Unary systems

Figure 3.11 Phase diagram for a one-component system (unary phase diagram).

Outlines the three important systems unary, binary, and ternary... 

Further, according to Ricci, although a single substance must behave as a one-component system, unary behaviour does not guarantee that a material is a single substance (9, 165). Finally, the phase rule approach doesn t always make a clear-cut distinction between unary and binary systems or between compound and solution (125). 

In the case of a unary or one-component system, only temperature and pressure may be varied, so the coordinates of unary phase diagrams are pressure and temperature. In a typical unary diagram, as shown in Figure 3.11, the temperature is chosen as the horizontal axis by convention, although in binary diagrams temperature is chosen as the vertical axis. However, for a one-component system, the phase rule becomes F=l-P+2 = 3-P. This means that the maximum number of phases in equilibrium is three when F equals zero. This is illustrated in Figure 3.11 which has three areas, i.e., solid, liquid, and vapour In any... 

Notice that the structures presented in this paragraph are unary structures, that is one species only is present in all its atomic positions. In the prototypes listed (and in the chemically unary isostructural substances) this species is represented by a pure element. In a number of cases, however, more than one atomic species may be equally distributed in the various atomic positions. If each atomic site has the same probability of being occupied in a certain percentage by atoms X and Y and all the sites are compositionally equivalent, the unary prototype is still a valid structural reference. In this case, from a chemical point of view, the structure will correspond to a two-component phase. Notice that there can be many binary (or more complex) solid solution phases having for instance the Cu-type or the W-type structures. Such phases are formed in several metallic alloy systems either as terminal or intermediate phases. 

A phase diagram is often considered as something which can only be measured directly. For example, if the solubility limit of a phase needs to be known, some physical method such as microscopy would be used to observe the formation of the second phase. However, it can also be argued that if the thermodynamic properties of a system could be properly measured this would also define the solubility limit of the phase. The previous sections have discussed in detail unary, single-phase systems and the quantities which are inherent in that sjrstem, such as enthalpy, activity, entropy, etc. This section will deal with what happens when there are various equilibria between different phases and includes a preliminary description of phase-diagram calculations. 

The unary phase diagram is seldom used in solid state syntheses. However, the unary diagram forms the basis for the phase diagrams of multicomponent systems. Since there are no composition variables, the only externally controllable variables in a unary system are simply the temperature and pressure. For this... 

Because there is an added term, the composition, binary systems are inherently more complex than unary systems. In order to completely represent the phase diagram of a binary system a three dimensional pressure-temperature-composition (P-T-x) diagram can be constructed. However, it is a more common... 

For the unary diagram, we only had one component, so that composition was fixed. For the binary diagram, we have three intensive variables (temperature, pressure, and composition), so to make an x-y diagram, we must fix one of the variables. Pressure is normally selected as the fixed variable. Moreover, pressure is typically fixed at 1 atm. This allows us to plot the most commonly manipulated variables in a binary component system temperature and composition. 

Much of what we need to know abont the thermodynamics of composites has been described in the previous sections. For example, if the composite matrix is composed of a metal, ceramic, or polymer, its phase stability behavior will be dictated by the free energy considerations of the preceding sections. Unary, binary, ternary, and even higher-order phase diagrams can be employed as appropriate to describe the phase behavior of both the reinforcement or matrix component of the composite system. At this level of discussion on composites, there is really only one topic that needs some further elaboration a thermodynamic description of the interphase. As we did back in Chapter 1, we will reserve the term interphase for a phase consisting of three-dimensional structure (e.g., with a characteristic thickness) and will use the term interface for a two-dimensional surface. Once this topic has been addressed, we will briefly describe how composite phase diagrams differ from those of the metal, ceramic, and polymer constituents that we have studied so far. 

Unlike the unary, binary, and ternary phase diagrams of the previous sections, there are no standardized guidelines for presenting phase information in composite systems. This... 

Stability of Liquid/Solid Interface during Solidification of a Unary System... 

In phase rule systems are categorized according to the number of components unary systems with only one component, binary systems with two components and (in this book) finally ternary systems with three components. The behaviour of the components in a system is determined by variables pressure, temperature and composition. 

Three kinds of systems can be represented in the composition triangle 1. The vertices on the triangle represent the unary system with the pure components. 

Phase changes are effected by three externally controllable variables. These are pressure, temperature and composition. In a one-component system, or unary system, however, the composition does not vary, but must always be unity. Therefore there are only two variables which can vary pressure and temperature. Every possible combination of temperature and pressure can be readily represented by points on a two-dimensional diagram. 

This is not a true unary system, but a binary system of A and the inert gas. In this case, the vapor pressure of A will be adjusted so that the gaseous A at 0.8 atm exists in equilibrium with the liquid A at 7j. The partial pressure of the inert gas will be 0.2 atm to maintain the total pressure of 1 atm. 

Figure 2.1. Generalized phase relations in the unary system CaCC>3. "A" -aragonite "I" through "V - calcite polymorphs with metastable fields indicated by (). Dash-dot line at 800°C represents transition encountered on cooling runs solid line at lower T represents transition encountered on heating runs. (After Carlson, 1980.)...

The phase rule(s) can be used to distinguish different types of equilibria based on the number of degrees of freedom. For example, in a unary system, an invariant equilibrium (/ = 0) exists between the liquid, solid, and vapor phases at the triple point, where there can be no changes to temperature or pressure without reducing the number of phases in equilibrium. Because / must equal zero or a positive integer, the condensed phase rule (/ = c — p + 1) limits the possible number of phases that can coexist in equilibrium within one-component condensed systems to one or two, which means that other than melting, only allotropic phase transformations are possible. Similarly, in two-component condensed systems, the condensed phase rule restricts the maximum number of phases that can coexist to three, which also corresponds to an invariant equilibrium. However, several invariant reactions are possible, each of which maintains the number of equilibrium phases at three and keeps / equal to zero (L represents a liquid and S, a solid) ... 

Interactions in the system under consideration is convenient to split up into two terms one-body (or unary) and pair (or binary) potential. The former describes the ion-wall interaction, and the latter represents interactions between ions in electrolyte solution, and between ions and images. 

Once the unary and binary potentials, which describe interactions in the wall-ion system, are specified, distribution of ions near the wall, and between slabs can be calculated. We will further employ an approximation based upon the distribution function formalism, but first the definitions of equilibrium ion densities and corresponding distribution functions have to be introduced. 

Unary phase diagrams are two-dimensional graphs that display the phases of singlecomponent systems (e.g. elements) as a function of both temperature (abscissa) and pressure (ordinate). Since there is only one component, it is not necessary to specify composition. Figure 11.2 shows the phase diagram for sulfur, which exists in two allotropes at 1 atm of pressure, rhombic (T < 368 K) and monoclinic T > 368 K). 

It is possible in many cases to predict highly accurate phase equihbria in multi-component systems by extrapolation. Experience has shown extrapolation of assessed (n — 1) data into an nth order system works well for n < 4, at least with metallurgical systems. Thus, the assessment of unary and binary systems is especially critical in the CALPHAD method. A thermodynamic assessment involves the optimization of aU the parameters in the thermodynamic description of a system, so that it reproduces the most accurate experimental phase diagram available. Even with experimental determinations of phase diagrams, one has to sample compositions at sufficiently small intervals to ensure accurate reflection of the phase boundaries. 

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