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

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


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


== Absorption Length ==
 
Alternatively ''Attenuation Length'' is defined as the distance into a material where the x-ray beam intensity has decreased to 1 / e, or about 63% of the incident beam.  The X-ray beam intensity at depth x into a material is calculated by Beer-Lambert law:
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))
   
   
<math>
  1 = mu * x
  \operatorname{erfc}(x) =
   
  \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt =
  x = 1/mu
  \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}}
 
</math>
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)


I(x) = e^(-x/lambda)
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%


ln(1/e) = ln(e ^-x/lambda)
In general, a ''mu*R'' of ~ 1.0 is desired for capillary transmission x-ray samples.


1 = x/Lambda
== 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


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


1/mu = x
== 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:


== Links ==
https://subversion.xray.aps.anl.gov/trac/pyFprime/


* [http://11bm.xor.aps.anl.gov/absorb/absorb.php '''Absorb''': compute X-ray absorption for powder XRD capillary samples (11BM page)]
=== Fprime ===
computes and plots elemental scattering factors.


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

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).

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