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Ultrasonic studies on ternary TeO2–V2O5–Sm2O3 glasses
Materials Chemistry and Physics 61 (1999) 103±109
Ultrasonic studies on ternary TeO2±V2O5±Sm2O3 glasses M.A. Sidkey, A. Abd El-Moneim*, L. Abd El-Latif National Institute for Standards, Giza, Egypt Received 30 June 1998; received in revised form 3 December 1998; accepted 28 February 1999
Abstract Longitudinal and shear wave velocities were measured in different compositions of the ternary glass system; 65TeO2±(35 ÿ x)V2O5± xSm2O3 at room temperature and at 4 MHz frequency using pulse echo technique. The densities of the glasses were measured by the displacement method using toluene as immersion liquid. The elastic moduli, Debye temperature, softening temperature, and micro-hardness were then calculated and have been used to obtain quantitative details about the structure of these glasses. The effect of adding Sm2O3, on the expense of V2O5, was investigated in terms of the number of network bonds of the glass. The average atomic ring size of the network was also calculated and it was found that it depends on the concentration of the modi®er. The results obtained showed that these glasses become more stable and compact when modi®ed with the rare earth oxide Sm2O3. This in turn increases the number of network bonds per unit volume and decrease the average atomic ring size of the network and consequently increases the elastic properties of these glasses. # 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Tellurite glasses; Elastic moduli; Debye temperature
1. Introduction Tellurite glasses posses interesting glass-forming ability, glass structure, no hygroscopic properties, and low melting point. Previous studies [1,2] on vanadium tellurite glasses showed that they are semiconducting glasses and they switch when a high electrical ®eld is applied. They also have high refractive index [3], high infrared transmittance [4], and large third order non-linear susceptibility [5,6]. The mechanical structure of TeO2±V2O5 glasses depends on the percentage of V2O5. When the V2O5 concentration is below 20 mol%, the three-dimensional tellurite network is partially broken by the formation of TeO3 trigonal pyramids which in turn reduce the glass rigidity. When V2O5 concentration is above 20 mol%, the glass structure changed from the continuous tellurite network to the continuous vanadate network. The velocities of ultrasonic waves in these glasses as well as the elastic properties are practically very useful for describing glasses as a function of composition since they give information about the microstructure and all the dynamics of glass. Moreover, the elastic properties are related to microscopic properties through the behavior of *Corresponding author. Present address: Physics Department, Faculty of Science, Zagazing University, Zagazing, Egypt.
the network and the modi®er. This work aims to throw more light on the previous work reported on binary, and ternary tellurite glasses [7±11]. 2. Experimental Glass samples were prepared in the form 65TeO2± (35 ÿ x)V2O5±xSm2O3, where x 0.1, 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0 mol%, by mixing together speci®c weights of tellurite oxide, vanadium pentaoxide, and samarium oxide (Aldrich Chemicals 99.99%) in a covered crucible. In order to reduce tendency to volatilization, mixture was kept at 3008C for 1 h. The crucible was then transferred to a muf¯e furnace which was controlled at a temperature in the range from 7208C to 7508C depending on the composition of the sample. The crucible was left in the furnace for 30 min. The melt was casted in a room temperature steel mold, and annealed at 3008C for 1 h. Two opposite sides of each glass sample were polished to obtain optically ¯at and parallel faces. The densities of the glass samples were measured accurately to the third decimal by the displacement method using toluene as immersion liquid. The ultrasonic velocities were measured, using pulse echo technique, by measuring the elapsed time between the initiation and the receipt of the
0254-0584/99/$ ± see front matter # 1999 Published by Elsevier Science S.A. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 9 9 ) 0 0 0 6 7 - X
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M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
