- Email: [email protected]
Study of the structural relaxation of Pd82Si18 metallic glass by thermal expansion and viscous flow measurements
Materials Science and Engineering, A133 (1991) 529-531
529
Study of the structural relaxation of Pd82Si18metallic glass by thermal expansion and viscous flow measurements Liljana Stojanova* and Krassimir Russew Institute for Metal Science and Technology, Bulgarian Academy of Sciences, 1574 Sofia (Bulgaria)
Emilia IIlekova Institute of Physics of EPRC, Slovak Academy of Sciences, Dubravska Cesta 9, 842 28 Bratislava (Czechoslovakia)
Abstract The temperature dependences of the viscosity r/ and of the thermal expansion coefficient ctt of asquenched and relaxed ribbons of Pd82Si18glassy alloy are studied. The experimental results obtained are treated on the basis of the hole theory of liquids, modified by Wachter and Sommer. Information is gained about the nature of relaxation phenomena in the amorphous alloy studied.
1. Introduction The structure of amorphous alloys changes to more stable amorphous configurations upon annealing. As a result, most of their properties change too [1-5]. The changes of the temperature dependence of the thermal expansion coefficient a e as well as of the viscosity ~/of glassy Pd82Si18 alloy due to different relaxation pre-annealings are studied in this article. Structural relaxation phenomena in this glassy alloy are discussed.
2. Experimental procedure The Pd82Si18 alloy studied was obtained in an amorphous state by the planar flow casting method, being 5.5 mm wide by 0.025 mm thick, The viscosity measurements were carried out on 1 mm narrow ribbons cut out from the initial wide ribbon. Specimens from the wide ribbon were used in order to determine the temperature dependence of the thermal expansion coefficient a e of the alloy in the as-quenched state as well as after relaxation pre-annealings at 473, 523 and 563 K for 50 min. More details about the experimental techniques for viscosity measurements are given in our previous paper [6]. Both the thermal *Present address: c/o Dr. E. Fromm, Max-Planck-Institut f/ir Metallforschung, Seestrasse 92, D-7000 Stuttgart 1, F.R.G. 0921-5093/91/$3.50
expansion and viscosity measurements were carried out under continuous heating conditions at a heating rate of 20 K min-1 with the aid of a Perkin-Elmer TMS-2 Thermomechanical Analyzer.
3. Experimental results and discussion The temperature dependence of the thermal expansion coefficient of the alloy studied is shown in Fig. 1. For comparison purposes, the total lifetime of positrons in Pds0Si20 glassy alloy measured by Tanigawa e t al. [7] after relaxation pre-annealing at different elevated temperatures is shown in the same figure. It can be seen that the high-temperature relaxation pre-annealing at 563 K leads to a temperature dependence of a t which up to 600 K is very similar to the temperature dependence of the thermal expansion coefficient of the crystallized alloy. After reaching 630 K (Tg) a rapid increase of at and a practically identical temperature dependence of the thermal expansion coefficient of all amorphous specimens, independent of their preliminary thermal history, is observed. The conclusion could be drawn that after 50 min relaxation at 563 K the alloy studied is brought to an internal quasiequilibrium amorphous state (metastable isoconfigurational structural state), whereas the pre-annealings at lower temperatures (473 and © Elsevier Sequoia/Printed in The Netherlands
530 TOc IOO
27
2OO
9
300
o
2
I 25
CRYST.
I
L
7
24
6
a~
"{
16o ~
.
~ 2z ~
~
TI I
120~D 22
Fig. I i
400
i
4~0
5O0 T, K
" 7 - - 525 ~ 55O =
80
6~0
Fig. 1. Temperature dependence ( ) of the apparent thermal expansion coefficients at of Pd82Si,s glassy alloy, depending on the thermal history of the specimens used. The curve ( - - - ) represents the total lifetime of positrons in Pd80Si20 glassy alloy as a function of the temperature of isothermal pre-annealing according to Tanigawa et al. [7].
