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The velocity of sound in the liquid S–Se alloy
Journal of Non-Crystalline Solids 250±252 (1999) 468±472
www.elsevier.com/locate/jnoncrysol
The velocity of sound in the liquid S±Se alloy Y. Tsuchiya b
a,* ,
R. Satoh a, F. Kakinuma
b
a Department of Physics, Faculty of Science, Niigata University, Ikarashi, 2-8050, Niigata 950-2181, Japan Department of Information and Electronic Engineering, Niigata Institute of Technology, 1719 Fujihashi, Kashiwazaki 945-1195, Japan
Abstract The sound velocity was measured to investigate the polymerization transition in the liquid S±Se alloy. The onset temperature, Tk , of polymerization transition could be found up to 10 at.% of Se, which decreases with increasing Se fraction at the rate of ÿ5.5 0.6 (K/at.%). The results indicate that Tk in liquid Se may not be observed in a ®nite temperature range in contradiction to the previous theoretical calculation. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction There has been a long standing interest in the polymerization transition in liquid sulfur (l-S) [1]. Liquid sulfur consists of S8 ring molecules at the melting point (Tm 118.2°C) and transforms at Tk 160°C to a liquid consisting of chain molecules of which the average molecular weight is assumed to be more than 105 [1]. The existence of long chain molecules is inferred from the viscosity of l-S above Tk [1]. The viscosity of liquid Se (l-Se) is also of the same magnitude and shows similar dependence on temperature as l-S. Eisenberg and Tobolsky [2] estimated the parameters for a model calculation predicting the polymerization of l-Se, from which the onset was calculated to be 77°C. Although the predicted Tk is just beyond a temperature experimentally accessible, no investigation to detect the onset of polymerization transition in l-Se is reported to our knowledge.
* Corresponding author. Tel.: +81-25 262 6146; fax: +81-25 263 3961; e-mail: [email protected]
The relaxation time, s, of structural rearrangement around Tk in l-S is of the order of 10 min and more [3]. Since a conventional transient method like DSC requires very fast sweep of temperature as compared with s, it is not possible to determine the onset of polymerization in thermal equilibrium. In this paper, we report investigation of the polymerization transition in the liquid S±Se alloy by measuring the sound velocity, because sound velocity can be measured in a material at constant temperature. Our results indicate that Tk in l-Se would not be reached at a ®nite temperature range in contradiction to the theoretical calculation [2]. The molar volume, thermal expansion coecient, speci®c heat and compressibility were measured to complement the information obtained by sound velocity measurements.
2. Experimental procedure The velocity of sound, vs , was measured with a standard pulse technique. Since the details have been reported elsewhere [4], only essential points are described in the following. A closed cell
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 1 2 7 - 1
Y. Tsuchiya et al. / Journal of Non-Crystalline Solids 250±252 (1999) 468±472
assembly made of fused silica was used to reduce the preferential evaporation of S. The sound velocity was determined with reference to the one in distilled water in the cell at 0°C. It was taken to be 1402.71 m/s. The absolute temperature uncertainty was 3°C, although the relative temperatures were accurate to better than 0.2°C and the stability at a temperature was better than 0.1°C. Density measurements were carried out with a c-ray attenuation method and the constant speci®c heat, CP , was measured with an adiabatic scanning calorimeter. Then, the molar volume, V, thermal expansion coecient, aP , constant volume speci®c heat, CV , adiabatic compressibility, jS and isothermal compressibility, jT , were evaluated, using thermodynamic relations. 3. Results The velocity of sound is plotted as a function temperature in Fig. 1. An in¯ection is observed in
Fig. 1. Sound velocity as a function of temperature in liquid S±Se alloy. The lines through the data are a guide for the eye.
469
the data of l-S, which can be resolved in the data for an alloy up to 10 at.% Se. Fig. 2 shows V as a function of temperature. At the polymerization temperature V of l-S has an in¯ection while V of lSe changes approximately linearly in our temperature range. The temperature dependence of V smoothly changes from Se to S. Fig. 3 shows composition dependences of the molar volume, V, thermal expansion coecient, aP , speci®c heat, CP and CV , and compressibility, jS and jT , at 200 and 400°C. All of them change smoothly from S to Se. To investigate the polymerization transition in a dilute S alloy, sound velocity measurements were done for compositions ranging from 1±10 at.% Se in 1 at.% increments. The results for 5 at.% Se alloy are compared with those for pure S in Fig. 4(a). We note that the temperature at which the in¯ection occurs decreases by about 30°C. Moreover the in¯ection appears to occur over a range of temperatures. To determine Tk ,
Fig. 2. Molar volume as a function of temperature for liquid S±Se alloy. The lines through data have been determined with either linear ®tting (l-Se) or quadratic ®tting from which the thermal expansion coecient has been calculated. The correlation coecient was larger than 0.998 for all the alloys.
