# Optical phonons in fcc-lattice

• johannes919
In summary: So, in summary, diamond has two optical modes while Al has one. Diamond has a simpler lattice than Al, which is why diamond has optical modes while Al does not. Diamond also has two atoms per cell while Al has one, and this is why diamond has an extra acoustical mode in the extended zone scheme.
johannes919
Aluminium has an fcc structure, which is a simple cubic lattice with four Al-atoms in the basis.

On the other hand, diamond has a diamond structure, which is a simple cubic lattice with 8 atoms in basis.

Now, diamond has optical modes in addition to acoustical, while Aluminium does not. What is the reason for this?

Because diamond is a simple cubic lattice with two atoms per cell while Al is a fcc lattice with one atom per cell.
Note that the fcc lattice is a lattice on its own different from the primitive cubic lattice and that a primitive cell is smaller than the cubic cell you have in mind.

johannes919
Ah, ok. So the reason is that the primitive unit cell of the fcc lattice only consists of one atom, while the primitive unit cell of diamond consists of two?

DrDu said:
Because diamond is a simple cubic lattice with two atoms per cell while Al is a fcc lattice with one atom per cell.
Note that the fcc lattice is a lattice on its own different from the primitive cubic lattice and that a primitive cell is smaller than the cubic cell you have in mind.
Don't you mean FCC lattice with a base of two atoms?

You are certainly right, thank's for correcting this. The main point is that optical phonons will only occur if there are more than one atoms in the primitive cell as the optical mode is a motion where these atoms move relative to each other, while in the accoustical mode all atoms in the basis move in unison (well, this is exactly true only at the Gamma point, i.e. the center of the Brillouin zone).

Why do you always have 3 modes for each atom in the basis?

So, I get that there are two atoms in the primitive cell of the Diamond lattice, while there's only one in the fcc lattice. But do we get optical modes if the two atoms are identical?

Referring to your answer in Wminus' post, it would seem to me that as the atoms in the primitive cell are equal, we shouldn't get optical modes, but we would see an "extra" acoustical mode in the extended zone scheme?

To your first point: As nasu pointed out, diamond, like aluminium, also crystallizes in a fcc lattice. There is no diamond lattice, only a diamond crystal structure. Diamond and aluminium both have a fcc lattice, but the former one has a basis with two atoms while the latter one a basis comprising only one atom. In Wminus's post, you can still call the upper mode an optical one if you like.
However in this example, the two atoms are not only equal but there positions are additionally spaced by a lattice vector. Therefore the two modes are degenerate at the zone boundary, i.e. there is no band gap between them.
In the case of diamond, the two atoms in the elementary cell cannot be made coincident via a shift by a lattice vector. This has the effect that the bands are not degenerate on the zone boundary (maybe with the exception of isolated points).

nasu and johannes919
Thanks!

## 1. What is an optical phonon in an fcc-lattice?

An optical phonon in an fcc-lattice is a type of lattice vibration that involves the displacement of ions in a face-centered cubic (fcc) crystal structure. It is characterized by the movement of ions along the high-symmetry directions of the lattice, resulting in a change in the dipole moment of the crystal.

## 2. What is the difference between an optical phonon and an acoustic phonon?

The main difference between an optical phonon and an acoustic phonon is the direction of the lattice vibration. Optical phonons involve movement along high-symmetry directions, while acoustic phonons involve movement along any direction in the crystal lattice. Additionally, optical phonons are typically higher in energy compared to acoustic phonons.

## 3. How do optical phonons contribute to the properties of a material?

Optical phonons can contribute to various properties of a material, such as its thermal and electrical conductivity, as well as its optical and mechanical properties. The presence of optical phonons can also affect the scattering of electrons, which can have implications for the material's electrical conductivity.

## 4. How are optical phonons experimentally observed?

Optical phonons can be observed through various experimental techniques, such as Raman spectroscopy, infrared spectroscopy, and inelastic neutron scattering. These techniques involve shining light or neutrons onto a material and measuring the energy of the scattered particles, which can provide information about the vibrational modes of the crystal lattice.

## 5. Can optical phonons be controlled or manipulated?

Yes, optical phonons can be controlled and manipulated through various methods, including applying external electric or magnetic fields, changing the temperature of the material, and introducing defects or impurities into the crystal lattice. These techniques can alter the energy and frequency of the optical phonons, which can have implications for the material's properties and behavior.

• Atomic and Condensed Matter
Replies
5
Views
2K
• Atomic and Condensed Matter
Replies
4
Views
3K
• Atomic and Condensed Matter
Replies
2
Views
6K
• Atomic and Condensed Matter
Replies
2
Views
1K
• Atomic and Condensed Matter
Replies
1
Views
5K
• Atomic and Condensed Matter
Replies
5
Views
7K
• Chemistry
Replies
1
Views
798
• Atomic and Condensed Matter
Replies
1
Views
30K
• Atomic and Condensed Matter
Replies
1
Views
4K
• Atomic and Condensed Matter
Replies
3
Views
2K