# Unit Cells Let’s look at two different ways to visualize the structure of a solid.

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Unit Cells Let’s look at two different ways to visualize the structure of a solid.

Simple Cubic Unit Cell A simple cubic unit cell has an atom at each corner of a cube.

Simple Cubic Unit Cell Each atom in a simple cubic unit cell is shared by 8 unit cells. Therefore only 1/8 of the volume of each atom is in each unit cell.

Simple Cubic Unit Cell Therefore, one simple cubic unit cell actually only represents 1 atom. Because: (1/8) * 8 = 1 atom

Simple Cubic Unit Cell The coordination number is the number of atoms that each atom touches. In a simple cubic unit cell, each atom touches 6 other atoms.

Simple Cubic Unit Cell The black line is the radius of one atom.

Body-Centered Cubic Unit Cell This picture shows the atoms spread out more than they really are. Build your model with the atoms touching. Notice the central atom (body) is totally in the unit cell.

Body-Centered Cubic Unit Cell The corner atoms are the same as a simple cubic unit cell; each atom is shared by 8 other unit cells and therefore they represent 1 atom.

Body-Centered Cubic Unit Cell Since the atom in the middle is 1 atom and the 8 on the corners represent 1 atom; this means the body centered until cell represents 2 total atoms.

Body-Centered Cubic Unit Cell Notice the 8 corner atoms touch the central atom. This is true for all the atoms in a body centered cubic unit cell. The coordination number of a body centered unit cell is 8.

Body-Centered Cubic Unit Cell Body centered unit cells are more dense than simple cubic unit cells. Look at the models of each, there is a lot less empty space due to the atom in the center.

Face-Centered Cubic Unit Cell This picture is of a FCC unit cell. All of the atoms are of the same element, even though they show different colors in this picture.

Face-Centered Cubic Unit Cell This picture is of 2 FCC unit cells. Notice how they share one of the face atoms. Therefore, ½ the volume of the face atom is in each unit cell.

Face-Centered Cubic Unit Cell With 6 face atoms in each unit cell, this means the face atoms represent a total of 3 atoms. (1/2) * 6 = 3 atoms

Face-Centered Cubic Unit Cell Each corner atom is shared by 8 unit cells, so only 1/8 of there volume is contributed to each unit cell. Just like with simple cubic, the 8 corner atoms represent the volume of just one atom.

Face-Centered Cubic Unit Cell Therefore the net number of atoms represented by a FCC unit cell is 4. 3 from face atoms + 1 from corner atoms 4 total atoms

Face-Centered Cubic Unit Cell The coordination number of a FCC unit cell is 12, that means that each atom touches 12 other atoms. Notice the red atom in the center of this lattice. Click to the next slide to see how it touches 12 other atoms.

Face-Centered Cubic Unit Cell The four yellow atoms touch the red atom.

Face-Centered Cubic Unit Cell These four yellow atoms touch the red atom.

Face-Centered Cubic Unit Cell All 12 of the yellow atoms touch the red atom when they are packed together.

Table Salt - NaCl This is a model of NaCl. Can you see that the red sodium atoms are in a FCC unit cell? This diagram doesn’t show size, but the Na + ion is smaller than the Cl - because it loses an energy level when it loses it’s one electron.

NaCl – great on fries!!! This is a better representation of a sodium chloride molecule. The chlorine atoms are FCC and the sodium atoms are filling the gaps, also FCC.

Hexagonal Closest Packing Another way of looking at the structures of solids is to look at how they are packed together. The diagram to the right shows a hexagonal closest packed structure.

Hexagonal Closest Packing Notice how this is a repeated pattern of 2 different layers. These are all the same element, the different colors just help show the different layers. ABABAB pattern

Hexagonal Closest Packing Look at the center red atom. Can you see that it is touching 6 red atoms, 3 blue atoms above it and 3 blue atoms below it. This gives HCP a coordination number of 12.

Cubic Closest Packing Notice that Cubic Closest Packing has 3 layers that alternate. The center red atom is still touching 12 other atoms, so it has a coordination number of 12, just like HCP and FCC.

Big Finale Now stack the atoms as shown in figure C and D on your worksheet and take it to Mr. Calhoun. This ends the program, please log off and enjoy the rest of the day.

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