Two Dimensional Crystals

A crystal is, most simply, an arrangement of particles showing long-range order and held in place by the forces between the particles. Particles tend to arrange themselves in such a way as to minimize their potential energy. Most solids are crystalline to some extent or another, forming strong bonds in lattice formations. Some liquids also exhibit long-range order, though less than that of solids.

This website is about two-dimensional crystals— orderly arrangements of particles constrained to lie on a surface. More specifically, we discuss spherical crystals. The theory is applicable to any group of particles on the surface of a sphere and interacting via mainly repulsive forces. We concern ourselves particularly with colloids, small solid particles dispersed in a liquid. These can form the relevant crystals at the interface between two fluids, if it takes on a curved shape.

Briefly, it is important to know that most crystals (2D or 3D) contain defects, places where the crystal structure is different from its usual form. These defects are important physically and chemically, as they provide a preferred location on the crystal for interactions of all types to take place. Spherical crystals are different from plane or cubic crystals in that they must contain defects due to their topological form. This poses fascinating questions for physicists to study and has many interesting ramifications.

This website is currently under construction. It is intended to provide an introduction to the theory of topological defects in two-dimensional crystals. It is designed to be readable by someone without a very deep background in physics, although a high school or introductory college class may be helpful. Links will be provided to more advanced discussions of the topics. The pages in the left sidebar are designed to be read in order.