1. Lecture 12 (10/30/2006) Crystallography Part 5: Internal Order and 2-D Symmetry Plane Lattices Planar Point Groups Plane Groups

2. Internal Order and Symmetry  Repeated and symmetrical arrangement (ordering) of atoms and molecules in minerals creates a 3-dimensional lattice array  Arrays are generated by translation of a unit cell – smallest unit of lattice points that define the basic ordering  Spacing of lattice points (atoms) are typically measured in angstroms (=10 -8 cm); scale of ionic radii

3. Two-Dimensional Plane Lattice Translation in two directions: x and y axes Angle between axes:  Translation distance: a along x and b along y Replacing motifs with points (or nodes) creates a plane lattice Generating an 2D Lattice Array (Plane Lattice) involves translation of a motif in two directions; non-unique Unit Cell

4. 5 Types of Plane Lattices Preferred

5. Defining a Unit Cell Choose: Smallest Most orthogonal Most in line with symmetry 2 Nodes per Lattice Vector Most Primitive (non-centered)

6. Symmetry Elements of Planar Motifs 10 Possible symmetry combinations; called Planar Point Groups Same limitations of rotational symmetries (1,2,3,4, & 6) as Point Groups (crystal classes)

7. Symmetry Elements of Plane Lattices glide line

8. 17 Plane Groups

9. Next Lecture