Sample inhomogeneity

In the case of substantially inhomogeneous samples, very different signals may be measured depending on the sample positioning. The measured signal, in fact, arises from the portion of the sample corresponding to the intersection between the 

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BeryUium aUoys ate usuaUy analyzed by optical emission or atomic absorption spectrophotometry. Low voltage spark emission spectrometry is used for the analysis of most copper-beryUium aUoys. Spectral interferences, other inter-element effects, metaUurgical effects, and sample inhomogeneity can degrade accuracy and precision and must be considered when constmcting a method (17). 

There are advantages to direct solid sampling. Sample preparation is less time consuming and less prone to contamination, and the analysis of microsamples is more straightforward. However, calibration may be more difficult than with solution samples, requiring standards that are matched more closely to the sample. Precision is typically 5% to 10% because of sample inhomogeneity and variations in the sample vaporization step. 

The aspect of sample preparation and characterization is usually hidden in the smallprint of articles and many details are often not mentioned at all. It is, however, a very crucial point, especially with surface and interface investigations since there might be many unknown parameters with respect to surface contaminations, surface conformations, built-in stresses, lateral sample inhomogeneities, roughness, interfacial contact etc. This is in particular important when surfaces and interfaces are investigated on a molecular scale where those effects may be quite pronounced. Thus special care has to be taken to prepare well defined and artifact free specimens, which is of course not always simple to check. Many of these points are areas of... 

Unlike non-radiometric methods of analysis, uncertainty modelling in NAA is facilitated by the existence of counting statistics, although in principle an additional source of uncertainty, because this parameter is instantly available from each measurement. If the method is in a state of statistical control, and the counting statistics are small, the major source of variability additional to analytical uncertainty can be attributed to sample inhomogeneity (Becker 1993). In other words, in Equation (2.1) ... 

The sampling variance of the material determined at a certain mass and the number of repetitive analyses can be used for the calculation of a sampling constant, K, a homogeneity factor, Hg or a statistical tolerance interval (m A) which will cover at least a 95 % probability at a probability level of r - a = 0.95 to obtain the expected result in the certified range (Pauwels et al. 1994). The value of A is computed as A = k 2R-s, a multiple of Rj, where is the standard deviation of the homogeneity determination,. The value of fe 2 depends on the number of measurements, n, the proportion, P, of the total population to be covered (95 %) and the probability level i - a (0.95). These factors for two-sided tolerance limits for normal distribution fe 2 can be found in various statistical textbooks (Owen 1962). The overall standard deviation S = (s/s/n) as determined from a series of replicate samples of approximately equal masses is composed of the analytical error, R , and an error due to sample inhomogeneity, Rj. As the variances are additive, one can write (Equation 4.2) ... 

Relatively poor repeatability precision (sample inhomogeneity ng range)... 

Table 8.60 shows the main features of GD-MS. Whereas d.c.-GD-MS is commercial, r.f.-GD-MS lacks commercial instruments, which limits spreading. Glow discharge is much more reliable than spark-source mass spectrometry. GD-MS is particularly valuable for studies of alloys and semiconductors [371], Detection limits at the ppb level have been reported for GD-MS [372], as compared to typical values of 10 ppm for GD-AES. The quantitative performance of GD-MS is uncertain. It appears that 5 % quantitative results are possible, assuming suitable standards are available for direct comparison of ion currents [373], Sources of error that may contribute to quantitative uncertainty include sample inhomogeneity, spectral interferences, matrix differences and changes in discharge conditions. 

Minimisation of sample preparation is the main bottleneck in polymer/additive analysis. The importance of sample preparation increases with miniaturisation of the separation techniques. However, there is no point in improving instrumentation when the true sources of errors in measurement are sampling, sample inhomogeneity or sample instability. 

