constants Module¶

X-ray fluorescence data¶

The c library xraylib provides a programmatic interface to x-ray fluorescence constants. We provide dictionary-like wrapping classes to provide easy access to the data. For the most part users should access this data through the Element object which manages the creation and access to these objects.

Converting \(2\theta\) between wavelengths¶

Given that

\[\frac{\lambda_c}{2 a} \sqrt{h^2 + k^2 + l^2} = \sin\left(\frac{2\theta_c}{2}\right)\]

If we multiply both sides by \(\frac{\lambda_n}{\lambda_c}\) then we have

\[\frac{\lambda_n}{2 a} \sqrt{h^2 + k^2 + l^2} = \frac{\lambda_n}{\lambda_c} \sin\left(\frac{2\theta_c}{2}\right)\]\[\sin\left(\frac{2\theta_n}{2}\right) = \frac{\lambda_n}{\lambda_c} \sin\left(\frac{2\theta_c}{2}\right)\]

which solving for \(2\theta_n\) gives us

\[2\theta_n = 2 \arcsin\left(\frac{\lambda_n}{\lambda_c} \sin\left(\frac{2\theta_c}{2}\right)\right)\]