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Thermal stability and crystallisation of a Zr55Cu30Al10Ni5 bulk metallic glass studied by in situ ultrasonic echography
Intermetallics 10 (2002) 1289–1296 www.elsevier.com/locate/intermet
Thermal stability and crystallisation of a Zr55Cu30Al10Ni5 bulk metallic glass studied by in situ ultrasonic echography Vincent Keryvina,*, Marie-Laure Vaillanta, Tanguy Rouxela, Marc Hugerb, Thierry Gloriantc, Yoshihito Kawamurad a
LARMAUR, UPRES-JE 2310, Universite´ de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France b GEMH, ENSCI, 47 av. A. Thomas, 87065 Limoges Cedex, France c GRCM, INSA de Rennes, UPRES-EA 2620, 20 Av. des Buttes de Coe¨smes, CS 14315, 35043 Rennes Cedex, France d Department of Mechanical Engineering and Materials Science, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
Abstract An original in situ ultrasonic echography technique was used to study the thermal stability and crystallisation of a Zr55Cu30Al10Ni5 bulk metallic glass between RT and 630 C. Changes in Young’s modulus with temperature were reported allowing to study the supercooled-liquid state and the crystallisation process. Investigations of viscoelastic properties gave information on the correlation factor (hierarchically correlated motion theory) and three distinct crystallisation stages were observed. Their kinetics were studied using Voigt’s and Reuss’ approximations for a two-phase material and comparisons with the Johnson–Mehl– Avrami–Kolmogorov theory allowed us to consider a mixed surface/internal nucleation for the first stage and a surface nucleation for the two last stages. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: B. Glasses, metallic; Thermal stability
1. Introduction The recent discoveries of bulk metallic glasses [1,2] led to materials with very useful properties, such as high strength, a good stiffness or good soft-magnetic properties. Moreover, in their large supercooled-liquid state, workability and production of large-scaled specimens by powder metallurgy [3] due to their superplastic behaviour give them tremendous potential applications. Though extensively studied for their interesting properties, many efforts are required to study the behaviour of bulk metallic glasses and to understand the complex mechanisms occuring from RT to high temperatures (before melting). Interesting topics such as the homogeneous/heterogeneous deformation process, viscous behaviour, crystallisation or welding are under study. In this paper, thermal stability and crystallisation of a Zrbased alloy (Zr55Cu30Al10Ni5) are studied by an original in situ ultrasonic pulse-echo method technique. It is shown that this technique is a powerful tool to study the temperature-dependent behaviour of bulk metallic * Corresponding author. Tel./fax: +33-2-23-23-57-17/63-59. E-mail address: [email protected] (V. Keryvin).
glasses. Besides data collected for the changes in Young’s modulus with temperature between RT and 630 C, attention is focused on the supercooled-liquid state and the crystallisation issue is addressed.
2. Experimental methods The Zr55Cu30Al10Ni5 (at.%) bulk metallic glass was used in this study, obtained by the copper mould casting technique (described for example in [4]). Some ingots were first prepared by arc-melting a mixture of pure elements then remelted in an evacuated quartz tube using an induction-heating coil and eventually injected through a nozzle into a copper mould using a high purity argon gas. The plate obtained, 1.6 mm thick, was cut into small specimens by means of a high-speed diamond/copper saw, and each specimen was then mirrorpolished by standard metallographic techniques using SiC and diamond containing grids. The density was measured by the Archimedes technique using CCl4. Hardness was determined by Vickers indentation (load of 2.942 N during 15 s). Elastic moduli (Young’s modulus E and Poisson’s ratio ) were
0966-9795/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(02)00150-4
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determined from the density and from the ultrasonic longitudinal VL and transversal VT wave velocities using piezo-electric transducers (10 MHz) in contact, via a coupling gel, with a specimen whose width is larger than the longitudinal and transverse wavelengths (respectively around 0.62 and 0.23 mm); in this case, values for the elastic moduli for the infinite mode are:
Young’s modulus E can be calculated from the density and the longitudinal wave velocity VL according to:
3V 2 4V 2 E ¼ L 2 T VL 1 VT
Material properties at room temperature are presented in Table 1.
and
¼
3VL2 4VT2 1 2 VL2 VT2
E ¼ V2L
ð2Þ
3. Results
ð1Þ
3.1. Differential scanning calorimetry DSC curves for different linear heatings (from 5 to 50 C /min) are plotted in Fig. 1. Results show both a glass transition (not evidenced on these plots by choice) and the existence of three different crystallisation peaks. Values for these temperatures are given in Table 2 (the second crystallisation temperature is not determined because the two first peaks tend to overlap). Taking the 5 C/min plot as a reference (label 1 in Fig. 1), two peaks are visible, the first one at T1=463 C and the other one at T3=553 C. Increasing the heating rate, the first peak reveals to be double while the second peak shifts to higher temperatures (which is not visible for heating rates greater than 5 C /min). Kissinger plots [7] of both glass transition and first crystallisation temperatures are shown in Fig. 2 (the slopes have the same sign by choice of presentation).
