Correction of Matrix Effects

The process to convert experimental XRF data into analytically useful information (usually in the form of concentration values of elemental constituents whose X-ray peaks are visible above the background in the spectrum) can be divided into two steps first the evaluation of the spectral data, whereby the net height or the net intensity of the X-ray peaks is determined, taking care to correct for peak overlap (if any) between X-ray lines of different elements and secondly the conversion of the net X-ray intensities into concentration data, i. e. the quantification. In this last step, especially, the appropriate correction of matrix effects is a critical issue. 

Analyte dilution sacrifices sensitivity. Matrix matching can only be applied for simple matrices, but is clearly not applicable for complex matrices of varying composition. Accurate correction for matrix effect is possible only if the IS is chosen with a mass number as close as possible to that of the analyte elements). Standard addition of a known amount of the element(s) of interest is a safe method for samples of unknown composition and thus unknown matrix effect. Chemical separations avoid spectral interference and allow preconcentration of the analyte elements. Sampling and sample preparation have recently been reviewed [4]. 

Conventional XRF analysis uses calibration by regression, which is quite feasible for known matrices. Both single and multi-element standards are in use, prepared for example by vacuum evaporation of elements or compounds on a thin Mylar film. Comparing the X-ray intensities of the sample with those of a standard, allows quantitative analysis. Depending on the degree of similarity between sample and standard, a small or large correction for matrix effects is required. Calibration standards and samples must be carefully prepared standards must be checked frequently because of polymer degradation from continued exposure to X-rays. For trace-element determination, a standard very close in composition to the sample is required. This may be a certified reference material or a sample analysed by a primary technique (e.g. NAA). Standard reference material for rubber samples is not commercially available. Use can also be made of an internal standard,... 

A correction for matrix effects is usually required. Difficulties in PIXE quantitation may be relieved by complementary information from RBS [290], or FTIR and elastic backscattering (EBS) analysis [291], FTIR can give a rough estimation of the elemental composition, while EBS or RBS can deliver information on the major-element composition. 

Vandecasteele et al. [745] studied signal suppression in ICP-MS of beryllium, aluminium, zinc, rubidium, indium, and lead in multielement solutions, and in the presence of increasing amounts of sodium chloride (up to 9 g/1). The suppression effects were the same for all of the analyte elements under consideration, and it was therefore possible to use one particular element, 115indium, as an internal standard to correct for the suppressive matrix effect, which significantly improved experimental precision. To study the causes of matrix effect, 0.154 M solutions of ammonium chloride, sodium chloride, and caesium chloride were compared. Ammonium chloride exhibited the least suppressive effect, and caesium chloride the most. The results had implications for trace element determinations in seawater (35 g sodium chloride per litre). 

Many instruments utilize a double beam principle in that radiation absorbed or emitted by the sample is automatically compared with that associated with a blank or standard. This facilitates the recording of data and corrects for matrix effects and instrumental noise and drift. Instrumentation for the generation of radiation is varied and often peculiar to one particular technique. It will be discussed separately in the relevant sections. Components (b) and (c), however, are broadly similar for most techniques and will be discussed more fully below. 

Interferences have been handled, traditionally, by the use of a matrix compensation response curve. Basically, the system is a series of standard additions to samples of a matrix and the use of these supplementations as the standards in a response curve. Thus, the recoveries of antibiotics, affected positively or negatively, can be corrected for matrix effects over a wide range of concentrations. Absolute recoveries are, of course, determined against standards in buffer. 

Electron microprobes can be used in spot mode to measure the chemical compositions of individual minerals. Mineral grains with diameters down to a few microns are routinely measured. The chemical composition of the sample is determined by comparing the measured X-ray intensities with those from standards of known composition. Sample counts must be corrected for matrix effects (absorption and fluorescence). The spatial resolution of the electron microprobe is governed by the interaction volume between the electron beam and the sample (Fig. A.l). An electron probe can also be operated in scanning mode to make X-ray maps of a sample. You will often see false-color images of a sample where three elements are plotted in different colors. Such maps allow rapid identification of specific minerals. EMP analysis has become the standard tool for characterizing the minerals in meteorites and lunar samples. 

The correct sequential transfer of values down the hierarchy requires measurement specificity and selectivity of each measurement procedure and commutability of each calibrator, i.e. it has the same behaviour towards the preceding and following measuring systems, working according to their respective measurement procedures, as have the routine samples. Lack of fulfilment of these requirements breaks the traceability chain. Unfortunately, the respective causes are often subsumed under the concept of "matrix effect". 

The accuracy of the method was considered by determination of the concentration of chloride, nitrate and sulphate in an EPA nutrient/ mineral standard. The results are shown in Table 2.10. The proximity of the chromatographic values to the EPA values indicates that corrections for matrix effects, due to additional constituents present in this standard, are unnecessaiy. 

When matrix effect exists, it is usually preferable to coeluate the analyte and its internal standard to better reduce the impact of matrix effect on quantitation. The more their chromatographic peaks overlap, the better the correction is. Since the concentration of the analyte varies while the amount of IS added is constant, a choice must be made as to match which part of a calibration curve. Usually, the segment between 1/3 and 1/2 of the ULOQ is most important because this segment is expected to cover the average Cma for most drugs and metabolites. This is probably why other researchers have proposed to use IS concentrations around 1/3 or 1/2 of the ULOQ of an analyte. 

