Wavelength-dispersive X-ray spectroscopy
method used to count the number of X-rays of a specific wavelength diffracted by a crystal
Wavelength-dispersive X-ray spectroscopy (WDXS or WDS) is a non-destructive analysis technique used to obtain elemental information about a range of materials by measuring characteristic x-rays within a small wavelength range. The technique generates a spectrum in which the peaks correspond to specific x-ray lines, and elements can be easily identified. WDS is primarily used in chemical analysis, wavelength dispersive X-ray fluorescence (WDXRF) spectrometry, electron microprobes, scanning electron microscopes, and high-precision experiments for testing atomic and plasma physics.
Theory
Wavelength-dispersive X-ray spectroscopy is based on known principles of how the characteristic x-rays are generated by a sample and how the x-rays are measured.
X-ray generation
X-rays are generated when an electron beam of high enough energy dislodges an electron from an inner orbital within an atom or ion, creating a void. This void is filled when an electron from a higher orbital releases energy and drops down to replace the dislodged electron. The energy difference between the two orbitals is characteristic of the electron configuration of the atom or ion and can be used to identify the atom or ion.
The lightest elements, hydrogen, helium, lithium, beryllium up to atomic number 5, do not have electrons in outer orbitals to replace an electron displaced by the electron beam and thus cannot be detected using this technique.
X-ray measurement
According to Bragg's law, when an X-ray beam of wavelength "λ" strikes the surface of a crystal at an angle "θ" and the crystal has atomic lattice planes a distance "d" apart, then constructive interference will result in a beam of diffracted x-rays that will be emitted from the crystal at angle "θ" if
2d sin θ = nλ,
where n is an integer equal to the n-order diffraction peak that was detected.
In practice, the Bragg's angle of the first-order diffraction peak is used, as this has the greatest intensity and signal, meaning n = 1 with regard to Bragg's law, and therefore n is effectively canceled in the equation.
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