Point defects experimental determination

Although this estimate of the interaction energy between defects is simplistic, it demonstrates that a fair number of defects may cluster together rather than remain as isolated point defects, provided, of course, that they can diffuse through the crystal. It is difficult, experimentally, to determine the absolute numbers of point defects present in a crystal, and doubly so to determine the percentage that might be associated rather than separate. It is in both of these areas that theoretical calculations are able to bear fruit. 

If the coupling of the electrons to certain centers is strong, their spectra may be distinguished from that of the crystal as a whole (point defect color centers in ionic crystals, polarons in semiconductors). The spectra of defects can therefore be used for analytical or even kinetic investigations. In principle, it should be possible to construct devices which have, under favorable conditions, a sufficient spatial resolution to experimentally determine the basic kinetic quantity c,( , t). 

K. Goto, T. Hondoh, and A. Higashi, Experimental determinations of the concentration and mobility of interstitials in pure ice crystals in Point Defects and Defect Interactions in Metals, eds. J. Takamura, M. Doyama, and M. Kiritani, University of Tokyo Press, 1982, p. 174. 

Here the narrow prescription of Chapter 1 is widened to deal with more chemically complex phases, in which the materials may contain mixtures of A, B and X ions as well as chemical defects. In these cases, using an ionic model, it is only necessary that the nominal charges balance to obtain a viable perovskite composition. In many instances these ions are distributed at random over the available sites, but for some simple ratios they can order to form phases with double or triple perovskite-type unit cells. The distribution and valence of these ordered or partly ordered cations and anions are often not totally apparent from difEraction studies, and they are often clarified by use of the bond valence sums derived from experimentally determined bond distances. Information on the bond valence method is given in Appendix A for readers unfamiliar with it Point defects also become significant in these materials. The standard Kroger- fink notation, used for labelling these defects, is outlined in Appendix B. 

Table 4.7 Boron carbide Comparison between theoretical electronic properties, experimental characterization and intrinsic point defects determined experimentally. 

The experimentally determined temperature range of the formation of microvoids in crystals with a large diameter is 1403... 1343 K (Kato et al, 1996 Itsumi, 2002). In this respect, the approximate calculations for the solution in terms of the model of point defect dynamics were performed at temperatures in the range 1403...1073 K. The computational model uses the classical theory of nucleation and formation of stable clusters and, in strict sense, represents the size distribution of clusters (microvoids) reasoning from the time process of their formation and previous history. 

It is well known that defects play an important role in determining material properties. Point defects play a major role in all macroscopic material properties that are related to atomic diffusion mechanisms and to electronic properties in semiconductors. Line defects, or dislocations, are unquestionably recognized as the basic elements that lead to plasticity and fracture (Fig. 20.1). Although the study of individual solid-state defects has reached an advanced level, investigations into the collective behavior of defects under nonequilibrium conditions remain in their infancy. Nonetheless, significant progress has been made in dislocation dynamics and plastic instabilities over the past several years, and the importance of nonlinear phenomena has also been assessed in this field. Dislocation structures have been observed experimentally. 

The quantitative relations between the point defect concentrations and the compound activities are very useful in interpreting electrical properties of sohd electrolytes and MIECs. The point defect-composition relations also define the electrolytic domain of a solid electrolyte, and hence determine experimental conditions to be fiilfilled in order for the materials to be applicable in solid state electrochemical devices. 

In the absence of extended defects, i.e., no interaction between point defects. Equations (14.61) to (14.64) may be used with the aid of experimentally determined equilibrium constants to constmct the Kr6ger- fink defect diagram, from which expressions for the partial conductivities of the mobile ionic and electronic defects can be derived. 

In previous studies (Kato et al., 2009a, 2011b 2011c), the stoichiometric compositions in (U,Pu)02 have been determined based on defect chemistry. The relationship between oxygen partial pressure and deviation x from stoichiometric composition has been analyzed in non-stoichiometric oxides. Kosuge (1993) used statistical thermodynamics considerations for description of non-stoichiometric compounds, and Karen (2006) reported a point-defect scheme for them. Recently their methods have been applied for nonstoichiometric (U,Pu)02, and experimental data, accurately measured in the near stoichiometric region, were analyzed as a function of temperature. In this report the measurement data and the measurement technique were reviewed and analysis results based on defect chemistry were summarized. 

Table 8 Calculated Electron Deficiencies for the Valence Bands of Idealized Crystal Structures and Experimentally Determined Point Defect Concentrations in the Real Crystals...

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