Diffusion-controlled morphology

Figure 1.55. The relationships between the concentration product, (Ba " )i(S04 )i, at the initiation of barite precipitation, and morphologies of barite crystals (Shikazono, 1994). The dashed line represents the boundary between dendritic barite crystals and well-formed rhombohedral, rectangular, and polyhedral barite crystals. The 150°C data are from Shikazono (1994) the others from other investigations. D dendritic (spindle-like, rodlike, star-like, cross-like) barite Dp feather-like dendritic barite W well-formed rectangular, rhombohedral, and polyhedral barite. The boundary between the diffusion-controlled mechanism (Di) and the surface reaction mechanism (S) for barite precipitation at 25°C estimated by Nielsen (1958) The solubility product for barite in 1 molal NaCl solution at 150°C based on data by Helgeson (1969) and Blount (1977). A-B The solubility product for barite in 1 molal NaCl solution from 25 to 150°C based on data by Helgeson (1969).

Proceeding systematically, diffusion controlled a-fi transformations of binary A-B systems should be discussed next when a and / are phases with extended ranges of homogeneity. Again, defect relaxations at the moving boundary and in the adjacent bulk phases are essential for their understanding (see, for example, [F. J. J. van Loo (1990)]). The morphological aspects of this reaction type are dealt within the next chapter. 

Let us finally comment on the morphological stability of the boundaries during metal oxidation (A + -02 = AO) or compound formation (A+B = AB) as discussed in the previous chapters. Here it is characteristic that the reaction product separates the reactants. 1 vo interfaces are formed and move. The reaction resistance increases with increasing product layer thickness (reaction rate 1/A J). The boundaries of these reaction products are inherently stable since the reactive flux and the boundary velocity point in the same direction. The flux which causes the boundary motion pushes the boundary (see case c) in Fig. 11-5). If instabilities are occasionally found, they are not primarily related to diffusional transport. The very fact that the rate of the diffusion controlled reaction is inversely proportional to the product layer thickness immediately stabilizes the moving planar interface in a one-... 

The Avrami analysis was performed on the crystallization data. The DLI measurements provided high Avrami exponents in the blends, but the analysis on the DLI data is extremely inaccurate because of all the difficulties inherent to the method. The IR measurements show Avrami exponents that range from 2.5 to 1.5 for PET and PBT. These studies were made on the diffusion-controlled region. It is our belief that the Avrami analysis strongly depends on the method used to follow the crystallization and always has to be accompanied with direct observations on the morphology. 

Anyway, the structure of copper deposits obtained at overpotentials of 800 and 1,000 mV with a quantity of the electricity of 20 mA h cm-2 was similar to those obtained at lower overpotentials before the beginning of dendritic growth. The absence of copper dendrites at overpotentials of 800 and 1,000 mV after the electrodeposition with 20 mAh cm-2, as well as the similarity of the obtained morphologies of copper deposits with those obtained at lower overpotentials before dendritic growth initiation clearly indicates that there is really lower degree of diffusion control at these overpotentials than at overpotentials of 550 and 700 mV respectively. 

This concept can be also applied for the case of the electrodeposition of copper. As mentioned earlier, the morphology of the copper deposit obtained at cathodic potential of -500 mV/SCE under the parallel field was of cauliflower-like structure (Fig. 12b), while the morphology of the copper deposit obtained without the applied magnetic field had very dendritic structure (Fig. 12a). It is known that dendritic structures are main characteristic of electrodeposition in conditions of full diffusion control, while cauliflower-like structures are a characteristic of a dominant diffusion in mixed control of electrodeposition process.13... 

Jiang et al. studied the electrodeposition and surface morphology of aluminum on tungsten (W) and aluminum (Al) electrodes from 1 2 M ratio of [Emim]CI/AlCl3 ionic liquids [165,166]. They found that the deposition process of aluminum on W substrates was controlled by instantaneous nucleation with diffusion-controlled growth. It was shown that the electrodeposits obtained on both W and Al electrodes between -0.10 and -0.40 V (vs. AI(III)/A1) are dense, continuous, and well adherent. Dense aluminum deposits were also obtained on Al substrates using constant current deposition between 10 and 70 mA/cm. The current efficiency was found to be dependent on the current density varying from 85% to 100%. Liu et al. showed in similar work that the 20-pm-thick dense smooth aluminum deposition was obtained with current density 200 A/m for 2 h electrolysis [167],... 

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