Phase diagrams quaternary

Phase diagrams are mostly determined by thermal analysis. We now discuss one-component systems to show how it works. The more complicated diagrams for binary, ternary or quaternary alloys are determined by the same method. 

An example for a partially known ternary phase diagram is the sodium octane 1 -sulfonate/ 1-decanol/water system [61]. Figure 34 shows the isotropic areas L, and L2 for the water-rich surfactant phase with solubilized alcohol and for the solvent-rich surfactant phase with solubilized water, respectively. Furthermore, the lamellar neat phase D and the anisotropic hexagonal middle phase E are indicated (for systematics, cf. Ref. 62). For the quaternary sodium octane 1-sulfonate (A)/l-butanol (B)/n-tetradecane (0)/water (W) system, the tricritical point which characterizes the transition of three coexisting phases into one liquid phase is at 40.1°C A, 0.042 (mass parts) B, 0.958 (A + B = 56 wt %) O, 0.54 W, 0.46 [63]. For both the binary phase equilibrium dodecane... 

A listing of ternary, quaternary and higher order systems is found in Table 1. An extensive and more detailed compilation concerning the structural chemistry and phase equilibria in the low-T phase diagrams of the (Mre, MrExXM i, Mj )4B4 type is available , along with a discussion of the physical properties and low-T behavior of these alloys (i.e., superconductivity and magnetism) - " . 

In each of the composition diagrams in Fig. 14.2, the numbers represent a series of reactions run at a defined composition and temperature. These are isometric sulfur slices through three-dimensional K/P/RE/S quaternary phase diagrams. As just one example of what we have studied. Table 14.1 identifies the compositions at each point and the resulting phase(s). We have rigorously studied how phase formation is dependent upon the compositions of reactions for the rare-earth elements Y, Eu, and La and we have also discovered key structural relationships between the rare-earth elements, indicating a significant dependence on rare-earth and alkali-metal size for sulfides and selenides. 

Figure 4.20 Tetrahedron space model for the phase diagram of the quaternary system A-B-C-D. The isotherms T], 72, T3 are shown for the primary phase volume of component A [17]. Reprinted with permission of The American Ceramic Society, www.ceramics.org. Copyright [1984]. All rights reserved.

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. 

Following the seminal formulation of electrolytes based on carbonates by Tarascon and Guyomard, - a lot of effort had been made to modily those binary lithium ion electrolytes. Often, ternary, quaternary, and even higher order solvent systems were proposed, and the difficulty in constructing the phase diagrams for these systems increased dramatically... 

SLE of quaternary ammonium ILs in alcohols, hydrocarbons, and water have been measured for many salts. Systematic studies of SLE phase diagrams for quaternary ammonium salts [(Cj)2C2HOC2N]Br, [(Ci)2C3HOC2N]Br, [(Cj)2C4HOC2N]Br, and [(Ci)2CgHOC2N]Br in water and alcohols have been published [52,79]. Other anions including [BFJ, [PFg], [dca] , and [TfjN] have also been investigated [53]. 

The importance of solvents and their effects play roles in electrochemistry as well. The properties of a family of novel quaternary ammonium salts based on the bis(triflu-oromethylsulfonyl)imide and triflate anions are reported in a paper by Sun (Sun et al., 1998). Binary phase diagrams for some of their mixtures and their electrochemical windows of stability were reported. The highest conductivity observed in the pure salt systems at 25°C was 7 x 10 S cm-1. An electrochemical window of stability of up to 5V was measured on graphite electrodes. The effect of salt structure and solvent on conductivity of the salts is also discussed. 

The thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

Liquid-Solution Models. The simple-solution model has been used most extensively to describe the dependence of the excess integral molar Gibbs energy, Gxs, on temperature and composition in binary (142-144, 149-155), quasi binary (156-160), ternary (156, 160-174), and quaternary (175-181) compound-semiconductor phase diagram calculations. For a simple multicomponent system, the excess integral molar Gibbs energy of solution is expressed by... 

This chapter presents a review of the current data on phase diagrams and crystal structures of binary, ternary and quaternary metal antimonides with the R elements (R = Sc, Y and the lanthanides). 

These observations on the sulfuric acid catalyst arc full in line with the general thermodynamic behaviour of fused catalyst systems. The mctastablc solid in Figure 2 has to be replaced in this case by a cascade of the partly reduced vanadium ternary sulfates. The processes sketched above occur under thermodynamic control in a quaternary phase diagram, vanadium-oxygen-sulfur-alkali, as illustrated by the reversibility of the exsolution of the partly reduced vanadium compounds under suitable partial pressures of oxygen... 

Schomacker compared the use of nonionic microemulsions with phase transfer catalysis for several different types of organic reactions and concluded that the former was more laborious since the pseudo-ternary phase diagram of the system had to be determined and the reaction temperature needed to be carefully monitored [13,29]. The main advantage of the microemulsion route for industrial use is related to the ecotoxicity of the effluent. Whereas nonionic surfactants are considered relatively harmless, quaternary ammonium compounds exhibit considerable fish toxicity. 

L9 was built from the combination of five elements (Pt, Ru, Os, Ir, and Rh) in a quaternary phase diagram (combinations of up to four elements from the five possible 57). Thequaternary phase diagram can be represented by a 10 x lOx lOx 10 tetrahedron (Fig. 11.12), where the 4 vertices represent the pure elements, the 48 positions on the edges (6 x 8) represent the binary alloys, the 112 positions on the faces (4 x 28) represent the ternary alloys, and the 56 inner positions represent the quaternary alloys to give a total of 220 different compositions. The addition of a fifth element increased the library composition by 1 (element) -1- 32 (4 x 8, binary alloys) + 168 (6 x 28, ternary alloys) -1- 224 (4 x 56, quaternary alloys) = 425 different compositions, giving a total number of 645 library individuals for L9 (Fig. 11.12). 

The phase diagram of the quaternary system, n-tetradecane, water, A-B-A block copol3nner (where A Is poly— (12-hydroxystearlc acid) and B Is poly(ethylene oxide)) and n-butanol was Investigated at 7, 23 and 47 C. Two A-B-A polymer concentrations of 10 and 20Z were used. 

Figure 1 Phase diagrams for the quaternary system tetradecane, butan-l-ol, water, B246 at 7°C (a), 23°C (b) and 40°C (c). Total concentration of B246 is 10%.

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