Introduction to Crystallography and Mineral Crystal Systems PD Dr. Andrea KoschinskyGeosciences and Astrophysics

Definition of CrystallographyCRYSTALLOGRAPHY is the study of crystals.CRYSTALLOGRAPHY is a division of the entire study of mineralogy.Geometrical, physical, and chemical CRYSTALLOGRAPHY

A CRYSTAL is a regular polyhedral form, bounded by smooth faces, which is assumed by a chemical compound, due to the action of its interatomic forces, when passing, under suitable conditions, from the state of a liquid or gas to that of a solid.Polyhedral form: solid bounded by flat planes (CRYSTAL FACES). During the process of crystallization, crystals assume various geometric shapes dependent on the ordering of their atomic structure and the physical and chemical conditions under which they grow.

CRYSTALLOGRAPHIC AXES6 large groups of crystal systems:

(1) CUBIC(2) TETRAGONAL(3) ORTHORHOMBIC(4) HEXAGONAL(5) MONOCLINIC(6) TRICLINIC

MILLER INDICESMathematical system for describing any crystal face or group of similar faces (forms) developed by William H. Miller (1801-1880).

ELEMENTS OF SYMMETRYPLANES OF SYMMETRYAny two dimensional surface that, when passed through the center of the crystal, divides it into two symmetrical parts that are MIRROR IMAGES is a PLANE OF SYMMETRY

AXES OF SYMMETRYAny line through the center of the crystal around which the crystal may be rotated so that after a definite angular revolution the crystal form appears the same as before is termed an axis of symmetry. Depending on the amount or degrees of rotation necessary, four types of axes of symmetry are possible when you are considering crystallography:

When rotation repeats form every 60 degrees, then we have sixfold or HEXAGONAL SYMMETRY.

When rotation repeats form every 90 degrees, then we have fourfold or TETRAGONAL SYMMETRY.

When rotation repeats form every 120 degrees, then we have threefold or TRIGONAL SYMMETRY.

When rotation repeats form every 180 degrees, then we have twofold or BINARY SYMMETRY.

The crystal face arrangement symmetry of any given crystal is simply an expression of the internal atomic structure. The relative size of a given face is of no importance, only the angular relationship or position to other given crystal faces.

CRYSTAL FORMS AND SYMMETRY CLASSESHABIT is the correct term to indicate outward appearance. Habit, when applied to natural crystals and minerals, includes such descriptive terms as tabular, equidimensional, massive, reniform, drusy, and encrusting.

A FORM is a group of crystal faces, all having the same relationship to the elements of symmetry of a given crystal system. These crystal faces display the same physical and chemical properties because the ATOMIC ARRANGEMENT (internal geometrical relationships) of the atoms composing them is the same.Note: Crystals, even of the same mineral, can have differing CRYSTAL FORMS, depending upon their conditions of growth.

There are 32 forms in the nonisometric (noncubic) crystal systems and another 15 forms in the isometric (cubic) system.

Introduction to the atomic arrangement of crystal form Crystal Lattice Structures

Simple Cubic and Related Structures

Schematic diagram of an atom of the element carbon. The nucleus contains six protons and six neutrons. Electrons orbiting the nucleus are confined to specific orbits called energy-level shells. Three-dimensional representation showing the first energy-level shells. The first shell can contain two electrons, the second eight. B. Two-dimensional representation of the carbon atom to show the number of protons and neutrons in the nucleus and the number of electrons in the energy-level shells. The first energy-level shell is full because it contains two electrons. The second shell contains four electrons and so is half full.

To form the compound lithium fluoride, an atom of the element lithium combines with an atom of the element fluorine. The lithium atom transfers its lone outer-shell electron to fill the fluorine atom's outer shell, creating an Li+ cation and a F- anion in the process. The electrostatic force that keeps the lithium and fluorine ions together in the compound lithium fluoride is an ionic bond.Model for the ionic compound LiF

The arrangement of ions in the most common lead mineral, galena (PbS). Lead, the Pb part, is a cation with a charge of 2+, and sulfur, S, is an anion with a charge of 2-. To maintain a charge balance between the ions, there must be an equal number of Pb and S ions in the structure. B. The packing arrangement of ions is repeated continuously through a crystal. The ions are shown pulled apart along the black lines to demonstrate how they fit together.Mineral structure of PbS

A.Anion with the four oxygens touching each other in natural position. Silicon (dashed circle) occupies central space. B. Exploded view showing the relatively large oxygen anions at the four corners of the tetrahedron, equidistant from the relatively small silicon cation.

The tetrahedron-shaped silicate anion SiO4(-4)

Polymerization of complex silicate anions

Polymerization of complex silicate anions

Summary of the way silicate anions polymerize to form the common silicate minerals. The most important polymerizations are those that produce chains, sheets, and three-dimensional networks.