The article presents investigations of Ti40Cu36Zr10Pd14 bulk metallic glass crystallization process heated with the rates of 10, 60, 100 and 140 K/min. High heating rates experiments were performed in a new type of differential scanning calorimeter equipped with a fast responding thermal sensor. Phase composition and microstructure were studied with x-ray diffraction and transmission electron microscopy. The observed crystallization proceeded in two separate steps. Applied high rates of heating/cooling resulted in the crystallization of only one CuTi phase, replacing typical multi-phase crystallization. The microstructure after crystallization was polycrystalline with some amount of amorphous phase retained. Kinetic parameters were determined with the use of the Kissinger and Friedman iso-conversional analysis and Matusita–Sakka iso-kinetic model. The kinetic analysis supplies results concerning autocatalytically activated mechanism of primary crystallization with decreasing activation energy and small density of quenched-in nuclei, in good agreement with previous structural investigations. The mechanism of secondary crystallization required dense nuclei site, increasing activation energy and large nucleation frequency. The amorphous phase of Ti40Cu36Zr10Pd14 BMG revealed high thermal stability against crystallization. Application of high heating rates in DSC experiments might be useful for the determination of mechanism and kinetic parameters in investigations of metallic glasses crystallization, giving reasonable results.
Introduction
Metallic glasses remain a current subject of the investigations in material sciences. Especially bulk metallic glasses, requiring relatively low critical cooling rates to form amorphous phase, are promising materials for some applications (Ref 1). A lot of attention has been given to finding amorphous equivalents of Al- and Ti-based light alloys. The Ti-based crystalline alloys are characterized by high specific strength and low density. Another important property of both crystalline and amorphous Ti alloys is their biocompatibility which enables their application as different types of implants (Ref 2-4). The mechanical properties of BMGs may be better adapted to parameters required for human implants than those of crystalline alloys (Ref 5).
The Ti40Zr10Cu40−xPd10+x amorphous alloys were identified as bio-acceptable metallic glasses (Ref 1, 5, 6). The Pd compositions of 10, 14 and 20 at.% were first invented by the Inoue group and later widely studied (Ref 7-9). The BMGs reveal quite wide supercooled liquid range ΔT, between glass transition Tg and primary crystallization temperature Tx1, and good glass-forming ability (GFA). Most of the published investigations concentrated on the alloys with 14 at.% of Pd, because of high glass-forming ability and large critical diameter available (Ref 5). Further development of TiZrCuPd alloys focused on attempts to increase the critical diameter of bulk glassy samples by small additions of the other element, preserving their biocompatibility. Small amounts of Sn (Ref 5, 7) and Nb were investigated (Ref 10). The small Nb content successfully improved the strength of the alloys but also promoted the precipitation of the composition-dependent Pd3Ti phase.
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From the point of view of application, the main weakness of BMGs as a constructive material remains poor deformability at room temperature in the range of heterogeneous deformation. However, formability may be good in the supercooled liquid range, in which metallic glasses may deform by homogenous flow mechanism (Ref 11). The precise knowledge of crystallization mechanism of particular BMG, including nucleation and growth, is important for the perspective of applications.
The crystallization mechanism of TiZrCuPd BMGs with 10-20 at.% Pd is quite complex, including at least two stages, primary and secondary crystallizations. After completed crystallization, the phases were identified as Cu8Zr3 and Cu4Ti3 (Ref 5) or Cu8Zr3, CuTi and PdTi2 (Ref 7). However, the phases identification based on XRD is not easy due to large number of lines in the patterns and a low symmetry of the phases. Small additions of Sn and Nb further modify the crystallization mechanism (Ref 5, 7, 10). Moreover, the issue of microstructure and phase composition after primary crystallization remains unclear. It was shown in Ref 12, in that the primary crystallization of the Ti40Zr10Cu40Pd10 glassy alloy proceeded by diffusion of Ti and Cu between amorphous and crystalline phases and the formation of 1-2 nm clusters growing into 5-nm crystallites, identified as Cu8Zr3, Cu2Ti and Cu3Pd phases. After the primary crystallization, a large part of the amorphous phase may be retained, even after the relatively long annealing time of 600 s at 750 K temperature (Ref 13). High-resolution microscopy (HREM) shows that the amorphous phase separates into two slightly different compositions (Ref 13) which should influence the primary crystallization process as well. Thermo-mechanical analysis, conducted with small constant loads and at 5 K/min heating rate, confirmed that due to the large part of the retained amorphous phase, deformation by the homogenous flow also overlapped the temperature range of primary crystallization (Ref 13).
