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Mixed alkali effect in optical properties of lithium–potassium bismuth borate glass system
Materials Letters 58 (2004) 694 – 698 www.elsevier.com/locate/matlet
Mixed alkali effect in optical properties of lithium–potassium bismuth borate glass system A. Agarwal a,*, V.P. Seth b, S. Sanghi a, P. Gahlot b, S. Khasa c a
Department of Applied Physics, G.J. University, Hisar 125001, India b Department of Physics, M.D. University, Rohtak 124001, India c Department of Physics, Government College, Bahadurgarh 124 507, India Received 28 April 2003; accepted 10 June 2003
Abstract The mixed alkali effect (MAE) has been investigated in the glass system (30 x)Li2OxK2O20Bi2O350B2O3 (0 V x V 30, mol%) through optical properties. The optical absorption and reflection spectra were recorded at room temperature in the wavelength range 400 – 800 and 450 – 800 nm, respectively. From the absorption edge studies, the values of optical band gap (Eopt) and Urbach energy (DE) have been evaluated. The values of Eopt lie between 2.21 and 2.55 eV for indirect allowed transitions, and for indirect forbidden transitions, the values vary from 1.86 to 2.31 eV. The values of Eopt show nonlinear behavior upon substitution of one alkali ion by another with a minima at x = 15 mol% because the glass structure in the mixed alkali region may be having more nonbridging oxygens than in the dilute foreign alkali regions. The theoretical analysis of optical absorption indicates that the present glass system behaves as an indirect gap semiconductor. The refractive index (n) and optical dielectric constant (e) have been evaluated from the reflection spectra. n and e also show nonlinear variation in their values with maxima at x = 15 mol%, which supports the existence of MAE in the optical properties of the present glass system. D 2003 Elsevier B.V. All rights reserved. PACS: 42.70.C; 61.43.F; 78.20.C Keywords: Glasses; Quenching; Optical materials and properties; Optical band gap; Mixed alkali effect; Indirect semiconductor
1. Introduction Glasses based on heavy metal oxides viz., Bi2O3, PbO and Ga2O3 have wide applications in the field of glass ceramics, layers for optical and electronic devices, thermal and mechanical sensors, reflecting windows, etc. [1,2]. Because of small field strength of Bi3 + ions, bismuth oxide cannot be considered as network former, however, in combination with B2O3, glass formation is possible in a relatively large composition range [3]. The large glass formation region in boro-bismuthate glasses has been attributed to the high polarizability of the Bi3 + cations. This property of Bi3 + ions also makes the glass suitable as nonlinear optical/photonic material with high nonlinear optical susceptibility [4]. Chemical durability is also enhanced on the addition of Bi2O3 to the conventional glass * Corresponding author. Tel.: +91-1662-263176; fax: +91-1662276240. E-mail address: [email protected] (A. Agarwal). 0167-577X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2003.06.007
formers. Many investigations have been reported on the optical properties of phosphate, borate, and silicate glasses, which contain alkali and/or alkaline earth oxides [5 – 11]. When two types of alkali metal ions are introduced into a glassy network, a phenomenon known as mixed alkali effect (MAE) is observed. It represents the nonlinear variations in many physical properties associated with alkali ion movement and structural properties, when one type of alkali ion in an alkali glass is gradually replaced by another, while total alkali content in the glass being constant [12,13]. The most evident manifestation of this effect has been observed in electrical dc conductivity as a function of composition where a deep minimum is observed in the intermediate mixing ratio of alkali ions [14,15]. Mixed alkali glasses are unique from the point of view that certain properties change much more than normally anticipated from what appears to be a structurally and compositionally simple substitution of one alkali oxide for another. Mixed alkali effect in different physical properties is observed in silicate, borate, and phosphate glasses [16 –
A. Agarwal et al. / Materials Letters 58 (2004) 694–698
695
Table 1 Glass composition of the samples in (30 x)Li2OxK2O20Bi2O350B2O3 glass system
temperature by pouring and pressing between two carbon plates.
