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Structural relaxation and crossover effect in a metallic glass
Journal of Non-Crystalline Solids 33 (1979) 291-297 © North-Holland Publishing Company
STRUCTURAL RELAXATION AND CROSSOVER EFFECT IN A METALLIC GLASS A.L. GREER and J.A. LEAKE Dept. o f Metallurgy and Materials Science, University o f Cambridge, Pembroke Street, Cambridge, CB2 3QZ, UK
Received 22 November 1978
1. Introduction On annealing metallic glasses, changes occur in the glassy state before the onset of crystallization. These changes, collectively known as relaxation, affect many properties, but one of the most convenient to measure and most sensitive to relaxation is the Curie temperature, T c. In this letter the variation of T c on annealing a metallic glass is compared with the variation of refractive index of oxide glasses, in particular, a "crossover" experiment has been performed and the results have been analysed in terms of a two-relaxation-time model.
2. The effect of annealing on the Curie temperature of metallic glasses Metallic glasses containing a high (typically around 80%) atom fraction of magnetic species are ferromagnetic and exhibit a sharp Curie transition [1]. On annealing the Curie temperature rises significantly, even at times and temperatures substantially below those necessary to cause crystallization [2], [3] and [4]. Fig. 1 shows this effect for the alloy FeaoB2o (Allied Chemical Corporation: Metglas 2605). In this case the Curie temperatures have been determined by differential scanning calorimetry as described in a previous paper [4]. At any annealing temperature Tc rises rapidly at first and then levels off at an equilibrium value. As may be seen from fig. 1, the lower the annealing temperature, the slower is the approach to equilibrium, but the higher the final equilibrium value of T c. Egami [5] and Greer and Leake [4] have shown that it is possible to move reversibly between equilibrium states attained on annealing at different temperatures.
291
292
A.L. Greer, J.A. Leake / Structural relaxation and crossover effect 368
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,' 0
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Fig. 1. The effect of isothermal annealing on the Curie temperature of amorphous FesoB2o. The dashed lines are extrapolations of equih~rium values to longer times: crystallization of the alloy prevented measurement of the Curie temperature at these longer times.
25o.o'c 1.462
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B203 gloss
1.454 0
10 Annealing
20 ,Time
30
40
50
{ hr )
Fig. 2. The effect of isothermal annealing on the refractive index of B203 glass previously stabilized at 310.5°C (after Boesch et al. [6]).
A.L. Greer, J.A. Leake / Structural relaxation and crossover effect
293
3. The effect of annealing on the refractive index of oxide glasses Annealing of oxide glasses causes the refractive index, RI, to change, and particularly excellent data exist for B203 glass. Boesch et al. [6] annealed specimens of B203 glass, previously stabilized (i.e., brought to equilibrium) at 310.5°C, at selected lower temperatures. The approach curves of RI to the equilibrium values at the annealing temperatures are shown in fig. 2. The variation shown is very similar to that of Curie temperature shown in fig. 1. Thus the as-quenched metallic glass behaves as though stabilized at a temperature considerably higher than any annealing temperature yet used.
4. The crossover experiment Boesch et al. [6] stabilized a specimen of B203 glass at 310.5°C, then held it at 225°C until its RI reached the equilibrium value for 259.7°C. The specimen was then annealed at 259.7°C and the subsequent change in RI is shown in fig. 3. We have performed a similar experiment on the metallic glass FeaoB2o. A specimen was annealed at 300°C until the Curie temperature reached the equilibrium value for 400°C. The variation of T c on subsequent annealing at 400°C is shown in fig. 4. Again the results for metallic and oxide glasses are of the same form. The crossover
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Fig. 3. The change of refractive index on annealing at 259.7°C a sample of B203 glass previously stabilized at 310.5°C and annealed at 225.5°C until its RI reached the equilibrium value for 259.7°C. The solid line is computed on the two-relaxation-time model, taking times of 118 rain and 768 min (after Boesch et al. [6]).
