X-ray absorption & fluorescence

X-Ray Absorption

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

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 the links and tables listed below.

The Absorption Length (or Attenuation Length) is then 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

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).