Materials Science and Engineering A304–306 (2001) 357–361
Kinetics of crystallization of a ternary titanium based amorphous alloy Arun Pratap a,∗ , K.G. Raval b , A.M. Awasthi c a
Applied Physics Department, Faculty of Technology and Engineering, MS University of Baroda, Vadodara 390 001, India b Electronics Department, Narmada College of Science and Commerce, Zadeshwar, Bharuch 392011, India c Inter-University Consortium for DAE Facilities, Khandwa Road, Indore 452 017, India
Abstract Temperature-modulated differential scanning calorimetry (DSC) has been used to study the crystallization kinetics of Ti50 Cu20 Ni30 metallic glass. The method of Matusita and Sakka for the kinetic study of crystallization seems to be still applicable despite the temperature modulation on four various linear heating rates (5, 10, 15 and 20◦ C/min) as it utilizes fractional crystallization at various temperatures of the crystallization curve in a continuous temperature domain. The modified Kissinger equation, on the other hand, underestimates the activation energy of crystallization as it incorporates particular discrete temperature points, i.e. peak crystallization temperatures at different heating rates. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Crystallization; Ternary titanium based amorphous alloy
1. Introduction Titanium based alloys are one of the important engineering materials. Among them, Ti–Ni alloys are excellent shape memory alloys. The unique shape memory effect exhibited by these alloys is caused by a reversible thermoelastic martensitic transformation. Cu can be substituted upto 20 at.% for Ni and these Ti50 Ni50−x Cux (x = 0–20) alloys show the shape memory effect [1,2]. Owing to the special characteristics of amorphous phase which are not obtained for crystalline alloys, a number of Ti-based alloys have been reported to be amorphized by melt spinning [3]. The study of crystallization of amorphous alloys has been a subject of lot of interest to estimate the supercooled region and the stability of glassy phase required to be known from their application viewpoint. Nickel based systems viz. Zr–Al–Ni [4] and Ln–Al–Ni [5] amorphous alloys exhibit a wide supercooled liquid region before crystallization. Cu50 Ti50 [6] glass has been earlier crystallized and its crystallization kinetics study prompted us to take up the present study in which Cu has been replaced by Nickel forming the ternary system namely Ti50 Cu20 Ni30 . Differential scanning calorimeter (DSC) is an extensively used analytical tool for studying the kinetics of chemical reactions [7,8] and the crystallization of glasses [9–11]. Recently, Reading et al. [12], in conjunction with TA Instru∗ Corresponding author. E-mail address:
[email protected] (A. Pratap).
ments, have extended the conventional DSC technique to permit a small sinusoidal modulation of temperature superimposed on the linearly programmed temperature changes that are used in the conventional DSC. The simultaneous exposure of the sample to these two different heating rates, provides both good resolution and sensitivity in the same experiment. Owing to the stimulation created by recently reported results on few amorphous metallic alloys [13,14], the authors have made an attempt to explore the possibility of studying the kinetics of crystallization of Ti50 Cu20 Ni30 glassy system using the existing equations of Matusita and Sakka [16] and the modified Kissinger equation [17] extensively used in normal DSC to the case of modulated DSC (MDSC).
2. Experimental The specimens of Ti50 Cu20 Ni30 ternary glass alloy have been prepared by single roller melt spinning technique in argon atmosphere at Institute of Materials Research, Sendai (Japan). The amorphous nature of the ribbons is ensured by X-ray diffraction (XRD) and transmission election microscopy (TEM) [18]. The crystallization kinetics of this glassy alloy is studied using DSC 2910 (TA Instruments Inc. USA) system in modulated DSC mode. The samples were heated with various heating rates with sinusoidal temperature modulation to study non-isothermal kinetics. The crystallized volume
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fraction at various temperatures in thermograms taken at different heating rates are utilized to study the growth dynamics during recrystallization assuming that the phase transformations are diffusion controlled processes.
