Binary phase diagrams equilibria

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

When two metals A and B are melted together and the liquid mixture is then slowly cooled, different equilibrium phases appear as a function of composition and temperature. These equilibrium phases are summarized in a condensed phase diagram. The solid region of a binary phase diagram usually contains one or more intermediate phases, in addition to terminal solid solutions. In solid solutions, the solute atoms may occupy random substitution positions in the host lattice, preserving the crystal structure of the host. Interstitial soHd solutions also exist wherein the significantly smaller atoms occupy interstitial sites... 

Figure 2.12a. Building blocks of binary phase diagrams examples of single-phase (two-variant) and two-phase (mono-variant) fields. In the figure the indication is given of the phases existing in the various fields and respectively of their number. The phase equilibrium composition in the two-phase fields is defined by the boundary (saturation) lines of the single-phase regions. (Pt), (Ag),...

Figure 2.12b. Building blocks of binary phase diagrams examples of two-phase (mono-variant) reactions. On the left the transformation, on cooling, from the a phase to (3 is shown. For the composition in equilibrium conditions the transformation starts at temperature 7) and ends at Tf. Notice that at an intermediate temperature as Tm only a partial transformation has been carried out a certain quantity of a (having the composition corresponding to a ) will coexist with [3 (of composition [3 ). On the right, the a phase undergoes, on cooling, a de-mixing in the two a and a" phases having at temperature 7) the compositions x and x", at temperature T2 the compositions x2, xt2, etc.

A major complication in the analysis of convection and segregation in melt crystal growth is the need for simultaneous calculation of the melt-crystal interface shape with the temperature, velocity, and pressure fields. For low growth rates, for which the assumption of local thermal equilibrium is valid, the shape of the solidification interface dDbI is given by the shape of the liquidus curve Tm(c) for the binary phase diagram ... 

Fig. 14 Binary phase diagram for C246H494 in octacosane. The top curve shows the equilibrium liquidus for extended-chain crystals, and the bottom line the metastable liquidus for once-folded crystals. Experimental dissolution temperatures are fitted to the Flory-Huggins equation with / = 0.15 (solid lines). Vertical dotted lines (a) and (b) indicate the concentrations at which the growth rates were determined as a function of Tc in [29]. Horizontal dotted lines indicate the temperatures at which the rates were determined in [45] as a function of concentration. G(c) at Tc = 106.3 °C, measured along line (c), is shown in Fig. 12. The shading indicates schematically the crystal growth rate (black = fast), and the dashed line the position of the growth rate minimum...

By combining the thermodynamic data with those on the structure of the equilibrium binary phase diagram, R. Pretorius et al 261,262 were able to improve the accuracy of predicting the sequence of compound-layer formation in the transition metal-aluminium systems. For this, they used the values of the standard enthalpies (heats) of formation of the compounds. 

Figure 4.6 (a) Portion of a binary-phase diagram illustrating equilibrium solidification (b) nonequilibrium (rapid) solidification, which results in a chemical composition gradient in the crystals, a condition known as coring. (After Lalena and Cleary, 2005. Copyright John Wiley Sons, Inc. Reproduced with permission.)... 

BINARY PHASE DIAGRAMS FOR VAPOR-LIQUID EQUILIBRIUM 3.15... 

Figure 9. (opposite) Liquidus and separation surfaces of the copper-tin-lead system after Ref, 13. Tne appropriate portions of the phase equilibrium diagrams for Cu-Sn and Cu-Pb appear on the sides of the triangle, ( ), Intersection of the liquidus contours with the liquidus of the binary phase diagrams. One should really picture this as a solid triangular prism viewed from the top the sides of the prism would show the binary phase equilibrium diagrams. 

The results of the crystallization trials are summarized in Table 11-3. The acetone/water binary phase diagram was used to approximate equilibrium conditions for the solvent systems at the freeze crystallization conditions in the absence of a multicomponent phase diagram for the acetone/water/imipe-nem/NaHCOp system. 

Equilibrium Binary Phase Diagrams of Alumina with Other Oxides... 

The change of halide ion results in weaker acidic properties for LnCl3 as compared with LnF3. This means that equilibrium (1.1.41) with the participation of alkali metal halide should be shifted to the left as compared with the fluoride complexes. That is, lithium chloride does not react with chlorides of the rare-earth elements with the formation of any compounds the binary phase diagrams are characterized by one simple eutectic. The same situation is observed for the binary diagrams for lithium- and rare-earth bromides. 

A phase diagram is a map that indicates the areas of stability of the various phases as a function of external conditions (temperature and pressure). Pure materials, such as mercury, helium, water, and methyl alcohol are considered one-component systems and they have unary phase diagrams. The equilibrium phases in two-component systems are presented in binary phase diagrams. Because many important materials consist of three, four, and more components, many attempts have been made to deduce their multicomponent phase diagrams. However, the vast majority of systems with three or more components are very complex, and no overall maps of the phase relationships have been worked out. 

AC or BC, which melts at a higher temperature than either of the pure elements (except for the InSb-Sb case). The binary phase diagram consists of two simple eutectic systems on either side of the compound (e.g., the A-AC and the AC-C systems). The third binary phase diagram represents solid-liquid equilibrium between elements from the same group. In Figure 1 the A-B portion of the ternary phase diagram is depicted as being isomorphous... 

The iron-iron carbide phase diagram is probably the most important of all binary phase diagrams. Why is the diagram not a true equilibrium diagram Does it matter ... 

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