Introduction to Computational Materials Science Fundamentals to Applications

An automaton is defined as a “a mechanism that is relatively self-operating; especially: robot” or as a “machine or control mechanism designed to follow automatically a predetermined sequence of operations or respond to encoded instructions” [226]. A classic cellular automaton is like an algorithmic robot. The cellular automata method describes the evolution of a discrete system of variables by applying a set of deterministic rules that depend on the values of the variables as well as those in the nearby cells of a regular lattice. Despite this simplicity, cellular automata show a remarkable complexity in their behavior.

Cellular automata have been used to model a number of effects in materials, mostly recrystallization, corrosion, and surface phenomena, with other applications ranging from hydration in cement to friction and wear, many of these applications being discussed below. Numerous applications extend classic cellular automata to include probabilistic rules, more complex lattice geometries, and longer-ranged rules. With the use of probabilistic rules, the distinction between cellular automata methods and Monte Carlo methods become a bit blurred, as will be discussed below.

In this chapter we will introduce the basic ideas behind cellular automata, using as examples some of the classic applications of the method. We will then go through a few applications of the methods to materials issues, highlighting the power of the method to model complex behavior. Much more detail about a range of applications, both in materials research and elsewhere, can be found elsewhere [68, 268, 269].