# What does a high Debye temperature signify?

• ajl1989

#### ajl1989

What does a high Debye temperature mean? I know it's related to the phonon contribution to heat capacity at low temperatures, but that's about it. Specifically, why is the Debye temperature of copper so much higher than that of lead? (I'm working on this in lab right now and can't find an explanation in any of my textbooks)

T_D ~ c n^1/2

where c is the speed of sound and n is the number density.

c ~ sqrt(k/m)

where k is the bond strength and m is the atomic mass.

So in fact, you should expect T_D to rise with falling mass.

T_D ~ c n^1/2

where c is the speed of sound and n is the number density.

c ~ sqrt(k/m)

where k is the bond strength and m is the atomic mass.

So in fact, you should expect T_D to rise with falling mass.
So Debye doesn't only apply to plasmas?

In the Debye model of the phonon density of states the Debye frequency (omega_debye) is the limit to the integral needed to ensure that all modes are active. The Debye temperature is T_db=hbar/k_boltzmann*omega_debye.

You can physically picture the Debye temperature as the temperature needed to activate all the phonon modes in a crystal.

A crystal with a large Debye temperature is going to be a stiffer crystal (Diamond is larger than Silicon is larger than Copper is larger than Lead). This is because the optical phonons have a higher frequency and therefore require greater energy to activate.