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Extended rigidity percolation and chemical thresholds in Ge–Te–Pb glasses as revealed by MDSC
Solid State Communications 129 (2004) 765–768 www.elsevier.com/locate/ssc
Extended rigidity percolation and chemical thresholds in Ge –Te –Pb glasses as revealed by MDSC P. Zaheerudeen Sahebb, B.H. Sharmilaa, S. Asokana,*, K. Appaji Gowdab a
Department of Instrumentation, Indian Institute of Science, Bangalore 560012, India b Department of Physics, Bangalore University, Bangalore 560056, India
Received 6 October 2003; received in revised form 27 November 2003; accepted 24 December 2003 by A.K. Sood
Abstract Thermal analysis of Ge20Te802xPbx ð2 # x # 8Þ glasses has been undertaken using modulated differential scanning calorimetry (MDSC). The compositional dependence of thermal parameters is investigated. The crystallization temperatures ðTc Þ estimated from the total heat flow show detectable changes at compositions x ¼ 4; 6.5 and 7.5. Further, the heat capacity change at the glass transition temperature, measured from the reversible heat flow curve ðDCpR Þ; is found to exhibit a maximum and an inflexion at compositions x ¼ 4 and 6.5 and minimum at x ¼ 7:5; respectively. Also, the relaxation enthalpy, estimated from the area under the non-reversing heat flow curve ðDH NR Þ; exhibits similar features at the said compositions. From the observed MDSC results, it has been proposed that the compositions x ¼ 4 and x ¼ 6:5 denote to the onset and completion of rigidity percolation and x ¼ 7:5 corresponds to the chemical threshold of the system. q 2004 Elsevier Ltd. All rights reserved. PACS: 61.43.Fs; 64.70.Pf; 67.80.Gb; 65.40. þ g; 64.75. þ g; 72.80.Ng Keywords: A. Disordered systems; D. Heat capacity; D. Thermodynamic properties
1. Introduction The differential scanning calorimetry (DSC) is extensively used in studying the thermal events that occur when a sample is subjected to a temperature regime. The recent technique of modulated differential scanning calorimetry (MDSC) uses the deconvolution procedure in which the total heat flow is resolved into a component that tracks the temperature modulation leading to the reversing heat flow and the other which does not track the temperature modulation giving rise to the non-reversing heat flow. This information provides unique insights into the structure of glassy materials [1]. Chalcogenide glasses are known to exhibit two network topological thresholds namely, the rigidity percolation * Corresponding author. Tel.: þ91-80-3344411; fax: þ 91-803341683. E-mail address: [email protected] (S. Asokan). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.12.043
threshold (RPT) and the chemical threshold (CT). The former is indicative of a transformation from a floppy polymeric glass to a rigid amorphous solid [2 –8], whereas the later corresponds to an ordered glass with only heteropolar bonds [2– 5,8]. DSC studies are routinely used to identify the network topological thresholds in chalcogenide glasses. The recent MDSC studies have revealed that the rigidity percolation may span over a range of compositions/average coordination numbers [9,10], contrary to the earlier understanding that the rigidity percolation is sharp occurring at a definite composition (RPT). An extended rigidity percolation leads to an intermediate phase existing between the floppy and the rigid phases. The presence of an intermediate phase is however, not revealed in many investigations other than MDSC. The earlier electrical studies on Ge– Te – Pb glasses [11] have revealed the signature of rigidity percolation, though the occurrence of an intermediate phase has not been
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noticed. In the present work, MDSC measurements have been carried out to explore the possibility of extended topological thresholds in Ge20Te802xPbx glasses.
