View source for X-ray Absorption and Fluorescence

== Background ==
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== X-Ray Absorption ==


See the Wiki page about preparing samples with strong X-ray absorption. 

Considerations for strongly absorbing samples are discussed below. 

, see the X-ray Absorption Information (11BM page)
http://11bm.xor.aps.anl.gov/absorption.html


https://wiki-ext.aps.anl.gov/ug11bm/index.php/Samples_with_Strong_X-Ray_Absorption

=== Absorption Length ===
The X-ray beam intensity ''I(x)''  at depth ''x'' in a material is a function of the attenuation coefficient ''mu'', and can be calculated by the Beer-Lambert law:

 I(x) = Io e^(-mu * x)

The attenuation coefficient ''mu'' is typical given in inverse length units of 1/cm, and is a function of the incident wavelength, material chemistry and density. It can be calculated or estimated using resources below.

The ''Absorption Length'' (or ''Attenuation Length'') is defined as the distance into a material where the x-ray beam intensity has decreased to a value of ''1/e'' (~ 40%) of the incident beam intensity (''Io'').

Recall that Euler's number ''e'' = 2.72.

This is a convenient description, as absorption length ''x'' = 1/mu, as shown below:

 (1/e) = e^(-mu * x)
 
 ln(1/e) = ln(e^(-mu * x))
 
 1 = mu * x
 
 x = 1/mu

as a simple example, consider a solid Nickel metal sample at room temperature probed by X-rays of energy = 30 KeV (Lambda = 0.41 A). 

For Ni with density = 8.908 g*cm-3, we can calculate (using resources below) that ''mu'' ~ 85.0 cm-1.

Then absorption length ''x'' = 1/85 = 0.011 cm = 110 microns.

=== Capillary Transmission ===

Continuing with the above example for capillary transmission X-ray diffraction experiments, we can consider a cylindrically shaped solid Nickel metal sample of radius ''R'' = 0.055 mm (or 0.0055 cm).  The diameter of this sample is then 2*R = 0.011 cm (see ''absorption length'' above)

Since ''mu'' = 85 cm-1, then ''mu*R'' = 0.935, therefore the % total incident x-rays transmitted through the sample is = e^(-2*muR) = ~ 40%

In general, a ''mu*R'' of ~ 1.0 is desired for capillary transmission x-ray samples.

== Web Resources ==
=== WebAbsorb ===
a web based calculator to estimate X-ray absorption for powder XRD capillary samples (11BM page)
http://11bm.xor.aps.anl.gov/absorb/absorb.php 

===MuCal ===
calculate X-ray absorption, fluorescence and more (by C. Segre @ IIT/ANL)
http://csrri.iit.edu/mucal.html

=== NIST X-Ray Mass Attenuation Coefficient Tables ===
Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients
http://www.nist.gov/pml/data/xraycoef/index.cfm

== Software == 

The two python GUI programs described below compute approximate x-ray scattering cross sections (f, f' and f") for individual elements using the Cromer & Liberman algorithm.

downloaded both here:

https://subversion.xor.aps.anl.gov/trac/pyFprime/

=== Fprime ===
computes and plots elemental scattering factors.

=== Absorb ===
computes scattering and absorption for a given composition and makes an attempt to estimate density as well. WebAbsorb provides a web based utility based on this program (see http://11bm.xor.aps.anl.gov/absorb/absorb.php).