ENERGY AND PACKING. Chapter 3 CRYSTAL STRUCTURE & PROPERTIES MATERIALS AND PACKING METALLIC CRYSTALS ISSUES TO ADDRESS...
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1 Chapter 3 CRYSTAL STRUCTURE & PROPERTIES ISSUES TO ADDRESS How do s assemble into solid structures? (For now, focus on metals) ENERGY AND PACKING non dense, random packing bond energy Energy bond length r 2. How does density depend on the structure? 3. When do material properties vary with sample (i.e., part) orientation? Anderson dense, regular packing bond energy Energy bond length Dense, regular packed structures tend to have lower energy r Anderson MATERIALS AND PACKING METALLIC CRYSTALS Crystalline s pack in periodic, 3D arrays typical of: -metals -many ceramics -some polymers Noncrystalline (amorphous) s have no periodic packing occurs for: -complex structures -rapid cooling crystalline SiO2 Si Oxygen Tend to be densely packed Reasons: -Typically, only one element (i.e., all ic radii are the same) -Bonding is not directional -Small nearest neighbor distances lower energy Have simplest crystal structures. We will look at three such structures... Noncrystalline SiO2 Anderson Anderson
2 Simple Cubic Structure (SC) Rare due to poor packing (only Po has this structure): 8 s 1 Atomic Packing Factor (APF) Volume of s in * Volume of *assume hard spheres For simple cubic structure... (contains 8 x 1/8 = 1 ) Coordination Number = 6 (number of nearest neighbors) Anderson a directions contains 8 x 1/8 = 1/ R=0.5a 0.52 for simple cubic π (0.5a)3 a 3 Anderson Body-Centered Cubic Structure (BCC) Materials Science: A Multimedia Approach, by John C. Russ Anderson Body-Centered Cubic Structure (BCC) 1 directions: length = 4R = 3 a Coordination Number = 8 contains x 1/8 = 2s/ s R π ( 3a/4)3 a 3 a One of 4 directions 0.68 for BCC Anderson
3 Face-Centered Cubic Structure () Materials Science: A Multimedia Approach, by John C. Russ Anderson Face-Centered Cubic Structure () a directions: length = 4R = 2 a Coordination Number = 12 contains 6 x 1/2 + 8 x 1/8 = 4s/ s 4 3 π ( 2a/4)3 4 a 3 Materials Science: A Multimedia Approach, by John C. Russ 0.74 for Anderson Structure: ABCABC Stacking Sequence... Hexagonal Close Packed Structure (HCP) ABABAB...Stacking Sequence A sites B sites C sites A B B C A B B B C C B B A B C Unit Cell 2D projection A sites B sites A sites Coordination Number = for HCP Top layer Middle layer Bottom layer Anderson Anderson
4 Compounds have Similar Structures (sometimes more complicated) example: NaCl Materials Science: A Multimedia Approach, by John C. Russ Anderson THEORETICAL DENSITY, ρ # s/ ρ = n A Atomic weight (g/mol) (units = mass/) V c N A Volume/ Avogadro's number (cm 3 /) (6.023 x s/mol) Example: Copper from Table inside from cover of Callister (see next slide): crystal structure = 4 s/ ic weight = g/mol (1 amu = 1 g/mol) Atomic radius R = nm (1nm = 10-7 cm) Vc = a 3 ; For a = 4R/ 2 ; Vc = 4.75 x cm 3 Result: theoretical ρ Cu = 8.89 g/cm 3 actual: 8.94 g/cm 3 Anderson Characteristics of Selected Elements (inside cover-callister) At. Weight Element Symbol (amu) g/cm 3 Crystal Atomic radius (nm) Aluminum Al Argon Ar Barium Ba Beryllium Be Boron B Bromine Br Cadmium Cd Calcium Ca Carbon C Cesium Cs Chlorine Cl Chromium Cr Cobalt Co Copper Cu Flourine F Gallium Ga GermaniumGe Gold Helium Hydrogen Au He H BCC HCP Rhomb HCP Hex BCC BCC HCP Ortho Dia. cubic Anderson DENSITIES OF MATERIAL CLASSES ρ metals ρ ceramics ρ polymers Why? Metals have... close-packing 5000 (metallic bonding) ρ large ic masses Ceramics have... (kg/m 3 ) less dense packing 1000 (covalent bonding) 500 often lighter elements (oxygen, carbon) Polymers have... poor packing 100 (often amorphous) lighter elements (C, H, O) Composites-average values 30 Ceramics WC TiC ZrC SiC Cement Ice from M.F. Ashby, Engineering Materials I Metals Platinum Gold Lead Iron Aluminum Beryllium Polymers PTFE PVC Polyethylene Foamed polymers Composites Cermets GFRPs CFRPs Common woods Anderson
5 Crystals are the Building Blocks of Many Engineering Materials diamonds (single crystals) Most Engineering Materials are Polycrystals Low carbon steel. Each grain is itself a single crystal. As each is randomly oriented, overall component is not directional. Diamond facets: Certain crystal planes pull apart (fracture) more easily. Some engineering applications require single crystals gems semi-conductors turbine blades Anderson µm Crystals typically range from 1 nm to 2 cm ( from a few to 10 8 ic layers) Anderson Single vs. Poly Crystals Single crystals Properties vary with direction Anisotropic material Example of anisotropy: BCC iron Polycrystals Properties may/may not vary with direction Example: Common steel is polycrystalline. If grains are random isotropic (E ~ 210 GPa) If grains are textured anisotropic. E (diagonal) = 272 GPa E (edge) = 125 GPa random grain orientation textured (from rolling) Anderson X-Rays can confirm we have crystals extra distance travelled by wave 2 θ detected x-ray intensity θ c θ λ spacing d between planes d=nλ/2sinθ c θ reflections must be in phase to detect signal Anderson
6 Scanning Tunneling Microscopy confirms crystals Images of s in a MoSi2 coating! DEMO 1: HEATING AND COOLING AN IRON WIRE This demonstrates polymorphism the same s can have more than one crystal structure. figs from: Liquid BCC Stable longer Anderson Stable 914 BCC Stable Tc 768 shorter! longer! magnet falls off shorter Anderson Summary-Crystal Structure & Properties Atoms may pack in -periodic arrays (crystals) -nonperiodic (amorphous) structures Theoretical density can be calculated based on: -crystal structure -ic radius The ranking of density generally follows... -metals: largest -ceramics: intermediate -polymers: smallest -composites: intermediate Single crystals: generally anisotropic. Polycrystals w/randomly oriented crystals: isotropic Anderson
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