The process of amorphous alloys crystallization is usually studied with differential scanning calorimetry (DSC), in continuous heating regime with relatively high rates β, from 20 to 40 K/min. Slower heating rates may cause preliminary nano-crystallization in the supercooled liquid temperature range. Phase composition observed after DSC cycle may also be influenced by diffusion processes which undergo during relatively slow cooling of the calorimeter. The DSC experiments enable the determination of kinetic parameters, commonly the activation energy Ea for nucleation and crystallization. The activation energy for primary crystallization of the Ti40Zr10Cu36Pd14 BMG was determined to be 287.6 kJ/mol (Ref 7).
New types of DSC calorimeters, equipped with fast responding thermal sensors enabling much faster heating and cooling, are now available. Such equipment was applied to study the crystallization process of the Ti40Cu36Zr10Pd14 BMG with DSC measurements performed at high rates of heating and cooling, 60, 100 and 140 K/min. Also the x-ray phase analysis (XRD) and transmission electron microscopy (TEM) were used in order to compare the results with the mechanism of crystallization deduced from the experiment performed with relatively small heating rate 10 K/min and suggested by results presented in the papers (Ref 12-14).
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Simple methods of kinetic parameters determination widely used in the literature concerning metallic glasses were applied for the interpretation of DSC results. The results of the activation energy Ea were calculated by the Kissinger and Friedman methods. Also, the non-iso-conversional kinetic method of Matusita–Sakka, frequently used in case of metallic glasses, was applied, in spite of the fact that the method was invented for very slow processes of crystallization proceeding in Li2O·2SiO2 glasses (Ref 15, 16). The intention of the authors was to verify whether the models might give reasonable results in the case of high rates of heating used in part of the DSC experiments.
Materials and Methods
Master alloy of nominal composition Ti40Cu36Zr10Pd14 was prepared by cold crucible levitation melting under a high-purity argon atmosphere (Ref 17). The glass samples were prepared by cooper mold injection casting method. They were 3 mm in diameter and 40 mm long. All samples were amorphous, as confirmed by XRD, TEM and HREM.
The transition of glass into crystalline morphology was studied in DSC calorimeters. The DSC Netzsch 214 Polyma was used for the experiments with the heating and cooling rates β 60, 100 and 140 K/min. The Netzsch DSC 214 has a new construction and is equipped with the fast responding thermal sensor enabling registration of the heat flux with high heating rates up to the temperature of 900 K. The DSC experiment with β 10 K/min was performed using another calorimeter, Netzsch DSC F1 Pegasus. The calorimeters were calibrated according to the Netzsch calibration procedure. The temperature calibration was performed through the melting of the 4 or 5 commonly used standards, In, Sn, Zn, Al and Ag for each heating rate separately in case of the DSC F1 Pegasus. Cell constants were determined from the Zn heat of fusion, calculated from each heating rate. Samples with mass of about 30 mg were used in the form of disks, 3 mm in diameter and about 2 mm in height. The Cu pans were used to improve the thermal contact of the samples with the calorimeter and as standards. The measurements were taken in an atmosphere of high-purity argon.
The microstructure and phase composition after crystallization were determined with x-ray diffraction (XRD) and transmission electron microscopy (TEM). For the XRD measurements, the D2 Phaser (Brukers) with X Flash detector and Cu Kα radiation was used. TEM experiments were performed with the electron microscope TECNAI (FEI, G2 FEG/200 kV) equipped with the EDAX Phoenix system for microanalysis.
Results
Results of DSC Experiments
The DSC curves of the BMG crystallized with heating rates of 60, 100 and 140 K/min are presented in Fig. 1 and with low heating rate 10 K/min in Fig. 2. The characteristic temperatures and enthalpies determined from the DSC are presented in Table 1. In the case of high heating rates, the crystallization was manifested by two exothermic effects preceded by an endothermic one resulting from glass transition and heat capacity increase in the supercooled liquid range, ΔT. Since crystallization is a diffusion-controlled process, peak temperatures Tp increased together with the increase in the heating rates. In effect, the second thermal effect could not be completely registered for the rate of 140 K/min, approaching the temperature limit of the Netzsch DSC 214 Polyma. Kinetic models requiring complete peak shape could not be applied for this peak. It may be noticed that the first exothermic peak related to primary crystallization at the high-temperature side reveals broadening, which may be related to a prolonged, relatively slow crystallization process or/end large thermal lag, while the secondary crystallization peak is much narrower and symmetrical. The last observation suggests a single crystallization event. The enthalpy increase in the primary crystallization (Table 1) brought about by the rise of the heating rate from 100 to 140 K/min is very small, not exceeding 1%, while the difference in enthalpy between the crystallization proceeding with the rates 60 and 100 K/min is much larger, about 10% (Table 1). The different sensitivity of the first and the second steps of crystallization for increasing heating rates suggests the different character of the respective crystallization mechanisms.
