11.2 X-ray fluorescence

X-ray fluorescence (XRF) is a technique for determining the chemical composition of rocks, minerals, and other geological materials. It works by hitting a sample with high-energy X-rays, which causes atoms in the sample to emit their own characteristic X-rays. By measuring those secondary X-rays, you can figure out which elements are present and in what concentrations.

XRF covers major, minor, and trace elements, and it's non-destructive, meaning the sample stays intact after analysis. That combination of broad elemental coverage and sample preservation makes it one of the most widely used tools in geochemistry for everything from petrology to environmental monitoring.

Principles of X-ray fluorescence

The core idea behind XRF is straightforward: high-energy X-rays knock inner-shell electrons out of atoms in your sample. When outer-shell electrons drop down to fill those vacancies, they release X-rays with energies unique to that element. Measuring those emitted X-rays tells you what's in the sample.

Electromagnetic spectrum basics

X-rays sit in the high-energy region of the electromagnetic spectrum, between ultraviolet and gamma rays. Their wavelengths range from about 0.01 to 10 nanometers, corresponding to energies between roughly 100 eV and 100 keV.

The relationship between energy and wavelength is given by:

$E = \frac{hc}{\lambda}$

where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J·s), $c$ is the speed of light, and $\lambda$ is wavelength. Shorter wavelength means higher energy, which is why X-rays carry enough energy to eject inner-shell electrons from atoms.

X-ray production mechanisms

There are several ways to generate X-rays, and each matters for different XRF applications:

• Bremsstrahlung radiation is produced when electrons decelerate upon hitting a target material. This creates a continuous spectrum of X-ray energies (the "background" radiation in an X-ray tube).
• Characteristic X-rays come from electron transitions between specific atomic energy levels in the target material. These appear as sharp peaks superimposed on the bremsstrahlung continuum.
• K-shell transitions produce the most intense characteristic X-rays and are the primary lines used in XRF analysis.
• Synchrotron radiation is generated by accelerating charged particles in a storage ring. It produces highly intense, tunable X-ray beams used in specialized research facilities.

Interaction with matter

When X-rays hit your sample, four main interactions can occur:

• Photoelectric absorption is the key process for XRF. An X-ray photon with sufficient energy ejects an inner-shell electron from an atom, creating a vacancy.
• Fluorescence follows when an outer-shell electron drops into that vacancy, releasing a secondary X-ray with energy characteristic of the element. This is the signal you actually measure.
• Compton scattering is an inelastic collision where the X-ray transfers some energy to a loosely bound electron, shifting to a longer wavelength. This contributes to spectral background.
• Rayleigh scattering is an elastic collision with no energy loss. The X-ray bounces off without changing wavelength.

The ratio of fluorescence to other de-excitation processes (like Auger electron emission) is called the fluorescence yield, and it increases with atomic number. This is one reason heavier elements are generally easier to detect by XRF.

XRF instrumentation

An XRF spectrometer has three essential components: an X-ray source to excite the sample, a sample holder, and a detector system to measure the emitted X-rays. How each of these is configured determines what elements you can analyze and how precisely.

X-ray sources

• X-ray tubes are the standard source in laboratory instruments. Electrons are accelerated toward a metal anode (commonly rhodium, tungsten, or molybdenum), and the choice of anode material determines the energy range of the primary X-rays.
• Synchrotron facilities provide extremely intense, monochromatic beams that can be tuned to specific energies, enabling specialized applications like micro-XRF and XANES.
• Radioisotope sources such as americium-241 or iron-55 are used in portable XRF devices. They don't need a power supply for X-ray generation, which makes true field deployment possible.

Sample preparation techniques

Sample prep has a huge effect on data quality. The goal is to present a homogeneous, flat surface to the X-ray beam.

1. Pressed pellets: The sample is ground to a fine powder (typically <75 μm), mixed with a binding agent, and pressed into a pellet. This reduces particle size effects and improves homogeneity.
2. Fused glass beads: The powdered sample is mixed with a lithium borate flux and heated to ~1000°C. The resulting glass bead eliminates mineralogical and particle size effects almost entirely, giving the most accurate results for major elements.
3. Liquid samples: These need minimal preparation and can often be analyzed directly or after dilution.
4. Unprepared solids: Solid samples can be analyzed as-is for non-destructive screening, but surface roughness and heterogeneity will reduce accuracy.

