Transcript Lecture 12 (10/30/2006) Crystallography Part 5: Internal Order and 2-D Symmetry

Lecture 12 (10/30/2006)
Crystallography
Part 5:
Internal Order and 2-D Symmetry
Plane Lattices
Planar Point Groups
Plane Groups
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

Two-Dimensional Plane Lattice
Generating an 2D Lattice Array (Plane
Lattice) involves translation of a motif in two
directions; non-unique
Translation in two directions: x and y axes
Angle between axes: g
Translation distance: a along x and b along y
Replacing motifs with points (or nodes)
creates a plane lattice
Unit Cell
5 Types of Plane Lattices
Preferred
Defining a Unit Cell
Choose:
Smallest
Most orthogonal
Most in line with symmetry
2 Nodes per Lattice Vector
Most Primitive (non-centered)
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)
Symmetry Elements of Plane Lattices
glide line
17 Plane Groups
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