pulse appearing on the screen of a ¯aw detector (USM3Krautkramer) by standard electronic circuit (PM 3055 Philips). The velocity was therefore obtained by dividing the round trip distance by the elapsed time. Random errors in the measuring were 100 m sÿ1 for longitudinal velocity and 60 m sÿ1 for shear velocity. X-ray diffraction examination was carried out using Philips PW/1710 with Ni®lter, Cu radiation ( 1.5424) at 40 kV, 30 mA and a scanning speed of 0.02% sÿ1. 3. Results and discussions X-ray diffraction pattern of the investigated glass showed the halo expected for the amorphous state of these glasses. As seen from Table 1, the variation of the glasses densities with Sm2O3 mol% concentration shows a linear increase in density with the substitution of V2O5 by Sm2O3 from 4.376 to 4.689 g cmÿ3. Molar volume (VM) of these glasses decrease with increasing Sm2O3 content from 38.32 to 37.5 cm3. The variations in these parameters accompanying the addition of Sm2O3 are related to the change in the atomic mass and atomic volume of the constituent elements (vanadium and samarium). The atomic mass of vanadium and samarium is 50.94 and 150.37 g, respectively, and their respective atomic volumes are 8.37 and 20 cm3 g-atÿ1. The replacement of vanadium atoms by samarium atoms explains the observed linear increase in density with increasing Sm2O3 content. Fig. 1 shows the variation of longitudinal and shear ultrasonic wave velocities with Sm2O3 concentration. Both velocities increase with the increase of Sm2O3 content and a
Table 1 Density, molar volume, and micro-hardness of 65TeO2±(35 ÿ x)V2O5± xSm2O3 Sm2O3 (mol%)
Density (g cmÿ3)
Molar volume VM (cm3)
Micro-hardness H (GPa)
0.1 0.5 1.0 2.0 3.0 4.0 5.0
4.376 4.393 4.436 4.512 4.531 4.659 4.689
38.32 38.33 38.14 38.86 38.07 37.39 37.50
3.85 3.88 3.93 4.00 4.10 4.21 4.32
linear relation is observed. Figs. 2 and 3 depict the variation of elastic moduli (longitudinal, shear and Young's) with Sm2O3 mol% concentration. The replacement of transition metal oxide V2O5 by the rare earth oxide Sm2O3; in the ternary glasses under investigation increases the rigidity of these glasses which in turn increases the ultrasonic wave velocities. Debye temperature D were calculated using the equation D 251:2Vm
1=3 nM
(1)
where Vm, (km sÿ1) is the mean ultrasonic velocity, n is the number of atoms in the chemical formula, M is the effective molecular weight. and is the density. Debye temperature represents the temperature at which nearly all modes of vibration in a solid are excited and its increase implies an increase in the rigidity of the glass. Fig. 4 describes the variations of Debye temperature with samarium oxide concentration in TeO2±V2O5±Sm2O3 glasses. The Debye tem-
Fig. 1. Variation of ultrasonic wave velocities (longitudinal and shear) as a function of Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
105
Fig. 2. Variation of elastic moduli (longitudinal and shear) as a function of Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
perature increases gradually as the samarium oxide increases which indicates the increase in the rigidity of these glasses. The increase in Debye temperature is attributed to the increase in the number of atoms in the chemical formula of the glass and the increase in the mean ultrasonic velocity.
Softening temperature Ts were calculated from the expression given by Anderson [12] as, Ts
Vt2 M C2 n
(2)
where Vt is the shear velocity, M is the effective molecular
Fig. 3. Dependence of Young's modulus on Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
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M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
Fig. 4. Debye temperature dependence on Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
weight, n is the number of atoms in the chemical formula, and C is the constant of proportionality and equals to 0.5074 105 cm sÿ1 Kÿ1/2. The softening point is the temperature at which viscous ¯ow changes to plastic ¯ow. In actual practice, it plays a crucial role in determining the temperature stability of glass. The higher the value of softening temperature of a glass, the greater is the stability of its elastic properties. From Fig. 5 it can be seen that softening temperature increases as Sm2O3 content increases
and these glasses become more stable as the network modi®er content increases. Micro-hardness H was obtained from the equation H
1 ÿ 2E 6 1
(3)
where is Poisson's ratio, and E is Young's modulus. Micro-hardness expresses the stress required to eliminate the free volume (deformation of the network) of the glass.
