Binary phase diagrams hypothetical

Figure 2 Portion of a hypothetical A-B binary phase diagram showing a simple eutectic solidification reaction. Compositional variations can occur within the liquid during solidification as a result of relative kinetics of growth of solids a and f. In this case, a grows more easily. When dendrites of phase a grow, the remaining liquid solution becomes more B-rich (Ci). f forms in the resulting hypereutectic liquid, causing the liqidd composition to make small oscillations about the initial composition with time (inset). Eventually eutectic solid fills in the spaces around all primary phases.

Figure 4.1 Hypothetical lyotropic binary phase diagram where phase transitions can be induced by varying water content or temperature. The indicated mesophases are L(,-lamellar, laid, Pn3m or Imlm-direct and inverted bicontinuous cubic (V and Vn, respectively), Fd3m-direct and inverted...

Fig. 34. Hypothetical representation of the binary phase diagram at regions of very dilute concentrations of amphiphilic compound. Small pollywog-like creations represent molecules of an amphiphilic compound, such as a detergent. The orderly array in zone Z represent crystals. The spherical array in zone Y represent micelles. In zone X only individual molecules are present. For explanation of A, B, C, and D see text.

Differential thermal analysis (DTA) is a commonly used method to determine the location of phase boundaries. Figure 8.3 shows a hypothetical binary phase diagram and the DTA curves that would be expected for several compositions within the system. The endothermic melting and solidi-solid2 first-order transformations during heating are clearly evident. These peaks are due to the temporary... 

A hypothetical binary-phase diagram is shown in Figure 4.5. The pure components are A and B. 

DTA is especially suited in the construction of unknown phase diagrams of binary compounds. A hypothetical phase die am and the DTA curves which would be used to construct it are shown in the followii diagram, given as 7.2.1. on the next p e. 

Figure 4.10 (a)-(i) Phase diagrams of the hypothetical binary system A-B consisting of regular solid and liquid solution phases for selected combinations of Q q and Qs°l. The entropy of fusion of compounds A and B is 10 J K 1 mol-l while the melting temperatures are 800 and 1000 K. 

Figure 2.34. For a hypothetical binary system, possible trends of equilibrium (E) and kinetic (K) phase diagram are shown. (M) indicates the appearance of transformations which could be observed in a metastable situation (adapted from Chvoj etal. 1991).

Figure 2.2 Phase diagram for a hypothetical eutectic binary system. There are three single-phase fields (a, fi, and L) and three two-phase fields (a + 3, a + L, and 3 + L).

Figure 2.3 (a) Isometric projection (solid diagram) for a hypothetical ternary system (b) isotherm (horizontal section) (c) binary-phase subset (d) liquidus surface. 

The use of the differential thermal analysis in the phase diagram determination is illustrated in Figure 3.52. A hypothetical binary eutectic system A-B with the formation of the incongmently melting compound A4B was chosen. There are three thermograms (a) to (c) shown as examples. In thermogram (a), the first heat effect at temperature ai... 

FIGURE 15.24 Hypothetical phase diagram of a binary mixture forming a solid solution over the whole compositional range. The X-axis gives the mass fraction of the higher melting component. For situations between the liquidus and the solidus curve, a mixture of liquid and solid (compound crystal) material is present. 

Massalski (1990) presented the hypothetical Sc-Eu phase diagram based on thermodynamic calculations of Miedema (1976). They predict the occurrence of a broad immiscibility gap in liquid and solid alloys and the absence of binary compounds in this system. 

Nowotny and Auer-Welsbach (1961) synthesized the ternary compound ScTi3C4 isotypic with NaCl (fl=4.5 A). Velikanova et al. (1989) evaluated the hypothetical projection of the solidus surfaces of the phase diagram. A wide range of continuous solid solutions between the isotypic binary carbides ScCi t and TiCi c (ST NaCl) was predicted by them. It might be that the ternary phase observed by Nowomy and Auer-Welsbach is a part of this solid solution, and possibly not an individual ternary compound. Recently this prediction was confirmed experimentally by Ilyenko et al. (1996) who confirmed a complete mutual solubility of ScCi c and TiCi- . These authors reported also that the ScCi j phase is in equilibrium with all the phases of the solidus surface. However, the paper by Ilyenko et al. does not contain a figure of the phase equilibria. 