Thermal stability was studied by Differential Scanning Calorimetry (DSC 111 SETARAM) under an inert Argon atmosphere for different heating rates from 5 C/min to 50 C/min. Both glass transition and crystallisation temperatures are determined for each test. An ultrasonic technique was used to follow the change in Young’s modulus E as a function of temperature between RT and 630 C. It consists [5,6] in calculating Young’s modulus E from the velocity of an ultrasonic pulse propagating in a long, thin and refractory wave-guide sealed to a specimen (about 0.61.645 mm3). A magnetostrictive transducer (350 kHz) was used and experiments were conducted under an inert Argon atmosphere with heating rates either of 1 or 5 C/min. In the present case, the longitudinal wave velocity is about 3500 m/s at room temperature and it follows that the wavelength is about 10 mm, that is much greater (at least more than five times) than the characteristic dimension of the specimen cross section. The condition of very long wavelength, in comparison with the scale of the microstructure, is thus satisfied and the long beam mode approximation holds, so that
Table 1 Material properties of the as-cast Zr55Cu30Al10Ni5 bulk glassa (g/cm3)
E (GPa)
v
Hv (kg/mm2)
Hv (GPa)
6.7720.006
81.643
0.3780.003
474 21
4.60.2
a , E, v and Hv stand respectively for the density, Young’s modulus, Poisson’s ratio and Vickers hardness.
Fig. 1. DSC curves at different heating rates. Labels 1–6 stand respectively for 5, 10, 20, 30, 40 and 50 C/min heating rates.
Table 2 Glass transition and crystallisation temperatures determined by DSC and ultrasonic echography (US) at different linear heating ratesa Technique
DSC
Heating rate ( C/min)
5
10
Tg ( C) Tx1 ( C) Tx2 ( C) Tx3 ( C)
388 463
398 412 476 490 Not determined 590 616
a
553
20
The ‘X’ indicates that the two first crystallisation processes overlapped.
US 30
40
50
1
5
422 504
427 513
430 523
370 425 X 490
375 430 435 540
Not determined
V. Keryvin et al. / Intermetallics 10 (2002) 1289–1296
1291
Fig. 2. Kissinger plots for the glass transition and the first crystallisation temperature. a stands for the heating rate, Tg and Tx are respectively the glass transition and the first crystallisation temperatures. The signs of the two slopes are the same by choice of presentation.
The apparent activation energies determined by taking the slope of the fitting lines are respectively 191 kJ/mol for Tg (endothermic) and 174 kJ/mol for Tx1 (exothermic). 3.2. Change in Young’s modulus E with temperature 3.2.1. A monotonous heat-treatment Changes in Young’s modulus with temperature at a heating rate of 5 C/min are plotted in Fig. 3. Tendencies during heating can be described in three stages. During the first one, the glassy state, the decrease of Young’s modulus is gentle. Then there is a steep transition between a slow softening rate (14 MPa/ C) and a faster one (89 MPa/ C) at the glass transition temperature. These values are completely similar with those for a window glass [8]. Sketching the conventional method applied to thermal expansion experiments, a method to estimate this transition temperature from the E(T) curves is to determine the intersection between the lines associated with both regimes, which gives a temperature close to 375 C. This transition is the beginning of the supercooled liquid state where the specimen starts to soften quite rapidly. This second stage lasts until a second very steep transition occurs when the slope changes from negative to high positive values (1.21 GPa/ C). This rapid transition, corresponding to the first crystallisation process, starts at a temperature Tx1 (around 430 C) and lasts for a very short temperature range (around 10 C) and is followed, starting at a temperature (around 435 C), by a continuous increase in Young’s modulus with a lower, but quite strong, positive slope (around 230 MPa/ C) during 20 C before
Fig. 3. Change in Young’s modulus during a linear heating (then cooling) at 5 C/min.
reaching a plateau. This plateau longs until a temperature Tx3 (around 540 C ) where another strong increase of stiffness starts and lasts, unlike the short process between Tx1 and Tx2, for 50 C with an average slope of 400 MPa/ C. Then another plateau is reached and no further stiffening is observed till 630 C. During cooling, a quasi linear and monotonic increase in E indicates, for this technique, that there is no residual glassy phase left (no glass transition is observed). The whole crystallisation process results after cooling to a 48% increase in Young’s modulus, from 81.4 to 121 GPa. The glass transition and first crystallisation temperatures are reported in Table 2 for two linear heatings (1 and 5 C/min).
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3.2.2. Isothermal annealings In order to investigate the crystallisation kinetics, annealing treatments were carried out at different temperatures, these being reached with a rather rapid heating rate of 5 C/min. The time–temperature diagram is reported on Fig. 4. Each time no change in Young’s modulus was observed during half an hour, an increase in the plateau-temperature was made by 10–30 C. The results (Fig. 4) show three crystallisation stages. At a temperature of 430 C, the same rapid stiffening (+12 GPa in 1.5 h), as for the monotonous heat-treatment was observed, while at a temperature of 470 C, a very long process occured (+ 14 GPa in 16.7 h). Eventually, at 520 C a last stiffening (+ 4 GPa in 3.8 h) was observed.
