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Reading:
Crystal Structures with Cubic Unit Cells
Revised 5/3/04
1
CRYSTAL STRUCTURES WITH CUBIC UNIT CELLS
Crystalline solids are a three dimensional collection of individual atoms, ions, or whole
molecules organized in repeating patterns.
These atoms, ions, or molecules are called
lattice points
and are typically visualized as round spheres.
The two dimensional layers
of a solid are created by packing the lattice point “spheres” into square or closed packed
arrays.
(Figure 1).
Which packing arrangement makes the most efficient use of space?
square array
closepacked array
Figure 1:
Two possible arrangements for identical atoms in a 2D structure
Stacking the two dimensional layers on top of each other creates a three dimensional
lattice point arrangement represented by a unit cell.
A
unit cell
is the smallest collection
of lattice points that can be repeated to create the crystalline solid.
The solid can be
envisioned as the result of the stacking a great number of unit cells together.
The unit
cell of a solid is determined by the type of layer (square or close packed), the way each
successive layer is placed on the layer below, and the
coordination number
for each
lattice point (the number of “spheres” touching the “sphere” of interest.)
Primitive (Simple) Cubic Structure
Placing a second square array layer directly over a first square array layer forms a
"simple cubic" structure.
The simple “cube” appearance of the resulting unit cell (Figure
3a) is the basis for the name of this three dimensional structure.
This packing
arrangement is often symbolized as "AA.
..", the letters refer to the repeating order of the
layers, starting with the bottom layer.
The coordination number of each lattice point is
six.
This becomes apparent when inspecting part of an adjacent unit cell (Figure 3b).
The unit cell in Figure 3a appears to contain eight corner spheres, however, the total
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Crystal Structures with Cubic Unit Cells
Revised 5/3/04
2
number of spheres within the unit cell is 1 (only 1/8
th
of each sphere is actually inside the
unit cell).
The remaining 7/8
ths
of each corner sphere resides in 7 adjacent unit cells.
Figure 3a:
Square Array Layering
Figure 3b:
Simple Cubic
Figure 3c:
Space Filling Simple Cubic
The considerable space shown between the spheres in Figures 3a is misleading:
lattice
points in solids touch as shown in Figure 3b.
For example, the distance between the
centers of two adjacent metal atoms is equal to the sum of their radii.
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This note was uploaded on 11/20/2010 for the course CHEMISTRY Chem 1LE taught by Professor Dr.kimberlyedwards during the Spring '10 term at UC Irvine.
 Spring '10
 Dr.KimberlyEdwards
 Atom, Mole

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