Internal Order and 2-D Symmetry Internal Order and 2-D Symmetry Plane Lattices Plane Groups
Repeated and symmetrical arrangement (ordering) of atoms and ionic complexes in minerals creates a 3-dimensional lattice array Repeated and symmetrical arrangement (ordering) of atoms and ionic complexes in minerals creates a 3-dimensional lattice arrayArrays are generated by translation of a unit cell – smallest unit of lattice points that define the basic orderingSpacing of lattice points (atoms) are typically measured in Angstroms (= 10-10 m) About the scale of atomic and ionic radii
The lattice and point group symmetries interrelate, because both are properties of the overall symmetry pattern
The lattice and point group symmetry interrelate, because both are properties of the overall symmetry pattern The lattice and point group symmetry interrelate, because both are properties of the overall symmetry pattern
There is a new 2-D symmetry operation when we consider translationsThe Glide Line, g:and translation
There are 5 unique 2-D plane lattices. There are 5 unique 2-D plane lattices.
3-D Internal Order & Symmetry Space (Bravais) Lattices Space Groups 3-D Internal Order & Symmetry Space (Bravais) Lattices Space GroupsSo far we examined the five 2-D plane lattices and combined them with the 10 planar point groups to generate the 17 2-D plane (space) groups. Next we study the 14 Bravais 3-D lattices and combine them with the 32 3-D point groups to generate 230 3-D space groups.
Different ways to combine 3 axes Different ways to combine 3 axesTranslations compatible with 32 3-D point groups (~ crystal classes)32 Point Groups fall into 6 systems
Different ways to combine 3 axes Different ways to combine 3 axesTranslations compatible with 32 3-D point groups (~ crystal classes)32 Point Groups fall into 6 Crystal Systems
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