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Critical sound propagation in liquid Ag–Ag2Te alloys
Journal of Non-Crystalline Solids 250±252 (1999) 373±376
www.elsevier.com/locate/jnoncrysol
Critical sound propagation in liquid Ag±Ag2Te alloys F. Kakinuma a
a,* ,
Y. Tsuchiya b, K. Suzuki
c
Department of Information and Electronic Engineering, Niigata Institute of Technology, 1719 Fujihashi, Kashiwazaki 945-1195, Japan b Department of Physics, Niigata University, Ikarashi 2-8050, Niigata 950-2181l, Japan c Institute for Advanced Materials Research, Moniwadai 2-6-8, Taihaku-Ku, Sendai 980-0252, Japan
Abstract Sound velocity measurements were carried out in Ag100ÿx Tex alloys in the range of concentration of x 0±33.33. The sound velocity in an alloy with a miscible gap deviates from a linear temperature dependence and the deviation increases as the two-melt phase boundary is approached, while it decreases almost linearly with temperature in miscible alloys. It is shown that the two-melt phase region is smaller than assumed. We attribute the anomalous temperature dependence to the critical phenomena associated with the two-melt phase separation. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Recently anomalous temperature dependence of sound velocity in several binary alloys with a miscibility gap have been reported [1±3]. Their anomaly becomes larger as the critical composition is approached. We suggest that the anomalous temperature dependence of the sound velocity is due to the two-melt phase separation which aects various physical properties at temperatures greater than that of the phase boundary. It is known that liquid Ag2 Te is a typical liquid semiconductor [4]. The electrical conductivity has a minimum in the concentration dependence at the composition of Ag2 Te. In the Ag±Te system, there is a miscibility gap in a concentration range between Ag and Ag2 Te [5]. The bond properties of Ag2 Te is ionic [4]. In a mixture of Ag and Ag2 Te the bonding changes with increasing Ag concentration. * Corresponding author. Tel.: +81-257 238 163; fax: +81-257 238 163; e-mail: [email protected]
Sound velocity investigation as a probe to the change in the bonding properties [6] and the associated structural change is now well established. In this paper, we report the results of sound velocity measurements for liquid Ag100ÿx Tex in the range of concentration of x 0±33.33 and analyze them on the basis of the Fixman theory [7].
2. Experimental The experimental details of the sound velocity measurements were essentially the same as described before [8]. To study an alloy with the critical temperature of these alloys, a closed cell assembly made from fused quartz crucible was used despite the larger uncertainty in determining the absolute magnitude of the velocity of sound. The crucible had parallel side walls, one of which was the end surface of a buer rod about 10 cm long. For an alloy in the two-melt phase, the sound velocity on either of the coexistent alloys could be
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 2 6 7 - 7
374
F. Kakinuma et al. / Journal of Non-Crystalline Solids 250±252 (1999) 373±376
measured by adjusting the position of a meniscus with respect to the buer end. The frequency of the sound was 8 MHz. The temperature was controlled by a digital temperature controller which could maintain a temperature within 0.5°C. The vertical temperature gradient over a specimen was less than 1°C. An eort to determine the absolute temperature very accurately was not made. The path length was determined by measuring the sound velocity in distilled water at 0°C. It was taken as 1402.71 m/s [9]. 3. Results Fig. 1 shows the sound velocity, vS , as a function of temperature. The sound velocities in liquid Ag, Ag90 Te10 and Ag2 Te decrease linearly with increasing temperature. On the other hand, the velocities of sound in alloys with a miscibility gap deviate from linear dependence as the phase Fig. 2. Composition dependence of sound velocity at 900°C, 1000°C and 1100°C. Curves are drawn as guides for the eye.
boundary is approached. The two-phase region is smaller than supposed [5] as seen in Fig. 1. Fig. 2 shows the concentration dependence of the sound velocity at several temperatures. The deviations from a linear dependence becomes larger in the concentration with a miscibility gap with decreasing temperature. 4. Discussion
Fig. 1. Sound velocity in alloys between Ag and Ag2 Te. Lines are drawn as guides for the eye.