Fig. 1
DSC curves for the Ti40Cu36Zr10Pd14 BMG, applied heating rates β: 60, 100 and 140 K/min. The DSC Netzsch 214 Polyma
Fig. 2
DSC curves for the Ti40Cu36Zr10Pd14 BMG, applied low heating rate 10 K/min. DSC Netzsch F1 Pegasus
Table 1
Characteristic temperatures of glass transition (Tg), crystallization (Tx), peak temperature (Tp), supercooled liquid range (ΔT), and enthalpies (ΔH) determined from the DSC curves
Heating rates, K/min
Tg, K
Tx1, K
ΔT, K
Tp1, K
ΔH1, J/g
Tx2, K
Tp2, K
ΔH2, J/g
10
674.0
696.0
22
706.0
17.0
802.0
811.0
75.0
60
710.0
732.0
22
739.0
25.0
813.0
821
75.0
100
721.0
742.0
21
748.0
27.0
824.0
828.0
87.0
140
725.0
749.0
24
757.0
28.0
829.0
834.0
…
Indexes 1 and 2 denote the first and the second exothermic peaks related to the primary and secondary crystallizations of the BMG.
×
×
The DSC curve of the BMG crystallization process with the heating rate 10 K/min is shown in Fig. 2. It is visible that except two thermal effects mentioned previously, an additional one is present at 772 K temperature. It is slightly lower than the start temperature of the secondary crystallization Tx2. Results presented in Table 1 show that in spite of the wide range of heating rates the supercooled liquid temperature range ΔT remains nearly constant, the enthalpy of primary crystallization is similar for high heating rates but lower for β 10 K/min, while enthalpy of the secondary crystallization established from the second exothermic effect remains stable for rates 10-60 K/min. The additional peak observed for β 10 K/min decays in the DSC curves for rates 20 and 30 K/min, not presented here.
The Structure and Phase Composition After Crystallization
The XRD investigations of phase composition of the samples crystallized in DSC with high rates of heating 60, 100 and 140 K/min proved the great influence of heating rates on the samples’ phase composition (Fig. 3a). As opposed to the samples crystallized with low rate (20 K/min) (Fig. 3b), all the diffraction peaks of samples crystallized at high heating rates could be identified as resulting from the presence of a single CuTi phase (Fig. 3a), which is tetragonal with lattice parameters a = 3.115 and c = 5.947 (Ref 18). Except the crystalline phase, large intensities observed at about 2Θ-40° and increasing with the heating rate are due to some amount of amorphous phase retained after crystallization. It is visible in Fig. 3(b) that crystallization with the rate of β—20 K/min leads to the appearance of many other phases apart from the CuTi phase. They were identified as CuTi2, Cu3Ti2, Cu8Zr3 (orthorhombic, a = 7.869, b = 8.147, c = 9.977), PdTi, PdZr, Pd3Zr (hexagonal, a = 5.611, c = 9.232) and Ti2Zr. Also, some evidence for the presence of ternary CuZrTi phase (tetragonal, a = 3.097, c = 11.036) exists. The phases Cu8Zr3 and CuTi are especially well documented in the literature (Ref 5, 7).
Fig. 3
XRD pattern after complete crystallization in DSC, heated up to 900 K, at rate β (a) 20 K/min, (b) 60, 100 and 140 K/min
×
The TEM microstructures of the samples after crystallization, heated with the rates of 60 and 140 K/min, are shown in Fig. 4. The morphology was very similar, except that lighter crystals and smaller average dimensions of the grains were noticed in the case of the sample heated with β 140 K/min. The electron diffraction patterns for both samples are shown in Fig. 5. They reveal strongly polycrystalline character, while the first rings of intensity, very intensive and widened, suggest some amount of amorphous phase retained after crystallization. In both cases, all calculated dhkl distances between crystalline planes fit the CuTi phase (Fig. 5). No other phases were identified in TEM investigations.