4. Discussion
correlated motion [9,10] and considers that the faster molecular movements occur before, and trigger, the slower ones. Let t be the characteristic relaxation time of the simplest elementary motions involved in the deformation process, an Arrhenius-type equation for its thermal behaviour writes: DGa ¼ 0 exp ð3Þ RT where Ga is the free activation enthalpy associated with the process, T is the temperature, R the gas constant and 0 a multiplicative constant. Then the characteristic time for molecular mobility in the disordered condensed matter mol (corresponding to the mean duration of a structural unit jump over a distance equal to its dimension—experimentally available) is given by [9,10]: 1
4.1. The glass transition stage (from glassy to supercooled-liquid) Values for the glass transition temperature, depending on both the technique used and the heating rate, are summarised in Table 2. The transition temperatures found by ultrasonic echography lies systematically at lower temperatures than those obtained by DSC. A similar trend was already noticed on other glasses [8] due mainly to the fact that for ultrasonic echography, the transition temperatures are clearly defined unlike those obtained by DSC. Note that, nevertheless, during the ultrasonic echography experiment, the temperature is measured above the sample in the oven and a 5 C difference may exist with the sample temperature. 4.2. The supercooled-liquid state At least two ways of studying this stage do exist. The first method is based on the concept of hierarchically
mol ¼ A b
ð4Þ
where A is a constant and b is the so-called correlation factor which can be regarded as a structural parameter characterising the correlation between the different atomic or molecular movements occuring in the glass: when b=0 any movement of a structural unit requires the motion of all the other units (maximum order, perfect correlation), while when b=1 all the movements are independent on each other (the maximum disorder corresponding to a Maxwell model for relaxation, or to a single characteristic time of the classical Debye relaxation process). In oxide glasses, b tends towards values as low as 0.2–0.5 below Tg but gets closer to 1 as the temperature increases in the supercooled-liquid state. Differentiation of Eq. (4) with respect to temperature, recalling that the directly available thermodynamic parameter is the activation enthalpy Ha ¼ @1n1mol , and @ RT
further assuming that Ga and b change little with temperature (which is generally the case above the transition range) [8], one obtains:
Ga ¼ b Ha
ð5Þ
The second method is based on the classical theory of thermally activated flow phenomena, which considers the existence of two independent contributions acting together to overcome the free energy barrier, G0, associated with the flow process. One of these contributions, Ga, has a purely thermal origin and is derived from the thermally activated atomic, or molecular, movements; the other, Wa, is due to the applied stress so that:
G0 ¼ Ga þ Wa
Fig. 4. Change in Young’s modulus during isothermal treatments.
ð6Þ
Following Schoeck [11] who considered that the height of the barrier, G0, to be overwhelmingly of
V. Keryvin et al. / Intermetallics 10 (2002) 1289–1296
elastic origin, G0 is taken to be proportional to the shear modulus and even proportional to Young’s modulus (by considering the classical assumption that Poisson’s ratio does not vary with temperature in the supercooled-liquid state). Other asumptions that can be found in [8] lead to:
Ga ¼
1
Ha T @E 1 E @T
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consistent with both mechanical spectroscopy and stress relaxation methods [8]. The reasons for the difference between the results for the bulk metallic glass are still under study. 4.3. The crystallisation processes
ð7Þ
Results of both the DSC and Young’s moduli analyses reveal the existence of three distinct crystallisation stages. Their onset and their kinetics are now discussed.
A correspondence between these two methods [Eqs. (5) and (7)] lead to the value of the correlation factor, b, as follows:
4.3.1. Change in the crystallised fractions with time In the case of a two phase material, it is possible to link the elastic moduli with the volume fractions of the phases by means of Voigt’s and Reuss’ approximations [13]. The analysis was developed for the shear moduli and gives the boundaries corresponding to the limit cases where the two phases experience the same strain (Voigt) or the same stress (Reuss). Both results are transposable to Young’s moduli when Poisson’s ratios are known. As it is supposed that these latter remain constant during each crystallisation stage (the temperature is kept constant), the expressions can be directly written with Young’s moduli. The fact that crystallised specimens exhibit Poisson’s ratios close to one of the as-cast glass supports this hypothesis (Vaillant [14]). For a volume fraction, X, of crystallised phase, the expressions for Young’s modulus of the material corresponding to Voigt’s and Reuss’ models, EV and ER are:
b¼
1 T @E 1 E @T
ð8Þ
The evaluation of Eq. (8) was performed using the E(T) data of Fig. 3 and two other experiments carried out at 1 and 5 C /min. Results are illustrated in Fig. 5. Values between 0.6 and 0.75 for b are found in a range of validity for T/Tg between 1.04 and 1.12 (so very close to the validity range found by Rouxel [8] for glasses with much larger supercooled-liquid states). This scattering is common for the correlation factor in amorphous solids and a mean value of 0.67 is obtained. Other techniques for measuring include mechanical spectroscopy and stress relaxation experiments. The first method [12] on a Zr–Ti–Cu–Ni–Be glass and a Pd–Ni– Cu–P glass) leads to b-values around 0.4, thus lower from our values. The method we used was already used for window glasses and oxynitride glasses and were very
E V ¼ E G ð1 XÞ þ E C X ER ¼
E C E G E G X þ E C ð1 XÞ
ð9Þ
where EG and EC are respectively Young’s modulus of the glass during the first crystallisation stage (or of the glassy matrix and the previously crystallised crystal supposed to remain unchanged) and of the crystallised phase. EG is thus assumed to be constant during crystallisation though it is likely that the crystallisation of a particular phase affects the composition of the residual glass and thus its properties. It is reciprocally possible, from a measured value of Young’s modulus E, to get bounds for the crystalline phase volume fraction, XV and XR. E EG EC EG EC EG E XR ¼ E ðE G E C Þ XV ¼
Fig. 5. Evolution of the correlation factor with temperature. Three sets of data corresponding to two different linear heatings (1 and 5 C /min) are superimposed. No influence of the heating rate is noticeable.
