Weak reflections

These stmctures do not diffract as weH as smaH molecules, and as a result, there are many weak reflections and data coHection takes much longer than for smaH molecules. Also, the solution of the phase problem is more difficult and usuaHy requires the coHection of data sets with monochromatic radiation at several different wavelengths. Because of the much longer data coHection times, area detectors are almost always used. Also because of the long... 

Now (200) gave a very weak reflection, so that S2o must be small. This is true only for ut + =, for which... 

On calculating intensities of reflection for these parameter values, it was found that the general agreement with observation for all except the very weak reflections was excellent, as is shown by the data in Table IV for useful reflections from 45° oscillation photographs from (100) with... 

All intensity values from 5 to 150 are those assigned by Shechtman and Blech2. For most peaks the values of d are calculated from the values of 29 printed on the diffractometer record. The exceptions are the weak reflections 4, 10, 11, 12 and 16. 

Experiments were carried out during several runs of DORIS III (E = 4.5 GeV). The beam size was 1 x 1 mm2, the sample-detector distance was 1200 mm and the detector aperture 9x9 mm2, co stepscans were applied with 1 s per step for the stronger and 3 s per step for the weak reflections. The sample was a sphere of 190 pm diameter. 

Table 1. Flipping ratios of strong and weak reflections obtained using the standard (std) and cyclic (eye) methods (total measurement time of 180 s). As expected, an improvement is observed for the strong reflection. 

Table 2. Flipping ratios of strong and weak reflections measured starting from different time proportions (three steps of 60s). When using the optimised method, the standard deviation c(R) does not depend on the initial conditions. 

The only problem with this method is observed for weak reflections where (+)/(-) count-rates are similar (i.e. R 1). The (+)/(-) optimised counting-time proportions must be 50%/50%, but with low count-rates, we have observed that the lack of precision may lead to proportions which are not optimum (e.g. 47%/53%). The same behaviour has been observed for peak to background proportions. In fact, when measuring a flipping ratio in many steps, we observe oscillations of the time proportions which slow the decrease of the standard deviation. Of course, these time variations have no sense, and one should calculate the variances of the optimised counting-times (Equations (16)) to avoid such spurious fluctuations ... 

There are three types of monochromators in common use, depending on the age and cost of the CAM. Least expensive and easiest to use is the continuous interference filter composed of very thin, alternating layers of strong-reflecting and weakly reflecting materials. These create inter-... 

When the Fe-MnO catalyst is analyzed after use in the Fischer-Tropsch reaction (the synthesis of hydrocarbons from CO and H2), the XRD pattern in Fig. 6.2 reveals that all metallic iron has disappeared. Instead, a number of weak reflections are visible, which are consistent with the presence of iron carbides, as confirmed by Mossbauer spectroscopy [7]. The conversion of iron to carbides under Fischer-Tropsch conditions has been studied by many investigators and has been discussed in more detail in Chapter 5 on Mossbauer spectroscopy. 

Further development of the Flory-Huggins method in direction of taking into account the effects of far interaction, swelling of polymeric ball in good solvents [4, 5], difference of free volumes of polymer and solvent [6, 7] leaded to complication of expression for virial coefficient A and to growth of number of parameters needed for its numerical estimation, but weakly reflected on the possibility of equation (1) to describe the osmotic pressure of polymeric solutions in a wide range of concentrations. 

When the 4 strongest independent reflections (in total 6 reflections including symmetry-related ones) are added, the map already shows some indication of where the atoms should be located within the unit cell (Fig. Ig). After the strongest 1/3 (11) of all the independent reflections has been included, all the atoms appear in the map (as white dots) (Fig. Ih). The map generated from all the 33 unique reflections (Fig. li) is only slightly better, because the 22 reflections further added in are weaker and so do not contribute very much to the Fourier map. The weak reflections are, however, equally important as the strong ones in the last step of a structure determination, the refinement. 

These uncertain atoms remain to be verified by a careful structure refinement. For a structure refinement, as many reflections as possible should be included. The phases are not needed at the refinement stage, but if possible complete 3D data out to 1 A resolution should be used. Strong and weak reflections are equally important. Such data can be obtained by electron diffraction, which is not affected by the contrast transfer function of the electron microscope, but suffers from dynamical scattering. The higher the accuracy of the amplitudes, the more accurate will the atomic positions become. 

The reflections involved in these triplets have i u and iii.u large but l i small. This differs from the other figures of merit in that it establishes a consistency between the amplitudes and phases of the strong reflections with a small set of weak reflections. Correct phase sets usually give a value of To close to unity. 

The true phases of the structure factors will, in general, be different from the phases calculated with the independent-atom model. In centrosymmetric structures, with phases restricted to 0 or n, only very few weak reflections are affected. In acentric structures, only the reflections of centrosymmetric projections, such as the hkO, hOl, and Okl reflections in the space group P212,21, are invariant. 

Asbrink, S. (1980). The crystal structure of and valency distribution in the low-temperature modification of V3O5. The decisive importance of a few very weak reflections in a crystal structure determination. Acta Cryst. B36,1332-9. 

Exposures may be shortened by putting a fluorescent screen behind and in contact with the film, so that the optical fluorescence reinforces the direct X-ray effect on the photographic emulsion or two screens might be used, one in front and one behind the film. (Note that the intensity relations are much changed by the optical fluorescence weak reflections come out relatively much too weak.)... 

The third arc is composed of reflections from 111 planes. The sheets of chlorine ions which define these planes are interleaved by sheets of ammonium ions (Fig. 118) hence, the situation is the same as for 001 waves from the ammonium ions oppose those from the chlorine ions, and a weak reflection is the result. 

For reflections of this type (weak or absent in the observed diffraction pattern, medium or strong in the calculations), there is no doubt about the sign of the discrepancy, and only a small uncertainty in its magnitude, arising from a doubt whether the weak reflection should have the same sign as the calculated value or not however, if the calculated F is +29 and the observed F is 3, the discrepancy is either... 

X-ray diffraction of 114 analcite at 25 °C revealed two weak reflections at d = 3.80 (at 23.4° 20) and 3.24 A (at 27.5 26) indexed as (320) and (411), respectively. These forbidden, weak reflections disappear from the pattern on heating the zeolite above 200° C. Their disappearance correlated closely with the pronounced second-order break in the dehydration curve at 200° C and suggests a randomization of the partially ordered distribution of 16Na+ ions over the 24Na+ sites (Vs, 0, x/4) in the unit cell. At the decomposition temperature, 916° C, the apparent cell edge is 13.69 A. 

This section reviews briefly the results of the preliminary paper. In the early stages of the work, reflections weaker than two times the standard deviation for all reflections (2a) were omitted from Fourier syntheses, because of greater uncertainty in the measurements of weak reflections. Table 8.2 is discussed later. 

The threshold intensity (relative to 100.0) for reporting reflections has been decreased to 0.01. This means that more weak reflections tend to be listed for the high-symmetry structures. If there are too many reflections to list on one page, the intensity threshold is increased so that only the 165 most intense reflections out to 50° 26 are listed. 

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