2. Experimental Bulk Ge20Te802xPbx glasses ð2 # x # 8Þ were prepared by melt quenching technique. The samples were confirmed for the amorphous nature by X-ray diffraction. MDSC studies were undertaken using a TA Instruments MDSCe (model 2910). The base line correction was done with an empty pan and the calibration for enthalpy and temperature was performed using high purity indium. The calibration for specific heat was achieved with high purity sapphire. All calibrations were conducted using the same experimental parameters that were used for the samples. Samples of about 10 – 16 mg in weight were ground into a powder and were subsequently transferred to an Al pan and sealed; an empty pan was taken as a reference. The sample was initially equilibrated at 30 8C for 2 min with the data storage capability switched on. The MDSC experiments were carried out with the heating rate maintained at 5 8C per min, the modulation amplitude at ^1.00 8C and modulation period of 60 s. The temperature evolution of the MDSC signals was deconvoluted from the modulated heat flow into the total heat flow, reversing heat flow and the non-reversing heat flow. The thermal parameters, namely the glass transition temperature ðTg Þ and the crystallization temperature ðTc Þ were estimated from the various MDSC curves; the change in specific heat was established from the step transition in the glass transition region from the reversing heat flow ðDCpR Þ; the relaxation enthalpy was calculated by measuring the area under the non-reversing heat flow curve ðDH NR Þ:
3. Results and discussion
Fig. 1. Variation with composition/average coordination number of (a) Crystallization temperature ðTc Þ obtained from total heat flow. (b) Heat capacity jump during glass transition obtained from the reversible heat flow ðDCpR Þ: (c) Relaxation enthalpy obtained from the non-reversing heat flow ðDH NR Þ:
Fig. 1(a) shows the variation of crystallization temperature ðTc Þ of the Ge– Te – Pb glasses, obtained from the total heat flow curve, with the composition/average coordination number ðkrlÞ: Here, for the calculation of krl; the coordination numbers of Ge and Te are taken to be 4 and 2, respectively. Based on the Kastner’s proposition that metal impurities in chalcogenide glasses coordinate tetrahedrally [12], a coordination of 4 has been assumed for Pb. However, there is no clear experimental evidence for the actual coordination of Pb in Ge– Te – Pb glasses. Hence, the average co-ordinations used here are only suggestive and it may be more appropriate to use the actual compositions. It can be seen from Fig. 1(a) that the crystallization temperature of Ge20Te802xPbx glasses increases with composition, exhibiting a maximum at x ¼ 4 ðkrl ¼ 2:48Þ: The Tc decreases subsequently and a cusp is seen in Tc at
x ¼ 6:5 ðkrl ¼ 2:53Þ: Beyond this, there is a sharp decrease in Tc which culminates in a minimum at x ¼ 7:5 ðkrl ¼ 2:55Þ: In the recent study by Boolchand et al., [10,13,14] it has been proposed that the rigidity percolation transition occurs over a range of mean coordination numbers leading to three distinct phases namely; floppy, intermediate and rigid. The occurrence of extended rigidity percolation has been observed in glasses such as Si– Se [10], As– Se [14] and Ge– Se [15]. Based on the present results, we propose that the floppy– rigid transition in Ge20Te802xPbx glasses occurs over a range of average coordination numbers/composition with the existence of an intermediate phase. Here, the composition x ¼ 4 ðkrl ¼ 2:48Þ corresponds to the onset and x ¼ 6:5 ðkrl ¼ 2:53Þ to the completion of rigidity percolation. The composition x ¼ 7:5 ðkrl ¼ 2:55Þ at which a
P. Zaheerudeen Saheb et al. / Solid State Communications 129 (2004) 765–768
