Defects fraction

We refer the actual defect fraction to the equilibrium value as a reference state by setting Nj = Nv = N° + <5. Equation (1.6) then reads... 

Figure 2-1. Point defect fractions Nd and nonstoichiometry S for A, <5X at given P and T (Kroeger-Vink diagram) a) as a function of the X component chemical potential, b) the same information in form of a titration curve .

To be more specific, consider an ionic crystal with the following characteristics a, = 10 6(Qcm)-1 D,= l0 6cm2/s Em = 20cm3 e=10 7"=1000K. These numbers lead to a bulk point defect fraction Nj = 10 5 and a Debye length LD of 80 A. If an interface is formed inside the crystal, the necessary charge transfer per... 

We mentioned before that not all fast ionic conductors possessing a large fraction of disordered ions arrive at the disordered state via a phase transformation. SrF2, BaF2, and, in particular, FbF2 are increasingly disordered in the anionic sublattice. The defect fraction amounts to 10%, 20%, and 40% respectively at 700 K [M.H. Dickens, et al. (1980)]. In a strict and systematic sense, this type of disorder is not... 

The -terms refer to differential defect fractions defined via the corresponding conservative ensembles according to... 

To take an example, suppose that in our first sample of 1000 there were 100 defectives (fraction defective 10%) and in the second sample of 500 there were 60 defectives (fraction defective 12%). Are we justified in taking it as reasonably certain that the populations represented by these two samples are different ... 

At thennal equilibrium, the defect fraction, , in a perfect crystal is given by a Boltzmann relationship ... 

The fuel failure and fission product release rates at the upper 95 percent bound are determined by a full-core propagation-of-errors analysis comparable to that described in Reference 11. The uncertainties in the as-manufactured fuel attributes (e.g., defect fractions as defined in Table 4.2-4), the core operating conditions, the fuel failure models, and the fission product transport properties are combined by conventional statistical techniques to determine the total variances in the fuel failure and fission product release rates from which the upper 95 percent bound values can be calculated. 

FIGURE 13.4 Mass defect [fractional mass change (fine)] consequent upon a typical... 

Tantalum ( Ta) (7=7/2). The perturbed angular correlation (PAC) spectroscopy was used to measure the electric quadrupole interactions (QIs) of the nuclear probes Ta and Cd in Hf02 and Zr02 as a function of temperature and a hydrate surface layer with a H content of 5-10% was detected by MAS NMR. A defect component involving 30-40% of the probe nuclei appears in the Ta PAC spectra by cooling from T> 1200 K. It was found that the temperature dependence of the Ta defect fraction is consistent with a Ta impurity level at Ed 0.9 and 0.6 eV below the hafnia and zirconia conduction band, respectively. 

Equation (10.9) predicts that the equilibrium defect fraction n/N) increases exponentially with increasing temperature. The defect fraction profile given by eq. (10.9) is shown in Figure 10.4 for several values of the enthalpy change. Observe that n/N is strongly dependent on the temperature above 800°C for selected values of the enthalpy change (AHf). 

Figure 10.5 Theoretical profiles for the defect fraction in solid crystals.

Alloy Composition (mass fraction %) Defect Fraction ... 

Comparison made between the observed defect fraction and a prediction based on a linear equation for defect fraction as a function of composition. 

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