Standardless methods

Best with standards, although standardless methods are widely used... 

The standardless approach attempts to apply first principles descriptions of X-ray production to the calculation of interelement relative sensitivities. Several of the key parameters necessary for first principles calculations are poorly known, and the accuracy of the standardless method often suffers when different X-ray families must be used in measuring several elemental constituents in a specimen. 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

The question of precision and accuracy in QPA via XRD is a difficult one. It is simple enough to calculate errors on the basis of replication or precision in the mathematical fit. However, determination of the actual accuracy of the analysis is no trivial task in a standardless method. In fact, it cannot be achieved without recourse to some other measure of the sample that does incorporate standards. Too often, analysts will report Rietveld errors (see Appendix A) calculated during refinement as the errors in the final quantification. These numbers relate purely to the mathematical fit of the model and have no bearing on the accuracy or otherwise of the quantification itself. 

All the methods previously cited (and others like the external standard or standardless methods), based on intensity-concentration for single lines, are the traditional techniques used for QPA in the recent past ... 

Quantitation in XRF was reviewed [225], as well as standardless analytical methods using an extended FPM for the determination of sample compositions [244,245]. 

Quantitative and standardless (absolute method no calibration curves)... 

For a given detector and a given pair of elements the last two factors give a single constant (Icab) that can be treated as a relative sensitivity factor. Both that factor and the method obtained their names after the two people who introduced them, Cliff and Lorimer (1975). The simplicity originates from the fact that the Uab factor does not depend either on the rest of elements also present in the sample or on the other parameters of the sample (thickness, density), as far as the thin film criterion is fulfilled. The Cliff-Lorimer factors can either be calculated using the known parameters of the detector or can be measured if a well-characterized thin film sample (standard) is available. In the first case the method is standardless. In the second case the known weight fractions and the measured intensity ratio provides the Cliff-Lorimer factor for the pair of elements. 

An analytical method has been developed that allows easy standardless semiquantitative measurements of elemental composition from single shot analysis by LA-ICP-ToFMS to identify alloys of different elemental composition.27 28 This method directly compares adjusted ion signals of... 

The fundamental parameters approach has been recently implemented in some of the current programs. It gives, to a certain extent, physical meaning to the parameters involved in pattern decomposition. This method attempts to model the contributions from various instrumental components (such as monochromators, slits) and geometry to the observed peak profile shapes. Since this is done considering the relevant physics involved from the generation, diffraction, and detection of PXRD, it leads to more physical meaning than the two methods described earlier. This method can be used not only to perform full pattern decomposition, but also effectively to do a standardless refinement of the sample effects such as crystallite size and microstrain. 

It is often difficult to assess properly the accuracy of a SDVtS analysis because there are no techniques capable of calibration analysis of very dilute analytes. Standardless SIMS analyses, e.g. using exponential ion yield relationships, are subject to sizeable errors, perhaps as much as factors of 2-3 [144]. Empirical methods of quantitative analysis can be applied to the problem of SIMS analysis to achieve useful levels of accuracy. The availability of standards is then critical. External standardisation is absolutely insufficient, and the use of internal standards is necessary. These standards must be introduced into the surface during preparation. When a suitable standards suite is available, an effective approach to quantitative SIMS analysis can be achieved through the use of the empirical method of relative elemental sensitivity factors. Detection sensitivity factors cover a wide range (six decades). 

The thermogravimetric analysis (TGA) can be also used as a standardless alternative to determine the proximate analysis within approximately 80 min. In TGA, a small coal sample (20 mg) is heated under a flow of nitrogen with 80K/min until 160 °C is reached and held on this temperature until all moisture is removed. An increase of the temperature to 950 °C removes the volatiles and after stabilization of the curve, air is finally introduced to convert the remaining fixed carbon. Relating to the original mass of the sample, the moisture, volatile matter, fixed carbon, and ash content are determined within the error limits of the standard method. 

Alternatively, standardless fundamental parameter (FP) techniques are based on built-in mathematical algorithms that describe the physics of the detector response to pure elements. In this case, the typical composition of a sample must be known, while the calibration model may be verified and optimized by one single standard sample. The techniques include the fundamental parameter method,the influence coefficient method, and the empirical coefficient method. 

The method of standard additions efficiently compensates for matrix effects but not for drift. If the latter is also present (for instance because of gradual clogging), internal standardization may also be required. The best method to compensate for both matrix effects and drift is isotope dilution analysis. However, it is only applicable to elements with at least two isotopes (stable and/or long-lived radioactive) free of spectroscopic interferences. Because of mass discrimination, this normally standardless technique requires a prior determination of mass bias using standards of known isotopic composition in order to correct the measured isotope ratios for mass discrimination. 

In TEM, EDS quantification is done using the standardless Cliff-Lorimer method (Cliff and Lorimer 1975 Lorimer G.W. 1987). This method stipulates that the above-background intensity ratio between two peaks is proportional to their weight fraction as... 

Low elemental concentrations, below 1 at.%, are difficult to quantify by EDS analysis. The standardless quantification methods used in STEM may mean that low concentrations cannot be as accurately measured as by SEM, as illustrated in the following example. The alite studied contained aluminium and magnesium and Al-rich and Mg-rich clusters and can be identified as indicated by the BSE image of a polished section in Figure 8.55. 

Quantitative Results for Paint Chip Analysis Bulk Method Standardless Acquired 03"Jun"2009, 20.0 keV 10 eV/channel... 

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