pronounced minimum is seen in Tc is likely to correspond to the chemical threshold of the system. The composition dependence of Tc (at which the material devitrifies) can be compared with the composition dependence of crystallization pressures ðPT Þ: The earlier studies have revealed that PT of many chalcogenide glasses exhibit a sharp maximum at the rigidity percolation threshold and a minimum at the chemical threshold [16], which are consistent with the present observation. Fig. 1(b) shows the variation of the change in specific heat capacity during the glass transition, obtained from the reversing heat flow curve ðDCpR Þ as a function of composition/average coordination number. It can be seen from this figure that a maximum and an inflexion is seen in DCpR at the onset and the completion of the rigidity percolation. Further, a minimum is observed at the proposed chemical threshold of the system. The change in the specific heat ðDCp Þ at the glass transition is the manifestation of the configurational degrees of freedom of the system characteristic of the liquid state above the transition [17]. The motions available in the liquid state, which are locked in below the glass transition are exclusively configurational and DCp ; which reflects these, is therefore known as the configurational heat capacity. An ideal glass is expected to show only small configurational changes as it is taken through the supercooled liquid state. When a glass is heated along the transition region, the liquid like configuration is regained which is registered as a small change in DCp : Tatsumisago et al., [18] in the studies on composition dependence of thermal properties of Ge– As –Se glasses have interpreted that DCp values could be related to the ease of glass formation. The smaller DCp is a characteristic feature of a fragile glass, which has a greater glass forming ability, whereas higher DCp corresponds to a strong glass, which has a lesser glass-forming tendency. In this context it is interesting to compare the composition dependence of glass forming difficulty (GFD, which is inverse of glass forming ability) of GexSe1002x glasses. The GFD of these samples exhibits a minimum around the rigidity percolation threshold and a maximum at the chemical threshold [5], which is consistent with our conclusion that the maximum and minimum seen in DCpR is associated with rigidity percolation and chemical threshold, respectively. It is interesting to note here that earlier studies on GexSb5Se952x ð12:5 # x # 35Þ; GexSb10Se902x, ð10 # x # 32:5Þ and Ge10AsxTe902x ð15 # x # 50Þ glasses [19] have revealed similar maxima and minima in DCp values at the rigidity percolation and chemical threshold, respectively. It is also suggested by Boolchand et al. [20] that a minimum in DCp indicates the maximization of hetero-polar bonds occurring near this composition (chemical threshold of the system). Enthalpy of relaxation measures the latent heat (configuration energy changes) between the glassy and liquid states, and it vanishes (or leads to a minimum) when the network is optimally constrained [21]. Fig. 1(c) shows the
767
compositional dependence of the relaxation enthalpy for Ge20Te802xPbx glasses obtained from the non-reversing heat flow curve ðDH NR Þ; during a heating scan. It can be seen that DH NR shows two distinct maxima at x ¼ 4 and 6.5, similar to the crystallization temperature, followed by a global minimum at x ¼ 7:5: The minimum or vanishing of the DH NR at x ¼ 7:5 is usually taken as an evidence for the absence of network stress [22]; the global minimum seen in DH NR also confirms that x ¼ 7:5 is the chemical threshold for the present system.
4. Conclusion Thermal analysis of Ge20Te802xPbx ð2 # x # 8Þ glasses has been undertaken using modulated differential scanning calorimetry (MDSC). The crystallization temperatures ðTc Þ estimated from the total heat flow show detectable changes at compositions x ¼ 4; 6.5 and 7.5. Further, the heat capacity change at the glass transition temperature, measured from the reversible heat flow curve ðDCpR Þ; exhibits a maximum and an inflexion at compositions x ¼ 4 and 6.5 and minimum at x ¼ 7:5; respectively. Also, the relaxation enthalpy, estimated from the area under the nonreversing heat flow curve ðDH NR Þ; exhibits similar variations at the said compositions. Based on the present results, it has been proposed that the composition x ¼ 4 and 6.5 denote to the onset and completion of rigidity percolation and x ¼ 7:5 corresponds to the chemical threshold of the system.
