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research
Adiabatic and Non-Adiabatic Contributions to the Free Energy from the Electron-Phonon Interaction for Na, K, Al, and Pb
Authors
D. C. Wallace
D. C. Wallace
+11Â more
D. Coffey
Duane C. Wallace
G. Grimvall
G. M. Eliashberg
M. Born
M. Born
N. Bock
N. W. Ashcroft
P. B. Allen
P. H. Dederichs
V. L. Moruzzi
Publication date
22 December 2005
Publisher
'American Physical Society (APS)'
Doi
Cite
View
on
arXiv
Abstract
We calculate the adiabatic contributions to the free energy due to the electron--phonon interaction at intermediate temperatures,
0
⩽
k
B
T
<
ϵ
F
0 \leqslant k_{B} T < \epsilon_{F}
0
⩽
k
B
​
T
<
ϵ
F
​
for the elemental metals Na, K, Al, and Pb. Using our previously published results for the nonadiabatic contributions we show that the adiabatic contribution, which is proportional to
T
2
T^{2}
T
2
at low temperatures and goes as
T
3
T^{3}
T
3
at high temperatures, dominates the nonadiabatic contribution for temperatures above a cross--over temperature,
T
c
T_{c}
T
c
​
, which is between 0.5 and 0.8
T
m
T_{m}
T
m
​
, where
T
m
T_{m}
T
m
​
is the melting temperature of the metal. The nonadiabatic contribution falls as
T
−
1
T^{-1}
T
−
1
for temperatures roughly above the average phonon frequency.Comment: Updated versio
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Last time updated on 10/12/2019