For the purpose of determining a function that fits the transmission data well, we used a very simplistic EXAFS model that incorporates features from the independent particle model developed by Stern 1978, Lee and Pendry 1975, and Stern et al. 1975. Our model considers only interference effects from the nearest atomic shell.
The EXAFS component 
is defined as the oscillating part of the mass
absorption coefficient and is given by
where 
is the smoothly varying part of the mass absorption
coefficient corresponding to an isolated atom, 
is
the change in the mass absorption coefficient over the absorption edge,
and k is the wavenumber of the scattered photoelectron, given by
The model used to fit the oscillatory component of the transmission has the form
The term 
represents the phase shift of a photoelectron
as it traverses the distance 2R, where R is the interatomic separation, and
and 
account for phase shifts in the presence of potentials,
disorders, and
thermal vibrations of atoms about their average distance R from the central
atom. Near-edge structure in our transmission data is modeled with the term
. Equation 5
does not take into
account the nonlinear dependence of the phase shift and the dependence
of the backscattering amplitude on k.
For our modeling purposes j takes the values j=0 for the Al-K edge and j=1
for the C-K edge. We define the function 
,
as follows,
In the plots above we show fits of our
simple EXAFS model to the regions above the
Al-K and C-K edges. Because of the limitations of the multilayer
monochromator the EXAFS above the N-K and O-K edge were not resolved.
In the left panel we also show the relevant energy boundaries used in our model.
defines the energy of the absorption K edge, 
, 
, 
,
, 
,
, define the boundaries of
the first, second and third term of equation (5) respectively.
Figure 1: Top Panel: Al-K EXAFS with model fit.
Lower Panel:
Difference between data and model .
Figure 2: Top Panel: C-K EXAFS with model fit.
Lower Panel:
Difference between data and model .