Sr. no.
x (mol%)
Glass composition
Code
2.2. Optical measurements
1 2 3 4 5 6 7
0 5 10 15 20 25 30
30Li2O20Bi2O350B2O3 25Li2O5K2O20Bi2O350B2O3 20Li2O10K2O20Bi2O350B2O33 15Li2O15K2O20Bi2O3 10Li2O20K2O20Bi2O350B2O3 5Li2O25K2O20Bi2O350B2O3 30K2O20Bi2O350B2O3
LK1 LK2 LK3 LK4 LK5 LK6 LK7
18]. However, there has been no attempt to observe the MAE in optical properties, particularly in optical band gap studies. Therefore, a systematic study has been performed to understand the variation of optical band gap as a function of composition in mixed alkali bismuth borate glasses. Further, some physical parameters viz., refractive index and dielectric constant have also been evaluated and their variation as a function of composition has been taken into account to supplement the results of MAE in optical properties.
The as-prepared glasses were grinded and finely polished to a thickness of 0.5– 1.0 mm to make them suitable for recording absorption and reflection spectra. The optical absorption and reflection spectra of the polished samples were recorded at room temperature in the wavelength range of 400– 800 and 450– 800 nm, respectively, using Perkin Elmer UV – VIS spectrometer (Lambda 20).
3. Results The optical absorption spectra of the glass samples (LK1 –LK7) are shown in Fig. 1. The non-sharp edges in
2. Experimental 2.1. Glass preparation The mixed alkali bismuth borate glasses were prepared by normal melt quenching. The starting materials used were analar (AR) grade reagents of Li2CO3, K2CO3, H3BO3 and Bi2O3. The mixtures corresponding to the desired composition (Table 1) were melted in a porcelain crucible at about 1100 jC. The fused materials were kept at melting temperature for 30 min and shaken frequently to make the mixture homogeneous. The melts were then quickly cooled at room
Fig. 1. Optical absorption spectra for (30 x)Li2OxK2O20Bi2O350B2O3 glasses at room temperature.
Fig. 2. Tauc’s plot for (30 x)Li2OxK2O20Bi2O350B2O3 glasses (a) for r = 2, (b) for r = 3.
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A. Agarwal et al. / Materials Letters 58 (2004) 694–698
Table 2 Cutoff wavelength, kcutoff; optical band gap, Eopt; Urbach’s energy, DE; band tailing parameter, B; refractive index, n; and dielectric constant, e in (30 x)Li2O.xK2O.20Bi2O3.50B2O3 glass system Sample code
kcutoff (nm)
Eopt (eV)
B (cm eV) 1
r=2 LK1 LK2 LK3 LK4 LK5 LK6 LK7
440 430 405 410 410 425 390
2.21 2.37 2.28 2.19 2.41 2.50 2.55
Eopt (eV)
B (cm eV) 1
DE (eV)
r=3 13.46 18.04 15.02 12.02 22.05 25.56 18.66
1.86 2.00 1.90 1.81 2.14 2.27 2.31
the figure give a clear indication of the amorphous nature of the samples. The optical absorption coefficient near the fundamental absorption edge of each curve in Fig. 1 was calculated at different wavelengths by using the formula aðmÞ ¼ 1=dlnðI0 =It Þ
ð1Þ
where I0 and It are the intensities of the incident and transmitted beams, respectively, and d is the thickness of the glass samples. The factor ln(I0/It) corresponds to absorbance. Mott and Davis [19] and Tauc and Menth [20] relate this data to the optical band gap, Eopt, through the following general relation proposed for amorphous materials. r
aðmÞ ¼ Bðhm Eopt Þ =hm
ð2Þ
where the index r takes different values depending on the mechanism of interband transitions [19,21], B is a constant and hm is the photon energy of incident photon. In various glasses, Eq. (2) depicts a straight line for r = 2 and is associated with indirect allowed transitions. Fig. 2(a) represents the Tauc’s plot {(ahm)1/2 vs. (hm)} for different samples. The Eopt has been estimated from the linear regions of
Fig. 3. Variation of Eopt with {xK2O/[(30 x)Li2O + xK2O]}.