References [1] P.S. Gill, S.R. Sauerbrunn, M. Reading, J. Therm. Anal. 40 (1993) 931. [2] J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. [3] J.C. Phillips, J. Non-Cryst. Solids 43 (1981) 37. [4] J.C. Phillips, J. Non-Cryst. Solids 44 (1981) 17. [5] J.C. Phillips, in: M.F. Thorpe, P.M. Duxbury (Eds.), Rigidity Theory and Applications, Kluwer Academic/Plenum, New York, 1999, p. 155. [6] J.C. Phillips, M.F. Thorpe, Solid State Commun. 53 (1985) 699. [7] U. Senapathi, A.K. Varshneya, J. Non-Cryst. Solids 185 (1985) 289. [8] R. Arvinda Narayanan, A. Kumar, Phys. Rev. B 60 (1999) 11859. [9] D. Selvanathan, W.J. Bresser, P. Boolchand, B. Goodman, Solid State Commun. 111 (1999) 619. [10] D. Selvanathan, W.J. Bresser, P. Boolchand, Phys. Rev. B 61 (2000) 15061. [11] P.Z. Saheb, S. Asokan, K.A. Gowda, Appl. Phys. A 77 (2003) 665. [12] M. Kastner, Phil. Mag. 37 (1978) 127. [13] P. Boolchand, J. Optoelect. Adv. Mater. 3 (2001) 703.
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[14] D.G. Georgiev, P. Boolchand, M. Micoulaut, Phys. Rev. B 62 (2000) R9228. [15] X. Feng, W.J. Bresser, P. Boolchand, Phys. Rev. Lett. 78 (1997) 4422. [16] S. Asokan, G. Parthasarthy, E.S.R. Gopal, Phys. Rev. B 35 (1987) 8269. [17] C.A. Angell, Pure Appl. Chem. 63 (1991) 1387. [18] M. Tatsumisago, B.L. Halfpap, J.L. Green, S.M. Lindsay, C.A. Angell, Phys. Rev. Lett. 64 (1990) 1549.
[19] A. Srinivasan, K. Nandakumar, Phys. Chem. Glasses 40 (1999) 40. [20] P. Boolchand, D.G. Georgiev, T. Qu, F. Wang, L. Cai, S. Chakravorty, C.R. Chimie 5 (2002) 1. [21] Y. Wang, J. Wells, D.G. Georgiev, P. Boolchand, K. Jackson, M. Micoulaut, Phys. Rev. Lett. 87 (2001) 185501–185503-1. [22] T. Wagner, S.O. Kasap, Phil. Mag. B 74 (1996) 667.
Extended rigidity percolation and chemical thresholds in Ge –Te –Pb glasses as revealed by MDSC P. Zaheerudeen Sahebb, B.H. Sharmilaa, S. Asokana,*, K. Appaji Gowdab a
Department of Instrumentation, Indian Institute of Science, Bangalore 560012, India b Department of Physics, Bangalore University, Bangalore 560056, India
Received 6 October 2003; received in revised form 27 November 2003; accepted 24 December 2003 by A.K. Sood
Abstract Thermal analysis of Ge20Te802xPbx ð2 # x # 8Þ glasses has been undertaken using modulated differential scanning calorimetry (MDSC). The compositional dependence of thermal parameters is investigated. The crystallization temperatures ðTc Þ estimated from the total heat flow show detectable changes at compositions x ¼ 4; 6.5 and 7.5. Further, the heat capacity change at the glass transition temperature, measured from the reversible heat flow curve ðDCpR Þ; is found to exhibit a maximum and an inflexion at compositions x ¼ 4 and 6.5 and minimum at x ¼ 7:5; respectively. Also, the relaxation enthalpy, estimated from the area under the non-reversing heat flow curve ðDH NR Þ; exhibits similar features at the said compositions. From the observed MDSC results, it has been proposed that the compositions x ¼ 4 and x ¼ 6:5 denote to the onset and completion of rigidity percolation and x ¼ 7:5 corresponds to the chemical threshold of the system. q 2004 Elsevier Ltd. All rights reserved. PACS: 61.43.Fs; 64.70.Pf; 67.80.Gb; 65.40. þ g; 64.75. þ g; 72.80.Ng Keywords: A. Disordered systems; D. Heat capacity; D. Thermodynamic properties
1. Introduction The differential scanning calorimetry (DSC) is extensively used in studying the thermal events that occur when a sample is subjected to a temperature regime. The recent technique of modulated differential scanning calorimetry (MDSC) uses the deconvolution procedure in which the total heat flow is resolved into a component that tracks the temperature modulation leading to the reversing heat flow and the other which does not track the temperature modulation giving rise to the non-reversing heat flow. This information provides unique insights into the structure of glassy materials [1]. Chalcogenide glasses are known to exhibit two network topological thresholds namely, the rigidity percolation * Corresponding author. Tel.: þ91-80-3344411; fax: þ 91-803341683. E-mail address: [email protected] (S. Asokan). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.12.043
