Relook on fitting of viscosity with undercooling of glassy liquids

Abstract

The present approach is on the modification of viscosity fitting of undercooled liquid as a function of undercooling. The method consists of finding analytical solution of three arbitrary constants of the Vogel-Fulcher-Tamman (VFT) equation by choosing three viscosity data at three critical temperatures for an undercooled liquid. Three critical temperatures are liquidus temperature (T l), crystallization onset temperature (T x) and glass transition temperature (T g). The experimental viscosity data at or very near to these three critical temperatures (depending on the availability in literature) have been utilized to achieve the analytical solution. The analytical solution of VFT equation is further examined by selecting the experimental data points away from the critical temperatures in order to check their (T l , T x and T g) significance towards the solution. Total absolute error (TAE) and total squared error (TSE) values obtained from the present method with respect to the experimental viscosity data in the temperature range between T l and T g are very much comparable and in most of the cases lower than that of existing 'best-fit' cited in the literature for a number of glassy alloys. Moreover, this method interestingly enables us to find the fragility parameters for a number of glassy alloys and convincingly explain their true glass forming abilities (GFA).

Critical evaluation of glass forming ability criteria

“…However, it could not decide GFA for a number of alloys as well. Recently, the present authors 47 have proposed a new route of estimation of viscosity of a glassy alloy or compound according to VFT equation. 47 Equation ( 22) contains three arbitrary constants (g 0 , D and T 0 ).…”

“…Recently, the present authors 47 have proposed a new route of estimation of viscosity of a glassy alloy or compound according to VFT equation. 47 Equation ( 22) contains three arbitrary constants (g 0 , D and T 0 ). Thus, three sets of viscosity-temperature data (viscosity data at three different temperatures) can analytically solve equation ( 22) for its three arbitrary constants.…”

“…Afterwards, the D values, where the complete data are available, are examined with respect to Z max , separately. According to the work by the authors, 47 the solution with the three data points of equation ( 22) is far more accurate. Thus, available D values in the literature as well as refined D values obtained using the analytical solution approach of VFT equation are used for examining fitting with Z max .…”

“…Category A consists of criteria depending on critical temperatures of glass forming alloys, category B shows the criteria depending on the thermodynamic parameters calculated based on Miedema's approach, [22][23][24][25][26][27][28] category C enlists the GFA criteria based on internal atomic structure and atomic arrangement of constituting elements in a glass forming alloy [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] and the category D suggests the criteria depending on the kinetic properties of the glassy materials. [45][46][47][48][49][50][51][52][53][54] Only those GFA criteria are listed where one criterion has been applied on various bulk metallic glass (BMG) forming systems and has been proven for its compatibility. If a criterion is proposed and proven only on the basis of one single alloy system with varying compositions or is proven on only a particular order of alloys (say binary alloys), then that GFA criterion has not been considered for this present comparison.…”

“…The present paper carefully examines the utility of different criteria from all the above four categories while predicting GFA of a number of glassy alloys, oxides and organic glasses with an aim to find out universality of performance by GFA criteria. Recently, a new technique has been proposed by the current authors 47 for the evaluation of viscosity in the form of Vogel-Fulcher-Tamman (VFT) equation in the temperature range of T l to T g . In the present work, a modified fragility parameter of the VFT equation is considered to understand the GFA.…”