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

Simple Cubic
  In the Simple Cubic (SC) unit cell there is one lattice point at each of the eight  corners of a cube.  Unit cells in which there are lattice points only at the eight corners are called primitive.  In general, the number of lattice points is denoted by the letter "Z"; thus, for SC, Z = 1. 
Let a host atom of radius r occupy each lattice point, and assume that each atom touches as many adjacent atoms as possible (in this case, there are six such contacts).  Then each of the three unit cell edges is equal to the sum of two atomic radii: a = b = c = 2r.  The volume of the cell is thus
Vc = 8r3
In a simple cubic cell, there is one host atom wholly inside the cube, because each of the eight corner atoms contributes one eighth of an atom to the cell interior.  In general, the total volume of the cell which is occupied by the host atoms is
Vs = 4/3pr3.Z.
The packing efficiency of a lattice is defined as the ratio Vs:Vc.  Thus, for SC, the packing efficiency is about 52%.
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Steven F. Watkins, Department of Chemistry, Louisiana State University