294
A.L. Greet, J.A. Leake / Structural relaxation and crossover effect
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Fig, 4. The change of Curie temperature on annealing at 400°C a sample of amorphous FeaoB2o previously annealed at 300°C until its Tc reached the equilibrium value for 400°C. The solid line is computed on the two-relaxation-time model, taking times of 3 s and 90 s. The contributions of the two mechanisms are shown by dotted lines.
experiments show that neither RI nor Tc is uniquely related to the structural state of the relevant glass. In describing the variation of RI of oxide glasses on annealing (fig. 2) account has to be taken of the possibilities of a distribution of relaxation times and also of non-linear effects in which the relaxation times change with distance from equilibrium. Boesch et al. [6] use a simple model to explain the results of the crossover experiment: this assumes two relaxation mechanisms of equal strength, each having a single relaxation time and both leading to the same values of equilibrium RI. The effect of annealing is as shown in fig. 5: the actual (measured) RI follows the average of the values given by the two mechanisms and rises from the stabilized value at temperature To to the equilibrium value for the annealing temperature TI. If, however, the annealing is stopped when the RI has reached the equilibrium value for a higher annealing temperature T2 (fig. 5), the fast mechanism has an RI value higher than the equilibrium and the slow mechanism a lower value; thus on annealing at T2 the fast mechanism is reversed, lowering its contribution to the RI and causing a temporary overall decrease, while the slow mechanism continues to cause the RI to rise and it eventually attains the new equilibrium value. The solid curve in fig. 3 has been calculated using the model. We have applied the same model to describe the crossover effect in the metallic
A.L. Greet, J.A. Leake / Structural relaxation and crossover effect
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Fig. 5. The two-relaxation-time model. On annealing at TI each mechanism, Mt andM2, would
cause the Curie temperature or refractive index to rise from the old value, stabilized at TO, to the new equilibrium value, but at different rates. The actual RI rises as their average (after Boesch etal. [6]).
glass, substituting Tc for RI. Thus in fig. 4 the solid curve has been calculated using the model and is the sum o f the relaxation curves for the two mechanisms which are also shown. The longer relaxation time is 90-+ 10 s. It is difficult to obtain accurate data at short annealing times and consequently only a rough estimate o f the relaxation time o f the faster mechanism is possible;it is less than or equal to 3 s.
5. Discussion As-quenched metallic glasses have relatively low values of To, characteristic of stabilization at a high temperature. The effective stabilization or "fictive" [7] temperature, though difficult to estimate, appears to be well above the crystallization temperature for conventional annealing treatments. This is a corollary o f the fact that high quench rates are required to produce these glasses, as compared to oxide glasses. For a particular composition the T c in the as-quenched state should be a measure of the quench rate used; its variation with quench rate may explain some o f the discrepancies in published data. The crossover experiment, however, shows that two samples of metallic glass having the same composition and Curie temperature can be in different structural states. Thus the concept of a fictive temperature [7], which assumes that the structural state of a glass can be completely described by a single parameter, is not sufficient to describe the contribution of thermal his-
296
A.L. Greer, J.A. Leake / Structural relaxation and crossover effect
tory to the effect of annealing. This conclusion is the same as for oxide glasses and similar results have also been obtained for polymers [8]. The equilibrium values of RI of oxide glasses and Tc of metallic glasses both decrease with increasing annealing temperature, so that the variations of these two properties on annealing are of similar form. The behaviour remains similar even on complicated annealing treatments such as a crossover experiment. Although the physical origins of RI and Tc are different, and with different atomic structure the relaxation mechanisms must be different, the similar behaviour points to fundamental characteristics of the glassy state. Many of the theories developed to explain the relaxation behaviour of oxide [6,9] and polymeric [8] glasses may be applicable also to metallic glasses. The ratio of errors to changes in Tc in metallic glasses is, however, greater than the corresponding ratio with RI of oxide glasses, so that the metallic glass data provide a less critical test of the theories. The crossover experiments demonstrate that the behaviour of Tc and RI on annealing can be described as a relaxation process provided that (at least) two relaxation times are considered. The existence of more than one relaxation time does not necessarily imply more than one independent atomic mechanism [10]. In the case of the metallic glass, however, the crossover data are well fitted by a two-relaxation-time model for which the ratio of relaxation times is large, approximately thirty, and we suggest that these two times may correspond to two distinct processes of atomic rearrangement; a fast process involving the (displacive) variation of equilibrium free volume with temperature and a slow process involving the (reconstructive) variation of equilibrium chemical ordering. Direct evidence supporting this suggestion is not yet available. Hitherto in this paper the similarities between metallic glasses and oxide glasses have been emphasized. Notable differences are firstly that the ratio of relaxation times in oxide glasses (a value independent of temperature) is almost seven, approximately one quarter of our estimate for metallic glasses, and secondly that the onset of crystallization places a much more stringent limit on possible heat treatments for metallic glasses.
