Direct comparison method

This method does not require a sample of the pure phase whose composition is being determined because the required reference line comes from another phase in the mixture. 

The direct comparison method is of greatest metallurgical interest because it can be applied directly to polycrystalline aggregates. Since its development by Averbach and Cohen [14.7], it has been widely used for measuring the amount of retained austenite in hardened steel and will be described here in terms of that specific problem, although the method itself is quite general. 

Assume that a hardened steel contains only two phases, martensite and austenite. The problem is to determine the composition of the mixture, when the two phases have the same composition but different crystal structure. The external standard method cannot be used, because it is usually impossible to obtain a reference sample of pure austenite, or of known austenite content, of the same chemical composition as the austenite in the unknown. Instead, we proceed as follows. In the basic intensity equation, Eq. (14-1), we put 

The value of c jc can therefore be obtained from a measurement of 7 /4 and a ealculation of Ry and R. (Note that the calculation of R values requires a knowledge of the crystal structures and lattice parameters of both phases.) Once Cy/c, is found, the value of Cy can be obtained from the additional relationship  

We can thus make an absolute measurement of the austenite content of the steel by direct comparison of the integrated intensity of an austenite line with the integrated intensity of a martensite line. By comparing several pairs of austenite-martensite lines, we can obtain several independent values of the austenite content. 

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The external standard method needs peak intensities of a particular phase in its pure form. The internal standard method needs a series of standard mixtures in which the particular phase contents are known. The direct comparison method is of the most interest and is easy to use because it does not have either of these restrictive requirements that is, it does not require samples of pure substances or standard mixtures of known phase content. The principles of the direct comparison method are introduced as follows. 

The direct comparison method enables us to estimate the weight fraction of a particular phase by comparing peak intensities between phases in a mixture. For example, we have a mixture of phases a and /9. We may rewrite Equation 2.12 for a peak intensity of a phase in a mixture. 

The three main methods of analysis differ in what is used as a reference line (1) external standard method (a line from pure a), (2) direct comparison method (a line from another phase in the mixture), and (3) internal standard method (a line from a foreign material mixed with the specimen). 

Other analytical problems to which the direct comparison method has been applied include the determination of mixed iron oxides in the oxide scale on steel [14.10], the beta phase in titanium alloys [14.11], and mixed uranium and plutonium carbides [14.12]. 

Microabsorption and extinction, if present, can seriously decrease the accuracy of the direct comparison method, because this is an absolute method. Fortunately, both effects are negligible in the case of hardened steel. Inasmuch as both the austenite and martensite have the same composition and only a 4 percent difference in density, their linear absorption coefficients are practically identical. Their average particle sizes are also roughly the same. Therefore, microabsorption does not occur. Extinction is absent because of the very nature of hardened steel. The change in specific volume accompanying the transformation of austenite to martensite sets up nonuniform strains in both phases so severe that both kinds of crystals can be considered highly imperfect. If these fortunate circumstances do not exist, and they do not in most other alloy systems, the direct comparison method should be used with caution and checked by some independent method. 

The next level of compositional interpretation is the quantitative estimation of the abundances of the gases present. If the constituent is believed to be uniformly mixed in the atmosphere, then an attempt can be made to determine the single parameter describing the amount of gas present, that is, the constant mole fraction or the column abundance above some level. If the gas is not uniformly mixed, but the spectral information is minimal, then a one-parameter description, such as the vertical mean mole fraction, may still be used. If a significant amount of spectral information is available, it may be possible to obtain a detailed description of the vertical distribution of the gas. Many different approaches have been devised to obtain abundance information from measured spectra. As discussed earlier in this chapter it is convenient to divide these into two groups direct comparison methods and inversion methods. 

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