Best-Value Lattice Parameters

The availability of eaqperlmental cold, clean, green lattice parameters for a lattice almost identical to the N lattice makes It possible to normalize tdieoretleal methods and determine best values for the lattice parameters cf the actual II lattice. Feat . s such as process tube differences, graphite purity differences, hellum-vs.-air atmosphere, cross-cooling tubes, 

TABia 2.6.1 - A CX)MPARlSQiy OF DlMmSIOHS AKD OTHER PHTSIGAL PROPBRPIBS H-UTTICE8 V3. BXEBRIMEnrEAX MOCKUP IA ETICBS 

Cladding used In. experimenis vas noi Ponded io fuel elements theses are 0 D or I D of clad uhlchever Is alpproprlate Luclte spacers vere used vhlch effectively moch up vater. 

Best Yalna Cold Cleaa Sreen lattice Parameters Parameter Value 

The agreement vlth experimental values is good except for, ubere the differeiwb lies in the definition of The derivation of dr from the measurement of f is base m the older definition of vhioh is the nuefber of neutrons vhioh slow down the Vr fission threshold for each neutron produced by thermal fission (See Reference 12). An average for the RPR startup element is 0.067. 

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The values used for e n, lattice parameters for argon and xenon at 0° K. The values of the parameters used in the calculation are listed in Table I. The potential functions which were obtained when these parameters were substituted in Equation 4.1 are shown in Figures 2 and 3. The potential energy at z — zm is plotted as a function of x (or y), the displacement of an adsorbed atom from the site center parallel to a site edge. It was found that the best simple representation of eT in the neighborhood of a site center on a face-centered cubic crystal is... 

For reasons to be discussed in Chap. 11, the observed values of sin 6 always contain small systematic errors. These errors are not large enough to cause any difficulty in indexing patterns of cubic crystals, but they can seriously interfere with the determination of some noncubic structures. The best method of removing such errors from the data is to calibrate the camera or diffractometer with a substance of known lattice parameter, mixed with the unknown. The difference between the observed and calculated values of sin 6 for the standard substance gives the error in sin 9, and this error can be plotted as a function of the observed values of sin 6. Figure 10-1 shows a correction curve of this kind, obtained with a particular specimen and a particular Debye-Scherrer camera. The errors represented by the ordinates of such a curve can then be applied to each of the observed values of sin 0 for the diffraction lines of the unknown substance. For the particular determination represented by Fig. 10-1, the errors shown are to be subtracted from the observed values. 

To compare the experimental lattice parameter more conveniently with the quantum-mechanical and also the classically derived ones, these are all found together in Table 3.1. Indeed, all of them agree, with respect to the [NaCl]-type lattice parameter, to lie around 4.81 A. The best value is the one derived from the empirical ionic radii but it may be argued that the latter data were, in fact, fitted to match the experimental crystal-structure results. The GGA result further allows us to estimate the classical predictions for the h)q5othetical lattice parameters of the [ZnS]/[CsCl] types, and here the fit is acceptable, too, for [ZnS] (fl 5.2 A) and [CsCl] a 3.0 A), with the only exception for the volume-increment method, in particular the [ZnS] entry. Obviously, we have already gone beyond the limits of this simplistic method and will therefore not consider it any further for the present system. 

An important, but subtle, factor influencing the B-values of the MAX phases is their stoichiometry, and more specifically their vacancy concentrations. This effect is best seen in the B-values of Ti2AlN, where theory and experiment show a decrease in lattice parameters as C is substituted for by N. Given that the lattice parameters shrink, it is not surprising that theory predicts that this substitution should increase the B-value, when, in fact, experimentally it decreases with increasing N-content [42]. This paradox is resolved when it is appreciated that B is a strong function of vacancies, and that the addition of N results in the formation of vacancies on the A1 and/or N sites. As discussed below, the presence of these defects also influence other properties [43, 44]. 

The crystallographic data for the five cerium allotropic phases are summarized in table 4.2. The lattice parameters listed are those we feel are the best values for each of the five allotropes taking into account the chemical and phase purities of the samples and the X-ray techniques employed. The metallic radii and atomic volumes were calculated from the lattice parameters and thus correspond to the conditions given in table 4.2. 

When calculating the lattice parameter, the diffraction peak data Kai and Ka2 of the sample should be separated first, and then peak values can be calculated by parabola function fitting method. As the accuracy of the determination of lattice parameters is determined by the precision of the angle measured, so in order to enhance the accuracy when reading value of angles and to avoid errors caused by human factors, as shown in Fig. 7.26, in the vicinity of peak 20m, 10 to 15 data of diffraction intensity are collected, with parabola equation fitting near the peak intensity distribution curve by the least square method to obtain the best 20 peak value. With known lattice parameters of the silica powder and sample together, the test results are obtained under the same condition to establish curve correction. 

W to S, and the lattice parameter Z are all that are required for obtaining the full dependence of the preferential solvation of P on the solvent composition x (i) = /(Xs). The lattice parameter Z, in turn, is obtained from fitting the curve. Setting the variables P = I -exp -e Jk T) and Q = -Ax y yields the value of Z that fits best the excess Gibbs energy of mixing curve [68] ... 

BEST VALUE COLD. aSAN. GREEN LATTICE PARAMETERS ... 

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