Applicability of calibration

The mediods in tiiis chapter will be illustrated as applied to the spectroscopy of mixtures as tiiis is a common and highly successful application of calibration in chemistry. However, similar principles apply to a wide variety of calibration problems. 

Another feature illustrated by the above discussed Ms studies is the need to avoid casual, uncritical application of calibrations based on synthetic materials to natural materials. It was discerned by Guidotti et al. (1992) that even the very small compositional differences between synthetic K-Na Ms samples and natural A1-, Si-, and Ti-saturated Ms samples from low P parageneses were enough to systematically offset the curves for d(oo2) vs. Na/(Na+K) based on each group of samples. 

Figure 6. Applicability of calibration using polystyrenes and IGEPALS for aromatic hydrocarbons, acids, and naphthalenes, see Experimental for a description of the compounds.

Since a standard additions calibration curve is constructed in the sample, it cannot be extended to the analysis of another sample. Each sample, therefore, requires its own standard additions calibration curve. This is a serious drawback to the routine application of the method of standard additions, particularly in laboratories that must handle many samples or that require a quick turnaround time. For example, suppose you need to analyze ten samples using a three-point calibration curve. For a normal calibration curve using external standards, only 13 solutions need to be analyzed (3 standards and 10 samples). Using the method of standard additions, however, requires the analysis of 30 solutions, since each of the 10 samples must be analyzed three times (once before spiking and two times after adding successive spikes). 

In the experiment was determined that for linear calibration curve for CrKa in GSO PG24-PG31 the standai d error was 0.045%. The application of theoretical corrections method enables a decrease of that value to the level of 0.013%. In case when for the analytical parameter is taken the ratio L /L the standai d deviation decreases to 0.002%. 

The same results were gained for Cr analysis in high alloyed steels. The error of linear calibration in this case is 0.28%. The application of theoretical corrections decreases this error to 0.07%. The standard error of the linear calibration on the base of the analytical pai ameter Ici.j,yipj,j,p is 0.23% and the application of the theoretical corrections in this case gives error 0.04%. 

Over the last seventeen year s the Analytical center at our Institute amassed the actual material on the application of XRF method to the quantitative determination of some major (Mg, Al, P, S, Cl, K, Ti, Mn, Fe) and trace (V, Cr, Co, Ni, Zn, Rb, Sr, Y, Zr, Nb, Mo, Ba, La, Ce, Pb, Th, U) element contents [1, 2]. This paper presents the specific features of developed techniques for the determination of 25 element contents in different types of rocks using new Biaiker Pioneer automated spectrometer connected to Intel Pentium IV. The special features of X-ray fluorescence analysis application to the determination of analyzed elements in various types of rocks are presented. The softwai e of this new X-ray spectrometer allows to choose optimal calibration equations and the coefficients for accounting for line overlaps by Equant program and to make a mathematic processing of the calibration ai ray of CRMs measured by the Loader program. 

Because of the complex nature of the discharge conditions, GD-OES is a comparative analytical method and standard reference materials must be used to establish a unique relationship between the measured line intensities and the elemental concentration. In quantitative bulk analysis, which has been developed to very high standards, calibration is performed with a set of calibration samples of composition similar to the unknown samples. Normally, a major element is used as reference and the internal standard method is applied. This approach is not generally applicable in depth-profile analysis, because the different layers encountered in a depth profile of ten comprise widely different types of material which means that a common reference element is not available. 

AFM through force or displacement modulation techniques. Numerous methods have evolved that take advantage of the greater sensitivity modulation techniques provide, allowing dissipative processes to be examined. However, evaluation of the probe/sample response requires care with test protocols and instrument calibration, as well as application of appropriate contact mechanics models only a few of these techniques have evolved into quantitative methods. 

Calibration of apparatus and application of corrections. All instruments (weights, flasks, burettes, pipettes, etc.) should be calibrated, and the appropriate corrections applied to the original measurements. In some cases where an error cannot be eliminated, it is possible to apply a correction for the effect that it produces thus an impurity in a weighed precipitate may be determined and its weight deducted. 

The construction of calibration curves is recommended in nephelometric and turbidimetric determinations, since the relationship between the optical properties of the suspension and the concentration of the disperse phase is, at best, semi-empirical. If the cloudiness or turbidity is to be reproducible, the utmost care must be taken in its preparation. The precipitate must be very fine, so as not to settle rapidly. The intensity of the scattered light depends upon the number and the size of the particles in suspension, and provided that the average size of particles is fairly reproducible, analytical applications are possible. 

