Thermally activated transformations

Most ceramics are thermally consoHdated by a process described as sintering (29,44,68,73—84), ia which thermally activated material transport transforms loosely bound particles and whiskers or fibers iato a dense, cohesive body. 

Bhattacharya et al.30b have shown that the transformation depicted in Scheme 5 is also readily achieved via thermal activation by substituting chloranil ( red = 0.02 V versus SCE) with a high-potential quinone such as... 

If Dh is indeed time dependent as in eq. (5) it is not obvious that C(x, t) will follow an error function expression as in eq. (3) or that >H will be thermally activated as in eq. (4). We now show that eqs. (3) and (4) still apply with a time dependent diffusion coefficient, by making a coordinate transformation (Kakalios and Jackson, 1988). The one-dimensional diffusion equation... 

In Chapter 3 we described the structure of interfaces and in the previous section we described their thermodynamic properties. In the following, we will discuss the kinetics of interfaces. However, kinetic effects due to interface energies (eg., Ostwald ripening) are treated in Chapter 12 on phase transformations, whereas Chapter 14 is devoted to the influence of elasticity on the kinetics. As such, we will concentrate here on the basic kinetics of interface reactions. Stationary, immobile phase boundaries in solids (e.g., A/B, A/AX, AX/AY, etc.) may be compared to two-phase heterogeneous systems of which one phase is a liquid. Their kinetics have been extensively studied in electrochemistry and we shall make use of the concepts developed in that subject. For electrodes in dynamic equilibrium, we know that charged atomic particles are continuously crossing the boundary in both directions. This transfer is thermally activated. At the stationary equilibrium boundary, the opposite fluxes of both electrons and ions are necessarily equal. Figure 10-7 shows this situation schematically for two different crystals bounded by the (b) interface. This was already presented in Section 4.5 and we continue that preliminary discussion now in more detail. 

We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

Let us compare the probabilities of tunnel electron transfer from singly and doubly charged metallic nanoparticles (Z — —l and Z = —2) to an adsorbed molecule. In the general case, tunnel electron transfer occurs in three stages (i) thermal activation of an electron in the metal, (ii) tunneling of the electron through the barrier to a molecular level, and (iii) transformation of the adiabatic potential of the molecule. 

The metathetic transformation of enynes in the presence of ruthenium precursors provide conjugated cycloalkenes, which are reactive under Diels-Alder reaction conditions with dienophiles. Many examples of such thermally activated [2 + 4] cycloadditions have been reported in the literature [51-59], and the beneficial effect of a ruthenium catalyst has been shown when the reaction was performed in one pot without isolation of the diene [60]. 

Thermal activation of alkyne-substituted clusters frequently results in the loss of one or more carbon monoxide ligands (418, 445, 446). Concomitant with this loss is an alteration in the bonding mode of the organic ligand in order to retain the electron balance within the molecule (107). Such a reaction is shown in Fig. 41, where an osmacyclopentadiene ring is transformed into a trisubstituted-f/5-cyclopentadienyl system. Metal-metal bond formation may take place in some examples (446, 447). 

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