Abstract
This paper describes a simple form, the theory to determine the crystallization fraction during the phase transformation of a solid, at a constant heating rate, from data obtained by impedance spectroscopy, where the change of the applied alternating voltage and measured current are proportional to the microstructural changes at the sample, corresponding to the volume fraction of a series layer model of two phases. To determine the volume fraction of each phase present in the sample, electrical data are obtained: conductivity and permittivity at DC, which are modeled by an electrical circuit composed by 2-RC, taking into that the permittivity and the occupied volume correspond to the filling fraction of each phase. By Cathodic Ersion or Sputtering, samples were obtained in film form of about 500 in thickness, composed of an alloy of Sb2Te3, in amorphous phase. To ensure the existence of the phase transformation in the sample, phase transition tests are performed by changes in: Reflection Optics, Electrical Resistivity and X-Ray Diffraction, showing clearly the presence of such a transformation. In the final part of this work, it completely shows the experimental results, giving a clear and precise idea of the kinetics of phase transformation of Sb2Te3 alloy, by impedance spectroscopy technique, which proves to be a simple and practical calculation tool.
Highlights
It is observed that any substance or material element when subjected to changes in temperature or pressure, is obtained different states or phases of the same material with the same chemical composition, called “Aggregate states of matter”
For isothermal processes when plotting In[In(1 − x)] versus Int is obtained n, another option to calculate the kinetic exponent of the system are the contributions made by Borchardt [8] and Pilotan [9], which involve differentiation with respect to time in Equation (4), later determined by Augis and Bennett [10], which are not discussed in this work, but worth mentioning as an alternative form
Changes in the optical reflection of a sample are clearly observed in the representative graph of Figure 7, where in an optical reflection behavior typical low, caused by the presence of the initial amorphous phase, which is maintained until 70 ̊C, subsequently microstructural changes occur due to oxide present in the material and y and around 80 ̊C a sudden increase is generated in the optical reflection of the material, produced by the transition to the crystalline phase of the specimen
Summary
The volume fraction of phase transformation (x), may be calculated by a different thermal history using experimental techniques, such as: DSC (Differential scanning calorimetry), DTA (Differential thermal Analysis), electrical resistivity, optical properties (reflection and transmission), hardness measurements, X-Ray Diffraction. EN y EG, are energy nucleation and energy growth respectively, k B is the Boltzmann constant and T is the absolute temperature, substituting these values in Equation (1) and integrating, we obtain: k This is the basic Equation for calculating the transformed volume fraction, redefining constants; we obtain the general relation for isothermal transformations proposed by Avrami. The increase in the use of different techniques helped simplify and obtain useful data with the aid of thermo-analytical methods simple These methods are certainly useful tools, as long as aptly used in the analysis of experimental data, for this reason large number of mathematical calculations have been proposed based on transformation kinetics theory and totally different assumptions. For isothermal processes when plotting In[In(1 − x)] versus Int is obtained n, another option to calculate the kinetic exponent of the system are the contributions made by Borchardt [8] and Pilotan [9], which involve differentiation with respect to time in Equation (4), later determined by Augis and Bennett [10], which are not discussed in this work, but worth mentioning as an alternative form
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