Extinction correction

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. 

Coppens P, Hamilton WC (1970) Anisotropic extinction corrections in the Zachariasen approximation. Acta Crystallogr A 26 71-83... 

It will now be clear that the accuracy that may be attained in crystal analysis depends on the number of observed reflections and on the precision with which their intensities can be measured. (We assume that the structure is not complicated by any randomness or disorder, and that the necessary absorption and extinction corrections can be made.) A very useful discussion of the requirements necessary for determining bond lengths to within a limit of error of 0-01 A has been given by Cruickshank (1960). This is, of course, a very ambitious limit, but if it could be achieved it would enable the predictions of the molecular-orbital and valence-bond theories in aromatic hydrocarbons to be distinguished. It is pointed out that at the 0-1% level of significance a bond length difference must be 3-3 times the standard deviation to be accepted as genuine, so the limit of error of 0-01 A would require an e.s.d. (estimated standard deviation) of 0-003 A or better in the bond difference, or a coordinate e.s.d. of 0-0015 A or better. 

Extinction, which is the failure of the kinematic scattering theory (Ihki hki) is only a minor problem in X-ray diffraction. In neutron diffraction, extinction is serious and pervasive throughout the whole data, as shown by the examples in Thble 3.2. The best methods available for extinction correction require careful measurement of crystal dimensions. Although somewhat empirical, it has proved to be very effective [184, 185]. At least one, and sometimes six, additional extinction parameters, gis0 or gij, have to be added to the variable parameters. Uncertainty in the validity of these extinction parameters appears to have very little effect on atomic positional coordinates, but may influence the absolute values of the atomic temperature factors. This is important in charge density or electrostatic potential... 

If not, incorrect conclusions about magnetic moment reductions and the shapes of form factors may be made. Discussion of the extinction corrections (52) in form factor determinations has recently been given in the case of Tb(OH)s (55) where the intensity of some reflections was reduced by as much as 90%, and K2NaCrFe (22). Because of the small crystal size, extinction has not been observed to be significant in any work with polycrystalline samples, which is one of the principal advantages of the latter technique. Preferred orientation can be a nuisance in powder work (especially with X-rays) but does not appear to have been significant in the experiments discussed below. 

The advantage of using polarized neutrons to determine weak magnetic reflections is clearly apparent. For example, if T =0.01 then the magnetic contribution to the intensity in an unpolarized beam experiment is 0.01 percent, but R Ri 1.04, i.e., there is a 4 percent effect on changing the incident neutron polarization. It is necessary to know the nuclear scattering amplitude accurately if an accurate magnetic amplitude is to be obtained and extinction corrections in particular must be accurately performed. 

Fig. 37. Experimental values for Tb(OH)3 in the ordered state at 2.6K, after making extinction corrections. The broken curve is derived from nonrelativistic free ion wave functions. The solid curve is the best fit to the experimental points and falls directly on the relativistic free ion form factor. All curves are normalized to a magnetic moment of 8.9 jUs/Tb atom [after Ref. (757)]...

Limiting the refinement to the 1207 data for which / > 3a(/) reduced theRto 0.033, An extinction correction of the form Rq =Ro[F0 + e X /] where e = 1.6 X 10" was applied to correct for discrepancies of hi -intensity reflections. This correction resulted in a final R value of 0.029 for the nonzero weighted data. Including zero-weighted data, R was 0.054 for 1945 data, and the standard deviation of an observation of unit weight was 1.09. The final weighted ... 

Finally, as may be established by a trial-and-error approach, a small extinction correction further improves the agreement between the observed... 

In fact, SHELXL is not necessarily right when it suggests the performance of an extinction correction. Other effects can mimic extinction and SHELXL cannot easily distinguish between certain bulk solvent effects and extinction. 

Accuracy of intensity measurement Inadequate too many corrections required Better than Laue Standard method but extinction correction necessary Best photographic method Very accurate few corrections but of limited applicability Fairly good... 

Among 2452 independent reflections in the range 2 <20<7O , 1973 ones with intensities larger than three times their estimated standard deviations (e.s.d. s) were used for the structure analysis Lp-corrected but no absorption and extinction corrections. The crystal data are ... 

Diffraction is controlled by Equation (14) if the kinematic theory is viewed as completely valid (n = 2). and by Equation (16) if the dynamic theory (/i = l) is applied. Normally, neither of these extremes is exactly fulfilled, and there is a combination of both. The kinematic theory is usually adopted, with dynamic contributions being handled by an extinction correction, although this (like the absorption correction) often proves unnecessary for measurements of standard level. 

Fig. 23. Variation of nucleotide content of B. cereua cells with the phase of growth. Curve 1, growth curve (no. of bacteria/ml. = n) 2, extinction at 257 ma 3, extinction corrected for nonspecific absorption 4, dn/n dt. (Malmgren Heden, 1947.)...

Carry out the method exactly as described in Section F paragraphs 1-4 using the 1-, 5-, or 10-cm cells that are appropriate. Add the concentrated ammonium chloride solution to 100 ml of redistilled water in a clean Erlenmeyer flask and use a column previously flushed with at least 50 ml of dilute ammonium chloride solution just before use. The blank extinction corrected by any cell-to-cell blank should not exceed about 0.1 using a 10-cm cell. 

J. H. Lee, Determination of Extinction Corrections in Infrared Analysis of Gaseous Hydrocarbon Mixtures, Anal, Chem. 18, 659, 1946. 

We confirm the presence of an extended or multiple (0.5" size, 0.02pc) object within 0.15" of SgrA. It s integrated flux is K=12 and H=13.9. After extinction correction, but ignoring possible local extinction, it has a blue color and a luminosity of l-5xl0 (Te///35,000 K) L . An identification of... 

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