Temperature-composition phase diagrams experimental

This paper describes the results of an experimental study of condensed phase equilibria in the system MoFe-UFo carried out by thermal analysis and x-ray diffraction analysis. A temperature-composition phase diagram is constructed from the temperatures of observed thermal arrests in MoFe-UFe mixtures, and the basis for the formation of this particular type of diagram is traced to the physical properties of the pure components. The solid-solubility relations indicated by the diagram are traced to the crystal structures of the pure solids. 

Fig. 6.4. Experimental temperature-composition phase diagrams for several representative binary systems (a) Cu-Au (adapted from Massalski (1990)), (b) Ti-Al (adapted from Asta et at. (1992)), (c) Si-Ge (adapted from Massalski (1990)), (d) Al-O (adapted from Massalski (1990)).

Temperature-composition phase diagrams such as this are often mapped out experimentally by observing the cooling curve (temperature as a function of time) along isopleths of various compositions. This procedure is thermal analysis. A break in the slope of a cooling curve at a particular temperature indicates the system point has moved from a one-phase liquid area to a two-phase area of liquid and solid. A temperature halt indicates the temperature is either the freezing point of the liquid to form a solid of the same composition, or else a eutectic temperature. 

Experimental results describing limited mutual solubility are usually presented as phase diagrams in which the compositions of the phases in equilibrium with each other at a given temperature are mapped for various temperatures. As noted above, the chemical potentials are the same in the equilibrium phases, so Eqs. (8.53) and (8.54) offer a method for calculating such... 

Experimental and theoretical studies, as well as computer simulators, all require knowledge of the number and compositions of the conjugate phases, and how these change with temperature, pressure, and/or overall (k ., system) composition. In short, all forms of enhanced oil recovery that use amphiphiles require a detailed knowledge of phase behavior and phase diagrams. 

For phase diagrams, a phase boundary is one end of a tie-line and, therefore, is dependent on the phase which exists at the other end of the tie-line. In a binary system, two independent measurements are therefore needed to define the tie-line in the case of a liquid/solid phase boundary this would be and Xg at temperature T. Ideally it would be desirable to have these two compositions as independent variables giving rise to two independent equations of error. The Lukas programme does this by making two equations but where the dependence of error on one of the measurements is weak. This is important if the two concentrations have different accuracies. For some types of experimental values newer versions of the Lukas programme offer different kinds of equations of error (Lukas and Fries 1992). 

The science dealing with phase transitions is thermodynamics. Using thermodynamics, we may discuss which phase will eventually be formed when a material (of composition c and phase p) is maintained under the same conditions for an infinite time, and the phase reaches the minimum energy state (equilibrium state) under given thermodynamic conditions (temperature and pressure). Experimentally, a phase diagram (equilibrium phase diagram) is prepared, and we may use the data... 

Determination of T y. In the formulation of the phase equilibrium problem presented earlier, component chemical potentials were separated into three terms (1) 0, which expresses the primary temperature dependence, (2) solution mole fractions, which represent the primary composition dependence (ideal entropic contribution), and (3) 1, which accounts for relative mixture nonidealities. Because little data about the experimental properties of solutions exist, Tg is usually evaluated by imposing a model to describe the behavior of the liquid and solid mixtures and estimating model parameters by semiempirical methods or fitting limited segments of the phase diagram. Various solution models used to describe the liquid and solid mixtures are discussed in the following sections, and the behavior of T % is presented. 

In addition to the molecular weight of the free polymer, there axe other variables, such as the nature of the solvent, particle size, temperature, and thickness of adsorbed layer which have a major influence on the amount of polymer required to cause destabilization in mixtures of sterically stabilized dispersions and free polymer in solution. Using the second-order perturbation theory and a simple model for the pair potential, phase diagrams relat mg the compositions of the disordered (dilute) and ordered (concentrated) phases to the concentration of the free polymer in solution have been presented which can be used for dilute as well as concentrated dispersions. Qualitative arguments show that, if the adsorbed and free polymer are chemically different, it is advisable to have a solvent which is good for the adsorbed polymer but is poor for the free polymer, for increased stability of such dispersions. Larger particles, higher temperatures, thinner steric layers and better solvents for the free polymer are shown to lead to decreased stability, i.e. require smaller amounts of free polymer for the onset of phase separation. These trends are in accordance with the experimental observations. 

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