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CHANGE OF YOUNG’S MODULUS DURING STRUCTURAL RELAXATION IN AMORPHOUS
FeB, FeNiB, FeNiP AND FeNiPB
E. Huizer, A. van den Beukel
To cite this version:
E. Huizer, A. van den Beukel. CHANGE OF YOUNG’S MODULUS DURING STRUCTURAL
RELAXATION IN AMORPHOUS FeB, FeNiB, FeNiP AND FeNiPB. Journal de Physique Colloques,
1985, 46 (C8), pp.C8-561-C8-565. �10.1051/jphyscol:1985889�. �jpa-00225242�
JOURNAL DE PHYSIQUE
Colloque C8, supplément au n°12, Tome 46, décembre 1985 page C8-561
CHANGE OF YOUNG'S MODULUS DURING STRUCTURAL RELAXATION IN AMORPHOUS FeB, FeNiB, FeNiP AND FeNiPB
E. Huizer and A. van den Beukel
Laboratory of Metallurgy, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands
Résumé - Nous présentons des mesures de variation du module d'Young au cours de la relaxation structurale d'alliages amorphes FeB, FeNiB, FeNiP et FeNiPB.
Le comportement du module d'Young est qualitativement identique dans les quatre alliages. Les résultats sont discutés sur la base d'une compétition entre deux processus de relaxation : une mise en ordre chimique à courte distance (CSRO) décrite par le modèle AES /2/ et une mise en ordre topologique à courte dis- tance (TSRO) décrite par un modèle du volume libre /3, 4/.
Abstract - Changes in Young's modulus were measured during structural relaxation of FeB, FeNiB, FeNiP and FeNiPB amorphous alloys. The behaviour of the Young's modulus in the four alloys is found to be qualitatively the same. The results are discussed in terms of relaxation consisting of two processes: Compositional Short Range Ordering, described by AES-model /2/ and Topological Short Range Ordering, described by the extended free volume model /3,4/.
I - INTRODUCTION
Annealing of metallic glasses below the glass temperature Tg causes changes in a number of physical properties /1/. This so-called structural relaxation is generally devided into two processes:
- Chemical Short Range Ordering (CSRO), describing reversible changes in the local surroundings of a given atom, and
- Topological Short Range Ordering (TSRO), describing the irreversible decrease of the free volume.
As metallic glasses are produced by rapid quenching from the melt the as-quenched glass will contain a large amount of free volume and the degree of short range order that is frozen in will be low. Structural relaxation during isothermal annealing of an as-quenched glass will normally result in a decrease of the amount of free volume (TSRO) and an increase of the degree of short range order (CSRO). There is a large amount of experimental evidence /l/ that at suitable annealing temperatures the chemical order parameter increases to new temperature dependent equilibrium values and that subsequent annealing at higher temperatures causes a decrease in the state of local order. CSRO is therefore a reversible process. It contains a spectrum of activation energies, which is qualitatively in agreement with the Activation Energy Spectrum model (AES) of Gibbs et al. /2/.
Due to the very nature of its kinetic TSRO cannot reach equilibrium under most experimental conditions before crystallization occurs. Therefore TSRO will be regarded as a non-reversible process. In the free volume model /3,4/, expressions are given for the decay of free volume during structural relaxation. In a previous paper /5/ measurements were presented of the change of length and Young's modulus during structural relaxation of Fe40Ni40B20 which allowed a quantitative test of the model and a separation of the contributions of CSRO and TSRO to the property changes observed. The parameters governing the kinetics of free volume decay were derived Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985889
JOURNAL DE PHYSIQUE
Fig. 1 - Isothermal changes in v2 for as-quenched specimens at 503 K.
* FeNiPB o FeNiB a FeNiP
0 FeB
Fig. 2
-
Isothermal changes in v 2 at 578 K after preannealing during l o 5 s at 503 K.from the experimental results.
The aim of the present paper is to investigate the influence of composition and different annealing treatments on CSRO and the so-called cross-over effect.
A pulse-echo technique /6/ was used to measure the longitudinal velocity of sound v, as Young's modulus E is given by E = pv2, where p is the density. In this paper changes in E are presented as changes in v2 as the corresponding change in p was found to be negligible. All measurements were performed at 300 K.
The alloys used were supplied in ribbon form:
-
the Fe40Ni40B20 alloy (Vitrovac 0040) by Vacuumschmelze- the Fe80B20 (Metglas 2605) and Fe40Ni40P14B6 (Metglas 2826) by Allied Chemical - the Fe40Ni40P20 by our own laboratory.
111 - RESULTS AND DISCUSSION
Changes resulting from isothermal annealing of as-quenched specimens of different compositions at 503 K are shown in fig. 1 . The change in v2 is presented on a relative scale (v2/vo2), where vo is the measured velocity at t = 0. For all materials v2 increases upon structural relaxation. According to the AES model /2/
CSRO consists of a spectrum of activation energies ranging from Qmin to Qmax.