threshold (RPT) and the chemical threshold (CT). The former is indicative of a transformation from a floppy polymeric glass to a rigid amorphous solid [2 –8], whereas the later corresponds to an ordered glass with only heteropolar bonds [2– 5,8]. DSC studies are routinely used to identify the network topological thresholds in chalcogenide glasses. The recent MDSC studies have revealed that the rigidity percolation may span over a range of compositions/average coordination numbers [9,10], contrary to the earlier understanding that the rigidity percolation is sharp occurring at a definite composition (RPT). An extended rigidity percolation leads to an intermediate phase existing between the floppy and the rigid phases. The presence of an intermediate phase is however, not revealed in many investigations other than MDSC. The earlier electrical studies on Ge– Te – Pb glasses [11] have revealed the signature of rigidity percolation, though the occurrence of an intermediate phase has not been
766
P. Zaheerudeen Saheb et al. / Solid State Communications 129 (2004) 765–768
noticed. In the present work, MDSC measurements have been carried out to explore the possibility of extended topological thresholds in Ge20Te802xPbx glasses.
2. Experimental Bulk Ge20Te802xPbx glasses ð2 # x # 8Þ were prepared by melt quenching technique. The samples were confirmed for the amorphous nature by X-ray diffraction. MDSC studies were undertaken using a TA Instruments MDSCe (model 2910). The base line correction was done with an empty pan and the calibration for enthalpy and temperature was performed using high purity indium. The calibration for specific heat was achieved with high purity sapphire. All calibrations were conducted using the same experimental parameters that were used for the samples. Samples of about 10 – 16 mg in weight were ground into a powder and were subsequently transferred to an Al pan and sealed; an empty pan was taken as a reference. The sample was initially equilibrated at 30 8C for 2 min with the data storage capability switched on. The MDSC experiments were carried out with the heating rate maintained at 5 8C per min, the modulation amplitude at ^1.00 8C and modulation period of 60 s. The temperature evolution of the MDSC signals was deconvoluted from the modulated heat flow into the total heat flow, reversing heat flow and the non-reversing heat flow. The thermal parameters, namely the glass transition temperature ðTg Þ and the crystallization temperature ðTc Þ were estimated from the various MDSC curves; the change in specific heat was established from the step transition in the glass transition region from the reversing heat flow ðDCpR Þ; the relaxation enthalpy was calculated by measuring the area under the non-reversing heat flow curve ðDH NR Þ:
3. Results and discussion
Fig. 1. Variation with composition/average coordination number of (a) Crystallization temperature ðTc Þ obtained from total heat flow. (b) Heat capacity jump during glass transition obtained from the reversible heat flow ðDCpR Þ: (c) Relaxation enthalpy obtained from the non-reversing heat flow ðDH NR Þ:
Fig. 1(a) shows the variation of crystallization temperature ðTc Þ of the Ge– Te – Pb glasses, obtained from the total heat flow curve, with the composition/average coordination number ðkrlÞ: Here, for the calculation of krl; the coordination numbers of Ge and Te are taken to be 4 and 2, respectively. Based on the Kastner’s proposition that metal impurities in chalcogenide glasses coordinate tetrahedrally [12], a coordination of 4 has been assumed for Pb. However, there is no clear experimental evidence for the actual coordination of Pb in Ge– Te – Pb glasses. Hence, the average co-ordinations used here are only suggestive and it may be more appropriate to use the actual compositions. It can be seen from Fig. 1(a) that the crystallization temperature of Ge20Te802xPbx glasses increases with composition, exhibiting a maximum at x ¼ 4 ðkrl ¼ 2:48Þ: The Tc decreases subsequently and a cusp is seen in Tc at