Fig. 5. Variation of softening temperature as a function of Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
dium atoms, with coordination number nf 5 and cross link density per cation nc 3, by the rare earth samarium atoms, with higher coordination number nf 7 and cross link density per cation nc 5. The average cross link density nc and the number of network bonds per unit volume nb are also calculated according to the expressions given by Higazy and Bridge [14] as; X nc nc Nc i (8)
As seen from Table 1, the micro-hardness increases as Sm2O3 content increases indicating the increase in the glass rigidity. An attempt to interpret the experimental results obtained from the study of elastic properties of the glass system of 65TeO2±(35 ÿ x)V2O5±xSm2O3 based on bond compression bulk modulus is attempted. The theoretical bond compression bulk modulus Kbc for some structures gives a fair approximation to the observed compressibility [13] although it is usually larger than the experimental modulus Ke. For a three-dimensional structure network, Kbc can be calculated from an equation given by Bridge et al. [13] as NA X xnf r 2 Fi (4) Kbc 9VM i
i
nb
is the average stretching force constant of the glass where F and is given by the equation [14] as P P xnf f i (6) F i xnf i The theoretical Poisson's ratio th was calculated from the equation [14] 0:28
(7)
nc 0:25
NA X nf xi VM i
(9)
where is the total number of cations per glass formula unit, nc is the number of cross link per cation de®ned as the number of bridging bonds per cation minus two, and Nc is number of cations per glass formula unit. The values of the constants used in these calculations are listed in Table 3. The increase of samarium oxide concentration on the expense of vanadium oxide from 0.1 to 5.0 mol% leads to an increase in both the average cross link density nc from 2.52 to 2.67 and the number of network bonds per unit volume nb from 6.84 1028 to 7.l5 1028 mÿ3. Meanwhile, the average stretching force constant decreased from 240.3 to 228.0 N mÿ1 (Table 2). Since Ke is less than Kbc, compression proceeds via a mechanism requiring much less energy than that required for pure compression of network bonds series [13]. This in turns results in a more cross-linked and compact structure and this explains the observed increase in Kbc values. The decrease in the average atomic ring size l from 0.532 to 0.509 nm with increasing samarium oxide content is due to the gradual increase in the average cross link density nc.
where x is the mole fraction of component oxide, nf is the coordination number of cation, r is the bond length, f is the stretching force constant of oxide, NA is Avogadro's number, and i denotes the component oxide. Moreover, the average atomic ring size l, de®ned as ring perimeter, (number of bonds in ring multiplied by bond length divided by ) is expressed according to the equation [13] 0:26 F l 0:0106 Ke
th
107
The calculated values of the average stretching force constant F, the atomic ring size l, the ratio Kbc/Ke, number of bonds per unit volume nb, average cross link density, nc and theoretical Poisson's ratio th are given in Table 2. It is quite clear from Table 2 that the calculated values of Kbc increase with increasing Sm2O3 content from the calculated values 67.3 to 69.0 GPa. This increase in Kbc values is related to the replacement of the transition metal vana-
Table 3 Coordination number of cross link density per cation, bond length, stretching force constant of the oxide Oxide
nf
nc
r (nm)
f (N mÿ1)
Reference
TeO2 V2O5 Sm2O3
4 5 7
2 3 5
0.199 0.183 0.249
216 277 110
[13] [15] [16]
Table 2 Average stretching force constant, atomic ring size, (Kbc/Ke) ratio, number of network bond per unit volume, average cross link density, and theoretical Poisson's ratio Sm2O3 (mol%)
(N mÿ1) F
l (nm)
Kbc/Ke
Nb 1028 (mÿ3)
nc
th
0.1 0.5 1.0 2.0 3.0 4.0 5.0
240.3 239.3 238.0 235.5 233.0 230.6 228.0
0.532 0.531 0.528 0.523 0.520 0.513 0.509
2.33 2.32 2.30 2.25 2.21 2.17 2.12
6.84 6.85 6.89 6.98 6.98 7.14 7.15
2.52 2.53 2.55 2.58 2.61 3.64 2.67
0.222 0.222 0.222 0.221 0.221 0.220 0.219
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M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
Fig. 6. Kbc/Ke ratio versus Sm2O3 mol% content.
Fig. 6 describes the dependence of Kbc/Ke ratio on Sm2O3 mol% content. It is clear from the ®gure that Kbc/Ke decreases gradually as the samarium oxide concentration increases. The relatively small value of (Kbc/Ke) 2.12 indicates a relatively close three-dimensional network structure. Alternatively, a high value of (KbC/Ke) could imply the existence of layer or chain network [13]. The dependence of samarium oxide content on the atomic ring size l (shown in
Fig. 7) is quite similar to that observed in Fig. 6 while Fig. 8 illustrates the variation of the estimated atomic ring size l with the value of (Kbc/Ke) for some oxide glasses. The ratio Kbc/Ke for the studied glasses lies on the curve and very near to silicon dioxide. Theoretical Poisson's ratio th of the studied glasses (Table 2) changes from 0.222 to 0.219. The main factor affecting Poisson's ratio is the average cross link density nc.
