1 Introduction

   

autobk[1] removes the background from x-ray absorption data in a reliable and reasonably easy-to-use manner. The XAFS is formed using the relation  $$\index{{{\ensuremath{\chi}}} definition} {{\ensuremath{\chi... ...nsuremath{\mu(E)}}} - \mu_{0}(E)]} \over{\Delta \mu_{0}(E_0)}},$$
where is the absorption edge energy, is the measured absorption coefficient, is the smooth, atomic-like absorption coefficient past the edge, and is the jump in the absorption coefficient at the edge step. , a function of photo-electron energy, is converted into , a function of photo-electron momentum using $k^2= {2m(E-E_0)/\hbar^2}$  . The autobk requires very little prior knowledge of the system being studied to extract from . The resulting has the atomic-like absorption contributions removed, but retains essentially all the local structural information about the near-neighbor environment of the absorbing atom. It is then ready for a more careful analysis of the effect of the local structure on the XAFS.

The important steps of background removal can be seen from Eq. (1) to be:

1.

Determine the edge energy .

2.

Determine the normalization constant .

3.

Determine the post-edge background function .

Steps 1 and 2 are not difficult, and will be discussed further in chapter 4. Step 3 is the hard part. The problem is that the true atomic-like absorption (that is, the non-XAFS absorption) will have some smooth energy dependence, but nobody knows its form. The absorption of an isolated central atom isn't good enough - (the so-called embedded atom absorption) is the absorption of the central atom in the electronic environment of the solid but without the scattering from the neighboring atoms. Since it is not usually possible to measure directly, it is approximated by a smooth function which has some flexibility and which can be adjusted to give some sort of fit to the measured absorption data.

autobk finds using concepts from Fourier signal analysis to assist the fundamental physical ideas behind the separation of XAFS and background. A piecewise polynomial, or spline, is used to approximate . The spline is adjusted so that the low-R components of the resulting XAFS (that is, after a Fourier Transform of )are optimized. This optimization is discussed in more detail in chapter 5 -- the idea is to eliminate the non-structural parts of at low-R . autobk controls the stiffness of internally, as determined by the size of the low-R ``background'' range. This gives a fairly clear definition of the background (as the low-R components of the absorption), and reduces the subjectivity inherent in background removal. The result is that autobk will find a reasonably good background without a lot of playing around with the data. In fact, only one parameter in the program has a profound effect on , and this (the endpoint of the low-R range) has at least some physical significance.

autobk is not the only method of XAFS background removal, of course. Most standard reviews [2,3] describe background removal, and an excellent description of the ``classic'' method of background removal is given by Sayers and Bunker [4]. There have been a variety of approaches to improve this method. Stern, Livins, and Zhang [5] used the temperature-dependence of to measure a few selected points of the background for pure Pb (unfortunately, this method requires temperature-dependent XAFS data for a system dominated by single scattering). A more general approach by Cook and Sayers [6] smooths the measured to get an approximation of . A technique by Li, Bridges, and Brown [7] uses feff calculations of the XAFS to determine the background as a smoothed version of - . autobk has some obvious similarities to each of these methods. Finally, attempts to calculate from first principles [8] have been partially successful, and show promise for practical data analysis. Such theoretical advancements have not been included in autobk.