ð10Þ
At time t=0, X(t)=0 and E=E0=EG. At time t=+1, X(t)=X1, where X1 is the maximum volume fraction of crystallised phase with respect to the experimental duration, to which a value E1 of E is associated. Following Besson [15], it is thus convenient
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to use a normalised crystallised volume fraction x(t), defined as the ratio between X(t) and X1. Eq. (10) write then: X V ðtÞ EðtÞ E0 ¼ XV E1 E0 R X ð t Þ E 1 ðEðtÞ E0 Þ xR ¼ ¼ R X1 EðtÞ ðE1 E0 Þ xV ¼
ð11Þ
With these expressions, one can draw Hill’s bounds for the three crystallisation stages (see Fig. 6) by plotting the normalised crystallised volume fractions with respect to the annealing time. All curves are very close and a mean value will be used for the following of the study. The kinetics of the first crystallization process has the three classical distinct stages: a slow one corre-
sponding to nucleation, a fast one corresponding to the growth of the nuclei and a final and slow one. As far as the other crystallization stages are concerned, the diagrams look similar but rather different from the first one, that is a fast behaviour followed by a slower one. 4.3.2. Crystallisation kinetics The conventional Johnson–Mehl–Avrami–Kolmogorov model is commonly used to describe the crystallisation kinetics of amorphous materials [16]. Assuming a random distribution of the crystallised precipitates, the normalised crystallised volume fraction, x, corresponding to an annealing time t is given by: xðtÞ ¼ 1 exp½ðKtÞn
ð12Þ
Fig. 6. Crystallisation kinetics as calculated with Voigt’s and Reuss’ approximations from E(T) data during isothermal treatments presented in Fig. 4. x(t) stands for the normalised crystallised volume fraction.
V. Keryvin et al. / Intermetallics 10 (2002) 1289–1296
where n is the reaction rate order, or Avrami’s exponent, and K is the overall reaction rate which is assumed to have an Arrhenius’ temperature dependence: KðTÞ ¼ K0 exp
Ea RT
ð13Þ
where Ea is the effective activation energy for the crystallistion process. When crystallisation proceeds by steps, Eq. (12) can be used for the primary crystallisation step [17] but the validity for the two other stages is controversial. Nevertheless, Eq. (12) can be rewritten as: ln½lnð1 xðtÞÞ ¼ nlnt þ nlnK
ð14Þ
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and plots of ln [ln(1x(t))] versus ln t are drawn on Fig. 7 where least-squares fitting lines are superimposed allowing to derive estimations for Avrami’s exponents. Values of 1.93, 0.88 and 0.8 were respectively determined this way for n corresponding to the three crystallisation sequences respectively. Unlike previous results on a very similar glass [17], the linear Johnson– Mehl–Avrami–Kolmogorov model agrees very well with our data. The usual hypotheses for the use of the JMAK model [16] are not known to be verified for bulk metallic glasses, but let us allow ourselves to compare our Avrami’s exponents with the usual physical meanings found for other glasses. Avrami’s exponents range usually in glasses from 1 for surface nucleation to 3 for internal nucleation; thus our first crystallisation could
Fig. 7. Determination of Avrami’s exponent for isothermal treatments. The correlation factor is 0.98. x(t) stands for the normalised crystallised volume fractions and t is time.
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V. Keryvin et al. / Intermetallics 10 (2002) 1289–1296
be a mixed surface and internal nucleation (surface nucleation could be triggered by the thin oxide layer) while the two other ones could be a pure surface nucleation (this surface nucleation could this time take place on the surface of the previously formed crystallysed phases). It is known that the only use of linear fittings to analyse phase transformation kinetics through the experimental values of Avrami’s exponent can give misleading interpretations for the transformation mechanisms; therefore, microscopic studies are needed to validate these hypotheses. Note that our Avrami’s exponents differ sensibly from the ones found by Inoue [4] (between 3 and 3.7, indicating a threedimensional homogeneous internal nucleation) for the Zr65Al7.5Cu27.5 glass. Eventually, besides the fact that it is particularly noteworthy difficult to give a physical meaning to the parameters of the JMAK model for bulk metallic glasses, it is known that a metastable phase is observed during the first crystallisation of our glass [18] that transforms later into the Zr2Cu phase. That metastable phase is supposed to be a polymorphic phase and since it is known that the linear form of the JMAK model is not valid for polymorphic transformations [19], the crystallisation issue for our glass, and more generally for bulk metallic glasses, calls for further investigations.
5. Conclusion An original in situ ultrasonic technique was carried out to study thermal stability and crystallisation of a Zr55Cu30Al10Ni5 bulk metallic glass. Besides the very interesting data collected for Young’s moduli between RT and 630 C, this technique allowed us to have some insight into both viscoelastic and crystallisation processes, as evidenced by the comparison with DSC measurements. Concerning the supercooled liquid state, an original correspondence between the theories of hierarchically correlated motion and thermally activated phenonema was used to calculate the correlation factor. However, some differences were found with mechanical spectro-
scopy results. Other comparisons must be made with other techniques such as creep and stress relaxation. Eventually, as far as the crystallisation issue is concerned, three different crystalli-sation stages were evidenced and their kinetics studied. Major differences on the kinetics were reported between stage 1 and stages 2 and 3. Comparisons with the classical JMAK theory made us suppose a mixed surface/internal nucleation for stage 1 and a surface nucleation for both stages 2 and 3. Nevertheless, microscopic studies are needed to have a deeper insight on the crystallisation mechanisms as well as on the crystallised phases.