The adiabatic compressibility has been deduced using the thermodynamic relation, jS qÿ1 VS2 , where q is the mass density [10]. It was measured with a high energy c-ray attenuation method. The results are plotted against ln T ÿ TC in Fig. 3, where TC denotes the critical temperature. The adiabatic compressibility increases as ln T ÿ TC towards the phase boundary in accord with the formal theory [11]. Thus it is reasonable to assume that the anomalous temperature dependence of the sound velocity for Ag±Te alloys above the phase
F. Kakinuma et al. / Journal of Non-Crystalline Solids 250±252 (1999) 373±376
375
g r a=r exp ÿjr:
3 2
The Debye relation is usually assumed for j as a function of temperature: j2 6=l2 T ÿ TC =TC ;
Fig. 3. Adiabatic compressibility as a function of ln(TÿTC ) for alloys with a miscibility gap. The line is drawn as a guide for the eye.
4
where l is the Debye short-range correlation length between atoms. Then d varies with temperature simply as T ÿ TC =TC . Since it was not possible to evaluate all the parameters involved in the theory, the experimental data were ®tted to Eq. (1) to obtain H and d0 , where we assumed phenomenologically a linear temperature dependence of v0 . The reduced sound velocity, ÿ1 2 v ÿ v0 v0 H , for Ag80 Te20 and Ag77:5 Te22:5 alloys are compared with the Fixman theory in Fig. 4. The theory can adequately explain the anomalous temperature dependence of the sound velocity above the two-melt phase boundary. It should be noted that the eects of two melt separation on the sound velocity remain over a
boundary originates from the critical phenomena associated with the two-melt phase separation. The Fixman theory [7] gives the following expression for the variation of velocity, v ÿ v0 , due to the presence of ¯uctuations associated with the two-melt phase separation: v ÿ v0 =v0 ÿ1=2 HR d;
1
where v0 is the sound velocity expected in the absence of phase separation. H is a constant depending on the frequency, x/2p, of the sound and the critical temperature, TC . R(d) is the real part of a de®nite integral which can be calculated analytically. The corresponding expression for the absorption coecient is given in terms of the imaginary part of the integral [7]. The critical property of the temperature dependence arises through the argument d j2 h=x1=2 ;
2
where h is a constant involving parameters a and j which determine the long-range correlation function,
Fig. 4. Reduced sound velocity as a function of d. Fixman theory [7] is represented by a smooth curve through the data.
376
F. Kakinuma et al. / Journal of Non-Crystalline Solids 250±252 (1999) 373±376
data fall between the line corresponding to l0 1.1 and 1.8. As seen in Fig. 5, alloys may be divided 1=2 1=2 into two groups on the H =d0 ÿ TC plane. The 0 values of l for alloys with a chalcogen element as 1=2 one component are located at the area of H =d0 > 0:4 and between l0 1.1 and 1.4. On the other hand, those for metal±metal binary alloys have 1=2 H =d0 < 0:3 and between l0 1.4 and 1.8. The observed feature seems to be related to the liquid structure associated with the nature of bond between elements. 5. Conclusion The critical sound-wave propagation has been found in a homogeneous alloy above the phase boundary which becomes more evident as the critical composition is approached. The Fixman theory can satisfactorily explain the critical sound wave propagation in a metallic alloy with a miscibility gap. Fig. 5. Plots of H=d01=2 against TC1=2 . Straight lines are the relation of Eq. (5) for l0 1.1, 1.3, 1.5 and 1.8. Numbers indicate as follows; 1. Ag80 Te20 , 2. Sn65 Se35 , 3. Tl80:7 Te19:3 , 4. Ag80 Se20 , 5. Tl80 Se20 , 6. Zn82 Bi18 , 7. Ga66:7 Bi33:3 and 8. Ga50:3 Hg49:7 .