Detectors and analyzers

The two main detector types define the two categories of XRF instruments:

• Energy-dispersive (ED-XRF) detectors measure X-ray energies directly. They allow simultaneous detection of all elements, making analysis fast. Modern silicon drift detectors (SDDs) offer good energy resolution (~125 eV) and high count rates.
• Wavelength-dispersive (WD-XRF) detectors use diffracting crystals (based on Bragg's Law: $n\lambda = 2d\sin\theta$) to separate X-rays by wavelength. This gives much better energy resolution (~5–20 eV) and lower detection limits, but analysis is sequential and slower.

A multichannel analyzer converts the detector output into a digital spectrum, plotting X-ray intensity versus energy (or wavelength) for element identification and quantification.

Qualitative analysis

Qualitative analysis answers the question: which elements are in this sample? It's typically the first step before any quantitative work.

Characteristic X-ray energies

Every element emits X-rays at specific, predictable energies when excited:

• K-series lines (Kα, Kβ) result from transitions into the innermost electron shell. These are the strongest lines for elements up to about barium (Z = 56).
• L-series and M-series lines involve transitions to outer shells. For heavier elements like rare earths and actinides, L-lines are often used because K-line energies are too high for standard XRF instruments to excite efficiently.

Moseley's Law provides the systematic relationship between atomic number and characteristic X-ray energy:

$E = k(Z - \sigma)^2$

where $Z$ is the atomic number, and $k$ and $\sigma$ are constants specific to each spectral series. This law is why the XRF spectrum is so orderly: elements with higher atomic numbers produce higher-energy characteristic X-rays.

Element identification methods

• Peak matching compares observed peak positions against reference databases of known characteristic energies.
• Spectral deconvolution mathematically separates overlapping peaks. This is critical when elements have closely spaced lines (e.g., titanium Kβ overlaps with vanadium Kα).
• Automated software handles most routine identification, but you should always review results manually, especially for complex geological matrices.

Spectral interpretation

A few practical points for reading XRF spectra:

• Energy calibration must be verified regularly so that peak positions correspond to the correct energies.
• Background subtraction removes the bremsstrahlung continuum, making weak peaks easier to identify.
• Spectral artifacts can fool you. Escape peaks appear at energies equal to the true peak minus the detector's silicon Kα energy (~1.74 keV). Sum peaks appear at twice the energy of an intense peak. Recognizing these prevents misidentification.

Quantitative analysis

Quantitative analysis converts measured X-ray intensities into actual elemental concentrations. This is where calibration and matrix corrections become critical.

Calibration methods

• Empirical calibration uses a set of standards with known compositions to build intensity-versus-concentration curves. This is the most common approach and works well when your standards closely match your unknowns.
• Fundamental parameter (FP) method calculates theoretical X-ray intensities from first principles (X-ray physics, sample composition, instrument geometry). It requires fewer standards but depends on accurate knowledge of instrument parameters.
• Standard-less analysis uses FP calculations with no external standards at all. It's convenient for screening but typically less accurate than calibrated methods.
• Internal standardization adds a known amount of a reference element to correct for matrix effects. This is more common in solution analysis.

Matrix effects

Matrix effects are the biggest source of error in quantitative XRF. They arise because the X-rays you're measuring have to travel through the sample matrix, which can alter their intensity:

• Absorption: Elements in the matrix can absorb the fluorescent X-rays before they reach the detector, reducing measured intensity. For example, iron strongly absorbs chromium Kα X-rays.
• Enhancement (secondary fluorescence): Characteristic X-rays from one element can excite fluorescence in another, artificially increasing its measured intensity. Iron Kα X-rays can enhance chromium fluorescence in the same sample.
• Particle size effects: In pressed pellets, coarser grains cause more scattering and uneven absorption. This is why grinding to a uniform fine particle size matters.
• Mineralogical effects: The same element in different mineral structures can produce slightly different X-ray intensities due to differences in density and bonding.