References [1] Inoue A, Zhang T, Masumoto T. Mater Trans JIM 1990; 31(5):425. [2] Peker A, Johnson WL. Appl Phys Lett 1993;63:2342. [3] Kawamura Y, Kato H, Inoue A, Masumoto T. Int J Powder Metall 1997;33:50. [4] Inoue A. Bulk amorphous alloys. Switzerland: Trans Tech Publications; 1998. [5] Papadakis EP, Fowler KA, Lynnworth LC, Robertson A, Zysk AD. J Appl Phys 1974;45(6):2409. [6] Huger M, Fargeot D, Gault C. J Am Ceram Soc 1994; 77(10):2554. [7] Kissinger H. Anal Chem 1957;29:1702. [8] Rouxel T, Sangleboeuf JC, Huger M, Gault C, Besson JL, Testu S. Acta Mater 2002;50:1669. [9] Palmer RG, Stein DL, Abrahams E, Anderson PW. Phys Rev Lett 1984;53:958. [10] Pelletier JM, Perez J, Soubeyroux JL. J Non Cryst Sol 2000; 274:301. [11] Schoeck G. Phys Stat Sol 1965;8:499. [12] Pelletier JM, Van de Moorte`le B, Liu IR. In: Risø Int Symp Materials Science 22. Roskilde, Denmark 2001;359. [13] Hill R. J Mech Phys Sol 1963;11:357. [14] Nishiyama N, Horino M, Inoue A. Mater Trans JIM 2000; 41:1432. [15] Besson JL, Lemercier H, Rouxel T, Trolliard G. J Non Cryst Sol 1997;211:1. [16] Zanotto ED, Galhardi A. J Non Cryst Sol 1988;104:73. [17] Xing LQ, Eckert J, Lo¨ser W, Schultz L, Herlach DM. Phil Mag A 1999;79(5):1095. [18] Yavari AR, Le Moulec A, Botta WJ, Inoue A, Rejmankova P, Kvick A. J Non Cryst Sol 1999;247:31. [19] Kelton KF. J Non Cryst Sol 1993;163:283.
Thermal stability and crystallisation of a Zr55Cu30Al10Ni5 bulk metallic glass studied by in situ ultrasonic echography Vincent Keryvina,*, Marie-Laure Vaillanta, Tanguy Rouxela, Marc Hugerb, Thierry Gloriantc, Yoshihito Kawamurad a
LARMAUR, UPRES-JE 2310, Universite´ de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France b GEMH, ENSCI, 47 av. A. Thomas, 87065 Limoges Cedex, France c GRCM, INSA de Rennes, UPRES-EA 2620, 20 Av. des Buttes de Coe¨smes, CS 14315, 35043 Rennes Cedex, France d Department of Mechanical Engineering and Materials Science, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
Abstract An original in situ ultrasonic echography technique was used to study the thermal stability and crystallisation of a Zr55Cu30Al10Ni5 bulk metallic glass between RT and 630 C. Changes in Young’s modulus with temperature were reported allowing to study the supercooled-liquid state and the crystallisation process. Investigations of viscoelastic properties gave information on the correlation factor (hierarchically correlated motion theory) and three distinct crystallisation stages were observed. Their kinetics were studied using Voigt’s and Reuss’ approximations for a two-phase material and comparisons with the Johnson–Mehl– Avrami–Kolmogorov theory allowed us to consider a mixed surface/internal nucleation for the first stage and a surface nucleation for the two last stages. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: B. Glasses, metallic; Thermal stability
1. Introduction The recent discoveries of bulk metallic glasses [1,2] led to materials with very useful properties, such as high strength, a good stiffness or good soft-magnetic properties. Moreover, in their large supercooled-liquid state, workability and production of large-scaled specimens by powder metallurgy [3] due to their superplastic behaviour give them tremendous potential applications. Though extensively studied for their interesting properties, many efforts are required to study the behaviour of bulk metallic glasses and to understand the complex mechanisms occuring from RT to high temperatures (before melting). Interesting topics such as the homogeneous/heterogeneous deformation process, viscous behaviour, crystallisation or welding are under study. In this paper, thermal stability and crystallisation of a Zrbased alloy (Zr55Cu30Al10Ni5) are studied by an original in situ ultrasonic pulse-echo method technique. It is shown that this technique is a powerful tool to study the temperature-dependent behaviour of bulk metallic * Corresponding author. Tel./fax: +33-2-23-23-57-17/63-59. E-mail address: [email protected] (V. Keryvin).
glasses. Besides data collected for the changes in Young’s modulus with temperature between RT and 630 C, attention is focused on the supercooled-liquid state and the crystallisation issue is addressed.
2. Experimental methods The Zr55Cu30Al10Ni5 (at.%) bulk metallic glass was used in this study, obtained by the copper mould casting technique (described for example in [4]). Some ingots were first prepared by arc-melting a mixture of pure elements then remelted in an evacuated quartz tube using an induction-heating coil and eventually injected through a nozzle into a copper mould using a high purity argon gas. The plate obtained, 1.6 mm thick, was cut into small specimens by means of a high-speed diamond/copper saw, and each specimen was then mirrorpolished by standard metallographic techniques using SiC and diamond containing grids. The density was measured by the Archimedes technique using CCl4. Hardness was determined by Vickers indentation (load of 2.942 N during 15 s). Elastic moduli (Young’s modulus E and Poisson’s ratio ) were
0966-9795/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(02)00150-4
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V. Keryvin et al. / Intermetallics 10 (2002) 1289–1296
determined from the density and from the ultrasonic longitudinal VL and transversal VT wave velocities using piezo-electric transducers (10 MHz) in contact, via a coupling gel, with a specimen whose width is larger than the longitudinal and transverse wavelengths (respectively around 0.62 and 0.23 mm); in this case, values for the elastic moduli for the infinite mode are:
Young’s modulus E can be calculated from the density and the longitudinal wave velocity VL according to:
3V 2 4V 2 E ¼ L 2 T VL 1 VT
Material properties at room temperature are presented in Table 1.
and
¼
3VL2 4VT2 1 2 VL2 VT2
E ¼ V2L
ð2Þ
3. Results
ð1Þ
3.1. Differential scanning calorimetry DSC curves for different linear heatings (from 5 to 50 C /min) are plotted in Fig. 1. Results show both a glass transition (not evidenced on these plots by choice) and the existence of three different crystallisation peaks. Values for these temperatures are given in Table 2 (the second crystallisation temperature is not determined because the two first peaks tend to overlap). Taking the 5 C/min plot as a reference (label 1 in Fig. 1), two peaks are visible, the first one at T1=463 C and the other one at T3=553 C. Increasing the heating rate, the first peak reveals to be double while the second peak shifts to higher temperatures (which is not visible for heating rates greater than 5 C /min). Kissinger plots [7] of both glass transition and first crystallisation temperatures are shown in Fig. 2 (the slopes have the same sign by choice of presentation).
