A non-linear diffusion of amorphous Pt studied using a variable-order fractional model

A predictive understanding of the phase transition process from amorphous to crystalline in as-deposited films is critical for electronics and optoelectronic device applications. However, anomalous diffusion is frequently observed during the phase transition, making the prediction of device properties challenging. In this study, the diffusion procedure of amorphous Pt models, which was accompanied by the crystallization process, was investigated using a variable-order fractional (VOF) model. The competition between atom rearrangement and migration resulted in a non-linear diffusion. The diffusion procedure was divided into three stages based on variable-order exponent β(t) from the VOF model: amorphous-keeping, rapid-conversion, and slow-conversion; the diffusion coefficient K demonstrated the effects of temperature, component, and substrate on the diffusion properties. The VOF model captured features of the time-dependent diffusion of phase transition with a few parameters, allowing the quantitative comparison among distinct diffusion modes, and inspired the analysis of the complex non-linear diffusion procedure.