Crystal Structure
Introduction
Crystal structure is a unique arrangement of atoms, ions, or molecules in a crystalline material. Ordered atomic structure is a defining characteristic of crystals, which differentiates them from amorphous substances that lack long-range order. The study of crystal structures is a fundamental part of crystallography, a branch of science that deals with the geometric properties of crystals and their internal arrangement of atoms.
Crystal Lattice and Unit Cell
A crystal lattice is a three-dimensional, repeating arrangement of atoms, ions, or molecules. Each repeating part of the lattice is known as a unit cell, which is the smallest divisible unit of the crystal that retains the properties of the entire crystal. The unit cell is defined by its lattice parameters, which include the lengths of the cell edges (a, b, c) and the angles between them (α, β, γ). The crystal lattice can be classified into seven crystal systems based on the values of these parameters.
Crystal Systems
The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral (also known as trigonal), hexagonal, and cubic. Each system is distinguished by its unique combination of edge lengths and interaxial angles. The cubic system, for example, has equal edge lengths and all interaxial angles are 90 degrees. In contrast, the triclinic system has unequal edge lengths and none of the interaxial angles are 90 degrees.
Bravais Lattices
In addition to the seven crystal systems, there are 14 possible types of lattice arrangements, known as Bravais lattices. Named after the French physicist Auguste Bravais, these lattices are distinguished by their symmetry properties. The Bravais lattices include primitive (P), body-centered (I), face-centered (F), and base-centered (C) lattices.
Crystallographic Defects
Despite the idealized image of perfect order within a crystal, real-world crystals often contain defects. These defects can be point defects, line defects, or planar defects. Point defects include vacancies (missing atoms) and interstitials (extra atoms). Line defects, also known as dislocations, occur when atoms are misaligned. Planar defects, such as grain boundaries, occur between crystals in a polycrystalline material.
Crystallographic Directions and Planes
In crystallography, specific directions and planes within the crystal lattice are often referred to using Miller indices. Named after the British mineralogist William Hallowes Miller, these indices provide a shorthand notation to describe the orientation of a plane or direction in the crystal lattice.
X-ray Crystallography
X-ray crystallography is a widely used technique for determining the atomic and molecular structure of a crystal. By measuring the angles and intensities of diffracted X-rays, researchers can produce a three-dimensional picture of the electron density within the crystal, which can be used to determine the positions of the atoms.
Applications of Crystal Structure Knowledge
Understanding crystal structures is crucial in many fields of science and engineering. In materials science, the properties of a material are often directly related to its crystal structure. In mineralogy and geology, the crystal structure is a key tool for identifying minerals. In chemistry and biology, the crystal structure of complex molecules and proteins can provide insight into their function.