1. Space Filling Geometry and Materials Science & Engineering Terry A. Ring University of Utah

2. Materials Science and Engineering Study of Materials Structure, Properties and Processing Manipulating the Geometry of Atoms

3. Packing of Spheres in a Box Cubic (Percentage Filled 52%) - Iodine, Uranium Body Centered Cubic (68%) - Iron, Chromium Face Centered Cubic (74%) - Silicon, Aluminum, Copper Random Close Packed (61-64%) - glass Cubic BodyCentered Face Centered

4. Measure Packing Structure by X-ray diffraction X-ray Scattering - Sycrotron Neutron Diffraction Light Scattering –opal –Photonic Crystals Optical Semiconductors

5. Atom Packing Gives Properties of Material Changes with Temperature –Higher temperatures less density. Gives Form to crystals Different Energy for Different Packings

6. Packing Defects Equilibrium Defect Concentration at Temperature Alters properties of crystal –Color Ruby - Cr atoms added to Al 2 O 3 –Electrical Conductivity –Mechanical Properties Strength Wear

7. Real Materials Packing of Mixed Sized Spheres Packing of Non- Spherical Objects Packing of Mixtures of Non- Spherical Objects

8. Real Materials Monocrystals - Jet engine blades, Silicon Wafer, Watch Crystal –How would you make one? Poly-Crystals - Iron bar, Ceramic Cup –Two levels of packing atom packing into crystallites crystallite packing into microstructure Composites –Two levels of packing –Two materials Polymer + Ceramic - Carbon Fiber Epoxy Metal + ceramic - Al2O3 reinforced Aluminum

9. Odd Materials Fullerene Carbon nanotubes Fractal Aggregate Structures Stuck Together –Network of Fractal Aggregates