Mathematical Modeling of Interface Movement during Diffusional Bonding of Surfaces
The concentration profile of Cu is modelled using semi-infinite geometry for diffusion couples of α and β phases in Cu-Al system. The dimensionless interface movement parameter γ is calculated, for various combinations of time and temperature, by root bracketing, bisection and inverse quadratic interpolation. A computational procedure is presented to calculate the concentration profile where the interface velocity (dε/dt) is high and/or with steep concentration gradient of the specie in the shrinking phase. In all cases the interface compositions are set at the equilibrium values given in the phase diagram with fixed composition of end members. The calculated profile match well with the experimental concentration profile as reported by Romig .
D. J. Fisher
R. Ray "Mathematical Modeling of Interface Movement during Diffusional Bonding of Surfaces", Defect and Diffusion Forum, Vol. 272, pp. 71-78, 2007