MAC Set

Overview

The MAC Set (MAC standing for Mass Absorption Coefficient) Utility enables the calculation of the mass absorption coefficient of the substrate or matrix as a function of the element to be measured. To open the program, click on the ‘MAC Set’ button in the SX-AppBar.

Principles

Once they have been emitted inside the sample, the X-rays have to escape it before entering the spectrometers. Some of them are absorbed by the material before they escape the sample, due to photo-electrical effects (photo-ionization). The relative amount of absorbed photons dIX/IX is proportional to their path length in the sample; hence the reduction in emitted intensity through an elementary path “ds” can be expressed as follows:

\[\frac{dIX}{IX}=-µ.ds \]

where µ is the absorption coefficient (cm-1), which depends on the chemical composition of the sample.

With respect to the vertical depth axis z, the detected photons actually travel through \[ds=\frac{dz}{sin\theta} \] when crossing an elementary layer dz in the material.

As the coefficient µ is proportional to the material density θ, X-ray spectroscopy conventionally uses the Mass Absorption Coefficient (MAC) µ/θ instead of µ. The unit in which MAC is expressed then becomes cm2/g.

\[dI=-I.\left(\frac{µ}{\theta}\right).\left(\frac{d\theta z}{sin\theta}\right) \]

To evaluate the escaping part of the signal originally emitted at depth z in the sample, one has to integrate the equation above, which translates into:

Current functions

Several databases are available for these MAC lists as highlighted on the figure below. By default, there’s a database from Cameca, but one can choose others such as Chantler 1995, Chantler 2000, Henke 1982, Henke 1993, Thinh & Leroux, MAC30 and FFAST.

The MAC values (cm²/g) will only be displayed if, along with a selected database, a Measured element and an Absorbing element are chosen on their associated periodic tables. These values are automatically calculated for X-ray lines going from Kα to Mβ. A large attenuation coefficient means that the beam is rapidly weakened as it passes through the medium, while a small attenuation coefficient would indicate that the initial beam intensity remains relatively high (in %).