Diffusion-limited crystal growth in metallic glasses under continuous heating

摘要

Mathematical analysis for diffusion-limited growth of a spherical crystal in an infinite matrix under linear heating conditions has been performed, and the exact and approximated solutions of the problem have been obtained. The approximated expression derived for evolution of the growing crystal radius at constant heating rate q formally coincides with the well-known parabolic law derived for isothermal conditions if the real time is replaced by T-2/(qQ), with Q being the activation energy of diffusion. Despite a relatively large difference between the exact and approximated values of the crystal size, the accuracy of the volume fraction crystallized is within 1. A good agreement of the calculated results with the relevant experimental data for the Fe-B metallic glasses implies the validity of the simple analytical relations derived for description of the diffusion-limited crystal growth in metallic glasses at constant rate heating. (C) 2002 American Institute of Physics. References: 19