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Resistivity changes during structural relaxation of amorphous Fe40Ni40B20
Materials Science and Engineering, 97(1988) 505 508
505
Resistivity Changes During Structural Relaxation of Amorphous Fe40Ni40B20* E. KOKMEIJER, E. HUIZER, B. J. THIJSSE and A. VAn DEN BEUKEL
Laboratory q[' Metallurgy, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft (The Netherlands)
Abstract
The isothermal change in the electrical resistivity during structural relaxation in the temperature range 50~%600 K was measured j a r amorphous Fe4oNi4oB2o. The resistiHty changes were measured both at the annealing temperature T, and at 77K. In both cases the resistiHty o f as-quenched samples decreases continuously with increasing time, but the decrease is smaller by about a factor o f 2 when measured at 77K. The size q[" the effect measured at 77 K increases with increasing T,,, whereas the reverse is true when the effect is measured at T,. Analysis o f the data shows that structural relaxation can be separated into two parts: (1) topological shortrange ordering (TSRO), the annealing-out of free volume, which can be quantitatively described in terms o f a free-volume model with a single activation energy (E l = 250 k J m o l 1); (2) a " n o n - T R S O " part, which can be separated into an irreversible contribution and a reversible contribution, which occur simultaneously and cover the same wide range o f activation energies (130250 k J mol 1). The reversible part is ascribed to chemical short-range ordering (CSRO). An increase in chemical order yields an increase in the resistivity when measured at 77 K and a decrease in the resistivity at T,. In particular, the result that C S R O is accompanied by an irreversible process is new.
I. Introduction
The annealing of metallic glasses at temperatures below the glass temperature gives rise to a change in many physical properties, whereas the structure of the material as observed by X-ray diffraction remains amorphous. This is generally attributed to atomic rearrangements within the amorphous state, and the process is called "structural relaxation". In a series of previous papers, experimental data have been presented on the change in Young's modulus [1], length [1], viscosity [2], electrical resistivity [3] and Curie temperature [4] during the structural *Paper presented at the Sixth International Conference on Rapidly Quenched Metals, Montr6al, August 3 7, 1987. 0025-5416/88/$3.50
relaxation of (mainly) Fe40NiaoB2o. The data were summarized in ref. 5. It was shown that the relaxation phenomena can be described satisfactorily when the process is divided into two components. (I) Topological short-range ordering (TSRO) is the annealing-out of free volume. The contribution of this process to the measured property changes can be separated from the measured effects because it turns out to be the final part of the relaxation process. It is an irreversible process and is characterized by a single activation energy (Er = 250 kJ mol 1). It can be described quantitatively in terms of the free-volume model [6, 7]. The equation describing the decay of free volume as a function of temperature T and time t is exp(x 1) _ exp(xo- ') = Cot exp ~
(1)
where Co is a constant and x = vf/Tv* is the reduced free volume; vf is the free volume per atomic volume; ?,v* is a constant of the order of 0.1. Values of Co and x o (the reduced free volume at t = 0) can be obtained from the analysis in ref. 1. (2) A " n o n - T S R O " part remains after the TSRO contribution has been subtracted from the measured effects. This part covers a wide range of activation energies (130-250 kJ mol 1) and can be described in terms of the activation energy spectrum model, introduced by Gibbs and coworkers [8, 9]. In this model, the activation energy of the atomic rearrangements occurring after a time t at a temperature T is given approximately by E = R T In rot, where vo is a frequency factor. Recently it was shown by one of the present authors [5] that vo depends on activation energy according to v = vo exp(ctE/R). This replaces the expression for the activation energy by E-
RT 1-TTlnV°t
(2)
