1. Chapter 12 Unit Cells

2. X-ray crystallography
Solids can be amorphous or crystalline
Crystalline solids can be analyzed using X-ray crystallography
Firing X-rays at a crystal can produce diffraction patterns which can be analyzed to give a 3-D image of a compound

3. Chemical Analysis techniques
Mass spectrometry – Determine composition of a compound
IR spectroscopy – uses IR-rays to determine bond types in a structure based on bond energy
NMR spectroscopy – utilizes magnetic field to determine connectivity of atoms
X-ray crystallography – gives the 3-D image of the compound, which includes the composition, bond types, bond connectivity, as well as 3-D arrangement

4. Unit cells
Crystalline solids are aligned in a crystal lattice, where a unit cell is the repeating pattern throughout the lattice
Various types of unit cells, we focus on cubic unit cells

5. Unit cell characteristics
Atoms per unit cell – the amount of atoms per unit cell, (based on volume of atom)
Coordination number – the number of atoms in direct contact with an atom
Edge length – the length of an edge of a unit cell
Measured in r (radius of the atom)
Packing efficiency – the percentage of the volume of the unit cell occupied by the spheres

6. Simple cubic unit cell
Simple cubic – consists of a cube with one atom at each corner
Atoms touch along edges
Coordination number = 6
Atoms per unti cell = 1
Packing efficiency = 52%

7. Body-centered cubic unit cell
Body-centered cubic – consists of one atom at each corner and one atom in the very center of the cube
Atoms don’t touch along edges, but instead along the diagonal through the center of the cube
Coordination number = 8
Atoms per unit cell = 2
Packing efficiency = 68%

8. Face-centered cubic
Face-centered cubic – consists of one atom at each corner and one atom in the center of each cube face
Atoms touch along the face diagonal
Coordination number = 12
Atoms per unit cell = 4
Packing Efficiency = 74%

9. Closest-packed structures
Envisioning atoms as stacking in layers
Simple cubic can be seen as atom layers directly stacked on top of each other PE = 52%
If atoms in a layer are in a row are offset from the next by half a sphere, higher PE can be achieved
If layers are instead stacked where they are offset, PE can increase further

10. Hexagonal closest packing
Two types of closest packed structure with the previously mentioned offset scaffold
Hexagonal closest packing – ABAB layering pattern, where 1st and third layer are equivalent (layer A)
Forms from a hexagonal unit cell

11. Cubic closest packing
Cubic closest packing – An ABCABC layering pattern where 3rd layer is offset from the first
Also the same as face-centered unit cell structure

12. Chapter 12 Unit cells….The end