The simple cubic unit cell, often referred to as the primitive cubic unit cell, consists of atoms positioned at each of the eight corners of a cube, with no atoms located in the center. This configuration results in a total of 1 atom per unit cell. The reasoning behind this is that each corner contributes one-eighth of an atom to the unit cell, leading to the calculation: \( \frac{1}{8} \text{ atom} \times 8 = 1 \text{ atom} \).
The edge length, denoted as \( a \), is defined as the length of one side of the cube. It can be expressed in terms of the atomic radius \( r \) as \( a = 2r \). This relationship arises because the atoms at the corners touch each other along the edges of the cube, meaning the total length of the edge is the sum of the radii of two adjacent atoms.
In terms of packing efficiency, the simple cubic unit cell exhibits a relatively low packing efficiency of 52%. This means that only 52% of the volume of the unit cell is occupied by the atoms, while the remaining volume is empty space. Additionally, the coordination number, which indicates the number of nearest neighbor atoms surrounding a given atom, is 6 for the simple cubic structure. As the complexity of cubic unit cells increases, both the packing efficiency and coordination number tend to rise, reflecting a more efficient arrangement of atoms.
Understanding these characteristics of the simple cubic unit cell is essential for grasping the foundational concepts of crystal structures and their properties in materials science.