# Do solid particles vibrate?

##### 1 Answer

Yes. And in lattices, if the atoms themselves are heavier, they vibrate at lower natural frequencies, and vice versa.

This can be modeled by an infinite array of harmonic oscillators, i.e. balls and springs.

For simplicity, consider a segment of a 1D lattice of

The **position over time** for the

#x_j(t) = A_(kappa) e^(i(omega_(kappa)t + kappa aj))#

They would vibrate with an **angular frequency**

#omega_(kappa) = 2sqrt(k/m)|sin((kappa a)/2)|#

and, since **maximum frequency**, called the Debye frequency

#omega_D = 2sqrt(k/m)# ,where:

#k# is theforce constantbetween the two identical atoms in#"kg/s"^2# .#kappa# is thewave number(the number of waves for a unit distance).#m# is themassof each atom in#"kg"# .#a# is theposition coordinateof a given atom.

Above

In other words, the wavelength *lower than the width of the unit cell*, given by the Debye (minimum) wavelength