Use of gumbel distribution functions for the fitting and deconvolution of differential thermal analysis thermograms
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Abstract
We present a proposal for the empirical fit of curves corresponding to phase transitions in measurements obtained using Differential Thermal Analysis (DTA). The family of functions for fit is known as the Gumbel functions. These functions have asymmetrical characteristics that resemble those of typical DTA peaks, different from the symmetrical functions usually used for the adjustment of peaks (such as Gaussian or Lorentzian). The adjustment process was performed with DTA measurements carried out with samples of InxMn(1-x)Sb compounds, which show the presence of two phases, InSb and MnSb. In these phases, depending on the value of x, phase transitions are observed that may or may not be simultaneous in temperature. When working with individual phase transition curves, Gumbel functions fits the curves with linear correlation coefficients (R2) higher than 0.98 –for both fusion and solidification transitions– which demonstrates the experimental data’s proper fit. This type of fit’s value is demonstrated by its use in a system where there are simultaneous phase transitions in temperature. In this case it is shown how, with the Gumbel functions, it is possible to separate these superimposed signals. These independent signals may provide access to information such as the phase transition temperature and the enthalpy of transformation for each of the compounds present in the mixture, something presently difficult to attain in simultaneous DTA signals.
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