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Lorentz-polarization factor

The Lorentz factor takes into account two different geometrical effects and it has two components. The first is owing to finite size of reciprocal lattice points and finite thickness of the Ewald s sphere, and the second is due to variable radii of the Debye rings. Both components are functions of 0. [Pg.190]

The polarization factor arises from partial polarization of the electromagnetic wave after scattering. Considering the orientation of the electric vector, the partially polarized beam can be represented by two components one has its amplitude parallel (Ay) to the goniometer axis and another has the amplitude perpendicular (Ax) to the same axis. The diffracted intensity is proportional to the square of the amplitude and the two projections of the partially polarized beam on the diffracted wavevector are proportional to 1 for (A ) and cos 20 for (Ax). Thus, partial polarization after scattering yields the following overall factor (also see Thomson equation in the footnote on page 140)  [Pg.191]

When a monochromator is employed, it introduces additional polarization, which is accounted as  [Pg.191]

The Lorentz and polarization contributions to the scattered intensity are nearly always combined together in a single Lorentz-polarization factor, which in the case when no monochromator is employed is given as  [Pg.191]


Hall and Pass used a rather different method (8), whereby the intensity was measured on a 25pm lattice of points covering the entire area of a reflection. From this an intensity contour map of the reflection was created and its total intensity determined by measuring the area within each contour line, multiplying this area by the intensity difference between adjacent contours, and summing these products for all contour areas within the boundary of the reflection. The measured intensity was corrected by application of the value at the centre of the reflection of the Lorentz-polarization factor. [Pg.338]

The factors that are included when calculating the intensity of a powder diffraction peak in a Bragg-Brentano geometry for a pure sample, composed of three-dimensional crystallites with a parallelepiped form, are the structure factor Fhkl 2=l/ TS )l2, the multiplicity factor, mm, the Lorentz polarization factor, LP(0), the absorption factor, A, the temperature factor, D(0), and the particle-size broadening factor, Bp(0). Then, the line intensity of a powder x-ray diffraction pattern is given by [20-22,24-26]... [Pg.38]

Figure 2.47. Lorentz-polarization factor as a function of Bragg angle the solid line represents calculation using Eq. 2.70 (no monochromator), and the dash-dotted line is calculated assuming graphite monochromator and Cu Ka radiation with K = 0.5 (Eq. 2.71). Figure 2.47. Lorentz-polarization factor as a function of Bragg angle the solid line represents calculation using Eq. 2.70 (no monochromator), and the dash-dotted line is calculated assuming graphite monochromator and Cu Ka radiation with K = 0.5 (Eq. 2.71).
Intensity gain due to Lorentz-polarization factor (see Chapter 2, section 2.10.4) is partially offset by the requirement of reduced divergence slit opening (see sections 3.5,3 and 3.6.3), provided all other things remain constant, including the brightness of the incident beam. [Pg.325]

This in turn is combined with the polarization factor + cos 26) of Sec. 4-2 to give the combined Lorentz-polarization factor which, with a constant factor of i omitted, is given by... [Pg.131]

In this case, A = 1.542 A (Cu Ka) and a = 3.615 A (lattice parameter of copper). Therefore, multiplication of the integers in column 3 by A /4o = 0.0455 gives the values of sin 6 listed in column 4. In this and similar calculations, three-figure accuracy is ample. Column 6 Needed to determine the Lorentz-polarization factor and (sin 0)/A. [Pg.141]

The agreement obtained here between observed and calculated intensities is satisfactory. Note how the value of the multiplicity p exerts a strong control over the line intensity. The values of F and of the Lorentz-polarization factor vary smoothly with 6, but the values ofp, and therefore of /, vary quite irregularly. [Pg.142]

