Intensities of X-ray reflections

A reasonable interpretation can be given to the curve of Fig. 2, with its two discontinuities in slope namely, that there exist ordered phases PbTls and PbTl,. Direct evidence from the intensities of X-ray reflections is not obtained for ordering in this case, because of the approximate equality in / values of lead and thallium. We can, however, discuss the probable structures of the ordered phases. The powder patterns given by these alloys show no splitting of lines. We estimate that the... 

There seem to be many binary metallic systems in which there are phases of this sort. In the sodium-lead system there are two such phases. One of them, based on the ideal structure Na3Pb, extends from 27 to 30 atomic percent lead, with its maximum at about 28 atomic percent lead and the other, corresponding to the ideal composition NaPb3, extends from 68 to 72 atomic percent lead, with maximum at about 70 atomic percent. The intensities of X-ray reflection have verified that in the second of these phases sodium atoms occupy the positions 0, 0, 0, and the other three positions in the unit cell are occupied by lead atoms isomorphously replaced to some extent by sodium atoms (Zintl Harder, 1931). These two phases are interesting in that the ranges of stability do not include the pure compounds Na8Pb and NaPb3. 

Wasserman [186] has described the use of both low-angle X-ray reflectivity and ellipsometry for the determination of thickness of Cio-Cig SAMs prepared on surface silanol groups of silicon plates. Ellipsometry is based on the reflection of polarized light from a sample and depends on the sample s thickness and refractive index. X-ray reflectivity measures the intensity of X-rays reflected from a surface (or interference pattern) that is characteristic of the distance between interfaces. The thickness of the SAMs was consistent with fully extended alkyl chains with all-trans conformations and excellent agreement was observed between the two methods. 

Diffraction symmetry in relation to point-group symmetry. So far, in our consideration of the intensities of X-ray reflections in the process of discovering the general arrangement in a crystal, we hare dealt only with reflections of zero intensity, and we have seen that when certain types of reflections have zero intensity the presence... 

Rubinshtein and associates (67) found that as Pt is dispersed more and more on carbon, the rate of dehydrogenation of cyclohexane parallels the intensity of X-ray reflections from the (111) faces and not from the others. 

It is difficult to obtain sedimentary chlorites of sufficient purity for reliable chemical analyses however, reasonably accurate estimates of chemical composition can often be made from X-ray data. If the difference in scattering power and size of the various atoms in the chlorite species is sufficiently large, the positions and intensities of X-ray reflections are measurably affected. The b and c parameters are the most useful. 

Definition rocking curve (RC) is a function of the total intensity of X-rays reflected by a sample versus its angular position in rotation around the axis perpendicular to the diffraction plane. The sample is adjusted to have diffracting crystallographic planes perpendicular to the diffraction plane. 

Mechanical activation brings to a decrease of the intensity of X-ray reflections of all the phases except quartz. Permanent presence of Si02 phase can be the sequence of its stability to deformations as well as the result of its formation from mechanically decomposed silicates. The initial phase, Si02, serves as a nuclei for its growth from amorphous phases during mechanical activation of silicates. 

An important support of the sextet model was obtained by Rubinstein et al. (209) they found that catalytical activity for dehydrogenation of cyclohexane falls regularly with the decrease of the intensity of X-ray reflections from the (HI) facets of platinum on coal. 

In principle, the absolute measurement of the intensities of x-ray reflections from a crystal is all that is required to determine the electron density distribution within the unit cell, which should provide, in principle, detailed information about the bonds between the atoms. The charge density, a, at any point within the unit cell (volume V) is... 

Now, the problem of determining the crystal structure can be reahzed. As the structure amphtude Fhki can be derived from the measurement of intensity of X-ray reflection, the phase angle hki cannot be directly determined and if these phases of the structure factor are known, then the crystal structure is known as one can compute the electron density from (8.4) and hence the positions of the atoms giving rise to the measured electron densities. Therefore, the lack of knowledge of the phases of the structure factors prevents from directly computing the electron density map and hence determines the positions of the atoms. Patterson suggested as an aid the use of the following equation instead of (8.4) [1,6,7] ... 

Knowing the arrangement of atoms in a crystal, it is easy to calculate the intensity of X-ray reflection. More difficult, however, is the problem of calculating the arrangement of atoms in a crystal from an experimentally measured diffraction picture. This problem is the essence of modem X-ray crystal structure analysis for which M. von Laue (1914) and W.L. and W.H. Bragg (1915) were awarded Nobel Prizes. 

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