with Vo=6.6 × 106s i and ~ = 9 . 7 x 10 4 K 1. A further rationalization of this expression can be found in ref. 10. The " n o n - T S R O " part of the relaxation process was ascribed to chemical short-range ordering (CSRO), because it was observed that in this range the physical properties can be varied reversibly with ,'~ Elsevier Sequoia/Printed in The Netherlands
506
temperature. This means that, when at a temperature Tj equilibrium order is attained, the specimen can be cycled between temperatures 7"1 and T2 and the physical property (corrected for the TSRO effect which continues to proceed in one direction) changes reversibly between two values corresponding to the states of equilibrium order at T2 and T2. However, in a recent detailed investigation [ 11] on reversible and irreversible length changes during structural relaxation, it was shown that the assignment of the "non-TSRO" part of the relaxation to CSRO only cannot be maintained. In particular, the "non-TSRO" length change of as-quenched specimens cannot be accounted for by a reversible CSRO effect only but must contain a substantial irreversible part. This point is also the subject of the present paper, where the problem is studied by electrical resistivity measurements. The new element is that the resistivity changes during annealing at a temperature T~ were measured at two different temperatures, Ta and 77 K. It will be shown that this gives rise to the observation of substantially different effects, in both magnitude and sign, and that this is helpful in separating the "non-TSRO" part of the relaxation into a reversible (CSRO) and irreversible component. 2. Experimental details The material used in this investigation was amorphous Fe4oNi4oB2o, supplied by Vacuumschmelze (Vitrovac 0040) in ribbon form. The specimen dimensions were 50 mm x 1 mm × 30 #m. The resistance was measured using a 30 Hz a.c. Thompson bridge. For annealing treatments at a temperature Ta, the specimen was brought quickly into a furnace which was kept at Ta with a stability of _ 0.2 K. The time required for the specimen to adjust to the furnace temperature was about 5 s. For isothermal resistance measurements at Ta, the resistance of the specimen was continuously recorded during the anneal. For measurements at 77 K, after each annealing treatment the specimen was rapidly moved from the furnace into a liquid nitrogen bath. The estimated accuracy of the resistance determined in this way is about 100 ppm. In a previous paper [3], it was shown that relative changes in resistance obtained can be identified with relative changes in resistivity, because effects due to the change in specimen dimensions can be neglected.
&
x
o
4- 4-
~ -2000
The isothermal relative change AR/Ro in the resistance of as-quenched Fe40Ni40B20 is plotted in Figs. I
°o
D o []
-4000
xx
oo
+ ++
o**
×
O~o ° °o
o
A z~
° ° o ~il m 6
o o
-6000
z~
o
+
+
i~
oo zxz~ oo
+
++
+ "/~ #tlm~
°o
+
°Oo ~
-8000
o o
%
-10.000
•
1(3
10'
lb'
16'
~5 time
10' (s}
Fig. I. Relative change in resistance of as-quenched FeaoNi4oB2o vs. time at various annealing temperatures: x, 503 K; ©, 525 K; +, 546 K; ,, 578 K; I~, 587 K; A, 600 K. The measurement temperature is 77 K. and 2 at the indicated annealing temperatures Ta. The resistance was measured at 77 K in Fig. I and at Ta in Fig. 2. In order to separate the TSRO contribution to the decrease in resistance from the measured effect, a procedure first introduced by Woldt et al. [ 12] was applied. It was assumed that the relative change in resistance due to TSRO is proportional to the change in reduced free volume:
where AR is a constant. The quantity Ax can be calculated as a function of time from eqn. (1). In Fig. 3 and
0 x
• x
o
2
" - -2000 o~
x x
4.
o
x x o
4.+
x o
ii
-4000
o
x
4-+
0
o
+4-+ Dtlt o
-6000
• x
o
+
x
••
o
++
x
o
@
% ~.
x
o
++
D•
om~
-8000
• x
o
444-
°t3~i
+4-
eo x
o +
• x
•
o ÷
t 3 ~o
-10.000
x
+ ~
I02
x
o
o ~o o1~
I0
3. Results and discussion
x x x Xxx x x Oo ° ° ° o o x x XXx Xx °° o xx + °° Xxx x
I03
o ++
x
+4- o
~,~-wi~i~,+~t +~.+o 10'
10s time
106 (s)
Fig. 2. As for Fig. 1: Q, 4?5 K; x, 500 K; ©, 525 K; + , 546 K;
• , 578 K; D, 587 K. The resistance measurement took place at the annealing temperature.