n
e
(at 633 nm) 4.21 4.91 4.44 3.82 6.40 7.42 5.94
0.254 0.258 0.386 0.294 0.253 0.206 0.281
2.12 2.22 2.42 2.60 2.55 2.29 2.21
4.49 4.93 5.86 6.76 6.50 5.24 4.88
the curves by extrapolating them to meet the hm axis at (ahm)1/2 = 0 and the values are listed in Table 2 for all the samples. The plot for r = 3 has been shown in Fig. 2(b). This corresponds to indirect forbidden transitions and the calculated values for Eopt in this case have also been included in Table 2. The variation of Eopt with composition {[xK2O]/ [(30 x)Li2O + xK2O]} for the two types of transitions (for r = 2, 3) is shown separately in Fig. 3. The values of B were determined from the linear regions of the Tauc’s plot for r = 2 and 3, and are also presented in Table 2. The fundamental absorption edge usually follows the Urbach rule [22] am ¼ Cexpðhm=DEÞ
ð3Þ
where C is a constant, DE is a measure of the band tailing and is known as Urbach energy. The values of Urbach energy (DE) were calculated by taking the reciprocals of the slopes of the linear portion of the ln a(m) vs. hm curves in the lower photon energy regions. These values of DE are also included in Table 2 for all the samples. Fig. 4 represents the optical reflection spectra of some of the samples. These spectra have been used to calculate the
Fig. 4. Optical reflection spectra for (30 x)Li2OxK2O20Bi2O350B2O3 glasses at room temperature.
A. Agarwal et al. / Materials Letters 58 (2004) 694–698
Fig. 5. Variation of (a) refractive index and (b) dielectric constant with mol% of K2O.
values of linear refractive index, n, and the dielectric constant, e. The optical dielectric constant and the refractive index are related through the following equation: e ¼ n2 ¼ ½ð1 þ R1=2 Þ=ð1 R1=2 Þ
ð4Þ
The variation of n and e (for k = 633 and 750 nm) with composition is presented in Fig. 5. It has been observed that the composition dependence of n and e show qualitatively similar behavior for different wavelengths.
4. Discussion The analysis of optical absorption spectra (Fig. 1) shows that the fundamental absorption edge is not sharply defined, which characterizes the glassy nature of the samples. The position of fundamental absorption edge varies with increase in the content of K2O in the glass system. This variation in the cutoff wavelength is not regular as can be seen from the values mentioned in Table 2. It is reported that the fundamental absorption edge shifts towards longer wavelengths in single alkali borate glasses with an increase in alkali content [5,11], whereas in the present mixed alkali
697
glasses, the shift in fundamental optical absorption edge is irregular when Li2O is replaced by K2O. The variation in the values of optical band gap in the present glass system is shown in Figs. 2 and 3. The values vary from 2.21 to 2.55 eV and from 1.86 to 2.31 eV for r = 2 and 3, respectively, when Li2O is replaced by K2O. A minimum in Eopt values at x = 15 mol%, where the content of both the alkalis is same, has been observed. This nonlinear variation in the Eopt with decrease in Li2O/K2O ratio indicates the existence of mixed alkali effect in optical properties of the present glass system. In single alkali borate glasses, the Eopt decreases monotonically with the content of alkali ions and has been attributed to the formation and increase in the nonbridging oxygens [5,8]. However, the existence of a minimum in Eopt at x = 15 mol%, in the mixed alkali glasses may be due to the formation of large number of nonbridging oxygens at this particular composition in comparison to dilute foreign alkali regions [23]. The analysis of optical spectra of all the samples shows that the fitting curves of Fig. 2(a) give a very good fit for r = 2, indicating indirect allowed transitions. The same