Vacancy mechanism, description

As an example, consider the study by Banerjee et al. (1984) on the effect of electron irradiation on the order-disorder transformation in (DIJ Ni4Mo. Electron micrographs and diffraction patterns were obtained during in situ electron irradiations at 50-1050 K in a HVEM. At temperatures below 200 K, the alloy completely disorders. At 200-450 K, only SRO was observed, and the transition between LRO and SRO, which occurs via the completely disordered state, is consistent with the concentration-wave description of the SRO structure and supports the concept of spinodal ordering. It is believed that an interstitial mechanism is responsible for maintaining the SRO. Above 450 K, LRO persisted for samples initially in this state and SRO was only preserved up to 550 K for samples initially in that state. Between 550 and 720 K, a mixed SRO-LRO state occurred, and at temperatures above 720 K a complete transition to SRO was obtained. It is believed that maintenance of LRO requires a vacancy mechanism. At temperatures below 800 K the SRO-LRO transition occurred in a continuous fashion, while above 800 K a nucleation and growth mechanism was operative. This behavior is characteristic of an ordering transition of the first kind below and above the coherent instability temperature. 

Self-diffusion in materials occurs by repeated occupation of defects. Depending on the defects involved one can distinguish between (1) vacancy, (2) interstial, and (3) interstitialcy mechanisms [107], As an example, different diffusion paths for oxygen interstitials are illustrated in Fig. 1.16 [129]. For a detailed description of diffusion paths for oxygen vacancies, zinc vacancies and zinc interstitials the reader is also referred to literature [129,130]. 

An isolated CS plane is referred to as a Wadsley defect and a random array of CS planes is considered to constitute planar (extended) defects which are entirely different from point defects. It is obvious that when CS planes occur at regular intervals, the composition of the crystal is stoichiometric, whereas a random array of CS planes results in nonstoichiometric compositions. While we have invoked anion vacancies which are later annihilated in our description of CS plane formation, we must point out that vacancies are not essential precursors for the formation of CS planes. Accommodating anion-deficient nonstoichiometry through CS mechanism is a special feature restricted to d° metal oxides such as W03, Nb205 and TiOz which exhibit soft phonon modes. Soft phonon modes in metal oxides arise from soft metal-orxygen potentials which permit large cation relaxation. The latter... 

These alternative descriptions of shear-plane formation will be valuable in our discussion of mechanism in Section 4. In the account now presented of the relative stabilities of shear plane and point defect structures we will assume that vacancies are the predominant point defects. However, the arguments we present could be adapted for metal interstitial defect structures. 

The proposed mechanisms of additive action depend on the structural formula used for description of transition aluminas. According [27] the general formula for y-alumina is Ab[ ]m0.3 v/2 (OH)v< >i-v/2. The incorporation of a foreign cation M(z+), either in an Al(3+) site or in a divalent vacancy, leads to a modification of the stoichiometry of different structural elements as... 

Last but not least, the fundamental understanding of the permeation mechanisms within perovsldte and more extensively MIEC membranes is still in its infancy. The most extended models are based on the Nernst-Planck equations (e.g., the Wagner equation) providing a macroscopic view of the permeation process itself. These models usually cannot afford the description of heterogeneous materials including impurities and occluded bubbles, as is the case for most real perovskite layers. To this aim, the development of meso- or microscale models with a proper description of diffusion effects and vacancy generation would be desirable. 

Stochastic models are also able to capture complicated pattern formation seen in chemically reacting media and can be used to study the effects of fluctuations on chemical patterns and wave propagation. The mesoscopic dynamics of the FHN model illustrates this point. In order to formulate a microscopically based stochastic model for this system, it is first necessary to provide a mechanism whose mass action law is the FHN kinetic equation. Some features of the FHN kinetics seem to preclude such a mechanistic description for example, the production of u is inhibited by a term linear in V, a contribution not usually encountered in mass action kinetics. However, if each local region of space is assumed to be able to accommodate only a maximum number m of each chemical species, then such a mechanism may be written. We assume that the chemical reactions depend on the local number of molecules of the species as well as the number of vacancies corresponding to each species, in analogy with the dependence of some surface reactions on the number of vacant surface sites or biochemical reactions involving complexes of allosteric enzymes that depend on the number of vacant active sites. 

For better understanding the diverse relaxation behavior of confined polymers, researchers have utilized models or simulation tools to capture the kinetic features of the material at the molecular level, aiming to represent the results observed in experiments. The FVHD model, which has been widely employed in characterizing physical aging in bulk polymers, is reformulated to describe the relaxation behavior of polymers under nanoconfinement. A dual mechanism combines the effect of vacancy diffusion and lattice contraction, and was recently applied with time-dependent internal length scales to characterize the free volume reduction in the aging process [169]. The dual mechanism model (DMM) fits the data of thin film permeability fairly well. The potential predictive capability of the DMM model depends on the accuracy of the relationship between the internal length and time scale on the description of complex material dynamics [161]. 

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