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

Tetrahedral Interstices
  When spheres of equal size (radius r) are packed together as closely as possible by stacking layers of hexagonally closest packed planes, the spheres themselves occupy 74% of the available space. The cavities of empty space ("holes" or "interstices") are found between layers.

For example, consider any two successive planes in a closest packed lattice. One atom in the A layer nestles in the triangular groove formed by three adjacent atoms in the B layer, and the four atoms touch along the edges of a regular tetrahedron. The edges of the tetrahedron are of length 2r, and the center of the tetrahedron is a cavity called the Tetrahedral  hole (a common symbol for "tetrahedral" is Td). If a guest sphere in that cavity is in contact with all four host spheres, its radius is  about 0.22r


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