Mineralogy
Crystal structure

The crystal structure is the arrangement of atoms in a crystal. It is represented by a lattice of points which repeats a basic pattern, called a unit cell, in three dimensions. The lattice can be characterized by its symmetries and by the dimensions of the unit cell. These dimensions are represented by three Miller indices. The lattice remains unchanged by certain symmetry operations about any given point in the lattice: reflection, rotation, inversion, and rotary inversion, a combination of rotation and reflection. Together, they make up a mathematical object called a crystallographic point group or crystal class. There are 32 possible crystal classes. In addition, there are operations that displace all the points: translation, screw axis, and glide plane. In combination with the point symmetries, they form 230 possible space groups.

Most geology departments have X-ray powder diffraction equipment to analyze the crystal structures of minerals. X-rays have wavelengths that are the same order of magnitude as the distances between atoms. Diffraction, the constructive and destructive interference between waves scattered at different atoms, leads to distinctive patterns of high and low intensity that depend on the geometry of the crystal. In a sample that is ground to a powder, the X-rays sample a random distribution of all crystal orientations. Powder diffraction can distinguish between minerals that may appear the same in a hand sample, for example quartz and its polymorphs tridymite and cristobalite.

Isomorphous minerals of different compositions have similar powder diffraction patterns, the main difference being in spacing and intensity of lines. For example, the Na Cl (halite) crystal structure is space group Fm3m; this structure is shared by sylvite (K Cl), periclase (Mg O), bunsenite (Ni O), galena (Pb S), alabandite (Mn S), chlorargyrite (Ag Cl), and osbornite (Ti N).
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