Most probable defect size

Fig. 2.5. The function F n) gives the probability of occurrence of a defect with size smaller than n. The maximum of the derivative appears for nc, which is the most probable size for a defect.

We shall now investigate the influence of the sample size. As discussed earlier, it is related to the notion of the most dangerous defect in the sample. In the present case, the most dangerous defect is a cell of the infinite cluster with length in the direction parallel to the current and /max in the perpendicular direction. The total probability of getting a defect of size I is given (using g l) from eqn. 1.23b) by... 

The iron oxides in natural surface environments are often poorly crystalline. i. e. the crystals are nano-sized (>100 nm), do not clearly exhibit the typical morphology of well-crystalline forms, are rich in defects and contain impurities. All this is most probably the result of their formation at low-temperature and in contaminated environments. Due to their striking colors (ranging from red to yellow) and their high surface area, small... 

The pyrochlore structure is three-dimensional framework of corner-shared (Ti,Ta,Nb)06 octahedra. The A site lies within this framework and is 8-coordinated. The octahedra can articulate to allow for a fair range in sizes of the A cation, which accounts for the variable compositions of most of these compounds. Part of the structure is depicted in Fig. 5. The A coordination is a distorted cube, the size and degree of distortion depending on the amount of tipping of the B octahedra. Many pyrochlores show deviations from the/42 206(0,OH,F) stoichiometry, some of which are probably defect structures that result from charge balance effects and coupled substi-... 

Impurity atoms can form solid solutions in ceramic materials much as they do in metals. Solid solutions of both substitutional and interstitial types are possible. For an interstitial, the ionic radius of the impurity must be relatively small in comparison to the anion. Because there are both anions and cations, a substitutional impurity substitutes for the host ion to which it is most similar in an electrical sense If the impurity atom normally forms a cation in a ceramic material, it most probably will substitute for a host cation. For example, in sodium chloride, impurity Ca and ions would most likely substitute for Na and Cl ions, respectively. Schematic representations for cation and anion substitutional as well as interstitial impurities are shown in Figure 12.21. To achieve any appreciable sohd solubility of substituting impmity atoms, the ionic size and charge must be very nearly the same as those of one of the host ions. For an impurity ion having a charge different from that of the host ion for which it substitutes, the crystal must compensate for this difference in charge so that electroneutrality is maintained with the solid. One way this is accomplished is by the formation of lattice defects—vacancies or interstitials of both ion types, as discussed previously. 

The size effect of the engineering properties of material is connected with the probability of meeting the most critical defect, which is obviously increased by the increase of structural size [2]. 

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