507 free-volume contribution, given by eqn. (3), from the total measured effect:
~.-4000
%
~g
%
+o~
(A~0) cor ------ARRo(A~o) fv -6000
-8000
i 001
0
o 0.02
lax]
Fig. 3. The data in Fig. 1 plotted vs. the calculated change in relative free volume Ax: +, 546 K; *, 578 K; [7, 587 K; A, 600 K. Fig. 4, the observed A R / R o (from Fig. 1 and Fig. 2 respectively) is plotted vs. the calculated Ax. In all cases, at the end, straight lines can be drawn through the data points. In both Fig. 3 and Fig. 4, this yields a parallel set of straight lines with slopes A R of 0.21 and 0.17 respectively. These results confirm the validity ofeqn. (1) for the final part of the resistance decrease. This is also in accordance with the results of a similar analysis of Young's modulus data on the same metallic glass [5]. It is concluded that the final part of the relaxation process is the annealing-out of free volume (TSRO), as described by eqn. (1). The remaining effect of structural relaxation on the resistance can now be obtained by subtracting the
In earlier work (eqn. (5)), this part was ascribed to CSRO. At first sight, this interpretation seems to be in qualitative agreement with the present results. The final value of A R / R o due to this effect is given by the intercept of the straight lines in Figs. 3 and 4 with the AR/ Ro axis. In Fig. 4 it is seen that the magnitude of the intercept increases with decreasing T a. This is in accordance with the idea of CSRO, because the increase in order at Ta should increase with increasing T f - T,, where Tf is the so-called fictive temperature, the temperature at which the equilibrium state of order is frozen in during the quench of the specimen. From Fig. 4, it is found that this effect, in the temperature range of the experiments (525-587 K), amounts to about - 35 p p m K - ]. The surprising feature of the present data is found in the results in Fig. 3. When measured at 77 K, the intercept of the straight lines with the AR/ Ro axis decreases with decreasing Ta. In this case the effect amounts to about + 12 ppm K-1. At first sight, this can be explained by assuming that the change in resistance due to a certain change in order has the opposite sign when measured at 77 K and T, respectively. This idea, however, cannot explain why the overall change in resistance is negative in both cases, being only smaller in magnitude at 77 K.
,-~
U
&
×e x x×
o~.....+ + ~ , ~
"-~-2000
~-7000
(4)
E
o~
-LO00
%
•
[] +
'~
~o
i-'o * o
"-
.,t%
ore
o
-... j~+ ~o ~.~. t"
,
R,---_2
~+~
T~--"Y'.* o + ~#,o
-BOO0
~.o ++
\O\o
x
***~'x x~\
~o ~
~ + .""4..+ * ~ "
~o "~o ,m~,,
[]
002 IAxl
Fig. 4. The data in Fig. 2 plotted vs. the calculated change in relative free volume Ax: O, 525 K; +, 546 K; *, 578 K; IS], 587 K.
i
1so
1">o
40
i
21o
x g o og,
+ +÷
o
130
0.01
o
Tm=Ta
-10000
-11000
~
o
~. " % . o
+o o,~,%~ma
4
-6000
_0000 o++
4'x3e ' ~
++ ++
o
o oo
2~0
' 25O E (kJ/mote)
Fig. 5. The data in Figs. 1 and 2 corrected for the free-volume contribution and plotted vs. the activation energy calculated from eqn. (2) at 77 K ( x , 503 K; O, 505 K, +, 546 K ; . , 578 K; I~, 587 K; A, 600 K) and at the annealing temperature (@, 475K; x, 500K; O, 525K; +, 546K;., 578K; El, 587 K).
508 In order to find a better interpretation, let us look at Fig. 5. Here the resistance change (AR/Ro)co r corrected for the T S R O contribution is plotted vs. the activation energy given by the activation energy spectrum model (eqn. (2)). Again it is seen, and indicated in the figure, that the magnitude of the effect increases with decreasing Ta when measured at Ta and decreases with decreasing Ta when measured at 77 K. This can be qualitatively understood by assuming that the effect represented in Fig. 5 is due to the superposition o f two contributions: ( 1 ) a n irreversible effect, indicated by the broken line, which yields a decrease in resistance independent o f the measuring temperature Tm, just as in the case of the free-volume effect; (2) superposed on this, a reversible effect, due to CSRO, which yields with increasing order a decrease in resistance when measured at Ta and an increase in resistance at 77 K. This means that our earlier idea (see for example ref. 5) that the part o f structural relaxation preceding T S R O is due to a reversible C S R O effect has to be modified. The present view can be summarized as follows: the final part of structural relaxation is due to the annealing-out o f free volume (TSRO) and can be quantitatively described by the free-volume model (eqn. (I)) with a single activation energy (250 kJ t o o l - l ) . The remaining part covers a b r o a d spectrum of activation energies (130-250 kJ/mol 1) (Fig. 5) and consists o f two simultaneous processes: an irreversible process and a reversible process (CSRO). This conclusion agrees with that obtained in a recent paper [ I l] from the analysis of length changes during structural relaxation. 4. Conclusions (1) The first part o f structural relaxation in Fe40Ni4oB2o consists of two simultaneous, p r o b a b l y interconnected processes: an irreversible process and a reversible process. They both cover the same wide range o f activation energies, 130-250 kJ mol 1. The reversible process is ascribed to CSRO.
