By geometry, the length of the diagonal is a √3. 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. the apf of fcc and hcp structures is 0.74, and 0.54 for. 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. Explanation: the density of packing in a crystal is determined using the atomic packing factor (apf).

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: Use the analyses of a bcc structure on page 534 and the fcc structure in Exercise 139 to determine the percent voids in the packing-of-spheres arrangement found in the foc. We don’t have your requested question, but here is a suggested video that might help. 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. Calculate the Atomic Packing Factor for the SC, FCC, BCC, and HCP crystal structures. Compare the calculated value with the actual density of 2.70 g/cc. Avogadro's number - 6.022 x 1023 atoms/mol. Calculate the density of Aluminum, FCC structure, atomic size 286 pm in diameter, atomic weight 26.98 g/mol. Face-centered cubicįor a face-centered cubic unit cell, the number of atoms is four. Show that the atomic packing factor for BCC is 0.68. This problem has been solved Youll get a detailed solution from a subject matter expert that helps you learn core concepts.

The side of the unit cell is of length 2 r, where r is the radius of the atom.

Simple cubicįor a simple cubic packing, the number of atoms per unit cell is one. 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