Thermodynamics interfacial defects

Although the emphasis here will, by necessity, be placed on more recent data, several key reviews of transport in nanocrystalline ionic materials have been presented, the details of which will be outlined first. An international workshop on interfacially controlled functional materials was conducted in 2000, the proceedings of which were published in the journal Solid State Ionics (Volume 131), focusing on the topic of atomic transport. In this issue, Maier [29] considered point defect thermodynamics and particle size, and Tuller [239] critically reviewed the available transport data for three oxides, namely cubic zirconia, ceria, and titania. Subsequently, in 2003, Heitjans and Indris [210] reviewed the diffusion and ionic conductivity data in nanoionics, and included some useful tabulations of data. A review of nanocrystalline ceria and zirconia electrolytes was recently published [240], as have extensive reviews of the mechanical behavior (hardness and plasticity) of both metals and ceramics [13, 234]. 

The question arises, why do bi- or multi-phasic catalysts generally show better activity and selectivity than the active phase alone The aim of this paper is to answer this question by exploring the role of interfacial effects. We shall examine first how the thermodynamic and structural properties of one phase influence its interactions, not only with the gaseous reactants, but also with coexisting solid phases as a result of its bulk, surface, and defect structure. We will also examine the conditions necessary for these interactions and set up a structural classification of the main components of mild oxidation catalysts. This will lead finally to a discussion of the role of interfacial effects in catalyst performance using some illustrative examples. Thermodynamic and Structural Properties of Single Phase Catalysts... 

The above treatment assumes that the defects are mobile and distributed in response to the thermodynamic driving force. It should be mentioned that this is not always the case ceramics often contain defects frozen in from higher tanperature treatment (e.g. sintering), in which case some of the defect concentrations will be fixed. The two cases, respectively known as the Debye and Schottky cases, produce different interfacial properties, including different characteristic lengths. For a concise discussion of the two cases see Maier [1996]. Further relevant information can be found in Kim et al. [2003] and Maier [2004]. 

A key parameter is the point defect concentration (co) directly adjacent to the interfacial core containing the information on the second phase. From a thermodynamic viewpoint, we better express Cq in terms of surface charge density or even better in terms of the energy levels as the real invariants (see Fig. 1) [12],... 

Based on a global energy analysis, if the decrease in interfacial energy can compensate the increase in energy due to defects, the formation of a twin plane is then thermodynamically favorable. This relationship among these energy terms can be depicted in the following equation ... 

It most clearly shows that neglect of one partial rate (% or %) is associated with nonlinear behaviour ( ArG RT). The inherent nonlinearity of chemical kinetics is the key to our understanding of biology. As has been discussed, it does not just make possible the durability of biological structures, it also leads to the variety of nature and the appearance of dissipative structures [94,339,340], which is after all what we are in a thermodynamic sense. As is well known, nonequilibrimn defects play a fundamental role in evolution. In our context, the fact that the nonlinearity of chemical reactions is indispensable for the individuality and complexity of interfacial reactions is of particular interest. Typical nonlinear phenomena are discussed in more detail at the end of this diapter. 

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