Fig. 7. Variation of atomic ring size l with Sm2O3 mol% content.
M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
109
Fig. 8. Variation of the estimated average atomic ring size l with the value of Kbc/Ke.
The observed decrease in Poisson's ratio with increasing Sm2O3 is mainly due to the increase in cross link density in these glasses from 2.52 to 2.67. 4. Conclusions The room temperature measurements on ultrasonic velocities and densities of the ternary TeO2±V2O5±Sm2O3 glasses showed that: (1) Ultrasonic velocity as well as elastic moduli and Debye temperature increase as Sm2O3 mol% content increases from 0.1% to 5.O% which indicates a strengthening of the binding energy in the network, (2) the observed increase in density of the investigated glass with increasing Sm2O3 content is attributed to the replacement of vanadium atoms by samarium atoms and (3) although the agreement between calculated bulk modulus and Poisson's ratio is not satisfactory, we were able to calculate ring diameter of the present network, average cross linking and stretching force constant to determine the critical factors affecting the elasticity of the glasses.
References [1] V.I. Gaman, V.A. Penznikov, N.I. Fedyainova, uzv. Vyssh Ucheb. Zaved. Fiz. 2 (1972) 57. [2] C. Rhee, S.W. Yoon, H.J. Lim, in: Proc. 10th Int. Cong. on Glass Kyoto, Japan, 7 (1974) 51. [3] J.E. Stanworth, Nature 169 (1952) 581. [4] H. Burger, W. Vogel, V. Kozhukharov, Infrared Phys. 25 (1985) 395. [5] H. Nasu, O. Matsushita, K. Kamiya, H. Kobayashi, K. Kubodera, J. Non-Cryst. Solids 124 (1990) 275. [6] S.H. Kim, T. Yoko, S. Sakka, J. Am. Ceram. Soc. 76 (1993) 2486. [7] E.F. Lambson, G.A. Saunders, B. Bridge, R. El Mallawany, I. NonCryst. Solids 69 (1984) 117. [8] R. El Mallawany, G.A. Saunders, J. Mater. Sci. Lett. 6 (1987) 443. [9] R. El Mallawany, G.A. Saunders, J. Mater. Sci. Lett. 7 (1988) 870. [10] R. El Mallawany, J. Appl. Phys. 73 (1993) 4878. [11] R. El Mallawany, M.A. Sidkey, A. Khafagy, H. Afifi, Mater. Chem. Phys. 37 (1994) 295. [12] O.L. Anderson, in: W.P. Mason (Ed.), Physical Acoustics, vol. 3B, Academic Press, New York, 1965. [13] B. Bridge, N.D. Patel, D.N. Waters, Phys. Stat. Sol. 177 (1983) 655. [14] A.A. Higazy, B. Bridge, Phys. Chem. Glasses 17 (1986) 1. [15] M.A. Sidkey, R. El-Mallawany, R.I. Nakhla, A. Abd El-Moneim, J. Non-Cryst. Solids 215 (1997) 75. [16] R. El Mallawany, J. Mater. Res. 5 (1990) 2218.
Ultrasonic studies on ternary TeO2±V2O5±Sm2O3 glasses M.A. Sidkey, A. Abd El-Moneim*, L. Abd El-Latif National Institute for Standards, Giza, Egypt Received 30 June 1998; received in revised form 3 December 1998; accepted 28 February 1999
Abstract Longitudinal and shear wave velocities were measured in different compositions of the ternary glass system; 65TeO2±(35 ÿ x)V2O5± xSm2O3 at room temperature and at 4 MHz frequency using pulse echo technique. The densities of the glasses were measured by the displacement method using toluene as immersion liquid. The elastic moduli, Debye temperature, softening temperature, and micro-hardness were then calculated and have been used to obtain quantitative details about the structure of these glasses. The effect of adding Sm2O3, on the expense of V2O5, was investigated in terms of the number of network bonds of the glass. The average atomic ring size of the network was also calculated and it was found that it depends on the concentration of the modi®er. The results obtained showed that these glasses become more stable and compact when modi®ed with the rare earth oxide Sm2O3. This in turn increases the number of network bonds per unit volume and decrease the average atomic ring size of the network and consequently increases the elastic properties of these glasses. # 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Tellurite glasses; Elastic moduli; Debye temperature
1. Introduction Tellurite glasses posses interesting glass-forming ability, glass structure, no hygroscopic properties, and low melting point. Previous studies [1,2] on vanadium tellurite glasses showed that they are semiconducting glasses and they switch when a high electrical ®eld is applied. They also have high refractive index [3], high infrared transmittance [4], and large third order non-linear susceptibility [5,6]. The mechanical structure of TeO2±V2O5 glasses depends on the percentage of V2O5. When the V2O5 concentration is below 20 mol%, the three-dimensional tellurite network is partially broken by the formation of TeO3 trigonal pyramids which in turn reduce the glass rigidity. When V2O5 concentration is above 20 mol%, the glass structure changed from the continuous tellurite network to the continuous vanadate network. The velocities of ultrasonic waves in these glasses as well as the elastic properties are practically very useful for describing glasses as a function of composition since they give information about the microstructure and all the dynamics of glass. Moreover, the elastic properties are related to microscopic properties through the behavior of *Corresponding author. Present address: Physics Department, Faculty of Science, Zagazing University, Zagazing, Egypt.
