The effect of tensile stress on the crystallization kinetics of metglas® 2826 Fe40Ni40P14B6

Materials Science and Engineering, 55 (1982) 1 - 7

1

The Effect of Tensile Stress on the Crystallization

Kinetics of Metglas ® 2826

Fe4oNi4oP14B6 R. S. TIWARI*, J. C. CLAUS and M. VON HEIMENDAHL

Institut fiir Werkstoffwissenschaften I, Universita't Erlangen-Niirnberg, Martenstrasse 5, 8520 Erlangen (F.R.G.) (Received August 24, 1981)

SUMMARY

Transmission electron microscopy was used to investigate the influence o f tensile stress on the crystallization kinetics o f Metglas ® 2826. The nucleation rate o f the eutectic crystals was f o u n d to increase markedly with increasing stress, whereas no influence was detected on growth rate. These results were explained in terms o f non-linear viscous f l o w and the difference between the diffusion mechanisms responsible for the processes o f nucleation and growth. The decrease in strain rate during isothermal creep was f o u n d to occur as a result o f the combined effect o f relaxation and volume fraction o f crystallization.

1. INTRODUCTION

Although the thermal stability of metallic glasses has been the subject of numerous investigations [1, 2], relatively little is k n o w n a b o u t the dependence of stress on the crystallization [ 3 - 5 ]. It has been reported that for Pds0Si20 a tensile stress accelerates the crystallization while a compressive stress retards it [3, 4]. Recently, using different ranges of tensile stress, t w o groups of workers have reported different results for Metglas ® 2826 [5 - 7]. Patterson and Jones [5, 6 ] , who have taken tensile stresses in the range 120 - 220 N mm -2, reported a decrease in activation energy for crystallization with increasing stress. In contrast, Anderson and Lord [ 7 ] , who applied a stress of only 10 N mm -2 for their creep experiment, did n o t find any influence of stress on crystallization. In the above*On leave from Department of Physics, University College, Kurukshetra University, Haryana, India. 0025-5416/82/0000-0000/$02.75

mentioned studies, crystallization has generally n o t been monitored by the same experimental technique in stressed and unstressed (reference) samples. The crystallization kinetics of metallic glasses have been generally analysed in terms of the nucleation and growth of crystals [ 1, 2, 8 - 10]. However, the influence of stress on these processes has not been studied so far. The aim of this paper is to report the observation of the nucleation and growth of crystals in stressed and reference samples of Metglas ® 2826 using quantitative electron microscopy. It has been reported previously that, for this alloy, crystallization proceeds by homogeneous nucleation and linear growth of eutectic crystals [2, 10]. Although the linear growth of the crystals is believed to be controlled by short-range diffusion, the nucleation process has been shown to be controlled b y volume diffusion [ 11]. Thus, it would be interesting to study the effect of tensile stress on the different diffusional processes. Furthermore, in refs. 6 and 7 the decrease in strain rate d with time has been attributed to relaxation of the amorphous material and the volume fraction of crystallization respectively. In the present study, the verification of these explanations was also considered.

2. EXPERIMENTAL DETAILS

The apparatus used in the present study for annealing amorphous alloy ribbons while they are under a tensile stress is shown schematically in Fig. 1. A tensile stress was applied to Metglas ® 2826 ribbon samples 40 mm long via two specially designed grips in a balance-like device. Elongation of the sample was measured by t w o linear variabledifferential transducers by recording the © Elsevier Sequoia/Printed in The Netherlands

7

quantitative metallography has been reported previously in refs. 9 and 10. For optical microscopy, samples were m o u n t e d transversely in cold-curing polymer (Technovit ® 4000). After the samples had been polished, they were etched in a solution of 85% methanol and 15% nitric acid for 1 - 5 min.

3 ~

5

3. RESULTS AND DISCUSSION Fig. 1. Schematic diagram of the creep apparatus: 1, salt bath; 2, sample grips; 3, inductive strain recorders; 4, force-measuring cell; 5, sample; 6, dashpot; 7, weight.

distance between the two grips. The strain and strain rate are corrected for changes in cross section o f the sample using a c o m p u t e r program. The load was checked by a forcemeasuring cell and controlled with an accuracy of + 3%. All the annealing was done in a salt bath with a temperature accurate to + 1 K. Annealing of the alloy under stresses of 50, 100 and 200 N m m -2 was carried o u t at 618, 628, 638 and 648 K for various times. It was n o t possible to use loads higher than 200 N m m -2 because the sample failed as a result of elongation before a sufficient volume fraction o f crystallization had occurred in this temperature range. The m e t h o d of sample preparation for transmission electron microscopy (TEM) and

3.1. Strain measurement Figure 2 shows a typical strain curve for a tensile stress of 100 N mm -2 at 638 K. After various time intervals, samples were taken out and examined to determine the microstructures of the stressed and reference sample. Typical micrographs of a sample after it had been annealed for 50, 80 and 100 min are also shown in Fig. 2. The strain rates ~ obtained from Fig. 2 are shown in Fig. 3, together with the strain rates corresponding to the two stresses, 50 and 200 N m m -2. It was found that there was always an initial rapid change in ~ which was followed by a steady state or linearly decreasing strain rate depending on the values of stress and temperature. As shown in Fig. 3, the ~ value corresponding to a stress of 200 N m m -2 attains a steady state whereas the ~ value corresponding to stresses of 100 and 50 N mm -2 decreases linearly with time.

