1. Unit Cell:
* Shape and symmetry: The basic building block of a crystal structure is the unit cell, which is a repeating three-dimensional pattern. Geologists classify unit cells based on their shape and symmetry, using seven crystal systems:
* Cubic: Equal lengths on all axes, all angles 90 degrees (e.g., halite, pyrite)
* Tetragonal: Equal lengths on two axes, different length on the third, all angles 90 degrees (e.g., cassiterite, rutile)
* Orthorhombic: All axes have different lengths, all angles 90 degrees (e.g., sulfur, topaz)
* Monoclinic: Two axes have different lengths, the third is different and oblique, one angle not 90 degrees (e.g., gypsum, pyroxene)
* Triclinic: All axes have different lengths, all angles are different (e.g., plagioclase feldspar, turquoise)
* Hexagonal: Three equal axes at 120 degrees, one axis perpendicular to the others (e.g., quartz, beryl)
* Trigonal (Rhombohedral): Three equal axes at 120 degrees, one axis perpendicular to the others, but also with 3-fold rotational symmetry (e.g., calcite, corundum)
* Lattice parameters: This includes the lengths of the unit cell axes (a, b, c) and the angles between them (α, β, γ). These parameters are used to precisely define the geometry of the unit cell.
2. Bravais Lattices:
* Atom arrangement: Within the unit cell, atoms occupy specific positions. Geologists use Bravais lattices to describe the possible arrangements of these points in space. There are 14 possible Bravais lattices, representing all the unique ways to arrange points in a three-dimensional space.
3. Point Groups:
* Symmetry elements: Crystals often exhibit symmetry elements like planes of symmetry, axes of rotation, and inversion centers. These elements are used to define the crystal's point group, which is a group of symmetry operations that leave the crystal unchanged. There are 32 possible point groups.
4. Space Groups:
* Combined symmetry: Space groups are a more complete description of crystal symmetry, considering both point group symmetry and the translational symmetry of the lattice. They combine the information from Bravais lattices and point groups, resulting in 230 possible space groups.
5. Crystal Structure:
* Detailed arrangement: A complete crystal structure description defines the exact positions of all atoms within the unit cell. This includes information about the type of atom, its coordinates, and the bond lengths and angles.
Example:
Take halite (NaCl), common table salt. It belongs to the cubic crystal system with a face-centered cubic Bravais lattice. Its point group is m3m, and space group is Fm3m. This means it has:
* Cubic: Equal lengths on all axes, all angles 90 degrees.
* Face-centered cubic: Atoms are located at the corners and the center of each face of the cube.
* m3m: The crystal has multiple planes of symmetry, axes of rotation, and an inversion center.
* Fm3m: The crystal has a combination of the face-centered cubic lattice and the m3m point group symmetry.
By knowing these details, geologists can understand the fundamental properties of a crystal, such as its physical and optical properties, and relate these properties to its chemical composition and formation environment.
