Single phase stability

Notice, that the critical point (Vr = 1, Pr = 1) is the upper limit of metastability (i.e., Pr < as the limit of single phase stability. 

Identify the limits of single-phase stability on the Gibbs energy versus mole fraction curve. 

In systems where the value of the X parameter is positive but the mixture is still in the range of single phase stability, defined by... 

Pure metallic cobalt has a soHd-state transition from cph (lower temperatures) to fee (higher temperatures) at approximately 417°C. However, when certain elements such as Ni, Mn, or Ti are added, the fee phase is stabilized. On the other hand, adding Cr, Mo, Si, or W stabilizes the cph phase. Upon fcc-phase stabilization, the energy of crystallographic stacking faults, ie, single-unit cph inclusions that impede mechanical sHp within the fee matrix, is high. 

The thermodynamic phase stability diagrams appear to be preferred by corrosion scientists and technologists for the evaluation of gas-metal systems where the chemical composition of the gaseous phase consisting of a single gas or mixture of gases has a critical influence on the formation of surface reaction products which, in turn, may either stifle or accelerate the rate of corrosion. Also, they are used to analyse or predict the reason for the sequence of formation of the phases in a multi-layered surface reaction product on a metal or alloy. 

Case II. Raising the pressure increases the solubility of the gas such that the solubility curve intersects a part of the coexistence curve. The stability criteria do not allow the existence of a single phase inside the coexistence curve therefore, a liquid-liquid region and a vapor-liquid-liquid region are formed, as illustrated in Fig. 28b. 

It is sometimes convenient to fix the pressure and decrease the degrees of freedom by one in dealing with condensed phases such as substances with low vapour pressure. The Gibbs phase rule for a ternary system at isobaric conditions is Ph + F = C + 1=4, and there are four phases present in an invariant equilibrium, three in univariant equilibria and two in divariant phase fields. Finally, three dimensions are needed to describe the stability field for the single phases e.g. temperature and two compositional terms. It is most convenient to measure composition in terms of mole fractions also for ternary systems. The sum of the mole fractions is unity thus, in a ternary system A-B-C ... 

The polyoxoanion-stabilized Rh(0) nanoclusters were investigated in anisole hydrogenation [6,95]. The catalytic reactions were carried out in a single phase... 

The final measure of crystallization effects is assessed by appropriate rigorous stability data (for example, 6 months accelerated stability at 40°C and 75% RH). This may seem excessive, but measuring the degree of crystallinity is inherently difficult because of low analytical sensitivity (for example, of amorphous components below 5% w/w), and pure single-phase standards are difficult to prepare and subsequently measure. 

C) within the analyzer. This option is mainly applicable to single-phase hqnid eqnilibrinm process streams - and is the de facto standard for rehnery hydrocarbon apphcations where the eqnilibrinm (non time-dependant) sample condition is met and where the qnantitative stability and reprodncibihty aspects of the application demand the highest level of samphng control (Fignre 5.23). 

Basically, whenever isotopic exchanges occur between different phases (i.e., heterogeneous equilibria), isotopic fractionations are more appropriately described in terms of differential reaction rates. Simple diffusion laws are nevertheless appropriate in discussions of compositional gradients within a single phase— induced, for instance, by vacancy migration mechanisms, such as those treated in section 4.10—or whenever the isotopic exchange process does not affect the extrinsic stability of the phase. 

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