Annealing during a time t p at a temperature T, results in ordering of the part of the spectrum with activation energies I Qp, with
Q = R.T .ln(v
P P oatp) (Qp s Qmax) (1)
and vo a frequency factor. The corresponding change in v2 is given by:
nv2 = ~(Q).R.T. ln(vo.t) (2)
Where p(Q) is related to the number of processes available for relaxation in the energy range Q to Q + dQ. If p ( Q ) is constant (box distribution), (2)
predicts a linear dependence of v2 versus ln(t) which is observed indeed (figure I) for all four alloys. The slope, which is proportional to p(0) increases from FeB to FeNiPB.
Subsequent annealing at a higher temperature Ta (Ta > T ) results in:
- a decrease In the degree of order, and therefore a decrease of v2, for the part P of the spectrum ,< Qp, which was already ordered at T
-
ordering of that part of the spectrum with activation energies Q, where P Qp < Q I Qa withQ = R . T .ln(v . t )
o a (Qa Qmax ) (3)
This results in an increase of v 2
.
When QT < Qmax this results in a minimum in the plot of Young's modulus versus annealing time. If Qp = Qmax a minimum is still observed as TSRO also gives rise to an increase of v2.
Figure 2 shows the minima for all four alloys after a preanneal for 105 s at 503 K and subsequent annealing at 578 K. Using (I) + (3) and taking vo = l0I9 Hz /2/ the time of the minimum has been calculated; it is indicated in figure 2 with an arrow.
It can be seen that the measured time for the minima agrees well with the time calculated according to the AES model. After about 104 s the curves of the different materials seem to converge, indicating that the same kind of process is taking place in all four alloys, which in our interpretation is TSRO and can be described by the free volume model. The TSRO contribution, calculated with the parameters for FeNiB obtained in ref. 151, is shown in figure 2 as a dotted curve and describes the rising part of all four curves beyond the minimum quite well.
The depth of the minimum is smallest for FeB and largest for FeNiPB. This is in agreement with the minimum being ascribed to CSRO, as it is to be expected that in a four component alloy there are more processes available for relaxation, resulting
JOURNAL DE PHYSIQUE
Fig. 3
-
Isothermal changes in v2 at 578 K after preannealing at 503 K for the indicated times. FeNiA.Fig. 4
-
Isothermal changes in v2 at 623 K after preannealing at 578 K for the indicated times. FeNiB.in a larger factor p(Q), than in a two component alloy.
In figure 3 a series of measurements on FeNiB is presented, preannealed at 503 K for the indicated times and annealed at Ta = 578 K. According to Van den Beukel et al.
151 Qmax = 250 kJ/mole for FeNiB. Substituting this in (I), it is found that complete CSRO at 503 K will be established after 107 s. The minima in figure 3 can therefore be ascribed to CSRO and, according to the AES-model, longer preannealing times should thus lead to an increase in:
- the time at which the minimum occurs (tmin). The calculated tmin according to the AES-model are indicated with arrows in the figure
- the depth of the minimum (v2(ta = 0) - v2(ta = tmin) + €fv, where cfv is a correction for the change in Young's modulus due to the annealing out of free volume up to t = tmin).
The measurements in figure 3 show both these effects and thus support the fact that the minima are governed by CSRO.
At a preannealing temperature of 578 K, according to ( I ) , the equilibrium CSRO will have been established after about 1000 s. Figure 4 shows a series of measurements for specimens (FeNiB) preannealed at 578 K for times longer than 1000 s and
subsequently annealed at 623 K. In this case the minima are governed by CSRO as well as TSRO. The dotted lines represent the calculated change in v2 caused by the annealing out of free volume according to /5/. The fits clearly indicate that the increase of v2 beyond the minimum can be well described by the free volume model.
Only datapoints above 7000 s are somewhat too high. This is probably due to crystallisation which is re orted by Luborsky /7/ to start at about that time.
The depth of the minimum (v4(ta = 0) - v2(ta = tmin) + rfv) can easily be found from the difference between the datapoint and the dotted line at ta = 0 , and it is found to be constant rather than increasing. The times at which the minima should occur according to the AES-model (vo = 1019 Hz) are indicated with arrows. They do not, correspond well with the measured times at the minima. These two facts support the prediction (equation (I)) that equilibrium CSRO was attained during preannealing.
IV - CONCLUSIONS
The behaviour of the Young's modulus upon preannealing and or annealing in FeB, FeNiB, FeNiP and FeNiPB is qualitatively the same in the CSRO part as well as in the TSRO part of structural relaxation. The quantitative effect of Compositional Short Range Ordering on the Young's modulus is dependent on the composition
,
increasing with increasing number of components.Structural relaxation can be accurately described by the extended free volume model /4/ together with the AES-model. The AES-model aloneis apparently not sufficient.
REFERENCES --
/I/ Egami, T., Ann. N.Y. Acad. Sc. 371 (1981) 238.
/2/ Gibbs, M.R. J., Evetts, J.E. a n d x a k e , J.A., J. Mat. Sc. - 18 (1983) 278.
131 Spaepen, F., Acta Metall.
25
(1977) 407./4/ Van den Beukel, A. and Radelaar, S., Acta Metall.
31
(1983) 419./5/ Van den Beukel, A., Mulder, A.L. and Van der Zwaag, S., Acta Metall.
2
( 1 984) 1895./6/ Mulder, A.L., Van der Zwaag, S., Snijders, J., Internal Report, Delft University of Technology (1984).
/7/ Luborsky, F.E., Mater. Sci. Eng.
