Equilibrium constitution and phase diagrams

Whenever you have to report on the structure of an alloy - because it is a possible design choice, or because it has mysteriously failed in service - the first thing you should do is reach for its phase diagram. It tells you what, at equilibrium, the constitution of the alloy should be. The real constitution may not be the equilibrium one, but the equilibrium constitution gives a base line from which other non-equilibrium constitutions can be inferred. 

An alloy is a metal made by taking a pure metal and adding other elements (the alloying elements ) to it. Examples are brass (Cu -t- Zn) and monel (M -i- Cu). 

The components of an alloy are the elements which make it up. In brass, the components are copper and zinc. In monel they are nickel and copper. The components are given the atomic symbols, e.g. Cu, Zn or Ni, Cu. 

An alloy system is all the alloys you can make with a given set of components the Cu-Zn system describes all the alloys you can make from copper and zinc. A binary alloy has two components a ternary alloy has three. 

A phase is a region of material that has uniform physical and chemical properties. Phases are often given Greek symbols, like a or fi. But when a phase consists of a solid solution of an alloying element in a host metal, a clearer symbol can be used. As an example, the phases in the lead-tin system may be symbolised as (Pb) - for the solution of tin in lead, and (Sn) - for the solution of lead in tin. 

---

DEF. An equilibrium-constitution diagram or equilibrium diagram for short (or, shorter still, phase diagram), is a diagram with T and Xg (or Wg) as axes. It shows the results of experiments which measure the equilibrium constitution at each T and Xg (or Wg). 

The state variables define a point on the diagram the "constitution point". If this point is given, then the equilibrium number of phases can be read off. So, too, can their composition and the quantity of each phase - but that comes later. So the diagram tells you the entire constitution of any given alloy, at equilibrium. Refer back to the definition of eonstitution (p. 311) and check that this is so. 

The equilibrium constitution of a one-component system is fixed by the variables p and T and so the equilibrium phases can be shown on a diagram with p and T axes. The one shown in Fig. A1.6 has only one solid phase. Some, like ice, or iron, have several. 

The phase diagram describes the equilibrium constitution of the alloy - the one given by very slow cooling. In the last example all the liquid should have solidified at the point marked 2 on Fig. A 1.35, when all the solid has moved to the composition Xp = 80% and the temperature is 255°C. Rapid cooling prevents this the solid has not had time to move to a composition Xpp = 80%. Instead, it has an average composition about half-way between that of the first solid to appear (Xpp = 90%) and the last (Xpp = 80%), that is, an average composition of about Xpp = 85%. This "rapid cooling" solidus lies to... 

The liquid line and vapor line together constitute a binary (vapor + liquid) phase diagram, in which the equilibrium (vapor) pressure is expressed as a function of mole fraction at constant temperature. At pressures less than the vapor (lower) curve, the mixture is all vapor. Two degrees of freedom are present in that region so that p and y2 can be varied independently. At pressures above the liquid (upper) curve, the mixture is all liquid. Again, two degrees of freedom are present so that p and. v can be varied independently/... 

Gels are obtained for concentrations shown in the temperature-concentration phase diagram (Figure 1). Electron spin resonance (ESR) shows (10) that for a given temperature only a fraction (p) of the initial steroid concentration is transferred from the solution to the gel network. The picture of this gel is thus of a supersaturation gel there is a dynamic equilibrium between free molecules in solution and aggregated steroid molecules included in the long objects which constitute the gel network. The free steroid molecules concentration at a temperature where the gel state is stable is (1-p), while C p is the steroid concentration within the solid-iike gel aggregates. 

Phase diagrams arc condensed presentations of a large amount of information. They provide quantitative information on the phases present under given conditions of alloy composition and temperature and, to the experienced metallurgist, a guide to the distribution of the phases in the microstructure of the alloy. They also dictate what alterations in phase constitution will occur w ith changing conditions, whether these be alteration of alloy composition, temperature, pressure or atmosphere in equilibrium with the material. 

Two components present in a single phase constitute a tervariant system, characterized by three degrees of freedom. The equilibrium condition between two phases is a bivariant system, while three phases in equilibrium would be invariant. For a system of two components to be invariant, there must be four phases in equilibrium. From the phase rule, one immediately concludes that there cannot be more than four phases in equilibrium under any set of environmental conditions. The graphical expression of phase relationships on a two-dimensional surface will require the a priori specification of a number of conditions. Fortunately, for the two component systems of greatest interest to pharmaceutical scientists (hydrates and their anhydrates), the normal studies are conducted at atmospheric pressure, which immediately fixes one of the variables. For phase equilibria, this allows the construction of the usual planar diagrams. 

ZAF Zafarani-Moatlar, M.T., Hamzehzadeh, S., and Hosseinzadeh, S., Phase diagrams for liquid-hquid equilibrium of ternary poly(ethylene glycol) + disodium tartrate aqueous system and vapor-liquid equilibrium of constituting binary aqueous systerrrs at r = (298.15, 308.15, and 318.15) K. Experiment and correlation. Fluid Phase Equil, 268, 142, 2008. 

Koe] Koster, W., Haehl, W.-D., The Real Constitution Diagram and the Obtention of Equilibrium in the Ternary System Iron-Cobalt-Niekel (in German), Arch. Eisenhuettenwes., 40(7), 569-574 (1969) (Phase Diagram, Phase Relations, Experimantal, 13)... 

---