Thermal stability was studied by Differential Scanning Calorimetry (DSC 111 SETARAM) under an inert Argon atmosphere for different heating rates from 5 C/min to 50 C/min. Both glass transition and crystallisation temperatures are determined for each test. An ultrasonic technique was used to follow the change in Young’s modulus E as a function of temperature between RT and 630 C. It consists [5,6] in calculating Young’s modulus E from the velocity of an ultrasonic pulse propagating in a long, thin and refractory wave-guide sealed to a specimen (about 0.61.645 mm3). A magnetostrictive transducer (350 kHz) was used and experiments were conducted under an inert Argon atmosphere with heating rates either of 1 or 5 C/min. In the present case, the longitudinal wave velocity is about 3500 m/s at room temperature and it follows that the wavelength is about 10 mm, that is much greater (at least more than five times) than the characteristic dimension of the specimen cross section. The condition of very long wavelength, in comparison with the scale of the microstructure, is thus satisfied and the long beam mode approximation holds, so that
Table 1 Material properties of the as-cast Zr55Cu30Al10Ni5 bulk glassa (g/cm3)
E (GPa)
v
Hv (kg/mm2)
Hv (GPa)
6.7720.006
81.643
0.3780.003
474 21
4.60.2
a , E, v and Hv stand respectively for the density, Young’s modulus, Poisson’s ratio and Vickers hardness.
Fig. 1. DSC curves at different heating rates. Labels 1–6 stand respectively for 5, 10, 20, 30, 40 and 50 C/min heating rates.
Table 2 Glass transition and crystallisation temperatures determined by DSC and ultrasonic echography (US) at different linear heating ratesa Technique
DSC
Heating rate ( C/min)
5
10
Tg ( C) Tx1 ( C) Tx2 ( C) Tx3 ( C)
388 463
398 412 476 490 Not determined 590 616
a
553
20
The ‘X’ indicates that the two first crystallisation processes overlapped.
US 30
40
50
1
5
422 504
427 513
430 523
370 425 X 490
375 430 435 540
Not determined
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Fig. 2. Kissinger plots for the glass transition and the first crystallisation temperature. a stands for the heating rate, Tg and Tx are respectively the glass transition and the first crystallisation temperatures. The signs of the two slopes are the same by choice of presentation.
The apparent activation energies determined by taking the slope of the fitting lines are respectively 191 kJ/mol for Tg (endothermic) and 174 kJ/mol for Tx1 (exothermic). 3.2. Change in Young’s modulus E with temperature 3.2.1. A monotonous heat-treatment Changes in Young’s modulus with temperature at a heating rate of 5 C/min are plotted in Fig. 3. Tendencies during heating can be described in three stages. During the first one, the glassy state, the decrease of Young’s modulus is gentle. Then there is a steep transition between a slow softening rate (14 MPa/ C) and a faster one (89 MPa/ C) at the glass transition temperature. These values are completely similar with those for a window glass [8]. Sketching the conventional method applied to thermal expansion experiments, a method to estimate this transition temperature from the E(T) curves is to determine the intersection between the lines associated with both regimes, which gives a temperature close to 375 C. This transition is the beginning of the supercooled liquid state where the specimen starts to soften quite rapidly. This second stage lasts until a second very steep transition occurs when the slope changes from negative to high positive values (1.21 GPa/ C). This rapid transition, corresponding to the first crystallisation process, starts at a temperature Tx1 (around 430 C) and lasts for a very short temperature range (around 10 C) and is followed, starting at a temperature (around 435 C), by a continuous increase in Young’s modulus with a lower, but quite strong, positive slope (around 230 MPa/ C) during 20 C before
Fig. 3. Change in Young’s modulus during a linear heating (then cooling) at 5 C/min.
reaching a plateau. This plateau longs until a temperature Tx3 (around 540 C ) where another strong increase of stiffness starts and lasts, unlike the short process between Tx1 and Tx2, for 50 C with an average slope of 400 MPa/ C. Then another plateau is reached and no further stiffening is observed till 630 C. During cooling, a quasi linear and monotonic increase in E indicates, for this technique, that there is no residual glassy phase left (no glass transition is observed). The whole crystallisation process results after cooling to a 48% increase in Young’s modulus, from 81.4 to 121 GPa. The glass transition and first crystallisation temperatures are reported in Table 2 for two linear heatings (1 and 5 C/min).
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3.2.2. Isothermal annealings In order to investigate the crystallisation kinetics, annealing treatments were carried out at different temperatures, these being reached with a rather rapid heating rate of 5 C/min. The time–temperature diagram is reported on Fig. 4. Each time no change in Young’s modulus was observed during half an hour, an increase in the plateau-temperature was made by 10–30 C. The results (Fig. 4) show three crystallisation stages. At a temperature of 430 C, the same rapid stiffening (+12 GPa in 1.5 h), as for the monotonous heat-treatment was observed, while at a temperature of 470 C, a very long process occured (+ 14 GPa in 16.7 h). Eventually, at 520 C a last stiffening (+ 4 GPa in 3.8 h) was observed.
