Lorentz-polarization factor table

Derivation of the Structure.—The observed intensities reported by Ludi et al. for the silver salt have been converted to / -values by dividing by the multiplicity of the form or pair of forms and the Lorentz and polarization factors (Table 1). With these / -values we have calculated the section z = 0 of the Patterson function. Maxima are found at the positions y2 0, 0 1/2, and 1/21/2. These maxima represent the silver-silver vectors, and require that silver atoms lie at or near the positions l/2 0 2,0 y2 z, V2 V2 z. The section z = l/2 of the Patterson function also shows pronounced maxima at l/2 0,0 y2, and y2 x/2, with no maximum in the neighborhood of y6 ys. These maxima are to be attributed to the silver-cobalt vectors, and they require that the cobalt atom lie at the position 0 0 0, if z for the silver atoms is assigned the value /. Thus the Patterson section for z = /2 eliminates the structure proposed by Ludi et al. 

The overall intensities of the peaks are related to the abundance of each phase in the sample. For each phase, the relative intensities may be determined by the calculation of structure factors, multiplicity factors, preferred orientation, and Lorentz/polarization factors. The latter two are normally tabled as a function of the scattering angle. The atomic arrangement within the cell also influences individual peak intensities via structure factor. 

To separate the ciystalline peak only, the background and non-ciystalline scattering should be subtracted. The shape of the peak can be corrected using the correction coefficient, K(0), which includes the Lorentz-polarization factor and initial intensity of the X-ray beam. Finally, averaged sizes and standard deviation are calculated. Comparative results of the calculation of the crystallite sizes using Scherrer s and updated equations are shown in Table 7.3. 

Observed and calculated intensities of reflections on two oscillation photographs, one of which is reproduced in Fig. 5, are given in Table III. The first number below each set of indices (hkl) is the visually estimated observed intensity, and the second the intensity calculated by the usual Bade-methode formula with the use of the Pauling-Sherman /0-values1), the Lorentz and polarization factors being included and the temperature factor omitted. No correction for position on the film has been made. It is seen that the agreement is satisfactory for most of the... 

Table G Definitions of the Electric Field E, the (Di)electric Polarization P, the Electric Displacement D, the Magnetic Field H, the Magnetization M, the Magnetic induction or flux density B, statement of the Maxwell equations, and of the Lorentz Force Equation in Various Systems of Units rat. = rationalized (no 477-), unrat. = the explicit factor 477- is used in the definition of dielectric polarization and magnetization c = speed of light) (using SI values for e, me, h, c) [J.D. Jackson, Classical Electrodynamics, 3rd edition, Wiley, New York, 1999.]. For Hartree atomic u nits of mag netism, two conventions exist (1) the "Gauss" or wave convention, which requires that E and H have the same magnitude for electromagnetic waves in vacuo (2) the Lorentz convention, which derives the magnetic field from the Lorentz force equation the ratio between these two sets of units is the Sommerfeld fine-structure constant a = 1/137.0359895...

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