One-component unary systems

In a one-component, or unary, system, only one chemical component is required to describe the phase relationships, for example, iron (Fe), water (H2O) or methane (CH4). There are many one-component systems, including all of the pure elements and compounds. The phases that can exist in a one-component system are limited to vapour, liquid and solid. Phase diagrams for one-component systems are specified in terms of two variables, temperature, normally specified in degrees centigrade, 

Understanding solids the science cf materials. Richard J. D. Tilley 2004 John Wiley Sons, Ltd ISBNs 0 470 85275 5 (Hbk) 0 470 85276 3 (Pbk) 

On the phase boundaries, two phases coexist indefinitely, ice and water, water and steam, or ice and steam. If a variable is changed, the two-phase equilibrium is generally lost. In order to preserve a two-phase equilibrium, one variable, either pressure or temperature, can be changed at will, but the other must also change, by exactly the amount specified in the phase diagram, to maintain two phases in coexistence and so to return to the phase boundary. 

The critical point of water, at 374 °C and 218 atm, is the point at which water and steam become identical. The triple point is found at 0.01 C and 0.006 atm (611 Pa). At this point and only at this 

Glasses, which fonn in systems in which nucleation is difficult or prevented, are called supercooled liquids, because they reach the solid state before crystallisation. 

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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. 

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) ... 

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... 

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

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. 

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. 

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). 

In the systems hitherto discussed (except sulphur and phosphorus), the components behaved, or were regarded as behaving, as strictly unary substances that is, the molecules of each component in all the phases in which it occurred were identical both physically and chemically. Each component formed only one molecular species, and the number of molecular species was, therefore, equal to the number of the components. The systems were purely unary (one-component) or purely binary (two-component). 

A phase diagram is a map that indicates the areas of stability of the various phases as a function of external conditions (temperature and pressure). Pure materials, such as mercury, helium, water, and methyl alcohol are considered one-component systems and they have unary phase diagrams. The equilibrium phases in two-component systems are presented in binary phase diagrams. Because many important materials consist of three, four, and more components, many attempts have been made to deduce their multicomponent phase diagrams. However, the vast majority of systems with three or more components are very complex, and no overall maps of the phase relationships have been worked out. 

The two variables that can affect the phase equilibria in a one-component, or unary, system are temperature and pressure. The phase diagram for such a system is therefore a temperature-pressure equilibrium diagram. 

Perhaps the simplest and easiest type of phase diagram to understand is that for a one-component system, in which composition is held constant (i.e., the phase diagram is for a pure substance) this means that pressure and temperature are the variables. This one-component phase diagram (or unary phase diagram, sometimes also called a pressure-temperature [or P-T diagram) is represented as a two-dimensional plot of... 

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). 

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. 

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. 

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. 

The subject matter is introduced by a short exposition of the Gibbs phase rule in Sec. 8.2. Unary component systems are discussed in Sec. 8.3. Binary and ternary systems are addressed in Secs. 8.4 and 8.5, respectively. Sec. 8.6 makes the connection between free energy, temperature, and composition, on one hand, and phase diagrams, on the other. 

When we consider the phase relations in systems having two components instead of one, we add one dimension to our diagrams. That is, in unary diagrams all phases have the same composition, and so we don t need an axis showing compositions - we can use both dimensions available on a sheet of paper for physical parameters, and we choose T and P. With two... 

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