Fig. 4
TEM microstructures of samples crystallized in DSC at rates: 60 K/min (a) bright-field (BF) technique, (b) dark-field (DF) technique; 140 K/min (c) (BF), (d) (DF)
Fig. 5
Comparison of the selected area diffraction patterns of the samples crystallized in DSC at rates (a) 60 K/min, (b) 140 K/min. All dhkl lattice confirms the appearance of CuTi phase
×
×
HREM microstructures shown in Fig. 6(a) and (b) present crystalline particles in the amorphous matrix identified by the fast Fourier transform (FFT) as CuTi phase, always observed with common orientation [100] or [221] (Fig. 6c, d, e and f).
Fig. 6
HREM images, fast Fourier transforms FFT and corresponding IFFT images of the samples crystallized in DSC at rates: 60 K/min (a) image, (b) FFT, (c) IFFT from the selected area; 140 K/min (d) image, (e) FFT, (f) IFFT from the selected area
×
The example of the microstructure of the individual CuTi crystalline particle is shown in Fig. 7(a), together with the corresponding SADP (Fig. 7b) with the [100] zone axis of the lattice, revealing a monocrystalline type of electron diffraction.
Fig. 7
TEM microstructure of sample crystallized at rate β 60 K/min, micrographs: (a) bright-field image (BF), (b) selected area diffraction (SADP) pattern from the dark particle, CuTi phase, zone axis [100]
×
The XRD and TEM results proved a large difference between the crystallization mechanisms of the Ti40Cu36Zr10Pd14 BMG with the heating rates β from 60 to 140 K/min, compared with the commonly used rate β 20 K/min. The crystallization process proceeding with high heating rates proved to be much simpler, reduced only to the single, CuTi phase, replacing multiphase crystallization at lower heating rates β 10-30 K/min, commonly presented in the literature (Ref 5, 7). At the same time, a noticeable amount of the amorphous phase was retained. The main difference between the microstructures of the samples crystallized with the heating rates 60 and 140 K/min was larger dispersion of the crystalline particles in the case of the higher heating rate.
Kinetic Parameters of Crystallization
Activation energy Ea is one of the basic kinetic parameters useful for the description of metallic glasses crystallization. The value of Ea may depend on the transformed fraction, which means that the crystallization mechanism represented by respective peaks in the DSC curve undergoes modification. Determination of Ea also enables establishing another valuable parameter, which is nucleation frequency Znf (Ref 19, 20). It is assumed that nucleation and growth processes participate in both steps of crystallization of the experimentally detected CuTi phase. The activation energy Ea was determined with the Kissinger and Friedman methods.
The Kissinger method (Ref 21) takes into account only peak temperature Tp and heating rate β. The results for the primary and secondary crystallizations, for the heating rates 60, 100 and 140 K/min, are presented in the first row of Table 2. The activation energy Ea of the primary crystallization was determined to be 218 kJ/mol. For the secondary crystallization, Ea was slightly larger, 352 kJ/mol. It was interesting to verify whether the Ea value may be consistently determined using a small heating rate such as 10 K/min, as well (Fig. 2; Table 1). The ln(β/Tp2) = f(Tp−1) relation, shown in Fig. 7, used for the determination of Ea in Kissinger method remains linear, giving possibility for the determination of activation energy for all, small and large heating rates with a good fitting parameter of 0.995 or better (Fig. 8; Table 2). The Ea values calculated for all heating rates are larger by 50 kJ/mol than the values calculated for only high heating rates in the case of the primary crystallization peak. However, the difference is only 8 kJ/mol for the secondary crystallization peak (Table 2). This suggests a difference in the crystallization mechanism of the primary crystallization proceeding with the small and large β. The nucleation frequency Znf was calculated with the use of the formula:
where β is the heating rate and R gas constant (Ref 19, 20).
Table 2
Activation energy (Ea) at the peak temperature (Tp) and nucleation frequency (Znf) in dependence on the included heating rates (β)—Kissinger method
Heating rates β
Ea, kJ/mol
Ea, kJ/mol
Znf—nucleation frequency
Znf—nucleation frequency
K/min
Peak 1
Peak 2
Peak 1
Peak 2
60, 100, 140
217.9
352.2
1.28exp(14)
1.71 exp(21)
10, 60, 100, 140
266.9
360.4
4.10exp(17)
5.78 exp(21)
Fig. 8
Determination of the activation energy for crystallization according to Kissinger relation (Ref 21) for primary (a) and secondary crystallizations (b)
×
Table 2 shows that the nucleation frequency of the primary crystallization is smaller than of the secondary one and clearly increases from 1.3exp(14) to 4.1exp(17) when small heating rate was included. The nucleation frequency of the secondary crystallization proved to be not sensible to heating rate remaining in the range of (1.7-5.8)exp(21).
