Mutual solubility diagrams

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... 

The phase diagrams we have shown are based upon the fact that A and B form solid mutually soluble solid state solutions. If they do not, i.e.- they are not mutually soluble in the solid state, then the phase diagram becomes more complicated. As an example, consider the following, which is the case of limited solid solubility between A and B. (N.B.- study the following diagrams carefully)"... 

Most hydrophobic substances have low solubilities in water, and in the case of liquids, water is also sparingly soluble in the pure substance. Some substances such as butanols and chlorophenols display relatively high mutual solubilities. As temperature increases, these mutual solubilities increase until a point of total miscibility is reached at a critical solution temperature. Above this temperature, no mutual solubilities exist. A simple plot of solubility versus temperature thus ends at this critical point. At low temperatures near freezing, the phase diagram also become complex. Example of such systems have been reported for sec-butyl alcohol (2-butanol) by Ochi et al. (1996) and for chlorophenols by Jaoui et al. (1999). 

Chapter 18 - The determination region of solubility of methanol with gasoline of high aromatic content was investigated experimentally at temperature of 288.2 K. A type 1 liquid-liquid phase diagram was obtained for this ternary system. These results were correlated simultaneously by the UNIQUAC model. By application of this model and the experimental data the values of the interaction parameters between each pair of components in the system were determined. This revealed that the root mean square deviation (RMSD) between the observed and calculated mole percents was 3.57% for methylcyclohexane + methanol + ethylbenzene. The mutual solubility of methylcyclohexane and ethylbenzene was also demostrated by the addition of methanol at 288.2 K. 

The diagrams that will be mainly considered are those concerning the behaviour of the alloys in the liquid and solid states that is, melting and solid-state transformation diagrams. A number of different diagram types can be defined and classified on the basis of the different mutual solubility of the components (in the liquid and in the solid state with the formation of more or less extended liquid and/or solid solutions) and of their reactivity, resulting in the formation of various, so-called intermediate phases . 

Figure 2.1. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the solid and in the liquid states (L liquid field, S solid field). The melting behaviour of the Mo-V, Cs-Rb and Ca-Sr alloys is presented. Notice the different ranges of temperature involved. The melting points of the pure metal components are shown on the corresponding vertical axes. The Cs-Rb is an example of a system showing a minimum in the melting temperature. In the Sr-Ca system complete mutual solid solubility is shown in both the allotropic forms a and (3 of the two metals.

Figure 2.9. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the liquid state and, at high temperature only, in the solid state. By lowering the temperature, however, the continuous solid solution decomposes into two phases. In (d) a schematic representation of NiAu or PtAu type diagrams is shown as formed by two generic components A and B.

A similar behaviour (complete mutual solubility in the liquid state and partial solubility in the solid state) is presented also by the Pt-Au and Ba-Ca systems (Fig. 2.9(b) and (c)). Notice in the Pt-Au diagram the closeness (mainly for compositions near 40 at.% Au) between the melting and the de-mixing equilibria. 

The Ba-Ca diagram has a different appearance because Ca (in its high-temperature form) and Ba are completely mutually soluble, while only a partial solid solubility is observed for Ba in the low-temperature modification of Ca. 

Figure 2.11. The Au-Si diagram is an example of a simple eutectic system with complete mutual solubility in the liquid state and no (or negligible) solubility in the solid state at a temperature of 363°C the liquid having the composition of 18.6 at.% Si solidifies with the simultaneous crystallization of the practically pure gold and silicon mechanically mixed. In the Cr-U system a slightly more complex situation due to the solid-state transformations of uranium is shown.

Solubility Diagrams effects of atomic properties on mutual solubility. The effect on mutual solubility of the atomic properties of the components (and therefore of their relative positions on the map shown in Fig. 2.8) may be considered on the basis also of different diagrams. 

All the phase diagrams reported above show a complete mutual solubility in the liquid state. The formation of a single phase in the liquid state corresponds to behaviour frequently observed in intermetallic (binary and complex) systems. Examples, however, of a degree of immiscibility in the liquid state are also found in selected intermetallic systems. Fig. 2.16 shows a few binary systems in which such immiscibility can be observed (existence of miscibility gaps in the liquid state). All the three... 

Binary data can be represented with a T—x diagram that shows the mutual solubility as function of temperature. Most of the binary systems belong to one of the classes in Fig. 10.1. For ternary systems, experimental data are usually obtained at constant temperature and given in ternary diagrams. There are many types of systems, but more than 95% belong to one of the two classes shown in Fig. 10.1. 