(2) The sign and magnitude o f resistance changes due to C S R O strongly depend on the measuring temperature. Increasing order yields an increase in resistance when measured at 77 K and a decrease in the resistance at the annealing temperature (500-
600 K). (3) Resistance changes due to the irreversible relaxation are nearly independent o f the measuring temperature. (4) The final part of structural relaxation is the annealing-out of free volume (TSRO). The effect of this process on resistance (this work) and other physical properties (earlier work) can be quantitatively described by the formalism of the free-volume model with a single activation energy ( E r = 250 kJ mol 1).
References 1 A. van den Beukel, S. van der Zwaag and A. L. Mulder, Acta Metall., 32(1984) 1895. 2 A. van den Beukel, E. Huizer, A. L. Mulder and S. van der Zwaag, Acta Metall., 34 (1986) 483. 3 J. Melissant, E. Huizer and B. J. Thijsse, Proc. 6th Int. Conf. on Liquid and Amorphous Metals, Garmisch-Partenkirchen, 1986, in Z. Phys. Chem., 156-157(1987). 4 E. Huizer, A. L. Mulder and A. van den Beukel, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, NorthHolland, Amsterdam, 1985, p. 639. 5 A. van den Beukel, in P. W. Lee and S. Carbonara (eds.), Rapidly Quenched Materials, American Society for Metals, Metals Park, OH, 1986, p. 193. 6 F. Spaepen, Acta Metall., 25(1977) 407. 7 A. van den Beukel and S. Radelaar, Acta Metall., 31 (1983) 419. 8 M. R. J. Gibbs, J. E. Evetts and J. A. Leake, J. Mater. Sci., 18(1983) 278. 9 M. R. J. Gibbs and J. E. Evetts, in T. Masumoto and K. Suzuki (eds.), Proc. 4th Int. Conf. on Rapidly Quenched Metals, Sendai, August 1981, Japan Institute of Metals, Sendai, 1982, pp. 479, 513. 10 A. van den Beukel, J. Non-Cryst. Solids, 83(1986) 134. 11 E. Huizer and A. van den Beukel, Acta Metall., to be published. 12 E. Woldt and J. A. Leake, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, North-Holland, Amsterdam, p. 687.
505
Resistivity Changes During Structural Relaxation of Amorphous Fe40Ni40B20* E. KOKMEIJER, E. HUIZER, B. J. THIJSSE and A. VAn DEN BEUKEL
Laboratory q[' Metallurgy, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft (The Netherlands)
Abstract
The isothermal change in the electrical resistivity during structural relaxation in the temperature range 50~%600 K was measured j a r amorphous Fe4oNi4oB2o. The resistiHty changes were measured both at the annealing temperature T, and at 77K. In both cases the resistiHty o f as-quenched samples decreases continuously with increasing time, but the decrease is smaller by about a factor o f 2 when measured at 77K. The size q[" the effect measured at 77 K increases with increasing T,,, whereas the reverse is true when the effect is measured at T,. Analysis o f the data shows that structural relaxation can be separated into two parts: (1) topological shortrange ordering (TSRO), the annealing-out of free volume, which can be quantitatively described in terms o f a free-volume model with a single activation energy (E l = 250 k J m o l 1); (2) a " n o n - T R S O " part, which can be separated into an irreversible contribution and a reversible contribution, which occur simultaneously and cover the same wide range o f activation energies (130250 k J mol 1). The reversible part is ascribed to chemical short-range ordering (CSRO). An increase in chemical order yields an increase in the resistivity when measured at 77 K and a decrease in the resistivity at T,. In particular, the result that C S R O is accompanied by an irreversible process is new.