The Friedman iso-conversional analysis enables the determination of the relation between transformed fraction dx and activation energy Ea, from equation (Ref 22):
where dx is the transformed fraction, t time, T temperature, R gas constant and A constant.
Also, in this case the calculations of Ea were done separately for heating rates β 60, 100 and 140 K/min and including the β 10 K/min. The results for primary and secondary crystallizations are presented in Tables 3 and 4 and in Fig. 9 and 10, while the example of the respective DSC curves and integrated area fractions with dx specific for Tp marked by the arrows for the β 60 K/min between 33 and 26% are presented in Fig. 11.
Table 3
Numerical values of Ea achieved from Friedman analysis for the heating rates (β) 60, 100 and 140 K/min
Partial area
Activation energy Ea, kJ/mol
Primary crystallization
Secondary crystallization
0.020
248.98 ± 1.17
287.54 ± 25.33
0.050
241.34 ± 6.64
317.47 ± 21.78
0.100
226.88 ± 15.67
362.36 ± 29.31
0.200
202.18 ± 24.82
465.22 ± 86.75
0.300
182.51 ± 25.10
481.46 ± 43.10
0.400
170.31 ± 20.82
386.26 ± 14.84
0.500
163.57 ± 14.71
301.50 ± 3.33
0.600
159.69 ± 7.78
244.04 ± 22.04
0.700
155.14 ± 0.88
214.41 ± 35.50
0.800
152.51 ± 8.19
209.08 ± 47.15
0.900
167.29 ± 3.43
230.63 ± 63.84
0.950
209.71 ± 7.29
270.42 ± 69.91
0.980
251.51 ± 37.08
356.92 ± 45.21
Table 4
Numerical values of Ea achieved from Friedman analysis for the heating rates (β) 10, 60, 100 and 140 K/min
Partial area
Activation energy Ea kJ/mol
Primary crystallization
Secondary crystallization
0.020
389.81 ± 29.95
368.02 ± 19.36
0.050
369.69 ± 28.08
364.77 ± 12.56
0.100
344.95 ± 26.55
360.04 ± 6.84
0.200
309.54 ± 24.77
372.95 ± 28.55
0.300
282.66 ± 23.10
371.55 ± 28.35
0.400
261.48 ± 21.04
340.25 ± 12.48
0.500
243.56 ± 18.60
307.52 ± 1.82
0.600
228.38 ± 16.32
283.59 ± 12.53
0.700
213.01 ± 14.11
269.57 ± 19.07
0.800
198.63 ± 11.50
266.26 ± 24.00
0.900
185.93 ± 2.55
282.25 ± 33.53
0.950
177.41 ± 14.92
310.19 ± 39.48
0.980
190.14 ± 30.85
341.38 ± 24.55
Fig. 9
Friedman analysis for heating rates β 60-140 K/min: the relation between transformation rate dx/dt and reversed temperature (T − 1), revealing dependence of activation energy Ea upon transformed fraction (Ref 22)
Fig. 10
Friedman analysis: relation between activation energy Ea and transformed fraction dx calculated for heating rates β 10-140 and 60-140 K/min (Ref 19); (a) primary crystallization DSC peak, (b) secondary crystallization DSC peak. The values of the Ea determined by Kissinger method marked by arrows
Fig. 11
Relative integrals from the first (a) and the second (b) crystallization peak in the DSC curves, with β = 60 K/min. The fracture crystallized at peak temperature Tp marked by arrow
×
×
×
As results from Friedman method, the activation energy Ea of primary and secondary crystallizations reveals some dependence on the degree of conversion dx (Tables 3, 4; Fig. 9, 10), which means a complex reaction path. The values of Ea revealed the same dependence on β as achieved by the Kissinger method when low heating rate β 10 K/min was included in the calculations, the values of Ea increased (Fig. 10). However, for the primary crystallization (Fig. 10a) the Friedman analysis revealed the Ea decrease at two different ranges in both methods of Ea calculations. In the first one, the decrease was more rapid, up to the transformed fraction of about 30% (Fig. 11a). In the second range, at larger dx, Ea decreases very slowly or, in the calculations including only high heating rates, the Ea remains nearly constant (Fig. 10a). Consequently, it may be deduced that the first range of transformation predominantly related to nucleation has the character of an autocatalytically activated reaction. At larger transformed fractions dx, the nucleation frequency decreases slowly or stabilizes.
