For all three of the cubic lattices (unit cells), what two things are the same size?
In the three-dimensional space, there are three types of cubic lattices: primitive cubic, face-centered cubic (FCC), and body-centered cubic (BCC). In each cubic lattice, there are two things that are the same size: the edge length of the unit cell and the distance between adjacent lattice points.
To understand why this is the case, let's take a closer look at each type of cubic lattice.
1. Primitive Cubic:
In the primitive cubic lattice, also known as simple cubic, the unit cell consists of lattice points located only at the corners. Each corner atom contributes 1/8th of its volume to the unit cell. The distance between any two adjacent lattice points is equal to the edge length of the unit cell.
2. Face-Centered Cubic (FCC):
The face-centered cubic lattice has additional lattice points located at the center of each face of the cube, in addition to the corner points found in the primitive cubic lattice. These face-centered atoms contribute 1/2 of their volume to the unit cell. In the FCC lattice, the distance between adjacent lattice points is again equal to the edge length of the unit cell.
3. Body-Centered Cubic (BCC):
The body-centered cubic lattice contains one additional lattice point located at the center of the unit cell, in addition to the corner points found in the primitive cubic lattice. The central atom contributes its entire volume to the unit cell. Similar to the other two cubic lattices, the distance between adjacent lattice points in the BCC lattice is also equal to the edge length of the unit cell.
Therefore, for all three cubic lattices, the edge length of the unit cell and the distance between adjacent lattice points are the same size.