Difference between revisions of "X-ray absorption & fluorescence"

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== X-Ray Absorption ==
== X-Ray Absorption ==
For more info, see the X-ray Absorption Information (11BM page)
For more info, see the X-ray Absorption Information (11-BM site):
http://11bm.xor.aps.anl.gov/absorption.html
 
http://11bm.xray.aps.anl.gov/absorption.html
 
 
For more practical info about strongly absorbing samples see this wiki page:
 
https://wiki-ext.aps.anl.gov/ug11bm/index.php/Samples_with_Strong_X-Ray_Absorption


=== Absorption Length ===
=== Absorption Length ===
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  I(x) = Io e^(-mu * x)
  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 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'').


The ''Absorption Length'' (or ''Attenuation Length'') is then defined as the distance into a material where the incident x-ray beam intensity (Io) has decreased to 1 / ''e'', or about 40% of the incident beam (recall that Euler's number ''e'' = 2.72).
Recall that Euler's number ''e'' = 2.72.


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


  (1/e) = e^(-mu * x)
  (1/e) = e^(-mu * x)
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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).  
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 that ''mu'' ~ 85.0 cm-1.
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.
Then absorption length ''x'' = 1/85 = 0.011 cm = 110 microns.
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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%
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%


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


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


===MuCal ===
===MuCal ===
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downloaded both here:
downloaded both here:


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


=== Fprime ===
=== Fprime ===
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=== Absorb ===
=== 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).
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.xray.aps.anl.gov/absorb/absorb.php).

Latest revision as of 00:32, 22 February 2014

X-Ray Absorption

For more info, see the X-ray Absorption Information (11-BM site):

http://11bm.xray.aps.anl.gov/absorption.html


For more practical info about strongly absorbing samples see this wiki page:

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.xray.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.xray.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.xray.aps.anl.gov/absorb/absorb.php).