Liquid-solid phase transformations

Let us first consider the liquid-solid phase transformation. At the melting point (or more appropriately, fusion point for a solidification process), liquid and solid are in equilibrium with each other. At equilibrium, we know that the free energy change for the liquid-solid transition must be zero. We can modify Eq. (2.11) for this situation... 

Solidification. When the ingot or casting solidifies, there are three main possible microstructures that form (see Figure 7.5). We will describe here only the final structures the thermodynamics of the liquid-solid phase transformation have been described previously in Chapter 2. The outside layer of the ingot is called the chill zone and consists of a thin layer of equiaxed crystals with random orientation. 

Thermoporometry is a thermal method which is based on the thermal analysis of the liquid-solid phase transformation of a capillary condensate held inside the porous body under study. The technique was developed by Brun et... 

The highest internal order, that of a single crystal, is obtained when the tip temperature is above the liquidus of the substrate, yields a liquid tip, and proceeds by a vapor-liquid-solid phase transformation. The lowest internal order, that of an amorphous structure, is obtained when the tip temperature is below the glass transition temperature of the substrate. A solid tip yields a vapor solid phase transformation. Between the liquidus and the glass transition temperature of a substrate, intermediate internal order is that of a polycrystalline fiber. In this case, whisker growth is either governed by a VLS and/or by a VS phase transformation. 

The fate of metal catalyst particles during the growth of nanotubes parallels that observed for the metal catalyst particles during the growth of single crystal whiskers. This commonalty suggests that vapor-liquid-solid phase transformations are involved in the majority of cases. 

Solid-solid transformations tend to have smaller AGy than liquid-solid phase transformations, which also leads to an increase in AG. ... 

Because of these factors, solid-solid phase transformations rarely reaeh equilibrium. The retention of metastable phases is nearly guaranteed. In faet, the retention of metastable phases is purposely exploited in many material proeesses, for example, in steelmaking, to ereate intrieate eomposite mierostruetures with exceptional properties. In the diseussions of phase transformations that follow, you should therefore keep in mind the faet that ineomplete phase transformation and metastable phase retention is the rule, not the exception. Complete conversion to the equilibrium phase composition is rare in solid-solid phase transformations (and even in many liquid-solid phase transformations). 

The nucleation rate, growth rate, and transformation rate equations that we developed in the preceding sections are sufficient to provide a general, semiquantitative understanding of nucleation- and growth-based phase transformations. However, it is important to understand that the kinetic models developed in this introductory text are generally not sufficient to provide a microstructurally predictive description of phase transformation for a specific materials system. It is also important to understand that real phase transformation processes often do not reach completion or do not attain complete equilibrium. In fact, extended defects such as grain boundaries or pores should not exist in a true equilibrium solid, so nearly all materials exist in some sort of metastable condition. Many phase transformation processes produce microstructures that depart wildly from our equilibrium expectation. The limited atomic mobilities associated with solid-state diffusion can frequently cause (and preserve) such nonequilibrium structures. In this section, we will focus more deeply on solidification (a liquid-solid phase transformation) as a way to discuss some of these issues. In particular, we will examine a few kinetic concepts/models... 

Growth front instability during transformation can lead to cellular or dendritic microstructures, depending on the severity of the instability. Minor instability leads to the formation of primary protuberances, called cells, which advance perpendicular to the interface. If the instability increases, these primary protuberances can themselves spawn secondary protuberances perpendicular to the primary protuberances, and a dendritic microstmcture develops. Cellular and dendritic microstructures are most commonly observed in vapor-solid or liquid-solid phase transformations, although they can also be formed in solid-solid phase transformations. 

TG analysis also represents a powerful adjunct to DTA or DSC analysis, since a combination of either method with a TG determination can be used in the assignment of observed thermal events. Desolvation processes or decomposition reactions must be accompanied by weight changes, and can be thusly identified by a TG weight loss over the same temperature range. On the other hand, solid-liquid or solid-solid phase transformations are not accompanied by any loss of sample mass and would not register in a TG thermogram. 

A vast number of engineering materials are used in solid form, but during processing may be found in vapor or liquid phases. The vapor— solid (condensation) and liquid—>solid (solidification) transformations take place at a distinct interface whose motion determines the rate of formation of the solid. In this chapter we consider some of the factors that influence the kinetics of vapor/solid and liquid/solid interface motion. Because vapor and liquid phases lack long-range structural order, the primary structural features that may influence the motion of these interfaces are those at the solid surface. 

The superscript ° indicates that this equation is for a gas at the standard state of 1 bar. Standard states will be discussed in greater detail later in this chapter. For a solid, the calculation just includes the first integral (to 7), and for a liquid, the first two terms plus the second integral (to 7). If there are any solid-phase transformations at temperatures T, with heats of transformation A H, additional terms of the form A H/T must be included. 

In this book we are concerned only with mass transport, or diffusion, in solids. Self-diffusion refers to atoms diffusing among others of the same type (e.g., in pure metals). Interdiffusion is the diffusion of two dissimilar substances (a diffusion couple) into one another. Impurity diffusion refers to the transport of dilute solute atoms in a host solvent. In solids, diffusion is several orders of magnitude slower than in liquids or gases. Nonetheless, diffusional processes are important to study because they are basic to our understanding of how solid-liquid, solid-vapor, and solid-solid reactions proceed, as well as [solid-solid] phase transformations in single-phase materials. 

The above-described mixers are essentially low-viscosity devices. In many operations where the viscosity is high, when dealing with concentrated multiphase gas-liquid-solid binary or tertiary systems, or when liquid-to-solid phase transformation occurs during mixing, novel equipment designs are needed to intensify the heat/mass transfer processes. The multiphase fluids also represent an important class of materials that have microstructure developed during processing and subsequently frozen-in, ready for use as a product. To deliver certain desired functions, the control of microstructure in the product is important. This microstructure is developed in most cases by the interaction between the fluid flow and the fluid microstructure hence, uniformity of the flow field is important. 

Vapor-liquid-solid growth A vapor to liquid to solid phase transformation, the most common way to grow whiskers. 

LIQUID-SOLID AND SOLID-SOLID PHASE TRANSFORMATIONS... 

Liquid-solid and solid-solid phase transformations are also known as condensed-matter phase transformations. Condensed-matter phase transformations, like other kinetic processes, are driven by thermodynamics. When a region of matter can lower its total free energy by changing its composition, structure, symmetry, density, or any other phase-defining aspect, a phase transformation can occur. 

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