I. Introduction
The annealing of metallic glasses at temperatures below the glass temperature gives rise to a change in many physical properties, whereas the structure of the material as observed by X-ray diffraction remains amorphous. This is generally attributed to atomic rearrangements within the amorphous state, and the process is called "structural relaxation". In a series of previous papers, experimental data have been presented on the change in Young's modulus [1], length [1], viscosity [2], electrical resistivity [3] and Curie temperature [4] during the structural *Paper presented at the Sixth International Conference on Rapidly Quenched Metals, Montr6al, August 3 7, 1987. 0025-5416/88/$3.50
relaxation of (mainly) Fe40NiaoB2o. The data were summarized in ref. 5. It was shown that the relaxation phenomena can be described satisfactorily when the process is divided into two components. (I) Topological short-range ordering (TSRO) is the annealing-out of free volume. The contribution of this process to the measured property changes can be separated from the measured effects because it turns out to be the final part of the relaxation process. It is an irreversible process and is characterized by a single activation energy (Er = 250 kJ mol 1). It can be described quantitatively in terms of the free-volume model [6, 7]. The equation describing the decay of free volume as a function of temperature T and time t is exp(x 1) _ exp(xo- ') = Cot exp ~
(1)
where Co is a constant and x = vf/Tv* is the reduced free volume; vf is the free volume per atomic volume; ?,v* is a constant of the order of 0.1. Values of Co and x o (the reduced free volume at t = 0) can be obtained from the analysis in ref. 1. (2) A " n o n - T S R O " part remains after the TSRO contribution has been subtracted from the measured effects. This part covers a wide range of activation energies (130-250 kJ mol 1) and can be described in terms of the activation energy spectrum model, introduced by Gibbs and coworkers [8, 9]. In this model, the activation energy of the atomic rearrangements occurring after a time t at a temperature T is given approximately by E = R T In rot, where vo is a frequency factor. Recently it was shown by one of the present authors [5] that vo depends on activation energy according to v = vo exp(ctE/R). This replaces the expression for the activation energy by E-
RT 1-TTlnV°t
(2)
with Vo=6.6 × 106s i and ~ = 9 . 7 x 10 4 K 1. A further rationalization of this expression can be found in ref. 10. The " n o n - T S R O " part of the relaxation process was ascribed to chemical short-range ordering (CSRO), because it was observed that in this range the physical properties can be varied reversibly with ,'~ Elsevier Sequoia/Printed in The Netherlands
506
temperature. This means that, when at a temperature Tj equilibrium order is attained, the specimen can be cycled between temperatures 7"1 and T2 and the physical property (corrected for the TSRO effect which continues to proceed in one direction) changes reversibly between two values corresponding to the states of equilibrium order at T2 and T2. However, in a recent detailed investigation [ 11] on reversible and irreversible length changes during structural relaxation, it was shown that the assignment of the "non-TSRO" part of the relaxation to CSRO only cannot be maintained. In particular, the "non-TSRO" length change of as-quenched specimens cannot be accounted for by a reversible CSRO effect only but must contain a substantial irreversible part. This point is also the subject of the present paper, where the problem is studied by electrical resistivity measurements. The new element is that the resistivity changes during annealing at a temperature T~ were measured at two different temperatures, Ta and 77 K. It will be shown that this gives rise to the observation of substantially different effects, in both magnitude and sign, and that this is helpful in separating the "non-TSRO" part of the relaxation into a reversible (CSRO) and irreversible component. 2. Experimental details The material used in this investigation was amorphous Fe4oNi4oB2o, supplied by Vacuumschmelze (Vitrovac 0040) in ribbon form. The specimen dimensions were 50 mm x 1 mm × 30 #m. The resistance was measured using a 30 Hz a.c. Thompson bridge. For annealing treatments at a temperature Ta, the specimen was brought quickly into a furnace which was kept at Ta with a stability of _ 0.2 K. The time required for the specimen to adjust to the furnace temperature was about 5 s. For isothermal resistance measurements at Ta, the resistance of the specimen was continuously recorded during the anneal. For measurements at 77 K, after each annealing treatment the specimen was rapidly moved from the furnace into a liquid nitrogen bath. The estimated accuracy of the resistance determined in this way is about 100 ppm. In a previous paper [3], it was shown that relative changes in resistance obtained can be identified with relative changes in resistivity, because effects due to the change in specimen dimensions can be neglected.
