Space Filling Geometry and Materials Science & Engineering

Terry A. RingUniversity of Utah

Materials Science and Engineering

• Study of Materials Structure, Properties and Processing

• Manipulating the Geometry of Atoms

Properties

Structure Processing

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 BodyCenteredFace Centered

Measure Packing Structure by

• X-ray diffraction• X-ray Scattering - Sycrotron• Neutron Diffraction• Light Scattering

– opal– Photonic Crystals

• Optical Semiconductors

Angle

Atom Packing

• Gives Properties of Material• Changes with Temperature

– Higher temperatures less density.

• Gives Form to crystals• Different Energy for Different

Packings

Packing Defects

• Equilibrium Defect Concentration at Temperature• Alters properties of crystal

– Color • Ruby - Cr atoms added to Al2O3

– Electrical Conductivity– Mechanical Properties

• Strength• Wear

Real Materials

• Packing of Mixed Sized Spheres

• Packing of Non-Spherical Objects

• Packing of Mixtures of Non-Spherical Objects

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

Odd Materials

• Fullerene

• Carbon nanotubes

• Fractal Aggregate Structures Stuck Together– Network of Fractal Aggregates