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Structural relaxation of Pd82Si18 and Cu53.5Zr44.3Nb2.2 glassy systems
Materials Science and Engineering, A133 (1991) 523-525
523
Structural relaxation of Pd82Si18and Cu53.5Zr44.3Nb2.2glassy systems L. Kubi6fir, J. Spigiak and P. Duhaj Institute of Physics, Slovak Academy of Sciences, 842 28 Bratislava (Czechoslovakia)
Abstract Thermophysical parameters of glassy systems strongly depend on their thermodynamic state. A high value of the specific heat of the "as-quenched" samples is caused by the anharmonicity of the interatomic potential. The thermal diffusivity is influenced through microstresses which are induced by production. The ribbon is inhomogeneous from the thermodynamic point of view in the period after production. This inhomogeneity vanishes through "ageing" or heat treatment.
1. Introduction Relaxation phenomena have been studied by various measuring techniques on different materials for a long time but up till now the universal model for describing the relaxation processes has not been found although all anomalies should have the same cause, i.e. the regrouping of atoms from a specified non-equilibrium state to a less non-equilibrium one. A number of papers are devoted to the investigation of the relaxation processes of Pd-Si and C u - Z r glassy systems [1-6]. This contribution .will deal with the investigation of the thermophysical parameters (specific heat-thermodynamic parameter, thermal diffusivity-transport parameter) in different stages of the structural relaxation of Pd82Si18 and Cu53.sZr44.3Nb2.2 glassy systems.
2. Experimental The master alloy Pd82Si18 was prepared in a vacuum furnace by induction heating of the elements palladium and silicon of 99.8% and semiconducting purity, respectively. The alloy Cu53Zr,4.3Nb2. 2 w a s prepared by arc melting. The purity of copper was of OFHC standard; that of zirconium and niobium were 99.8%. Amorphous ribbons 6 mm wide and 25/~m thick were prepared by planar flow casting in helium atmosphere. A modification of the pulse method with line heat source was used for measuring specific heat and thermal diffusivity [7]. The principle of the method is based on measuring the tempera0921-5093/91/$3.50
ture response to the heat pulse. An automatic apparatus for measuring thermophysical properties in the range from 0 to 600 °C was used [7]. The size of the sample was 6 x 20 mm 2. The width and the output energy of the heat pulse were 0.7 s and 20 J m -1, respectively. Relative values of the specific heat were estimated only because of difficulties with calibration of the sample holder. All measurements were performed in vacuum. The combinations of various isotherms with the heating or cooling of the sample were used for measuring the thermophysical parameters in the temperature range from 5 to 600 °C.
3. Results The samples of the amorphous ribbon Pd82Si~8 were cut from various parts of the middle region of the ribbon length. The initial values of the specific heat and thermal diffusivity corresponding to room temperature of different samples measured in the course of time after production are listed in Table 1. The thermophysical properties change in time. The values of the specific h e a t and thermal diffusivity of the samples measured earlier differ markedly from each other. The thermophysical parameters of the samples measured later have nearly the same value which corresponds to the relaxed state [8]. The relaxed state can be reached through heat treatment. The results of such process are shown in Table 2 where the thermophysical parameters © Elsevier Sequoia/Printed in The Netherlands
524 TABLE 1
TABLE 3
Thermophysical parameters of the "as-quenched" samples of Pds2Sils glassy system
Thermophysical parameters of the "as-quenched" samples of the Cus3.sZr44.aNb2.2 glassy system
Sample no.
Time (months)
a X 106 (m 2 s-l)
c (a.u.)
Sample no.
Time (months)
a X 106 (m 2 s- 1)
C (a.u.)
1 2 3 4 5 6 7 8 9 10
9.6 10.3 10.5 10.8 11.7 18.0 18.3 20.3 21.1 22.4
4.12 5.33 4.67 5.05 5.12 4.20 3.72 4.01 3.97 4.04
5.50 5.86 7.49 7.99 5.12 3.35 7.38 4.07 3.7.0 3.81
1 2 3 4 5 6 7 8 9
20.6 23.5 26.6 26.8 29.0 29.2 29.7 29.7 31.0
2.36 2.99 3.12 2.89 3.22 2.97 2.55 2.92 3.27
22.9 28.9 5.19 6.39 8.72 8.74 12.6 10.0 9.66
20
TABLE 2 Thermophysical parameters of Pd82Si~8 glassy system at various relaxation stages a x 10 6 (m2s - ' )
C (a.u.)