A different Ea dependence results from Friedman analysis of the secondary crystallization presented in Fig. 10(b). As demonstrated, the Ea increases up to dx specific for the Tp, and decreases at higher transformed fractions dx. The behavior is more pronounced for the crystallization with high heating rates. When low β 10 K/min was considered, the calculated Ea was smaller and its increase more moderate. All this suggests much larger Ea required for the crystallization of only single CuTi phase in comparison with the multi-phase process proceeding with small heating rates.
The respective Ea values determined by the Kissinger method at Tp for the primary crystallization (Table 2), marked in Fig. 10(a), revealed values to be in good agreement with those determined from the Friedman analysis, taking into account the respective range of the crystallized fraction. In case of the secondary crystallization, the Kissinger Ea values are underestimated if calculated with high heating rates, but fit very well to the Ea determined from the Friedman analysis calculated taking into account all the heating rates (Table 2; Fig. 10b).
The Matusita–Sakka (Ref 15, 16) method was applied to both steps of crystallization. There are two parameters to be determined: Avrami parameter n and dimensional parameter m, both related by the equation:
enables the determination the m parameter (Ref 15, 16). The way in which the parameter n was determined is shown in Fig. 12(a), while the example of the m parameter determination for the heating rate 60 K/min is shown in Fig. 12(b).
Fig. 12
Determination of n and m parameters for the Matusita–Sakka kinetic model; (a) determination of n parameter as function of heating rate β and temperature T, (b) determination of m parameter for heating rate β 60 K/min. P1—primary crystallization and P2—secondary crystallization peak in the DSC curve
×
The n values determined on the basis of the model are presented in Table 5, for both the primary and secondary crystallizations. As the values vary with temperature, the average values nav 4.8 for the primary crystallization and 3.8 for the secondary crystallization were calculated. According to the model, the dimensional parameter m may take values n − 1 or m = n. The calculated m parameter together with the interpretation is presented in Table 6 for each heating rate and all crystallization steps. It is visible that the n parameter determined for the first peak of crystallization and heating rate β 60 K/min is too large because the m parameter exceeds 3D. In all other cases, n and m parameters remain reasonable. The crystallizing particles are always three-dimensional. Also, the dense nuclei sites should not appear in the primary crystallization. In the case of the second step of crystallization, the model suggests that the dense nuclei sites are present provided the rates are the highest: 100 and 140 K/min (Ref 15, 16). The results seem to be in a good qualitative agreement with the nucleation frequency Znf, calculated based on the Kissinger activation energy Ea (Table 2), which is much smaller for the primary than for the secondary crystallization. It should be remembered that the values of Znf are averaged over all heating rates, while the m parameter of the Matusita-Sakka model is determined for each heating rate separately.
Table 5
Values of (n) parameter determined based on the model of Matusita–Sakka (Ref 15, 16)
Peak 1
Peak 2
T, K
n
nav
T, K
n
nav
743
7.9
4.8
823
6
3.8
748
5.4
828
4.8
753
3.4
833
2.8
785
2.3
838
1.8
nav Average value.
Table 6
Values of (m) parameter, dimensions of growing particles (D) and interpretation of nucleation mechanism determined based on model of Matusita–Sakka (Ref 15, 16)
β, K/min
Peak 1
Peak 2
n = m + 1 or m = n
m
D
m
D
Peak 1
Peak 2
60
3.7
3D?
3.1
3D
m + 1=4.7 = n
m + 1=4.1 ≈ n
…
No dense nuclei site
100
3.0
3D
2.8
3D
n > m + 1 = 4.0
m = 3.8 = n
No dense nuclei site
Dense nuclei site
140
2.6
3D
2.7
3D
n > m + 1 = 3.6
m = 3.7 = n
No dense nuclei site
Dense nuclei site
β Heating rate.