The use of a monochromator produces a change in the relative intensities of the beams diffracted by the specimen. Equation (4-19), for example, was derived for the completely unpolarized incident beam obtained from the x-ray tube. Any beam diffracted by a crystal, however, becomes partially polarized by the diffraction process itself, which means that the beam from a crystal monochromator is partially polarized before it reaches the specimen. Under these circumstances, the usual polarization factor (1 - - cos 26)12, which is included in Eqs. (4-19) through (4-21), must be replaced by the factor (1 + cos 2a cos 20)/(l -I- cos 2a), where 2a is the diffraction angle in the monochromator (Fig. 6-16). Since the denominator in this expression is independent of 6, it may be omitted the combined Lorentz-polarization factor for crystal-monochromated radiation is therefore (1 + cos 2a cos 20)/sin 6 cos 6. This factor may be substituted into Eqs. (4-19) and (4-20), although a monochromator is not often used with a Debye-Scherrer camera, or into Eq. (4-21), when a monochromator is used with a diffractometer (Sec. 7-13). But note that Eq. (4-20) does not apply to the focusing cameras of the next section. [Pg.183]

We have already seen that the intensity of a superlattice line from an ordered solid solution is much lower than that of a fundamental line. Will it ever be so low that the line cannot be detected We can make an approximate estimate by ignoring the variation in multiplicity factor and Lorentz-polarization factor from line to line, and assuming that the relative integrated intensities of a superlattice and fundamental line are given by their relative F values. For fully ordered AuCus, for example, we find from Eqs. (13-1) that... [Pg.391]

Usually not taken into account is the variation of the structure factor due to the variation of the diffusion factor (X-ray), or of the Lorentz-polarization factor. [Pg.152]

The term X /sin 20 is referred to as the Lorentz factor, the Lorentz-polarization factor, which is the product of the two previous expressions, is also commonly used. [Pg.37]

Lp is the Lorentz polarization factor, A and E are absorption and extinction factors, and IF /1 the absolute magnitude of the structure factor. The sign or phase of the structure factor, a /, is not directly determinable from the diffraction experiment. [Pg.168]

Structure factors were computed for all crystallographic planes possible, and the values thus obtained (with the exception of those for the meridional reflections) were then corrected for multiplicity and for the Lorentz polarization factor, in the usual maimer,in order to obtain the calculated intensities for all reflections. The meridional reflections were not used, as the Lorentz factor does not apply to them, and, in general, the meridional intensities found experimentally are unreliable. [Pg.453]

The Debye function and the Lorentz polarization factor were calculated on a Razdan computer. [Pg.37]

To determine the coordinates of these atoms, the intensities of about 300 structurally independent reflections of the hkO and Okf type were measured and anal3 ed. The reflection intensity was measured by the ionization method. The measurements were made on a spherical crystal of 0.51-mm diameter. The spherical shape was obtained by rolling [6]. Corrections were made for the absorption and for the Lorentz-polarization factor. [Pg.4]

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. [Pg.217]

To correct the diffractogram, the total intensity at the angle 20 is divided into the correction coefficient, K 9 ), that includes the Lorentz-polarization factor (LP] and initial intensity of the X-ray beam J -. [Pg.207]

The intensities are first converted to structure factor amplitudes by correcting for absorption, Lorentz-polarization factors, and multiplicity. In general the structure factors are complex, but only the amplitude can be measured experimentally, and not the phase angle. The so-called phase problem has prevented X-ray crystallography from becoming a routine procedure, although the development of powerful analytic techniques makes this less true now than in the past. [Pg.460]

The angular factor 0 represents a combination of the Lorentz polarization factor and the geometrical factor, and its mathematical form depends on the experimental technique that is used. For reflections given by a small single crystal or by one face of a large crystal, the factor has the form... [Pg.272]


See other pages where Lorentz-polarization factor is mentioned: [Pg.24]    [Pg.125]    [Pg.293]    [Pg.553]    [Pg.94]    [Pg.190]    [Pg.192]    [Pg.325]    [Pg.131]    [Pg.131]    [Pg.139]    [Pg.396]    [Pg.479]    [Pg.524]    [Pg.67]    [Pg.389]    [Pg.101]    [Pg.241]   
See also in sourсe #XX -- [ Pg.191 , Pg.192 ]

See also in sourсe #XX -- [ Pg.131 ]

See also in sourсe #XX -- [ Pg.66 ]




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