Material scientists describe the vibrations in a crystal in terms of the normal modes of the crystal. They specify the normal modes by publishing a phonon dispersion relation and/or a phonon density of states. You can search for

<crystal name> phonon dispersion

or

<crystal name> phonon density of states

in a browser and find the information about the normal modes of any common crystal.

The Materials Project lists the phonon dispersion and phonon density of states for many crystals. Use the Materials Explorer to find a crystal and then select 'Properties'. If there is a phonon calculation for that crystal, there will be a 'Phonon' tab that will show the phonon dispersion and phonon density of states.

The phonon density of states is used to calculate the thermodynamic properties of a crystal. Sometimes it is useful to have the phonon density of state in tabular form. Below are some links to tables of the phonon density of states of some crystals.

Ag-fcc, Al-fcc, AlN, Fe-bcc, GaN, Mg-hcp, Mo-bcc, Si-diamond, α-Sn, β-Sn, Ta-bcc, Tb-hcp, Ti-hcp, W-bcc, ZnO (rocksalt), ZnO (zincblende), ZnO (wurtzite), Zr-hcp

Some simple models: linear chain, Einstein model, Debye model, linear chain with two masses