Comments
4.12 4.45
5.50 3.71
4.46
3.72
' ~ s quenched" Heating up to 320 °C and free cooling to room temperature Heating up to 250 °C and free cooling to room temperature
5o o 10
5
i
240
are listed in various stages of relaxation together with the history of the heat treatment regimes. The thermophysical parameters reach the values corresponding to the relaxed state. The thermodynamic state of this sample is equivalent to the state of the samples which were measured in a later period (Table 1). The Cu53.5Zr44.3Nb2.2amorphous ribbon exhibits similar properties. The initial values of the specific heat and thermal diffusivity corresponding to room temperature of different samples are listed in Table 3. The differences between the relaxed and non-relaxed samples are greater in comparison to the Pd828i18 system. The influence of the heat treatment on the crystallization temperature of Pd825i18 a m o r p h o u s alloy is shown in Fig. 1 where the specific heat is plotted against temperature for samples which were in different stages of relaxation. The designation of the curves in Fig. 1 corresponds to the one in Table 1, although their thermodynamic state is different. The heating rate of all samples was in the range of 2 K min -1. The sample (10) has the most relaxed state and the corresponding data set was obtained in the following way: (1) the heat treatment was performed to obtain the lowest value of the specific heat;
t
i
i
280
i
i
i
I
i
i
320
i
I
360
i
i
i
i
400
i
i
i 440
T (*C)
Fig. 1. Specific heat of Pds2Si18 samples relaxed to different stages. Numbers 2, 4, 9, 10 correspond to the notation in Table 1.
(2) the sample temperature was promptly set to 283 °C and the measurement has started at heating rate 2 K min -1 . The chosen temperature regime of the sample (4) has allowed the relaxed state corresponding to room temperature to be preserved temporarily at higher temperatures. The crystallization temperature depends strongly on the relaxation stage and it changes from 345 °C to 383 °C. 4. Discussion
The interatomic potential of the glassy state has a complicated form. The double well potential model is frequently used to elucidate various physical phenomena during the relaxation [9]. Tunnelling will play an important role at low temperatures; anharmonic effects and reorientational jumps will predominate at medium and higher temperatures [8]. The specific heat and thermal diffusivity depend on the thermodynamic state of materials. Generally, the specific heat above
525
room temperature consists of three contributions, c = ce + cv + Cr, where ce is the electronic part, Cv the vibrational part and cr is created by the reorientational jumps of the atoms. The electronic part of the specific heat plays a negligible role at room temperature (the molar value of the electronic specific heat of copper has form ce - 1 0 - 4 kT where k is the Boltzmann constant). The contribution to the specific heat from the reorientational jumps may create a substantial part above the softening point or in the measuring regimes where the heating rate is high enough to initiate a high rate of the regrouping jumps, This part may reach in limit form (i.e. for ideal gas) the value 2/3 k. The vibrational part consists of two contributions, namely a harmonic and anharmonic one Cv= Ch+ Ca. The harmonic contribution may reach at room temperatures the value ch = 3k. The anharmonic contribution will depend on the form of the interatomic potential. The thermal diffusivity has an electronic part and a phonon part. The electronic part plays a predominant role in energy transport at room temperature. Nevertheless, the changes of this part are in the range of 1% due to relaxation [10]. the phonon thermal diffusivity is a function of mean free path of phonons as well as of the acoustic velocity of phonons. This part is influenced by the phonon-phonon scattering due to U-processes and by the microstresses induced by production. The metallic glasses are produced in thermodynamic state which is far from equilibrium. Such materials age in time or they relax from a specific non-equilibrium state to a less non-equilibrium one from the physical point of view. The "asquenched" Pd82Sil8 and Cu53.sZr44.aNb2. 2 glassy metals have a highly non-equilibrium state immediately after production. Analysis of the data in Tables 1 and 3 gives high values of the specific heat of the samples which were measured after their production. The question arises as to what
contributions cause these anomalous values of the specific heat. Careful analysis yields that this contribution should be caused by the anharmonic effects only. The specific heat reaches higher values through the anlaarmonic contribution. The thermal diffusivity changes by removing the microstresses inside the ribbon. The specific heat and thermal diffusivity decrease in the process of ageing and increase with heat treatment. This is supported by the data in Table 2. Then the changes of thermophysical parameters are caused by changes of the interatomic potential. The potential acquires a less anharmonic form. The relaxation processes are represented by a small adjustment of the atoms in the glassy structure. The ribbon is inhomogeneous from the thermodynamic point of view in the period after production. This inhomogeneity vanishes through "ageing" or heat treatment.
