1 / 16

INTRODUCTION TO CERAMIC MINERALS

INTRODUCTION TO CERAMIC MINERALS. ATOMIC STRUCTURE AND PACKING Lattice Constant, a & Atomic Packing Factor, APF. INTRODUCTION TO CERAMICMINERALS. Learning Outcomes Calculate lattice constant Calculate the atomic packing factor Calculate the ionic packing factor

matsu
Download Presentation

INTRODUCTION TO CERAMIC MINERALS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. INTRODUCTION TO CERAMIC MINERALS ATOMIC STRUCTURE AND PACKING Lattice Constant, a & Atomic Packing Factor, APF

  2. INTRODUCTION TO CERAMICMINERALS Learning Outcomes • Calculate lattice constant • Calculate the atomic packing factor • Calculate the ionic packing factor • Definition of coordination number • Determine the total atom in unit cell

  3. Lattice Constant, a : BCC √3 . a r a 2r r √2 . a Given, ( Fe )radius, r = 0.124nm 4r = √3. a a = 4r / √3 = 4(0.124) / √3 = 0.2864 nm

  4. INTRODUCTION TO CERAMIC MINERALS COORDINATION NUMBER, CN = the number of closest neighbors to which an atom is bonded = number of touching atoms,

  5. INTRODUCTION TO CERAMIC MINERALS ATOMIC PACKING FACTOR (APF) = fraction of volume occupied by hard spheres = Sum of atomic volumes / Volume of unit cell

  6. SIMPLE CUBIC STRUCTURE (SC) • Rare due to poor packing (only Po has this structure)  Does NOT occur in common engineering metals • Close-packed directions are cube edges. • Coordination # = 6 (# nearest neighbors) (Courtesy P.M. Anderson)

  7. ATOMIC PACKING FACTOR: SC • APF for a simple cubic structure = 0.52 Coordination #:6

  8. BODY CENTERED CUBIC STRUCTURE (BCC) • Close packed directions are cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. • Coordination # = 8 Adapted from Fig. 3.2, Callister 6e. (Courtesy P.M. Anderson) 7

  9. BODY CENTERD CUBIC STRUCTURED, BCC BCC • The hard spheres touch one another along cube diagonal . • The cube edge length, a= 4R/√3 • The coordination number, CN = 8 • Number of atoms per unit cell, n = 2 • Center atom (1) shared by no other cells: 1 x 1 = 1 • 8 corner atoms shared by eight cells: 8 x 1/8 = 1 • Atomic packing factor, APF = 0.68 • Corner and center atoms are equivalent

  10. ATOMIC PACKING FACTOR: BCC • APF for a body-centered cubic structure = 0.68 Adapted from Fig. 3.2,Callister 6e. 8

  11. FACE CENTERED CUBIC STRUCTURE (FCC) • Close packed directions are face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. • Coordination # = 12 9

  12. Figure 25: FCC atomic packing FACE CENTERED CUBIC STRUCTURE, FCC Share with 2 cells Share with 8 cells a= 2R√2 CN= 12 • The cube edge length, a= 2R√2 • The coordination number, CN = 12 • Number of atoms per unit cell, n = 4. (For an atom that is shared with m adjacent unit cells, we only count a fraction of the atom, 1/m). • 6 face atoms shared by two cells: 6 x 1/2 = 3 • 8 corner atoms shared by eight cells: 8 x 1/8 = 1 • Atomic packing factor (APF) = (Sum of atomic volumes)/(Volume of cell) = 0.74 (maximum possible)

  13. ATOMIC PACKING FACTOR: FCC • APF for a body-centered cubic structure = 0.74 Adapted from Fig. 3.1(a), Callister 6e. 10

  14. Figure 26: HCP closed-pack HEXAGONAL CLOSE-PACKED STRUCTURE, HCP HCP is one more common structure of metallic crystals • Number of atoms per unit cell, n = 6. • The coordination number, CN = 12 (same as in FCC) • 3 mid-plane atoms shared by no other cells: 3 x 1 = 3 • 12 hexagonal corner atoms shared by 6 cells: • 12 x 1/6 = 2 • 2 top/bottom plane center atoms shared by 2 cells: • 2 x 1/2 = 1 • Unit cell has two lattice parameters a and c. Ideal ratio c/a = 1.633 • Atomic packing factor, APF = 0.74 (same as in FCC) • Cd, Mg, Zn, Ti have this crystal struct

  15. HEXAGONAL CLOSE-PACKED STRUCTURE (HCP) • ABAB... Stacking Sequence • 3D Projection • 2D Projection Adapted from Fig. 3.3, Callister 6e. • APF = 0.74 • Coordination # = 12 12

  16. Calculate the atomic factor (APF) for the BCC unit cell, assuming the atoms to be hard spheres. APF = vol of atoms in BCC unit cell vol of BCC unit cell V atoms= 2 x 4/3πR3 V unit cell = a3 √3a = 4R or a = 4R √3 APF = 2 x 4/3πR3 / a3 = (8/3 πR3 ) / ( 4R3/ √3) = 0.74

More Related