the network and the modi®er. This work aims to throw more light on the previous work reported on binary, and ternary tellurite glasses [7±11]. 2. Experimental Glass samples were prepared in the form 65TeO2± (35 ÿ x)V2O5±xSm2O3, where x 0.1, 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0 mol%, by mixing together speci®c weights of tellurite oxide, vanadium pentaoxide, and samarium oxide (Aldrich Chemicals 99.99%) in a covered crucible. In order to reduce tendency to volatilization, mixture was kept at 3008C for 1 h. The crucible was then transferred to a muf¯e furnace which was controlled at a temperature in the range from 7208C to 7508C depending on the composition of the sample. The crucible was left in the furnace for 30 min. The melt was casted in a room temperature steel mold, and annealed at 3008C for 1 h. Two opposite sides of each glass sample were polished to obtain optically ¯at and parallel faces. The densities of the glass samples were measured accurately to the third decimal by the displacement method using toluene as immersion liquid. The ultrasonic velocities were measured, using pulse echo technique, by measuring the elapsed time between the initiation and the receipt of the
0254-0584/99/$ ± see front matter # 1999 Published by Elsevier Science S.A. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 9 9 ) 0 0 0 6 7 - X
104
M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
pulse appearing on the screen of a ¯aw detector (USM3Krautkramer) by standard electronic circuit (PM 3055 Philips). The velocity was therefore obtained by dividing the round trip distance by the elapsed time. Random errors in the measuring were 100 m sÿ1 for longitudinal velocity and 60 m sÿ1 for shear velocity. X-ray diffraction examination was carried out using Philips PW/1710 with Ni®lter, Cu radiation ( 1.5424) at 40 kV, 30 mA and a scanning speed of 0.02% sÿ1. 3. Results and discussions X-ray diffraction pattern of the investigated glass showed the halo expected for the amorphous state of these glasses. As seen from Table 1, the variation of the glasses densities with Sm2O3 mol% concentration shows a linear increase in density with the substitution of V2O5 by Sm2O3 from 4.376 to 4.689 g cmÿ3. Molar volume (VM) of these glasses decrease with increasing Sm2O3 content from 38.32 to 37.5 cm3. The variations in these parameters accompanying the addition of Sm2O3 are related to the change in the atomic mass and atomic volume of the constituent elements (vanadium and samarium). The atomic mass of vanadium and samarium is 50.94 and 150.37 g, respectively, and their respective atomic volumes are 8.37 and 20 cm3 g-atÿ1. The replacement of vanadium atoms by samarium atoms explains the observed linear increase in density with increasing Sm2O3 content. Fig. 1 shows the variation of longitudinal and shear ultrasonic wave velocities with Sm2O3 concentration. Both velocities increase with the increase of Sm2O3 content and a
Table 1 Density, molar volume, and micro-hardness of 65TeO2±(35 ÿ x)V2O5± xSm2O3 Sm2O3 (mol%)
Density (g cmÿ3)
Molar volume VM (cm3)
Micro-hardness H (GPa)
0.1 0.5 1.0 2.0 3.0 4.0 5.0
4.376 4.393 4.436 4.512 4.531 4.659 4.689
38.32 38.33 38.14 38.86 38.07 37.39 37.50
3.85 3.88 3.93 4.00 4.10 4.21 4.32
linear relation is observed. Figs. 2 and 3 depict the variation of elastic moduli (longitudinal, shear and Young's) with Sm2O3 mol% concentration. The replacement of transition metal oxide V2O5 by the rare earth oxide Sm2O3; in the ternary glasses under investigation increases the rigidity of these glasses which in turn increases the ultrasonic wave velocities. Debye temperature D were calculated using the equation D 251:2Vm
1=3 nM
(1)
where Vm, (km sÿ1) is the mean ultrasonic velocity, n is the number of atoms in the chemical formula, M is the effective molecular weight. and is the density. Debye temperature represents the temperature at which nearly all modes of vibration in a solid are excited and its increase implies an increase in the rigidity of the glass. Fig. 4 describes the variations of Debye temperature with samarium oxide concentration in TeO2±V2O5±Sm2O3 glasses. The Debye tem-
Fig. 1. Variation of ultrasonic wave velocities (longitudinal and shear) as a function of Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