temperature interval of about 50°C above the phase boundary. The parameters H and d0 obtained in this way satisfy the relation [7], p 1=2 1=2 5 H =d0 3 6 c ÿ 1R= 2p2 CP0 nl3 TC ; where c is the speci®c heat ratio, R is the gas constant, C0P is the non-critical constant-pressurespeci®c heat and n is the number density. Since CP0 3Rc and c 1:1 to an approximation, 1=2 Eq. (5) reduces to H =d0 0:034l0ÿ3 T 1=2 , where 0 l is scaled by an interatomic distance. The obtained l0 is 1.14 for Ag80 Te20 which is close to the critical composition. Fig. 5 shows the plot of 1=2 1=2 H =d0 against TC for several binary alloys. The
References [1] Y. Tsuchiya, F. Kakinuma, J. Phys.: Condens. Matter 4 (1992) 2117. [2] Y. Tsuchiya, J. Non-Cryst. Solids 156±158 (1993) 700. [3] Y. Tsuchiya, J. Non-Cryst. Solids 205±207 (1996) 94. [4] M. Cutler, Liquid Semiconductors, Academic Press, New York, 1977, p. 163. [5] T.B. Massalski, H. Okamoto, P.R. Subramanian, L. Kacprzak, Binary Alloy Phase Diagrams, 2nd ed., AMS International, Metals Park, OH, 1992. [6] D. Sette, Physics in Simple Liquids, ch. 9, North-Holland, Amsterdam, 1967. [7] M. Fixman, J. Chem. Phys. 48 (1962) 1961. [8] Y. Tsuchiya, J. Phys. C 21 (1988) 5473. [9] M. Greenspan, C.E. Tschiegg, J. Res. Nat. Bur. Stand. 59 (1957) 249. [10] E.A. Guggenheim, Thermodynamics, North-Holland, Amsterdam, 1967. [11] C.E. Chase, R.C. Williamson, L. Tisza, Phys. Rev. Lett. 13 (1964) 467.
www.elsevier.com/locate/jnoncrysol
Critical sound propagation in liquid Ag±Ag2Te alloys F. Kakinuma a
a,* ,
Y. Tsuchiya b, K. Suzuki
c
Department of Information and Electronic Engineering, Niigata Institute of Technology, 1719 Fujihashi, Kashiwazaki 945-1195, Japan b Department of Physics, Niigata University, Ikarashi 2-8050, Niigata 950-2181l, Japan c Institute for Advanced Materials Research, Moniwadai 2-6-8, Taihaku-Ku, Sendai 980-0252, Japan
Abstract Sound velocity measurements were carried out in Ag100ÿx Tex alloys in the range of concentration of x 0±33.33. The sound velocity in an alloy with a miscible gap deviates from a linear temperature dependence and the deviation increases as the two-melt phase boundary is approached, while it decreases almost linearly with temperature in miscible alloys. It is shown that the two-melt phase region is smaller than assumed. We attribute the anomalous temperature dependence to the critical phenomena associated with the two-melt phase separation. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Recently anomalous temperature dependence of sound velocity in several binary alloys with a miscibility gap have been reported [1±3]. Their anomaly becomes larger as the critical composition is approached. We suggest that the anomalous temperature dependence of the sound velocity is due to the two-melt phase separation which aects various physical properties at temperatures greater than that of the phase boundary. It is known that liquid Ag2 Te is a typical liquid semiconductor [4]. The electrical conductivity has a minimum in the concentration dependence at the composition of Ag2 Te. In the Ag±Te system, there is a miscibility gap in a concentration range between Ag and Ag2 Te [5]. The bond properties of Ag2 Te is ionic [4]. In a mixture of Ag and Ag2 Te the bonding changes with increasing Ag concentration. * Corresponding author. Tel.: +81-257 238 163; fax: +81-257 238 163; e-mail: [email protected]
Sound velocity investigation as a probe to the change in the bonding properties [6] and the associated structural change is now well established. In this paper, we report the results of sound velocity measurements for liquid Ag100ÿx Tex in the range of concentration of x 0±33.33 and analyze them on the basis of the Fixman theory [7].
