1. Crystal Structures & X-ray Diffraction Chemistry 123 Spring 2008 Dr. Woodward

2. Crystals

3. Crystalline Solids 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. CaF 2 Unit Cell

4. 3D Crystal Systems (7) Cubic Tetragonal Hexagonal Rhombohedral Orthorhombic Monoclinic Triclinic 14 Bravais Lattices Cubic The crystal systems each have distinctive symmetry and unit cell dimensions

5. X-ray Diffraction

6. 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

7. Bragg’s Law When we use Bragg’s Law we generally set n=1. The extra path length traveled by wave B (shown in red) is equal to 2d sin , where d is the spacing between planes. Constructive interference will only occur if this distance is an integer multiple of the wavelength (n ). When we use Bragg’s Law we generally set n=1. A B d

8. Symmetric Structures Simple X-ray Pattern Ex. Gold – Face centered cubic structure Low symmetry Structures Complex X-ray Pattern Ex. CuSO 4 5H 2 O (triclinic structure)

9. (a) CsCl(b) NaCl(c) Zinc blende Simple Cubic Crystal Structures Decreasing coordination number

10. X-Ray Powder Diffraction Pattern (Ex. Magnesium Sulfide, MgS) Each peak corresponds to scattering from a different set of lattice planes. Two planes are shown above for MgS, which has the same structure as NaCl. 020 planes 220 planes

11. MgS with the NaCl structureZnS with the Zinc Blende structure

12. Two Component Phase Diagram Mole %ZnS 0255075100 Liquid 2-phase region MgS(ss) +ZnS(ss) MgS(ss) + Liquid ZnS(ss) + Liquid MgS(ss) ZnS(ss) Temperature (  C) PureZnSPureMgS A B C Eutectic Point D Mole % 0255075100 Liquid 2-phase region (ss) +(ss) ( ) + Liquid (ss) + Liquid (ss) Temperature (  C) Pure Eutectic Point

13. Rock salt type Mg 1-x Zn x S Zinc Blende type Zn 1-x Mg x S X-ray Powder Diffraction Pattern Microscopic View Region A MgS-type solid solution Region B ZnS-type solid solution Region C Two-phase region Microscopic View