The use of stable isotope labeled (SIL) version of the target analyte as an internal standard (IS) is theoretically considered to be the best approach to compensate or correct for matrix effects and minimize their influence on the accuracy and precision of ESI-MS quantitative assays. 

For these samples, matrix corrections were not made. The matrix effects are most severe at the lower energy levels and are considered to be of almost negligible importance for elements having an atomic weight greater than that of iron. Thus, concentrations of Al, Si, S, and Cr may be in error by up to 50% of the amount present because of matrix effects and relatively poor counting statistics. All other reported elements are estimated to be accurate to within 10% of the correct values. 

Physical and chemical effects can be combined for identification as sample matrix effects. Matrix effects alter the slope of calibration curves, while spectral interferences cause parallel shifts in the calibration curve. The water-methanol data set contains matrix effects stemming from chemical interferences. As already noted in Section 5.2, using the univariate calibration defined in Equation 5.4 requires an interference-free wavelength. Going to multivariate models can correct for spectral interferences and some matrix effects. The standard addition method described in Section 5.7 can be used in some cases to correct for matrix effects. Severe matrix effects can cause nonlinear responses requiring a nonlinear modeling method. 

In Sections 5.2.1 and 5.2.2, it was stated that the samples must be matrix-effect-free for univariate models, e.g., inter- and intramolecular interactions must not be present. The standard addition method can be used to correct sample matrix effects. It should be noted that most descriptions of the standard addition method in the literature use a model form, where the instrument response signifies the dependent variable, and... 

Standard addition is used to quantify the concentration in unknown samples when matrix interferences are present. The use of standard addition has been extensively discussed by Rodriguez et al., Cardone, and Honorato et al. [23-26]. Exact amounts of the analyte in increasing concentrations are added to the sample. The response (Y) is plotted vs. the added concentration (X). A straight line is regressed through the data points. The concentration of the analyte in the sample is given by the intercept on the X-axis (Xsample = a/b). Standard addition is probably the best way to correct for matrix effects. Rodriguez et al. have described the statistical techniques that can be used for the validation of analytical methods with standard addition [23],... 

To correct for matrix effects the absorption of X-rays by the matrix must be calculated. If 6 is the angle of the axis of the spectrometer to the surface of the sample, a photon created at a mass depth pr has a probability of [1 - exp (-p/p.p.r. cosec 0)] of being absorbed (p/p is the mass absorption coefficient of the sample for the radiation under consideration, p is the density of the material crossed and z is the thickness crossed). 

All these methods for attenuation or compensation of matrix effects can be optimised by correcting the residual matrix effects using the alpha coefficient method. In this case, the mathematical equation becomes ... 

The apparent concentrations thus obtained constitute, in certain specific cases (such as where matrix effects are negligible), a good approximation of the mass concentrations of the elements present in the sample. Nevertheless, in the majority of cases, calculations are required to correct for matrix effects because the influence of the matrix elements on the measured characteristic signal generally differs between the sample and the standard. The measured apparent concentration levels (A-ratios) then serve as a basis for an iterative process for correcting matrix effects. 

Accuracy is the ability of any assay to provide the correct result. Ideally, the assay should detect all of the analyte (100% recovery) and nothing else (no interference or cross-reactivity). To estimate the method accuracy, a comparison of method results with tme sample concentrations must be completed. A straightforward procedure involves the use of a standard reference material, in which the analyte concentration is known with high accuracy and precision. Standard reference materials are not generally available for biochemical analytes, however. When a reference material is not available, accuracy can be established by comparison with alternative previously validated analytical techniques, or currently accepted methods. Intralaboratory tests of matrix effects and interferences are also conducted in order to establish the accuracy of a new method. 

The only correct quantitation of results from the proanthocyanidin assay is to use purified procyanidin fractions from the matrix under analysis. Calibrations should be prepared in the extracts themselves to correct for matrix effects as much as possible. A similar approach has been used by Li et al. [67] who produced a calibration curve with purified... 

As with all analytical determinative techniques, interelement and matrix interferences exist and accurate quantitative determinations of concentration involve corrections for matrix effects. X-ray spectrometers comprise an excitation source, a means for the separation and isolation of emission lines, a device for intensity measurement, and typically a dedicated computer for calculation and applying corrections. The two basic types are wavelength-dispersive (in which the X-rays are characterized by wavelength) and energy-dispersive (in which the X-rays are measured by their energy levels) spectrometers. A disadvantage, as with many (all) other methods of analysis is the complication caused by the chemical composition of the matrix and as well by granulation, i.e., particle size. It remains the view... 

With proper correction for matrix effects. X-ray fluorescence spectrometry is one of the most powerful tools available for the rapid quantitative determination of all but the lightest elements in complex samples. For example. Rose, Bornhorst. and Sivonon have demonstrated that twenty-two elements can bo determined in powdered rock samples with a commercial EDXRF spectrometer in about 2 hours (1 hour instrument time), including grinding and pellet preparation. Relative standard deviations for the method are better than 1% for major elements and better than y/o for trace elements. Accuracy and detection limits as determined by comparison to results from international standard rock samples were comparable or better than other published procedures. For an e.xcellent overview of XRF analysis of geological materials, see the paper by Anzelmo and Lindsay. ... 

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