Lab-2 Crystallography in Materials Science
- 1. Lab# 02 Basic Introduction to Crystallography By Yousaf Haroon Lab Engineer FMCE
- 2. Contents of lab 2 • Crystallography and crystal systems. • Lattice and motif • Unit cell • Coordination number • How to find CN of SC,FCC and BCC. • Number of atoms in a unit cell ( SC,FCC,BCC) • Atomic Packing Factor (SC, FCC,BCC)
- 3. The branch of science concerned with the structure and properties of crystals.
- 4. Crystal structure The atomic arrangement inside a crystalline material is called crystal structure.
- 5. Why do we study crystal structure? 1. Properties 2. Applications Similar materials having different properties and applications?
- 6. Fundamental concepts Crystalline/Non crystalline materials • A crystalline material is one in which the atoms have a 1. Repeating or periodic array over large atomic distances 2. Long-range order exists. 3. Repetitive three-dimensional pattern, in which each atom is bonded to its nearest-neighbor atoms. 4. All metals, many ceramic materials, and certain polymers Amorphous material?
- 7. Hard sphere model • When describing crystalline structures, atoms (or ions) are thought of as being solid spheres having well-defined diameters. • This is termed the atomic hard sphere model in which spheres representing nearest-neighbor atoms touch one another.
- 8. Lattice and motif Three dimensional (infinite) array of regularly spaced points. Crystal structure= lattice + motif Lattice points are the connection points in a unit cell Arrangement of the building blocks(atoms) of the unit cell
- 9. CRYSTAL SYSTEMS • Lattice parameters •Axis and angles a, b, c & •α,ꞵ,γ •Seven possible combinations of a, b, c & α,ꞵ,γ resulting in seven crystal systems
- 11. Unit cell •Small repeating entities •Unit cells for most crystal structures are parallelepipeds or prisms having three sets of parallel faces.
- 12. Coordinate number and point coordinates • Number of nearest- neighbors or touching atoms • The position of any point located within a unit cell may be specified in terms of its coordinates as fractional multiples of the unit cell edge lengths (i.e., in terms of a, b, and c)
- 13. Number of atoms in a unit cell
- 14. The Crystal Structure of Metals Metals usually have crystal structures: 1. Simple cubic 2. Body centered cubic 3. Face centered cubic
- 15. 15 • Rare due to low packing density (only Po has this structure) • Close-packed directions are cube edges. • Coordination # = 6 (# nearest neighbors) Simple Cubic Structure (SC) No. of atoms/unit cell : 8 corners x 1/8 = 1
- 16. 16 • Coordination # = 8 • Atoms touch each other along cube diagonals. Body Centered Cubic Structure (BCC) ex: Cr, W, Fe (), Tantalum, Molybdenum 2 atoms/unit cell: 1 center + 8 corners x 1/8
- 17. 17 • Coordination # = 12 • Atoms touch each other along face diagonals. Face Centered Cubic Structure (FCC) ex: Al, Cu, Au, Pb, Ni, Pt, Ag 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
- 18. Hexagonal close-packed Coordination # = 12 ex: Cd, Mg, Ti, Zn 6 atoms/unit cell: 3 center + ½ x 2 top and bottom + 1/6 x 12 corners
- 19. Atomic packing factor •How closely atoms are packed in a unit cell. •How much portion an atom occupy. • The APF is the sum of the sphere volumes of all atoms within a unit cell!
- 20. 20 • APF for a simple cubic structure = 0.52 APF = a3 4 3 p (0.5a) 3 1 atoms unit cell atom volume unit cell volume Atomic Packing Factor (APF) APF = Volume of atoms in unit cell* Volume of unit cell *assume hard spheres close-packed directions a R=0.5a contains 8 x 1/8 = 1 atom/unit cell
- 21. 21 Atomic Packing Factor: BCC a APF = 4 3 p ( 3a/4)3 2 atoms unit cell atom volume a3 unit cell volume length = 4R = Close-packed directions: 3 a • APF for a body-centered cubic structure = 0.68 a R a 2 a 3
- 22. 22 • APF for a face-centered cubic structure = 0.74 Atomic Packing Factor: FCC maximum achievable APF APF = 4 3 p ( 2a/4)3 4 atoms unit cell atom volume a3 unit cell volume Close-packed directions: length = 4R = 2 a Unit cell contains: 6 x1/2 + 8 x1/8 = 4 atoms/unit cell a 2 a Adapted from Fig. 3.1(a), Callister & Rethwisch 3e.
- 24. 24 A sites B B B B B B B C sites C C C A B B sites • ABCABC... Stacking Sequence • FCC Unit Cell FCC Stacking Sequence B B B B B B B B sites C C C A C C C A A B C
- 25. 25 • Coordination # = 12 • ABAB... Stacking Sequence • APF = 0.74 Adapted from Fig. 3.3(a), Callister & Rethwisch 3e. Hexagonal Close-Packed Structure (HCP) 6 atoms/unit cell • c/a = 1.633 c a A sites B sites A sites Bottom layer Middle layer Top layer