**4. Conclusion**

Based on the analysis of thermo-analytical data, the very obvious and straight forward question is: which is better, iso-conversional or iso-kinetic?

Iso-conversional methods provide activation energy values, *E* as a function of conversion,α*.*  The iso-kinetic methods, on the other hand, are used considering the crystallization mechanism to be the same throughout the entire conversion (crystallization) and give single constant value of activation energy. For metallic glasses, the thermally activated phase transformations are more physical than chemical. In fact, crystallization is a complex process involving nucleation and growth and on rigorous grounds, it can not be considered to be a single-step process. The iso-kinetic analysis always leads to a single activation energy (rather say, apparent activation energy) giving an overall picture of the crystallization process. However, the difficulty (and hence uncertainty) in choosing the proper reaction model persists in isokinetic analysis. Therefore, the isoconversional methods are definitely

Nano-structures can be synthesized by controlled crystallization of metallic glasses also

The selected area diffraction (SAD) pattern shows characteristic rings with discontinuity.

Fig. 11. Nano-phases present in Ti20Zr20Cu60 metallic glass after annealing at 673 K for

question is: which is better, iso-conversional or iso-kinetic?

Based on the analysis of thermo-analytical data, the very obvious and straight forward

Iso-conversional methods provide activation energy values, *E* as a function of conversion,

The iso-kinetic methods, on the other hand, are used considering the crystallization mechanism to be the same throughout the entire conversion (crystallization) and give single constant value of activation energy. For metallic glasses, the thermally activated phase transformations are more physical than chemical. In fact, crystallization is a complex process involving nucleation and growth and on rigorous grounds, it can not be considered to be a single-step process. The iso-kinetic analysis always leads to a single activation energy (rather say, apparent activation energy) giving an overall picture of the crystallization process. However, the difficulty (and hence uncertainty) in choosing the proper reaction model persists in isokinetic analysis. Therefore, the isoconversional methods are definitely

The plot of α\* and β\* gives the true values of *E* and *A*.

The phases can also be idetified as seen from fig.11.

known as de-vitrification method.

4 hours

**4. Conclusion** 

superior to the isokinetic methods as far as the determination of *E* is concerned (Pratap et al, 2007). Nonetheless, accurate determination of E is not the only issue in the kinetic analysis of crystallization process in metallic glasses. The micro-structural evolution during the nonisothermal heating of the metallic glasses is also important. For the determination of the dimensionality of the growth and the grain size, one needs to know a precise reaction model that closely follows the crystallization process. A reaction model independently proposed by John-Mehl- Avrami-Kolmogorov (JMAK) is found to be the most suitable for describing the nucleation and growth process during the non- isothermal crystallization of metallic glasses. This model does help to determine of the kinetic parameters, like the dimensionality of growth (apart from *E* and *A*). The model-free isoconversional methods are definitely superior to the isokinetic methods for the accurate determination of kinetic parameters like E and A. However, the knowledge of accurate E and A is not sufficient for the detailed investigations of the dimensionality of the growth and the grain size using thermal analysis. A precise reaction model accounting for the phase transformations during the crystallization process is a prerequisite for deriving such micro-structural information. This could be a valid proposition if it is explicitly related to the phase transformations involving significant chemical changes. One can find numerous publications where JMAK formalism has been found to be the most appropriate for the description of kinetics of nucleation and growth processes in metallic glasses. Therefore, in our opinion, isokinetic methods (despite its limited applicability) are important and useful for the analysis of non-isothermal crystallization data. So, as far as the study of thermally activated phase transformation in metallic glasses is concerned, both the types of methods are complementary and provide not only useful data, but also pave way into the insight of the crystallization process.