Hypothetical projections of the solidus surfaces of the Sc-M-C (M=Zr, Hf, V, Nb, Ta) phase diagrams are proposed in a paper of Velikanova et al. (1989). A complete miscibility of the binary carbides ScCi- and MCi- (M=Zr, Hf, V, Nb, Ta) crystallizing in the NaCl type structure, and the absence of ternary compounds in each of these ternary systems is predicted. However, these data need to be confirmed experimentally. Recently Ilyenko et al. (1996) reported the existence of continuous solid solutions between ScCi x and MC] x (M=Zr, Hf), and accordingty these solid solutions are in equilibria with all the phases of the solidus surface. The same authors reported that the VCi x binary carbidedissolves at least 15at.% Sc while the V solubility in ScC x is at least 17at.%. These data reject the earlier prediction of a complete miscibility of the NaCl-t5q)e binary carbides in the system Sc-V-C. However, no figures of the phase equilibria are presented in the brief communication of Ilyenko et al. 

In the context of a hypothetical binary system. Figure 3.9 illustrates how the liquidus and solidus lines in the phase diagram can be derived from DSC plots of different mixtures of the two components. In the lower part of the figure, the phase diagram of the system is given in the upper part, the DSC curves of particular compositions are shown together with the derived liquidus fine. 

Figure 1.8 Phase diagrams for a hypothetical binary system in the form of a Type 1 (rversus a ) diagram, a Type 2 (T versus Xb) diagram and a Type 3 (S versus Xb) diagram.

Figure 1.8 presents the phase equilibria in a hypothetical binary eutectic system similar to that in Figure 1.7, represented on each of the three types of diagrams. This diagram is similar to those for the Ag-Cu and Ni-Cr systems. The plot of T versus ub is a Type 1 diagram and the three-phase equilibrium a-L-(3 is represented by a point. The plot of T versus Ab is a Type 2 diagram and the a-L-(3 equilibrium is represented by three points on a line, the eutectic isotherm. The plot of S versus Xb is a Type 3 diagram and the a-L-(3 equilibrium is represented by an area. Note that the forms of these diagrams correspond to those for the unary system in Figure 1.4. (Numerous examples of the three types of phase diagrams are given for unary, binary and ternary systems in Chapter 13 of Reference [2], Reference [5] and Chapter 2 of Reference [8].

FIGURE 5.6 Top The phase diagram for a hypothetical binary system of a solvent and second molecule with N=2. Bottom The free energy versus volume fraction 0, at various temperatures, from which the phase diagram is constructed. Dashed lines show examples of how the phase diagram relates to the free energy functions. 

Figure 4.26 Sequence of phases observed on increasing solvent content, in a binary amphiphile-solvent system, representing a hypothetical phase diagram where phase transitions are controlled by solvent content only. Here a, b, c and d indicate intermediate phases (for example the bicontinuous cubic structure shown in Fig. 4.25d), L2 denotes the inverse micellar solution, Hn is the inverse hexagonal phase, L is the lamellar phase. Hi is the normal hexagonal phase and Li is the normal micellar phase. In practice, the full sequence of phases is rarely observed, and in reality the phase transitions depend on temperature as well as concentration...

Inasmuch as precipitation hardening results from the development of particles of a new phase, an explanation of the heat treatment procedure is facilitated by use of a phase diagram. Even though, in practice, many precipitation-hardenable alloys contain two or more alloying elements, the discussion is simplified by reference to a binary system. The phase diagram must be of the form shown for the hypothetical A-B system in Figure 11.22. 

Figure 5 Phase diagram of a hypothetical aqueous binary. The 7g -vs-c(w) curve represents the boundary between low and high molecular mobility regions lettering is specified in the text.

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