The isokinetic behavior in diffusion controlled growth processes

Abstract

The isokinetic behaviour of crystallization processes controlled by diffusion is analysed under both isothermal and continuous cooling/heating conditions. The kinetic function is computed employing an approximate expression for the so called exponential integral. Diffusion controlled 3D growth of homogeneously nucleating crystalline grains is an isokinetic reaction if the nucleation and diffusion activation energies are identical. In the non isokinetic range, the kinetic functions in both continuous heating and isothermal transformations are the same except for a factor which depends on the nucleation and diffusion activation energies ratio. This development is applied to the crystallization of AgGeSe glasses. The primary crystallization kinetic of glasses with compositions (Ge25Se75)100−y Agy (with y = 10, 15, 20 and 25 at. %) was studied in a previous work using differential scanning calorimetry and X-ray diffraction. The analysis is grounded on the Kolmogorov-Johnson-Mehl-Avrami model generalized to account for the compositional changes of the parent phase, responsible for the decreasing of both the nucleation frequency and the growth rate of the primary grains. The kinetic study of the crystallization process from continuous heating calorimetric data has been performed applying the master curve method. The primary crystallization product is the ternary phase γ-Ag8GeSe6. The values of apparent activation energy Ea, obtained are in the range: 2.0 eV/at < Ea < 2.6 eV/at. A model of diffusion controlled 3D growth with decreasing homogeneous nucleation and soft impingement has been developed that reproduces the rate of transformation obtained experimentally for the studied alloys.