Binary systems with three phases

A binary system with three phases has only one degree of freedom and eannot be represented by an area on a two-dimensional phase diagram. Instead, there is a horizontal boundary line between areas, with a speeial point along the line at the junction of several areas. The compositions of the three phases are given by the positions of this point and the points at the two ends of the line. The position of the system point on this line does not uniquely specify the relative amounts in the three phases. 

To understand the reculiarities of multiple layer formation, it suffices to consider the A-B binary system with three chemical compounds ApBq, ArBs and AiBn on the equilibrium phase diagram (Fig. 3.1). The scheme of analysis of the process of their occurrence at the A-B interface is analogous to that of two compound layers (see Chapter 2). First of all, the equations of partial chemical reactions taking place at phase interfaces must be written. These are as follows. 

The most significant advantage of these more quantitative methods is that, in a binary system, only one sample is needed to determine the position of both phase boimdaries in a two-phase field. Further, if the alloy lies in the two-phase field over a wide range of temperatures, it is feasible that only one alloy need be used to fix the phase boundaries over this range of temperature. In a ternary system the analogous position is found with three-phase fields and, as these also define the limiting tie-lines of the three sets of two-phase fields, substantial information can be gained from the accurate determination of only one alloy. More recently transmission electron microscopy (TEM) has been used which is particularly valuable when microstructures are very fine as, for example, found in yTiAl alloys (Chen et al. 1994). 

In the following, we will often be concerned with ternary systems. Heterogeneous binary systems have two phases in equilibrium and are nonvariant (at given P and T). When two ternary phases are in contact, the system still has one (thermodynamic) degree of freedom. A ternary phase has three independent transport coefficients iee., Ln,L22, and /. ). 

By Gibbs Phase Rule illustrated in this chapter s introduction, a second intensive variable is needed (in addition to either temperature or pressure) to specify the three-phase binary system with an inhibitor (F = 3 — 3 + 2). Typically, the concentration of the inhibitor in the free water phase is specified as the second intensive variable. Substances that have considerable solubility in the aqueous phase, such as alcohols, glycols, and salts, normally act as inhibitors to hydrate formation. The colligative mechanism of formation inhibition is aided by increased competition for water molecules by the dissolved inhibitor molecule or ion through hydrogen bonding for alcohols or glycols, or via Coulombic forces (for salt ions). 

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. 

If a binary system is multiphase, then the layer of the same chemical compound can obviously grow in different reaction couples consisting of elementary substances A and B and their other compounds. To show how its growth rate depends on the composition of initial phases, it suffices to consider a system with three compounds ApBq, ArBs and AtBn (see Fig. 3.1). 

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. 

Whereas in Fig. 17a the binary system has two phases, three phases are present in Fig. 17b and in accordance with the phase rule, the system will be monovariant. 

Figure 4J29. Binary phase diagrams of intermetallics in the Ni/Ti/Al system (a) The phase diagram of the Al/Ni system, (b) The phase diagram of the Ti/Al system, (c) The phase diagram of the Ti/Ni system with three intermetallic compounds. From J. H. Westbrook and R. L. Fleischer (eds.). Intermetallic Compounds. Copyright John Wiley Sons (1995). Reproduced with permission.

L Earlier Observations on Unexpected Fluid Phase Behavior Patton et al. [4] found unexpected fluid multiphase behavior for the system CO2 + 1-decanol + tetradecane. The two binary border systems CO2 + 1-decanol and CO2 + tetradecane both show type-III fluid phase behavior, see [41] and [10,43], respectively, in the classification of Scott and Van Konynenburg [14,30] (section 2), with its characteristic UCEP For the ternary system, the three-phase surface Ug is... 

Ternary systems with binary subsystems of types 1 and 2. If the binary subsystems with a volatile component belong to type la and have a single (uninterrupted) three-phase solubility curves for each solid phase, as in the case of H2O -NaCl - KCl system, the three-phase solubility surfaces of ternary system are also smooth and uninterrupted. However, if one of the binary subsystems belongs to type 2 with the... 

Quatemized P4VP core PS shell/poly(methacrylic acid) (PMA) core/PS shell type microsphere binary blend systems have a common PS sequence in the shell. Material with three-phase separated microdomains, such as both dispersed P4VP (positively charged region) and PMA (negatively charged region) spheres in a PS matrix, was obtained in this blend film [51]. 

W. G. Moffatt, The Handbook of Binary Phase Diagrams, General Electric Co., Schenectady, NY, 1977. Lxxiseleaf system in three volumes with regular updating. Contains excellent index to material contained in refs. 1-3. 

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