470
Y. Tsuchiya et al. / Journal of Non-Crystalline Solids 250±252 (1999) 468±472
Fig. 3. (a) Adiabatic (jS ) and isothermal (jS ) compressibility at 200 and 400°C. (b) constant pressure (CP ) and constant volume (CV ) at (jS ) at 200 and 400°C. (c) Molar volume (V) and thermal expansion coecient (aP ) at 200 and 400°C. The lines through data are a guide for the eye.
the logarithmic derivative of vs was calculated, and is shown in Fig. 4(b). At the onset of polymerization, the logarithmic derivative of vs increases stepwise. We assumed that the midpoint of the step corresponds to the onset of a transition. The onset temperature determined in this way is plotted against S composition in Fig. 5. It decreases with increasing Se composition. The rate of decrease determined by ®tting all the data to a linear relation, ax b (x: at.% Se), is ÿ5.5 0.6 (K/at.%). The correlation coecient was 0.998.
Fig. 4. (a) Sound velocity in S and S95 Se5 around the onset temperature of polymerization. (b) Logarithmic derivative of the sound velocity with respect to temperature. The contribution from the thermal expansion coecient is drawn by solid line.
4. Discussion First we consider the dependences on composition of thermodynamic quantities plotted in Fig. 3(a) and (b). All the thermodynamic quantities change smoothly from those for S to those for Se. The heat of mixing of this system has an endothermic parabolic form and is almost independent of temperature [5]. The interchange parameter is estimated to be 5.03 kJ/mol which is comparable to the thermal energy, R (R is the universal gas constant and T the temperature). Those results indicate, though they are rather indirect, that a S±Se alloy forms an almost random mixture at any composition. Based on neutron diraction experiments Winter et al. have sug-
Y. Tsuchiya et al. / Journal of Non-Crystalline Solids 250±252 (1999) 468±472
471
model for a polymerization transition in l-Se [2]. It has been predicted [2] that the onset of polymerization transition would take place at 77°C [2]. As plotted in Fig. 5, the onset temperature decreases linearly with Se composition at a rate of ÿ5.5 0.6 (K/at.%). If this rate is not changed considerably in the Se-rich composition range, the onset temperature in l-Se would not be reached in a ®nite temperature range in contradiction to the theoretical calculation [2]. Finally we mention the temperature dependence of the logarithmic derivative of vs with respect to temperature plotted in Fig. 4(b). For l-S, the derivative diverges as Tk , is approached from temperature greater than Tk . The logarithmic derivative of Vs with respect to temperature is given by ÿ1 vÿ1 s dvs =dT 1=2 jS djS =dT ÿ aP :
Fig. 5. Dependence on composition of the onset temperature, Tk , of polymerization transition in dilute S alloy. The broken line represents the liquidus line [10].