data of optical spectra were applied for r = 3, which corresponds to indirect forbidden transitions (Fig. 2(b)). It has been observed that out of these curves, the latter provides a much better fit for the optical data. Therefore, it is concluded that whatever is the mechanism of transitions, the glass system under study behaves as an indirect gap semiconductor. The values of B, the band tailing parameter, have been evaluated from the slope of the curves of Fig. 2. These values lie between 12.02 and 25.56 (cm eV) 1 and between 3.82 and 7.42 (cm eV) 1 for r = 2 and 3, respectively, and are in agreement with the reported values [10,24]. The values of Urbach’s energy, DE, are shown in Table 2. It is observed that for most materials, the width of absorption tail (just below the conduction band), DE ranges from 0.006 to 0.014 eV which is a broad range to draw any conclusive remark about any specific mechanism of absorption edge operative in a particular material. However, it is generally assumed [25] that the exponential tail observed in various materials and in their different structures must have the same physical origin. This origin can be attributed to the phonon-assisted indirect electronic transitions. In the present glass system, the values of DE lie between 0.206 and 0.386 eV and these results are in accordance with those reported for inorganic glasses [11]. It has been reported [26] that the linear refractive index of alkali borate glasses increases with increase in alkali content and it has also been reported [27] that the values of n increases with increase in Bi2O3 content in Bi2O3B2O3 glasses. In 30Li2O70B2O3 glass samples, the reported values of n at 633 nm is 1.546 and in 30K2O70B2O3 glass samples, it is 1.585 [26]. In the present study, the values of n at 633 nm for the glass samples LK1 and LK7 is 2.12 and 2.21, respectively, which are higher than the pure alkali borate glasses due to the presence of Bi2O3. In addition to this, the variation in n is not linear with decrease in Li2O/
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K2O ratio. It increases from 2.12 at x = 0 mol% and reaches a maximum value of 2.60 at x = 15 mol%, thereafter, it starts decreasing and at x = 30 mol%, its value is 2.21 (Fig. 5). Similar behavior in the values of e is observed. This nonlinear variation of n and e also supports the existence of mixed alkali effect in optical properties in the present glass system.
5. Conclusions The optical properties of the(30 x)Li2OxK2O20Bi2 O350B2O3 glasses (0 V x V 30, mol%) have been studied. The optical band gap values have been determined and from the theoretical fitting of the experimental absorption coefficient for all the glass samples, it is concluded that both indirect allowed and indirect forbidden transitions are involved. Hence, the present glass system acts as an indirect gap semiconductor. Further, a minimum in the optical band gap values and a maximum in the refractive index values at x = 15 mol% show that the mixed alkali effect is prevailing in the glass system under study. The values of Urbach energy confirm the existence of phononassisted transitions.
Acknowledgements The work was supported by CSIR, UGC and DST (FIST scheme) New Delhi (India).
