Crystal Lattice Structures
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Introduction

Simple Cubic

Body Centered Cubic

Face Centered Cubic

Primitive FCC

Simple Hexagonal

Hexagonal Closest Packing

HCP Coordination

Cubic Closest Packing

CCP Coordination

Rhombohedral

2- & 3-Layer repeats

4-layer repeats

Tetrahedral Holes

Octahedral Holes

CsCl

NaCl

Halite

Fluorite

Zinc Blende

Exercises
Primitive Face Centered Cubic
  In any lattice it is always possible to choose a primitive (Z = 1) unit cell.  In fact, there is an infinite number of such choices, and it can be shown that all of the primitive unit cells on a lattice have the same volume.  However, only one of these primitive unit cells has the three shortest cell edges (a,b,c), and this unit cell is called the standard reduced cell.

In a FCC lattice, the standard reduced cell is a rhombohedron, with a = b = c = 2r.  The three interior angles formed between unit cell edges are called:

a (alpha, between edges b & c)
b (beta, between edges a & c)
g (gamma, between edges a & b)
In the FCC rhombohedral standard reduced cell, it can be shown that a = b = g = 60o.  Note that a cube is a just a special rhombohedron, with a = b = g = 90o.

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Steven F. Watkins, Department of Chemistry, Louisiana State University