AN ANALYSIS OF NON-ISOTHERMAL PRIMARY CRYSTALLIZATION KINETICS OF FE95SI5 AMORPHOUS ALLOY

The paper describes the primary crystallization of metallic Fe95Si5 glass which was studied by differential scanning calorimetry (DSC) with non-isothermal methods. The activation energy of crystal transformation was calculated with the equations proposed by Kissinger, Mahadevan and a modified version of the equation developed by Augis and Bennett. Activation energy was determined at Ea = 242.0 254.2 kJ / mol, subject to the applied method. The Avrami exponent of crystallization in the amorphous phase n was determined in the range of n = 2.40 2.52, depending on the method of calculating the transformation of activation energy.


Introduction
Amorphous alloys, also known as metallic glass, have numerous industrial applications due to their excellent soft magnetic properties. The properties of amorphous alloys continue to be investigated (Li et al. 2008, Sahingoza et al. 2004, nobuyuki et al. 2007.
Thermal treatment and nanocrystallization improve the properties of metallic glass. The crystallization of amorphous alloys can be controlled, which is particularly important consideration in the production of materials with a specific structure. These processes require a thorough understanding of the crystallization kinetics of metallic glass.
The crystallization kinetics of chalcogenide glass can be analyzed by isothermal and non-isothermal methods, and the results can be interpreted with the use of several theoretical models (kiSSinger 1957, ozawa 1970, MatuSita et al. 1979, MatuSita et al. 1980, kong et al. 2011. In recent years, new isoconversional methods have been applied to determine the crystallization parameters of amorphous alloys during non-isothermal heating , anSariniya et al. 2018, Jaafari et al. 2018.
Isothermal analyses involve the JMA equation which is a primary method for determining crystallization parameters. However, non-isothermal techniques have also been used in numerous experiments. Different values of crystallization kinetic parameters were reported in Fe-based amorphous alloys. For example, the estimated values of the Avrami exponent ranged from 1.0 to 4.0 (gibSon et al. 1987, SantoS et al. 2002. The activation energy of the same alloy can also be calculated with the use of different models and equations. The aim of the present study was to determine the activation energy of the primary crystallization process based on the equations proposed by Kissinger and Mahadevan and the modified version of the equation developed by Augis and Bennett. The Avrami exponent of crystallization kinetics n which describes the mechanism of crystalline phase formation was also calculated.

Theory
The analyses of the crystallization kinetics of amorphous alloys generally involve two parameters: activation energy E a and the Avrami exponent of crystallization kinetics n.
Both isothermal and non-isothermal methods can be used in calorimetric measurements. Most methods rely on the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation of isothermal transformation kinetics (Málek 2000(Málek , wang et al. 2014: where: x(t) -volume fraction transformed after time t, n -the Avrami exponent exponent which reflects the nucleation rate and the growth morphology, K -the reaction rate constant.
The temperature dependence of the reaction rate is usually determined with the use of the Arrhenius equation: where: E a -the activation energy for the crystallization reaction, K 0 -the frequency factor, R -the gas constant.
Non-isothermal crystallization is characterized by a constant heating rate. The relationship between sample temperature T and heating rate β can be expressed by the following equation: The activation energy of primary crystallization can be determined using the models developed by Kissinger (kiSSinger 1957), Ozawa (ozawa 1970), Mahadevan (Mahadevan et al. 1986) and Augis-Bennett (augiS et al. 1978). These methods are based on the JMAK theory (Eq. 1) and the logarithmic form of Equation 2. These models account for the fact that the volume of the crystallized fraction at the top of the crystallization peak in DSC is x p =0.63. When the highest rate of transformation is applied at maximum peak approximations, the relevant equations can be interpreted as follows: a) Kissinger model c) Modified version of the Augis and Bennett model where: T p -peak temperature, β=dT/dt -the heating rate.
The partial values of ln(K 0 R/E a ), ln(K 0 E a /R) and ln(K 0 ) in Equations 4, 5 and 6 are constant. From it is possible to derive The value of activation energy E a and pre-exponential factor K 0 of the crystallization process can be derived from the slope and the intercept of the straight line (Equations 4, 5, 6), respectively.
The Avrami exponent n is also an important crystallization parameter, and it can be determined with the use of various methods. In the model developed by Ozawa, time in Equation 1 was replaced by temperature in Equation 3 to produce the following equation: Double logarithmic transformation can be applied to produce the following equation: The values of ln [−ln (1 -x)] are plotted against ln(β) from various DSC thermograms, and the Avrami exponent n is derived from the slope of the straight line (Eq. 8). The Avrami exponent n can also be determined with the following equation (gao et al. 1986(gao et al. , Jakubczyk et al. 2008): where: (dx/dt) p -the maximum crystallization rate.