3. Results and discussion Fig. 1 shows a typical thermogram of ‘total’ heat flow of Ti50 Cu20 Ni30 at a linear heating rate of 10◦ C/min with a temperature modulation of ±3◦ C in modulated DSC mode taken under nitrogen flow at 45 cc/min. The peak crystallization temperature occurs at 753.51 K. Similar curves are obtained at three other heating rates. From the following equation suggested [16] for nonisothermal crystallization, the activation energy for crystallization Ec can be evaluated. ln[−ln(1 − x)] = −n ln(α) − 1.052
mEc + const. RT
(1)
where x is the fractional crystallization at any temperature T and α is heating rate. The thermogram of the sample in normal DSC mode at the same heating rate of 10◦ C/min under the same flow rate of nitrogen is shown in Fig. 2. It is clear from the two figures that measurement of weak transitions such as the glass transition, Tg is difficult by conventional DSC (Fig. 2). But, the same transition temperature is clearly observed (T g = 674.13 K) in Fig. 1 in modulated DSC mode. MDSC eliminates these problems by providing a high instantaneous heating rate and by separating the baseline effects from heat capacity measurement. There is shift in baseline before and after crystallization because the thermal properties of the
low temperature form (i.e. before crystallization) and high temperature (i.e. after crystallization) are different. So, the common tangent has been used as prescribed [19] to find out the area under the curve. For the evaluation of the order parameter n, ln[−ln(1−x)] was plotted in Fig. 3 as a function of lnα. The value of n derived from the plot at 750 K comes out to be 2.9, whereas the n value from the line at 756 K comes out to be 2.5. The parameter n characterizing the mechanism of nucleation and growth is known [15] to have far from a single constant value. Rather, this parameter is supposed to show a functional dependence of strongly decreasing character from 4 to 1 with increasing degree of crystallinity. In the present study, as we go from the plot at 750 to that at 756 K, we are going towards higher crystallinity and growth being diffusion limited, the value of n decreases from 2.9 to 2.5. Since no particular heat treatment was given to nucleate the samples before thermal analysis, the dimensionality of growth m is taken to be equal to (n − 1) [16]. So, in present case, the growth is assumed to be twodimensional. Furuya et al. [20] have studied the microstructures observed by TEM in the melt-spun Ti50 Ni35 Cu15 alloy aged at 973 K for 230 h. In the as-spun specimen only needle-like martensitic twins are observed in the matrix, however, a very fine precipitate of Cu-rich compound and recrystallized grains were observed with increasing aging time. The aging of the amorphous melt-spun ribbons at high temperature being a thermal annealing process is similar to developing crystallites by continuous heating. However, it is not possible to draw any information regarding the dimensionality of growth during recrystallization from the TEM micrograph of Furuya et al.
Fig. 1. A typical thermogram of total heat flow at a heating rate of 10◦ C/min ± 3◦ C in MDSC mode.
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Fig. 2. Normal DSC thermogram showing the recrystallization of Ti50 Cu20 Ni30 at a heating rate of 10◦ C/min.
In order to characterize the microstructural changes with increasing temperature, SEM (Leo, Cambridge, 440i) with EDAX from Oxford instruments was used to study the sample after recrystallization. No prominent crystallites were observed in the micrograph. However, in order to characterize the phases formed, analytical electron microscopy based on energy dispersive X-ray spectroscopic analysis (EDS) was performed. EDS scan of the whole surface of the specimen gives an average composition of this alloy as 51.34 at.% Ti, 29.32 at.% Ni and 19.34 at.% Cu. This value is close to the nominal composition, Ti50 Cu20 Ni30 in the prepared alloy which reflects simultaneous precipitation of the crystallites of the entire system in one step.
Fig. 3. ln[−ln(1 − x)] as a function of lnα showing straight line plots for T1 = 750 K (n = 2.9) and T2 = 756 K (n = 2.5).