gested [6] that the structure of l-S above Tk may consist of small spherical molecules rather than long chain polymer molecules. If this is the case, a random mixture of S and Se would not be expected because of the geometrical constraint imposed by chains of Se [7]. Fig. 3(b) shows the constant volume speci®c heat, CV , as a function of composition. With increasing temperature, CV of l-S decreases from 4.5 at 200°C to 3.5 (Rÿ1 ) at 400°C (R is the gas constant), and CV of the alloy becomes almost independent of Se composition. As has been shown in Ref. [1], l-S above the polymerization temperature consists of various long chains in addition of S8 ring molecules. The average chain length becomes shorter with increasing temperature [1]. Liquid Se has a similar structure and temperature dependence though the extent of molecular structure is smaller compared with that of l-S [7]. Therefore the observed temperature composition dependence of CV is due to the rate of change with temperature of relative population of various molecular species in the mixture. Using the data on the dissolution of amorphous Se in CS2 , Eisenberg and Tobolsky presented a
1
Since the contribution from aP is about 10% of the right-hand side of Eq. (1) as plotted in Fig. 4(b), the derivative of the adiabatic compressibility with respect to temperature, diverges as Tk is approached. With addition of 5 at.% of Se, the peak in the derivative becomes much less resolved and the stepwise increase is also less resolved and occurs over a longer interval as compared with the results for l-S. Such eects may be related to the increase in the concentration ¯uctuations by alloying [8]. It has been reported [9] that the temperature dependence of the molar volume has a logarithmic singularity. However, it is localized on the very vicinity of Tk jT ÿ Tk j 2 0:1 K. Therefore, more detailed experiments would be required to observe the divergence in the derivative of the sound velocity, if a true thermodynamic singularity in the temperature dependence of jS around Tk is present. 5. Conclusions We have measured the sound velocity, molar volume and constant pressure speci®c heat. Main points are: (1) no indication has been observed for structural changes with composition which would be expected if l-S above Tk consisted of small spherical molecules, and (2) the onset of
472
Y. Tsuchiya et al. / Journal of Non-Crystalline Solids 250±252 (1999) 468±472
polymerization transition in dilute S alloy decreases at the rate of ÿ5.5 0.6 (K/at.%) by adding Se. References [1] [2] [3] [4]
B. Meyer, Chem. Rev. 76 (1976) 367. A. Eisenberg, A.V. Tobolsky, J. Polym. Sci. 46 (1960) 19. W. Klement Jr., J. Polym. Sci. 12 (1974) 815. Y. Tsuchiya, J. Phys. C 21 (1988) 5473.
[5] T. Maekawa, T. Yokokawa, K. Niwa, Bull. Chem. Soc. Jpn. 46 (1973) 761. [6] R. Winter, C. Szornel, W.-C. Pilgrim, W.S. Howells, P.A. Egelsta, T. Bodensteiner, Condens. Matter 2 (1990) 8427. [7] G. Lucovsky, in: E. Gerlach, P. Grosse (Eds.), The Physics of Selenium and Tellurium, Springer, Berlin, 1979, p. 178. [8] M. Shimoji, Liquid Metals, Academic Press, New York, 1977. [9] H. Patel, L.B. Borst, J. Chem. Phys. 54 (1971) 822. [10] M. Hansen, K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York, 1958.
www.elsevier.com/locate/jnoncrysol
The velocity of sound in the liquid S±Se alloy Y. Tsuchiya b
a,* ,
R. Satoh a, F. Kakinuma
b
a Department of Physics, Faculty of Science, Niigata University, Ikarashi, 2-8050, Niigata 950-2181, Japan Department of Information and Electronic Engineering, Niigata Institute of Technology, 1719 Fujihashi, Kashiwazaki 945-1195, Japan
Abstract The sound velocity was measured to investigate the polymerization transition in the liquid S±Se alloy. The onset temperature, Tk , of polymerization transition could be found up to 10 at.% of Se, which decreases with increasing Se fraction at the rate of ÿ5.5 0.6 (K/at.%). The results indicate that Tk in liquid Se may not be observed in a ®nite temperature range in contradiction to the previous theoretical calculation. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction There has been a long standing interest in the polymerization transition in liquid sulfur (l-S) [1]. Liquid sulfur consists of S8 ring molecules at the melting point (Tm 118.2°C) and transforms at Tk 160°C to a liquid consisting of chain molecules of which the average molecular weight is assumed to be more than 105 [1]. The existence of long chain molecules is inferred from the viscosity of l-S above Tk [1]. The viscosity of liquid Se (l-Se) is also of the same magnitude and shows similar dependence on temperature as l-S. Eisenberg and Tobolsky [2] estimated the parameters for a model calculation predicting the polymerization of l-Se, from which the onset was calculated to be 77°C. Although the predicted Tk is just beyond a temperature experimentally accessible, no investigation to detect the onset of polymerization transition in l-Se is reported to our knowledge.
* Corresponding author. Tel.: +81-25 262 6146; fax: +81-25 263 3961; e-mail: [email protected]
The relaxation time, s, of structural rearrangement around Tk in l-S is of the order of 10 min and more [3]. Since a conventional transient method like DSC requires very fast sweep of temperature as compared with s, it is not possible to determine the onset of polymerization in thermal equilibrium. In this paper, we report investigation of the polymerization transition in the liquid S±Se alloy by measuring the sound velocity, because sound velocity can be measured in a material at constant temperature. Our results indicate that Tk in l-Se would not be reached at a ®nite temperature range in contradiction to the theoretical calculation [2]. The molar volume, thermal expansion coecient, speci®c heat and compressibility were measured to complement the information obtained by sound velocity measurements.
