Numerical simulation of transient liquid phase bonding with variable diffusion coefficient in planar, cylindrical and spherical systems
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Date
2019-01-16
Authors
Ghanbar, Amin
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Abstract
A new finite difference numerical model with variable diffusion coefficient is developed by using an explicit-fully-implicit hybrid method and Landau transformation with adaptable spatial discretization to study TLP bonding kinetics in planar and non-planar systems. The results of the numerical model developed in this research, which are verified with experimental data available in the literature, reveal key reasons for why the extent of isothermal solidification deviates from linear relationship with √t, i.e. deviation from parabolic behavior. The deviation occurs when the concentration dependency of D changes with time. In non-planar systems (cylindrical and spherical), however, deviation from the parabolic behavior can occur even when D is independent of both concentration and time, solely by geometry-induced effect. Moreover, the kinetics of solute penetration into the substrate during isothermal solidification is different from the solute penetration kinetics that occur during homogenization process that follows the isothermal solidification stage.
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Keywords
Numerical Simulation, Transient Liquid Phase Bonding, Variable Diffusion Coefficient