Kinetics of Ionic Single Crystals

One of the first uses of the SECM was as a fabrication tool to form dissolution channels and growth hillocks on materials at the micrometer to submicrometer level. This area is dealt with in greater detail in Chapter 13. For these studies, the feedback mode of the device was predominantly utilized. Because the purpose was only to alter the topographical features of a substrate, little information was provided on the rates or nature of the dissolution processes. In this section we describe how the equilibrium perturbation mode can be employed to initiate, and quantitatively monitor, dissolution reactions, providing unequivocal information on the kinetics and mechanism of the 

12 Principles of SECM-induced dissolution using copper sulfate pentahydrate as an example substrate. Note that the diagram is not to scale as the tip-crystal separation is typically 0.01 r.. 

The key features of this technique, which result in considerable advantages over conventional methodologies, are as follows  

Mass transfer in the tip-substrate gap is well defined, variable, and calculable, enabling the role of interfacial undersaturation in the dissolution process to be quantified (2-8). 

Extremely high mass transfer rates can be generated using close tip-substrate separations and small-radii UMEs (42,43) facilitating the study of fast reactions (2-8). 

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When an ionic single crystal is immersed in solution, the surrounding solution becomes saturated with respect to the substrate ions, so, initially the system is at equilibrium and there is no net dissolution or growth. With the UME positioned close to the substrate, the tip potential is stepped from a value where no electrochemical reactions occur to one where the electrolysis of one type of the lattice ion occurs at a diffusion controlled rate. This process creates a local undersaturation at the crystal-solution interface, perturbs the interfacial equilibrium, and provides the driving force for the dissolution reaction. The perturbation mode can be employed to initiate, and quantitatively monitor, dissolution reactions, providing unequivocal information on the kinetics and mechanism of the process. 

Instead of continuous modulation, single thermal pulses have been imposed by laser beams. This can be seen as a continuation and an expansion of the temperature-jump technique which had been introduced to study kinetics of ionic processes [36]. The method has found application preferably with single-crystal electrodes [65-70]. Many fundamental quantities have been determined, among them the potential of zero charge (Fpzc) of Au(l 11) [65], the potential of maximum entropy [66, 70], the process of hydrogen adsorption at platinum surfaces [67, 68] and the entropy of double-layer formation [69]. This quantity also has been... 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

The kinetics of dissolution of ionic solids has traditionally been studied via the measurement of bulk concentration changes in, for example, stirred suspensions. Using the equilibrium perturbation mode of the SECM, the experimenter can control directly the interfacial undersaturation and make measurements at single crystal surfaces or with micrometer spatial resolution [24]. 

He T, Kreuer KD, Baikov YM, Maier J (1997) Impedance spectroscopic study of thermodynamics and kinetics of Gd-doped BaCeOs single crystal. Solid State Ionics 95 301-308... 

Most simple halides, ionic or covalent, melt unchanged on heating. Crystal defects have been identified as being important in the decompositions of C0F3 [48] and Cdlj [49]. Barret [50] studied the decomposition of CuBrj - CuBr + /2BT2 and discussed the role of diffusion within the mass of reactant particles on the overall kinetic behaviour. HF.LiF and HF.NaF decompose [51] before melting, in a single... 

As for the valence band, the picture is relatively complicated. Considering a single hole near the top of the Fg valence band (for zinc blende crystal structure) and the magnetic ion with five d orbitals occupied by N electrons, the Hamiltonian that is applicable would have ionic, crystal, and hybridization components. The p-d hybridization mediated kinetic exchange depends on the filling of only the orbitals, not all the one-electron d-orbitals of the magnetic ion. The spin-dependent part of the exchange Hamiltonian for interaction between the Fg valence band p-like electrons and all the three d-orbitals occupied by one electron can be described as... 

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