Normative calculations

RAT grinding operations. This surface layer was removed except for a remnant in a second grind. Spectra - both 14.4 keV and 6.4 keV - were obtained on the undisturbed surface, on the bmshed surface and after grinding. The sequence of spectra shows that nanophase Oxide (npOx) is eiu-iched in the surface layer, while olivine is depleted. This is also apparent from a comparison of 14.4 keV spectra and 6.4 keV spectra [332, 346, 347]. The thickness of this surface layer was determined by Monte-Carlo (MC)-Simulation to about 10 pm. Our Monte Carlo simulation program [346, 347] takes into account all kinds of absorption processes in the sample as well as secondary effects of radiation scattering. For the MC-simulation, a simple model of the mineralogical sample composition was used, based on normative calculations by McSween [355]. 

The first step in the model is a normative calculation (table 6.12) to establish the molar amounts of the various melt components. For each component, the molar Gibbs free energy at the standard state of pure component at T and P of interest is given by... 

A bar graph representing the results of the Mackenzie and Garrels (1966) mass-balance calculation. The bar length is the total number of moles of the ion delivered to the ocean in 100 million years. The dark region of the bar is the portion of that flux accounted for by the normative calculation in Table 2.4. 

A normative mineral calculation - or norm - is a casting of a rock analysis into a hypothetical assemblage of standard minerals (12-14). The norm should be distinguished from the mineral assemblage that is actually present which is termed the mode. Some simplifications are used to calculate a norm (12). The important assumptions for this paper are that anhydrous conditions prevail so no hydrous phases are formed and that ferromagnesium minerals are free of Al2(>3 and all the Al2(>3 goes to feldspars. Although a norm calculation is hypothetical, it often shows a close... 

In industry, many manufacturing or processing lines are controlled by measurement of chemistry alone simply because these values can be readily obtained to a high degree of accuracy and precision. When quantification of crystal form, or phase, is used in plant optimization and control it is often derived from bulk chemical analysis rather than being measured directly. This is achieved by normative calculation where particular elements are assigned to specific phases based on an assumed knowledge of individual phase composition. 

Indirect methods - these are usually based on the measurement of total chemistry which is then apportioned according to an assumed composition for each phase. A very widely used form of this normative calculation is the Bogue method for the estimation of Portland cement phases. The limitations in this approach arise when the actual compositions of individual phases vary from those assumed in the calculation. This frequently occurs in the cement industry, where variance in local materials and production conditions can affect detailed phase compositions. In addition, normative calculation has the potential to be unstable when several phases in the mixture have similar chemical composition. 

In the example above, the phases are such that the chemistry is unambiguous and the phase quantification could have been derived by normative calculation from bulk elemental analysis (XRF). This is not often the case, but it is frequently possible to establish the composition of each phase within a system via electron probe microanalysis or similar and conduct the inverse of a normative calculation to derive the bulk chemistry from the XRD QPA. This can then be compared with the results of a standards based technique such as XRF to obtain a measure of the accuracy of the XRD analysis. Examples of such calculations are given later in the sections dealing with application in mineralogical and industrial situations. Where this is not possible or practical, it is better to consider XRD QPA as a semi-quantitative technique at best. 

The composition of feldspar in a particular rock as calculated from the major element chemistry of the rock using a specific set of rules - the (CIPW) normative calculation. The feldspar content is expressed in terms of the weight % proportion of the Na-, K- and Ca-feldspars (Albite (Ab), Orthoclase (Or) and Anorthite (An)) Basalt from an arc environment which typically has about 20 wt% Al203, rather than the ca. 15 wt% found in oceanic basalts... 

Rules for the CIPW norm calculation after Kelsey (1965) and Cox et at. (1979)... 

It is helpful to use a standard form when calculating a norm by hand. This may be done by laying out the oxides (with their molecular weights and therefore the molecular proportions) as columns along the top of the page and the more common normative minerals as rows along the left-hand margin. The boxes of the fable are filled as the calculation is made and can be used to keep a check on when an element is totally used up. Constants used in the CIPW norm calculation are listed below. 

A particular dlfBculty with the norm calculation is that it is very sensitive to the oxidation state of the iron. This is more of a problem in mafic rocks where the Fe content is much higher than that of most fdsic rocks. Middlemost (1989) has proposed a range of oxidation ratios (Fe203/Fe0) for use with volcanic rocks drawn from the geological literature. His data are presented by rock type on a TAS diagram m Figure 3.6. 

Normative calculations A procedure for determining the concentration of hypothetical ideal (normative) minerals in a specimen, determined by calculation from the total... 

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