1. Crystalline Solids CaF2 Unit Cell
Crystal Lattice – A 3D array of points where each point has an identical environment.
Unit Cell – The repeating unit (a unit cell is to a crystal, like a “brick” is in a house). In a given crystal all unit cells are identical.

2. Ionic radii and coordination number
Cation
Anion
Large cation & Large anion
r(Cation)/r(Anion) ~0.72
Small cation & Large anion
r(Cation)/r(Anion) ~0.3
Anions and cations want to stay in contact with each other, but when the cation becomes much smaller than the anion, anion-anion contacts prevent this.
The solution is to lower the coordination number

3. Coordination Geometry
Radius Ratio Rules
r(cation)/r(anion)
Coordination Number
Coordination Geometry
 0.73 8
Cube
 0.41 6
Octahedron
 0.22 4
Tetrahedron
 0.15 3
Trigonal Planar
These are only meant to be used as rough guidelines, but the coordination number does goes down as the radius ratio [r(cation)/r(anion)] decreases.

4. Ionic Crystal Structures
(a) CsCl
(b) NaCl
(c) Zinc blende
Decreasing coordination number
Decreasing r(cation)/r(anion)

5. Cell Edge vs. Radii 4rFe = √3 a 2rRe + 2rO = a 4rAg = √2 a
Body centered cubic metal (i.e. Fe)
Face centered cubic metal (i.e. Ag)
ReO3 structure a
diag a
diag a
4rFe = √3 a
2rRe + 2rO = a
4rAg = √2 a
Atoms touch along the body diagonal of the cubic unit cell
Atoms touch along a face diagonal of the cubic unit cell
Atoms touch along an edge of the cubic unit cell

6. Optical Diffraction Experiment
Laser
Diffraction Slide
Diffraction Spots

7. Diffraction Demo Take home message
The diffraction pattern is related but not equal to the grid pattern
Diffraction is most effective for monochromatic light whose wavelength is similar to the spacing of “slits”
For crystals X-rays have a wavelength comparable to spacings of atoms

8. Single Crystal X-ray Diffraction

9. Bragg’s Law A B d
The extra path length traveled by wave B (shown in red) is equal to 2d sin q, where d is the spacing between planes. Constructive interference will only occur if this distance is an integer multiple of the wavelength (nl).

10. X-ray Powder Diffractionq 2q
Horizontal Diffraction Circle
Divergent
X-ray
Source
Detector
Divergence Slit
Antiscatter Slit
Receiving Slit
Horizontal
Soller Slits
Sample (Vertical Flat Plate)

11. X-ray Powder Diffraction Pattern