References 1 A. Sadoc and J. C. Lasjaunias, J. Phys. F: 15 (1985) 1021. 2 J. R. Matey and A. C. Anderson, J. Non-Cryst. Sol., 23 (1977) 129. 3 R. O.Suzuki and P. H. Shingu, J. Non-Cryst. Sol., 61 &62 (1984) 1003. 4 A. Ravex, J. C. Lasjaunias and O. Bethoux, J. Phys. F: 14 (1984) 329. 5 H. S. Chen and A. Inoue, J. Non-Cryst. Sol., 61 & 62 (1984) 805. 6 A. Sadoc, Y. Calvayac, A. Quivy, M. Harmelin and A. M. Flank, J. Non-Cryst. Sol., 65 (1984) 109. 7 L. Kubi~ir, in G. Svehla (ed.), Wilson & Wilson's Comprehensive Analytical Chemistry, Elsevier, Amsterdam; Veda, Bratislava, 1990, pp. 370. 8 L. Kubir~ir, in P. Duhaj, P. Mrafko and P. gvec (eds.), 2nd Int. Conf. on Metallic Glasses, Smolenice, May 22-26, 1989 (Trans Tech Publications, Switzerland, Germany, UK, USA, 1990),p. 165. 9 W. A. Philips, Amorphous Solids at Low Temperatures, Springer, New York, 1981, p. 160. 10 G. Riontino and M. Baricco, PhiL Mag. B, 61 (1990) 715.
523
Structural relaxation of Pd82Si18and Cu53.5Zr44.3Nb2.2glassy systems L. Kubi6fir, J. Spigiak and P. Duhaj Institute of Physics, Slovak Academy of Sciences, 842 28 Bratislava (Czechoslovakia)
Abstract Thermophysical parameters of glassy systems strongly depend on their thermodynamic state. A high value of the specific heat of the "as-quenched" samples is caused by the anharmonicity of the interatomic potential. The thermal diffusivity is influenced through microstresses which are induced by production. The ribbon is inhomogeneous from the thermodynamic point of view in the period after production. This inhomogeneity vanishes through "ageing" or heat treatment.
1. Introduction Relaxation phenomena have been studied by various measuring techniques on different materials for a long time but up till now the universal model for describing the relaxation processes has not been found although all anomalies should have the same cause, i.e. the regrouping of atoms from a specified non-equilibrium state to a less non-equilibrium one. A number of papers are devoted to the investigation of the relaxation processes of Pd-Si and C u - Z r glassy systems [1-6]. This contribution .will deal with the investigation of the thermophysical parameters (specific heat-thermodynamic parameter, thermal diffusivity-transport parameter) in different stages of the structural relaxation of Pd82Si18 and Cu53.sZr44.3Nb2.2 glassy systems.
2. Experimental The master alloy Pd82Si18 was prepared in a vacuum furnace by induction heating of the elements palladium and silicon of 99.8% and semiconducting purity, respectively. The alloy Cu53Zr,4.3Nb2. 2 w a s prepared by arc melting. The purity of copper was of OFHC standard; that of zirconium and niobium were 99.8%. Amorphous ribbons 6 mm wide and 25/~m thick were prepared by planar flow casting in helium atmosphere. A modification of the pulse method with line heat source was used for measuring specific heat and thermal diffusivity [7]. The principle of the method is based on measuring the tempera0921-5093/91/$3.50
ture response to the heat pulse. An automatic apparatus for measuring thermophysical properties in the range from 0 to 600 °C was used [7]. The size of the sample was 6 x 20 mm 2. The width and the output energy of the heat pulse were 0.7 s and 20 J m -1, respectively. Relative values of the specific heat were estimated only because of difficulties with calibration of the sample holder. All measurements were performed in vacuum. The combinations of various isotherms with the heating or cooling of the sample were used for measuring the thermophysical parameters in the temperature range from 5 to 600 °C.
