Space Filling Geometry and Materials Science & Engineering

Terry A. Ring

University 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