Based on the thermograms in Figs. 1 and 2 and EDS analysis, it is found that this amorphous alloy undergoes sequential of structural changes of structural relaxation, followed by glass transition, supercooled liquid and then crystallization. Crystallization of this glassy alloy takes place through a single-stage exothermic reaction leading to the simultaneous precipitation of more than two kinds of intermetallic compound. There is a wide supercooled region with ∆T = (T p − T g ) value being 79.38 K. The general tendency [21] of the amorphous alloy exhibiting a wide supercooled liquid region to crystallize only through a single-stage exothermic reaction is also satisfied with the present glassy system. From the slope of the linear part of ln[−ln(1 − x)] versus (1/T) data (Fig. 4) mEc was calculated using Eq. (1). It may be noted that this plot based on Eq. (1) is linear only for the region in which the value of x is away from 1 because Eq. (1) is derived assuming x to be away from 1 by Matusita and Sakka [16]. Despite the fact that a sinusoidal temperature is modulated on linear heating, reasonably consistent values of Ec are obtained. This may be due to the fact that overall temperature is considered in deriving Ec taking constant value of heating rate (Fig. 4.) The Ec values at various heating rates are tabulated in Table 1. For the evaluation of activation energy of crystallization Ec the modified Kissinger equation [22] is used independently and it is given by the following expression ! mEc αn + lnK (2) =− ln 2 RTp Tp where K is constant and the shift in peak crystallization
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in modulated DSC. Though linear fitting has been attempted between ln(α n /Tp2 ) and (l/T) in Fig. 5, non-linearity enters which is shown by the dotted curve in Fig. 5. In fact, the temperature change in MDSC follows the following equation T (t) = T0 + αt + AT sin(ωt)
(3)
where AT = amplitude of temperature modulation (±◦ C). Its values for different linear heating rates are listed in Table 1, ω = 2π/P the modulation frequency (s−1 ), P = period (s) (60 s in present case) and the measured heating rate (dT/dt) is (α + ωAT cos(ωt)).
4. Conclusion
Fig. 4. ln[−ln(1 − x)] as a function of 1/T showing curvature towards x → 1.
Table 1 Activation energy values at various heating rates From ln[−ln(1 − x)] vs. 1/T data Heating rate with modulation amplitude
1.052 mEc (kJ/mol)
Ec (kJ/mol)
5◦ C/min ± 2.5◦ C 10◦ C/min ± 3.0◦ C 15◦ C/min ± 4.0◦ C 20◦ C/min ± 5.0◦ C
2617.65 3561.42 2932.94 3324.00
1246.5 1695.9 1396.6 1582.9
In using modulated DSC, it is clear that the heating rate is not constant due to modulation and hence the normal equations used for constant heating rates may not be strictly applicable. However, one would expect that Eq. (1) which uses large temperature domain for analysis, is still applicable in the case of MDSC since the average heating rate is considered to be constant. Modified Kissinger equation given by Eq. (2), is based on the shift of peak crystallization temperature with heating rate. This expression utilizes discrete temperature, i.e. particular temperature points instead of a domain. Due to non-linear heating profile in the modulated DSC mode, the peak-shift with heating rate does not follow linear trend. This non-linearity is shown by dotted curve in the same figure.
Acknowledgements temperature Tp with heating rate α is used to determine Ec . mEc value derived by using Eq. (2) is 1089.84 kJ/mol which is much lower than the values obtained using Eq. (1) shown in Table 1. The reason for this anomaly is due to the fact that various heating rates α used in expression (2) are not linear
The authors are extremely thankful to Prof. T. Masumoto, Institute for Materials Research, Sendai (Japan), for very kindly supplying the above samples and to Dr. P. M. Raole of Institute for Plasma Research, Gandhinagar (India) for carrying out the SEM investigations. References
Fig. 5. ln(α n /Tp2 ) as a function of l/T showing linear fit alongwith deviation of experimental points from linearity by dotted line.
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