Quantitative analysis of multicomponent additive packages in polymers is difficult subject matter, as evidenced by results of round-robins [110,118,119]. Sample inhomogeneity is often greater than the error in analysis. In procedures entailing extraction/chromatography, the main uncertainty lies in the extraction stage. Chromatographic methods have become a ubiquitous part of quantitative chemical analysis. Dissolution procedures (without precipitation) lead to the most reliable quantitative results, provided that total dissolution can be achieved follow-up SEC-GC is molecular mass-limited by the requirements of GC. Of the various solid-state procedures (Table 10.27), only TG, SHS, and eventually Py, lead to easily obtainable accurate quantitation. 

It must be considered, though, that limits derived from the SNR characterize mainly instrumental noise and do not, as a rule, include chemical noise, viz such variations of measurement values which come from sample inhomogeneities, sample preparations in the course of the entire analytical... 

Taylor and Zeitlin [43] described an X-ray fluorescence procedure for the determination of total sulfur in seawater. They studied the matrix effects of sodium chloride, sodium tetraborate, and lithium chloride and show that the X-ray fluorescence of sulfur in seawater experiences an enhancement by chloride and a suppression by sodium that fortuitously almost cancel out. The use of soft scattered radiation as an internal standard is ineffective in compensating for matrix effects but does diminish the effects of instrument variations and sample inhomogeneity. 

Since about 1990, however, inductively coupled plasma (ICP, see Section 2.1.5) has become increasingly popular at the expense of TI in this area of application [9]. Although TI can provide better results for some analyses, ICP is more versatile and requires less sample preparation effort. Moreover, the advantage of better precision for TI is often compromised by the sample, for example, sample inhomogeneity. Nevertheless, there are still many examples where TI is used, such as for isotope analysis [10-13] and geochronology [14]. 

It may also be an underestimate due to sample inhomogeneity or matrix variations... 

Real samples. The move to analyze real samples represents a move toward the unknown. Not only are the results of the analysis unknown ahead of time, but other variables relating to sample inhomogeneity, sample preparation variables, additional sources of error, etc. are introduced. A large number (>30) of duplicate samples should be analyzed so that a reliable standard deviation and a reliable control chart can be established. The ultimate purpose of this work is to characterize what is a typical analysis for this kind of sample so that one can know when the method is under statistical control and when... 

Absolute accuracy has no real meaning in this experiment critical information consists of significant changes in mass loss or temperature of mass loss between samples. Inhomogeneity of samples, sample geometry, and sample size differences can have adverse effects on the reproducibility of data. 

These can be independent of our circulated samples. Inhomogeneity of of the samples should be carefully controlled and assessed. 

It should be noted that the activation energies for motional processes in the same crosslinked polymer gel calculated from line widths in 13C NMR spectra are higher than those calculated from 1H NMR spectra under the magic angle conditions (residual line width). These findings indicate that 13C line widths (which are of the order of 10 Hz) are probably more affected by sample inhomogeneity and by relatively small residual chemical shift anisotropies 162). 

Third, the reference method results should be compared with measurements on an equivalent amount of material, particularly if the sample is not homogeneous. In many instruments, Raman spectra are collected only from the sample located in a small focal volume. If that material is not representative of the bulk, then the Raman results will appear to be biased or erroneous. To avoid this problem, multiple sequential spectra are added together to represent an effectively larger composite sample. Alternatively, a larger area could be sampled if the instrument design permits it. If it were desired to study within-sample inhomogeneity, short acquisition times could be used. 

A study by Rasemann et al. demonstrated to what extent mercury concentrations depend on the method of handling soil samples between sampling and chemical analysis for samples from a nonuniformly contaminated site [152], Sample pretreatment contributed substantially to the variance in results and was of the same order as the contribution from sample inhomogeneity. Welz et al. [153] and Baxter [154] have conducted speciation studies on mercury in soils. Lexa and Stulik [155] employed a gold film electrode modified by a film of tri-n-octylphosphinc oxide in a PVC matrix to determine mercury in soils. Concentrations of mercury as low as 0.02 ppm were determined. 

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