Discussion
According to the results from the DSC experiments, low heating rate 10 K/min of the Ti40Cu36Zr10Pd14 BMG did not lead to nanocrystallization observed in the supercooled liquid temperature range (Fig. 2). The XRD and TEM results proved that the crystallization process performed with high heating rates from 60 to 140 K/min was simplified. The multi-phase crystallization was replaced by the crystallization of single-phase CuTi. This phase was also suggested previously in case of the CuTiZrPd BMGs crystallization (Ref 7). The result proves that, in thermodynamic terms, the CuTi phase reveals the largest driving force for the nucleation and growth for the investigated composition range of the amorphous alloys. The refinement of the polycrystalline microstructure shown by TEM also revealed its dependence on heating rate. The problem of the selection of crystallizing phases in the case of the metallic glasses is not easy to explain and must be directed to both thermodynamics and kinetics. Because of selected CuTi crystallization at the high heating rates, only some suggestions may be given. Ti and Cu atoms are the main components of the alloy, statistically most probable near neighbors in disordered amorphous matrix which reduces the required diffusion distance. There is no solubility of Cu in Ti, while other components reveal solubility in one of the components, which increases tendency for the intermetallic Cu–Ti phase formation. Also, in many amorphous compositions Cu atoms reveal strong tendency for the clustering in liquid phase. As was shown in case of the FINMET alloy (Ref 26), such clusters are the place for the crystalline phase nucleation. Together with the surrounding Ti atoms, such clusters may play the role of the nuclei in the amorphous matrix. As is visible from the experiments, the nucleation and growth kinetics are going to be decisive at high heating rates.
The activation energy of crystallization and growth Ea, determined with the use of different methods, concerns only CuTi phase which transformed because of the decrease in amorphous phase thermal stability at high heating rates. The Ea is usually determined with Kissinger method (Ref 7, 8, 20, 23). It was revealed that the straight line obtained for the Ea evaluation refers not only to the high heating rates but also to heating rates from 10 to 140 K/min. The values of Ea were calculated both for high heating rates separately and including the heating rate of 10 K/min. Table 2 and Fig. 10(a) show that the Ea determined by Kissinger method is significantly larger for the primary crystallization performed with 10 K/min rate. This means higher activation energy of nucleation when the multi-phase crystallization with the low heating rate proceeds in the primary crystallization range. This also suggests a relation with the nucleation process occurring with much higher frequency Znf, of multi-phase nucleation. It is not the case when the secondary crystallization is considered, since no significant differences of Ea and Znf in the calculation by Kissinger method were noticed (Table 2; Fig. 10b).
Essentially, the Kissinger method supplies the Ea values for the fraction transformed at peak temperature Tp, which slightly depends on higher heating rates. This means that Ea values determined by the method are averaged for the transformed fractions between 20 and 40% (Fig. 11). The Friedman method of Ea determination reveals the dependence of Ea on the transformed fraction. Figure 10 shows that Ea of both primary and secondary crystallizations exhibits some dependence on crystallized fraction, which suggests that complicated, autocatalytic mechanism of crystallization is involved (Ref 22). The Ea of the primary crystallization decreases with the transformed fraction, which also indicates the decrease in the nucleation frequency Znf. Such a behavior fits in well with the crystallization mechanism including nuclei quenched-in from the liquid phase, followed by the moderate growth.
Another situation concerns secondary crystallization, during which the activation energy increases until the transformed fraction achieves the value corresponding to the peak temperature Tp, and later decreases. Such behavior is especially pronounced when only the CuTi phase appears (Fig. 11b), suggesting that the Ea required for the multi-phase crystallization at the secondary crystallization is much smaller than for the single-phase crystallization. The increase in Ea revealed the increase in the nucleation frequency, in the temperature range up to Tp. This also suggests formation of new nuclei and growth by the mechanism of diffusion in the amorphous phase, retained after primary crystallization. As the amount of amorphous phase decreases, the process requires the increase in Ea to be continued. Similar behavior of Ea was also observed in the kinetic analysis presented in Ref 23.
It should be noticed that the values of activation energy determined by Kissinger method fit very well with the values calculated with the Friedman method, taken as the average values for the properly estimated fractions crystallized at Tp (Fig. 11a and b). Moreover, the value of Ea 288 kJ/mol, reported in Ref 6 for the primary crystallization at moderate rates of heating, agrees well with the present results (Table 2; Fig. 11a).
