ABSTRACT
In addition, to keep the mathematics manageable, only solutions to the one-dimensional mass conservation equation ∂ ∂ = ∂ ∂C t D C x/ /( )2 2 are considered in this chapter but are, nevertheless, important in many applications. There are many books devoted to the solution to partial differential equations in general (e.g., Farlow 1982; Snider 2006). Then there are some that are
completely, or partially, focused on the solution to the broad range of diffusion or heat transfer equations (Morse and Feshbach 1953; Carslaw and Jaeger 1959; Crank 1975; Glicksman 2000). The intention is not to emulate the rigor and breadth of these works but rather to provide some straightforward and plausible approaches to solutions of a limited number of problems that a materials scientist or engineer might encounter. These and other works in the literature are excellent sources for specific solutions that might be of interest for a given application, provided one is familiar with these solutions and knows how and where to look for them. The goal of this chapter is to provide this familiarity by modeling solutions to Fick’s second law for infinite and semi-infinite boundary conditions. Chapter 12 develops models for solutions with finite boundary conditions.
