# X-ray Absorption and Fluorescence

## Contents

## Background

Practical tips on how to deal with samples exhibiting strong x-ray absorption can be found on the Wiki page Samples with Strong X-Ray Absorption.

## X-Ray Absorption

A brief discussion on X-Ray absorption is given below.

### 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).