Sensitivity and detection limits

• Detection limits depend strongly on atomic number. Heavier elements (higher Z) have higher fluorescence yields and produce stronger signals, so they're easier to detect.
• Typical lower limits of detection (LOD) range from ~1 ppm for heavy elements in WD-XRF to ~0.01 wt% for light elements in ED-XRF.
• Longer counting times improve precision by reducing statistical uncertainty (the relative error decreases as $1/\sqrt{N}$, where $N$ is the number of counts).
• Light elements (Na, Mg, Al) are challenging because their low-energy X-rays are easily absorbed by air, the sample matrix, and detector windows.

Applications in geochemistry

Elemental composition analysis

• Whole-rock analysis is the bread-and-butter application: determining major oxides ($SiO_2$, $Al_2O_3$, $Fe_2O_3$, $CaO$, etc.) and trace elements in igneous, sedimentary, and metamorphic rocks.
• Trace element ratios like Zr/Ti, Nb/Y, and La/Yb help discriminate tectonic settings and magma sources. These are plotted on classification diagrams widely used in petrology.
• Rare earth element (REE) patterns, when normalized to chondrite or primitive mantle values, reveal information about source composition and fractionation processes.
• Chemostratigraphy uses systematic elemental variations through a sedimentary section to correlate rock units across different locations, which is especially useful where biostratigraphy is limited.

Mineral identification

• Characteristic elemental ratios can help identify unknown minerals. For example, a grain with high Mg and Si but low Al and Ca is likely an olivine or pyroxene rather than a feldspar.
• Quantitative mineral chemistry from XRF supports phase equilibria studies and geothermometry/geobarometry calculations.
• Micro-XRF mapping reveals compositional zoning within individual mineral grains, such as core-to-rim variations in garnet or plagioclase.

Environmental monitoring

• Soil contamination: Portable XRF is widely used to screen for heavy metals like lead, arsenic, cadmium, and mercury in contaminated soils. The U.S. EPA Method 6200 specifically covers field-portable XRF for this purpose.
• Sediment cores: Analyzing elemental profiles down a lake or marine sediment core reconstructs pollution history over decades to centuries.
• Atmospheric particulates: XRF characterizes the elemental composition of airborne particles collected on filters, helping identify pollution sources.
• Water quality: Dissolved and suspended element concentrations can be measured after appropriate sample preparation (e.g., filtration and preconcentration).

Advantages and limitations

XRF vs other analytical techniques

Sample requirements

• Minimum sample size ranges from milligrams (micro-XRF) to several grams (conventional WD-XRF), depending on the instrument and required precision.
• Sample homogeneity is critical. Heterogeneous samples give unreliable results unless properly prepared (ground and pressed, or fused).
• Surface roughness affects X-ray absorption and scattering, so polished or flat surfaces are preferred for solid samples.
• Moisture must be controlled for light element analysis, since water absorbs low-energy X-rays. Samples are typically dried or a correction is applied.

Accuracy and precision considerations

• Matrix-matched standards are essential for accurate calibration. Using a basalt standard to calibrate a limestone analysis will introduce systematic errors.
• Precision improves with counting time. Doubling the measurement time reduces statistical error by a factor of $\sqrt{2}$.
• Spectral overlaps can reduce accuracy. Ti Kβ and V Kα overlap is a classic example that requires careful deconvolution.
• Light elements (Z < 11, i.e., below sodium) generally cannot be measured by conventional XRF. Elements like Na and Mg require vacuum or helium path conditions to prevent atmospheric absorption.

Data processing and interpretation

Spectral deconvolution

Raw XRF spectra contain overlapping peaks, background radiation, and detector artifacts that must be separated before quantification.

• Peak fitting uses mathematical functions (typically Gaussian or Voigt profiles) to model individual element peaks and separate overlapping contributions.
• Background modeling fits and subtracts the bremsstrahlung continuum, which varies with sample composition and tube settings.
• Artifact corrections account for escape peaks and sum peaks that are inherent to semiconductor detectors.
• Iterative refinement adjusts peak positions, widths, and intensities until the model matches the measured spectrum within statistical limits.

