What does it look like for two atoms per unit cell? Why does one speak of optical and acoustic branches?
To determine what a unit cell looks like with two atoms, we need to consider the crystal structure. Crystal structures can be broadly classified into two types: simple crystal structures and complex crystal structures.
In a simple crystal structure, the unit cell is repeated throughout the crystal lattice, and it contains one or more atoms per unit cell. When we talk about two atoms per unit cell, it means that each unit cell contains two atoms arranged in a specific pattern.
One example of a crystal with a simple structure is the face-centered cubic (FCC) structure. In this structure, each unit cell contains atoms at the corners of the cube and one atom at the center of each face. This arrangement leads to a total of two atoms per unit cell.
Now, let's move on to the concept of optical and acoustic branches. In crystal lattice vibrations, or phonons, there are two types of vibrational modes: optical and acoustic. These modes describe how the lattice atoms oscillate around their equilibrium positions.
The optical branches are associated with vibrations where the displacement of atoms in the crystal occurs in the same phase. This means that all atoms move together, resulting in higher energy vibrational modes. These modes are typically associated with the excitation of electromagnetic radiation and are strongly influenced by the presence of multiple atoms in a unit cell.
On the other hand, the acoustic branches are associated with vibrations in which the atoms vibrate in opposite directions within a unit cell. This means that some atoms move in one direction while the others move in the opposite direction. Acoustic modes are characterized by lower energy vibrations and are largely insensitive to the presence of multiple atoms in a unit cell.
So, the distinction between optical and acoustic branches arises from the different vibrational patterns of atoms in the crystal lattice. The presence of multiple atoms in a unit cell can affect the overall behavior of these vibrational modes, leading to different energy levels and characteristics.