Independent reflections

Physically the independence reflects the fact that dephasing is performed by weak long-range interactions, and rotational relaxation results mainly from short-range, repulsive forces. In other words the rotational state is changed solely when the distance between molecules becomes rather short, while the phase is frustrated in all cases and the contribution of frontal collisions is not so significant. 

A 3D potential map was calculated from the 144 independent reflections by inverse Fourier transformation (Figure 4)[9]. All 24 unique Si positions but no oxygens could be determined directly from the peaks in this 3D potential map. 

All six unit cell parameters of a lattice can be obtained from these two equations (lO)-(ll) by measuring the Dm and Buk values of at least three independent reflections with known Miller indices, all with different h and k and, at least one of which with / 0 in order to calculate c. ... 

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. 

After merging of the single zones, data sets of approx. 100-300 independent reflections can be obtained as described in chapter 2.5. In a first step a kinematical structure refinement should be performed using the program SHELXL [13]. The temperature factors for FAPPO were chosen as U = 0.06 for C, N and O as U = 0.10 for H atoms apart from H atoms situated at N with U = 0.12 A (Electron scattering factors [20]). To prevent the molecules from being distorted a refinement, where the whole molecule was kept rigid, was performed. This also improves the usually bad parameter/reflection ratio. In the case of modification I we obtained R-values of 31% (481 unique reflections with I > 2cr) for the 100 kV data and of 25% (385 unique reflections with I > 2a). The sparse 100 kV data of modification II was not analysed quantitatively. From 300 kV data we obtained an R-value of 23% (226 unique reflections with I > 2a). 

First of all, we analyzed the 2-dimensional structure projected on the ab-plane in order to confirm the result of the analysis by electron diffraction. The 17 independent reflections on the equator were used (R=35%, B=0.075nm (isotropic)). The molecular conformation of the p-form was adopted because it lowered R. The mutual positions and orientations of molecular chains are almost identical to those analyzed by electron diffraction. In the 3-dimensional analysis, therefore, this structure in the aft-plane projection was basically fixed. 

Fig. 4. CTF curve calculated with U = 200 kV Cj = 0.5 mm, 0=10 nm corresponding to experimental images figure 4e. Seven independent reflections are expressed as vertical bars with the length proportional to the amplitude values.

The intensity data, uncorrected for absorption, were measured on a fully automated Hilger-Watts diffractometer (Ni-filtered Cu-A"2 radiation, 0-20 scans pulse-height discrimination) using a crystal of dimensions ca. 0.08 x 0.20 x 0.6 mm grown from methanol. Of 1763 independent reflections for 0 < 57°, 1518 were considered to be observed [7> 2.5o(7)]. The structure and relative stereochemistry of... 

Hirschfeld13t 132) has generated the algorithms which are necessary to use IRS to determine the optical constants of a sample from a pair of independent reflectivity measurements at each frequency. The optimum method is to determine the total reflectance at two polarizations at the same incidence angle. 

Each of the viscoelastic parameters G°, rj0, and Je° has associated with it a characteristic molecular weight which either measures an equivalent spacing of entanglement couples along the chain (Me, deduced from G with the kinetic theory of rubber elasticity), or marks the onset of behavior attributed to the presence of entanglements (Mc and AT, deduced from r/0 and Je° as functions of molecular weight). Table 5.2 lists Me, Mc, and M c for several polymers. Aside from certain difficulties in their evaluation, each is a rather direct and independent reflection of experimental fact. 

If the improper axis is of even order and [Pg.35]

Completeness to 9 = 30.22° Reflections collected Independent reflections Reflections with F2 > 2a Absorption correction Min. and max. transmission Structure solution Refinement method Weighting parameters a,b D ata/re straints/parameters Final R indices [F2 > 2a]... 

DM is easiest to explain for centrosymmetric crystals, for which all phase factors exp [IniQiXj + ky + Izj)] must be equal, individually, to either +1 or —1 that is, the only phase choice is which F i has a positive sign and which has a negative sign. Since a typical crystal structure is determined from about 2000 independent reflections (hkdobs and there may be 30 atoms to be found [for each, three positional parameters x , y , z and the six unique components of the second-rank thermal vibration tensor (thermal parameters) /irl, [122, P33, 12, P23, 31, i-e., a total of 30 x (3+6) = 270 parameters], the problem is overdetermined, by a comfortable ratio of 2000/270. It also uses the physical... 

Reflections collected Independent reflections Rl, WR2U > 2cr(/)] All data... 

The problem is that, in many cases for many systems, there may simply be no such thing as a truly independent variable. Out here in the real world, the phrase "independent" may often be oxymoronic. The very notion of independence reflects the world of Platonic idealism, a pure world populated by separate discrete things each with its essence, floating suspended in a sea of laws, rules governing the relations between these autonomous entities. 

E.g. analytical, numerical, empirical via -scans max. and min. transmission factors T must be specified, 0 < Tmin < Tmax < 1 Total number of measured reflections no of unique (independent) reflections after merging symmetrical equivalents no of observed reflections and the criterion for observed e.g 6896 measured refls., 4323 unique, 2544 observed refls. with I > 2a (/) ... 

Suitable small crystals of 2XeF,AsF, were obtained by sublimation under nitrogen (at atmos.) in sealed quartz AT-ray capillaries. A tablet measuring <01 mm. in any dimension was used for the intensity data. The crystals are monoclinic with unit-cell dimensions a = 16-443, b = 8-678, c = 20-888 A, )S = 90-13°, V = 2799 A -The space group is 12/a, and Z 12 Three-dimensional data, amounting to 1182 non-zero independent reflections, were obtained. Two xenon and one arsenic atoms were located with a three-dimensional Patterson map, and the remaining atomic p>ositions from subsequent electron-density maps. Full-matrix least-squares refinement led to a final conventional R-value of 0-066. 

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