What is calibration and why does an XRF spectrometer need it? 

An X-ray fluorescence (XRF) analyzer is a sophisticated measuring device that identifies the presence of elements from the periodic table in a sample and quantifies the mass fraction (concentration, percentage) of each element. For these measurements to be accurate and reliable, like any measuring instrument, an XRF spectrometer must be calibrated. But what exactly is calibration in this context? Let's simplify it using a ruler as an example. A ruler is a tool used to measure length (distance, dimensions). To create a ruler, one starts with a straight strip of metal or plastic. However, this strip cannot measure anything in this state. To transform it into a measuring device, it needs graduations marked in centimeters, millimeters, inches, etc. This is done using a standard, such as another ruler with pre-marked divisions or another method that ensures a correct outcome. Transferring the measurement unit from the standard to the measuring tool is called calibration. A similar, albeit more complex, calibration process is applied to the X-ray fluorescence spectrometer.

It's important to note that an XRF essentially measures two quantities. Besides the mass fraction of elements, the spectrometer also measures the energies of their characteristic X-ray lines. Therefore, XRF calibration is twofold – energy calibration (calibrating the X-axis of the X-ray spectrum) and quantitative calibration (converting the intensities of X-ray lines, plotted on the Y-axis of the spectrum, into mass fractions of the respective elements).

Energy scale calibration of the spectrometer is relatively straightforward. It requires a calibration sample with at least two energy-distant lines from known elements, such as chromium and molybdenum or copper and silver. Knowing the energies of these lines and considering that the spectrometer's energy scale is linear, it's simple to mark the entire scale in energy units (for XRF, this is kilo-electron volts, keV). After this, the spectrometer can determine which elements are present in an unknown sample by the energy of their lines in the X-ray spectrum.

The Challenge of Quantitative Calibration in XRF Analysis

Quantitative calibration, which converts the intensity of each element's X-ray line into its mass fraction, presents significant challenges. The complexity arises because the intensity of an element's line depends not only on its concentration in the sample but also on the concentrations of all other elements. This is known as the matrix effect, where the "matrix" refers to the complete elemental composition of the sample. The primary matrix effects include absorption, which weakens the intensity of the element being analyzed, and enhancement, which strengthens the intensity due to additional excitation of the atoms of the element being analyzed by the radiation of atoms with higher energy lines. 

Absorption is more pronounced in heavier matrices (for example, the iron line is absorbed much more in lead than in aluminum), while enhancement increases the line intensity through additional excitation (for instance, in stainless steel, the intensity of the iron line increases due to enhancement by the nickel line). This poses the question: How do we transfer the measurement unit of an element's mass fraction from a standard (a sample with a certified known content) to the spectrometer?

Empirical Calibration vs. Fundamental Parameters Method in XRF Analysis

To tackle quantitative calibration, which translates X-ray line intensity to element mass fraction, there are two alternative approaches: the empirical calibration method and the fundamental parameters method. The empirical approach is traditional, reminiscent of calibrating a new ruler by transferring marks from a standard one. Spectrometers record the spectra of standard samples (SS) with known element contents, then construct a calibration curve correlating element intensity with its content. Since an element's line intensity also depends on the matrix composition, additional terms accounting for the intensities of other matrix elements are included in the calibration formula. These formulas, known as regression models, employ various mathematical regression models to achieve the best results for a given material type. If the material contains many elements across a wide range of concentrations, constructing an adequate regression model requires a large number of SS of that material with varying element ratios. These SS sets are often difficult to access and expensive. Obviously, each material type needs its own set of standard samples; for instance, calibration using SS for platinum-palladium alloys cannot measure platinum and palladium content in used catalytic converters due to their entirely different matrices. This calibration method yields good results when the matrix is constant, and the element of interest varies within narrow limits, such as analyzing sulfur content in petroleum products in the 0 – 5% range or lead in polyethylene in the 0 – 0.2% range.

Addressing Complex Materials with the Fundamental Parameters Method

For more complex materials, such as metallic alloys or ores and minerals containing over a dozen elements ranging from 0 to 100%, constructing an adequate empirical calibration becomes nearly impossible. This is where the fundamental parameters method shines. In this approach, matrix effects of absorption and enhancement are accounted for theoretically, linking the mass fraction of an element in any matrix composition to its intensity through a single calibration coefficient. Thus, calibrating the spectrometer may only require one or a few standard samples. The quality of this calibration is determined by how accurately the spectrometer's software solves the fundamental parameters equation.

Elvatech pioneered the market in implementing the fundamental parameters method for the high-precision analysis of metallic alloy compositions and has been refining it for over 30 years. Currently, our spectrometers are capable of analyzing virtually any material with unparalleled accuracy using this method, offering a robust solution for handling materials with complex compositions.