Quantification algorithms

• The fundamental parameter method iteratively calculates expected intensities from an assumed composition, compares them to measured intensities, and adjusts the composition until convergence.
• Influence coefficient algorithms (e.g., the Lachance-Traill or de Jongh models) apply empirically or theoretically derived correction factors for inter-element effects.
• Compton normalization uses the intensity of the Compton scatter peak as an internal reference to correct for matrix absorption effects, particularly useful for trace element analysis.
• Machine learning approaches are increasingly used to improve quantification in complex or unusual matrices where traditional methods struggle.

Statistical analysis methods

• Principal component analysis (PCA) and cluster analysis identify geochemical groupings and trends in multi-element datasets.
• Correlation analysis reveals element associations that may reflect mineralogical controls (e.g., strong Ca-Sr correlation suggesting carbonate minerals).
• Error propagation calculates how uncertainties in individual measurements affect derived parameters like element ratios or normative mineral calculations.
• Outlier detection flags anomalous data points that may indicate analytical errors or genuinely unusual samples.

Advanced XRF techniques

Micro-XRF imaging

Micro-XRF uses focused X-ray beams to map elemental distributions at spatial resolutions down to a few micrometers. Polycapillary optics or Fresnel zone plates concentrate the beam onto a small spot, and the sample is rastered beneath it to build up 2D (or even 3D) elemental maps.

These maps are powerful for visualizing mineral zoning, alteration halos, and compositional boundaries that aren't visible optically. Combining micro-XRF maps with petrographic microscopy gives both chemical and textural context.

Synchrotron-based XRF

Synchrotron sources produce X-ray beams orders of magnitude more intense than laboratory tubes, enabling:

• Detection limits in the ppb range for some elements
• Spatial resolution below 100 nm with nano-focused beams
• XANES (X-ray Absorption Near-Edge Structure) spectroscopy, which determines oxidation states and chemical speciation of elements in situ. For example, you can distinguish $Fe^{2+}$ from $Fe^{3+}$ or identify whether arsenic is present as arsenate or arsenite.
• Confocal XRF, which uses two focusing optics to define a small analysis volume within a sample, enabling non-destructive 3D elemental mapping.

Portable XRF devices

Handheld XRF analyzers have transformed field geochemistry. These battery-powered instruments use miniaturized X-ray tubes and SDD detectors to deliver quantitative results in 30–120 seconds per measurement.

Common field applications include:

• Mineral exploration (lithogeochemical sampling, drill core logging)
• Soil contamination screening at brownfield sites
• Geochemical mapping in remote areas
• Cultural heritage and archaeological studies

Portable XRF has lower precision and higher detection limits than laboratory instruments, but the ability to analyze hundreds of samples per day in the field often outweighs those limitations for screening purposes.

Quality control and standards

Reference materials

• Certified reference materials (CRMs) from organizations like USGS, NIST, or GSJ provide independently verified elemental compositions for calibration and validation. Common geochemical CRMs include BHVO-2 (basalt), AGV-2 (andesite), and STM-2 (syenite).
• Matrix-matched standards are critical: calibrating a silicate rock analysis with carbonate standards will introduce systematic bias.
• Synthetic standards made from pure oxides or compounds are used for fundamental calibrations but don't capture real matrix effects.
• In-house reference materials are analyzed repeatedly over time to monitor long-term instrument stability and drift.

Instrument calibration

Calibration involves several steps that should be performed regularly:

1. Energy calibration assigns correct energies to detector channels, typically using known peaks from a reference material.
2. Intensity calibration establishes the relationship between measured count rates and elemental concentrations using standards.
3. Gain drift correction compensates for changes in detector response caused by temperature fluctuations or component aging.
4. Background calibration accounts for variations in continuum radiation from the X-ray tube.

Data validation procedures

• Replicate analyses (measuring the same sample multiple times) assess precision and reveal sample heterogeneity.
• CRM analysis as unknowns: Running a reference material as if it were an unknown sample checks whether your calibration is producing accurate results.
• Inter-laboratory comparisons (round-robin studies) evaluate whether your results are consistent with other labs using different instruments.
• Cross-validation with complementary techniques like ICP-MS or EPMA confirms XRF results for critical samples where accuracy is paramount.