(1) what does the atomic packing factor represent? (2) what is the atomic packing factor for the zinc blende…

(1) what does the atomic packing factor represent? (2) what is the atomic packing factor for the zinc blende crystal structure in which rc/ra = 0.225? hint: when rc/ra is 0.225, the tetrahedral sites are close - packed (i.e., as compact as possible). this means that the anions touch not only the cations, but also all adjacent anions. this means that the anions are in contact along the face diagonals of the unit cell. select select

(1) what does the atomic packing factor represent? (2) what is the atomic packing factor for the zinc blende crystal structure in which rc/ra = 0.225? hint: when rc/ra is 0.225, the tetrahedral sites are close - packed (i.e., as compact as possible). this means that the anions touch not only the cations, but also all adjacent anions. this means that the anions are in contact along the face diagonals of the unit cell. select select

Answer

Explanation:

Step1: Define atomic packing factor

The atomic packing factor (APF) is the fraction of the volume of the unit - cell that is occupied by "hard - sphere" atoms or ions. It represents the efficiency of packing of atoms or ions in a crystal structure.

Step2: Recall zinc - blende structure facts

In the zinc - blende (sphalerite) structure, the cations occupy tetrahedral holes in a face - centered cubic lattice of anions. When (r_C/r_A = 0.225), the tetrahedral sites are close - packed. The APF for the zinc - blende structure can be calculated considering the number of atoms per unit cell and their volumes. For zinc - blende, there are 4 cations and 4 anions per unit cell. The volume of a sphere is (V=\frac{4}{3}\pi r^{3}). The APF is calculated by summing the volumes of all atoms in the unit cell and dividing by the volume of the unit cell. For zinc - blende with close - packed tetrahedral sites at (r_C/r_A = 0.225), the APF is 0.476.

Answer:

(1) The atomic packing factor represents the fraction of the volume of the unit - cell occupied by atoms or ions. (2) 0.476