Crystal Formation Exploration by Computation

Introduction

A crystal is formed when the molecules that make up a solid substance are arranged in a regular, evenly-spaced lattice, or, grid. A lattice is a regular arrangement of objects, usually in some type of grid. These lattices represent mimimal energy states for the solid. However, there are a large number of other configurations, not quite as regular as a lattice, that are also low-energy (desirable) states.

It is generally the case that the most stable configuration of a system is the one which involves the least amount of stored energy. For example, nitroglycerine is a substance with a great deal of energy stored in its chemical bonds, and is therefore highly unstable. Cast iron, on the other hand, has very little energy stored and is a much more stable substance.

Depending on the surrounding conditions, a substance can be locked in to what is referred to as a local minimum, meaning that it is the lowest of any "nearby" or easily reached states. An example is when steel weapons are hardened by a blacksmith's plunging them into a bucket of water while the steel is still red hot. This has the effect of "freezing" the steel in an excited state. This state is a local minimum--if the steel is bent a little bit, it will return to this state. However, if it is stressed enough, it will break.

Small variations in the regularity of the lattice structure are known as defects. When you produce a crystal, you want it to have as few defects as possible. The program SimSurface simulates one method of attempting to create a defect-free crystal. The method, known as annealing, consists of heating the material which one desires to crystallize to a high enough temperature to liquefy it, then cooling it over a period of time, slowly reducingthe temperature until the material is completely solid, or, frozen. Annealing is the general term applied to the process a substance goes through as it hardens, or "freezes" into a solid state. The idea is to give the material time to "find" its lowest energy state. If the temperature is lowered too quickly, the material is likely to end up frozen in a local minimum.