Atomic packing factor

BCC, HCP, APF

1. Material Science and Technology Unit 1 Lecture 05 By: Saumy Agarwal Asst. Professor (MED) BTKIT Dwarahat

2. Body Centered Cubic Structure (BCC) In BCC, there are atoms at all eight corners of the cube and a single atom at the center of cube. Examples- α -Iron, δ -Iron, Cr, W, Mo

3. The atoms at each corner are shared with 8 unit cells and a single atom is located at the center of the unit cell. Thus, Number of atoms in a unit cell Co-ordination number= 8 ( the central atom is surrounded by eight nearest neighbors)  

4. Hexagonal Close-packed (HCP) Structure Unit cell is a hexagonal in shape. Atomic arrangement in HCP unit cell In most cases, c/a= 1.633

5. The top and bottom faces of the unit cell consist of six atoms that form regular hexagons and they surround a single atom at the center of the face. Between the top and bottom planes, a plane is situated that provides three additional atoms to the unit cell. Examples- Zn , Cd, Co, Mg, Ti

6. The corner atoms are shared with 6 unit cells and the atoms at the face center are shared by 2 unit cells. Number of atoms in a unit cell n  

7. One atom at the center of the top face is surrounded by: six neighbouring atoms in the plane of the face three central atoms of the lower unit cell, and three central atoms of the upper unit cell Co-ordination Number= 12

8. Atomic Packing Factor (APF) It is a fraction of volume occupied by all the atoms in a unit cell to the total volume of a unit cell . A simple cubic unit cell has APF= 0.52  

9. APF of a FCC unit cell: a= edge length r= radius of an atomic sphere In a FCC unit cell, n= 4  

10. APF of a BCC unit cell: a= edge length r= radius of an atomic sphere Length of body diagonal= 4r In a BCC unit cell, n= 2  

11. APF of a HCP unit cell: a= edge length of hexagon r= radius of an atomic sphere , r=0.5 a In a HCP unit cell, n= 6  

12. Density of crystal The density of a crystal can be calculated as: where, n is number of atoms in a unit cell, A is atomic weight, V C is the volume of unit cell, N A is Avogadro's number (6.023 10 23 atoms/ mol )