Acknowledgements The authors are indebted to Professor R.W.K. Honeycombe for encouragement and the provision of laboratory facilities, and to the Science Research Council for equipment. They would also like to thank Dr. P.H. Gaskell for helpful discussions. A.L.G. is grateful to the Northern Ireland Department of Education for a studentship in support of this work.
A.L. Greer, J.A. Leake / Structural relaxation and crossover effect
297
References [1] H.S. Chen, Phys. Stat. Solidi (a)17 (1973) 561. [2] H.H. Liebermann, C.D. Graham, Jr. and P.J. Flanders, IEEE Trans. Mag. MAG-13 (1977) 1541. [3] H.S. Chen, J. Appl. Phys. 49 (1978) 4595. [4] A.L. Greer and J.A. Leake, Proc. 3rd Int. Conf. on Rapidly Quenched Metals, University of Sussex, 3 - 7 t h July 1978, to be published, Metals Society, London. [5] T. Egami, Mat. Res. Bull. 13 (1978) 557. [6] L. Boesch, A. Napolitano and P.B. Macedo, J. Am. Ceram. Soc, 53 (1970) 148. [7] A.Q. Tool, J. Am. Ceram. Soc. 29 (1946) 240. [8] A.J. Kovacs, J.M. Hutchinson and J.J, Aklonis, The Structure of Non-Crystalline Materials, ed. P.H. Gaskell (Taylor and Francis, London, 1977) p. 153. [9] H.S.-Y.Hsich, J. Mat. Sci. 13 (1978) 750. [10] M. Goldstein, in: Modern Aspects of the Vitreous State, Volume 3, ed. J.D. Mackenzie (Butterworths, London, 1964).
STRUCTURAL RELAXATION AND CROSSOVER EFFECT IN A METALLIC GLASS A.L. GREER and J.A. LEAKE Dept. o f Metallurgy and Materials Science, University o f Cambridge, Pembroke Street, Cambridge, CB2 3QZ, UK
Received 22 November 1978
1. Introduction On annealing metallic glasses, changes occur in the glassy state before the onset of crystallization. These changes, collectively known as relaxation, affect many properties, but one of the most convenient to measure and most sensitive to relaxation is the Curie temperature, T c. In this letter the variation of T c on annealing a metallic glass is compared with the variation of refractive index of oxide glasses, in particular, a "crossover" experiment has been performed and the results have been analysed in terms of a two-relaxation-time model.
2. The effect of annealing on the Curie temperature of metallic glasses Metallic glasses containing a high (typically around 80%) atom fraction of magnetic species are ferromagnetic and exhibit a sharp Curie transition [1]. On annealing the Curie temperature rises significantly, even at times and temperatures substantially below those necessary to cause crystallization [2], [3] and [4]. Fig. 1 shows this effect for the alloy FeaoB2o (Allied Chemical Corporation: Metglas 2605). In this case the Curie temperatures have been determined by differential scanning calorimetry as described in a previous paper [4]. At any annealing temperature Tc rises rapidly at first and then levels off at an equilibrium value. As may be seen from fig. 1, the lower the annealing temperature, the slower is the approach to equilibrium, but the higher the final equilibrium value of T c. Egami [5] and Greer and Leake [4] have shown that it is possible to move reversibly between equilibrium states attained on annealing at different temperatures.
291
292
A.L. Greer, J.A. Leake / Structural relaxation and crossover effect 368
366
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~
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i
375 "C
///
&
.
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-
4oo'c
Metglos 26os
/// I error
358
0
10 '
20 '
Annealing
30 '
Time
,' 0
;o
,'o
( rain )
Fig. 1. The effect of isothermal annealing on the Curie temperature of amorphous FesoB2o. The dashed lines are extrapolations of equih~rium values to longer times: crystallization of the alloy prevented measurement of the Curie temperature at these longer times.
25o.o'c 1.462
I
B203 gloss
1.454 0
10 Annealing
20 ,Time
30
40
50
{ hr )
Fig. 2. The effect of isothermal annealing on the refractive index of B203 glass previously stabilized at 310.5°C (after Boesch et al. [6]).