3. Results The samples of the amorphous ribbon Pd82Si~8 were cut from various parts of the middle region of the ribbon length. The initial values of the specific heat and thermal diffusivity corresponding to room temperature of different samples measured in the course of time after production are listed in Table 1. The thermophysical properties change in time. The values of the specific h e a t and thermal diffusivity of the samples measured earlier differ markedly from each other. The thermophysical parameters of the samples measured later have nearly the same value which corresponds to the relaxed state [8]. The relaxed state can be reached through heat treatment. The results of such process are shown in Table 2 where the thermophysical parameters © Elsevier Sequoia/Printed in The Netherlands
524 TABLE 1
TABLE 3
Thermophysical parameters of the "as-quenched" samples of Pds2Sils glassy system
Thermophysical parameters of the "as-quenched" samples of the Cus3.sZr44.aNb2.2 glassy system
Sample no.
Time (months)
a X 106 (m 2 s-l)
c (a.u.)
Sample no.
Time (months)
a X 106 (m 2 s- 1)
C (a.u.)
1 2 3 4 5 6 7 8 9 10
9.6 10.3 10.5 10.8 11.7 18.0 18.3 20.3 21.1 22.4
4.12 5.33 4.67 5.05 5.12 4.20 3.72 4.01 3.97 4.04
5.50 5.86 7.49 7.99 5.12 3.35 7.38 4.07 3.7.0 3.81
1 2 3 4 5 6 7 8 9
20.6 23.5 26.6 26.8 29.0 29.2 29.7 29.7 31.0
2.36 2.99 3.12 2.89 3.22 2.97 2.55 2.92 3.27
22.9 28.9 5.19 6.39 8.72 8.74 12.6 10.0 9.66
20
TABLE 2 Thermophysical parameters of Pd82Si~8 glassy system at various relaxation stages a x 10 6 (m2s - ' )
C (a.u.)
Comments
4.12 4.45
5.50 3.71
4.46
3.72
' ~ s quenched" Heating up to 320 °C and free cooling to room temperature Heating up to 250 °C and free cooling to room temperature
5o o 10
5
i
240
are listed in various stages of relaxation together with the history of the heat treatment regimes. The thermophysical parameters reach the values corresponding to the relaxed state. The thermodynamic state of this sample is equivalent to the state of the samples which were measured in a later period (Table 1). The Cu53.5Zr44.3Nb2.2amorphous ribbon exhibits similar properties. The initial values of the specific heat and thermal diffusivity corresponding to room temperature of different samples are listed in Table 3. The differences between the relaxed and non-relaxed samples are greater in comparison to the Pd828i18 system. The influence of the heat treatment on the crystallization temperature of Pd825i18 a m o r p h o u s alloy is shown in Fig. 1 where the specific heat is plotted against temperature for samples which were in different stages of relaxation. The designation of the curves in Fig. 1 corresponds to the one in Table 1, although their thermodynamic state is different. The heating rate of all samples was in the range of 2 K min -1. The sample (10) has the most relaxed state and the corresponding data set was obtained in the following way: (1) the heat treatment was performed to obtain the lowest value of the specific heat;
t
i
i
280
i
i
i
I
i
i
320
i
I
360
i
i
i
i
400
i
i
i 440
T (*C)
Fig. 1. Specific heat of Pds2Si18 samples relaxed to different stages. Numbers 2, 4, 9, 10 correspond to the notation in Table 1.
