Perturbation Analysis of Amorphous Alloy Formation

Abstract

A moving boundary problem is formulated for heat and mass transfer in the solidification of glassy alloys. A similarity transformation is applied. The nonlinear system is linearized and a perturbation analysis is applied to evaluate the solution. Effects of the Fourier and Stefan numbers are obtained. This permits a closer examination of the effects of the surface conditions on the boundary layer and transition zone. A correlation is discovered for the boundary layer thickness and the glass transition temperature for many alloys in various groups of the Periodic Table, found through previously published data. In particular, the role of convective effects on the solution is used with the Biot number in the decoupling of the heat and mass components. A correlation of over 90% is found indicating a strong relationship between the Tg and the heat transfer thermodynamic inputs. This indicated the possibility of designing BMG alloys by adjusting certain parameters a priori.