I'm familiar with normal modes and their periodic nature. And I know that the term 'independent mode' is used to describe how each individual atom in a lattice can move (degrees of freedom).
But, what confuses me is the term 'random atomic motion'. Wikipedia discusses this in their Thermodynamics section (https://en.wikipedia.org/wiki/Phonon). Are random (thermal) atomic motions in a lattice (which move about their mean position) the same thing as 'independent modes'? If not, what are random/thermal atomic motions?
I ask because somewhere I've heard the random/thermal motions of atoms described as 'wiggling' and that would seem to define something different than the bending and stretching of independent modes.
I would more than appreciate clarification on this.