Crystal formation phase diagram

For sodium palmitate, 5-phase is the thermodynamically preferred, or equiUbrium state, at room temperature and up to - 60° C P-phase contains a higher level of hydration and forms at higher temperatures and CO-phase is an anhydrous crystal that forms at temperatures comparable to P-phase. Most soap in the soHd state exists in one or a combination of these three phases. The phase diagram refers to equiUbrium states. In practice, the drying routes and other mechanical manipulation utilized in the formation of soHd soap can result in the formation of nonequilibrium phase stmcture. This point is important when dealing with the manufacturing of soap bars and their performance. 

It would be incomplete for any discussion of soap crystal phase properties to ignore the colloidal aspects of soap and its impact. At room temperature, the soap—water phase diagram suggests that the soap crystals should be surrounded by an isotropic Hquid phase. The colloidal properties are defined by the size, geometry, and interconnectiviness of the soap crystals. Correlations between the coUoid stmcture of the soap bar and the performance of the product are somewhat quaUtative, as there is tittle hard data presented in the literature. However, it might be anticipated that smaller crystals would lead to a softer product. Furthermore, these smaller crystals might also be expected to dissolve more readily, leading to more lather. Translucent and transparent products rely on the formation of extremely small crystals to impart optical clarity. 

Fig. 1. Carbon-phase diagram where A, solvent-cataly2ed diamond growth B—G, diamond formation direcdy from graphite C, graphite formation from diamond, D, approximate region where formation of Lonsdaleite occurs from weU-ordered graphite crystals (7,8). To convert GPa to atm, multiply by...

Knowledge of phase diagrams is not only a prerequisite for efficient crystal-growth, but also provides information on the formation of solid solutions, in which, for example, physical properties may change continuously. The numerous publications concerning Group VA systems are summarized in Tables XXV-XXVII, together with the respective references and the most important information. Abbreviations used... 

Figure 2a shows a schematic phase diagram for lyotropic liquid crystals. This figure shows the formation of micelles, cubic phases, bicontinuous cubic phases, and lamellar phases as the concentration of surfactant increases. Also shown in this figure is a schematic diagram of an ordered bicontinuous cubic phase (Fig. 2b). Another interesting example in...

The potassium/caesium phase diagram is an example of a system involving the formation of mixed crystals with a temperature minimum (Fig. 4.4). The right and left halves of the diagram are of the same type as the diagram for antimony/bismuth. The minimum corresponds to a special point for which the compositions of the solid and the liquid are the same. Other systems can have the special point at a temperature maximum. 

Several phase diagrams of binary alloy systems have been shown (see for instance Fig. 2.18) in which the existence of intermediate phases may be noticed. In these systems we have seen the formation of AmB phases, which generally crystallize with structures other than those of the constituent elements, and which have negligible homogeneity ranges. Thermodynamically, the composition of any such phase is variable. In a number of cases, as those exemplified in Fig. 2.19, the possible variation in composition is very small (invariant composition phases or... 

Figure 6.10. A generic binary phase diagram is shown for an A-B system in which two compounds, AB and ABm, are formed. Different parts of the liquidus line are indicated. 1 is the line of primary crystallization of the terminal solid-solution based on the component A (which, on cooling, will be followed by the peritectic formation of AB ) 2 is the line of primary crystallization of the compound AB (to be followed by the eutectic crystallization of AB + ABm) 3 and 4 are lines of primary crystallization of ABm (to be followed, respectively, by the crystallization of the eutectic AB + ABm or of the eutectic AB, + B-based solid solution).

Figure 6.18. In-As phase diagram (at constrained pressure). Notice, (similarly to other III/V phase diagrams) the formation of the congruently melting 1 1 compound which gives two eutectics. The eutectic with In is practically coincident with In. As a consequence, for all the compositions from 0 up to 50 at.% As the primary crystallization of InAs may he obtained.

A very common occurrence in crystallization is the formation of clusters of non-diffracting crystals or crystalline precipitate that can not be improved by merely fine tuning the crystallization parameters. In such cases a working phase diagram can be constructed based on the conditions that give the low... 

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