References [1] D.W. Hall, M.A. Newhouse, N.F. Borrelli, W.H. Dumbaugh, D.L. Weidman, Appl. Phys. Lett. 54 (1989) 1293. [2] N. Sugi Moto, J. Am. Ceram. Soc. 85 (2002) 1083. [3] W.H. Dumbaugh, J.C. Lapp, J. Am. Ceram. Soc. 75 (1992) 2315. [4] K. Terashima, T.H. Shimato, T. Yoko, Phys. Chem. Glasses 38 (1997) 211. [5] R. Sheibani, C.A. Hogarth, J. Mater. Sci. 26 (1991) 429. [6] C. Dayanand, R.V.G.K. Serma, G. Bhikshamaiah, M. Salagram, J. Non-Cryst. Solids 167 (1994) 122. [7] S.A. Siddiqi, M. Masih, A. Mateen, Mater. Chem. Phys. 40 (1995) 69. [8] T. Suzuki, M. Hirano, H. Hosono, J. Appl. Phys. 91 (2002) 4149. [9] C. Dayanand, G. Bhikshamaiah, M. Salagram, Mater. Lett. 23 (1995) 69. [10] M. Chaudhary, M. Altaf, Mater. Lett. 34 (1998) 213. [11] K. Subrahmanyam, M. Salagram, Opt. Mater. 15 (2000) 181. [12] D.E. Day, J. Non-Cryst. Solids 21 (1976) 343. [13] M.D. Ingram, Phys. Chem. Glasses 28 (1987) 215. [14] A.G. Hunt, J. Non-Cryst. Solids 255 (1999) 47. [15] A.W. Imre, S. Voss, H. Mehrer, Phys. Chem. 4 (2002) 3219. [16] R.M. Hakim, D.R. Uhlmann, Phys. Chem. Glasses 8 (1967) 174. [17] H. Jain, H.L. Downing, N.L. Peterson, J. Non-Cryst. Solids 64 (1984) 335. [18] H.M.J.M. van Ass, J.M. Stevels, J. Non-Crystal. Solids 15 (1974) 215. [19] E.A. Davis, N.F. Mott, Phila. Mag. 22 (1970) 903. [20] J. Tauc, A. Menth, J. Non-Cryst. Solids 8 – 10 (1972) 569. [21] G.A. Khan, C.A. Hogarth, J. Mater. Sci. 26 (1991) 412. [22] F. Urbach, Phys. Rev. 92 (1953) 1324. [23] W. Soppe, J. Kleerebezem, H.W. den Hartog, J. Non-Cryst. Solids 93 (1987) 142. [24] Y.C. Ratnakaram, A.V. Reddy, J. Non-Cryst. Solids 277 (2000) 142. [25] K.L. Chopra, S.K. Bahl, Thin Solid Films 11 (1972) 377. [26] K. Terashima, S.H. Kim, T. Yoko, J. Am. Ceram. Soc. 78 (1995) 1601. [27] J.A. Ruller, J.E. Shelby, Phys. Chem. Glasses 33 (1992) 177.
Mixed alkali effect in optical properties of lithium–potassium bismuth borate glass system A. Agarwal a,*, V.P. Seth b, S. Sanghi a, P. Gahlot b, S. Khasa c a
Department of Applied Physics, G.J. University, Hisar 125001, India b Department of Physics, M.D. University, Rohtak 124001, India c Department of Physics, Government College, Bahadurgarh 124 507, India Received 28 April 2003; accepted 10 June 2003
Abstract The mixed alkali effect (MAE) has been investigated in the glass system (30 x)Li2OxK2O20Bi2O350B2O3 (0 V x V 30, mol%) through optical properties. The optical absorption and reflection spectra were recorded at room temperature in the wavelength range 400 – 800 and 450 – 800 nm, respectively. From the absorption edge studies, the values of optical band gap (Eopt) and Urbach energy (DE) have been evaluated. The values of Eopt lie between 2.21 and 2.55 eV for indirect allowed transitions, and for indirect forbidden transitions, the values vary from 1.86 to 2.31 eV. The values of Eopt show nonlinear behavior upon substitution of one alkali ion by another with a minima at x = 15 mol% because the glass structure in the mixed alkali region may be having more nonbridging oxygens than in the dilute foreign alkali regions. The theoretical analysis of optical absorption indicates that the present glass system behaves as an indirect gap semiconductor. The refractive index (n) and optical dielectric constant (e) have been evaluated from the reflection spectra. n and e also show nonlinear variation in their values with maxima at x = 15 mol%, which supports the existence of MAE in the optical properties of the present glass system. D 2003 Elsevier B.V. All rights reserved. PACS: 42.70.C; 61.43.F; 78.20.C Keywords: Glasses; Quenching; Optical materials and properties; Optical band gap; Mixed alkali effect; Indirect semiconductor
1. Introduction Glasses based on heavy metal oxides viz., Bi2O3, PbO and Ga2O3 have wide applications in the field of glass ceramics, layers for optical and electronic devices, thermal and mechanical sensors, reflecting windows, etc. [1,2]. Because of small field strength of Bi3 + ions, bismuth oxide cannot be considered as network former, however, in combination with B2O3, glass formation is possible in a relatively large composition range [3]. The large glass formation region in boro-bismuthate glasses has been attributed to the high polarizability of the Bi3 + cations. This property of Bi3 + ions also makes the glass suitable as nonlinear optical/photonic material with high nonlinear optical susceptibility [4]. Chemical durability is also enhanced on the addition of Bi2O3 to the conventional glass * Corresponding author. Tel.: +91-1662-263176; fax: +91-1662276240. E-mail address: [email protected] (A. Agarwal). 0167-577X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2003.06.007
