Absorption Corrections

Absorption Correction. The absorption correction factor (ACF) is the ratio of the effective sensitivity factor kAB to the true sensitivity factor kAB, and is given by  

In this expression, n/p] pec is the mass absorption coefficient of X-rays from element A in the specimen, a is the detector take-off angle, p is the density of the specimen 

Because the sample density and the values of p/p vary with the composition of the specimen, the complete absorption correction procedure is an iterative process. 

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CutshallNH, Larsen IL, Olsen CR. 1983. Direct analysis of 210Pb in sediment samples Self absorption corrections. Nucl Instrum Methods 206 309. 

International or in-house standards in combination with fundamental parameters software, lead to the same accuracy as conventional analysis using regression analysis of standards. Provided that accurate standards are available, the main factors that determine the accuracy of XRF are the matrix absorption correction and (in the case of EDXRF) the spectrum evaluation programme, i.e. correction for spectral overlap and background. 

Absorption Corrections. If T is the intensity of a collimated X-ray beam of initial intensity 7, after passing through a thickness x of material of density p, the... 

The denominator in this equation represents the area under the curve of Figure 5.12 and serves to normalise the expression, so that f(x) —> 1 as x 0- The absorption correction factor Ea is equal to 1 //(%). 

No absorption corrections were carried out. The correction for TDS was evaluated using TDSCOR [8]. Elastic constants were taken from Hallberg and Hanson [9]. 

These values were used to correct the intensities for nine representative data sets, organic crystals, organometallics and minerals, and the data compared with respect to systematic absences and space group assignment (i) with no corrections to the data, (ii) with an absorption correction (SADABS [9]), (iii) with only 1/2 correction, and (iv) with both absorption and X/2 correction. Analogously four different refinements per sample were carried out based on F2. 

The unit cell (Table 1) and orientation matrix were determined from the XYZ centroids of 8192 reflections with I > 20c(7). The intensities (SAINT [8]) were corrected for beam inhomogeneity and decay, and the esd s adjusted using SADABS [9]. An absorption correction was applied (Tmin 0.949, Tmsx 0.983) and symmetry and multiply measured reflections averaged with SORTAV [10]. 

Data collection Diffractometer Data collection method Absorption correction... 

De Titta, G. (1985) An absorption correction program for crystals enclosed in capillaries with trapped mother liquor, J. Appl. Cryst., 18, 75-79. 

Complex Anisotropy is studied in texture goniometers (p. 193) as a function of sample orientation. If the study is aiming at quantitative analysis of scattering data, the absorption correction may become an issue. Conversely, by choosing a special kind of scanning modus (e.g., symmetrical reflection SAXS SRSAXS), the absorption correction problem can be simplified. 

When reflection geometries are set up in modern scattering applications to study the structure of thin layers, the simplifying assumption of infinite sample thickness is not allowed, and the absorption correction becomes more difficult. Moreover, symmetrical-reflection geometry is utilized less frequently than asymmetrical-reflection geometry with fixed incident angle. Thus both cases are of practical interest. 

Special care has to be taken concerning data pre-evaluation if the scattering of highly oriented nanostructures are investigated in symmetrical reflection or at grazing incidence. Absorption correction is delicate (cf. Sect. 7.6.3). Even a refraction correction (Sect. 7.6.5) may be necessary118. 

Crystal data and parameters of the data collection (at -173°, 50 < 20 < 450) are shown in Table I. A data set collected on a parallelopiped of dimensions 0.09 x 0.18 x 0.55 mm yielded the molecular structure with little difficulty using direct methods and Fourier techniques. Full matrix refinement using isotropic thermal parameters converged to R = 0.I7. Attempts to use anisotropic thermal parameters, both with and without an absorption correction, yielded non-positive-definite thermal parameters for over half of the atoms and the residual remained at ca. 0.15. 

Characteristic fluorescence of x-rays of one element by the x-rays from another element in the specimen also can lead to errors in certain cases, e.g., CrK in an iron alloy. Although at times significant, this correction is usually much smaller than the absorption correction. The general formulation of the characteristic fluorescence correction factor is[12] ... 

An example is provided by the work of Valtasaari39 on solutions of cellulose in the coloured complex solvent FeTNa, which necessitates this correction even though the transmittance maximum of this solvent lies conveniently at X0 = 546 nm. In the absence of an absorption correction the molecular weight obtained will be lower than its true value. 

It can be seen that calculation of the absorption correction also needs the values of the sample density and the linear value of the absorption path length beside the mass absorption coefficients. It is also important to note that it is the difference of the absorption coefficients, what coimts in determining if the thin film criterion is fulfilled for a given sample (geometry). It frequently happens that the sample is thin for one pair of its components and thick if another pair of elements is considered from its components. 

An absorption correction was applied which resulted in transmission factors ranging from 0.891 to 0.991. Reflections with 20 < 50 were used for structure solution and refinement. 

In [59] the authors reported the structure of a tri-osmium complex containing a hydride and clearly stated that a low temperature X-ray diffraction experiment would not be useful to locate the hydride if an accurate absorption correction is not carried out. Curiously, a few years before they had contacted Prof A. Sironi and myself at the University of Milan proposing a low temperature data collection on that compound, with the purpose of locating the not so clearly visible hydride. As evident from [59], we were able to convince them on the real problems connected with the location of hydrogens close to heavy metals. 

In the diffraction experiment, Fhkl is available from the measured (and eventually absorption corrected) intensity of a reflection, Ihkt, according to equation 6, where L and p are geometric correction terms related to the diffraction experiment ... 

Before this information can be used, the data set has to undergo some routine corrections, this process is known as data reduction. The Lorentz correction, L, relates to the geometry of the collection mode the polarization correction, p, allows for the fact that the nonpolarized X-ray beam, may become partly polarized on reflection, and an absorption correction is often applied to data, particularly for inorganic structures, because the heavier atoms absorb some of the X-ray beam, rather than just scatter it. Corrections can also be made for anomalous dispersion, which affects the scattering power of an atom when the wavelength of the incident X-ray is close to its absorption edge. These corrections are applied to the scattering factor, 4 of the atom. 

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