Experimental
Amorphous samples were obtained by rapid solidification of melts using the melt-spinning method (Fig. 1). The obtained ribbon was 20 mm wide and and 0.03 mm thick. The nominal composition of Fe 95 Si 5 is presented in Figure 2. The crystallization process was investigated by differential scanning calorimetry (DSC) in a nitrogen atmosphere using the Netzsch DSC 204 differential scanning calorimeter. Temperature and energy calibrations were performed based on the melting temperatures and melting enthalpies of high-purity zinc and indium registered in the device. Sample mass in DSC measurements approximated several milligrams. The samples were heated from 340 K to 840 K at different heating rates (β = 5, 10, 20 and 30 K min -1 ).

Results and Discussion
The DSC thermograms for the crystallization of Fe 95 Si 5 at various heating rates are presented in Figure 3. The two crystallization peaks of Fe 95 Si 5 involve two resolved phase transformations. The position of both peaks shifted to higher temperatures with an increase in heating rate. The first peak corresponds to phase formation in α-Fe(Si) (Frączyk 2011). The observed shift of the onset of crystallization T x to higher temperatures is the result of the induction time of the nucleation process. There is a nucleation time during crystallization. When the heating rate increases, the onset of crystallization shifts to higher temperatures. Adam Frączyk,Krzysztof Kuś,Adam Wojtkowiak Fig. 3. DSC curves of Fe 95 Si 5 for several heating rates illustrating primary crystallization (first peak) and secondary crystallization (second peak) processes The activation energy E a of the primary crystallization of Fe 95 Si 5 metallic glass was calculated with the use of the models proposed by Kissinger and Mahadevan and the modified version of the Augis and Bennett model (4-6). For this purpose, the values of ln(β/T p 2 ) vs. 10 3 /T p (Fig. 4), ln(β) vs. 10 3 /T p (Fig. 5) and ln(β/T p 2 ) vs. 10 3 /T p (Fig. 6) were plotted for the amorphous alloy. The activation energy E a of an amorphous alloy can be derived from the slope (-E a /R) of the line. The line of best fit was determined with the least squares method. The arithmetic mean and standard deviation were calculated for activation energies. The results are presented in Table 1. The crystallized fraction x at temperature T was expressed as x(T ) = = Ax(T )/A, where A and Ax represent the total area and the partial area (at generic temperature T ) of the exothermic peak, respectively. The relationship between the crystallized volume fraction and the time of the first exothermic peak of amorphous Fe 95 Si 5 alloy is presented in Figure 7. In Figure 8, the data from Figure 5 were expressed as a function of time t to illustrate the relationship between crystallization rate dx/dt and temperature T.
The Avrami exponent n was calculated by substituting the maximum value of dx/dt into Equation 9 for different heating rates. The primary crystallization parameters are presented in Table 1.

Conclusions
The values of activation energy and the Avrami exponent n, which are associated with the first peak temperature in continuous heating DSC curves of amorphous Fe 95 Si 5 alloy, were estimated with the use of acclaimed methods. The values of Avrami exponent n indicate that during the first stages of the crystallization process a crystal growth controlled respectively by diffusion and by interface takes place.
In order compare the activation energy of different amorphous alloys the same equation or model should be applied.