formers. Many investigations have been reported on the optical properties of phosphate, borate, and silicate glasses, which contain alkali and/or alkaline earth oxides [5 – 11]. When two types of alkali metal ions are introduced into a glassy network, a phenomenon known as mixed alkali effect (MAE) is observed. It represents the nonlinear variations in many physical properties associated with alkali ion movement and structural properties, when one type of alkali ion in an alkali glass is gradually replaced by another, while total alkali content in the glass being constant [12,13]. The most evident manifestation of this effect has been observed in electrical dc conductivity as a function of composition where a deep minimum is observed in the intermediate mixing ratio of alkali ions [14,15]. Mixed alkali glasses are unique from the point of view that certain properties change much more than normally anticipated from what appears to be a structurally and compositionally simple substitution of one alkali oxide for another. Mixed alkali effect in different physical properties is observed in silicate, borate, and phosphate glasses [16 –
A. Agarwal et al. / Materials Letters 58 (2004) 694–698
695
Table 1 Glass composition of the samples in (30 x)Li2OxK2O20Bi2O350B2O3 glass system
temperature by pouring and pressing between two carbon plates.
Sr. no.
x (mol%)
Glass composition
Code
2.2. Optical measurements
1 2 3 4 5 6 7
0 5 10 15 20 25 30
30Li2O20Bi2O350B2O3 25Li2O5K2O20Bi2O350B2O3 20Li2O10K2O20Bi2O350B2O33 15Li2O15K2O20Bi2O3 10Li2O20K2O20Bi2O350B2O3 5Li2O25K2O20Bi2O350B2O3 30K2O20Bi2O350B2O3
LK1 LK2 LK3 LK4 LK5 LK6 LK7
18]. However, there has been no attempt to observe the MAE in optical properties, particularly in optical band gap studies. Therefore, a systematic study has been performed to understand the variation of optical band gap as a function of composition in mixed alkali bismuth borate glasses. Further, some physical parameters viz., refractive index and dielectric constant have also been evaluated and their variation as a function of composition has been taken into account to supplement the results of MAE in optical properties.
The as-prepared glasses were grinded and finely polished to a thickness of 0.5– 1.0 mm to make them suitable for recording absorption and reflection spectra. The optical absorption and reflection spectra of the polished samples were recorded at room temperature in the wavelength range of 400– 800 and 450– 800 nm, respectively, using Perkin Elmer UV – VIS spectrometer (Lambda 20).
3. Results The optical absorption spectra of the glass samples (LK1 –LK7) are shown in Fig. 1. The non-sharp edges in
2. Experimental 2.1. Glass preparation The mixed alkali bismuth borate glasses were prepared by normal melt quenching. The starting materials used were analar (AR) grade reagents of Li2CO3, K2CO3, H3BO3 and Bi2O3. The mixtures corresponding to the desired composition (Table 1) were melted in a porcelain crucible at about 1100 jC. The fused materials were kept at melting temperature for 30 min and shaken frequently to make the mixture homogeneous. The melts were then quickly cooled at room
Fig. 1. Optical absorption spectra for (30 x)Li2OxK2O20Bi2O350B2O3 glasses at room temperature.
Fig. 2. Tauc’s plot for (30 x)Li2OxK2O20Bi2O350B2O3 glasses (a) for r = 2, (b) for r = 3.
