Phase transition binary systems

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. 

We will be looking at first-order phase transitions in a mixture so that the Clapeyron equation, as well as the Gibbs phase rule, apply. We will describe mostly binary systems so that C = 2 and the phase rule becomes... 

An alloy is said to be of Type II if neither the AC nor the BC component has the structure a as its stable crystal form at the temperature range T]. Instead, another phase (P) is stable at T, whereas the a-phase does exist in the phase diagram of the constituents at some different temperature range. It then appears that the alloy environment stabilizes the high-temperature phase of the constituent binary systems. Type II alloys exhibit a a P phase transition at some critical composition Xc, which generally depends on the preparation conditions and temperature. Correspondingly, the alloy properties (e.g., lattice constant, band gaps) often show a derivative discontinuity at Xc. 

L. Kaufman, Coupled phase diagrams and thermochemical data for transition metal binary systems-VI, CALPHAD, 3 (1979) 45-76. 

Line compounds. These are phases where sublattice occupation is restricted by particular combinations of atomic size, electronegativity, etc., and there is a well-defined stoichiometry with respect to the components. Many examples occur in transition metal borides and silicides, III-V compounds and a number of carbides. Although such phases are considered to be stoichiometric in the relevant binary systems, they can have partial or complete solubility of other components with preferential substitution for one of the binary elements. This can be demonstrated for the case of a compound such as the orthorhombic Cr2B-type boride which exists in a number or refractory metal-boride phase diagrams. Mixing then occurs by substitution on the metal sublattice. 

A further method of producing amorphous phases is by a strain-driven solid-state reaction (Blatter and von Allmen 1985, 1988, Blatter et al. 1987, Gfeller et al. 1988). It appears that solid solutions of some transition metal-(Ti,Nb) binary systems, which are only stable at high temperatures, can be made amorphous. This is done by first quenching an alloy to retain the high-temperature solid solution. The alloy is then annealed at low temperatures where the amorphous phase appears transiently during the decomposition of the metastable crystalline phase. The effect was explained by the stabilisation of the liquid phase due to the liquid—>glass... 

The guest cations hitherto examined cover broadly uni- to trivalent and inorganic to organic ions that include alkali, alkaline earth, heavy and transition metal ions, as well as (ar)alkyl ammonium and diazonium ions. As to the complex stoichiometry between cation and ligand, both 1 1 stoichiometric and 1 2 sandwich complexes are analyzed. The solvent systems employed also vary widely from protic and aprotic homogeneous phase to binary-phase solvent extraction. 

In binary systems of a light gas and members of the n-alkane homologuous series in almost all cases type II phase behaviour is found for the lower members of the n-alkane series. With increasing carbon number type IV phase behaviour is found followed by type HI phase behaviour at high carbon numbers. Systems of CO2 + n-alkanes show type II phase behaviour for n-alkane carbon numbers 12, type IV phase behaviour for =13 and type HI phase behaviour for n S14 [11, 12]. This transition from type II to type HI phase behaviour via type IV phase behaviour seems to be the rule, allthough in most binary families type IV phase behaviour is only found at broken values of n in so-called quasi-binary systems [13, 14]. 

For binary systems, a variety of phase behaviours possible when partial immiscibility of liquids and gases, and the occurrence of solid phases is considered. Phase-behaviours are classified into six basic types, and transitions between them are possible. 

Chapters 6 and 7 dealt with solid state reactions in which the product separates the reactants spatially. For binary (or quasi-binary) systems, reactive growth is the only mode possible for an isothermal heterogeneous solid state reaction if local equilibrium prevails and phase transitions are disregarded. In ternary (and higher) systems, another reactive growth mode can occur. This is the internal reaction mode. The reaction product does not form at the contacting surfaces of the two reactants as discussed in Chapters 6 and 7, but instead forms within the interior of one of the reactants or within a solvent crystal. 

Let us regard a binary A-B system that has been quenched sufficiently fast from the / -phase field into the two phase region (a + / ) (see, for example, Fig. 6-2). If the cooling did not change the state of order by activated atomic jumps, the crystal is now supersaturated with respect to component B. When further diffusional jumping is frozen, some crystals then undergo a diffusionless first-order phase transition, / ->/ , into a different crystal structure. This is called a martensitic transformation and the product of the transformation is martensite. 

There is a large body of experimental work on ternary systems of the type salt + water + organic cosolvent. In many cases the binary water + organic solvent subsystems show reentrant phase transitions, which means that there is more than one critical point. Well-known examples are closed miscibility loops that possess both a LCST and a UCST. Addition of salts may lead to an expansion or shrinking of these loops, or may even generate a loop in a completely miscible binary mixture. By judicious choice of the salt concentration, one can then achieve very special critical states, where two or even more critical points coincide [90, 160,161]. This leads to very peculiar critical behavior—for example, a doubling of the critical exponent y. We shall not discuss these aspects here in detail, but refer to a comprehensive review of reentrant phase transitions [90], We note, however, that for reentrant phase transitions one has to redefine the reduced temperature T, because near a given critical point the system s behavior is also affected by the existence of the second critical point. An improper treatment of these issues will obscure results on criticality. 

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