Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege

1. Engineering 45 Crystalline MicroStructure Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Learning Goals • Learn How atoms assemble into solid structures • Use metals as Prototypical Example • Determine Relationship Between Material density and material MicroStructure • Understand how material properties vary with the sample (i.e., part) orientation

3. Properties of Solid Materials • Mechanical: Characteristics of materials displayed when Forces and/or Moments are applied to them. • Physical: Characteristics of materials that relate to the interaction of materials with various forms of Energy. • Chemical: Material characteristics that relate to the e− structure of a material. • Dimensional: Size, shape, and finish

4. Material Properties Chemical Physical Mechanical Dimensional Composition Melting Point Tensile properties Standard Shapes Microstructure Thermal Toughness Standard Sizes Phases Magnetic Ductility Surface Texture Grain Size Electrical Fatigue Stability Corrosion Optical Hardness Mfg. Tolerances Crystallinity Acoustic Creep Molecular Wt Gravimetric Compression Flammability

5. NonDense, Random Packing Energy typical neighbor bond length typical neighbor r bond energy Energy typical neighbor bond length r typical neighbor bond energy Energy and Atomic Packing • Dense Regular Packing • Regular Structures Tend to have LOWER Energy → Energetically Favored

6. Materials and Atomic-Packing • CRYSTALLINE Materials • atoms pack in periodic, 3D arrays • typical of: Metals, many Ceramics, and some Polymers • NONcrystalline Materials • atoms have no periodic packing • occurs for: • Complex structures • Rapid Cooling • "Amorphous"  Noncrystalline crystalline SiO2 noncrystalline SiO2

7. Crystalline Material atomic arrangement in solid: periodic and repeating 3D array Long Range Order lattice Crystal Basics • Unit Cell  Smallest Repeating Entity Within a Lattice • Geometry • Lattice Constants: a, b, c • interaxial angles: a, b, g

8. B Crystal Structure • Crystal Structure geometry + atom-positions • i.e.; the spatial arrangement of Atoms, Ions, or Molecules • Some Types polymer

9. Tab 3.2 In Text Shows the 7 Most Common Crystal Systems Some Examples Cubic a = b = c  =  =  = 90° Example Crystal Systems • Hexagonal • a = b  c •  =  = 90°,  = 120°

10. Simple Cubic Stucture (SC) • Rare due to poor packing (only Po has this structure) • Close-packed directions are cube edges. • Rotate • Coordination No. = 6 • CoOrd No. (CN) = the No. of Nearest Neighbors

11. HardSphere Model Polonium, Z = 84, SC Structure • Reduced Sphere Mod http://www.webelements.com/webelements/index.html http://www.webelements.com/webelements/elements/text/Po/key.html http://www.webelements.com/webelements/elements/text/Po/xtal.html • Note: 100 PicoMeters = 1 Å

12. Assuming HardSphere Model volume atoms atom 4 a 3 p unit cell (0.5a) 1 3 R=0.5a APF = 3 a volume close-packed directions unit cell contains 8 x 1/8 = 1 atom/unit cell Atomic Packing Factor, APF • APF For Simple Cubic Structure = 52%

13. HardSphere Model Body Centered Cubic (BCC) • Atoms per Unit Cell = 1 + (8 x 1/8) = 2 • CoOrd No. = 8 • 8 Atoms Touch the “Center” Atom • Rotate

14. Find Radius, r, in terms of Lattice Const, a Atomic Packing Factor: BCC • Thus r in Terms of a • And Vsphere = (4/3)R3 • So the BCC APF • Atoms Touch On Cube Diagonal, L • L = a3 = L = 4r

15. HardSphere Model Face Centered Cubic (FCC) • Atoms per Unit Cell = 6x½ + (8 x 1/8) = 4 • CoOrd No. = 12 • CN = 4top + 4bot + 4mid • Rotate

16. Find Radius, r, in terms of Lattice Const, a Atomic Packing Factor: FCC • Thus r in Terms of a • And Vsphere = (4/3)R3 • So the FCC APF • Atoms Touch on Face Diagonal, f • f = a2 = 4r

17. An ABCABC... Stacking Sequence The 2D projection B B B B C C C A A A B B B B B B B A sites C C C C C C B B sites sites B B B B C sites A B C FCC Stacking Sequence • The FCCUnit Cell

18. Built Up in an A-B Stacking Pattern c a Hexagonal Close Packed (HCP) • Exhibits NonCubic Symmetry on a & c axes • c:a Ratio  1.633 • Atoms per Cell = 6 • (12 x 1/6)corners + (2 x ½)top/bot + 3mid = 6 • APF and CN are the SAME as the FCC Structure • APF = 74.05% • Close Packed

19. For 3 Stacking Planes Below, Consider the CENTER Atom HCP CoOrdination Number • Observe The Center Atom’s Nearest Neighbors • 6 Surrounding in the Center Plane • 3 Touching From Below • 3 Touching From Above • Thus

20. Compounds: Often have similar close-packed structures NaCl Structure Ionic Radii Na+ = 116 pm Cl– = 167 pm Structure of Compounds • Expand Na+ ions to Reveal Close-Packed X-tal Structure

21. Atomic Radii for Crystals are Measured by X-Ray Diffraction Can use The Data From XRD Measurements to Calc Density for Crystals Theoretical Density, r Fcn of Ratom • On the Macro Scale Densities are Calc’d by Weight & Measure of Chunks of Crystals

22. For Copper Ratom = 128 pm Acu = 63.54 g/mol Xtal Structure = FCC Recall From FCC APF Calc Theoretical Density Example • FCC Cu has 4 atoms per Unit Cell; so r • And The VC = a3 • rmacro = 8940 kg•m-3 •  0.53% HIGHER than Theoretical Value

23. Characteristics of Some Elements at 20 °C 15

24. Densities Of Material Classes rmetals>rceramics>rpolymers Why? Metals have... • close-packing (metallic bonding) • large atomic mass Ceramics have... • less dense packing (covalent bonding) • often lighter elements Polymers have... • poor packing (often amorphous) • lighter elements (C,H,O) Composites have... • intermediate values Data from Table B1, Callister 6e. 16

25. Most Crystalline Materials Are Composed of many Small Crystals i.e., they are POLYcrystalline and exhibit a GRAIN Structure Grain Structure Introduces Weakness into the Material SINGLE Crystal Applications • But Making LARGE Single Crystals is Very Difficult; i.e., Expensive • Single Xtal Examples • SemiConductorwafers • Turbine Blades

26. 1-Material; Several Crystal Types • Polymorphism  More Than One Crystal Structure • Often Found in Compounds • Allotropy  Polymorphism in ELEMENTAL Solids • Examples • Carbon Allotropes • Graphite • Diamond • Bucky Balls/Tubes • Iron Allotropes • BCC Ferrite (RT) • FCC Austenite (> 912 °C) • BCC Delta (~TMelt)

27. Diamond - tetrahedral, covalent bonds, Single-Element Form; the ZincBlende Crystal structure • Graphite – Layers of Hexagonally Bonded C-atoms Cabon Allotropes • C60 Fullerenes

28. Example similar to P3.15 Uranium Orthorhombic Lattice Constants a = 286 pm b = 587 pm c = 495 pm ratom = 138.5 pm  = 19050 kg/m3 AU = 238.03 g/mol → FIND APF WhiteBoard Work SR Case

29. Uranium Unit Cell (BCR)

30. Uranium Unit Cell (BC)

31. Uranium Unit Cell (SR)

32. All Done for Today Uranium hasthe Highest ZOf Any NaturalElement

34. P3-15