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A. Agarwal et al. / Materials Letters 58 (2004) 694–698
Table 2 Cutoff wavelength, kcutoff; optical band gap, Eopt; Urbach’s energy, DE; band tailing parameter, B; refractive index, n; and dielectric constant, e in (30 x)Li2O.xK2O.20Bi2O3.50B2O3 glass system Sample code
kcutoff (nm)
Eopt (eV)
B (cm eV) 1
r=2 LK1 LK2 LK3 LK4 LK5 LK6 LK7
440 430 405 410 410 425 390
2.21 2.37 2.28 2.19 2.41 2.50 2.55
Eopt (eV)
B (cm eV) 1
DE (eV)
r=3 13.46 18.04 15.02 12.02 22.05 25.56 18.66
1.86 2.00 1.90 1.81 2.14 2.27 2.31
the figure give a clear indication of the amorphous nature of the samples. The optical absorption coefficient near the fundamental absorption edge of each curve in Fig. 1 was calculated at different wavelengths by using the formula aðmÞ ¼ 1=dlnðI0 =It Þ
ð1Þ
where I0 and It are the intensities of the incident and transmitted beams, respectively, and d is the thickness of the glass samples. The factor ln(I0/It) corresponds to absorbance. Mott and Davis [19] and Tauc and Menth [20] relate this data to the optical band gap, Eopt, through the following general relation proposed for amorphous materials. r
aðmÞ ¼ Bðhm Eopt Þ =hm
ð2Þ
where the index r takes different values depending on the mechanism of interband transitions [19,21], B is a constant and hm is the photon energy of incident photon. In various glasses, Eq. (2) depicts a straight line for r = 2 and is associated with indirect allowed transitions. Fig. 2(a) represents the Tauc’s plot {(ahm)1/2 vs. (hm)} for different samples. The Eopt has been estimated from the linear regions of
Fig. 3. Variation of Eopt with {xK2O/[(30 x)Li2O + xK2O]}.
n
e
(at 633 nm) 4.21 4.91 4.44 3.82 6.40 7.42 5.94
0.254 0.258 0.386 0.294 0.253 0.206 0.281
2.12 2.22 2.42 2.60 2.55 2.29 2.21
4.49 4.93 5.86 6.76 6.50 5.24 4.88
the curves by extrapolating them to meet the hm axis at (ahm)1/2 = 0 and the values are listed in Table 2 for all the samples. The plot for r = 3 has been shown in Fig. 2(b). This corresponds to indirect forbidden transitions and the calculated values for Eopt in this case have also been included in Table 2. The variation of Eopt with composition {[xK2O]/ [(30 x)Li2O + xK2O]} for the two types of transitions (for r = 2, 3) is shown separately in Fig. 3. The values of B were determined from the linear regions of the Tauc’s plot for r = 2 and 3, and are also presented in Table 2. The fundamental absorption edge usually follows the Urbach rule [22] am ¼ Cexpðhm=DEÞ
ð3Þ
where C is a constant, DE is a measure of the band tailing and is known as Urbach energy. The values of Urbach energy (DE) were calculated by taking the reciprocals of the slopes of the linear portion of the ln a(m) vs. hm curves in the lower photon energy regions. These values of DE are also included in Table 2 for all the samples. Fig. 4 represents the optical reflection spectra of some of the samples. These spectra have been used to calculate the
Fig. 4. Optical reflection spectra for (30 x)Li2OxK2O20Bi2O350B2O3 glasses at room temperature.
A. Agarwal et al. / Materials Letters 58 (2004) 694–698
Fig. 5. Variation of (a) refractive index and (b) dielectric constant with mol% of K2O.
values of linear refractive index, n, and the dielectric constant, e. The optical dielectric constant and the refractive index are related through the following equation: e ¼ n2 ¼ ½ð1 þ R1=2 Þ=ð1 R1=2 Þ
ð4Þ
The variation of n and e (for k = 633 and 750 nm) with composition is presented in Fig. 5. It has been observed that the composition dependence of n and e show qualitatively similar behavior for different wavelengths.