4. Discussion
correlated motion [9,10] and considers that the faster molecular movements occur before, and trigger, the slower ones. Let t be the characteristic relaxation time of the simplest elementary motions involved in the deformation process, an Arrhenius-type equation for its thermal behaviour writes: DGa ¼ 0 exp ð3Þ RT where Ga is the free activation enthalpy associated with the process, T is the temperature, R the gas constant and 0 a multiplicative constant. Then the characteristic time for molecular mobility in the disordered condensed matter mol (corresponding to the mean duration of a structural unit jump over a distance equal to its dimension—experimentally available) is given by [9,10]: 1
4.1. The glass transition stage (from glassy to supercooled-liquid) Values for the glass transition temperature, depending on both the technique used and the heating rate, are summarised in Table 2. The transition temperatures found by ultrasonic echography lies systematically at lower temperatures than those obtained by DSC. A similar trend was already noticed on other glasses [8] due mainly to the fact that for ultrasonic echography, the transition temperatures are clearly defined unlike those obtained by DSC. Note that, nevertheless, during the ultrasonic echography experiment, the temperature is measured above the sample in the oven and a 5 C difference may exist with the sample temperature. 4.2. The supercooled-liquid state At least two ways of studying this stage do exist. The first method is based on the concept of hierarchically
mol ¼ A b
ð4Þ
where A is a constant and b is the so-called correlation factor which can be regarded as a structural parameter characterising the correlation between the different atomic or molecular movements occuring in the glass: when b=0 any movement of a structural unit requires the motion of all the other units (maximum order, perfect correlation), while when b=1 all the movements are independent on each other (the maximum disorder corresponding to a Maxwell model for relaxation, or to a single characteristic time of the classical Debye relaxation process). In oxide glasses, b tends towards values as low as 0.2–0.5 below Tg but gets closer to 1 as the temperature increases in the supercooled-liquid state. Differentiation of Eq. (4) with respect to temperature, recalling that the directly available thermodynamic parameter is the activation enthalpy Ha ¼ @1n1mol , and @ RT
further assuming that Ga and b change little with temperature (which is generally the case above the transition range) [8], one obtains:
Ga ¼ b Ha
ð5Þ
The second method is based on the classical theory of thermally activated flow phenomena, which considers the existence of two independent contributions acting together to overcome the free energy barrier, G0, associated with the flow process. One of these contributions, Ga, has a purely thermal origin and is derived from the thermally activated atomic, or molecular, movements; the other, Wa, is due to the applied stress so that:
G0 ¼ Ga þ Wa
Fig. 4. Change in Young’s modulus during isothermal treatments.
ð6Þ
Following Schoeck [11] who considered that the height of the barrier, G0, to be overwhelmingly of
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elastic origin, G0 is taken to be proportional to the shear modulus and even proportional to Young’s modulus (by considering the classical assumption that Poisson’s ratio does not vary with temperature in the supercooled-liquid state). Other asumptions that can be found in [8] lead to:
Ga ¼
1
Ha T @E 1 E @T
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consistent with both mechanical spectroscopy and stress relaxation methods [8]. The reasons for the difference between the results for the bulk metallic glass are still under study. 4.3. The crystallisation processes
ð7Þ
Results of both the DSC and Young’s moduli analyses reveal the existence of three distinct crystallisation stages. Their onset and their kinetics are now discussed.
A correspondence between these two methods [Eqs. (5) and (7)] lead to the value of the correlation factor, b, as follows:
4.3.1. Change in the crystallised fractions with time In the case of a two phase material, it is possible to link the elastic moduli with the volume fractions of the phases by means of Voigt’s and Reuss’ approximations [13]. The analysis was developed for the shear moduli and gives the boundaries corresponding to the limit cases where the two phases experience the same strain (Voigt) or the same stress (Reuss). Both results are transposable to Young’s moduli when Poisson’s ratios are known. As it is supposed that these latter remain constant during each crystallisation stage (the temperature is kept constant), the expressions can be directly written with Young’s moduli. The fact that crystallised specimens exhibit Poisson’s ratios close to one of the as-cast glass supports this hypothesis (Vaillant [14]). For a volume fraction, X, of crystallised phase, the expressions for Young’s modulus of the material corresponding to Voigt’s and Reuss’ models, EV and ER are:
b¼
1 T @E 1 E @T
ð8Þ
The evaluation of Eq. (8) was performed using the E(T) data of Fig. 3 and two other experiments carried out at 1 and 5 C /min. Results are illustrated in Fig. 5. Values between 0.6 and 0.75 for b are found in a range of validity for T/Tg between 1.04 and 1.12 (so very close to the validity range found by Rouxel [8] for glasses with much larger supercooled-liquid states). This scattering is common for the correlation factor in amorphous solids and a mean value of 0.67 is obtained. Other techniques for measuring include mechanical spectroscopy and stress relaxation experiments. The first method [12] on a Zr–Ti–Cu–Ni–Be glass and a Pd–Ni– Cu–P glass) leads to b-values around 0.4, thus lower from our values. The method we used was already used for window glasses and oxynitride glasses and were very
E V ¼ E G ð1 XÞ þ E C X ER ¼
E C E G E G X þ E C ð1 XÞ
ð9Þ
where EG and EC are respectively Young’s modulus of the glass during the first crystallisation stage (or of the glassy matrix and the previously crystallised crystal supposed to remain unchanged) and of the crystallised phase. EG is thus assumed to be constant during crystallisation though it is likely that the crystallisation of a particular phase affects the composition of the residual glass and thus its properties. It is reciprocally possible, from a measured value of Young’s modulus E, to get bounds for the crystalline phase volume fraction, XV and XR. E EG EC EG EC EG E XR ¼ E ðE G E C Þ XV ¼
Fig. 5. Evolution of the correlation factor with temperature. Three sets of data corresponding to two different linear heatings (1 and 5 C /min) are superimposed. No influence of the heating rate is noticeable.
