Accuracy of structure determination

Before proceeding with a discussion of bond lengths and related details, it is essential to consider the inherent accuracies of structure determinations. In the usual X-ray diffraction experiment the scattering power of... 

The accuracy of experimentally determined structure factors is limited by various error sources, which may be introduced by the experimental method itself or during the data reduction stage. A reduction of those errors is expected by the use of high-energy synchrotron radiation (E(/ ) > 100 keV) as primary beam source, because absorption and extinction corrections are negligible in most practical cases. 

The EXAFS, which occurs at higher energies above the edge, is due to the interference between the outgoing and the backscattered photoelectron waves (10-14). EXAFS provides information about the local structure of the x-ray absorbing atom. Typically, nearest neighbor bond lengths and coordination numbers can be determined to 0.02 A (1%) and one atom in four (25%) (4 ). The accuracy of these determinations is somewhat worse for outer-shell atoms, for disordered systems, or for systems with asymmetric distributions of atoms within a shell (15,16). 

The difference in the two values is surprisingly large and is well within the accuracy of density determinations. The experimental value is in accord with a model that assumes vacancies on the iron positions, as are all results in Table 1.1, indicating that a formula Fe in which there are vacancies at some of the Fe positions, better reflects the structure. 

The relative retention a=k/ki is a measure of the separation selectivity for two compounds i and j with retention factors ki and kj, respectively, differing by one repeat structural unit, An=l.p in Equation 5.16 is the end-group contribution to the retention factor. The conventional theory describes adequately the retention of oligomers and lower homopolymers and copolymers up to the molar masses 10,000-30,000Da for higher polymers the accuracy of the determination of retention model parameters is too low [95]. 

In principle any physical constant may be useful for structural analysis of mixtures. For practical reasons those constants should be applied that can be easily determined. High demands should be made upon the accuracy of the determinations. For example the physical constants density, refractive index, kinematic viscosity, ultrasonic sound velocity and surface tension may be chosen. Combination of constants, e.g. in certain additive functions, is useful only when the constants in question have been determined with comparable accuracy. In this respect density and refractive index may be combined, whereas molecular weight, the determination of which is not so precise, cannot always be combined with refractive index and density. 

It should be pointed out that this method for ring analysis and branching analysis is based exclusively on reliable data of n, d, M and a of pure individual hydrocarbons, and holds, within the limits of accuracy of the determination, for widely differing types of branched as well as non-branched saturated hydrocarbon mixtures. It is particularly recommended for the structural analysis of saturated polymers, where other statistical methods (w- -M-method, v-n-d-method, etc.) fail because they have been developed for mineral oils, and are based on correlations of physical data of mineral oil fractions that always show approximately the same small degree of branching 1-2 branchings per molecular weight = 100. 

Very few complete investigations have as yet been carried out under such ideal conditions. There is therefore great scope for the future improvement of accuracy in structure determination. It is to be... 

The accuracy of structural parameters extracted from EXAFS depends on many factors such as the disorder, the extension of the experimental spectra and quality of these data. Typical accuracies for the determination of parameters are 1% for interatomic distances, 15% for the coordination numbers and 20% for Debye-Waller factors [6], But, in a situation more complex where several shells must be fitted simultaneously, one must be satisfied with much less accurate results. 

The oil phase, Soltrol 130, a refined kerosene, was doped with iodated oils of similar molecular structure. The dopants are strong photoelectric absorbers and increase the accuracy of saturation determination by increasing the X-ray attenuation. The refined, nearly single-component, oil was also used to insure complete first-contact miscibility. Because this is a single-component oil, multiple contact developed miscibility is not observed below the miscibility pressure. 

A caveat for relaxation matrix cedculations is that they may not sigi cantly reduce errors of structure determination because of the usual assumption of a single correlation time and lack of any motional averaging. The precision and accuracy of structures so determined are always limited by the approximations used in data analysis. 

Observation of spectra over a temperature range from —100 to +200 °C can be achieved in many laboratories with no impairment in accuracy of frequency determination. Assignment of subspectra in the low-temperature limit to structures suffers from the difficulties already discussed. 

The other alternative that can be used to obtain a structure from just three moments of inertia is that if the structure contains relatively few atoms, and hence relatively few coordinates to be determined, and if some parts of the geometry of the molecule are already known, or can be assumed from some other available information involving similar molecules, then the part of the structure that is not known can be determined (as long as only three pieces of data are required). This method usually contains considerable uncertainty because one is never quite sure just how accurately part of the structure can be transferred from another molecule. So the result is that the microwave method gives moments of inertia very accurately. However, one must make assumptions and approximations if one is going to determine a real molecular structure by this method. For this reason, the simultaneous use of microwave and electron diffraction data is most useful because if one can fit both of these kinds of data at the same time, one can normally increase very much the reliability and accuracy of the determination. 

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