4. Discussion The analysis of optical absorption spectra (Fig. 1) shows that the fundamental absorption edge is not sharply defined, which characterizes the glassy nature of the samples. The position of fundamental absorption edge varies with increase in the content of K2O in the glass system. This variation in the cutoff wavelength is not regular as can be seen from the values mentioned in Table 2. It is reported that the fundamental absorption edge shifts towards longer wavelengths in single alkali borate glasses with an increase in alkali content [5,11], whereas in the present mixed alkali
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glasses, the shift in fundamental optical absorption edge is irregular when Li2O is replaced by K2O. The variation in the values of optical band gap in the present glass system is shown in Figs. 2 and 3. The values vary from 2.21 to 2.55 eV and from 1.86 to 2.31 eV for r = 2 and 3, respectively, when Li2O is replaced by K2O. A minimum in Eopt values at x = 15 mol%, where the content of both the alkalis is same, has been observed. This nonlinear variation in the Eopt with decrease in Li2O/K2O ratio indicates the existence of mixed alkali effect in optical properties of the present glass system. In single alkali borate glasses, the Eopt decreases monotonically with the content of alkali ions and has been attributed to the formation and increase in the nonbridging oxygens [5,8]. However, the existence of a minimum in Eopt at x = 15 mol%, in the mixed alkali glasses may be due to the formation of large number of nonbridging oxygens at this particular composition in comparison to dilute foreign alkali regions [23]. The analysis of optical spectra of all the samples shows that the fitting curves of Fig. 2(a) give a very good fit for r = 2, indicating indirect allowed transitions. The same data of optical spectra were applied for r = 3, which corresponds to indirect forbidden transitions (Fig. 2(b)). It has been observed that out of these curves, the latter provides a much better fit for the optical data. Therefore, it is concluded that whatever is the mechanism of transitions, the glass system under study behaves as an indirect gap semiconductor. The values of B, the band tailing parameter, have been evaluated from the slope of the curves of Fig. 2. These values lie between 12.02 and 25.56 (cm eV) 1 and between 3.82 and 7.42 (cm eV) 1 for r = 2 and 3, respectively, and are in agreement with the reported values [10,24]. The values of Urbach’s energy, DE, are shown in Table 2. It is observed that for most materials, the width of absorption tail (just below the conduction band), DE ranges from 0.006 to 0.014 eV which is a broad range to draw any conclusive remark about any specific mechanism of absorption edge operative in a particular material. However, it is generally assumed [25] that the exponential tail observed in various materials and in their different structures must have the same physical origin. This origin can be attributed to the phonon-assisted indirect electronic transitions. In the present glass system, the values of DE lie between 0.206 and 0.386 eV and these results are in accordance with those reported for inorganic glasses [11]. It has been reported [26] that the linear refractive index of alkali borate glasses increases with increase in alkali content and it has also been reported [27] that the values of n increases with increase in Bi2O3 content in Bi2O3B2O3 glasses. In 30Li2O70B2O3 glass samples, the reported values of n at 633 nm is 1.546 and in 30K2O70B2O3 glass samples, it is 1.585 [26]. In the present study, the values of n at 633 nm for the glass samples LK1 and LK7 is 2.12 and 2.21, respectively, which are higher than the pure alkali borate glasses due to the presence of Bi2O3. In addition to this, the variation in n is not linear with decrease in Li2O/
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K2O ratio. It increases from 2.12 at x = 0 mol% and reaches a maximum value of 2.60 at x = 15 mol%, thereafter, it starts decreasing and at x = 30 mol%, its value is 2.21 (Fig. 5). Similar behavior in the values of e is observed. This nonlinear variation of n and e also supports the existence of mixed alkali effect in optical properties in the present glass system.
5. Conclusions The optical properties of the(30 x)Li2OxK2O20Bi2 O350B2O3 glasses (0 V x V 30, mol%) have been studied. The optical band gap values have been determined and from the theoretical fitting of the experimental absorption coefficient for all the glass samples, it is concluded that both indirect allowed and indirect forbidden transitions are involved. Hence, the present glass system acts as an indirect gap semiconductor. Further, a minimum in the optical band gap values and a maximum in the refractive index values at x = 15 mol% show that the mixed alkali effect is prevailing in the glass system under study. The values of Urbach energy confirm the existence of phononassisted transitions.
Acknowledgements The work was supported by CSIR, UGC and DST (FIST scheme) New Delhi (India).
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