**3.3.3 Amorphous thin films**

The crystallization kinetics in Ni50.54Ti49.46 film was studied by Liu et al. using differeantial scanning calorimetry through non-isothermal and isothermal techniques. Ni50.54Ti49.46 thin films were prepared by a mixed NiTi target using DC magnetron sputtering. The NiTi thin film was deposited on Si wafer and the substrate was unheated to achieve the amorphous structure. For non-isothermal analyses, a set of DSC scans was recorded at heating rates ranging from 5 to 50 °C/min. For isothermal analyses, the amorphous samples were first heated to a fixed temperature with 250 °C/min (between 793 and 823 K), and then held for a certain period of time until fully crystalline state was achieved.

Non-isothermal crystallization kinetic investigation of Se58Ge42-xPbx (*x* = 9, 12) alloy studied by Deepika et al. is given here as an example of the crystallization kinetics in amorphous alloys. In their study, glassy alloys of Se58Ge33Pb9 and Se58Ge30Pb12 were prepared by meltquenching technique and after realizing thermal analyses, the samples were annealed at 633 and 643 K, which lie between the first and second crystallization, respectively. The activation energy of crystallization for the first and second crystallization stages of Se58Ge33Pb9 and Se58Ge30Pb12 glassy systems was derived using the approximation methods developed by the Kissinger (Equation 58), Matusita (Equation 59), Augis and Bennett (Equation 60). The values of activation energy of crystallization of as-prepared and annealed

samples using different theoretical models are given in Table 3 (Deepika et al., 2009).

Activation energy of crystallization (kJ/mol) Se58Ge33Pb9 Se58Ge30Pb12 Before annealing After annealing Before annealing After annealing

I peak II peak I peak II peak Kissinger Model 167.06 ± 0.88 165.29 ± 0.45 144.97 ± 0.88 171.46 ± 1.19 146.15 ± 2.03 139.71 ± 1.13

Method 155.65 ± 1.37 168.20 ± 2.27 66.35 ± 0.77 195.66 ± 0.53 186.43 ± 3.12 134.22 ± 2.94 Matusita Model 330.34 ± 7.46 316.28 ± 2.0 237.58 ± 1.33 384.52 ± 3.79 412.39 ± 2.61 195.60 ± 1.96

From Table 3, it is observed that activation energy of crystallization decreases after annealing. This means that group of atoms in the glassy state requires less amount of energy to jump to crystalline state hence, making the sample less stable and more prone to crystallization. This is again an indication of the fact that annealing of glass leads it to a quicker crystallization. The crystallization mechanism of crystals decreases to one dimension from two and three dimensions after annealing, suggesting a decrease from bulk

It is also observed that activation energies of amorphous alloys calculated by means of the different theoretical models differ substantially from each other. This difference in the activation energy as calculated with the different models may be attributed to the different

The crystallization kinetics in Ni50.54Ti49.46 film was studied by Liu et al. using differeantial scanning calorimetry through non-isothermal and isothermal techniques. Ni50.54Ti49.46 thin films were prepared by a mixed NiTi target using DC magnetron sputtering. The NiTi thin film was deposited on Si wafer and the substrate was unheated to achieve the amorphous structure. For non-isothermal analyses, a set of DSC scans was recorded at heating rates ranging from 5 to 50 °C/min. For isothermal analyses, the amorphous samples were first heated to a fixed temperature with 250 °C/min (between 793 and 823 K), and then held for a

Table 3. Activation energy of crystallization of as-prepared and annealed samples of Se58Ge33Pb9 and Se58Ge30Pb12 glassy systems using different theoritical models

nucleation to surface nucleation in annealed samples.

certain period of time until fully crystalline state was achieved.

approximations used in the models.

**3.3.3 Amorphous thin films** 

**3.3.2 Amorphous alloys** 

Models applied

Augis–Bennett

(Deepika et al., 2009)

The activation energy for crystallization was determined to be 411 and 315 kJ/mol by Kissinger (Equation 58) and Augis & Bennett (Equation 60) method, respectively (Fig. 28a-b) (Liu & Duh, 2007). Comparing with this study, previous works on near equiatomic NiTi films showed that the activation energy was 370–419 kJ/mol (Chen & Wu 1999; Seeger & Ryder, 1994).

Fig. 28. Plot of the (a) Kissinger and (b) Augis & Bennett equations for the crystallization in Ni50.54Ti49.46 thin films (Liu & Duh, 2007)

The isothermal crystallization kinetics of amorphous materials is described by the Johnson– Mehl–Avrami (JMA) equation. The Avrami exponent n for different temperature ranges from 2.63 to 3.12 between 793 and 823 K (Fig. 29a), which indicates that the isothermal annealing was governed by diffusion-controlled three-dimensional growth for Ni50.54Ti49.46

Fig. 29. Plots of the (a) Avrami and (b) Arrhenius equations for the isothermal crystallization of Ni50.54Ti49.46 thin films(Liu & Duh, 2007)

Crystallization Kinetics of Amorphous Materials 157

the slopes of these lines the activation energies were determined as 373, 448 and 435 kJ/mol for *T*g, *T*x, *T*p, respectively. The apparent activation energy *E*x deduced from the Kissinger equation for onset crystallization is higher than that for crystallization peak, meaning that

