Broadening instrumental

Consideration of instrumental broadening is a merely technical issue. The instmmen-tal profile Hj (s) must be measured. It is the shape of any peak of a single crystal of infinite size and perfection. For application in the field of polymers, many inorganic crystals, e.g the common standard LaB6, are very good approximations to the ideal case. 

The effect of instrumental broadening can be eliminated by deconvolution (see p. 38) of the instrumental profile from the measured spectrum. If deconvolution shall be avoided one can make assumptions on the type of both the instrumental profile and of the remnant line profile. In this case the deconvolution can be carried out analytically, and the result is an algebraic relation between the integral breadths of instrumental and ideal peak profile. From such a relation a linearizing plot can be found (e.g., measured peak breadths v. peak position ) in which the instrumental breadth effect can be eliminated (Sect. 8.2.5.8). 

A diffraction line may be broadened as a result of instrumental effects, such as an imperfection in the collimation geometry, the finite width of the detector window, imperfect focusing, less than perfect monochromatization of the incident beam, etc. Suppose that I(s) represents the intensity pattern that could be obtained under an ideal instrumental condition producing no instrumental broadening, and f0bs(s) represents the smeared intensity pattern that is actually observed. The relationship between these two can be expressed in most cases as 

Therefore I(s) can be obtained as the inverse Fourier transform of the ratio J7 70bs (s) / G(s).  

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As previously stated, GPC is the method of choice for studying polymer degradation kinetics. The GPC trace, as given by the detector output, does not provide the true MWD due to various diffusion broadening processes inside the different parts of the equipment. The first step is to correct for instrument broadening if a precise evaluation of MWD is desired. Even with the best columns available, this correction may change the MWD significantly as can be visualized... 

The peak profile analysis techniques allow separating the intrinsic and extrinsic causes producing peak broadening and shift. Accurate peak profile analysis requires the instrumental broadening well characterized and, in general, significantly smaller than the one due to sample defects (size and strain). New high quality X-ray sources and... 

In the simplest approach T is the full width of the peak (measured in radians) subtended by the half maximum intensity (FWHM) corrected for the instrumental broadening. The correction for instrumental broadening is very important and can be omitted only if the instrumental broadening is much less than the FWHM of the studied diffraction profile, which is always the case in presence of small nanoclusters. The integral breadth can be used in order to evaluate the crystallite size. In the case of Gaussian peak shape, it is ... 

In order to properly take into account the instrumental broadening, the function describing the peak shape must be considered. In the case of Lorentzian shape it is Psize = Pexp - instr while for Gaussian shape p = Pl -Pl tr- In the case of pseudo-Voigt function, Gaussian and Lorentzian contributions must be treated separately [39]. 

Several peaks of interest (ideally higher order reflections of the same type hkl, 2h, 2k, 21, 3h, 3k, 31,. .., nh, nk, nl) are fitted by Fourier series the same procedure is applied to the diffraction lines of a reference sample, in which size and strain effects are negligible, in order to determine the instrumental line broadening. Such information is used in order to deconvolute instrumental broadening from sample effects (Stokes-Fourier deconvolution [36]). 

This approach also allows an easy correction of the diffraction peaks from the instrumental broadening that can be obtained by fitting the peak profile of a standard... 

Gugliotta, L. M., Vega, J. R., and Meira, G. R., Instrumental broadening correction in size exclusion chromatography. Comparison of several deconvolution techniques, /. Liq. Chromatogr., 13,1671, 1990. 

After H0bs has properly been extracted (cf. Sect. 2.2.2), the effect of instrumental broadening can be eliminated by numerical deconvolution (see p. 38). If the peaks shall be modeled by analytical functions (Sects. 8.2.5.7-8.2.5.8), the consideration... 

Elimination of Instrumental Broadening and Crystal Size Effect. Fourier transform of Eq. (8.13) turns the convolutions into multiplications (Sect. 2.7.8)... 

If, moreover, we consider a set of peaks with the index (h) counting the orders of reflections, then the effects of size and instrumental broadening are readily eliminated... 

Step 3 Guinier Plot Separation of Size and Distortion Effects. The inner part of the correlation functions y0bs(h) (T) s readily expanded into a power series. For this purpose we resort to Eq. (8.14). Assuming that instrumental broadening is already eliminated we have... 

Model Mixed Gaussian and Lorentzian Peaks. Even if one of the distributions must be modeled by a Gaussian and the other by a Lorentzian while the instrumental broadening is already eliminated, a solution has been deduced (Ruland [124], 1965). 

Lorentzians, Gaussians, and combinations of both like pseudo-Voigt functions 38Frequently the effect of instrumental broadening is tacitly considered as already eliminated. 

Think of instrumental broadening, finite lattice size. 

Here Bp describes the inevitable instrumental broadening by the known integral breadth of the primary beam16, and Bg is the true integral breadth of the orientation distribution. For the determination of (L) and Bg the relation is linearized... 

Baldwin, M.A. Derrick, P.J. Morgan, R.P. Correction of Metastable Peak Shapes to Allow for Instrumental Broadening and the Translational Energy Spread of the Parent Ion. Org. Mass Spectrom. 1976,11, 440-442. 

In the first section, the mechanisms involved in size exclusion chromatography are discussed this is an area where additional understanding and clarification still are needed. Data treatment with respect to statistical reliability of the data along with corrections for instrumental broadening is still a valid concern. Instrumental advances in the automation of multiple detectors and the developm.ent of a pressure-programmed, controlled-flow supercritical fluid chromatograph are presented. 

Maximum extinction coefficients will not do, even for non-rigorous discussions, since band widths differ so widely. Quantitative discussions should include corrections for instrumental broadening the procedures available are described in (59). 

Tung (55) has shown that the normalized observed SEC chromatogram, F(v), at retention volume v is related to the normalized SEC chromatogram corrected for instrument broadening, W(y), by means of the shape function G(v,y) through the relation... 

In this work, using ultrastyragel columns, it was found that instrumental broadening corrections were unnecessary. 

Correction for Instrumental Broadening in Size Exclusion Chromatography Using a Stochastic Matrix Approach... 

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