Experimental determination of phase diagrams

The experimental methods of determining phase diagrams will be only briefly commented upon, in order to give an idea of the problems involved and of the connection between phase diagram science and other disciplines. A few special points will be considered in Chapter 6, dedicated to the preparation of intermetallics. 

It must however be pointed out that a sound experimental definition of a phase diagram can be obtained from the results of a number of concerted investigations such as thermal analysis, thermodynamic analysis, micrographic examination and phase analysis and identification by means of techniques such as X-ray diffraction measurements, microprobe analysis, etc. 

Emphasis has already been placed on the different experimental methodologies, for instance by Hume-Rothery et al. (1953) who stressed the need to use different complementary techniques in the definition of ternary or more complex systems. The necessity of combining thermal analysis with microscopic techniques was especially highlighted, for example, in the determination of solid liquid equilibria. 

In any case, going back to the beginning of the past century we may mention the pioneering investigation carried out by Parravano and Sirovich (1912) and Parravano (1914) in the determination by thermal analysis of the phase diagrams of quaternary alloy systems, such as Cu-Fe-Mn-Ni, Bi-Cd-Pb-Sn, Ag-Au-Cu-Ni. 

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Phase diagrams give valuable information about the compounds that can form in a system of components. These compounds can then be prepared and studied. For the experimental determination of phase diagrams the following methods are used. In differential thermal analysis (DTA) a sample of a given composition is heated or cooled slowly... 

As for many other materials, phase diagrams are roadmaps not only for the description of these substances and of their reactions, but also for their processing and for research and development planning. The systematic experimental determination of phase diagrams, their assessment and compilation and their thermodynamic optimization and calculation are the essential steps in the development of materials science and make up one of the bases of the intermetallic disciplines. 

It is possible in many cases to predict highly accurate phase equihbria in multi-component systems by extrapolation. Experience has shown extrapolation of assessed (n — 1) data into an nth order system works well for n < 4, at least with metallurgical systems. Thus, the assessment of unary and binary systems is especially critical in the CALPHAD method. A thermodynamic assessment involves the optimization of aU the parameters in the thermodynamic description of a system, so that it reproduces the most accurate experimental phase diagram available. Even with experimental determinations of phase diagrams, one has to sample compositions at sufficiently small intervals to ensure accurate reflection of the phase boundaries. 

Experimental determination of phase diagrams is convenient by using the thermal analysis method at which the temperature of the investigated sample is registered at its cooling by a constant rate of 2-5°C/min. Due to the thermal effects connected with the phase transformations (crystallization, polymorphic transformation), breaks appear on the cooling... 

Muan, A. and Osborn, E.F. (1965) Phase Equilibria among Oxides in Steelmaking, Addison-Wesley Publishing. Co., Reading, MA. Reference for experimental determination of phase diagrams in ceramics. Inspirational with very helpful commentary a must see text. 

Polymer solutions and blends have been extensively studied,motivation being both the fundamental and technological interest 2. When one component is a liquid crystal polymer, synergy could produce exceptional properties due to the anisotropy of the mesomorphic polymer. It is important to determine the conditions for the existence of either a uniform, mesomorphic phase or an incompatible biphasic system. In such studies, the rigid or semi-rigid character of the chains and the anisotropic interaction between the chains play a role. The presence of mesomorphic macromolecules is labeled by their ability to align under certain conditions, a fact which can be exploited in the experimental determination of phase diagrams. 

Rom] Roming, A.D., Goldstein, J.I., Experimental Determination of Phase Diagrams with the Electron Microprobc and Scanning Transmission Electron Microscope , Nat Bur. Stand. Special Publ N° 496, Vol. 1, 462-482 (1977) (Experimental, Phase Diagram, Phase Relations, 33)... 

The inset to Fig. 3.6 shows the experimentally determined ( ), T) phase diagram for %CB together with the results of the LdG theory, indicated by the solid line [20]. At a given temperature, the phase boundary is determined... 

Concerning the rare-earth-based alloys there is a continuous increase in the volume of experimental work determination of phase diagrams, characterization of intermetallic compounds, and thermodynamic measurements. In some cases a good agreement between recent values obtained by different authors has finally allowed a decision to be made between several data with a laige scatter. 

Phase diagrams describe the phase relations in equilibrated systems of chemical substances. The determination of phase diagrams is one of the commonest research topics in physical chemistry. After about more than one hundred years work, a huge amount of experimental data has been accumulated. These experimental data have been recorded into many handbooks and databases. They are widely used in daily research work, plant design and other practical work in chemistry, chemical technology and materials science. 

The incremental capacity of an insertion electrode material used in ambient temperature batteries can be estimated from voltage spectroscopy measurements which can help to the determination of phase diagram of the insertion compotmd [1], In the first section, we examine the various aspects of electrochemical lithium insertion into a number of electrode materials. The experimental techniques of solid-state electrochemistry are presented in the second section. Voltage spectroscopy and phase diagram during Li intercalation into cathode materials are investigated. Finally, the experimental determination of the diffusion coefficient of ions in solid materials is investigated. 

Pal] Palm, M., Inden, G., Experimental Determination of Phase Equilibria in the Fe-Al-C System , Intermetallics, 3, 443-454 (1995) (Phase Relations, Phase Diagram, Experimental,, 33)... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Experimental determination of a temperature depending phase diagram LC / LV / LK... 

An interesting example of a one-component systems is SiOa, which can exist in five different crystalline forms or as a liquid or a vapor. As C = 1, the maximum number of phases that can coexist at equilibrium is three. Each phase occupies an area on the T P diagram the two-phase equilibria are represented by curves and the three-phase equilibria by points. Figure 13.1 (2, p. 123), which displays the equUi-brium relationships among the sohd forms of Si02, was obtained from calculations of the temperature and pressure dependence of AG (as described in Section 7.3) and from experimental determination of equUibrium temperature as a function of equilibrium pressure. 

EXPERIMENTAL DETERMINATION OF THERMODYNAMIC QUANTITIES AND PHASE DIAGRAMS 61... 

It can now be seen that if the thermodynamic properties of the liquid and f.c.c. phases could be determined it would be possible to calculate a phase diagram without the need for experimental determination of the phase diagram itself. Indeed, this was done by Pascoe and Mackowiak (1970, 1971) more than 25 years ago and the diagram was in good agreement with that observed experimentally. Ni-Cu presents... 

Experimental Determination of Thermodynamic Quantities and Phase Diagrams... 

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