105
Fig. 2. Variation of elastic moduli (longitudinal and shear) as a function of Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
perature increases gradually as the samarium oxide increases which indicates the increase in the rigidity of these glasses. The increase in Debye temperature is attributed to the increase in the number of atoms in the chemical formula of the glass and the increase in the mean ultrasonic velocity.
Softening temperature Ts were calculated from the expression given by Anderson [12] as, Ts
Vt2 M C2 n
(2)
where Vt is the shear velocity, M is the effective molecular
Fig. 3. Dependence of Young's modulus on Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
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M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
Fig. 4. Debye temperature dependence on Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
weight, n is the number of atoms in the chemical formula, and C is the constant of proportionality and equals to 0.5074 105 cm sÿ1 Kÿ1/2. The softening point is the temperature at which viscous ¯ow changes to plastic ¯ow. In actual practice, it plays a crucial role in determining the temperature stability of glass. The higher the value of softening temperature of a glass, the greater is the stability of its elastic properties. From Fig. 5 it can be seen that softening temperature increases as Sm2O3 content increases
and these glasses become more stable as the network modi®er content increases. Micro-hardness H was obtained from the equation H
1 ÿ 2E 6 1
(3)
where is Poisson's ratio, and E is Young's modulus. Micro-hardness expresses the stress required to eliminate the free volume (deformation of the network) of the glass.
Fig. 5. Variation of softening temperature as a function of Sm2O3 mol% content in TeO2±V2O5±Sm2O3 glass system.
M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
dium atoms, with coordination number nf 5 and cross link density per cation nc 3, by the rare earth samarium atoms, with higher coordination number nf 7 and cross link density per cation nc 5. The average cross link density nc and the number of network bonds per unit volume nb are also calculated according to the expressions given by Higazy and Bridge [14] as; X nc nc Nc i (8)
As seen from Table 1, the micro-hardness increases as Sm2O3 content increases indicating the increase in the glass rigidity. An attempt to interpret the experimental results obtained from the study of elastic properties of the glass system of 65TeO2±(35 ÿ x)V2O5±xSm2O3 based on bond compression bulk modulus is attempted. The theoretical bond compression bulk modulus Kbc for some structures gives a fair approximation to the observed compressibility [13] although it is usually larger than the experimental modulus Ke. For a three-dimensional structure network, Kbc can be calculated from an equation given by Bridge et al. [13] as NA X xnf r 2 Fi (4) Kbc 9VM i
i
nb
is the average stretching force constant of the glass where F and is given by the equation [14] as P P xnf f i (6) F i xnf i The theoretical Poisson's ratio th was calculated from the equation [14] 0:28
(7)
nc 0:25
NA X nf xi VM i
(9)
where is the total number of cations per glass formula unit, nc is the number of cross link per cation de®ned as the number of bridging bonds per cation minus two, and Nc is number of cations per glass formula unit. The values of the constants used in these calculations are listed in Table 3. The increase of samarium oxide concentration on the expense of vanadium oxide from 0.1 to 5.0 mol% leads to an increase in both the average cross link density nc from 2.52 to 2.67 and the number of network bonds per unit volume nb from 6.84 1028 to 7.l5 1028 mÿ3. Meanwhile, the average stretching force constant decreased from 240.3 to 228.0 N mÿ1 (Table 2). Since Ke is less than Kbc, compression proceeds via a mechanism requiring much less energy than that required for pure compression of network bonds series [13]. This in turns results in a more cross-linked and compact structure and this explains the observed increase in Kbc values. The decrease in the average atomic ring size l from 0.532 to 0.509 nm with increasing samarium oxide content is due to the gradual increase in the average cross link density nc.