2. Experimental procedure The velocity of sound, vs , was measured with a standard pulse technique. Since the details have been reported elsewhere [4], only essential points are described in the following. A closed cell
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 1 2 7 - 1
Y. Tsuchiya et al. / Journal of Non-Crystalline Solids 250±252 (1999) 468±472
assembly made of fused silica was used to reduce the preferential evaporation of S. The sound velocity was determined with reference to the one in distilled water in the cell at 0°C. It was taken to be 1402.71 m/s. The absolute temperature uncertainty was 3°C, although the relative temperatures were accurate to better than 0.2°C and the stability at a temperature was better than 0.1°C. Density measurements were carried out with a c-ray attenuation method and the constant speci®c heat, CP , was measured with an adiabatic scanning calorimeter. Then, the molar volume, V, thermal expansion coecient, aP , constant volume speci®c heat, CV , adiabatic compressibility, jS and isothermal compressibility, jT , were evaluated, using thermodynamic relations. 3. Results The velocity of sound is plotted as a function temperature in Fig. 1. An in¯ection is observed in
Fig. 1. Sound velocity as a function of temperature in liquid S±Se alloy. The lines through the data are a guide for the eye.
469
the data of l-S, which can be resolved in the data for an alloy up to 10 at.% Se. Fig. 2 shows V as a function of temperature. At the polymerization temperature V of l-S has an in¯ection while V of lSe changes approximately linearly in our temperature range. The temperature dependence of V smoothly changes from Se to S. Fig. 3 shows composition dependences of the molar volume, V, thermal expansion coecient, aP , speci®c heat, CP and CV , and compressibility, jS and jT , at 200 and 400°C. All of them change smoothly from S to Se. To investigate the polymerization transition in a dilute S alloy, sound velocity measurements were done for compositions ranging from 1±10 at.% Se in 1 at.% increments. The results for 5 at.% Se alloy are compared with those for pure S in Fig. 4(a). We note that the temperature at which the in¯ection occurs decreases by about 30°C. Moreover the in¯ection appears to occur over a range of temperatures. To determine Tk ,
Fig. 2. Molar volume as a function of temperature for liquid S±Se alloy. The lines through data have been determined with either linear ®tting (l-Se) or quadratic ®tting from which the thermal expansion coecient has been calculated. The correlation coecient was larger than 0.998 for all the alloys.
470
Y. Tsuchiya et al. / Journal of Non-Crystalline Solids 250±252 (1999) 468±472
Fig. 3. (a) Adiabatic (jS ) and isothermal (jS ) compressibility at 200 and 400°C. (b) constant pressure (CP ) and constant volume (CV ) at (jS ) at 200 and 400°C. (c) Molar volume (V) and thermal expansion coecient (aP ) at 200 and 400°C. The lines through data are a guide for the eye.
the logarithmic derivative of vs was calculated, and is shown in Fig. 4(b). At the onset of polymerization, the logarithmic derivative of vs increases stepwise. We assumed that the midpoint of the step corresponds to the onset of a transition. The onset temperature determined in this way is plotted against S composition in Fig. 5. It decreases with increasing Se composition. The rate of decrease determined by ®tting all the data to a linear relation, ax b (x: at.% Se), is ÿ5.5 0.6 (K/at.%). The correlation coecient was 0.998.
Fig. 4. (a) Sound velocity in S and S95 Se5 around the onset temperature of polymerization. (b) Logarithmic derivative of the sound velocity with respect to temperature. The contribution from the thermal expansion coecient is drawn by solid line.
