Chapter 2: Diffusion in Solids

The mathematical foundation of these processes is established through Fick's First Law, which relates atomic flux to concentration gradients under steady-state conditions, and Fick's Second Law, which describes how concentration profiles evolve with time in non-steady-state scenarios. These laws are applied to practical metallurgical problems, such as the homogenization of segregated castings and the carburization of steel surfaces, utilizing error function solutions to predict solute penetration depths. The chapter further explores the temperature dependence of diffusion coefficients using the Arrhenius equation, highlighting the roles of activation enthalpy, vibrational frequency, and entropy. A significant portion of the text is dedicated to diffusion in binary substitutional alloys, introducing the Kirkendall effect, where unequal diffusion rates between species result in a net flux of vacancies and a physical shift of the lattice planes relative to the ends of the specimen. This phenomenon leads to the derivation of Darken's equations, which connect individual intrinsic diffusion coefficients to the overall interdiffusion coefficient. The discussion expands to include atomic mobility and the thermodynamic driving forces of diffusion, emphasizing that atoms migrate down chemical potential gradients, which can occasionally lead to up-hill diffusion in systems with miscibility gaps. Additionally, the summary covers tracer diffusion techniques for measuring self-diffusion and impurity diffusion, as well as the influence of high-diffusivity paths such as grain boundaries and dislocations (pipe diffusion), which become dominant transport mechanisms at lower temperatures due to their lower activation energies compared to bulk lattice diffusion. Finally, the chapter addresses multiphase diffusion in binary systems, analyzing interface migration kinetics and phase layer growth in diffusion couples.