Boundary morphology

Figure A3.3.9 Time dependence of die domain boundary morphology for j = 0.48. Here the domam boundary is the location where / = 0. The evolution is shown for early-time t values of (a) 50, (b) 100, (c) 150, (d) 200, (e) 250 and (f) 300. From [29].

In Chapter 11, growth morphologies are dealt with and the question is raised as to which conditions make the moving phase boundaries morphologically stable or unstable during solid state reactions. One criterion for instability is met if the interface moves against the flux direction of the rate determining (slow) reaction partner. 

The definition of a solid state reaction implies that the reaction product is a solid. If, for example, one of the reactants is a fluid, no deviatoric stresses are transmitted across the common interface. This situation simplifies the mechanical boundary condition significantly and explains why studies on boundary morphology are often performed with solid/fluid systems. 

In a true binary system, the transport problem, which includes the boundary morphology, is completely defined by 1) the continuity equation (11.2) at the moving... 

Figure 11-6 defines the transport problem in a quasi-binary ionic system (A,B)X with a miscibility gap, if both chemical (V/i,) and electrical (Vp) driving forces act simultaneously (case 3)). If the chemical force is negligible, we are dealing with case 2) and the electrical drift flux of the cations shifts the boundary b in the direction of the flux. We can conclude that, in agreement with Figure 11-5 a, the boundary morphology is unstable if... 

Let us briefly outline the main concepts of a (linear) stability analysis and refer to the situation illustrated in Figure 11-7. If we artificially keep the moving boundary morphologically stable, we can immediately calculate the steady state vacancy flux, /v, across the crystal. The boundary velocity relative to the laboratory reference system (crystal lattice) is... 

The above approximation, however, is valid only for dilute solutions and with assemblies of molecules of similar structure. In the event that concentration is high where intemiolecular interactions are very strong, or the system contains a less defined morphology, a different data analysis approach must be taken. One such approach was derived by Debye et al [21]. They have shown tliat for a random two-phase system with sharp boundaries, the correlation fiinction may carry an exponential fomi. 

Fig. 8. Emulsion morphology diagram, illustrating where the microemulsion in various macroemulsion morphologies is a continuous phase or dispersed phase. Morphology boundaries (—), aqueous, continuous (--------------), oleic, continuous (--), microemulsion, continuous.

As the substrate temperature increases, the surface mobUity increases and the stmctural morphology first transforms to that of Zone T, ie, tightly packed fibrous grains having weak grain boundaries, and then to a full density columnar morphology corresponding to Zone 2 (see Fig. 7). 

To further characterize the event it is first necessary to identify critical features of the initial configuration that will strongly influence the process. For powder compacts, the most obvious features are the morphological characteristics of the powders, their microstructures, and the porosity of the compact. For solid density samples, the grain structure, grain boundaries, defect level, impurities, and inclusions are critical features. 

The lithium morphology at the beginning of the deposition was measured by in-situ atomic force microscopy (AFM) [42], When lithium was deposited at 0.6 C cm2, small particles 200-1000 nm in size were deposited on the thin lines and grain boundaries in LiC104-PC. Lump-like growth was observed in LiAsF6-PC along the line. 

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