Numerical methods of finding transient solutions to diffusion problems in two distinct phases that are separated by a moving boundary are reviewed and compared. A new scheme is developed, based on the Landau transformation. Finite difference equations are derived in such a way as to ensure that solute is conserved. It is applicable to binary alloys in planar, cylindrical, or spherical geometries.The efficiency of algorithms which implement the scheme is considered. Computational experiments indicate that the algorithms presented here are of first order accuracy in both time and space.

Diffusion in material of inhomogeneous composition can induce phase changes, even at a constant temperature. A transient liquid phase (TLP), in which a liquid layer is formed and subsequently solidifies, is one example of such an isothermal phase change. This phenomenon is exploited industrially in TLP bonding and sintering processes. Successful processing requires an understanding of the behaviour of the transient liquid layer in terms of both diffusion-controlled phase boundary migration and capillarity-driven flow.In this paper, a numerical model is presented for the simulation of diffusion-controlled dissolution and solidification in one dimension. The width of a liquid layer and time to solidification are studied for various bonding conditions. A novel approach is proposed, which generates results of a high precision even with coarse meshes and high interface velocities. The model is validated using experimental data from a variety of systems, including solid/solid diffusion couples. C 2005 Springer Science + Business Media, Inc.

An established mathematical model, describing the rate at which transient liquid phase bonding (TLP bonding) progresses in binary alloy systems, is subjected to careful scrutiny. It is shown that the process can be characterised using just two dimensionless parameters. An advantage of such dimensionless characterisation is demonstrated by analysis of the solution for solidification of semi-infinite systems. It is known that analytical formulae for the rate at which the liquid region solidifies are valid only for certain restricted cases. This is investigated by numerical modelling, and the requirements for the formulae to be applicable are rationalised. Maps presented here can be used to determine whether the semi-infinite solution would provide an acceptable approximation for any given system. Information is also presented concerning optimal combinations of phase diagram characteristics, diffusivities and system dimensions required for rapid TLP solidification, which can be used to identify the best melting point depressant (MPD) materials to use for particular TLP requirements. The analysis reveals that, as a consequence of their higher solubilities, elements forming substitutional solutes in the parent plates may often allow faster TLP solidification than those forming interstitial solutes, despite the fact that the latter group normally exhibits much higher diffusivities.