Phase diagram isothermal methods

Considering now a few common methods and techniques for the experimental definition of a phase diagram, it may be useful to refer to their usual classification into two groups polythermal and isothermal methods. 

Isothermal methods. In principle these methods imply the preparation of a certain number of alloy specimens of different compositions and their examination at the same given temperature. Important methods are those based on observations carried out under a microscope. An example of such an analysis is given in Fig. 2.41 where the photomicrographs of two alloys of the Cu-Mg phase diagram are shown. These pictures, taken with a reflection microscope, allow identification... 

The second section will concentrate on methods of determining phase diagrams. The first part will examine non-isothermal methods, such as differential thermal analysis and cooling curve determinations, while the second will concentrate on isothermal methods, such as metallography, X-ray measurements, etc. The various limitations of both methods will be discussed and some novel techniques introduced. 

This chapter s statistical mechanics method was used to generate phase diagrams as illustrations of multicomponent hydrate equilibria concepts at one isotherm, 277.6 K, the most common temperature in a pipeline on the ocean floor at water depths beyond 600 m. Section 5.2.1 shows the fit if the method to single (simple) hydrates, before the extension to binary hydrate guests in Section 5.2.2. Section 5.2.3 shows the final extension to ternary mixtures of CH4 + C2H6 + C3H8 and indicates an industrial application. Most of the discussion in this section was extracted from the thesis of Ballard (2002) and the paper by Ballard and Sloan (2001). 

Here we derive Eq. (7.2.14) on the basis of somewhat tortuous thermodynamic arguments. An alternative, simpler procedure is provided in the next section, but the present method is instructive and included for that reason. We base our considerations on the portion of the liquid-gas phase diagram very close to the critical point, shown in Fig. 7.3.1. One of the two isotherms is taken at the critical temperature Tc the other, at a lower temperature T very close to Tc. We investigate... 

In this chapter we describe the methods used to calculate solubility isotherms as well as the entire phase diagram for binary and ternary solute-SCF mixtures. The objective of the first part of the chapter is to discuss the relevant physical properties of the solute and solvent pair that are needed to describe the intermolecular forces in operation between molecules in a mixture that ultimately fix solubility levels. A brief description is provided on the application of solubility parameters to supercritical fluids. 

The experimental procedure can be understood by reference to the Fe-C phase diagram, Figure 2. The specimen is reacted with methane at temperatures of 750-850°C. Carbon dissolves in the metal until the saturation solubility has been exceeded at the gamma-Fe/FejC phase boundary, or alternatively the specimen is cooled to a temperature below the iron-carbon eutectoid (721°C or 738°C). The solid and dotted lines in Figure 2 indicate the alternative iron-Fe3C and iron-graphite phase boundaries respectively. Either method produces similar reaction products but the isothermal experiment is prefereably carried out at higher pressures, e.g. 50 Torr, to minimise run times. 

Sample phase diagrams collected using the two gradient methods are presented in Fig. 9 and 11. It is important to realize that in both cases only the location of phase boundaries are shown, while in fact, phase identification and structural characterization is available continuously along each isotherm and isopleth in the respective plots. 

Probably the simplest method to determine phase diagrams is to hold a carefully prepared mixture of known composition isothermally at elevated temperatures until equilibrium is achieved, quench the sample to room temperature rapidly enough to prevent phase changes during cooling, and then examine the specimen to determine the phases present. The latter is usually carried out by using a combination of X-ray diffraction and microscopy techniques. 

Figure 4.21 The method of determination of compositions on an isothermal phase diagram...

The bulk phase diagrams of pure hydrocarbons and mixtures are well known from the experiments. In the work by Sage et al. [3], the bubble point pressures of methane + n-butane mixtures are determined experimentally from the discontinuity of isothermal compressibility of constant-composition mixture at the point of phase transition. The composition of vapor phase is determined in that work from the residual specific volume of gas. Later experiments employ phase recirculation techniques [4] to achieve vapor-Uquid equilibrium [5, 6], and the phase compositions are analyzed by more advanced methods such as gas chromatography. 

The first calculation of the whole phase diagram by the CALPHAD method has been carried out by [1993Lee]. The results were presented as isothermal sections at 1000, 950, 900, 850, 800, 750 and 650° C and vertical section at 6, 16 and 28 mass% Mn. [1993Lee] has treated a phase as stoichiometric phase due to the lack of information. The thermodynamic parameters L for the Cr-Fe system and L for the Cr-Fe-Mn system in (aMn), (fiMn) and L for Cr-Fe-Mn in hep phases were given the value zero. 

The capacity for hydration of a substance in the crystalline state is a measure of its hydration capacity in solution. Sulphuric acid e. g., does form crystalline hydrates. In liquid mixtures of sulphuric acid and water, these hydrates, of course, are present as well. They are then dissolved in an excess of either water or sulphuric acid. In inorganic chemistry there are also numerous examples of solid substances forming chemically definite hydrates, though these cannot be detected by the common methods (X-ray diagram, isothermal or isobaric decomposition) which imply the existence of phases with crystalline order. According to R. Fricke (Walden, Handbuch d. allgemeinen Chemie, 9 (1937), 520), a typical example is chromium (3) hydroxide. In such cases the vapour pressure isotherms do not represent the typical step-ladder type but resemble those of solutions (R. Fricke, Naturwiss., 31 (1943) 469). 

The research method for the stable phase equilibria of salt-water system is isothermal dissolution method. It is worthy of pointing out that the status of the stable phase equilibrium of salt-water system is the in a sealed condition under stirring sufficiently, and the speed of dissolution and crystallization of equilibrium solid phase is completely equal with the marker of no change for the liquid phase composition. As to the thermodynamic stable equilibrium studies aiming at sea water system (Na - K - Mg - Cl - SO4 - H2O), J.H. Vant hollf (1912) was in the earliest to report the stable phase diagram at 293.15 K with isothermal dissolution method. 

We shall consider in detail some versions of p-V-T-x curve methods using schemes of typical isothermal and isobaric sections (Figure 1.10) of phase diagrams for binary systems. 

The sandwich-hke sample Al-Cd-Mg was treated at 575 K by the method of diffusion zones superposition [11]. A1 and Mg interacted through the Cd layer (0.2 xm). After isothermal aimealing for t = 10, 100, 200, 500, and 900 h and measuring the concentration distributions, the diffusion paths were built and thus the system s phase diagram was constructed (Figure 9.1b). In that, the first phase. 

The ternary solubility phase diagram of (S) - and (R) - propranolol hydrochloride in a mixed solvent of methanol and acetone was measured by isothermal method [25]. For isothermal method, enough amount of powder, namely lOfttO.lmg, was dissolved in the solvent of methanol in a test tube. Saturated solution samples were carefully withdrawn and filtered, and the concentration of which were analyzed by the HPLC system with employment of above-mentioned self-packed column. 

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