Phase field diagram

Fig. 1. Phase field diagram for the rare-earth oxides. After Foex and Traverse [/ ] Reprinted by permission of Societie Francaise de Mineralogie et al Crystallographie.

Since the crystallization fields for zeolites A and faujasite (X and Y) lie next to each other on the crystallization phase field diagram (Fig. 3) [5], they often grow in the same, or similar solutions. This is especially true when attempting to increase crystal sizes through the addition of complexing agents to the solutions (see Sect. 2.1.1). Hence, these two types of zeolites will be discussed together. 

Fig. 3.6. (a) The copper-nickel diagram is a good deal simpler than the lead-tin one, largely because copper and nickel are completely soluble in one another in the solid state. (b) The copper-zinc diagram is much more involved than the lead-tin one, largely because there are extra (intermediate) phases in between the end (terminal] phases. However, it is still an assembly of single-phase and two-phase fields. 

Pernod is a transparent yellow fluid consisting of water, alcohol and Evil Esters. The Evil Esters dissolve in strong water-alcohol solutions but precipitate out as tiny whitish droplets if the solution is diluted with more water. It is observed that Pernod turns cloudy at 60 wt% water at 0°C, at 70 wt% water at 20°C, and at 85 wt% water at 40°C. Using axes of T and concentration of water in wt%, sketch an approximate phase diagram (Fig. A1.3) for the Pernod-water system, indicating the single-phase and two-phase fields. 

The phase diagram for a binary alloy (Fig. A1.13) shows single-phase fields (e.g. liquid) and two-phase fields (e.g. liquid plus A). The fields are separated by phase boundaries. When a phase boundary is crossed, a phase change starts, or finishes, or both. 

Figure A1.19 shows the phase diagram for the copper-zinc system. It is more complicated than you have seen so far, but all the same rules apply. The Greek letters (conventionally) identify the single-phase fields. 

Most pairs of homopolymers are mutually immiscible, so that phase diagrams are little used in polymer science... another major difference between polymers on the one hand, and metals and ceramics on the other. Two-phase fields can be at lower or higher temperatures than single-phase fields... another unique feature. 

In addition to all the metallic phase diagrams, a series of volumes devoted to ceramic systems have been published since 1964 by the American Ceramic Society and is still continuing. The original title was Phase Diagrams for Ceramists, now it is named Phase Equilibria Diagrams. Some 25,000 diagrams, binary and ternary mostly, have been published to date. There is no compilation for polymeric systems, since little attention has been devoted to phase diagrams in this field up to now. 

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),...

The Te-S system is peculiar it is a simple eutectic-type diagram and shows (like an island completely surrounded by the single-phase field of the liquid) a small oval insolubility region situated between —37 and 41.5 at.% S and between two critical temperatures (upper Tc = 740°C and lower Tc = 690°C). This behaviour (often observed for instance in organic systems) among the different pairs of elements has been described only for Te-S. 

Figure 2.27. Isothermal section at 307°C of the Al-Zn-Si diagram. The boundary binary systems are shown. The isothermal section at 307°C is marked on the binary Al-Zn diagram. The corresponding single-phase (thick segment) and two-phase regions are indicated in the base edge of the triangle. By additions of Si (immiscible in the solid state in the other two elements) two- and three-phase fields are formed. ( ) = three-phase region. In the two-phase region on the left examples of tie-lines are presented.

Figure 2.29. Isothermal sections of ternary phase diagrams (a) Al-Er-Mg system at 400°C, Saccone et al. (2002) and, (b) Al-Cu-Ti system at 540°C from Villars et al. (1995). A number of single-phase regions (dark grey) may be noticed, both extending from binary compounds and as ternary intermediate phases (r) in the Al-Er-Mg system and the four phases Tj t2 t3 and t4 in the Al-Cu-Ti system. The three-phase fields are marked by an asterisk, in the Al-Er-Mg system a few tie-lines are indicated in the two-phase fields.

Figure 2.30. Typical one-component systems (a) Room temperature, room pressure region of the well-known PIT phase diagram of water (notice the logarithmic scale of pressure), (b) P-T phase diagram of elemental Fe. The fields of existence of the different forms of Fe are shown a (body-centred cubic Fe), (face-centred cubic), 6 (body-centred cubic, high-temperature form isostructural with a), e (hexagonal close packed), L (liquid Fe). The gas phase field, owing to the pressure scale and the not very high temperatures considered, should be represented by a very narrow region close to the T axis.

Figure 2.33. Ni-Co-O phase diagram (isothermal section at 1600 K). log p02 (oxygen partial pressure) is plotted against the molar fraction in the metallic alloy. The metallic alloy, (Ni, Co) solid solution is stable in (1) and the mixed oxide (Ni, Co)0 solid solution in (3). In the intermediate region (2) we have coexistence of alloy and oxide. For the value of the partial oxygen pressure corresponding to y, within the two-phase field, we will have the alloy of composition xt in equilibrium with an oxide containing the two metals in the ratio x2-...

More complex situations were shown in Figs. 2.26 and 2.27, where some typical examples of isobarothermal sections of ternary alloy phase diagrams were presented. In the case of ternary systems, several binary and ternary stoichiometric (Fig. 2.28) phases and/or different types of variable composition phases (Fig. 2.29) may be found. We may differentiate between these phases by using terms such as point compounds (or point phases, that is, phases represented in the composition triangle, or more generally in the composition simplex by points), Tine phases , field phases , etc. 

In the diagrams obtained in this way, the composition limits of each phase have been connected from one binary system to the next. A number of single-phase fields (shaded regions) have thus been obtained. These correspond to well-defined structure types, which are listed in the figure. 

Figure 4.44. Isothermal multi-diagram, at the reduced temperature Tred (see text), of the Mo-Me and Mo Me, Mc2 systems formed by Mo with a number of transition metals ( 7 ) of the 6th row. Single-phase fields are represented by the hatched regions. For the phase symbols see Fig.4.41.

Figure 5.26. Iron binary alloys. Examples of the effects produced by the addition of different metals on the stability of the yFe (cF4-Cu type) field are shown. In the Fe-Ge and Fe-Cr systems the 7 field forms a closed loop surrounded by the a-j two-phase field and, around it, by the a field. Notice in the Fe-Cr diagram a minimum in the a-7 transformation temperature. The iron-rich region of the Fe-Ru diagram shows a different behaviour the 7 field is bounded by several, mutually intersecting, two (and three) phase equilibria. The Fe-Ir alloys are characterized, in certain temperature ranges, by the formation of a continuous fee solid solution between Ir and yFe. Compare with Fig. 5.27 where an indication is given of the effects produced by the different elements of the Periodic Table on the stability and extension of the yFe field.

Figure 3.10(a) shows one of the simplest forms of phase diagram, a system with a miscibility gap. It is characterised by a high-temperature, single-phase field of a... 

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