A crystal is a solid material whose constituent particles (atoms, ions, or molecules) are arranged in a highly ordered, repeating pattern extending in all three dimensions. This systematic internal structure is known as a crystal lattice, and it gives crystalline solids their characteristic geometric shapes and physical properties. The scientific study of these structures is called crystallography.
The organization of a crystal’s internal structure directly dictates its macroscopic traits, such as hardness, electrical conductivity, and melting point. A systematic method of categorization is necessary to study their properties efficiently. Classification is approached using multiple criteria, moving from external shape to internal geometry and finally to the fundamental chemical forces that hold the structure together.
Classification Based on External Shape and Symmetry
The first broad method of classifying crystals is based on their external form and the geometric relationships between their crystallographic axes. This system groups all crystals into one of seven distinct categories known as the Crystal Systems. These systems are defined by the relative lengths of the three axes (a, b, and c) and the angles between them (\(\alpha\), \(\beta\), and \(\gamma\)).
The most symmetrical is the Cubic system, where all three axes are of equal length (\(a=b=c\)) and intersect at right angles (\(\alpha=\beta=\gamma=90^\circ\)). Slightly less symmetrical is the Tetragonal system, which retains three perpendicular axes but has one axis that is either longer or shorter than the other two (\(a=b\neq c\)). The Orthorhombic system further reduces symmetry by having three axes of unequal length, though all still intersect at \(90^\circ\) angles (\(a\neq b\neq c\)).
The remaining four systems involve angles other than \(90^\circ\). The Monoclinic system has three unequal axes, with two intersecting at right angles and the third inclined (\(\alpha=\gamma=90^\circ, \beta\neq 90^\circ\)). In the Triclinic system, the least symmetrical of all, all three axes are of unequal length, and none of the angles are equal to \(90^\circ\) (\(a\neq b\neq c, \alpha\neq \beta\neq \gamma\neq 90^\circ\)). Finally, the Hexagonal system features three equal axes lying in the same plane and intersecting at \(120^\circ\), with a fourth axis perpendicular to that plane. The Trigonal system is characterized by three equal axes that are equally inclined to one another, but not at \(90^\circ\).
Classification Based on Internal Unit Cell Arrangement
While the seven crystal systems categorize crystals based on outer symmetry, a more granular classification delves into the specific arrangement of atoms within the repeating structure. This internal arrangement is defined by the unit cell, which is the smallest repeating volume that, when stacked in all directions, generates the entire crystal lattice. A single crystal system can contain several ways the unit cell can be centered, which leads to a total of 14 distinct three-dimensional lattice types known as the Bravais Lattices.
These 14 lattices are derived by combining the geometric constraints of the seven crystal systems with four basic types of unit cell centering. The simplest is the Primitive (P) cell, which has lattice points only at the eight corners. A Body-Centered (I) cell adds an additional lattice point exactly in the center of the unit cell.
The Face-Centered (F) cell contains an extra lattice point in the center of each of the six faces. The final type, the Base-Centered (C) cell, has additional lattice points only on the center of two opposite faces. The various combinations of these centering types with the seven crystal systems result in the 14 Bravais lattices. For example, the Cubic system can accommodate Primitive, Body-Centered, and Face-Centered arrangements, but not the Base-Centered one.
Classification Based on the Types of Atomic Bonds
A classification independent of the crystal’s geometry is based on the chemical forces that bind the constituent particles together. This method groups crystalline solids into four main types, which directly influence their physical properties like melting point, hardness, and electrical conductivity.
Ionic Solids
Ionic solids, such as table salt (sodium chloride), are held together by strong electrostatic attraction between positively charged cations and negatively charged anions. This powerful attraction results in structures that are hard and brittle, with very high melting points. Because the ions are fixed in position, they are electrical insulators in the solid state, only becoming conductors when melted or dissolved.
Covalent Network Solids
Covalent Network solids consist of atoms linked by strong, directional covalent bonds in a continuous three-dimensional network. Diamond and quartz are prime examples. They are characterized by extreme hardness and extremely high melting points due to the strength of the extended bond network. These solids are generally poor conductors of electricity because their valence electrons are localized within the covalent bonds.
Metallic Solids
Metallic solids are formed from metal atoms held together by a unique “sea” of delocalized electrons shared across the entire structure. This arrangement, known as metallic bonding, allows for excellent electrical and thermal conductivity, as the electrons are free to move. Metallic crystals exhibit a wide range of melting points and are often malleable and ductile.
Molecular Solids
Molecular solids are composed of discrete molecules held together by relatively weak intermolecular forces, such as London dispersion forces, dipole-dipole interactions, or hydrogen bonds. Examples include frozen water and sugar (sucrose). They are characterized by soft structures and low melting points, often below room temperature. Since there are no free-moving charged particles or delocalized electrons, molecular solids are poor conductors of electricity.