Lecture 5 - Ch 3 pt 1

Lecture 5 - Ch 3 pt 1 - Ch. 3: The Structure of Crystalline...

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Unformatted text preview: Ch. 3: The Structure of Crystalline Solids ISSUES TO ADDRESS... • How do atoms assemble into solid structures? (initial focus on metals) • How does the density of a material depend on its structure? • When do material properties vary with the sample (i.e., part) orientation? Chapter 3 - 1 ANNOUNCEMENTS • Reading: Chapter 3: all sections except 3.8-3.11 and 3.16 • Midterm #1: Week TBA; Day TBA, Time TBA • Week 3 Recitations: Hand in #’s 2.14 & 2.20 (counts as Quiz 1) Team Project - Unit Cell Building (read ahead for NaCl, Diamond Cubic etc.) Problem Set #2: Chapter 3, #s 3.4, 3.5, 3.8, 3.9 and 3.14 Chapter 3 - 2 Here are the rules for the in-recitation Unit Cell building project: Each group will build ONE of the following unit cells: SC, BCC, FCC, HCP, NaCl, Diamond Cubic/Zinc Blende (ZnS) You need to understand/demonstrate the relationship between the following pairs: BCC and CsCl; Diamond Cubic and ZnS In week 3 each group/team will build and present their assigned unit cell. There will be 6 groups, so each will get ONE unit cell. “Present” means explaining to the rest of the class: i. How many atoms per unit cell ii. Which atoms touch, and where iii. The relationship between a and r Scoring/grading will be based on team voting ballots that will be given out and collected in Week 3 recitations. It will be a simple vote on: Aesthetics, accuracy and how well each group presents their structure and answers questions Chapter 3 - 3 Long + short range order The Big Picture Crystalline Solids Single Crystals PolyCrystals Combination Crystalline + Amorphous Some Polymers & Glass/Ceramics Short range order only Amorphous Solids Most polymers and inorganic glasses Chapter 3 - 4 Crystalline vs Amorphous e.g.: Ceramic compound SiO2 (aka Silica): Can be crystalline or amorphous (depends on cooling) Each Si atom bonds to 3 O atoms Quartz = Crystalline regular, ordered structure Fused silica = Amorphous disordered & irregular Chapter 3 - 5 Energy and Packing • Dense, ordered packing Energy typical neighbor bond length r typical neighbor bond energy • Non-dense, random packing Energy typical neighbor bond length typical neighbor bond energy Dense, ordered packed structures tend to have lower energies and are thus more stable! r Chapter 3 - 6 Materials & Packing Crystalline materials: Atoms pack in periodic, 3D arrays Typical of: Metals Many ceramics Some polymers Noncrystalline materials: Atoms have no periodic packing Occurs for: Complex structures Under rapid cooling Crystalline SiO2 Adapted from Fig. 3.22(a), Callister 7e. Si Oxygen Noncrystalline SiO2 “Amorphous” = Noncrystalline Adapted from Fig. 3.22(b), Callister 7e. Chapter 3 - 7 2-Dimensional Analogy Consider Tiles: What shape tiles can you imagine that completely cover a surface? squares? triangles? rectangles? hexagons? pentagons? Chapter 3 - 8 Section 3.7 – Crystal Systems Atomic order…small groups of atoms repetitive pattern Unit Cell: smallest repetitive (repeating) volume which contains the complete lattice pattern of a crystal: Represents symmetry of crystal structure Basic “building block” of crystal structure Generate entire structure via integer translations along each edge Unit cell geometry defined by 6 parameters: edge lengths a, b and c interaxial angles , and 7 crystal systems 14 crystal lattices a, b and c are the lattice constants Fig. 3.4, Callister 7e. Chapter 3 - 9 Highest symmetry Symmetry dictates what crystal a solid can be described by There are essentially only 7 types of bricks in Nature!! Lowest symmetry Chapter 3 - 10 Section 3.4 – Metallic Crystal Structures • How can we stack metal atoms to minimize empty space? 2-dimensions vs. Now stack these 2-D layers to make 3-D structures Chapter 3 - 11 Metallic Crystal Structures Tend to be densely packed Reasons for dense packing?: Typically, only one element is present, so all atomic radii are the same Metallic bonding is not directional Nearest neighbor distances tend to be small in order to lower bond energy Electron “cloud” shields ion cores from each other… metallic bond Have the simplest crystal structures We will consider 3 such structures… Well, 3-ish… Chapter 3 - 12 …and These Three Are… Simple Cubic, SC Body-centered cubic, BCC Face-centered cubic, FCC Hexagonal close-packed, HCP Chapter 3 - 13 So First…Simple Cubic Structure (SC) • Rare due to low packing density (only Polonium has this structure) • Close-packed directions are the cube edges • Coordination # = 6 (# nearest neighbors) (Courtesy P.M. Anderson) Chapter 3 - 14 Atomic Packing Factor (APF) Volume of atoms in unit cell* APF = Volume of unit cell *assume hard spheres • APF for a simple cubic (SC) structure = 0.52 atoms unit cell a R=0.5a APF = 1 4 3 a3 close-packed directions contains 8 x 1/8 = 1 atom/unit cell volume atom (0.5a) 3 volume unit cell Adapted from Fig. 3.23, Callister 7e. Chapter 3 - 15 Body-Centered Cubic Structure (BCC) • Atoms touch each other along cube body diagonals - Note: All atoms are identical; the body center atom is shaded differently only for ease of viewing. e.g.: Cr, W, Fe ( ), Tantalum, Molybdenum • Coordination # = 8 Adapted from Fig. 3.2, Callister 7e. 2 atoms/unit cell: 1 in center + 8 corners x 1/8 (Courtesy P.M. Anderson) Chapter 3 - 16 Atomic Packing Factor: BCC • APF for a body-centered cubic structure = 0.68 3a a 2a Adapted from Fig. 3.2(a), Callister 7e. R Close-packed directions: length = 4R = 3 a a atoms 4 2 unit cell 3 APF = ( 3a/4 ) 3 a3 volume atom volume unit cell Chapter 3 - 17 Face-Centered Cubic Structure (FCC) • Atoms touch each other along face diagonals - Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. e.g.: Al, Cu, Au, Pb, Ni, Pt, Ag • Coordination # = 12 Adapted from Fig. 3.1, Callister 7e. 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8 (Courtesy P.M. Anderson) Chapter 3 - 18 Atomic Packing Factor: FCC • APF for a face-centered cubic structure = 0.74 …the maximum achievable APF Close-packed directions: Length = 4R = 2 a 2a a Adapted from Fig. 3.1(a), Callister 7e. Unit cell contains: (6 x 1/2) + (8 x 1/8) = 4 atoms/unit cell atoms 4 4 unit cell 3 APF = ( 2a/4 ) 3 a3 volume atom volume unit cell Chapter 3 - 19 ...
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