Morphological instabilities

Let us assume that a small bulge appears on a rough, curved interface, and that for some reason the interface morphology is altered. Intervals between the lines of equal temperature or concentration become narrower at the bulge hence, the 

The problem of morphological instability was solved theoretically by Mullins and Sekerka [20], who proposed a linear theory demonstrating that the morphology of a spherical crystal growing in supercooled melt is destabilized due to thermal diffusion the theory dealt quantitatively with and gave linear analysis of the interface instability in one-directional solidification. 

Why polyhedral forms bounded by smooth interfaces can grow, whilst maintaining their polyhedral forms, was not properly accounted for until the layer-by-layer growth theory (which considers atomic process of crystal growth) formulated by Kossel and Stranski appeared. 

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Periodic oscillations have been observed as a morphological instability in several systems grown under various conditions [148]. The correspondence of the observed structures with results of theoretical modelling [139,149] is striking. 

P. Mahalingam, D. S. Dandy. Simulation of morphological instabilities during diamond chemical vapor deposition. Diamond Rel Mater d 1759, 1997. 

Aogaki et al,63-77 first examined from both theoretical and experimental viewpoints the morphological instability in which the mass flux of metal ions produced by shifting of the electrode potential to the less noble... 

In general, surface morphological instabilities driven by stresses are an important subject to investigate in connection with microelectronic applications. In particular, the degree of surface waviness in thin films as a consequence of surface and volume diffusion is a matter of pivotal importance. This topic has attracted considerable attention in the last two or so decades (11). Although surface diffusion is an important kinetic process, other kinetic processes may affect the evolution of stressed surfaces. Indeed, a possibility at high temperatures is the diffusion of atoms through the bulk. 

Figure 3.17. Relation between interface and lines of equal concentration in the ambient phase when morphological instability occurs.

Systematically speaking, so-called internal oxidation reactions of alloys (A,B) are extreme cases of morphological instabilities in oxidation. Internal oxidation occurs if oxygen dissolves in the alloy crystal and the (diffusional) transport of atomic oxygen from the gas/crystal surface into the interior of the alloy is faster than the countertransport of the base metal component (B) from the interior towards the surface. In this case, the oxidation product BO does not form a stable oxide layer on the alloy surface. Rather, BO is internally precipitated in the form of small oxide particles. The internal reaction front moves parabolically ( Vo into the alloy. Examples of internal reactions are discussed quantitatively in Chapter 9. 

A similar process occurs if we electrolyze the phase sequence AX/AY, using A-metal electrodes. AX and AY are immiscible ionic crystals. This time we focus on the AX/AY interface. Since there is always a finite electronic partial conductivity and the very small transference numbers te (AX) and te (AY) are normally different, the AX side of the AX/AY interface serves either as an anode (oxidizing) or as a cathode (reducing). The difference (te(AY)-te(AX)) is proportional to the anodic (cathodic) current in AX. The cathodic interface is expected to obtain similar morphologies as have been described for the A-metal cathode in the previous paragraph. It is immobile as long as Dx,Dy[Pg.286]

Figure 11-18. a) Morphological instability of the AgCI/KCl phase boundary in the electric field-driven transport couple, b) Morphological instability of the concentration profile of the AgCl-NaCI interdiffusion couple under the action of an electric field (see text) [S. Schimschal (1993)]. 

This chapter has been devoted to morphological, that is, geometrical instabilities. There is a second class of instabilities which may or may not be related to morphological instabilities. These instabilities occur in time (and space) and derive from nonlinear kinetics. They happen in two ways either as non-monotonous (periodic)... 

Once the particle grows to a size that exceeds R, morphological instabilities will set in. The minimum size for instabilities is found from the n = 2 spherical harmonic, giving R (n = 2) = 7Rc.5 Thus the theory predicts instabilities at very small precipitate sizes. 

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