Kinetics of transformation with nucleation and growth mechanism: Diffusion-controlled reactions

Abstract

Kinetics of phase transformations controlled by the diffusion of solute atoms has been studied by using a newly developed method based on probability theory. It is demonstrated that an exact solution considering the redistribution of the solute atoms can be achieved for a homogeneous one-dimensional system with all nuclei simultaneously generated at the beginning of the transformation. If the growth rate of the individual grains is not strongly correlated and obeys the square-root rule up to the very late stage, the equation describing the rate of the transformation as a function of time can be derived. The effect of the overlapping diffusion zones is discussed by numerically solving the diffusion function for the model systems. It can be concluded that the ''soft impingement,'' which is frequently argued in the works on the diffusion-controlled reaction, plays a role only in the final stage of the transformation and generally cannot cause bending of the curve in the Avrami-type plots.

Growth kinetics and crystallographic properties of polysilicon thin films formed by aluminium-induced crystallization

“…The driving force of the AIC process is still under discussion [22][23][24][25]. It should be mentioned that (re)crystallization and layer exchange were observed in various metal-semiconductor [20,26] systems and even if the Si supply is already completely or partially crystalline.…”

Analysis of soft impingement in nonisothermal precipitation

“…At sufficiently high undercooling or supersaturation, nucleation often saturates at a very early stage of continuous reactions 1 so that an assumption of site saturation in diffusion-controlled transformations is physically reasonable. 19 For site saturation, all the nuclei exist at the beginning of the transformation. For the nonisothermal case, it can be given as 14…”

“…(7) equal to Eq. (19) at the beginning of the soft impingement (i.e., T = T 1 ), C can be derived as 2[1 -(r z /r f ) d ] (see Fig. 2 for r f ).…”

Synthesis of normal and flattened rhombic dodecahedral Ag2S particles

“…Therefore, the growing stage might be more important in governing the final morphologies of the nanocrystals through a balance between the kinetic and thermodynamic growth regimes. 14,15 This understanding of the formation mechanism has been successfully used as a guideline for the preparation of those morphologically different materials mentioned above. However, to date, there are few reports on the synthesis of regularly polyhedral nanocrystals with low symmetry crystal structures due to the lack of precise calculation in terms of the reticular density and surface energy of a specific crystalline surface because of their relatively complex crystal structure.…”