2. Experimental The experimental details of the sound velocity measurements were essentially the same as described before [8]. To study an alloy with the critical temperature of these alloys, a closed cell assembly made from fused quartz crucible was used despite the larger uncertainty in determining the absolute magnitude of the velocity of sound. The crucible had parallel side walls, one of which was the end surface of a buer rod about 10 cm long. For an alloy in the two-melt phase, the sound velocity on either of the coexistent alloys could be
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 2 6 7 - 7
374
F. Kakinuma et al. / Journal of Non-Crystalline Solids 250±252 (1999) 373±376
measured by adjusting the position of a meniscus with respect to the buer end. The frequency of the sound was 8 MHz. The temperature was controlled by a digital temperature controller which could maintain a temperature within 0.5°C. The vertical temperature gradient over a specimen was less than 1°C. An eort to determine the absolute temperature very accurately was not made. The path length was determined by measuring the sound velocity in distilled water at 0°C. It was taken as 1402.71 m/s [9]. 3. Results Fig. 1 shows the sound velocity, vS , as a function of temperature. The sound velocities in liquid Ag, Ag90 Te10 and Ag2 Te decrease linearly with increasing temperature. On the other hand, the velocities of sound in alloys with a miscibility gap deviate from linear dependence as the phase Fig. 2. Composition dependence of sound velocity at 900°C, 1000°C and 1100°C. Curves are drawn as guides for the eye.
boundary is approached. The two-phase region is smaller than supposed [5] as seen in Fig. 1. Fig. 2 shows the concentration dependence of the sound velocity at several temperatures. The deviations from a linear dependence becomes larger in the concentration with a miscibility gap with decreasing temperature. 4. Discussion
Fig. 1. Sound velocity in alloys between Ag and Ag2 Te. Lines are drawn as guides for the eye.
The adiabatic compressibility has been deduced using the thermodynamic relation, jS qÿ1 VS2 , where q is the mass density [10]. It was measured with a high energy c-ray attenuation method. The results are plotted against ln T ÿ TC in Fig. 3, where TC denotes the critical temperature. The adiabatic compressibility increases as ln T ÿ TC towards the phase boundary in accord with the formal theory [11]. Thus it is reasonable to assume that the anomalous temperature dependence of the sound velocity for Ag±Te alloys above the phase
F. Kakinuma et al. / Journal of Non-Crystalline Solids 250±252 (1999) 373±376
375
g r a=r exp ÿjr:
3 2
The Debye relation is usually assumed for j as a function of temperature: j2 6=l2 T ÿ TC =TC ;
Fig. 3. Adiabatic compressibility as a function of ln(TÿTC ) for alloys with a miscibility gap. The line is drawn as a guide for the eye.
4
where l is the Debye short-range correlation length between atoms. Then d varies with temperature simply as T ÿ TC =TC . Since it was not possible to evaluate all the parameters involved in the theory, the experimental data were ®tted to Eq. (1) to obtain H and d0 , where we assumed phenomenologically a linear temperature dependence of v0 . The reduced sound velocity, ÿ1 2 v ÿ v0 v0 H , for Ag80 Te20 and Ag77:5 Te22:5 alloys are compared with the Fixman theory in Fig. 4. The theory can adequately explain the anomalous temperature dependence of the sound velocity above the two-melt phase boundary. It should be noted that the eects of two melt separation on the sound velocity remain over a
boundary originates from the critical phenomena associated with the two-melt phase separation. The Fixman theory [7] gives the following expression for the variation of velocity, v ÿ v0 , due to the presence of ¯uctuations associated with the two-melt phase separation: v ÿ v0 =v0 ÿ1=2 HR d;
1
where v0 is the sound velocity expected in the absence of phase separation. H is a constant depending on the frequency, x/2p, of the sound and the critical temperature, TC . R(d) is the real part of a de®nite integral which can be calculated analytically. The corresponding expression for the absorption coecient is given in terms of the imaginary part of the integral [7]. The critical property of the temperature dependence arises through the argument d j2 h=x1=2 ;
2
where h is a constant involving parameters a and j which determine the long-range correlation function,
Fig. 4. Reduced sound velocity as a function of d. Fixman theory [7] is represented by a smooth curve through the data.