523 K) for 50 min do not lead to complete relaxation. The anomalies of the temperature dependence of a t could be interpreted in this case on the basis of the similarity (see Fig. 1 ) between the total lifetime of positrons in Pd80Si20 at room temperatures as a function of the temperature of isothermal pre-annealing for 20 min [7] and the ae-temperature dependences for specimens preannealed at 473 and 523 K. Obviously, after these low-temperature pre-annealings and under the conditions of a repeated heating run at 20 K min -1 an additional relaxation takes place, leading in the temperature range 3 7 0 - 4 7 0 K to stress release in the amorphous regions with higher density. This is reflected by an increase of the apparent thermal expansion coefficient and of the total lifetime of positrons [7]. The additional relaxation which takes place in the temperature range 4 7 0 - 5 6 0 K is probably connected with stress release in the amorphous regions with lower density [7] and annealing out of the excess free volume of the amorphous structure. This is manifested by a decrease of the apparent thermal expansion coefficient and of the total lifetime of the positrons. Another possibility to interpret the observed anomalies of the thermal expansion coefficient a e is represented by the DNLR (Distribution of NonLinear Relaxation) model of Cunat et al. [8, 9] which will be the subject of another paper. As is seen from Fig. 1, at temperatures higher than 630 K (Tg) the relaxation rate becomes high enough and brings all the speci-
Q,r 1.55
,
,
1.60
IOO0/T, K -I
1.65
1.70
,,
Fig. 2. Temperature dependence of the viscosity t/ of Pd82Si~8 glass alloy: • as-quenched specimen, o fully relaxed at 563 K for 50 min specimen. The points • represent the temperature dependence of the volume thermal expansion coefficient av of Pd82Si,8 glassy alloy, fully relaxed at 563 K for 50 min, in the coordinates of the equation of Wachter and Sommer [11].
mens to a unique quasi-equilibrium structural state, which is preserved until the onset temperature of crystallization is reached. The temperature dependence of the viscosity r/ of as-quenched as well as of fully relaxed at 563 K specimens is shown in Fig. 2. In both cases two linear parts of this temperature dependence with different slopes are observed, the crossing points of which correspond to the glass transition temperatures Tg (633 and 628 K respectively) of the above-mentioned specimens. For temperatures lower than Tg the activation energies of viscous flow are 193.5 and 63 kJ mo1-1 for fully relaxed and as-quenched specimens, respectively. At temperatures higher than Tg an identical temperature dependence of ~/ is observed with an apparent activation energy of flow of 617 kJ mol-1, i.e. the conclusions made on the basis of the ae measurements are confirmed by the results of the viscous flow measurements. Based on the hole model of liquids [10], combined with some generally available thermodynamic properties, Wachter and Sommer [11] have derived the following expression for the volume expansion coefficient av: av=~T ~exp
[ ( -~-
1-
(1)
with n=Ua/Vh, Eh=formation enthalpy of one mole holes, v a = mean hard core volume of a t o m s and v h = hole volume. This expression is valid for
531
undercooled liquids and glasses in the thermal quasi-equilibrium state. Taking into account that av = 3ae, the temperature dependence of ctv of relaxed at 563 K specimens in the coordinates of eqn. (1) is plotted in Fig. 2. Also in this case two linear parts of the temperature dependence are observed, with crossing points corresponding to Tg (628 K). From the slopes and intercepts of these lines the values of E h and n were calculated. For T < Tg Eh=26.3 kJ mol -l, n=0.92; for T > Tg E h = 384 kJ mol- 1, n = 0.015. On the basis of these n-values the conclusion could be drawn that the hole size in the fully relaxed specimens practically coincides with the mean atomic size, which is physically meaningful and gives an explanation for the similarity of the at-temperature dependences of crystalline and fully relaxed amorphous specimens for T< Tg (see Fig. 1). The value of n for T> Tg suggests the existence of huge (vh=67va) holes in the structure of the undercooled melt. It is to some extent surprising, but corresponds very well to the experimentally observed increase of a t by an order of magnitude at temperatures higher than Tg. According to [11], the total activation energy of viscous flow Q~=RTVa/Vf+Eh, with uf the free volume per atom [12]. It follows from our results that E h (26.3 kJ mo1-1) is approximately 13% of Q, (193.5 kJ mol-1), in good agreement with the theoretically expected [11] E h/Q, ratio.
