# I Molecular vibrations

#### Iceking20

Summary
Do solid particles rotate or transit or they just vibrate?
Summary: Do solid particles rotate or transit or they just vibrate?

Do solid particles move rotationaly and transitionally or all of these for liquid and gas?

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Yes

#### mathman

To the best of my knowledge (this is not my field), the atoms in a solid form some sort of a lattice structure which holds them in place - no transit or rotation. I don't believe molecules exist independently.

#### TeethWhitener

Gold Member
Any N-particle system in 3 dimensions has 3N degrees of freedom. 3 are pure translations and 3 are pure rotations; hence the typical formula for molecules as having 3N-6 internal (vibrational) degrees of freedom.

For a macroscopic solid, N is huge (a solid weighing a few grams will have nearly Avogadro’s number of atoms), so the internal degrees of freedom dwarf the translations and rotations. But of course a finite object can still rotate and translate—it’s just that those motions don’t contribute significantly to the quantum description of the solid.

In the idealized case of an infinite crystal (like you might encounter in a class on solid state physics), nuclear motions are generally only considered over a single unit cell. In this case, if the unit cell contains N atoms, it still has 3N degrees of freedom (assuming the cell is 3-dimensional). But now the atomic motions of a unit cell are going to affect the motions of the neighboring cells. 3 of the modes will look like translational modes—these correspond to acoustic phonons and have zero energy at zero crystal momentum. The other 3N-3 modes correspond to optical phonons, which have a nonzero energy at zero crystal momentum.

Edit for clarity: in general, any atom in a crystal can move in any direction. However, these motions can be decomposed into a set of 3N normal modes—eigenstates of the vibrational Hamiltonian that are orthogonal to one another (that is, their $L^2$ inner product is zero).

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#### SpinFlop

When atoms condense into a solid, then, as TeethWhitener pointed out, the primary modes are acoustic and optical phonons. These are vibrations that move as a wave through the material, ie: they are collective modes due to long range coordination of the atoms. In fact, they are guaranteed to exist since they are the Goldstone mode associated with long range ordering of the crystalline lattice. So back to your question:
Do solid particles rotate or transit or they just vibrate?
When these phonons vibrate, this typically consists of small linear translations of the individual atoms. I am not sure if this is what you are asking when you use the word transit, but they definitely do not rotate.
However, it should be stressed that you can still sometimes find other modes in materials. For instance, there exist rattling modes where the crystal structure includes cages with atoms confined inside. These atoms can then rattle about which often leads to a glassiness or lifetime decay of the more traditional acoustic and optical phonons. Cages themselves can have a flexing or breathing like mode. These are effectively local modes with collective behavior confined to individual cages. This is in stark contrast to standard phonons that recruit atoms across many many unit cells. However, recently a material has been discovered where the collective phonon propagation across the material does actually consist of rotations referred to as chiral phonons. See this link for a gif of the material in action.
As a final example, you can also have single molecules that are embedded in a material that can rotate quasi-independent of the lattice. As an example, look at Fig 1 a,b of this paper:

#### mjc123

Some compounds whose molecules are roughly spherical in shape can form a plastic crystal, in which the molecules are fixed in their crystal positions (can't translate), but can freely rotate - kind of the opposite of a liquid crystal. E.g. sulfolane between 16 and 28°C.

"Molecular vibrations"

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