Nonequilibrium phase diagram

This nonequilibrium phase diagram is in the form of a cusp in (m,t,h) space (see Ref. 45 for definitions). It is a perfect analogue of a ferromagnetic phase transition if we interpret m,t,h as magnetization, temperature (minus its critical value), and applied magnetic... 

Matsumoto S., Sato Y., Tsutsumi M., Setaka N., Growth of diamond particles from methane-hydrogen gas. J. Mater. Sci. 17, (1982) pp.3106-3112. Nonequilibrium phase diagrams of ternary amorphous alloys (Springer, Heidelberg, 1997) 295 pages. 

Fig. 9 Two component nonequilibrium phase diagram for P3HT PCBM measured using differential scanning calorimetry. Reprinted (adapted) with permission from [121]. Copyright 2008 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim...

Phase diagrams can be used to predict the reactions between refractories and various soHd, Hquid, and gaseous reactants. These diagrams are derived from phase equiHbria of relatively simple pure compounds. Real systems, however, are highly complex and may contain a large number of minor impurities that significantly affect equiHbria. Moreover, equiHbrium between the reacting phases in real refractory systems may not be reached in actual service conditions. In fact, the successful performance of a refractory may rely on the existence of nonequilibrium conditions, eg, environment (15—19). 

For sodium palmitate, 5-phase is the thermodynamically preferred, or equiUbrium state, at room temperature and up to - 60° C P-phase contains a higher level of hydration and forms at higher temperatures and CO-phase is an anhydrous crystal that forms at temperatures comparable to P-phase. Most soap in the soHd state exists in one or a combination of these three phases. The phase diagram refers to equiUbrium states. In practice, the drying routes and other mechanical manipulation utilized in the formation of soHd soap can result in the formation of nonequilibrium phase stmcture. This point is important when dealing with the manufacturing of soap bars and their performance. 

Plot of the nonequilibrium solidus for an alloy of 1% B, superimposed on the phase diagram. 

As a consequence of these experiments one has to realize that care is required in situations where equilibrium phase diagrams are applied to nonequilibrium situations [113], Due to the coupling of heat and mass transport, the local... 

The coupling of the order parameter to the temperature gradient also leads to unexpected excursions along the concentration axis in the case of off-critical mixtures. As a consequence, equilibrium phase diagrams lose their usual meaning in thermal nonequilibrium situations, and even an off-critical blend with a temperature above the binodal can be quenched into phase separation by local heating with a laser beam. 

Figure 4.6 (a) Portion of a binary-phase diagram illustrating equilibrium solidification (b) nonequilibrium (rapid) solidification, which results in a chemical composition gradient in the crystals, a condition known as coring. (After Lalena and Cleary, 2005. Copyright John Wiley Sons, Inc. Reproduced with permission.)... 

They can be used to predict crystalline phase volume and which crystalline form (polymorph, hydrate, etc.) is expected in a food that has reached phase equilibrium. However, in foods that never attain equilibrium, the phase diagram by itself is of limited value. In recent years, certain aspects of nonequilibrium have been characterized using the state diagram approach (Slade and Levine 1991). 

Figure 2. Nonequilibrium (stationary) phase diagrams for C-H system with the existence of superequilibrium concentration atomic hydrogen (O, CJ and A are experimental data reported by Matsumoto [6], Sato[10], and Southworth [11] etc.).

Wang J.-T., Phase diagrams of stationary nonequilibrium states ---------... 

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