Introduction to Crystallography

1. Practical I - A Introduction toCrystallography

2. Crystallographic axis • One of three lines (sometimes four, in the case of a hexagonal crystal), passing through a common point, that are chosen to have definite relation to the symmetry properties of a crystal, and are used as a reference in describing crystal symmetry and structure. • The crystallographic axes are imaginary lines that we can draw within the crystal lattice.  • These will define a coordinate system within the crystal. • For 3-dimensional space lattices we need 3 or in some cases 4 crystallographic axes that define directions within the crystal lattices.  • Depending on the symmetry of the lattice, the directions may or may not be perpendicular to one another, and the divisions along the coordinate axes may or may not be equal along the axes.  • The lengths of the axes are in some way proportional to the lattice spacing along an axis and this is defined by the unit cell.

3. Crystal symmetry • Symmetrically arranged faces reflect the internal arrangement of atoms. The symmetry can be described according to three symmetry elements: • Centre of symmetry • A central point which is present when all faces or edges occur in parallel pairs on opposite sides of the crystal. • A point, within a crystal, through which any straight line also passes through two points on the edge of the figure at the same distance from the centre but on opposite sides. • The centre of symmetry at a point (0,0,0) operates on any point (x,y,z) to give an identical point at (-x,-y,-z). • Axis of symmetry • A line about which a crystal may be rotated through 360°/n until it assumes a congruent position (identical image is seen); n may equal 2, 3, 4 or 6 – depending on the number of times the congruent position is repeated, resulting in 2-fold (diad), 3-fold (triad), 4-fold (tetrad) and 6-fold (hexad) axes. • Plane of symmetry (also mirror plane) • A plane by which the crystal may be divided into two halves which are mirror images of each other. • Videos

4. Crystallographic classification system • Using the elements of symmetry discussed above, crystallographers have recognized • 32 Crystal classes (point groups) • Classified based on three symmetry operations • 6(7) Crystal systems • Classified based on lattice parameters (a, b, c and α, β, γ) • Symmetry is highest (high symmetry) in the cubic system, where many elements are repeated, and lowest (low symmetry) in the triclinic system, where only a centre of symmetry may be present (i.e. there may be no plane or axis of symmetry).

5. Crystal forms (230 space groups) • All known crystal forms fit into the above seven crystal systems. But why don't all crystals in a given set look the same? • Or, stated differently, why can't I learn seven crystal shapes and know all I need to know? • Well, crystals, even of the same mineral, have differing CRYSTAL FORMS, depending upon their conditions of growth. • Whether they grew rapidly or slowly, under constant or fluctuating conditions of temperature and pressure, or from highly variable or remarkably uniform fluids or melts, all these factors have their influence on the resultant crystal shapes, even when not considering other controls. • Video

6. Practical • Classify your own examples • Divide into groups and classify the models in front of you • Furthermore, work through the trays provided in order to understand the classification of more complex crystallographic forms • Lastly, complete the sheet provided, classifying and describing the unknown crystal models provided