THEORETICAL PREDICTION OF SELF-PROPAGATING, DIFFUSION-LIMITED AND DECOMPOSITION-LIMITED INTERMETALLIC REACTIONS

A method for predicting the steady-state structure and propagation velocity of an infinite, exothermic alloying process is presented. It is assumed that two unreacted solid-phase metals, one of which is assumed to be in a combined state with a gaseous species, are premixed in stoichiometric proportions. It is also assumed that the propagation of the reaction is limited not only by thermal and mass diffusion, but also by the need for the gaseous species to be completely driven off before the two metals can react. The governing ordinary differential system possesses an equilibrium point in the burned region at infinity, and an asymptotic analysis in this region shows the structure of the equilibrium point to be that of a saddle point. The unknown eigenvalue V*, the velocity of propagation of the reaction, is then uniquely determined from the requirement that the solution be bounded at infinity. The method is illustrated by considering both an idealized analytical example and a more realistic model requiring a numerical algorithm suggested by the analysis. © 1979.