Intensity slit-smeared

J (s) = Jl (s) dsi is the slit-smeared scattering intensity, P(t is the total primary beam intensity per slit-length element - a quantity determined by the moving slit device. R is the distance between sample and detector slit as measured on the optical axis of the camera. L is the (fixed and known) length of the detector slit in the registration plane. H is the (adjustable) height of the detector slit. exp(—jut) is the linear absorption factor of the sample19. 

Thereafter the slit-smeared scattering intensity is readily expressed in absolute units [7(x)/y] =e.u./nm4. 

The so-called Lupolen standard 25 is a well-known secondary standard in the field of SAXS. In conjunction with the Kratky camera it is easily used, because its slit-smeared intensity J(s) /V is constant over a fairly wide range, and this level is chosen as the calibration constant. In point-focus setups the SAXS of the Lupolen standard neither shows a constant intensity region, nor is the reported calibration constant of any use. 

The 2D projection / 2 (ai2) = J sn) in Table 8.3 is denoted by the symbol J(s) - the classical notation of a slit-smeared scattering intensity (Kratky camera). Instead of utilizing mathematics, the Kratky camera carries out the 2D projection by... 

For an ideal two-phase system haying sharply defined phase boundaries, according to Porod s law [5], the slit-smeared scattering intensity is given as [6]... 

Table 8.3 shows that there are Porod laws with exponents p =2, 3 and 4. The exponent p =4 shows up in materials which are isotropic (in 3D space). If we project such a scattering pattern to a plane, the corresponding slit-smeared intensity shows an exponent p =3. The projected scattering pattern is isotropic as well - in the 2D plane onto which it has been projected. Therefore any Porod law has an exponent of at least p =2. The reason is that the scattering of an isotropic ideal multiphase material with sharp edges is readily expressed in terms of the 2nd derivative of its radial correlation function (Merino and Tchoubar [118,141]). The derivative theorem yields the factor —An s for the scattering intensity, if in real space an isotropic second derivative or a non-isotropic Laplacian is applied (cf. Sect. 2.7.4). 

Fig. 12. Desmearing of J (m)(see Figs. 10,11 and Eq. (30) includes smearing by slit length and slit width) Crosses ii(m) empty circles J (m)(effect of slight width has been removed cf. Eq.(33)),filled circles desmeared intensities I(q)...

X-ray beam is rectangular, which occurs when slits are used to collimate the beam, the resulting pattern will show smearing of intensity due to the incident beam shape. Ibese effects must be removed by mathematically "desmearing" the pattern to obtain the corrected intensity. The topic of desmearing is extensively covered in the references (3-5). Least distortion of the measured intensity occurs when pinhole collimation is used. 

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