Phase transformations, energy cost

Spherical alumina can also be formed from commercial, low cost aluminum-oxides or even from aluminum-hydroxides. In the latter case energy of the plasma should provide not only the enthalpy of melting but that of dehydration and subsequent phase transformations of alumina as well. Under the aforementioned conditions particles below 45 pm have a good chance to be spherodized. Presumably the wide particle size distribution of starting gibbsite powder accounts for the less spheroidization rate of 70%. 

The energy cost to create surfaces/interfaces leads to a nucleation barrier in condensed-matter phase transformations. Therefore, nucleation-based phase transformations can only occur if the energy released by creating the new volume of the second phase sufficiently offsets the energy expended in creating the new interfacial area. This leads to a minimum viable nucleation size and thus helps determine the speed at which nucleation can proceed. These issues will be discussed in the next section ... 

The Fermi sphere for atoms with one valence electron per atom can easily fit in a bcc reciprocal lattice (fee direct lattice). If a divalent element is added, the additional electrons will increase the diameter of the Fermi sphere. When the Fermi sphere begins to touch the Brillouin zone, the additional electrons must either go to the unfilled states in the comers of the first Brillouin zone, which are higher energy states, go across the Brillion zone, which costs energy because of the energy gap, or imdergo a solid-phase transition to a new reciprocal lattice with a Brillouin that can accommodate more electrons. This model explains the solid-phase transformations of many mixed-valency binary alloys in which the phases progress from fee to bcc to hep as more divalent component is added. 

Because the trimerization of acetylene is so enormously exothermic (—143.6 kcal/mol) and is allowed by the Woodward-Hoffmann rules, one might expect a very low activation energy for this transformation. The decrease in entropy might be costly, but should not be prohibitive in intramolecular cases. Experimentally, acetylene undergoes reaction at 400 °C in the gas phase to give a wide variety of products, of which benzene constitutes only a small fraction26. ... 

Transition metal catalysts, specifically those composed of iron nanoparticles, are widely employed in industrial chemical production and pollution abatement applications [67], Iron also plays a cracial role in many important biological processes. Iron oxides are economical alternatives to more costly catalysts and show activity for the oxidation of methane [68], conversion of carbon monoxide to carbon dioxide [58], and the transformation of various hydrocarbons [69,70]. In addition, iron oxides have good catalytic lifetimes and are resistant to high concentrations of moisture and CO which often poison other catalysts [71]. Li et al. have observed that nanosized iron oxides are highly active for CO oxidation at low tanperatures [58]. Iron is unique and more active than other catalyst and support materials because it is easily reduced and provides a large number of potential active sites because of its highly disordered and defect rich structure [72, 73]. Previous gas-phase smdies of cationic iron clusters have included determination of the thermochemistry and bond energies of iron cluster oxides and iron carbonyl complexes by Armentrout and co-workers [74, 75], and a classification of the dissociation patterns of small iron oxide cluster cations by Schwarz et al. [76]. 

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