Lecture 6 - Ch 3 pt 2

Lecture 6 - Ch 3 pt 2 - FCC Stacking Sequence •...

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Unformatted text preview: FCC Stacking Sequence • ABCABC...stacking sequence • 2D Projection B B C A B B B A sites C C B sites sites B B C sites • FCC Unit Cell A B C Chapter 3 - 20 Hexagonal-Close Packed Chapter 3 - 21 Hexagonal Close-Packed Structure (HCP) • ABAB...stacking sequence • 3D Projection: • 2D Projection: Top layer A sites c Middle layer B sites Bottom layer A sites a Adapted from Fig. 3.3(a), Callister 7e. Coordination #: 12 APF = 0.74 c/a = 1.633 6 atoms/unit cell: (12 x 1/6) + (2 x 1/2) + (3 x 1) e.g.: Cd, Mg, Ti, Zn Chapter 3 - 22 Hexagonal Close-Packed Structure (HCP) Chapter 3 - 23 HCP Both are close-packed!! FCC Chapter 3 - 24 t01_03_pg41 Chapter 3 - 25 Theoretical Density, Density = = Mass of Atoms in Unit Cell Total Volume of Unit Cell = where nA VC NA n = number of atoms/unit cell A = atomic weight VC = Volume of unit cell = a3 for cubic NA = Avogadro’s number = 6.023 x 1023 atoms/mol Chapter 3 - 26 Theoretical Density, = Mass of Atoms in Unit Cell Total Volume of Unit Cell • Need to know 3 things: Which atoms touch, to give you the relationship between a and r (or R) Now many atoms there are per unit cell Mass of the atoms in the unit cell Chapter 3 - 27 Theoretical Density, • e.g: Cr (BCC) A = 52.00 g/mol R = 0.125 nm n=2 R atoms unit cell = volume unit cell a= a 2 52.00 a3 6.023 x 1023 g mol 4R = 0.2887nm 3 theoretical = 7.18 g/cm3 actual = 7.19 g/cm3 atoms mol Chapter 3 - 28 Densities of Material Classes In general: metals > ceramics > Metals/ Alloys polymers 20 Platinum Gold, W Tantalum 10 Silver, Mo Cu,Ni Steels Tin, Zinc less dense packing often lighter elements (g/cm 3) Metals have... Ceramics have... 5 4 3 2 Polymers have... low packing density (often amorphous) lighter elements (C,H,O) Composites have... intermediate values Composites/ fibers Polymers 30 Why?: close-packing (metallic bonding) often large atomic masses Graphite/ Ceramics/ Semicond 1 Titanium Aluminum Magnesium B ased on data in Table B1, Callister *GFRE, CFRE, & AFRE are Glass, Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers in an epoxy matrix). Zirconia Al oxide Diamond Si nitride Glass -soda Concrete Silicon G raphite PTFE Silicone PVC PET PC HDPE, PS PP, LDPE 0.5 0.4 0.3 Glass fibers GFRE* Carbon fibers CFRE* A ramid fibers AFRE * Wood Data from Table B1, Callister 7e. Chapter 3 - 29 Solidification Small crystallite nuclei Irregular shaped grains Crystallite growth & grain obstruction Grain boundaries Chapter 3 - 30 Crystals as Building Blocks • Some engineering applications require single crystals: - Diamond single crystals for abrasives - Turbine blades Fig. 8.33(c), Callister 7e. (Fig. 8.33(c) courtesy of Pratt and Whitney). (Courtesy Martin Deakins, GE Superabrasives, Worthington, OH. Used with permission.) • Properties of crystalline materials often related to crystal structure: e.g.: Quartz (SiO2) fractures more easily along some crystal planes than others • Si - the king of single crystals! (Courtesy P.M. Anderson) Chapter 3 - 31 Single vs Polycrystals Single Crystals: Properties vary with direction: anisotropic e.g.: modulus of elasticity (E) in BCC iron E (diagonal) = 273 GPa Data from Table 3.3, Callister 7e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.) E (edge) = 125 GPa Polycrystals: Properties may/may not vary with direction If grains are randomly oriented: isotropic (Epoly iron = 210 GPa) If grains are textured: anisotropic 200 μm Adapted from Fig. 4.14(b), Callister 7e. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) Chapter 3 - 32 Polycrystals • Most engineering materials are polycrystals Anisotropic Adapted from Fig. K, color inset pages of Callister 5e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany) 1 mm • Nb-Hf-W plate with an electron beam weld • Each “grain” is a single crystal • If grains are randomly oriented, Isotropic overall component properties are not directional. • Grain sizes typ. range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers). Chapter 3 - 33 SUMMARY • Atoms may assemble into crystalline or amorphous structures • Common metallic crystal structures are FCC, BCC and HCP. Coordination number (CN) and atomic packing factor (APF) are the same for both the FCC and HCP crystal structures • We can predict the density of a material, provided we know the atomic weight, atomic radius and crystal geometry (e.g., FCC, BCC, HCP, etc.). • Materials can be single crystals or polycrystalline • Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but are generally non-directional (i.e., they are isotropic) in polycrystals with randomly-oriented grains. Chapter 3 - 34 ...
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