ð10Þ
At time t=0, X(t)=0 and E=E0=EG. At time t=+1, X(t)=X1, where X1 is the maximum volume fraction of crystallised phase with respect to the experimental duration, to which a value E1 of E is associated. Following Besson [15], it is thus convenient
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to use a normalised crystallised volume fraction x(t), defined as the ratio between X(t) and X1. Eq. (10) write then: X V ðtÞ EðtÞ E0 ¼ XV E1 E0 R X ð t Þ E 1 ðEðtÞ E0 Þ xR ¼ ¼ R X1 EðtÞ ðE1 E0 Þ xV ¼
ð11Þ
With these expressions, one can draw Hill’s bounds for the three crystallisation stages (see Fig. 6) by plotting the normalised crystallised volume fractions with respect to the annealing time. All curves are very close and a mean value will be used for the following of the study. The kinetics of the first crystallization process has the three classical distinct stages: a slow one corre-
sponding to nucleation, a fast one corresponding to the growth of the nuclei and a final and slow one. As far as the other crystallization stages are concerned, the diagrams look similar but rather different from the first one, that is a fast behaviour followed by a slower one. 4.3.2. Crystallisation kinetics The conventional Johnson–Mehl–Avrami–Kolmogorov model is commonly used to describe the crystallisation kinetics of amorphous materials [16]. Assuming a random distribution of the crystallised precipitates, the normalised crystallised volume fraction, x, corresponding to an annealing time t is given by: xðtÞ ¼ 1 exp½ðKtÞn
ð12Þ
Fig. 6. Crystallisation kinetics as calculated with Voigt’s and Reuss’ approximations from E(T) data during isothermal treatments presented in Fig. 4. x(t) stands for the normalised crystallised volume fraction.
V. Keryvin et al. / Intermetallics 10 (2002) 1289–1296
where n is the reaction rate order, or Avrami’s exponent, and K is the overall reaction rate which is assumed to have an Arrhenius’ temperature dependence: KðTÞ ¼ K0 exp
Ea RT
ð13Þ
where Ea is the effective activation energy for the crystallistion process. When crystallisation proceeds by steps, Eq. (12) can be used for the primary crystallisation step [17] but the validity for the two other stages is controversial. Nevertheless, Eq. (12) can be rewritten as: ln½lnð1 xðtÞÞ ¼ nlnt þ nlnK
ð14Þ
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and plots of ln [ln(1x(t))] versus ln t are drawn on Fig. 7 where least-squares fitting lines are superimposed allowing to derive estimations for Avrami’s exponents. Values of 1.93, 0.88 and 0.8 were respectively determined this way for n corresponding to the three crystallisation sequences respectively. Unlike previous results on a very similar glass [17], the linear Johnson– Mehl–Avrami–Kolmogorov model agrees very well with our data. The usual hypotheses for the use of the JMAK model [16] are not known to be verified for bulk metallic glasses, but let us allow ourselves to compare our Avrami’s exponents with the usual physical meanings found for other glasses. Avrami’s exponents range usually in glasses from 1 for surface nucleation to 3 for internal nucleation; thus our first crystallisation could
Fig. 7. Determination of Avrami’s exponent for isothermal treatments. The correlation factor is 0.98. x(t) stands for the normalised crystallised volume fractions and t is time.
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be a mixed surface and internal nucleation (surface nucleation could be triggered by the thin oxide layer) while the two other ones could be a pure surface nucleation (this surface nucleation could this time take place on the surface of the previously formed crystallysed phases). It is known that the only use of linear fittings to analyse phase transformation kinetics through the experimental values of Avrami’s exponent can give misleading interpretations for the transformation mechanisms; therefore, microscopic studies are needed to validate these hypotheses. Note that our Avrami’s exponents differ sensibly from the ones found by Inoue [4] (between 3 and 3.7, indicating a threedimensional homogeneous internal nucleation) for the Zr65Al7.5Cu27.5 glass. Eventually, besides the fact that it is particularly noteworthy difficult to give a physical meaning to the parameters of the JMAK model for bulk metallic glasses, it is known that a metastable phase is observed during the first crystallisation of our glass [18] that transforms later into the Zr2Cu phase. That metastable phase is supposed to be a polymorphic phase and since it is known that the linear form of the JMAK model is not valid for polymorphic transformations [19], the crystallisation issue for our glass, and more generally for bulk metallic glasses, calls for further investigations.
5. Conclusion An original in situ ultrasonic technique was carried out to study thermal stability and crystallisation of a Zr55Cu30Al10Ni5 bulk metallic glass. Besides the very interesting data collected for Young’s moduli between RT and 630 C, this technique allowed us to have some insight into both viscoelastic and crystallisation processes, as evidenced by the comparison with DSC measurements. Concerning the supercooled liquid state, an original correspondence between the theories of hierarchically correlated motion and thermally activated phenonema was used to calculate the correlation factor. However, some differences were found with mechanical spectro-
scopy results. Other comparisons must be made with other techniques such as creep and stress relaxation. Eventually, as far as the crystallisation issue is concerned, three different crystalli-sation stages were evidenced and their kinetics studied. Major differences on the kinetics were reported between stage 1 and stages 2 and 3. Comparisons with the classical JMAK theory made us suppose a mixed surface/internal nucleation for stage 1 and a surface nucleation for both stages 2 and 3. Nevertheless, microscopic studies are needed to have a deeper insight on the crystallisation mechanisms as well as on the crystallised phases.
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