Relative Phase Abundances

The following section describes the derivation of errors in the quantitative phase abundances resulting from the Hill and Howard algorithm. Notably, these errors only reflect the uncertainty generated by the mathematical fitting process in the Rietveld minimization process. It should also be reiterated that other sources of error, such as the presence of microabsorption, may generate errors that exceed the magnitude of those calculated here. 

The variance in the weight fraction of phase a, Var(IEa), is calculated from  

The error in the determination of the weight fraction for phase a is then  

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The application of Equation (15) assumes that all phases are crystalline and included in the analysis with the result that the sum of the W/s is normalized to 1.0. While the technique leads to derivation of the correct relative phase abundances, the absolute values may be overestimated if non-identified or amorphous materials are present. The addition of an internal standard to the system allows calculation of the absolute amount of each phase [Equation (16)] and thus the derivation of the amount of amorphous and/or non-analysed components [Equation (17)] ... 

Equation (Al) can only be used to determine the relative phase abundance since the total of the measured weight fractions is summed to 1.0. The addition of an internal standard phase to the sample in a known amount can be used... 

Finally, a deep quantitative characterization of all corrosion products, which includes detailed identification and determination of relative phase abundances and physical properties, allows a better comprehension of possible mechanisms of formation of the iron phases. 

Xhe phase transitions in several MAX phases and their relative phase abundances at various temperatures as revealed by in-situ neutron diffraction is shown in Figure 1. A weight loss of - 4% was observed for decomposed Xi3SiC2 which may be attributed to the release of gaseous Si by sublimation during the decomposition process. For Xi3AlC2, its decomposition into XiC and Xi2AlC... 

The surface properties of three types of methanation catalysts obtained by oxidation of selected Intermetallics were examined In relation to their CO conversion activity. The first type (Ni Si, N1 A1 ) which corresponds to active phase-supporl iX the coXventionally prepared catalyst Is little affected by the oxidation treatment. The surface Nl is oxidized and relatively more abundant In the active solids. The second type (active phase-promoter ex Ni Th ) is extensively decomposed on oxidation. The transformation of these alloys Is accompanied by a surface enrichment in Nl. 

Figure 2. Noble gas M/ Kr abundance ratios in terrestrial planet atmospheres and volatile-rich meteorites, plotted with respect to solar relative abundances and compared to the range of elemental fractionations (with respect to ambient gas-phase abundance ratios) determined from laboratory adsorptive experiments and from analyses of natural sedimentary materials (Pepin 1991). These fractionations generally fall in the darker shaded area of the figure, except for a number of measurements on carbon black (Wacker 1989) displaying the smaller or reversed patterns within the lighter shading. Data from references cited in the text and in Pepin (1991).

Comet accretion models. Noble gases, as well as water, carbon, and nitrogen, could have been supplied to the inner planets by accretion of volatile-rich icy comets scattered inward from the outer solar system. Although noble gas isotopic distributions in comets are unknown, solar isotopic compositions would be expected in cometary gases acquired from the nebula. There is experimental evidence that the relative elemental abundances of heavier species (Xe, Kr, and Ar) trapped in water ice at plausible comet formation temperatures ( 30 K) approximately reflect those of the ambient gas phase, and trapped noble gas abundances per gram of water are substantial (Bar-Nun et al. 1985 Owen et al. 

The solid phase of soil contains particles of different sizes, and it has different textures. The granulometric analysis of the soil presents data about the relative (percentage) abundance of particles of a certain size and it serves as a basis for soil categorization. 

Consequently, instead of a chapter organization based primarily on genetic sequence (see Hofmanner, 1973 Chromy, 1974 Butt and Timashev, 1974 Ono, 1981, 1995 Chromy, 1982 and Gartner, 1985), the observations and interpretations in this chapter are listed first with some of the relatively large-scale features of clinkers and then, for the most part, according to phase abundance. Rather than in a lengthy narrative survey of interpretive details of clinker phases, stated by various authors in many published papers, the information is presented in tabular form. Table 7-1 presents, in a double column, a list of (a) clearly recorded observations on the left and (b) verbatim published interpretations, associations, or correlations on the right. This survey is not a critical review. 

In this work, the potential for application of Mossbauer spectrometry to corrosion studies was demonstrated for three accelerated corrosion tests in chloride environments. This technique allowed retrieving maximum information from the inherent properties of the rust layers. With VT-MS, it was possible to identify and determine the relative iron phase abundances from which three parameters could be calculated (i) a, (ii) (A + S)/(A + L + S), and (iii) PAI. Moreover, with the physical properties retrieved from the analysis of the hyperfine parameters, it was possible to discuss prospective mechanisms of formation and therefore to contribute to the understanding of the deterioration progress. These studies showed that some corrosion product is lost and/or the conversion of metallic ions into iron oxides may be incomplete, and that the relative iron phase abundances pointed out to a nonprotective and active type of rusts. More work is required on other types and chemistry (composition and abundance of alloying elements) of steels, other environmental conditions, and different exposure times. More efforts are needed to improve the fitting models for nonstoichiometric and substituted iron oxides in rust layers. 

Figure 10 Gas-phase abundances measured towards the star z Oph of various elements relative to atomic hydrogen (X/H) and normalized with respect to solar abundances (X/H)o plotted versus condensation temperature of these elements. The condensation temperature is the temperature at which 50% of that element is depleted from the gas phase into the solid phase. The error bars on the squares indicate measurement errors only. Representative uncertainties in the solar abundances, oscillator strength and condensation temperature are indicated in the lower left hand corner.

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