Chap 4-2a

The structure of solids can be described as if they were three dimensional analogs of
wallpaper. Wallpaper has regular repeating design that extends from one edge to the other.
Crystals have a similar repeating design, but in this case the design extends in three dimensions
from one edge of the solid to the other.
We can describe a three-dimensional crystal by specifying the size, shape, and contents
of the simplest repeating unit and the way these repeating units stack to form the crystal.
A crystal is an array of atoms packed together in a regular pattern.
Unit Cell
 The simplest repeating unit of a crystal is a unit cell. A unit cell of a pattern is a piece of
the pattern which, when repeated through space without rotation and without gaps or
overlaps, reconstruct the pattern to infinity.
 Each unit cell is defined in terms of lattice pointsthe points in space about which
particles are free to vibrate in a crystal.
In 1850, Auguste Bravais showed that crystals could be divided into 14 unit cells, which
meet the following criteria:
 The unit cell is the simplest repeating unit cell in the crystal.
 Opposite faces of a unit cell are parallel.
 The edge of the unit cell connects equivalent points.
The 14 Bravais unit cells are shown in the figure below.
These unit cells fall into 7 categories, which differ in the three unit-cell edge lengths (a, b,
and c) and three internal angles (, , and ), as shown in the table below.
We will focus on the cubic category, which includes the 3 types of unit cells simple cubic,
body-centered cubic, and face-centered cubic shown in the figure below.
These unit cells are important for 2 reasons:
A number of metals, ionic solids, and intermetallic compounds crystallize in cubic cells.
It is relatively easy to do calculations with these unit cells because the cell-edge lengths
are all the same and the cell angles are al 90.
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