x ¼ 6:5 ðkrl ¼ 2:53Þ: Beyond this, there is a sharp decrease in Tc which culminates in a minimum at x ¼ 7:5 ðkrl ¼ 2:55Þ: In the recent study by Boolchand et al., [10,13,14] it has been proposed that the rigidity percolation transition occurs over a range of mean coordination numbers leading to three distinct phases namely; floppy, intermediate and rigid. The occurrence of extended rigidity percolation has been observed in glasses such as Si– Se [10], As– Se [14] and Ge– Se [15]. Based on the present results, we propose that the floppy– rigid transition in Ge20Te802xPbx glasses occurs over a range of average coordination numbers/composition with the existence of an intermediate phase. Here, the composition x ¼ 4 ðkrl ¼ 2:48Þ corresponds to the onset and x ¼ 6:5 ðkrl ¼ 2:53Þ to the completion of rigidity percolation. The composition x ¼ 7:5 ðkrl ¼ 2:55Þ at which a
P. Zaheerudeen Saheb et al. / Solid State Communications 129 (2004) 765–768
pronounced minimum is seen in Tc is likely to correspond to the chemical threshold of the system. The composition dependence of Tc (at which the material devitrifies) can be compared with the composition dependence of crystallization pressures ðPT Þ: The earlier studies have revealed that PT of many chalcogenide glasses exhibit a sharp maximum at the rigidity percolation threshold and a minimum at the chemical threshold [16], which are consistent with the present observation. Fig. 1(b) shows the variation of the change in specific heat capacity during the glass transition, obtained from the reversing heat flow curve ðDCpR Þ as a function of composition/average coordination number. It can be seen from this figure that a maximum and an inflexion is seen in DCpR at the onset and the completion of the rigidity percolation. Further, a minimum is observed at the proposed chemical threshold of the system. The change in the specific heat ðDCp Þ at the glass transition is the manifestation of the configurational degrees of freedom of the system characteristic of the liquid state above the transition [17]. The motions available in the liquid state, which are locked in below the glass transition are exclusively configurational and DCp ; which reflects these, is therefore known as the configurational heat capacity. An ideal glass is expected to show only small configurational changes as it is taken through the supercooled liquid state. When a glass is heated along the transition region, the liquid like configuration is regained which is registered as a small change in DCp : Tatsumisago et al., [18] in the studies on composition dependence of thermal properties of Ge– As –Se glasses have interpreted that DCp values could be related to the ease of glass formation. The smaller DCp is a characteristic feature of a fragile glass, which has a greater glass forming ability, whereas higher DCp corresponds to a strong glass, which has a lesser glass-forming tendency. In this context it is interesting to compare the composition dependence of glass forming difficulty (GFD, which is inverse of glass forming ability) of GexSe1002x glasses. The GFD of these samples exhibits a minimum around the rigidity percolation threshold and a maximum at the chemical threshold [5], which is consistent with our conclusion that the maximum and minimum seen in DCpR is associated with rigidity percolation and chemical threshold, respectively. It is interesting to note here that earlier studies on GexSb5Se952x ð12:5 # x # 35Þ; GexSb10Se902x, ð10 # x # 32:5Þ and Ge10AsxTe902x ð15 # x # 50Þ glasses [19] have revealed similar maxima and minima in DCp values at the rigidity percolation and chemical threshold, respectively. It is also suggested by Boolchand et al. [20] that a minimum in DCp indicates the maximization of hetero-polar bonds occurring near this composition (chemical threshold of the system). Enthalpy of relaxation measures the latent heat (configuration energy changes) between the glassy and liquid states, and it vanishes (or leads to a minimum) when the network is optimally constrained [21]. Fig. 1(c) shows the
767
compositional dependence of the relaxation enthalpy for Ge20Te802xPbx glasses obtained from the non-reversing heat flow curve ðDH NR Þ; during a heating scan. It can be seen that DH NR shows two distinct maxima at x ¼ 4 and 6.5, similar to the crystallization temperature, followed by a global minimum at x ¼ 7:5: The minimum or vanishing of the DH NR at x ¼ 7:5 is usually taken as an evidence for the absence of network stress [22]; the global minimum seen in DH NR also confirms that x ¼ 7:5 is the chemical threshold for the present system.
