Stoichiometric vacancy concentration

At this point, it is instructive to examine both components of this equation and the likely contribution to the tracer diffusion coefficient for these perovskite materials. Here the term [F ] refers to the mobile vacancy concentration, which may be different from the stoichiometric vacancy concentration (i.e., that determined by the oxidation states of the constituent cations) because of vacancy trapping, as observed in the fluorite oxides [2], or due to vaeaney ordering [5]. contains the terms relevant to mobility of the vacancies, i.e., the ease with which the oxygen atoms can jump from an adjacent lattice site into a vacancy. Mizusaki et al. [6] have previously shown that data for D, the vacancy diffusivity, show remarkably little variation for a number of perovskite materials. This is a very interesting observation and one to which we return later. It is thus important to understand the changes that occur in the vacancy concentration in these materials and how this affects the oxygen self-diffusion coefficient. 

AHf affects the stoichiometric vacancy concentration whereas AH a affects the mobile vacancy concentration and A// only enters into the vacancy diffusion coefficient. Thus, if we can determine the stoichiometric vacancy concentration (or, more accurately, the mobile vacancy concentration), then we can extract the value of Dv, leading to a value for AHm. 

The close match of Dv from very different materials was obtained using the stoichiometric vacancy concentrations determined by Thermogravimetric Analysis (TGA) this implies that all these vacancies are mobile and hence that trapping is negligible. 

The value of the activation energy approaches 50000 near the stoichiometric composition. This diffusion process therefore approximates to the selfdiffusion of metals at stoichiometty where the vacancy concentration on the carbon sub-lattice is small. 

In the case of non-stoichiometric compounds, the vacancy concentration is mainly associated with their deficiency parameters.14185 When comparing the reaction- and self-diffusion coefficients of iron cations in Fe3.504, satisfactory results can be obtained simply by setting cv 3/4 for the growing Fe3 s04 phase and cy 8 for the non-growing one. The value of 8 characterising the cation deficiency of the crystal structure of this phase is known to be around 1.0 xlO 2,14 160 185 considerably higher than the concentration of thermal vacancies. The Fe3.g04 layer grows mainly at the expense of diffusion of iron cations, while the value of their reaction-... 

Lyon (5) proposed that A H may be affected by vacancy concentration, which varies from 14 to 15% (5) in samples of stoichiometric B-TiO obtained at normal pressure. Samples with vacancy concentrations dow to 0% have been prepared (6) at high pressure. PVT data (6) allowed calculation (5) of values of A H for Ti0(B, 0% vacancies) + TiO(B, 14% vacancies). These values, if valid, suggest that A H should be quite different for vacancy-free B-TiO and significantly different even for the normal range of vacancy concentrations. Ideal ordered a-TiO, containing 1/6 or 16.7% vacancies, should involve additional changes in volume ( ) and AjH . In summary, the discrepancy in a H may arise from sample differences - phase, composition and vacancy concentration - or from bias in the reaction calorimetry. 

The above results concerning the behaviour of non-stoichiometric AM03 y perov-skites are significant in that, for the first time, evidence of short-range ordering has been found for low-vacancy concentrations. 

In a previous study of non-stoichiometiy in ScS, [30] an analysis of the charge densities and partial densities of states for a series of low-energy structures with increasing vacancy concentration revealed very clearly the mechanism of intrinsic non-stoichiometry in that system. Despite the very obvious similarities of the ground states in these two systems compared to those of ScS, the details of the mechanism for non-stoichiometry appears to be different. An analysis of the partial densities of states(not shown here) for non-stoichiometric TiC and TiN did not reveal a mechanism for vacancy formation similar to that found for ScS—a somewhat puzzling result given the fact that the ground states in ScS are so closely related to those in TiC/N. At this point, we have not been able to determine the electronic mechanism that drives the formation of vacancies in TiC and TiN. This topic is a focus of our current research and will be discussed in a future publication. 

In this case the electronic properties within region IF are insensitive to composition, while the vacancy concentrations vary with composition. The stoichiometric composition corresponds to [F ] =... 

We consider an AB alloy which consists of an equal number of A and B sites. For the subsequent analysis, every site is uniquely associated with either an A or a B sublattive. The following is trivially generalised to A iBn alloys. The alloy is not quite stoichiometric, and has the composition A Bj.x, where for the validity of the independent defect approximation we must suppose x to be within a few percent of 0.5. Each site of each sublattice can be occupied by its own atom, an atom of the other kind (an antisite defect) or a vacancy. There are therefore six species for which we define the concentrations on each sublattice ... 

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