where x is the mole fraction of component oxide, nf is the coordination number of cation, r is the bond length, f is the stretching force constant of oxide, NA is Avogadro's number, and i denotes the component oxide. Moreover, the average atomic ring size l, de®ned as ring perimeter, (number of bonds in ring multiplied by bond length divided by ) is expressed according to the equation [13] 0:26 F l 0:0106 Ke
th
107
The calculated values of the average stretching force constant F, the atomic ring size l, the ratio Kbc/Ke, number of bonds per unit volume nb, average cross link density, nc and theoretical Poisson's ratio th are given in Table 2. It is quite clear from Table 2 that the calculated values of Kbc increase with increasing Sm2O3 content from the calculated values 67.3 to 69.0 GPa. This increase in Kbc values is related to the replacement of the transition metal vana-
Table 3 Coordination number of cross link density per cation, bond length, stretching force constant of the oxide Oxide
nf
nc
r (nm)
f (N mÿ1)
Reference
TeO2 V2O5 Sm2O3
4 5 7
2 3 5
0.199 0.183 0.249
216 277 110
[13] [15] [16]
Table 2 Average stretching force constant, atomic ring size, (Kbc/Ke) ratio, number of network bond per unit volume, average cross link density, and theoretical Poisson's ratio Sm2O3 (mol%)
(N mÿ1) F
l (nm)
Kbc/Ke
Nb 1028 (mÿ3)
nc
th
0.1 0.5 1.0 2.0 3.0 4.0 5.0
240.3 239.3 238.0 235.5 233.0 230.6 228.0
0.532 0.531 0.528 0.523 0.520 0.513 0.509
2.33 2.32 2.30 2.25 2.21 2.17 2.12
6.84 6.85 6.89 6.98 6.98 7.14 7.15
2.52 2.53 2.55 2.58 2.61 3.64 2.67
0.222 0.222 0.222 0.221 0.221 0.220 0.219
108
M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
Fig. 6. Kbc/Ke ratio versus Sm2O3 mol% content.
Fig. 6 describes the dependence of Kbc/Ke ratio on Sm2O3 mol% content. It is clear from the ®gure that Kbc/Ke decreases gradually as the samarium oxide concentration increases. The relatively small value of (Kbc/Ke) 2.12 indicates a relatively close three-dimensional network structure. Alternatively, a high value of (KbC/Ke) could imply the existence of layer or chain network [13]. The dependence of samarium oxide content on the atomic ring size l (shown in
Fig. 7) is quite similar to that observed in Fig. 6 while Fig. 8 illustrates the variation of the estimated atomic ring size l with the value of (Kbc/Ke) for some oxide glasses. The ratio Kbc/Ke for the studied glasses lies on the curve and very near to silicon dioxide. Theoretical Poisson's ratio th of the studied glasses (Table 2) changes from 0.222 to 0.219. The main factor affecting Poisson's ratio is the average cross link density nc.
Fig. 7. Variation of atomic ring size l with Sm2O3 mol% content.
M.A. Sidkey et al. / Materials Chemistry and Physics 61 (1999) 103±109
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Fig. 8. Variation of the estimated average atomic ring size l with the value of Kbc/Ke.
The observed decrease in Poisson's ratio with increasing Sm2O3 is mainly due to the increase in cross link density in these glasses from 2.52 to 2.67. 4. Conclusions The room temperature measurements on ultrasonic velocities and densities of the ternary TeO2±V2O5±Sm2O3 glasses showed that: (1) Ultrasonic velocity as well as elastic moduli and Debye temperature increase as Sm2O3 mol% content increases from 0.1% to 5.O% which indicates a strengthening of the binding energy in the network, (2) the observed increase in density of the investigated glass with increasing Sm2O3 content is attributed to the replacement of vanadium atoms by samarium atoms and (3) although the agreement between calculated bulk modulus and Poisson's ratio is not satisfactory, we were able to calculate ring diameter of the present network, average cross linking and stretching force constant to determine the critical factors affecting the elasticity of the glasses.
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