4. Conclusions Thermal expansion and viscous flow measurements could be used as sensitive methods for investigation of the structural relaxation phenomena in amorphous alloys. In the case of PdszSil8 amorphous alloy the relaxation in the low-temperature range 370-470 K is most probably connected with stress release in the amorphous regions with higher density, reflected by an increase of the apparent thermal expansion coefficient of the alloy studied by a repeated heating run. In the temperature range 470-560 K the relaxation in the alloy studied is connected with stress
release in the amorphous regions with lower density and annealing out of the excess free volume in the amorphous structure, manifested by a decrease of the apparent thermal expansion coefficient. The isothermal high-temperature relaxation at 563 K leads to a more uniform quasi-equilibrium amorphous structure with hole defects similar to the hole defects in the crystalline Pd82Si18 alloy. At temperatures higher than Tg a common structure of undercooled melt in the quasi-equilibrium state is established, manifested by a common temperature dependence of the viscosity and of the thermal expansion coefficient of the Pd82Sil8 amorphous alloy studied, independent of the thermal history of the specimens.
Acknowledgment The authors are indebted to the Alexander von Humboldt Foundation, ER.G., for donating the thermoanalytical equipment.
References 1 H.S. Chen, J. Appl. Phys., 49 ( 1978 ) 3289. 2 Th. Frechen, G. Dietz and F. Gans, J. Magn. Magn. Mater., 13 (1979) 85. 3 A. L. Mulder, J. W. Driver and S. Raclelaax, t'roc. Conf. Metallic Glasses, Budapest, Vol. 2 (1980) p. 299, 4 G. Dietz and K. Hiiller, J. Non-Cryst. Solids, 47 (1982) 377. 5 H. S. Chen and E. Coleman, Appl. Phys. Lett., 28 (1976) 245. 6 K. Russew and L. Stojanova, Mater. Sci. Eng. A, 123 (1990) 59. 7 S. Tanigawa and K. Shima, Proc. 4th Int. Conf. on Rapidly Quenched Metals, Sendai, Japan ( 1981 ) p. 501. 8 Ch. Cunat, Z. Phys. Chem. Neue Folge, 157(1988) 425. 9 E. Illekova, Ch. Cunat, E A. Kuhnast, A. Aharoune and J. M. Fiorani, J. Phys. (1990), submitted. 10 K. S. Dubey and P. Ramachandrarao, Acta Metall., 32 (1984) 91. 11 J. Wachter and E Sommer, J. Non-Cryst. Solids, 117/118 (1990) 890. 12 M. H. Cohen and D. Turnbull, J. Chem. Phys., 31 (1959) 1164.
529
Study of the structural relaxation of Pd82Si18metallic glass by thermal expansion and viscous flow measurements Liljana Stojanova* and Krassimir Russew Institute for Metal Science and Technology, Bulgarian Academy of Sciences, 1574 Sofia (Bulgaria)
Emilia IIlekova Institute of Physics of EPRC, Slovak Academy of Sciences, Dubravska Cesta 9, 842 28 Bratislava (Czechoslovakia)
Abstract The temperature dependences of the viscosity r/ and of the thermal expansion coefficient ctt of asquenched and relaxed ribbons of Pd82Si18glassy alloy are studied. The experimental results obtained are treated on the basis of the hole theory of liquids, modified by Wachter and Sommer. Information is gained about the nature of relaxation phenomena in the amorphous alloy studied.
1. Introduction The structure of amorphous alloys changes to more stable amorphous configurations upon annealing. As a result, most of their properties change too [1-5]. The changes of the temperature dependence of the thermal expansion coefficient a e as well as of the viscosity ~/of glassy Pd82Si18 alloy due to different relaxation pre-annealings are studied in this article. Structural relaxation phenomena in this glassy alloy are discussed.
2. Experimental procedure The Pd82Si18 alloy studied was obtained in an amorphous state by the planar flow casting method, being 5.5 mm wide by 0.025 mm thick, The viscosity measurements were carried out on 1 mm narrow ribbons cut out from the initial wide ribbon. Specimens from the wide ribbon were used in order to determine the temperature dependence of the thermal expansion coefficient a e of the alloy in the as-quenched state as well as after relaxation pre-annealings at 473, 523 and 563 K for 50 min. More details about the experimental techniques for viscosity measurements are given in our previous paper [6]. Both the thermal *Present address: c/o Dr. E. Fromm, Max-Planck-Institut f/ir Metallforschung, Seestrasse 92, D-7000 Stuttgart 1, F.R.G. 0921-5093/91/$3.50
expansion and viscosity measurements were carried out under continuous heating conditions at a heating rate of 20 K min-1 with the aid of a Perkin-Elmer TMS-2 Thermomechanical Analyzer.
