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THE RIGID MUFFIN-TIN APPROXIMATION FOR THE ELECTRON-PHONON INTERACTION
IN TRANSITION AETALS*W. H. Butler
MAS TEA
Metals and Ceramics Division, Oak Ridge National Laboratory,
Oak Ridge, Tennessee 37830 USA
1. Introduction
Substantial progress has been achieved in recent years in our ability
to calculate the electron-phonon parameters of transition metals. This
progress has been based primarily on one or the other of two ad hoc
prescriptions for the electron-phonon matrix elements, the "rigid
muffin-tin approximation" (RMTA) or the "fitted modified tight-binding
approximation" (FMTBA). Here, I shall mainly be concerned with the
R14TA. Comparisons between RMTA calculations and several types of
experiments show that the RMTA is remarkably accurate for average
electron-phonon properties such as the electron-phonon mass enhancement
X. There are indications, however, that the itMTA matrix elements may
be too small at low momentum transfers.
In this paper I shall attempt to demonstrate these assertions concerning
the accuracy of the RMTA and shall offer some simple observations which
may help to explain why they are true. I shall also try to place the
numerous electron-phonon calculations in a broader perspective by
showing how they can be used to explain the trends in the strength of
the electron-phonon coupling among the transition metals and the A-15
compounds.
2. Average Electron-Phonon Properties in the R11TA
The basic problem in the theory of the electron-phonon interaction is
the calculation of the transition rate between Bloch states 4'k and
k due to an infinitesimal atomic displacement 6R. The matrix element
for this transition is(1)
k-k = <IVk- 15V/l5Rc I Vk>
where SV/6Ra is the change in (self-consistent) crystal potential per
unit displacement due to the displacement of a single atom in direction
a. In the RI TA, 6V(r)/6Ra is replaced by the gradient of the usual
muffin-tin type potential which would enter an augmented plane wave or
Korringa-Kohn-Rostocker band calculation.
The MTA has been used to calculate a host of electron-phonon interaction
dependent properties for a wide variety of mat' -ials. Calculations of
<1->, the Fermi surface average of E Ik'k 2 have been extremely popu-
lar because Gaspari and Gyorffy (1972) showed how it could be obtained
rather simply in the course of a typical band structure calculation.
*
Research sponsored by the Division of Materials Sciences, U.S. Department
of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.?f 7 G4lIjMgur IS UNUMITuj
By acceptance of this article, the
publisher or recipient acknowledges
the U.S. Government's right to
retain a nonexclusive, royalty -ree
license in and to any copyright
covering the article.= t=
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Butler, W. H. Rigid muffin-tin approximation for the electron-phonon interaction in transition metals, article, January 1, 1980; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1055878/m1/1/: accessed June 9, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.