To use KBr discs for quantitative measurements it is best to employ an internal standard procedure in which a substance possessing a prominent isolated infrared absorption band is mixed with the potassium bromide. The substance most commonly used is potassium thiocyanate, KSCN, which is intimately mixed and ground to give a uniform concentration, usually 0.1-0.2 per cent, in the potassium bromide. A KBr/KSCN disc will give a characteristic absorption band at 2125 cm 1. Before quantitative measurements can be carried out it is necessary to prepare a calibration curve from a series of standards made using different amounts of the pure organic compound with the KBr/KSCN. A practical application of this is given in Section 19.9. 

Relationship between Ca2+ concentration and luminescence intensity. In the measurement of Ca2+ concentration with aequorin, the calibration of the relationship between Ca2+ concentration and luminescence intensity is essential. However, the application of this relationship is complicated by the chelator used to set the Ca2+ concentration, for the reason noted above. To minimize the complication, we used only a minimum amount of EDTA to protect aequorin in the measurements to obtain the relationship between Ca2+ -concentration and light intensity, and plotted the data as shown in Fig. 4.1.7 (Shimomura and Johnson, 1976). The concentration of EDTA was... 

It is important to understand that this material will not be presented in a theoretical vacuum. Instead, it will be presented in a particular context, consistent with the majority of the author s experience, namely the development of calibrations in an industrial setting. We will focus on working with the types of data, noise, nonlinearities, and other sources of error, as well as the requirements for accuracy, reliability, and robustness typically encountered in industrial analytical laboratories and process analyzers. Since some of the advantages, tradeoffs, and limitations of these methods can be data and/or application dependent, the guidance In this book may sometimes differ from the guidance offered in the general literature. 

In practical terms, we can usually develop satisfactory calibrations with training set concentrations, as determined by some referee method, that are accurate to 5% mean relative error. Fortunately, when working with typical industrial applications and within a reasonable budget, it is usually possible to achieve at least this level of accuracy. But there is no need to stop there. We will usually realize significant benefits such as improved analytical accuracy, robustness, and ease of calibration if we can reduce the errors in the training set concentrations to 2% or 3%. The benefits are such that it is usually worthwhile to shoot for this level of accuracy whenever it can be reasonably achieved. 

Classical least-squares (CLS), sometimes known as K-matrix calibration, is so called because, originally, it involved the application of multiple linear regression (MLR) to the classical expression of the Beer-Lambert Law of spectroscopy ... 

The trade-offs between direct calibration and standard addition are treated in Ref 103. The same recovery as is found for the native analyte has to be obtained for the spiked analyte (see Section 3.2). The application of spiking to potentiometry is reviewed in Refs. 104 and 105. A worked example for the application of standard addition methodology to FIA/AAS is found in Ref 106. Reference 70 discusses the optimization of the standard addition method. 

Overall control is provided by the PDP-11/44, running DEC S RSX-llM operating system. RSX-llM is a multi-user multi-task operating system, and a number of other analytical instruments are interfaced to this computer system and are running concurrently. The automated Instron software is menu-driven because our experience has shown that menu-driven software is particularly effective for applications of this type. To perform either test the user accesses a main menu from which separate menus for instrument calibration, tensile tests, and flexure tests can be reached. The tensile and flexure menus have equivalent options the choices pertaining to automated testing are as follows ... 

Flammable atmospheres can be assessed using portable gas chromatographs or, for selected compounds, by colour indicator tubes. More commonly, use is made of explos-imeters fitted with Pellistors (e.g. platinum wire encased in beads of refractory material). The beads are arranged in a Wheatstone bridge circuit. The flammable gas is oxidized on the heated catalytic element, causing the electrical resistance to alter relative to the reference. Instruments are calibrated for specific compounds in terms of 0—100% of their lower flammable limit. Recalibration or application of correction factors is required for different gases. Points to consider are listed in Table 9.10. 

Figure 4. Effect of maitotoxin (MTX, 2-6 x 10 g/mL) on the contractile response of guinea pig left (a) and right (b) atria. MTX was administered at the arrow. Numbers above the tracing indicate the times after the application of MTX. The horizontal calibration indicates 4 min for the tracing recorded at a slower sweep speed and 4 sec for that recorded at faster speed. (Reproduced with permission from Ref. 20. Copyright 1987 Elsevier)...

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

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