3. Experimental results and discussion The temperature dependence of the thermal expansion coefficient of the alloy studied is shown in Fig. 1. For comparison purposes, the total lifetime of positrons in Pds0Si20 glassy alloy measured by Tanigawa e t al. [7] after relaxation pre-annealing at different elevated temperatures is shown in the same figure. It can be seen that the high-temperature relaxation pre-annealing at 563 K leads to a temperature dependence of a t which up to 600 K is very similar to the temperature dependence of the thermal expansion coefficient of the crystallized alloy. After reaching 630 K (Tg) a rapid increase of at and a practically identical temperature dependence of the thermal expansion coefficient of all amorphous specimens, independent of their preliminary thermal history, is observed. The conclusion could be drawn that after 50 min relaxation at 563 K the alloy studied is brought to an internal quasiequilibrium amorphous state (metastable isoconfigurational structural state), whereas the pre-annealings at lower temperatures (473 and © Elsevier Sequoia/Printed in The Netherlands
530 TOc IOO
27
2OO
9
300
o
2
I 25
CRYST.
I
L
7
24
6
a~
"{
16o ~
.
~ 2z ~
~
TI I
120~D 22
Fig. I i
400
i
4~0
5O0 T, K
" 7 - - 525 ~ 55O =
80
6~0
Fig. 1. Temperature dependence ( ) of the apparent thermal expansion coefficients at of Pd82Si,s glassy alloy, depending on the thermal history of the specimens used. The curve ( - - - ) represents the total lifetime of positrons in Pd80Si20 glassy alloy as a function of the temperature of isothermal pre-annealing according to Tanigawa et al. [7].
523 K) for 50 min do not lead to complete relaxation. The anomalies of the temperature dependence of a t could be interpreted in this case on the basis of the similarity (see Fig. 1 ) between the total lifetime of positrons in Pd80Si20 at room temperatures as a function of the temperature of isothermal pre-annealing for 20 min [7] and the ae-temperature dependences for specimens preannealed at 473 and 523 K. Obviously, after these low-temperature pre-annealings and under the conditions of a repeated heating run at 20 K min -1 an additional relaxation takes place, leading in the temperature range 3 7 0 - 4 7 0 K to stress release in the amorphous regions with higher density. This is reflected by an increase of the apparent thermal expansion coefficient and of the total lifetime of positrons [7]. The additional relaxation which takes place in the temperature range 4 7 0 - 5 6 0 K is probably connected with stress release in the amorphous regions with lower density [7] and annealing out of the excess free volume of the amorphous structure. This is manifested by a decrease of the apparent thermal expansion coefficient and of the total lifetime of the positrons. Another possibility to interpret the observed anomalies of the thermal expansion coefficient a e is represented by the DNLR (Distribution of NonLinear Relaxation) model of Cunat et al. [8, 9] which will be the subject of another paper. As is seen from Fig. 1, at temperatures higher than 630 K (Tg) the relaxation rate becomes high enough and brings all the speci-
Q,r 1.55
,
,
1.60
IOO0/T, K -I
1.65
1.70
,,
Fig. 2. Temperature dependence of the viscosity t/ of Pd82Si~8 glass alloy: • as-quenched specimen, o fully relaxed at 563 K for 50 min specimen. The points • represent the temperature dependence of the volume thermal expansion coefficient av of Pd82Si,8 glassy alloy, fully relaxed at 563 K for 50 min, in the coordinates of the equation of Wachter and Sommer [11].
