### Unit Cells - Gordon State College

```Structures of Solids
Glass (SiO2)
Crystal
Solid
Noncrystal
Crystals
• Have an ordered, repeated structure.
• The smallest repeating unit in a crystal is a
unit cell, which has the symmetry of the
entire crystal.
• 3-D stacking of unit cells is the crystal lattice.
Chapter 11
Basis
Crystal structure
The basis may be a single atom or
molecule, or a small group of atoms,
molecules, or ions.
Unit cell: 2-D, at least a parallelogram
Unit cell is the building block of the crystal
: 3-D, at least a parallelepiped
(Simple cubic)
• Size of the cell
• Size of the atoms
• Number of atoms in a cell
X-ray diffraction
Next lecture
Count it now!
MODEL
• Close Packing of Spheres
Chapter 11
Most Common Types of Unit Cells based on Close Packing of
Spheres Model
• Simple Cubic
– 1 atom
• Body Centered Cubic (BCC)
– 2 atoms
• Face Centered Cubic (FCC)
– 4 atoms
Chapter 11
Number of Atoms in a Cubic Unit Cell
1
2
4
Unit Cells
Chapter 11
Sample Problem
• The simple cubic unit cell of a particular
crystalline form of barium is 2.8664 oA on
each side. Calculate the density of this form
of barium in gm/cm3.
Chapter 11
Steps to Solving the Problem
• (1.) Determine the # of atoms in the unit cell.
• (2.) Convert oA (if given) to cm. (3.) Find volume
of cube using Vcube = s3 = cm3
• (4.) Convert a.m.u. to grams. [Note: 1 gm=
6.02 x 1023 a.m.u.]
• (5.) Plug in values to the formula: D =
mass/volume
•
Chapter 11
Conversions
• Useful Conversions:
• 1 nm(nanometer = 1 x 10-7 cm
• 1 oA (angstrom)= 1 x 10-8 cm
• 1 pm (picometer) = 1 x 10-10 cm
• 1 gram = 6.02 x 10 23 a. m. u. (atomic mass
unit)
Chapter 11
Sample Problem
• LiF has a face-centered cubic unit cell (same as NaCl). [F- ion
is on the face and corners. Li+ in between.]
•
•
•
•
Determine:
1. The net number of F- ions in the unit cell.
2. The number of Li+ ions in the unit cell.
3. The density of LiF given that the unit cell is 4.02 oA on an
edge. (oA = 1 x 10-8 cm)
Chapter 11
Sample Problem
• The body-centered unit cell of a particular
crystalline form of iron is 2.8664 oA on each
side. (a.) Calculate the density of this form of
iron in gm/cm3. (b.)Calculate the radius of
Fe.
• Note: First determine:
• A. The net number of iron in the unit cell.
• B. 1 oA = 1 x 10-8 cm