0.O8

0.06

.c lOOmin

o.oh 80 t r ~

0.02

50min

0'1

i

I

J

I

100 time (minJ Fig. 2. Strain v s . time for Metglas ® 2826 under a stress of 100 N m m -2 at 648 K. Transmission electron micrographs of the sample crept for 50, 80 and 100 min are also shown. 0

20

40

60

80

10-~

~0 -

1 + 2.5x(t) ~ 0 0 N mm"2

.~10"5 ~ _ ~ O O N ram-2I

mm-21

ON 10-6

o

2o

60 /o time (m/n)

80

100

Fig. 3. Strain rate vs. time for Metglas® 2826 under stresses of 50, 100 and 200 N mm-2 at 638 K. It should be mentioned here that Patterson and Jones [ 5, 6 ] , w h o used relatively higher loads (between 120 and 1410 N mm-2), reported a steady state strain rate whereas Anderson and Lord [ 7], w h o applied a load of only 10 N mm -2, reported a linear decrease in strain rate. In fact, Anderson and Lord reported a linear increase in viscosity 77 which is related to the strain rate by 1 o ~?- 3 6

(1)

The observation of g shown in Fig. 3 is consistent with these results, i.e. low stresses only lead to a decrease in strain rate. As in the work reported in ref. 7 where a sudden increase in viscosity was attributed to the end of the incubation time, in Fig. 3 a deviation from linearity at the end of the curve should be noted. The microstructure shown in Fig. 2 clearly indicates that the end of the incubation time (which for Fig. 2 is nearly 40 min) cannot be detected in the creep curve, since the volume fraction of crystals is still very small. According to Figs. 2 and 3, a sudden decrease in ~ occurs only after crystallization has progressed somewhat (in Fig. 3 at the very end of the curves). This decrease can be explained in terms of the relation given by Einstein [12] for the flow of a medium containing a volume fraction x ( t ) of hard particles:

where e0 is the steady state strain rate. For a very small volume fraction of crystals the change in ~ would be negligibly small. Thus the decrease in ~ before the incubation time is only due to relaxation of the material whereas, after this time, both the relaxation and the volume fraction of crystallization cause the decrease in ~. It should be pointed o u t that, in the work reported in ref. 6, the decrease in ~ for the whole duration of the isothermal creep has been explained only in terms of eqn. (2). It appears from the present investigation that, when the decrease in ~ is interpreted (especially around the incubation time), both the relaxation and the volume fraction of crystallization should be considered. For amorphous alloys it has been indicated [13, 14] that the following relationship exists between the steady state strain rate e0 and the stress: do ~ o n

TABLE 1

n

648 1.86 + 0,2

638 1.79 -+ 0.2

(3)

where n is a dimensionless exponent. For newtonian viscous flow, by definition the value of n is taken to be unity whereas n values higher than unity indicate p o w e r law creep [ 1 4 ] . In the present observations, steady state creep was observed only for 200 N mm -2 (see Fig. 3). Therefore, n was calculated for lower stresses from ~ at the onset of crystallization at various temperatures. The value of n obtained from ln(~1/~2) = n ln(ol/o2) is given in Table 1. The onset of crystallization was taken as the time when the first crystal was visible during TEM. The average n value of 1.9 + 0.2 is in good agreement with the value of n reported previously [6]. However, it should be mentioned that, in ref. 6, ~ has been normalized to certain preannealing times. The Arrhenius plot of the strain rate at the onset of crystallization for t w o loads is shown

Stress e x p o n e n t s for Metglas ® 2826

Temperature (K)

(2)

628 2.11 + 0.2

618 1.8 -+ 0.2

-7

-9 -10

.,.~ -11 x

" •

(a)

-12

(b)

Fig. 5. Transmission electron micrographs of (a) the reference and (b) the crept sample after creep testing

for 20 m i n at 6 4 8 K under a stress o f 2 0 0 N mm-z

-13

-14

.~,

!