376
F. Kakinuma et al. / Journal of Non-Crystalline Solids 250±252 (1999) 373±376
data fall between the line corresponding to l0 1.1 and 1.8. As seen in Fig. 5, alloys may be divided 1=2 1=2 into two groups on the H =d0 ÿ TC plane. The 0 values of l for alloys with a chalcogen element as 1=2 one component are located at the area of H =d0 > 0:4 and between l0 1.1 and 1.4. On the other hand, those for metal±metal binary alloys have 1=2 H =d0 < 0:3 and between l0 1.4 and 1.8. The observed feature seems to be related to the liquid structure associated with the nature of bond between elements. 5. Conclusion The critical sound-wave propagation has been found in a homogeneous alloy above the phase boundary which becomes more evident as the critical composition is approached. The Fixman theory can satisfactorily explain the critical sound wave propagation in a metallic alloy with a miscibility gap. Fig. 5. Plots of H=d01=2 against TC1=2 . Straight lines are the relation of Eq. (5) for l0 1.1, 1.3, 1.5 and 1.8. Numbers indicate as follows; 1. Ag80 Te20 , 2. Sn65 Se35 , 3. Tl80:7 Te19:3 , 4. Ag80 Se20 , 5. Tl80 Se20 , 6. Zn82 Bi18 , 7. Ga66:7 Bi33:3 and 8. Ga50:3 Hg49:7 .
temperature interval of about 50°C above the phase boundary. The parameters H and d0 obtained in this way satisfy the relation [7], p 1=2 1=2 5 H =d0 3 6 c ÿ 1R= 2p2 CP0 nl3 TC ; where c is the speci®c heat ratio, R is the gas constant, C0P is the non-critical constant-pressurespeci®c heat and n is the number density. Since CP0 3Rc and c 1:1 to an approximation, 1=2 Eq. (5) reduces to H =d0 0:034l0ÿ3 T 1=2 , where 0 l is scaled by an interatomic distance. The obtained l0 is 1.14 for Ag80 Te20 which is close to the critical composition. Fig. 5 shows the plot of 1=2 1=2 H =d0 against TC for several binary alloys. The
References [1] Y. Tsuchiya, F. Kakinuma, J. Phys.: Condens. Matter 4 (1992) 2117. [2] Y. Tsuchiya, J. Non-Cryst. Solids 156±158 (1993) 700. [3] Y. Tsuchiya, J. Non-Cryst. Solids 205±207 (1996) 94. [4] M. Cutler, Liquid Semiconductors, Academic Press, New York, 1977, p. 163. [5] T.B. Massalski, H. Okamoto, P.R. Subramanian, L. Kacprzak, Binary Alloy Phase Diagrams, 2nd ed., AMS International, Metals Park, OH, 1992. [6] D. Sette, Physics in Simple Liquids, ch. 9, North-Holland, Amsterdam, 1967. [7] M. Fixman, J. Chem. Phys. 48 (1962) 1961. [8] Y. Tsuchiya, J. Phys. C 21 (1988) 5473. [9] M. Greenspan, C.E. Tschiegg, J. Res. Nat. Bur. Stand. 59 (1957) 249. [10] E.A. Guggenheim, Thermodynamics, North-Holland, Amsterdam, 1967. [11] C.E. Chase, R.C. Williamson, L. Tisza, Phys. Rev. Lett. 13 (1964) 467.