Using specific metal combinations, electrodeposited alloys can be made to exhibit hardening as a result of heat treatment subsequent to deposition. This, it should be noted, causes solid precipitation. When alloys such as Cu-Ag, Cu-Pb, and Cu-Ni are coelectrodeposited within the limits of diffusion currents, equilibrium solutions or supersaturated solid solutions are in evidence, as observed by x-rays. The actual type of deposit can, for instance, be determined by the work value of nucleus formation under the overpotential conditions of the more electronegative metal. When the metals are codeposited at low polarization values, formation of solid solutions or of supersaturated solid solutions results. This is so even when the metals are not mutually soluble in the solid state according to the phase diagram. Codeposition at high polarization values, on the other hand, results, as a rule, in two-phase alloys even with systems capable of forming a continuous series of solid solutions. 

Wh/kg. As indicated in the sodium-sulphur phase diagram given in Fig. 8.15, sodium pentasulphide and sulphur are not mutually soluble at the temperature of cell operation, so that two liquid phases are present in the cathode compartment and the cell voltage is invariant. As the discharge progresses and the available elemental sulphur is consumed, a series of reactions commences as the sodium pentasulphide is converted to lower polysulphides, all of which are mutually soluble ... 

On a ternary equilibrium diagram like that of Figure 14.1, the limits of mutual solubilities are marked by the binodal curve and the compositions of phases in equilibrium by tielines. The region within the dome is two-phase and that outside is one-phase. The most common systems are those with one pair (Type I, Fig. 14.1) and two pairs (Type II. Fig. 14.4) of partially miscible substances. For instance, of the approximately 1000 sets of data collected and analyzed by Sorensen and Arlt (1979), 75% are Type I and 20% are Type II. The remaining small percentage of systems exhibit a considerable variety of behaviors, a few of which appear in Figure 14.4. As some of these examples show, the effect of temperature on phase behavior of liquids often is very pronounced. 

The phase diagrams of two-component surfactant-water systems are typically quite different for nonionic and ionic compounds. As exemplified in Fig. 2.22 there are at low temperatures different liquid crystalline phases while at intermediate temperatures there may be a total mutual solubility of surfactant and water98. At higher temperatures, there is, as already noted, a separation into two phases with a very large two-phase region. One of the phases contains very little surfactant, while the other contains appreciable amounts of both components. The cloud-point curve can be described as a liquid-liquid solubility curve with a lower consolute tempera-... 

For a binary system in which two components are mutually soluble in all proportions in both the liquid and solid states, the possible phase diagram shapes are as shown below ... 

In the study of miscibility of partially miscible liquid pairs, the external pressure is kept constant and, therefore, the vapour phase is ignored. The mutual solubilities are represented by means of temperature-composition diagram. 

Iron-nickel alloys are known to dissolve in the aluminium melts non-selectively. " As seen from Table 5.3, during dissolution of a 50 mass % Fe-50 mass % Ni alloy the ratio, cFe cNi, of iron to nickel concentrations in the melt is 1.00 0.05, i.e. it is equal to that in the initial solid material. The same applies to other alloys over the whole range of compositions. Respective saturation concentrations are presented in Table 5.4. The data obtained display a strong mutual influence of the elements on their solubilities in liquid aluminium because in its absence the solubility diagram for a constant temperature would be like that shown by the dotted lines in Fig. 5.5, with the eutonic point, E, at 2.5 mass % Fe and 10.0 mass % Ni. The effect of iron on the nickel solubility is seen to be more pronounced than that of nickel on the iron solubility. 

The influence of different modifiers on extraction efficiency with a concentration of 4 mol% is pointed out in diagram 2. With pure supercritical carbon dioxide,only pentaerythrit-tetranitrate is recovered. Recovery of the other samples is below 1 %, indicating no mutual solubilities with supercritical carbon dioxide. Using modifiers, recoveries of nitro-triazole and cyclo-trimethylene-trinitramine can be greatly enhanced. 

Binary liquid-liquid equilibria are usually represented as temperature-vol-ume fraction diagrams. These diagrams give the mutual solubilities in the two coexisting liquid phases, as functions of temperature. Figure 2F-3 illustrates six types of phase behavior that have been observed in binary LLE. A horizontal line intersects the phase boundary curve at two points which give the compositions of the two phases in equilibrium at the corresponding temperature. 

Fig. 3 Phase diagram for two components, X and Y, which are miscible in the liquid phase and mutually soluble in the solid phase.

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