MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

Electronic and Magnetic Measurements 79
density of states, giving a γ of the order 1 mJ/mol/K 2 . Bad metals tend to
have narrow bands and high density of states providing the region of large γ
between semiconductors and metals.
3. 3. 2. 2 Phonon specific heat
The cubic term in the specific heat arises from the excitation of phonons in
the crystal lattice, and can be related to the Debye temperature Θ D :
-3
β = ΘD nkB 12π 4 /5. The Debye temperature varies like the spring constant
between neighboring atoms in the crystal: with Θ D being very large for light,
strongly bonded atoms such as diamond, and small for heavy, weakly bonded
atoms such as lead metal. Graphite, which has strong bonding in only two
dimensions, has a specific heat over a significant temperature range which is
proportional to T 2 instead of T 3 .
The Debye model does not account for the specific heat of optical phonons.
At higher temperatures this may become important. Using the Einstein
model the additional specific heat is proportional to nk
Θ E is the Einstein temperature.
B
2 Θ E ( ΘE
/ T) e
Θ E / T
( e − 1)
/ T
2
where