A single crystal is a regular and periodic arrangement of particles inside a crystal in three-dimensional space. The entire lattice of single crystals is continuous, and single crystals have important industrial applications. Ideal single crystals of a certain size are extremely rare in nature and difficult to produce in the laboratory due to entropy effects that lead to non-idealities in the solid microstructure, such as impurities, inhomogeneous strain, and crystal defects. Common single crystals contain aluminum oxide, niobium, and palladium.