![]() Knowing this and the formula for the volume of a sphere, it becomes possible to calculate the APF.įor the Hexagonal structure (HCP) the derivation is different, since the volume and the area of the faces change. Therefore, the length of each side of the BCC structure can be related to the radius of the atom by 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 4r, where r is the radius of an atom. Because the volume of the corner atoms are shared between adjacent cells, each BCC crystal only contains two whole atoms.Įach corner atom touches the center atom. The body-centered cubic crystal structure contains eight atoms on each corner of the cube and one atom in the center. For multiple-component structures, the APF can exceed 0.74. BCC has 2 atoms per unit cell lattice constant a 4R3 Coordination number CN 8 and Atomic Packing Factor APF 68. Of course there are still low-melting point metals with FCC HCP or BCC crystal structures because these are the most stable structures. In reality, this number can be higher given specific intermolecular factors. Atomic Packing Factor The ratio of atomic sphere volume to unit cell volume assuming a hard sphere model. ![]() It can be proven mathematically that one-component (one type of atom) close-packed structures, those that have the most dense arrangement of atoms, has an APF of 0.74. We are asked to show that the atomic packing factor for BCC is 0.68. Where N is the number of atoms in the crystal and V is the volume. Safe Weighing Range Ensures Accurate Results
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