X-Ray Fluorescence Analytical Techniques - CNSTN : Centre ...

each other. If the amplification condition “phase difference = a whole multiple of the
wavelength” (∆λ = nλ) is not precisely met, the reflected wave will interfere such that
cancellation occurs. All that remains is the wavelength for which the amplification condition
is met precisely. For a defined wavelength and a defined lattice plane distance, this is only
given with a specific angle, the Bragg angle (Figure IV.6).
Figure IV.6: Bragg’s Law.
Under amplification conditions, parallel, coherent X-ray light (1,2) falls on a crystal
with a lattice plane distanced ‘d’ and is scattered below the angle θ (1′,2′). The proportion of
the beam that is scattered on the second plane has a difference of ‘ACB’ to the proportion of
the beam that was scattered at the first plane.
The amplification condition is fulfilled when the phase difference is a whole multiple of
the wavelength λ. This results in Bragg’s Law:
2dsinθ= nλ;
(IV.2)
n = 1, 2, 3… Reflection order.
On the basis of Bragg’s Law, by measuring the angle θ, you can determine either the
wavelength λ, and thus chemical elements, if the lattice plane distance ‘d’ is known or, if the
wavelength λ is known, the lattice plane –value distance ‘d’ and thus the crystalline structure.
This provides the basis for two measuring techniques for the quantitative and qualitative
determination of chemical elements (XRF) and crystalline structures (molecules, XRD),
depending on whether the wavelength λ or the 2d-vale is identified by measuring the angle θ
(Table IV.1).
Table IV.1: Wavelength dispersive X-ray techniques.
Known Sought Measured Method Instrument type
d λ θ X-ray fluorescence Spectrometer
λ d θ X-ray diffraction Diffractometer
In X-ray diffraction (XRD) the sample is excited with monochromatic radiation of a
known wavelength (λ) in order to evaluate the lattice plane distance as per Bragg’s equation.
In XRF, the ‘d’-value of the analyzer crystal is known and we can solve Bragg’s
equation for the element characteristic wavelength (λ).