Constructing the Muffin-Tin Potential
The crystal is built up by placing the spherically averaged potentials
of the individual atoms at the lattice positions of the atoms. In order
to give definition to the crystal potential, the range of affect of each
potential is defined by the muffin-tin radius of the respective atom. In
this viewpoint, the atoms are treated as "hard" spheres of potential packed
together in a lattice (this is a surprisingly good approximation).
The choice of the muffin-tin radius for an atom is largely by chemical
intuition. There are tabulated tables of atomic, Pauling, and ionic radii
available. These can be correlated with knowledge of bond lengths in the
crystal lattice to determine a working radius of affect for an atom - the
muffin-tin radius of its potential. Generally, the muffin-tin spheres touch,
but must not overlap.
This crystal defined by muffin-tin radius spheres at the lattice positions
contains interstitial regions of potential that, by definition, belong
to no atom. An average value of the net total spherically averaged potential
in the interstitial region (taken from the overlap of neighboring atom
potentials) is found and taken to be the defined muffin-tin zero value
of the crystal potential. This shifts the energy zero of the entire crystal
to the average potential of the interstitial regions.
The muffin-tin potential is then
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Created: April 12, 1999 ---- Last Updated: April 12, 1999
By Mark D. Pauli