Numerical modelling of transient liquid phase bonding and other diffusion controlled phase changes

Abstract

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.

Numerical solutions of diffusion-controlled moving boundary problems which conserve solute

“…However, none of the proposed improvements actually render the algorithms conservative of solute. The authors of the present work have previously shown that conservative schemes can be derived by adopting a different approach to modelling the interfacial fluxes [31].…”

Modelling of transient liquid phase bonding in binary systems—A new parametric study

“…Once the liquid has become homogeneous, solidification takes place at a rate determined by the rate of diffusion within the solid phase. This assumption is supported by numerical simulations [4,6,20].…”

“…The present authors recently published [16,20] an algorithm designed to obtain approximate solutions to Eqs. (1)- (6), to any required accuracy.…”

Efficient Numerical Modeling of Field Diffusion in High-Temperature Superconducting Wires

“…The discretization points are defined by a fixed discretization of , , and they may be written as , . The finite volume discretization [8] of (11) is based on integration around the nodes and is fairly straightforward [9], [10]. The boundary conditions (8) and (10) The finite volume discretization for (12) and (13) immediately follows from the general form of the finite volume integral.…”