The cubic closed packed unit cell and face-center cubic cell have what coordination number?
The coordination number refers to the number of nearest neighboring atoms or ions surrounding a particular atom or ion within a crystal structure
The coordination number refers to the number of nearest neighboring atoms or ions surrounding a particular atom or ion within a crystal structure.
For the cubic closed packed (CCP) unit cell, also known as the face-centered cubic (FCC) cell, the coordination number is 12. This means that each atom in the CCP/FCC structure is surrounded by 12 nearest neighboring atoms.
To visualize this, imagine an atom at the center of the unit cell. It is in contact with all eight corner atoms of the unit cell, and each of these corner atoms is shared with eight adjacent unit cells, adding up to 8 x 1/8 = 1 atom per corner. Additionally, there is an atom at the center of each face of the unit cell, and each of these face atoms is shared with two adjacent unit cells, contributing 6 x 1/2 = 3 atoms per face. Altogether, the center atom is surrounded by 12 nearest neighbors, giving it a coordination number of 12.
It is important to note that the coordination number can vary depending on the crystal structure. For example, in a simple cubic lattice, the coordination number is 6, as each atom is in contact with six neighboring atoms. However, for CCP/FCC structures, including the unit cell itself, the coordination number is 12 due to the close packing arrangement.
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