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 A spectrum (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...

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 X-ray fluorescence (XRF) is the emission of characteristic "secondary" (or fluorescent) X-rays from a material that has been excited by being bombarded with high-energy X-rays or gamma rays. The phenomenon is widely used for elemental analysis ...

(WDXRF) spectrometry, electron microprobes,

scanning electron microscope A scanning electron microscope (SEM) is a type of electron microscope that produces images of a sample by scanning the surface with a focused beam of electrons. The electrons interact with atoms in the sample, producing various signals that ...

s, 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 In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon ato ...

of the atom or ion and can be used to identify the atom or ion. The lightest elements,

hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

helium Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...

lithium Lithium (from , , ) is a chemical element; it has chemical symbol, symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard temperature and pressure, standard conditions, it is the least dense metal and the ...

beryllium Beryllium is a chemical element; it has Symbol (chemistry), symbol Be and atomic number 4. It is a steel-gray, hard, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with ...

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 In physics, interference is a phenomenon in which two coherence (physics), coherent waves are combined by adding their intensities or displacements with due consideration for their phase (waves), phase difference. The resultant wave may have ...

will result in a beam of diffracted x-rays that will be emitted from the crystal at angle "θ" if : , where n is an

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

. This means that a crystal with a known lattice size will deflect a beam of x-rays from a specific type of sample at a pre-determined angle. The x-ray beam can be measured by placing a detector (usually a

scintillation counter A scintillation counter is an instrument for detecting and measuring ionizing radiation by using the Electron excitation, excitation effect of incident radiation on a Scintillation (physics), scintillating material, and detecting the resultant li ...

or a

proportional counter The proportional counter is a type of gaseous ionization detector device used to measure Charged particle, particles of ionizing radiation. The key feature is its ability to measure the Electronvolt, energy of incident radiation, by producing a det ...

) in the path of the deflected beam and, since each element has a distinctive x-ray wavelength, multiple elements can be determined by having multiple crystals and multiple detectors. To improve accuracy, the x-ray beams are usually collimated by parallel copper blades called a Söller collimator. The single crystal, the specimen, and the detector are mounted precisely on a

goniometer A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (''gōnía'') 'angle' and μέτρον (''métron'') ' me ...

with the distance between the specimen and the crystal equal to the distance between the crystal and the detector. It is usually operated under vacuum to reduce the absorption of soft radiation (low-energy photons) by air and thus increase the sensitivity for detection and quantification of light elements (between

boron Boron is a chemical element; it has symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the boron group it has three ...

and

oxygen Oxygen is a chemical element; it has chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen group (periodic table), group in the periodic table, a highly reactivity (chemistry), reactive nonmetal (chemistry), non ...

). The technique generates a spectrum with peaks corresponding to x-ray lines. This is compared with reference spectra to determine the elemental composition of the sample. As the atomic number of the element increases, there are more possible electrons at different energy levels that can be ejected, resulting in x-rays with different wavelengths. This creates spectra with multiple lines, one for each energy level. The most prominent peak in the spectrum is labelled K_α, the next K_β, and so on.

Applications

Applications include analysis of catalysts, cement, food, metals, mining and mineral samples, petroleum, plastics, semiconductors, and wood.

Limitations

* Analysis is generally limited to a very small area of the sample, although modern automated equipment often uses grid patterns for larger analysis areas. * The technique cannot distinguish between

isotope Isotopes are distinct nuclear species (or ''nuclides'') of the same chemical element. They have the same atomic number (number of protons in their Atomic nucleus, nuclei) and position in the periodic table (and hence belong to the same chemica ...

s of elements as the electron configuration of isotopes of an element is identical. * It cannot determine the valence state of the element, for example Fe²⁺ vs Fe³⁺. * In certain elements, the K_α line might overlap the K_β of another element and hence if the first element is present, the second element cannot be reliably detected (for example VK_α overlaps TiK_β)

References