(23

\ -151.50

~ ~55

1.60 I/7 (x 1~3 K-I)

1.65

Fig. 4. Arrhenius p l o t s o f ~ (at the end o f the incubation t i m e ) as a f u n c t i o n o f reciprocal t e m p e r a t u r e under stresses o f 1 0 0 N m m - 2 (X, ) and 2 0 0 N m m - 2 ( I , - - - --). T h e s e p l o t s were used t o o b t a i n an E,, value o f 620 -+ 3 0 kJ mo1-1. q

in Fig. 4. Near the end of the incubation time (where most of the relaxation has taken place and pronounced crystallization has y e t to start), d m a y be approximated by the equilibrium strain rate [15]. The activation energy E~ for creep (or viscous flow) obtained from Fig. 4 is 620 + 50 kJ mo1-1 which is in good agreement with the value reported in ref. 15. One remarkable feature shown in Fig. 4 is that there is a parallel shift in d at stresses o f 100 and 200 N m m -a, i.e. the activation energy for flow remains unchanged. The relevance of this will be discussed later. 3.2. N u c l e a t i o n a n d g r o w t h m e a s u r e m e n t s Figure 5 is a micrograph of a sample annealed at 648 K under a stress of 200 N m m -2 for 20 min and the corresponding reference sample. It is evident from Fig. 5 t h a t the number of crystals in the stressed sample is much higher than in the reference sample. From such pictures (both transmission electron and optical micrographs) the n u m b e r of nuclei and the average size of the crystals were determined. Figure 6 shows plots of the

(22

x

01

:b

~o

4'o

~

150

time (min)

Fig. 6. Number of crystals vs. time for Metglas® 2826 under stresses of 50 N mm-2 (v), 100 N mm-2 (×) and 200 N mm-2 (u) and for the reference sample (e) at 638 K.

n u m b e r Nv of crystals per unit volume against time for different loads at 638 K. As can be seen in Fig. 6, no significant difference between the number of nuclei for the reference sample and that for the 50 N mm -2 sample was found. As we have pointed out previously [ 10], the nucleation rate/;/v after the elapse of incubation and transient times attains a constant value and can be described for the narrow temperature range under investigation by the following relation: /(/v = constant X exp

~-~

(4)

where En is the apparent activation energy for nucleation. The Arrhenius plots for nucleation

rates at different stresses are given in Fig. 7. The activation energy E~ obtained from these plots was f o u n d to be 800 + 80 kJ mo1-1 and is approximately equal to our previously reported value of En [ 1 0 ] . It is interesting to note in Fig. 7 that the activation energy E , does n o t change within the limits of experimental error as the load is increased. It can be seen from Fig. 6 that there is no detectable change in nucleation rate for stresses lower than 100 N mm -2. In spite of the experimental limitations in detecting the effect of small stresses (much less than 100 N mm -2) on nucleation, it may still be argued that a low stress has no effect on the nucleation rate. Because nucleation is strongly viscosity dependent according to classical nucleation theory [16], no change in the nucleation rate under a low stress means that the viscosity 7? remains unchanged for these stresses o. In contrast, high stresses result in a viscosity change. This means a transition from newtonian to non-newtonian behaviour, because o is no longer proportional to ~ (see eqns. (1) and {3)). In fact, Takamori et al. [15] have found newtonian flow for this alloy at stresses 1 0

-3 -4 -5

. ~ -7 -8 -9

-10 -11

Fig. 7. A r r h e n i u s p l o t s o f the nucleation rate/V as a function of reciprocal temperature under s t r e s s e s o f 1 0 0 N m r n - 2 (X, - - ) a n d 2 0 0 N m m - 2 (1, - - - - - ) a n d f o r the reference sample ( e , - - - -). T h e s e plots were used to obtain an E n v a l u e o f 8 0 0 + 8 0 k J t o o l -1.

of much less than 100 N mm -2, whereas Gibeling and Nix [14] and Patterson and Jones [6] have found a non-newtonian flow at higher stresses. The activation energy En for nucleation reported here is higher than the activation energy EV for flow, 620 kJ mo1-1 (see above), and much higher than the previously reported values of activation energy Ec for crystallization and activation energy Eg for growth, 440 kJ mo1-1 and 345 kJ mo1-1 respectively [ 1 0 ] . A similar difference between the activation energy Ec for crystallization and that for the onset of crystallization has been reported by Scott and Ramchandrarao for F e - P - C amorphous alloy [ 1 7 ] . (The activation energy Eonset for the onset of crystallization is used by some researchers [17, 18]. Eonse t is n o t the same as En because as a result of experimental limitations a certain a m o u n t of crystal growth, governed by Eg, is necessary for detection. The more sensitive the experimental technique to detect onset is, the closer will Eonse t be to E~.) Scott and Ramchandrarao postulate that " t h e nucleation of the crystal in the amorphous matrix requires a viscous flow whereas the growth is governed only by the lower thermal activation Eg". The higher activation energy for both nucleation and flow of the material found in the present investigation conforms with this idea. Also, as En includes the activation energy for the transp o r t of the atoms at the nucleation site as well as the energy AG* to form a critical nucleus, E~ is expected to be higher than E~. As described in ref. 10, the growth rate of the crystals was determined by measuring the diameter of the largest crystal. Figure 8 shows that, within the limits of accuracy, the slopes of the lines for the reference and the stressed samples are the same. The points corresponding to the 200 and 100 N mm -2 sample are generally a little above those for the reference sample because of the earlier start of nucleation. Similar results have also been found at other temperatures, i.e. the growth rate remains unchanged under a tensile stress and therefore Eg also remains unchanged. It should be mentioned that some minor morphological change was found at higher stresses. The details of this effect are at present under investigation. In this study, no effect of stress on the activation energy En for nucleation and the

