Determination of the pre-exponential factor in the viscosity equation using the Lagrange polynomial and cubic splines

The article studies chalcogenide glasses of the Sb-Ge-Se and P-Se-Te systems to determine the pre-exponential factor η₀ in the viscosity equation. Two mathematical extrapolation methods were employed: Lagrange polynomial interpolation and cubic splines. These methods enabled the extrapolation of the logarithmic viscosity-inverse temperature dependence curve, lg η vs. (1/T), into the low-temperature region where experimental data are unavailable. The results showed that the lg η₀ values obtained using both methods were in close agreement, confirming the reliability of the approaches used. For the Sb-Ge-Se glass system, lg η₀ values ranged from 0.7 to 2.97, while for the P-Se-Te system, they ranged from -0.97 to 3.3. The article also revealed that the pre-exponential factor depends on the nature of the glass and confirmed its relationship with the activation volume Vη, which is defined by the ratio of the activation free energy Eη to the shear modulus G. The findings demonstrate that the variation in η₀ values is due to structural characteristics of the amorphous materials rather than inaccuracies in the extrapolation methods.