Composition of Phases

The composition of single-phase materials can be determined by a wide range of wet chemistry techniques and bulk analysis procedures, including such varied methods as atomic absorption spectroscopy. X-ray fluorescence, and magnetic resonance spectroscopy. For most materials, however, the chemical composition of each component in a complex microstructure is of interest. In order to ascertain this. 

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Thin-film XRD is important in many technological applications, because of its abilities to accurately determine strains and to uniquely identify the presence and composition of phases. In semiconduaor and optical materials applications, XRD is used to measure the strain state, orientation, and defects in epitaxial thin films, which affect the film s electronic and optical properties. For magnetic thin films, it is used to identify phases and to determine preferred orientations, since these can determine magnetic properties. In metallurgical applications, it is used to determine strains in surfiice layers and thin films, which influence their mechanical properties. For packaging materials, XRD can be used to investigate diffusion and phase formation at interfaces... 

Transmission electron microscopes (TEM) with their variants (scanning transmission microscopes, analytical microscopes, high-resolution microscopes, high-voltage microscopes) are now crucial tools in the study of materials crystal defects of all kinds, radiation damage, ofif-stoichiometric compounds, features of atomic order, polyphase microstructures, stages in phase transformations, orientation relationships between phases, recrystallisation, local textures, compositions of phases... there is no end to the features that are today studied by TEM. Newbury and Williams (2000) have surveyed the place of the electron microscope as the materials characterisation tool of the millennium . 

In Fig. 7.83 using the common tangent construction the equilibrium compositions of phase I-phase II at their boundary are found, from the points of contact, to be respectively Xg — A, and Xg = X2. 

These three diagrams show clearly how a very small change in the relative position of the AG-concentration curves for the different phases can have a dramatic effect on the composition and stability of the solid phases in the Fe,j,-Zn( system. A detailed discussion of these diagrams can be found elsewhere In addition, Fig. 7.86 shows that any physical effects in the solid phases, which can be expressed in terms of energy, can be added to the AG -concentration curves. Thus the curves can be corrected for these effects and the resulting new equilibria from the shift of the AG-concentra-tion curves (i.e. change in composition of phase, their stability, etc.) can be predicted simply by the use of the tangency rule. 

Figure 5.71A shows univariant equilibrium curves for various molar amounts of ferrous component in the orthopyroxene mixture. The P-T field is split into two domains, corresponding to the structural state of the coexisting quartz (a and j3 polymorphs, respectively). If the temperature is known, the composition of phases furnishes a precise estimate of the P of equilibrium for this paragenesis. Equation 5.277 is calibrated only for the most ferriferous terms, and the geobarometer is applicable only to Fe-rich rocks such as charnockites and fayalite-bearing granitoids. 

Process by which phase domains increase in size during the aging of a multiphase material. Note 1 In the coarsening at the late stage of phase separation, volumes and compositions of phase domains are conserved. 

The accuracy of some isothermal techniques, particularly those that rely on observation of phases, is limited by the number of different compositions that are prepared. For example, if two samples are separated by a composition of 2at%, and one is single-phase while the other two-phase, dien formally the phase boundary can only be defined to within an accuracy of 2at%. This makes isothermal techniques more labour intensive than some of the non-isothermal methods. However, because it is now possible to directly determine compositions of phases by techniques such as electron microprobe analysis (EPMA), a substantially more quantitative exposition of the phase equilibria is possible. 

This section will give examples of how CALPHAD calculations have been used for materials which are in practical use and is concerned with calculations of critical temperatures and the amoimt and composition of phases in duplex and multi-phase types of alloy. These cases provide an excellent opportunity to compare predicted calculations of phase equilibria against an extensive literature of experimental measurements. This can be used to show that the CALPHAD route provides results whose accuracy lies close to what would be expected from experimental measurements. The ability to statistically validate databases is a key factor in seeing the CALPHAD methodology become increasingly used in practical applications. 

Suppose the grain size for phase A is very small, leading to very large total surface area for reaction. That is, A >A . Then (w - 1) (w - 1), meaning the fluid composition is such that it is very close to the saturation composition of phase A, whereas phase B is significantly undersaturated. After solving for vA and w , the reaction rate of A and B can be calculated if lA and are known. 

In a primary solid solution M(O) (phase (I)) as appears in this system, the oxygen atoms take up positions between the lattice sites of metals, i.e. the interstitial positions. The chemical composition of phase (II) is usually expressed as In the case of <5 / 0, the crystal has various kinds of... 

Continuous changes in compositions of phases flowing in contact with each other are characteristic of packed towers, spray or wetted wall columns, and some novel equipment such as the FHGEE contactor (Fig. 13.14). The theory of mass transfer between phases and separation of mixtures under such conditions is based on a two-film theory. The concept is illustrated in Figure 13.15(a). 

On a ternary equilibrium diagram like that of Figure 14.1, the limits of mutual solubilities are marked by the binodal curve and the compositions of phases in equilibrium by tielines. The region within the dome is two-phase and that outside is one-phase. The most common systems are those with one pair (Type I, Fig. 14.1) and two pairs (Type II. Fig. 14.4) of partially miscible substances. For instance, of the approximately 1000 sets of data collected and analyzed by Sorensen and Arlt (1979), 75% are Type I and 20% are Type II. The remaining small percentage of systems exhibit a considerable variety of behaviors, a few of which appear in Figure 14.4. As some of these examples show, the effect of temperature on phase behavior of liquids often is very pronounced. 

Basically, compositions of phases in equilibrium are indicated with tielines. For convenience of interpolation and to reduce the clutter, however, various kinds of tieline loci may be constructed, usually as loci of intersections of projections from the two ends of the tielines. In Figure 14.1 the projections are parallel to the base and to the hypotenuse, whereas in Figures 14.2 and 14.6 they are horizontal and vertical. 

Therein, y(x) represents the equilibrium relation for the composition of phase ("), which is in general a function of the composition of phase ( ). 

Inside the reactive zone, chemical and phase equilibrium occur simultaneously. The composition of phases can be found by Gibbs free-energy minimization. The UNIQUAC model is adopted for phase equilibrium, for which interaction parameters are available, except the binary fatty-ester/water handled by UNIFAC-Dortmund. 

The first detailed studies of carbonitrides of iron were published by-Jack (17) in 1948. The nitrogen-rich carbonitride phases are isomorphous with y -, e-, and ("-nitrides, i.e., nitrogen has simply been replaced partially by carbon. The compositions of phases in the Fe-N-C system as given by Jack (17) are shown in Fig. 2. 

The application of Eq. (10.3) to specific phase-equilibrium problems requires use of models of solution behavior, which provide expressions for G or for the Hi as functions of temperature, pressure, and composition. The simplest of such expressions are for mixtures of ideal gases and for mixtures that form ideal solutions. These expressions, developed in this chapter, lead directly to Raoult s law, the simplest realistic relation between the compositions of phases coexisting in vapor/liquid equilibrium. Models of more general validity are treated in Chaps. 11 and 12. 

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