ectance spectroscopy study on a series of barium gallogermanate glasses [11], and concluded that the gallogermanate glasses are structurally analogous to the aluminosilicate glasses. By analogy with aluminosilicate, the band between 700 and 850 cmÿ1 is assigned to T±O stretching vibrations, where T represents a tetrahedrally coordinated cation [11]. Because of their similar masses and coordinations of Ge and Ga, we assign the band at 760 cmÿ1 to the combination of the T±O (T Ge or Ga) stretching vibration band in [GaOÿ 4 ] and [GeO4 ] tetrahedral network. The band at 510 cmÿ1 we attribute to a Ga±O± Ga bending vibration. This assignment agrees with previous observations on alkaline earth gallate glasses and lead gallosilicate glasses [12,13]. Not so many previous vibrational studies of the La-related structure have been performed. However, Yamaguchi et al. [14] and Takahashi and Ohtsuka [15] found the La±O related vibration mode in the 300±400 cmÿ1 range. Consequently, we assign the band at 370 cmÿ1 to La±O vibration mode in our samples.
Table 1 The density, q, index of refraction, n, longitudinal (VL ) and transverse (VT ) sound velocities of seven lanthanum gallogermanate samples and the SiO2 glass sample Sample
q (g/cm3 )
n (514.5 nm)
VL (m/s)
VT (m/s)
0.20La2 O3 ±GeO2 ±0.25Ga2 O3 0.25La2 O3 ±GeO2 ±0.25Ga2 O3 0.33La2 O3 ±GeO2 ±0.25Ga2 O3 0.50La2 O3 ±GeO2 ±0.25Ga2 O3 0.25La2 O3 ±GeO2 ±0.20Ga2 O3 0.25La2 O3 ±GeO2 ±0.33Ga2 O3 0.25La2 O3 ±GeO2 ±0.50Ga2 O3 SiO2
5.137 5.332 5.375 5.438 5.271 5.226 5.246 2.203
1.842 1.866 1.865 1.897 1.852 1.856 1.790 1.462
5203.2 5224.4 5242.3 5272.5 5280.2 5280.2 5340.8 5944.2
2717.8 2678.4 2659.0 2699.5 2693.2 2735.9 2764.3 3748.7
L.-G. Hwa et al. / Journal of Non-Crystalline Solids 231 (1998) 222±226
225
For pure longitudinal waves C11 qV2L , and for pure transverse waves C44 qV2T , where VL and VT respectively are the longitudinal and transverse velocities. The sound velocities also allow the determination of Young's modulus E, bulk modulus B, and Poisson's ratio r, by the following equations: 3V 2 ÿ 4VT2 ; 1 E qVT2 L2 VL ÿ VT2 Bq
3VL2 ÿ 4VT2 ; 3
2
VL2 ÿ 2VT2 : 3 2 VL2 ÿ VT2 Table 2 gives the calculated elastic constants (C11 , C44 and C12 ), the C44 /C12 ratio, Young's modulus, bulk modulus and Poisson's ratio for seven lanthanum gallogermanate samples and the SiO2 sample. The overall uncertainty for these calculated quantities is estimated to be 2%. The calculated elastic constants, C11 , of lanthanum gallogermanate samples are about two times larger than that of the SiO2 sample. This dierence implies that lanthanum gallogermanate samples possess a rigid lattice structure. The C44 /C12 ratio is less than unity for our samples. This C44 /C12 ratio is an indicator of the force ®eld: central forces if C44 /C12 1 and non-central forces if C44 /C12 ¹ 1. As the ratio of C44 /C12 approaches unity, the central force ®eld may reduce fraction of broken bonds in the glass structure. Poisson's ratio of the lanthanum gallogermanate samples is in the range of 0.31±0.33, whereas in SiO2 glass this ratio is 0.17. The larger Poisson's ratio may be due to ionic bonds, in comparison with SiO2 , which is predominantly covalent [16±18]. r
Fig. 4. The logarithm of absorption coecient versus frequency for a 0.2La2 O3 ±GeO2 ±0.25Ga2 O3 glass.
To understand the relation between the fundamental absorption (deduced from re¯ectivity measurements) and the multiphonon edge absorption, we plot the logarithm of absorption coecient versus frequency for a 0.2La2 O3 ±GeO2 ±0.33Ga2 O3 sample, as indicated in Fig. 4. The results show that this sample has two-to-three phonon absorption behavior. In a glass the elastic strain produced by a stress can be described by two independent elastic constants, C11 and C44 . The Cauchy relation 2C44 C11 ) C12 allows one to determine C12 .
