Errors Due to Heterogeneity

Another method which is employed is to change the vessel surface by using different vessel materials or by coating the walls with KCl, AgCl, 

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Safety in use of x-ray equipment, 332 Sample, errors due to heterogeneity of surface, 172, 175... 

Ks is expressed in the units of mass and is numerically equal to the sample mass necessary to limit the error due to sample heterogeneity (sampling uncertainty) to I % (with 68 % confidence). 

Formation of polynuclear lead species with parameters close to isolated lead bromophenoxides during DPC synthesis was found by EXAFS of frozen active reaction mixtures (Pb-0 = 2.34 A, Pb Pb = 3.83 A). Noteworthy, in samples of final reaction mixtures, where catalyst was inactive, short Pb Pb distances were absent. These polynuclear compounds have been tested as lead sources in large-scale runs (small scale reactions were inconclusive due to heterogeneity of reaction mixtures because these compounds are less soluble than PbO). It was found that the use of lead bromophenoxides instead of PbO increases both Pd TON (by 25-35%), and reaction selectivity (from 65 - 67 % to 75 - 84 %). Activity of different lead bromophenoxides was about the same (within experimental error) but the best selectivity was observed for complex Pb602(0Ph)6Br2. Therefore, the gain in selectivity vs. loss due to additional preparation step should be analyzed for practical application. 

One of the most conamon uses of the BET isotherm is for determining the surface area of finely divided solids by physical adsorption. Such information can be of great importance in a number of areas including heterogeneous catalysis and various sorption applications. While the BET model for multilayer adsorption contains several potential sources of error due to the assumptions of the absence of lateral interactions between adsorbed molecules, the... 

Conversion of a fluoride to the metal can leave areas of the metal with fluorine content much higher than the average composition. It is not uncommon in these cases for the determination of fluorine to be in error by two to three orders of magnitude. Rare earths prepared or purified in a vaporization step produce a condensed metal which, if sampled directly for analysis by SSMS, can yield erroneous data due to heterogeneous impurity content since only a few mg of sample are consumed in the analysis by SSMS (Svec and Conzemius, 1968). 

The common engineering strategy to improve the fit of experimental data to a model is to reduce the variance in the data as much as possible. However, in this particular case there are two sources of large variance to be dealt with. The first is experimental error. The experimental error arises from uncertainty in determining the true cell position from the micrographs. The second source of the variance is the actual variance in the speed within the cell population. This source of variance, due to heterogeneity in the cell speed, represents part of the biological response, and should therefore be conserved, rather than eliminated, in our analysis. 

Model errors are caused by travel-time prediction errors due to unknown velocity heterogeneities in the Earth and may introduce location bias. After phase identification errors are accounted for, model errors represent the most significant contribution to the error budget, especially at local and regional distances. Representing model errors as zero mean, Gaussian processes commonly lead to erroneous formal uncertainty estimates, as the distribution of model errors is not zero mean and is often multimodal. Because of their systematic nature (a velocity model will always produce the same travel-time prediction error along the same ray path), model errors can only be reduced by improved travel-time predictions that account for the 3D velocity structure of the Earth. 

Error introduced into an evaluation due to heterogeneity of populations. 

Houben [256] has compared the determination of flame-retardant elements Br, P, S, K, Cl and F in polycarbonate using commercial (X40 and UniQuant ) software. For the X40 method, a calibration line for each element in PC or PC/ABS blends was mapped for the conversion of intensities to concentrations. With the universal UniQuant method, sensitivity factors (ks) were calibrated with pure standards. The X40 method turned out to be more reliable than UniQuant for the determination of FRs in PC and PC/ABS blends, even in the case of calibration of k values with PC standards. Standard errors of 5 % were achieved for Br, P, S and K, and 20% for Cl and F the latter element could not be determined by means of UniQuant (Table 8.44). GFR PC cannot be quantified with these two methods, because of the heterogeneous nature of the composites. Other difficult matrices for XRF analysis are PBT, PS and PP compounds containing both BFRs and Sb203 (10-30wt %) due to self-absorption of Sb and interelement effects. 

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