A.L. Greer, J.A. Leake / Structural relaxation and crossover effect
293
3. The effect of annealing on the refractive index of oxide glasses Annealing of oxide glasses causes the refractive index, RI, to change, and particularly excellent data exist for B203 glass. Boesch et al. [6] annealed specimens of B203 glass, previously stabilized (i.e., brought to equilibrium) at 310.5°C, at selected lower temperatures. The approach curves of RI to the equilibrium values at the annealing temperatures are shown in fig. 2. The variation shown is very similar to that of Curie temperature shown in fig. 1. Thus the as-quenched metallic glass behaves as though stabilized at a temperature considerably higher than any annealing temperature yet used.
4. The crossover experiment Boesch et al. [6] stabilized a specimen of B203 glass at 310.5°C, then held it at 225°C until its RI reached the equilibrium value for 259.7°C. The specimen was then annealed at 259.7°C and the subsequent change in RI is shown in fig. 3. We have performed a similar experiment on the metallic glass FeaoB2o. A specimen was annealed at 300°C until the Curie temperature reached the equilibrium value for 400°C. The variation of T c on subsequent annealing at 400°C is shown in fig. 4. Again the results for metallic and oxide glasses are of the same form. The crossover
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i
i
i
i
600
1200
1800
2400
Annealing
Time
3000
( rnin )
Fig. 3. The change of refractive index on annealing at 259.7°C a sample of B203 glass previously stabilized at 310.5°C and annealed at 225.5°C until its RI reached the equilibrium value for 259.7°C. The solid line is computed on the two-relaxation-time model, taking times of 118 rain and 768 min (after Boesch et al. [6]).
294
A.L. Greet, J.A. Leake / Structural relaxation and crossover effect
365 Metglcts
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2605
364 363
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"~ 361 (J 360
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I
I
I
I
I
I
0
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2
3
z.
5
6
Anneoling
Time
( min )
Fig, 4. The change of Curie temperature on annealing at 400°C a sample of amorphous FeaoB2o previously annealed at 300°C until its Tc reached the equilibrium value for 400°C. The solid line is computed on the two-relaxation-time model, taking times of 3 s and 90 s. The contributions of the two mechanisms are shown by dotted lines.
experiments show that neither RI nor Tc is uniquely related to the structural state of the relevant glass. In describing the variation of RI of oxide glasses on annealing (fig. 2) account has to be taken of the possibilities of a distribution of relaxation times and also of non-linear effects in which the relaxation times change with distance from equilibrium. Boesch et al. [6] use a simple model to explain the results of the crossover experiment: this assumes two relaxation mechanisms of equal strength, each having a single relaxation time and both leading to the same values of equilibrium RI. The effect of annealing is as shown in fig. 5: the actual (measured) RI follows the average of the values given by the two mechanisms and rises from the stabilized value at temperature To to the equilibrium value for the annealing temperature TI. If, however, the annealing is stopped when the RI has reached the equilibrium value for a higher annealing temperature T2 (fig. 5), the fast mechanism has an RI value higher than the equilibrium and the slow mechanism a lower value; thus on annealing at T2 the fast mechanism is reversed, lowering its contribution to the RI and causing a temporary overall decrease, while the slow mechanism continues to cause the RI to rise and it eventually attains the new equilibrium value. The solid curve in fig. 3 has been calculated using the model. We have applied the same model to describe the crossover effect in the metallic
A.L. Greet, J.A. Leake / Structural relaxation and crossover effect
_ _ _ M~
.~
x
equilibrium
value
at
at
TI
295
1",
,
2
c.,~ n,"
0 Time
of
Anneot
Fig. 5. The two-relaxation-time model. On annealing at TI each mechanism, Mt andM2, would
cause the Curie temperature or refractive index to rise from the old value, stabilized at TO, to the new equilibrium value, but at different rates. The actual RI rises as their average (after Boesch etal. [6]).
glass, substituting Tc for RI. Thus in fig. 4 the solid curve has been calculated using the model and is the sum o f the relaxation curves for the two mechanisms which are also shown. The longer relaxation time is 90-+ 10 s. It is difficult to obtain accurate data at short annealing times and consequently only a rough estimate o f the relaxation time o f the faster mechanism is possible;it is less than or equal to 3 s.
