Transformation by Surface Nucleation and Growth

The total transfonnation of an initial solid A into a new solid B involves the two processes of nucleation and growth. It is thus advisable to estabUsh laws of evolution that consider the two processes. We will examine the most frequent case, when the nuclei are formed on the surface of the initial soUd. We will see in Appendix 9 the case with nucleation in the bulk. 

Note that these two processes present the same balance on the chemical point of view and will thns be represented consequently by the same expression of the reactioit They present a particular character by the fact that the growth can be achieved oidy after nucleation, which makes the two processes consecutive but nucleation can continne, simultaneously with the growth, at other points where the final phase is not yet present. 

Other processes can possibly be snperimposed on the two precedent cases during the transformation coalescence of the grains and enucleating. 

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Transformation by Surface Nucleation and Growth 347 If we remember that = we get the following equation for the rate ... 

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is beheved to occur by surface nucleation and ledge movement by face specific reactions (37). The soHd-state transformation from one polytype to another is beheved to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

The discussion in this paper appties to wide classes of phase transformations that occur by a nucleation and growth mechanism. Examples of such transformations indude many common transformations, such as boiling and freezing of a liquid and condensation of a vapor, as well as some much less well known transformations, such as oxidation of a metal surface and formation of voids in nudear reactor materials. There are some types of phase transformations, such as spinoidal decomposition, that occur as soon as they are thermodynamically allowed and do not require nudeation. 

Stranski-Krastanov growth has been documented for copper on Au(lll) [101, 102], Pt(100) and Pt(lll) [103], for silver on Au(lll) [104, 105], for cadmium on Cu(lll) [106] and for lead on Ag(100) and Ag(lll) [107-109]. In all of these examples, an active metal is deposited onto a low-index plane of a more noble metal. Since the substrate does not undergo electrochemical transformations at the deposition potential, a reproducible surface can be presented to the solution. At the same time, the substrate metal must be carefully prepared and characterized so that the nucleation and growth mechanisms can be clearly identified, and information can be obtained by variation of the density of surface features, including steps, defects and dislocations. 

By a change of temperature or pressure, it is often possible to cross the phase limits of a homogeneous crystal. It supersaturates with respect to one or several of its components, and the supersaturated components eventually precipitate. This is an additive reaction. It occurs either externally at the surfaces, or in the crystal bulk by nucleation and growth. Reactions of this kind from initially homogeneous and supersaturated solid solutions will be discussed in Chapter 12 on phase transformations. Internal reactions in the sense of the present chapter occur after crystal A has been brought into contact with reactant B, and the product AB forms isothermally in the interior of A or B. Point defect fluxes are responsible for the matter transport during internal reactions, and local equilibrium is often established throughout. 

In view of the importance of macroscopic structure, further studies of liquid crystal formation seem desirable. Certainly, the rates of liquid crystal nucleation and growth are of interest in some applications—in emulsions and foams, for example, where formation of liquid crystal by nonequilibrium processes is an important stabilizing factor—and in detergency, where liquid crystal formation is one means of dirt removal. As noted previously and as indicated by the work of Tiddy and Wheeler (45), for example, rates of formation and dissolution of liquid crystals can be very slow, with weeks or months required to achieve equilibrium. Work which would clarify when and why phase transformation is fast or slow would be of value. Another topic of possible interest is whether the presence of an interface which orients amphiphilic molecules can affect the rate of liquid crystal formation at, for example, the surfaces of drops in an emulsion. 

A 2D first order phase transition is unequivocally characterized by a discontinuity in the T E) isotherm at / = constant. At this special point in the r E) isotherm an expanded" 2D Meads phase is transformed into a more condensed" 2D Meads phase. Expanded and condensed Meads phases have to coexist. Therefore, 2D nucleation and growth occur in the presence of a preformed expanded but supersaturated Meads adsorbate. The surface concentration of the expanded Meads adsorbate, F, is continuously changing according to the actual polarization state of the UPD system. As long as corresponding -amounts (cf. eq. 3.4) contribute significantly to the overall measured -values, an identification of 2D nucleation and growth is not possible. 

The population balance approach to measurement of nucleation and growth rates was presented by Randolph and Larson (1971, 1988). This methodology creates a transform called population density [n(L)], where L is the characteristic size of each particle, by differentiating the cumulative size distribution N versus L. shown in Fig. 4-22, where N is the cumulative number of crystals smaller than L. Per unit volume, the total number of particles, total surface area, and total volume/mass are calculated as the first, second, and third moments of this distribution. 

At TT > TTg the relaxation phenomena for insoluble monolayers are caused by the transformation of a homogeneous monolayer phase into a heterogeneous monolayer-collapse phase system. However, some differences exist between saturated-LMWE and unsaturated-LMWE monolayers (Eigure 14.6b). Relaxation phenomena in saturated-LMWE monolayer are controlled predominantly by the collapse mechanism because the surface pressure relaxes to TTg. Eor these systems the monolayer collapses by nucleation and growth of critical nuclei. Unsaturated-LMWE monolayers behave differently to saturated-LMWE monolayers. As the surface pressure relaxes from the collapse value, which is close to TTg, towards values lower than TTg at longer times, the collapse competes with a desorption mechanism (Patino and Nino, 1999). 

The formation of bulk phases is most common in the case of oxygen. Transformation of the chemisorbed phase into oxide proceeds generally through a nucleation and growth mechanism. As an example. Fig. 2.26a shows an STM image from a Ru(0 001) surface that had been exposed to O2 at elevated temperature [41 ]. The right part is still the Ru(0 001) surface covered by a 1 x 1 O adlayer, while the left part had been transformed into a thin... 

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