The bright field TEM image and a corresponding selected area diffraction pattern (SADP) of the bulk specimen after annealing at 840 K for 900 seconds are shown in Fig. 31. The bright field image shows crystalline nanoparticles embedded in the amorphous matrix. The SADP consists of several ring patterns superimposed on a diffuse halo patterns, also indicating a mixture of nanocrystalline and residual amorphous phase. All the continuous rings can be analyzed into the ordered bcc structure phase with lattice parameter little larger than that of

Fig. 31. Bright-field TEM image (a) and selected-are eletron diffraction pattern, (b) of the Ni45Ti23Zr15Si5Pd12 bulk amourphus alloy annealed for 900 seconds at 840K (Qin, 2004)

In conclusion, crystallization of an amorphous material is a complex phenomenon involving nucleation and growth processes and it can be investigated by taking into account the structure and the kinetics of the crystallization reaction. Crystallization kinetics is crucial since it studies the effect of nucleation and growth rate of the resulting crystalline phase.

**4. Conclusion** 

nucleation process is more difficult than growth (Qin, 2004).

NiTi, which is in agreement with the realized XRD results (Qin, 2004).

thin films. The *E*A value was calculated from the Arrhenius equation and activation energy for crystallization was determined as 424 kJ/mol (Fig. 29b). This value is very similar to that from non-isothermal method as determined by the Kissinger analysis (411 kJ/mol). It isdemonstrated that the crystallization on both non-isothermal and isothermal methods induces a similar phase transformation mechanism (Liu & Duh, 2007).

#### **3.3.4 Amorphous nanomaterials**

The nanocrystallization kinetics of Ni45Ti23Zr15Si5Pd12 alloy has been investigated using differential scanning calorimetry by means of non-isothermal and isothermal techiques and the products of crystallization have been analyzed by transmission electron microscopy and X-ray diffraction. The bulk amorphous alloy has been prepared by copper mold casting. In the non-isothermal experiments, a set of DSC scans were obtained at a heating rate ranging from 10 to 40 K/min. For the isothermal analysis, the amorphous samples were first heated to a fixed temperature between 820 and 835 K at a rate of 200 K/min, then maintained for a certain period of time until the completion of exothermic process (Qin, 2004).

By using the values of glass transition, *T*g, crystallization onset, *T*x, and crystallization peak, *T*p, temperatures a Kissinger plot yields approximate straight lines as shown in Fig. 30. From

Fig. 30. Kissinger plots of the Ni45Ti23Zr15Si5Pd12 bulk amourphus alloy (Qin, 2004)

thin films. The *E*A value was calculated from the Arrhenius equation and activation energy for crystallization was determined as 424 kJ/mol (Fig. 29b). This value is very similar to that from non-isothermal method as determined by the Kissinger analysis (411 kJ/mol). It isdemonstrated that the crystallization on both non-isothermal and isothermal methods

The nanocrystallization kinetics of Ni45Ti23Zr15Si5Pd12 alloy has been investigated using differential scanning calorimetry by means of non-isothermal and isothermal techiques and the products of crystallization have been analyzed by transmission electron microscopy and X-ray diffraction. The bulk amorphous alloy has been prepared by copper mold casting. In the non-isothermal experiments, a set of DSC scans were obtained at a heating rate ranging from 10 to 40 K/min. For the isothermal analysis, the amorphous samples were first heated to a fixed temperature between 820 and 835 K at a rate of 200 K/min, then maintained for a

By using the values of glass transition, *T*g, crystallization onset, *T*x, and crystallization peak, *T*p, temperatures a Kissinger plot yields approximate straight lines as shown in Fig. 30. From

induces a similar phase transformation mechanism (Liu & Duh, 2007).

certain period of time until the completion of exothermic process (Qin, 2004).

Fig. 30. Kissinger plots of the Ni45Ti23Zr15Si5Pd12 bulk amourphus alloy (Qin, 2004)

**3.3.4 Amorphous nanomaterials** 

the slopes of these lines the activation energies were determined as 373, 448 and 435 kJ/mol for *T*g, *T*x, *T*p, respectively. The apparent activation energy *E*x deduced from the Kissinger equation for onset crystallization is higher than that for crystallization peak, meaning that nucleation process is more difficult than growth (Qin, 2004).

The bright field TEM image and a corresponding selected area diffraction pattern (SADP) of the bulk specimen after annealing at 840 K for 900 seconds are shown in Fig. 31. The bright field image shows crystalline nanoparticles embedded in the amorphous matrix. The SADP consists of several ring patterns superimposed on a diffuse halo patterns, also indicating a mixture of nanocrystalline and residual amorphous phase. All the continuous rings can be analyzed into the ordered bcc structure phase with lattice parameter little larger than that of NiTi, which is in agreement with the realized XRD results (Qin, 2004).

Fig. 31. Bright-field TEM image (a) and selected-are eletron diffraction pattern, (b) of the Ni45Ti23Zr15Si5Pd12 bulk amourphus alloy annealed for 900 seconds at 840K (Qin, 2004)