5. Discussion As-quenched metallic glasses have relatively low values of To, characteristic of stabilization at a high temperature. The effective stabilization or "fictive" [7] temperature, though difficult to estimate, appears to be well above the crystallization temperature for conventional annealing treatments. This is a corollary o f the fact that high quench rates are required to produce these glasses, as compared to oxide glasses. For a particular composition the T c in the as-quenched state should be a measure of the quench rate used; its variation with quench rate may explain some o f the discrepancies in published data. The crossover experiment, however, shows that two samples of metallic glass having the same composition and Curie temperature can be in different structural states. Thus the concept of a fictive temperature [7], which assumes that the structural state of a glass can be completely described by a single parameter, is not sufficient to describe the contribution of thermal his-
296
A.L. Greer, J.A. Leake / Structural relaxation and crossover effect
tory to the effect of annealing. This conclusion is the same as for oxide glasses and similar results have also been obtained for polymers [8]. The equilibrium values of RI of oxide glasses and Tc of metallic glasses both decrease with increasing annealing temperature, so that the variations of these two properties on annealing are of similar form. The behaviour remains similar even on complicated annealing treatments such as a crossover experiment. Although the physical origins of RI and Tc are different, and with different atomic structure the relaxation mechanisms must be different, the similar behaviour points to fundamental characteristics of the glassy state. Many of the theories developed to explain the relaxation behaviour of oxide [6,9] and polymeric [8] glasses may be applicable also to metallic glasses. The ratio of errors to changes in Tc in metallic glasses is, however, greater than the corresponding ratio with RI of oxide glasses, so that the metallic glass data provide a less critical test of the theories. The crossover experiments demonstrate that the behaviour of Tc and RI on annealing can be described as a relaxation process provided that (at least) two relaxation times are considered. The existence of more than one relaxation time does not necessarily imply more than one independent atomic mechanism [10]. In the case of the metallic glass, however, the crossover data are well fitted by a two-relaxation-time model for which the ratio of relaxation times is large, approximately thirty, and we suggest that these two times may correspond to two distinct processes of atomic rearrangement; a fast process involving the (displacive) variation of equilibrium free volume with temperature and a slow process involving the (reconstructive) variation of equilibrium chemical ordering. Direct evidence supporting this suggestion is not yet available. Hitherto in this paper the similarities between metallic glasses and oxide glasses have been emphasized. Notable differences are firstly that the ratio of relaxation times in oxide glasses (a value independent of temperature) is almost seven, approximately one quarter of our estimate for metallic glasses, and secondly that the onset of crystallization places a much more stringent limit on possible heat treatments for metallic glasses.
Acknowledgements The authors are indebted to Professor R.W.K. Honeycombe for encouragement and the provision of laboratory facilities, and to the Science Research Council for equipment. They would also like to thank Dr. P.H. Gaskell for helpful discussions. A.L.G. is grateful to the Northern Ireland Department of Education for a studentship in support of this work.
A.L. Greer, J.A. Leake / Structural relaxation and crossover effect
297
References [1] H.S. Chen, Phys. Stat. Solidi (a)17 (1973) 561. [2] H.H. Liebermann, C.D. Graham, Jr. and P.J. Flanders, IEEE Trans. Mag. MAG-13 (1977) 1541. [3] H.S. Chen, J. Appl. Phys. 49 (1978) 4595. [4] A.L. Greer and J.A. Leake, Proc. 3rd Int. Conf. on Rapidly Quenched Metals, University of Sussex, 3 - 7 t h July 1978, to be published, Metals Society, London. [5] T. Egami, Mat. Res. Bull. 13 (1978) 557. [6] L. Boesch, A. Napolitano and P.B. Macedo, J. Am. Ceram. Soc, 53 (1970) 148. [7] A.Q. Tool, J. Am. Ceram. Soc. 29 (1946) 240. [8] A.J. Kovacs, J.M. Hutchinson and J.J, Aklonis, The Structure of Non-Crystalline Materials, ed. P.H. Gaskell (Taylor and Francis, London, 1977) p. 153. [9] H.S.-Y.Hsich, J. Mat. Sci. 13 (1978) 750. [10] M. Goldstein, in: Modern Aspects of the Vitreous State, Volume 3, ed. J.D. Mackenzie (Butterworths, London, 1964).