legs are upper left front to lower left front. Since atoms are in contact along the body diagonals. This is called the simple cubic (SC) crystal structure-, hard-sphere and reduced-sphere models are shown, respectively, in Figures 33a and 33b. It is also possible to have a unit cell that consists of atoms situated only at the corners of a cube. look at the diagon from upper left front atom through the center atom to lower right rear atom. Body centered (bcc) Metal structure: two metal atoms/unit cell and the atomic packing factor of 0.68. Because the coordination number is less for BCC than for FCC, the atomic packing factor is also lower for BCC0.68 versus 0.74. the atoms touch on the diagonal of the cube. (edge length)² + (edge length)² = (face length)²Įdge length = 2/√2 x r = (2/√2) x (√2 /√2) x r = (2√2 / 2) x r = √2 rįor a bcc. In the FCC unit cell effective number of atoms 8 corner atoms x (1/8) (each atom is shared by 8 unit cells) + 6 face centered atoms x1/2 (each shared by two unit cells) 4 atoms.

so only 1/2 of each atom is in the cellĮach body centered atom is entirely in the cell.įor a simple cell.

so only 1/8 of each of those atoms is in the cellĮach face atom exists in 2 adjacent cells. By geometry, the length of the diagonal is a √3.APF = volume of atoms per cell / volume of the cellĮach corner atom exists in 8 adjacent cells. A line that is drawn from one corner of the cube through the center and to the other corner passes through 4 r, where r is the radius of an atom. Because the volume of each of the eight corner atoms is shared between eight adjacent cells, each BCC cell contains the equivalent volume of two atoms (one central and one on the corner).Įach corner atom touches the center atom. If you want to prove any of these numbers, check out my article about Atomic Packing Factor. The primitive unit cell for the body-centered cubic crystal structure contains several fractions taken from nine atoms (if the particles in the crystal are atoms): one on each corner of the cube and one atom in the center. Knowing this and the formula for the volume of a sphere, it becomes possible to calculate the APF as follows: Body-centered cubic Using geometry, and the side length, a can be related to r as: A line can be drawn from the top corner of a cube diagonally to the bottom corner on the same side of the cube, which is equal to 4 r. Face-centered cubicįor a face-centered cubic unit cell, the number of atoms is four. The side of the unit cell is of length 2 r, where r is the radius of the atom. For example, the only element exhibiting Simple Cubic structure is Po. Simple cubicįor a simple cubic packing, the number of atoms per unit cell is one. Lattice Points do not necessarily lie at the center of atoms. Packing factor or Atomic Packing factor (APF) can be defined as the ratio between the volume of the basic atoms of the unit cell (which represents the volume of all atoms in one unit cell ) to the volume of the unit cell itself.įor cubic crystals, it depends on the radius of atoms and the characterization of chemical bondings.

Atomic packing factor for bcc and fcc