How can I rotate phonon eigenvectors to make them parallel?

In summary, the conversation discusses the issue of rotating phonon eigenvectors in a 3-atom primitive cell. The speaker has calculated eigenvectors for two points in reciprocal space, but due to the degeneracy of transverse modes, they are not parallel. The solution suggested is to use a linear algebra library to calculate a rotation matrix to align one vector with the other. Further information about the desired outcome and constraints is needed for more specific assistance.
  • #1
zephyr213
1
0
Hi, can someone help me about rotating phonon eigenvectors?
Say I have a primitive cell with 3 atoms, so for each point in reciprocal space, there are 9 eigen frequency and eigenvectors. Each eigenvector is a 9-dimensional complex vector.

I calculated eigenvectors from a transverse branch for two points in reciprocal space say 0.5ax+0.5ay+0.0az and 0.7ax+0.7ay+0.7az from a software.

However, due to the degeneracy nature of transverse modes, the two eigenvectors are not parallel to each other. (longitudinal modes are) So I am wondering how can I apply a rotation to one vector to make it parallel with the other?
 
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  • #2
The answer depends on what you want to accomplish. If you just want to make them parallel, then the easiest way would be to use a linear algebra library such as Numpy or SciPy to calculate the rotation matrix that will rotate one vector into the direction of the other. If you need more specific help, please provide more information about what you're trying to do and what constraints you may have.
 

1. What are phonon eigenvectors and why are they important in science?

Phonon eigenvectors are mathematical representations of the vibrational modes of atoms in a crystal lattice. They are important in science because they help us understand and predict the behavior of materials and their properties, such as thermal conductivity and mechanical strength.

2. How are phonon eigenvectors related to phonon frequencies?

Phonon eigenvectors and frequencies are closely related, as the eigenvectors determine the direction and magnitude of the atomic displacements that result in a certain frequency of vibration. In other words, the eigenvectors describe the motion of atoms and the frequencies determine how fast they vibrate.

3. How do phonon eigenvectors change with temperature?

At higher temperatures, atoms in a crystal lattice have more thermal energy and therefore vibrate with larger amplitudes. This leads to a change in the phonon eigenvectors, as they represent the directions and magnitudes of atomic displacements. As temperature increases, the eigenvectors become more randomized and less organized.

4. Can phonon eigenvectors rotate in different directions?

Yes, phonon eigenvectors can rotate in different directions. In fact, this rotation is an important property of phonon eigenvectors as it allows us to understand the coupling between different vibrational modes in a crystal lattice.

5. How are phonon eigenvectors calculated and visualized?

Phonon eigenvectors can be calculated using mathematical methods such as density functional theory or molecular dynamics simulations. They are usually visualized using plots or animations that show the direction and magnitude of atomic displacements at each point in the crystal lattice.

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