Fundamental Parameter XRF analytical software

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X-ray fluorescence analysis (XRFA) is commonly used for relatively quick and non-destructive elemental analyses of samples. With the advent of small x-ray tubes and solid state detectors (Si pin diodes and Si drift detectors) that can be cooled electrically (Peltier cooling), tube excited energy dispersive (ED) XRFA has become one of the preferred methods. It is adapted to both hand portable devices, generally for qualitative analyses, and table top devices which are usually the choice for quantitative analyses. Variations on the method include total reflection XRFA, polarized XRFA both of which are used to increase the sensitivity and decrease the background.

Simple ED-XRFA is eminently suited to nondestructive analysis of a wide range of samples. If reliable measurements can be done with input count rates of the order of several 10s of thousands then the "rapid analysis" criteria can be met. With count rates of these orders measurement times of 1 to 2 minutes can result in relatively low limits of detection (LODs) of the order of 1 to a few ppm depending on their location in the spectrum relative to the scattered radiation. So can a simple quantitative ED-XRFA system be set up to run quickly and reliably? Much of the discussion below would apply to other XRF systems as well.

In order to obtain reliable element concentrations the analyst needs to understand how the method, equipment and data analysis package works as well as where limitations on the accuracy of the analysis can arise and thus what can be done in order to minimize these effects.

It is NOT sufficient to simply look at the output of your analysis program that has assigned a statistical accuracy (x) to the element concentrations (X) and say that we have determined that the concentration is X +- x. In an effort to get close to this level with any degree of certainty and reliability the analyst has to do a lot of careful preliminary work and probably will at best be able to say the the element concentration is X +-(x+s) where s represents some potential system limit on the accuracy of the measurement.

Analysis Methods

The two extreme methods that can be used to analyze x-ray spectra for element concentration values depend on either reference spectra curves alone or a "pure" fundamental parameters description of your system that in either case can be used to translate a peak area to an element concentration. Each method has its own set of problems and associated errors.

In a pure reference spectra method experimentally determined basis functions for each element are combined with experimental basis functions for the background (that is mostly scattered excitation radiation) and fit to indicate how much of each element is present in the sample via reference curves to multiple standards. The obvious issues here are the generation of the experimental basis functions, the closeness of the reference materials to the sample in composition, thickness, orientation etc all of which provides the basis for the validity of the basis functions for both elements and background, the frequency with which the reference standards are run and the overall stability of the system and thus repeatability of the measurement. A large number of standards spanning all sample types to be measured must be maintained and run on a regular basis in order for this method to produce accurate quantitative measurements with any degree of reliability.

In a pure fundamental parameters method no standards presumably need be run but in practice one or more will be run simply to confirm the validity of the system description. This method relies on a complete knowledge of the system, including the excitation radiation, the source-sample-detector geometry as well as intervening x-ray absorbers, the general sample makeup, the detector and associated electronics response function and the physics data base needed to translate all this information to a theoretical spectrum for comparison to the experimental spectrum. The experimental peak areas translate directly to elemental concentrations via the theoretical yields for each element in the sample. Probably one of the greatest limitations for the "pure FP" method is the assumed time invariance of the measurement system.

In practice, the optimal method for the widest range of general sample analyses by ED-XRFA is probably the fundamental parameter method modified to include one or more standards that are used to confirm the system description, as well as its stability. Inclusion of standards in the analysis allows for relatively simple handling of most of the accuracy limiting factors associated with the FP method.

How does the CSXRF Analysis Program Work?

Conceptually, the CSXRF program is basically a FP based program that uses one or more standards to confirm or calibrate the system description. The method employed is to fit a digitally filtered model x-ray spectrum to the digitally filtered data spectrum by means of a non-linear least squares algorithm. The model spectrum is generated using analytical functions to describe a series of characteristic x-ray lines based on FP x-ray energy and relative intensity information of the elements assumed to be in the sample. Each line is modeled as a Voigtian style peak (a system Gaussian component convoluted with the natural Lorentzian x-ray line shape) with any associated parameterized tailing. Usually a single parameter is used to model each series of x-ray lines, e.g., Fe K lines or Ag L lines, which along with four energy calibration parameters for centroid and peak width is sufficient to describe the spectrum. In the case of x-ray tube bremsstrahlung excitation radiation, with or without characteristic lines, no attempt is made to fit the scattered radiation but instead the digital filter is relied upon to remove the slowly varying scattered background radiation from the sample spectrum. Scattered characteristic line radiation will remain and is simply fitted as a normal element with the obvious proviso that this characteristic line radiation will make it difficult or impossible to determine accurately the concentration of that element in the sample.

Once the elemental peak areas have been estimated, a FP calculation of the theoretical yields of elements for the given system and sample is used to convert the peak areas to elemental concentration values. The CSXRF program allows the user to make use of an instrumental correction value (or curve) in this conversion based on measurements of one or more standards which can go a long way to minimizing any inaccuracies in the estimated concentration values.