(2) the sample temperature was promptly set to 283 °C and the measurement has started at heating rate 2 K min -1 . The chosen temperature regime of the sample (4) has allowed the relaxed state corresponding to room temperature to be preserved temporarily at higher temperatures. The crystallization temperature depends strongly on the relaxation stage and it changes from 345 °C to 383 °C. 4. Discussion
The interatomic potential of the glassy state has a complicated form. The double well potential model is frequently used to elucidate various physical phenomena during the relaxation [9]. Tunnelling will play an important role at low temperatures; anharmonic effects and reorientational jumps will predominate at medium and higher temperatures [8]. The specific heat and thermal diffusivity depend on the thermodynamic state of materials. Generally, the specific heat above
525
room temperature consists of three contributions, c = ce + cv + Cr, where ce is the electronic part, Cv the vibrational part and cr is created by the reorientational jumps of the atoms. The electronic part of the specific heat plays a negligible role at room temperature (the molar value of the electronic specific heat of copper has form ce - 1 0 - 4 kT where k is the Boltzmann constant). The contribution to the specific heat from the reorientational jumps may create a substantial part above the softening point or in the measuring regimes where the heating rate is high enough to initiate a high rate of the regrouping jumps, This part may reach in limit form (i.e. for ideal gas) the value 2/3 k. The vibrational part consists of two contributions, namely a harmonic and anharmonic one Cv= Ch+ Ca. The harmonic contribution may reach at room temperatures the value ch = 3k. The anharmonic contribution will depend on the form of the interatomic potential. The thermal diffusivity has an electronic part and a phonon part. The electronic part plays a predominant role in energy transport at room temperature. Nevertheless, the changes of this part are in the range of 1% due to relaxation [10]. the phonon thermal diffusivity is a function of mean free path of phonons as well as of the acoustic velocity of phonons. This part is influenced by the phonon-phonon scattering due to U-processes and by the microstresses induced by production. The metallic glasses are produced in thermodynamic state which is far from equilibrium. Such materials age in time or they relax from a specific non-equilibrium state to a less non-equilibrium one from the physical point of view. The "asquenched" Pd82Sil8 and Cu53.sZr44.aNb2. 2 glassy metals have a highly non-equilibrium state immediately after production. Analysis of the data in Tables 1 and 3 gives high values of the specific heat of the samples which were measured after their production. The question arises as to what
contributions cause these anomalous values of the specific heat. Careful analysis yields that this contribution should be caused by the anharmonic effects only. The specific heat reaches higher values through the anlaarmonic contribution. The thermal diffusivity changes by removing the microstresses inside the ribbon. The specific heat and thermal diffusivity decrease in the process of ageing and increase with heat treatment. This is supported by the data in Table 2. Then the changes of thermophysical parameters are caused by changes of the interatomic potential. The potential acquires a less anharmonic form. The relaxation processes are represented by a small adjustment of the atoms in the glassy structure. The ribbon is inhomogeneous from the thermodynamic point of view in the period after production. This inhomogeneity vanishes through "ageing" or heat treatment.
References 1 A. Sadoc and J. C. Lasjaunias, J. Phys. F: 15 (1985) 1021. 2 J. R. Matey and A. C. Anderson, J. Non-Cryst. Sol., 23 (1977) 129. 3 R. O.Suzuki and P. H. Shingu, J. Non-Cryst. Sol., 61 &62 (1984) 1003. 4 A. Ravex, J. C. Lasjaunias and O. Bethoux, J. Phys. F: 14 (1984) 329. 5 H. S. Chen and A. Inoue, J. Non-Cryst. Sol., 61 & 62 (1984) 805. 6 A. Sadoc, Y. Calvayac, A. Quivy, M. Harmelin and A. M. Flank, J. Non-Cryst. Sol., 65 (1984) 109. 7 L. Kubi~ir, in G. Svehla (ed.), Wilson & Wilson's Comprehensive Analytical Chemistry, Elsevier, Amsterdam; Veda, Bratislava, 1990, pp. 370. 8 L. Kubir~ir, in P. Duhaj, P. Mrafko and P. gvec (eds.), 2nd Int. Conf. on Metallic Glasses, Smolenice, May 22-26, 1989 (Trans Tech Publications, Switzerland, Germany, UK, USA, 1990),p. 165. 9 W. A. Philips, Amorphous Solids at Low Temperatures, Springer, New York, 1981, p. 160. 10 G. Riontino and M. Baricco, PhiL Mag. B, 61 (1990) 715.