Abstract
The Vogel-Fulcher-Tammann (VFT) equation has been used extensively in the analysis of the experimental data of temperature dependence of the viscosity or of the relaxation time in various types of supercooled liquids including metallic glass forming materials. In this article, it is shown that our model of viscosity, the Bond Strength—Coordination Number Fluctuation (BSCNF) model, can be used as an alternative model for the VFT equation. Using the BSCNF model, it was found that when the normalized bond strength and coordination number fluctuations of the structural units are equal, the viscosity behaviors described by both become identical. From this finding, an analytical expression that connects the parameters of the BSCNF model to the ideal glass transition temperature T0 of the VFT equation is obtained. The physical picture of the Kohlrausch-Williams-Watts relaxation function in the glass forming liquids is also discussed in terms of the cooperativity of the structural units that form the melt. An example of the application of the model is shown for metallic glass forming liquids.
Highlights
In order to check the exact fitting between the VFT equation and the Bond Strength—Coordination Number Fluctuation (BSCNF) model, in this analysis, we used the collection of fitting parameters by the VFT equation given in reference [4], where the values of BVFT, T0, Tg, and the fragility index m for various oxide glass forming materials are provided
All these results indicate that the BSCNF model could be an alternative to the VFT equation which has been widely used in the analysis of the temperature dependence of the viscosity
It was shown that in the case where the magnitudes of energy and coordination number fluctuations of the structural units are equal, the viscosity behavior described by the BSCNF model corresponds perfectly to that described by the VFT equation
Summary
The Vogel-Fulcher-Tammann (VFT) equation [1,2,3] is one of the most commonly used expressions for the analysis of the temperature dependence of viscosity [4,5,6,7,8,9], relaxation time [5,8,10,11], diffusion coefficient [5,6,7,9], and electrical conductivity [5,6,7], etc. One of the parameters of the VFT equation, the so-called ideal glass transition temperature T0 which indicates the dynamical divergence in the temperature dependence of the viscosity or relaxation time, is not observed in real systems [18]. Another point is that the values of the parameters of the VFT equation, obtained from the data analysis, have not been fully exploited. The correlation between the fragility index of various glass forming liquids and the stretched exponent of the Kohlrausch-Williams-Watts (KWW) relaxation function [36,37], is discussed in terms of the cooperativity which is defined by the BSCNF model
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