mens to a unique quasi-equilibrium structural state, which is preserved until the onset temperature of crystallization is reached. The temperature dependence of the viscosity r/ of as-quenched as well as of fully relaxed at 563 K specimens is shown in Fig. 2. In both cases two linear parts of this temperature dependence with different slopes are observed, the crossing points of which correspond to the glass transition temperatures Tg (633 and 628 K respectively) of the above-mentioned specimens. For temperatures lower than Tg the activation energies of viscous flow are 193.5 and 63 kJ mo1-1 for fully relaxed and as-quenched specimens, respectively. At temperatures higher than Tg an identical temperature dependence of ~/ is observed with an apparent activation energy of flow of 617 kJ mol-1, i.e. the conclusions made on the basis of the ae measurements are confirmed by the results of the viscous flow measurements. Based on the hole model of liquids [10], combined with some generally available thermodynamic properties, Wachter and Sommer [11] have derived the following expression for the volume expansion coefficient av: av=~T ~exp
[ ( -~-
1-
(1)
with n=Ua/Vh, Eh=formation enthalpy of one mole holes, v a = mean hard core volume of a t o m s and v h = hole volume. This expression is valid for
531
undercooled liquids and glasses in the thermal quasi-equilibrium state. Taking into account that av = 3ae, the temperature dependence of ctv of relaxed at 563 K specimens in the coordinates of eqn. (1) is plotted in Fig. 2. Also in this case two linear parts of the temperature dependence are observed, with crossing points corresponding to Tg (628 K). From the slopes and intercepts of these lines the values of E h and n were calculated. For T < Tg Eh=26.3 kJ mol -l, n=0.92; for T > Tg E h = 384 kJ mol- 1, n = 0.015. On the basis of these n-values the conclusion could be drawn that the hole size in the fully relaxed specimens practically coincides with the mean atomic size, which is physically meaningful and gives an explanation for the similarity of the at-temperature dependences of crystalline and fully relaxed amorphous specimens for T< Tg (see Fig. 1). The value of n for T> Tg suggests the existence of huge (vh=67va) holes in the structure of the undercooled melt. It is to some extent surprising, but corresponds very well to the experimentally observed increase of a t by an order of magnitude at temperatures higher than Tg. According to [11], the total activation energy of viscous flow Q~=RTVa/Vf+Eh, with uf the free volume per atom [12]. It follows from our results that E h (26.3 kJ mo1-1) is approximately 13% of Q, (193.5 kJ mol-1), in good agreement with the theoretically expected [11] E h/Q, ratio.
4. Conclusions Thermal expansion and viscous flow measurements could be used as sensitive methods for investigation of the structural relaxation phenomena in amorphous alloys. In the case of PdszSil8 amorphous alloy the relaxation in the low-temperature range 370-470 K is most probably connected with stress release in the amorphous regions with higher density, reflected by an increase of the apparent thermal expansion coefficient of the alloy studied by a repeated heating run. In the temperature range 470-560 K the relaxation in the alloy studied is connected with stress
release in the amorphous regions with lower density and annealing out of the excess free volume in the amorphous structure, manifested by a decrease of the apparent thermal expansion coefficient. The isothermal high-temperature relaxation at 563 K leads to a more uniform quasi-equilibrium amorphous structure with hole defects similar to the hole defects in the crystalline Pd82Si18 alloy. At temperatures higher than Tg a common structure of undercooled melt in the quasi-equilibrium state is established, manifested by a common temperature dependence of the viscosity and of the thermal expansion coefficient of the Pd82Sil8 amorphous alloy studied, independent of the thermal history of the specimens.
Acknowledgment The authors are indebted to the Alexander von Humboldt Foundation, ER.G., for donating the thermoanalytical equipment.
References 1 H.S. Chen, J. Appl. Phys., 49 ( 1978 ) 3289. 2 Th. Frechen, G. Dietz and F. Gans, J. Magn. Magn. Mater., 13 (1979) 85. 3 A. L. Mulder, J. W. Driver and S. Raclelaax, t'roc. Conf. Metallic Glasses, Budapest, Vol. 2 (1980) p. 299, 4 G. Dietz and K. Hiiller, J. Non-Cryst. Solids, 47 (1982) 377. 5 H. S. Chen and E. Coleman, Appl. Phys. Lett., 28 (1976) 245. 6 K. Russew and L. Stojanova, Mater. Sci. Eng. A, 123 (1990) 59. 7 S. Tanigawa and K. Shima, Proc. 4th Int. Conf. on Rapidly Quenched Metals, Sendai, Japan ( 1981 ) p. 501. 8 Ch. Cunat, Z. Phys. Chem. Neue Folge, 157(1988) 425. 9 E. Illekova, Ch. Cunat, E A. Kuhnast, A. Aharoune and J. M. Fiorani, J. Phys. (1990), submitted. 10 K. S. Dubey and P. Ramachandrarao, Acta Metall., 32 (1984) 91. 11 J. Wachter and E Sommer, J. Non-Cryst. Solids, 117/118 (1990) 890. 12 M. H. Cohen and D. Turnbull, J. Chem. Phys., 31 (1959) 1164.