4. Conclusion Thermal analysis of Ge20Te802xPbx ð2 # x # 8Þ glasses has been undertaken using modulated differential scanning calorimetry (MDSC). The crystallization temperatures ðTc Þ estimated from the total heat flow show detectable changes at compositions x ¼ 4; 6.5 and 7.5. Further, the heat capacity change at the glass transition temperature, measured from the reversible heat flow curve ðDCpR Þ; exhibits a maximum and an inflexion at compositions x ¼ 4 and 6.5 and minimum at x ¼ 7:5; respectively. Also, the relaxation enthalpy, estimated from the area under the nonreversing heat flow curve ðDH NR Þ; exhibits similar variations at the said compositions. Based on the present results, it has been proposed that the composition x ¼ 4 and 6.5 denote to the onset and completion of rigidity percolation and x ¼ 7:5 corresponds to the chemical threshold of the system.
References [1] P.S. Gill, S.R. Sauerbrunn, M. Reading, J. Therm. Anal. 40 (1993) 931. [2] J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. [3] J.C. Phillips, J. Non-Cryst. Solids 43 (1981) 37. [4] J.C. Phillips, J. Non-Cryst. Solids 44 (1981) 17. [5] J.C. Phillips, in: M.F. Thorpe, P.M. Duxbury (Eds.), Rigidity Theory and Applications, Kluwer Academic/Plenum, New York, 1999, p. 155. [6] J.C. Phillips, M.F. Thorpe, Solid State Commun. 53 (1985) 699. [7] U. Senapathi, A.K. Varshneya, J. Non-Cryst. Solids 185 (1985) 289. [8] R. Arvinda Narayanan, A. Kumar, Phys. Rev. B 60 (1999) 11859. [9] D. Selvanathan, W.J. Bresser, P. Boolchand, B. Goodman, Solid State Commun. 111 (1999) 619. [10] D. Selvanathan, W.J. Bresser, P. Boolchand, Phys. Rev. B 61 (2000) 15061. [11] P.Z. Saheb, S. Asokan, K.A. Gowda, Appl. Phys. A 77 (2003) 665. [12] M. Kastner, Phil. Mag. 37 (1978) 127. [13] P. Boolchand, J. Optoelect. Adv. Mater. 3 (2001) 703.
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[14] D.G. Georgiev, P. Boolchand, M. Micoulaut, Phys. Rev. B 62 (2000) R9228. [15] X. Feng, W.J. Bresser, P. Boolchand, Phys. Rev. Lett. 78 (1997) 4422. [16] S. Asokan, G. Parthasarthy, E.S.R. Gopal, Phys. Rev. B 35 (1987) 8269. [17] C.A. Angell, Pure Appl. Chem. 63 (1991) 1387. [18] M. Tatsumisago, B.L. Halfpap, J.L. Green, S.M. Lindsay, C.A. Angell, Phys. Rev. Lett. 64 (1990) 1549.
[19] A. Srinivasan, K. Nandakumar, Phys. Chem. Glasses 40 (1999) 40. [20] P. Boolchand, D.G. Georgiev, T. Qu, F. Wang, L. Cai, S. Chakravorty, C.R. Chimie 5 (2002) 1. [21] Y. Wang, J. Wells, D.G. Georgiev, P. Boolchand, K. Jackson, M. Micoulaut, Phys. Rev. Lett. 87 (2001) 185501–185503-1. [22] T. Wagner, S.O. Kasap, Phil. Mag. B 74 (1996) 667.