4. Discussion First we consider the dependences on composition of thermodynamic quantities plotted in Fig. 3(a) and (b). All the thermodynamic quantities change smoothly from those for S to those for Se. The heat of mixing of this system has an endothermic parabolic form and is almost independent of temperature [5]. The interchange parameter is estimated to be 5.03 kJ/mol which is comparable to the thermal energy, R (R is the universal gas constant and T the temperature). Those results indicate, though they are rather indirect, that a S±Se alloy forms an almost random mixture at any composition. Based on neutron diraction experiments Winter et al. have sug-
Y. Tsuchiya et al. / Journal of Non-Crystalline Solids 250±252 (1999) 468±472
471
model for a polymerization transition in l-Se [2]. It has been predicted [2] that the onset of polymerization transition would take place at 77°C [2]. As plotted in Fig. 5, the onset temperature decreases linearly with Se composition at a rate of ÿ5.5 0.6 (K/at.%). If this rate is not changed considerably in the Se-rich composition range, the onset temperature in l-Se would not be reached in a ®nite temperature range in contradiction to the theoretical calculation [2]. Finally we mention the temperature dependence of the logarithmic derivative of vs with respect to temperature plotted in Fig. 4(b). For l-S, the derivative diverges as Tk , is approached from temperature greater than Tk . The logarithmic derivative of Vs with respect to temperature is given by ÿ1 vÿ1 s dvs =dT 1=2 jS djS =dT ÿ aP :
Fig. 5. Dependence on composition of the onset temperature, Tk , of polymerization transition in dilute S alloy. The broken line represents the liquidus line [10].
gested [6] that the structure of l-S above Tk may consist of small spherical molecules rather than long chain polymer molecules. If this is the case, a random mixture of S and Se would not be expected because of the geometrical constraint imposed by chains of Se [7]. Fig. 3(b) shows the constant volume speci®c heat, CV , as a function of composition. With increasing temperature, CV of l-S decreases from 4.5 at 200°C to 3.5 (Rÿ1 ) at 400°C (R is the gas constant), and CV of the alloy becomes almost independent of Se composition. As has been shown in Ref. [1], l-S above the polymerization temperature consists of various long chains in addition of S8 ring molecules. The average chain length becomes shorter with increasing temperature [1]. Liquid Se has a similar structure and temperature dependence though the extent of molecular structure is smaller compared with that of l-S [7]. Therefore the observed temperature composition dependence of CV is due to the rate of change with temperature of relative population of various molecular species in the mixture. Using the data on the dissolution of amorphous Se in CS2 , Eisenberg and Tobolsky presented a
1
Since the contribution from aP is about 10% of the right-hand side of Eq. (1) as plotted in Fig. 4(b), the derivative of the adiabatic compressibility with respect to temperature, diverges as Tk is approached. With addition of 5 at.% of Se, the peak in the derivative becomes much less resolved and the stepwise increase is also less resolved and occurs over a longer interval as compared with the results for l-S. Such eects may be related to the increase in the concentration ¯uctuations by alloying [8]. It has been reported [9] that the temperature dependence of the molar volume has a logarithmic singularity. However, it is localized on the very vicinity of Tk jT ÿ Tk j 2 0:1 K. Therefore, more detailed experiments would be required to observe the divergence in the derivative of the sound velocity, if a true thermodynamic singularity in the temperature dependence of jS around Tk is present. 5. Conclusions We have measured the sound velocity, molar volume and constant pressure speci®c heat. Main points are: (1) no indication has been observed for structural changes with composition which would be expected if l-S above Tk consisted of small spherical molecules, and (2) the onset of
472
Y. Tsuchiya et al. / Journal of Non-Crystalline Solids 250±252 (1999) 468±472
polymerization transition in dilute S alloy decreases at the rate of ÿ5.5 0.6 (K/at.%) by adding Se. References [1] [2] [3] [4]
B. Meyer, Chem. Rev. 76 (1976) 367. A. Eisenberg, A.V. Tobolsky, J. Polym. Sci. 46 (1960) 19. W. Klement Jr., J. Polym. Sci. 12 (1974) 815. Y. Tsuchiya, J. Phys. C 21 (1988) 5473.
[5] T. Maekawa, T. Yokokawa, K. Niwa, Bull. Chem. Soc. Jpn. 46 (1973) 761. [6] R. Winter, C. Szornel, W.-C. Pilgrim, W.S. Howells, P.A. Egelsta, T. Bodensteiner, Condens. Matter 2 (1990) 8427. [7] G. Lucovsky, in: E. Gerlach, P. Grosse (Eds.), The Physics of Selenium and Tellurium, Springer, Berlin, 1979, p. 178. [8] M. Shimoji, Liquid Metals, Academic Press, New York, 1977. [9] H. Patel, L.B. Borst, J. Chem. Phys. 54 (1971) 822. [10] M. Hansen, K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York, 1958.