Table 2 The calculated elastic constants (C11 , C44 and C12 ), the C44 /C12 ratio, Young's modulus, E, bulk modulus, B, and Poisson's ratio, r, for lanthanum gallogermanate samples and a SiO2 glass sample Sample
C11 (GPa)
C44 (GPa)
C12 (GPa)
C44 /C12
E (GPa)
B (GPa)
r (GPa)
0.20La2 O3 ±GeO2 ±0.25Ga2 O3 0.25La2 O3 ±GeO2 ±0.25Ga2 O3 0.33La2 O3 ±GeO2 ±0.25Ga2 O3 0.50La2 O3 ±GeO2 ±0.25Ga2 O3 0.25La2 O3 ±GeO2 ±0.20Ga2 O3 0.25La2 O3 ±GeO2 ±0.33Ga2 O3 0.25La2 O3 ±GeO2 ±0.50Ga2 O3 SiO2
139.1 145.5 147.7 151.2 139.7 145.7 149.6 79.0
37.9 38.3 37.9 38.8 38.2 39.1 40.1 31.0
63.3 68.9 71.9 73.6 63.3 67.5 69.4 17.0
0.60 0.56 0.53 0.53 0.60 0.58 0.58 1.82
99.6 101.1 100.8 104.8 100.3 103.0 105.6 72.4
88.5 94.5 97.0 98.3 88.7 93.5 96.2 36.6
0.31 0.32 0.33 0.32 0.31 0.32 0.32 0.17
226
L.-G. Hwa et al. / Journal of Non-Crystalline Solids 231 (1998) 222±226
5. Conclusion We conclude that bonding in our lanthanum gallogermanate samples is mostly ionic. Both multiphonon edge absorption and elastic constant results are consistent with ionic bond eects in the glass structure. Acknowledgements The authors thank Ms S.Y. Lay of the department of physics, Fu-Jen Catholic University, for helping with the ultrasonic measurements, and Mr C.P. Shu of the department of physics, National Chung-Hsin University, for preparing glass samples used in this study. This work was supported in part by the National Science Council of R.O.C. under grant number NSC-86-2112-M-005-010. References [1] W.H. Dumbaugh, Phys. Chem. Glasses 27 (1986) 119. [2] T. Kokubo, Y. Inaka, S. Sakka, J. Non-Cryst. Solids 80 (1986) 518.
[3] T. Kokubo, Y. Inaka, S. Sakka, J. Non-Cryst. Solids 81 (1987) 337. [4] P.L. Higby, I.D. Aggarwal, J. Non-Cryst. Solids 163 (1993) 303. [5] B.H. Lindquist, J.E. Shelby, Phys. Chem. Glasses 35 (1994) 1. [6] S.P. Szu, C.P. Shu, L.G. Hwa, submitted to J. Non-Cryst. Solids, 1997. [7] B. Bendow, in: H. Ehrenreich, F. Seitz, D. Turnbull (Eds.), Solid State Physics, vol. 3, 1978, p. 249. [8] B. Bendow, M.G. Drexhage, H.G. Lipston, J. Appl. Phys. 52 (1981) 1460. [9] S.Y. Ko, L.G. Hwa, Chin. J. Mater. Sci. 27 (1995) 67. [10] L.G. Hwa, C.C. Chen, S.L. Hwang, Chin. J. Phys. 35 (1997) 78. [11] C.I. Merzbacher, Phys. Chem. Glasses 33 (1992) 233. [12] K. Fukumi, S. Sakka, J. Non-Cryst. Solids 94 (1987) 251. [13] J.A. Ruller, J.M. Jewell, J. Non-Cryst. Solids 175 (1994) 91. [14] O. Yamaguchi, H. Kawabata, H. Hashimoto, K. Shimizu, J. Am. Ceram. Soc. 70 (1987) C131. [15] J. Takahashi, T. Ohtsuka, J. Am. Ceram. Soc. 72 (1989) 426. [16] M.P. Brassington, T. Halling, A.J. Miller, G.A. Saunders, Mater. Res. Bull. 16 (1981) 613. [17] R. Ota, N. Soga, J. Non-Cryst. Solids 56 (1983) 105. [18] A.N. Streeram, A.K. Varshneya, D.R. Swiler, J. NonCryst. Solids 128 (1991) 294.