Single-phase field

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. 

DEF. When the constitution point lies in a single-phase region, the alloy consists of a single, homogeneous, phase. Its composition must (obviously) be that of the alloy. The phase composition and the alloy composition coincide in single-phase fields. 

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. 

The copper-zinc system shown in Fig. A1.38 has no fewer than five peritectic reactions. Locate them and ring the peritectic points. (Remember that when a single-phase field closes above at a point, the point is a peritectic point.)... 

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. 

The composition/temperature field is subdivided into three regions, as for instance in Fig. 2.1(a), at low temperature there is a single phase field (S) where all the temperature and composition values are collected for which only one solid phase is stable (a continuous solid solution field between Mo and V). 

In a similar way, another single-phase field (L) exists at high temperature the two components show, indeed, a mutual complete solubility in the liquid state also. 

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. 

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 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... 

Identification of unknown crystal structures and determination of phase fields by X-rays can be problematical if the characteristic patterns of the various phases are quite similar, for example in some b.c.c. A2-based ordered phases in noble-metal-based alloys. However, in many cases the characteristic patterns of the phases can be quite different and, even if the exact structure is not known, phase fields can still be well established. Exact determination of phase boundaries is possible using lattice-parameter determination and this is a well-established method for identifying solvus lines for terminal solid solutions. The technique simply requires that the lattice parameter of the phase is measured as a function of composition across the phase boimdary. The lattice parameter varies across the single-phase field but in the two-phase field becomes constant. Figure 4.12 shows such a phase-boundary determination for the HfC(i i) phase where results at various temperatures were used to define the phase boundary as a fimction of temperature (Rudy 1969). As can be seen, the position of is defined exactly and the method can be used to identify phase fields across the whole composition range. 

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).

The single-phase fields of a-zirconium, the y2 uranium-zirconium solid solution, and 8-zirconium hydride have well-defined phase boundaries. However, the exact limits of the single-phase fields of the y1 uranium-zirconium solid solution, a-uranium, and -uranium are not as certain. 

The possible types of invariant reactions were illustrated in Table 11.2. These reactions, or their absence, determine the positions and shapes of the areas, known as phase fields, in a phase diagram. Three-phase equilibrium is only allowed at a single point (an invariant point) in a binary system that is, three-phase fields are not allowed. Binary systems however, may contain both single-phase and two-phase fields, and when a two-phase field does exist, it must be located between two single-phase fields. 

Based on data by [1927Kas], [1988Ray] calculated the hquidus and solidus surfaces. The later is characterized by the wide single phase fields (6Fe) and (aCo,"yFe,Ni) and by a respective narrow two-phase region. Tentative hquidus surface shown in Fig. 1 is drawn after [1988Ray] but adjusted to the accepted binary systems. 

Consider the case of single-phase fields on the phase diagram (e.g., a, ji, and liquid regions). Because only one phase is present, P = 1 and... 

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