Mineralogy: Lattices and Point Groups

What is a node?

A specific spot on the unit cell

How do we use nodes?

We essentially ignore the unit cell, instead using a node to represent the volume it takes up

Lattice

Imaginary pattern of nodes, in which every node has an environment identical to every other node

How can the lattice move?

It can be shifted parallel to itself

What creates the lattice

repetition of nodes

2D Bravais Lattices

The five ways you can organize nodes in 2D

What are the five 2D bravais lattices?

general/oblique, rectangular, centered rectangular, square, and rhombic

How many 3D lattice arrangements are there, and what are they called?

14, also bravis lattices

Who discovered bravis lattices

Auguste BRavis

What is combined to make the 3D bravis lattices

2D bravis lattices, and the six crystal systems

What symmetry operations are used to create 3D bravis lattices

Glide, translation, and screw axes

What do space groups do

Cover all the ways motifs can be combined in 3D

What does P stand for in a space group

primative

What does A, B, or C stand for in a space group?

Face centered along an axis

What does I stand for in a space group?

Body centered

What does F stand for in a space group?

Face centered

What does R stand for in a space group?

Rhombohedral

What are space groups based on?

One of the 14 3D bravis lattices, plus symmetry content from one of the 32 point groups

To extend from a point to 3d, what can we do?

Substitute glide planes for mirror planes or screw axes

Types of glide

a/b/c, n, and d

a, b, or c glide

gliding along that axis

n glide

Diagonal glide between axes

d glide

Diamond glide