The Matusita–Sakka method was invented for DSC kinetics investigations for very low heating rates, for the chalcogenide glasses (Ref 15, 16). The method is iso-kinetic and involves double-logarithmic method to calculate the parameters. In spite of many doubts concerning the applicability and the sensitivity of the method (Ref 24), it is quite often used for the studies of BMG’s crystallization (Ref 23, 25). As was shown above, the m and n parameters are related to each other. The parameters achieved for the high heating rates used in our DSC experiments are in the range of expectations, except for the primary crystallization with β 60 K/min. The conclusions, which can be drawn from the parameters, summarized in Table 6, concern 3D growth of particles, which agrees well with the bulk character of the samples. The amorphous matrix does not contain a dense network of nuclei at the start of the crystallization and in the range of primary crystallization particles grow in three dimensions from very small sizes (Table 6). This agrees well with decrease in the Ea calculated by Friedman method and with the relatively small Znf values for primary crystallization determined by the Kissinger method (Table 2; Fig. 10a). All this suggests the predominant participation of the quenched-in nuclei at that primary stage of crystallization.
The secondary crystallization at the heating rates of 100 and 140 K/min, based on the parameters calculated from the model of Matusita-Sakka, proceeds by growth from small dimensions and from the existing dense lattice of nuclei which does not exist in the range of first DSC peak (Table 6) as results from the n parameter in Matusita–Sakka equation. It suggests that in the range of secondary crystallization, except some amount of the crystalline particles and nuclei supplied by the primary crystallization, also a new nucleation and growth process should proceed, including the new nuclei formation by the diffusion processes. This is in accordance with the Ea evaluation determined by Kissinger method.
All the conclusions from the kinetic parameters look quite reasonable when compared with the results of structural investigations presented in Ref 12-14 and in this paper. According to them, the amorphous phase decomposed into two different compositions in the range of primary crystallization. Relatively small amounts of clusters and nanoparticles crystallized in that temperature range, while a large quantity of the amorphous phase was retained. Even after short-time isothermal annealing at temperatures between the first and the second crystallization peaks in the DSC curves, the amorphous phase partially remained in the structure (Ref 12-14). The TEM observations presented above showed that the secondary crystallization led to the polycrystalline microstructure containing 3D crystals and some amount of the amorphous phase. The summary of the crystallization mechanism, detected from the determination of kinetic parameters and structural investigations, is presented in Table 7.
Table 7
Summary of results from analysis of kinetic parameters: heating rates (β), activation energy (Ea), nucleation frequency (Znf), peak temperature (Tp)
β, K/min
Friedman/Kissinger—activation energy/reaction
Primary crystallization
Secondary crystallization
60-140
Decreasing with transformed fraction
Increasing with transformed fraction till Tp
Ea ≈ 218
Ea ≈ 352
Small nucleation frequency
Large nucleation frequency
Znf (1.3exp(14));
Znf (1.7exp(21));
Complex reaction autocatalytic
Average Ea and Znf not sensitive for low
Increase in Ea and Znf for low β included
β included
β, K/min
Matusita-Sakka—nucleation and growth
Primary crystallization
Secondary crystallization
60
…
…
No dense nuclei site
3D growth from small dimensions
100
No dense nuclei site
(quenched in)
3D growth from small dimensions
Dense nuclei site
3D growth from small dimensions
140
Conclusions
1.
Application of the high heating rates, between 60 and 140 K/min in DSC experiments proved to be useful for the determination of crystallization mechanism and the kinetic parameters in CuZrTiPd metallic glass investigations.
2.
The XRD and TEM investigations showed that the crystallization process in Ti40Cu36Zr10Pd14 BMG with heating/cooling rates between 60 and 140 K/min led to replacing complicated multi-phase crystallization with single CuTi phase.
3.
The method of Kissinger of activation energy and nucleation frequency determination for nucleation and growth of the crystalline phase revealed larger Ea and Znf required for the secondary crystallization than for the primary one in the case of the high heating rates used. The method of Friedman revealed decrease in the activation energy with increased crystallized fraction for the primary crystallization and increase in Ea with transformed fraction in the secondary crystallization.
4.
The common Ea values calculated for small and large heating rates suggest that slower, multi-phase crystallization requires larger Ea for the primary crystallization and similar to these for high heating rates for the secondary crystallization.
5.
The results of Matusita–Sakka method suggest lack of the dense nuclei site in primary crystallization and dense nuclei site in the secondary one as well as 3D growth of the particles.
6.
The conclusions of the kinetic analysis remain in a good agreement with the structural investigations.
Acknowledgments
The work was financed by Grant No. 2013/11/B/ST8/04286 and partially by Grant NN507303940 of the Polish National Scientific Center. The studies were performed in the Accredited Testing Laboratories at the Institute of Metallurgy and Materials Science of the Polish Academy of Sciences.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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