&
x
o
4- 4-
~ -2000
The isothermal relative change AR/Ro in the resistance of as-quenched Fe40Ni40B20 is plotted in Figs. I
°o
D o []
-4000
xx
oo
+ ++
o**
×
O~o ° °o
o
A z~
° ° o ~il m 6
o o
-6000
z~
o
+
+
i~
oo zxz~ oo
+
++
+ "/~ #tlm~
°o
+
°Oo ~
-8000
o o
%
-10.000
•
1(3
10'
lb'
16'
~5 time
10' (s}
Fig. I. Relative change in resistance of as-quenched FeaoNi4oB2o vs. time at various annealing temperatures: x, 503 K; ©, 525 K; +, 546 K; ,, 578 K; I~, 587 K; A, 600 K. The measurement temperature is 77 K. and 2 at the indicated annealing temperatures Ta. The resistance was measured at 77 K in Fig. I and at Ta in Fig. 2. In order to separate the TSRO contribution to the decrease in resistance from the measured effect, a procedure first introduced by Woldt et al. [ 12] was applied. It was assumed that the relative change in resistance due to TSRO is proportional to the change in reduced free volume:
where AR is a constant. The quantity Ax can be calculated as a function of time from eqn. (1). In Fig. 3 and
0 x
• x
o
2
" - -2000 o~
x x
4.
o
x x o
4.+
x o
ii
-4000
o
x
4-+
0
o
+4-+ Dtlt o
-6000
• x
o
+
x
••
o
++
x
o
@
% ~.
x
o
++
D•
om~
-8000
• x
o
444-
°t3~i
+4-
eo x
o +
• x
•
o ÷
t 3 ~o
-10.000
x
+ ~
I02
x
o
o ~o o1~
I0
3. Results and discussion
x x x Xxx x x Oo ° ° ° o o x x XXx Xx °° o xx + °° Xxx x
I03
o ++
x
+4- o
~,~-wi~i~,+~t +~.+o 10'
10s time
106 (s)
Fig. 2. As for Fig. 1: Q, 4?5 K; x, 500 K; ©, 525 K; + , 546 K;
• , 578 K; D, 587 K. The resistance measurement took place at the annealing temperature.
507 free-volume contribution, given by eqn. (3), from the total measured effect:
~.-4000
%
~g
%
+o~
(A~0) cor ------ARRo(A~o) fv -6000
-8000
i 001
0
o 0.02
lax]
Fig. 3. The data in Fig. 1 plotted vs. the calculated change in relative free volume Ax: +, 546 K; *, 578 K; [7, 587 K; A, 600 K. Fig. 4, the observed A R / R o (from Fig. 1 and Fig. 2 respectively) is plotted vs. the calculated Ax. In all cases, at the end, straight lines can be drawn through the data points. In both Fig. 3 and Fig. 4, this yields a parallel set of straight lines with slopes A R of 0.21 and 0.17 respectively. These results confirm the validity ofeqn. (1) for the final part of the resistance decrease. This is also in accordance with the results of a similar analysis of Young's modulus data on the same metallic glass [5]. It is concluded that the final part of the relaxation process is the annealing-out of free volume (TSRO), as described by eqn. (1). The remaining effect of structural relaxation on the resistance can now be obtained by subtracting the
In earlier work (eqn. (5)), this part was ascribed to CSRO. At first sight, this interpretation seems to be in qualitative agreement with the present results. The final value of A R / R o due to this effect is given by the intercept of the straight lines in Figs. 3 and 4 with the AR/ Ro axis. In Fig. 4 it is seen that the magnitude of the intercept increases with decreasing T a. This is in accordance with the idea of CSRO, because the increase in order at Ta should increase with increasing T f - T,, where Tf is the so-called fictive temperature, the temperature at which the equilibrium state of order is frozen in during the quench of the specimen. From Fig. 4, it is found that this effect, in the temperature range of the experiments (525-587 K), amounts to about - 35 p p m K - ]. The surprising feature of the present data is found in the results in Fig. 3. When measured at 77 K, the intercept of the straight lines with the AR/ Ro axis decreases with decreasing Ta. In this case the effect amounts to about + 12 ppm K-1. At first sight, this can be explained by assuming that the change in resistance due to a certain change in order has the opposite sign when measured at 77 K and T, respectively. This idea, however, cannot explain why the overall change in resistance is negative in both cases, being only smaller in magnitude at 77 K.
