polarization in cubic materials

[Bruce Ravel <ravel@phys.washington.edu>]

Howdy folks,

Here is a question that turns up frequently in my inbox.  Indeed, I
believe that a similar question was asked in this forum a few months
ago.  It is a sufficiently common question that it seems worth putting
the answer in the feffusers archive.

Here is the relevant part of the email I received:

     We were discussing whether there is a difference in analyzing
     exafs when single crystals of cubic structure were measured. So
     far we did not care. But now we have tried to include the
     polarization card and had run feffit with different polarization
     directions for ZnTe at Zn edge, x y z = 0 0 1 and 1 1 0, e.g.,
     but the difference is so small, it is hard to believe. Do you
     have experience on that? Of course we get a variety of sub-paths,
     but in total practically no difference which surprised us. Is
     that so?  Perhaps you can give us a comment

And here is my response:


     I just looked up ZnTe on the Matt Newville's database of Atoms
     input files
     (http://cars9.uchicago.edu/~newville/adb/search.html).  ZnTe is
     cubic with very high point symmetry.  In such a lattice it does
     not matter in which direction you point the polarization vector.

     Let's look at a simpler example, simple cubic:

       O      O      O      O



       O      A      O      O



       O      *      B      O



       O      O      O      O


     Put the polarization vector at some arbitrary angle theta with
     respect to the x-axis and consider the atoms marked with an
     asterisk as the absorber.  In the absence of polarization, the
     contributions from scatterers A and B would be the same.
     However, with the angle theta and for a K edge, scatterer A is
     attenuated by sin^2(theta) and scatterer B by cos^2(theta).
     (Except very close to the edge where spherical wave effects are
     strong, but even then the sin^2:cos^2 approximation is good.)
     In an experiment, you would, of course, sum the contributions
     from A and B.  sin^2(theta) + cos^2(theta) is always 1 regardless
     of theta.  Thus, a simple cubic lattice is insensitive to the
     effect of polarization.  This argument is trivially extended into
     three dimensions.  (001) and (110) do indeed give the same exafs,
     just as you observed with feff.

     The ZnTe lattice is of sufficiently high symmetry that the same
     argument applies.


The one other comment I neglected to mention to the person who sent me
this email is that it is reasonable, as he observed, that the path
list is different for different polarization, even though the sum of
paths comes out the same.  The path filters consider path amplitude.
For example, for theta = 0 or 90 there are entire classes of paths
which have no amplitude because the cosine or the sine is strictly
zero.  Thus, intermediate angles will generate more non-zero paths,
but in any case the sum of paths will be the same (within numerical
precision, of course).

B


-- 
 Bruce Ravel  ----------------------------------- ravel@phys.washington.edu
 U.S. Naval Research Laboratory, Code 6134          phone: (1) 202 767 5947
 Washington DC 20375, USA                             fax: (1) 202 767 1697

 NRL Synchrotron Radiation Consortium (NRL-SRC)
 Beamlines X11a, X11b, X23b, X24c, U4b
 National Synchrotron Light Source
 Brookhaven National Laboratory, Upton, NY 11973

 My homepage:    http://feff.phys.washington.edu/~ravel 
 EXAFS software: http://feff.phys.washington.edu/~ravel/software/exafs/