found that both nucleation and growth are accelerated by the application of a tensile stress. Details of this investigation will be presented elsewhere [21].

25 30

×

4. CONCLUSION

i

0

,

20

40 time

60 (rain)

80

100

120

Fig. 8. Maximum diameter of the crystals vs. time for Metgl~ ~ 2826 under stresses of 50 N m m -2 (v), 100 N m m -2 (X) and 200 N m m -2 (") and for the reference sample (o) at 638 K.

activation energy Eg for growth was found. This indicates that the activation energy E c for crystallization should also not change (see the equations for E c given in refs. 9, 10 and 19). However, this result is contrary to the observations given in ref. 5 where a decrease in Ec with increasing stress (nearly 20%) has been reported. It should be pointed out that different experimental techniques for the reference and the stressed samples were used in the work described in ref. 5. These results can be explained in terms of Spaepen's [20] proposed mechanism of steady state flow of metallic glasses. According to his empirical deformation map, steady state homogeneous flow occurs above a certain stress level at which the creation of free volume overcomes the annihilation of free volume. In a recent paper [11] it was stated that, for Metglas ® 2826, nucleation starts by the formation of an (FeNi)3PB phase and hence requires volume diffusion (the amorphous matrix has 5% less metalloid than the (FeNi)aPB crystal first formed). Thus the volume diffusion (longrange diffusion) which is responsible for nucleation increases because of the increase in viscous flow. However, as the linear growth of the eutectic crystal is controlled by the movement of the atoms only across the crystal-matrix interface (short-range diffusion) it is not expected to be markedly affected by the smaller change in viscous flow. It should be added here that crystals of the metastable phase which is formed in Metglas ® 2826A and which grow by volume diffusion have been similarly studied [19]. It was

It has been found that the nucleation rate of eutectic crystallization in Metglas ® 2826 increased considerably with increasing load. However, the activation energy E n of 800 + 80 kJ mo1-1 for this process did not change. The activation energy E~ of 620 + 50 kJ mo1-1 for the flow and the activation energy E , of nucleation are much higher than that for crystallization. This indicates that viscous flow contributes significantly to the nucleation process. No influence was observed for the growth rate and this shows that shortrange diffusion remains unchanged under tensile stress. A decrease in the strain rate during isothermal creep is a result of both relaxation and the volume fraction of crystallization. Thus, when this decrease in ~ is interpreted, both relaxation and the volume fraction should be taken into account.

ACKNOWLEDGMENTS

The authors are very grateful to Professor B. Ilschner for useful discussions and for reading the manuscript. One of us (R. S. T.) is thankful to the Alexander yon Humboldt-Stiftung for financial assistance during the tenure of this work. Sincere thanks are extended to the Deutsche Forschungsgemeinschaft for financial support

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14 J. C. Gibeling and W. D. Nix, Scr. Metall., 12 (1978) 919. 15 T. Takamori, T. Mizoguchi and T. R. McGuire, Mater. Res. Bull., 15 (1980) 81. 16 D. R. Uhlmann, Mater. Sci. Res., 4 (1969) 17. 17 M. G. Scott and P. Ramchandrarao, Mater. Sci. Eng., 29 (1977) 137. 18 A. Kur§umovi6, E. Girt, E. Babid, B. Leontid and N. Njuhovi6, J. Non-Cryst. Solids, 44 (1981) 57. 19 M. von Heimendahl, R. S. Tiwari and J. C. Claus, in T. Masumoto and K. Suzuki (eds.), Proc. 4th Conf. on Rapidly Quenched Metals, Sendai, August 1981, Vol. 1, Japanese Institute of Metals, Sendai, 1982, p. 709. 20 F. Spaepen, Acta Metall., 25 (1977) 407. 21 J. C. Claus, Ph.D. Thesis, Erlangen, 1981 - 1982.