,-~
U
&
×e x x×
o~.....+ + ~ , ~
"-~-2000
~-7000
(4)
E
o~
-LO00
%
•
[] +
'~
~o
i-'o * o
"-
.,t%
ore
o
-... j~+ ~o ~.~. t"
,
R,---_2
~+~
T~--"Y'.* o + ~#,o
-BOO0
~.o ++
\O\o
x
***~'x x~\
~o ~
~ + .""4..+ * ~ "
~o "~o ,m~,,
[]
002 IAxl
Fig. 4. The data in Fig. 2 plotted vs. the calculated change in relative free volume Ax: O, 525 K; +, 546 K; *, 578 K; IS], 587 K.
i
1so
1">o
40
i
21o
x g o og,
+ +÷
o
130
0.01
o
Tm=Ta
-10000
-11000
~
o
~. " % . o
+o o,~,%~ma
4
-6000
_0000 o++
4'x3e ' ~
++ ++
o
o oo
2~0
' 25O E (kJ/mote)
Fig. 5. The data in Figs. 1 and 2 corrected for the free-volume contribution and plotted vs. the activation energy calculated from eqn. (2) at 77 K ( x , 503 K; O, 505 K, +, 546 K ; . , 578 K; I~, 587 K; A, 600 K) and at the annealing temperature (@, 475K; x, 500K; O, 525K; +, 546K;., 578K; El, 587 K).
508 In order to find a better interpretation, let us look at Fig. 5. Here the resistance change (AR/Ro)co r corrected for the T S R O contribution is plotted vs. the activation energy given by the activation energy spectrum model (eqn. (2)). Again it is seen, and indicated in the figure, that the magnitude of the effect increases with decreasing Ta when measured at Ta and decreases with decreasing Ta when measured at 77 K. This can be qualitatively understood by assuming that the effect represented in Fig. 5 is due to the superposition o f two contributions: ( 1 ) a n irreversible effect, indicated by the broken line, which yields a decrease in resistance independent o f the measuring temperature Tm, just as in the case of the free-volume effect; (2) superposed on this, a reversible effect, due to CSRO, which yields with increasing order a decrease in resistance when measured at Ta and an increase in resistance at 77 K. This means that our earlier idea (see for example ref. 5) that the part o f structural relaxation preceding T S R O is due to a reversible C S R O effect has to be modified. The present view can be summarized as follows: the final part of structural relaxation is due to the annealing-out o f free volume (TSRO) and can be quantitatively described by the free-volume model (eqn. (I)) with a single activation energy (250 kJ t o o l - l ) . The remaining part covers a b r o a d spectrum of activation energies (130-250 kJ/mol 1) (Fig. 5) and consists o f two simultaneous processes: an irreversible process and a reversible process (CSRO). This conclusion agrees with that obtained in a recent paper [ I l] from the analysis of length changes during structural relaxation. 4. Conclusions (1) The first part o f structural relaxation in Fe40Ni4oB2o consists of two simultaneous, p r o b a b l y interconnected processes: an irreversible process and a reversible process. They both cover the same wide range o f activation energies, 130-250 kJ mol 1. The reversible process is ascribed to CSRO.
(2) The sign and magnitude o f resistance changes due to C S R O strongly depend on the measuring temperature. Increasing order yields an increase in resistance when measured at 77 K and a decrease in the resistance at the annealing temperature (500-
600 K). (3) Resistance changes due to the irreversible relaxation are nearly independent o f the measuring temperature. (4) The final part of structural relaxation is the annealing-out of free volume (TSRO). The effect of this process on resistance (this work) and other physical properties (earlier work) can be quantitatively described by the formalism of the free-volume model with a single activation energy ( E r = 250 kJ mol 1).
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