Kratky camera

A Siemens Kratky camera system was utilized for small angle x-ray scattering (SAXS) measurements in conjunction with an M. Braun position sensitive detector from Innovative Technology Inc.. Wide angle x-ray diffraction was obtained utilizing a Philips table-top x-ray generator. 

The progress achieved is closely linked to the development of both powerful detectors and brilliant X-ray sources (synchrotron radiation, rotating anode). Such point-focus equipment has replaced older slit-focus equipment (Kratky camera, Rigaku-Denki camera) in many laboratories, and the next step of instrumental progress is already discernible. With the X-ray free electron laser (XFEL) it will become possible to study very fast processes like the structure relaxation of elastomers after the removal of mechanical load. 

In addition to point-focus apparatus there are scattering devices with an extremely elongated cross-section of the primary beam. Historically this geometry has been developed as a compromise between ideal collimation and insufficient scattering power. Their practical importance is decreasing as more powerful point-collimated sources become available. Kratky camera (Alexander [7], p. 107-110) and Rigaku-Denki camera (BaltA Vonk [22], p. 83) are the most frequent representatives of slit-focus devices. 

General Routes. If a SAXS beamline in normal transmission geometry is used, calibration to absolute intensity is, in general, carried out indirectly using secondary standards. Direct methods require direct measurement of the primary beam intensity under consideration of the geometrical setup of the beamline. On a routine basis such direct calibration was commercially available for the historic Kratky camera equipped with zero-dimensional detector and moving slit device 14. 

A Practical Hint20. In order to most accurately determine PI in Eq. (7.21), a mathematical theorem concerning convolution of a function with a shape function are helpful. The measured primary beam profile of the Kratky camera... 

For a 2D detector this is height and width of the detector pixels. For the Kratky camera with zerodimensional counter this is the height and length of the measuring slit. 

This procedure can only be applied for a Kratky camera with zero-dimensional detector. It shows the value of this classical step-scan device for studies of scattering in absolute intensity units. 

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. 

A proper calibration constant for any beamline geometry is the invariant Q. Thus, the Lupolen standard or any other semicrystalline polymer that previously has been calibrated in the Kratky camera can be made a secondary standard for a point-focus setup, after its invariant Q has been computed in absolute units - based on a measurement of its SAXS in the Kratky camera. 

Asymmetrical peaks with a steep decrease towards high scattering angle are typical for data recorded by a slit-focus (Kratky camera). An isotropic and infinitely sharp peak at s0, (J(s) = 8(s — so)), measured by means of an ideal slit becomes... 

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... 

A well-known device that performs a 2D projection of the scattering pattern is the Kratky camera. By integrating the intensity along the direction of the focus slit, it is collapsing the SAXS intensity on the plane that is normal to the slit direction. In general, 2D projections collapse the measured complete intensity not on a line, but on a plane. As in the case of the ID projections, the orientation of this plane can freely be chosen. The result of such a projection / 2 (Sj,Sk) is not a curve as was the case with the ID projection, but a 2D scattering pattern. Only in the case of 2D isotropy (i.e., / 2 (sjk) with sjk = Js2, + s ) the scattering pattern can be represented by a curve. 

The same equation is considered for the smearing of the classical Kratky camera. 

Figure 1. Collimation system of Kratky camera showing the beam geometry.

The mechanical stability of the Kratky Camera may be expressed as a change in the position of the center of gravity of the primary beam. This is less than 5 seconds of arc over a period of a few days. 

To calculate the absolute intensity it is necessary to know the strength of the primary beam. This can be achieved by using a specially prepared standard sample that scatters X-rays in a known way such that the absolute intensity scattered by any sample is determined by a simple comparison calculation. It must be sufficiently insensitive to the action of X-rays (18) as well as being homogeneous throughout. The standard sample used here is Lupolen (a polyethelene platelet) supplied with the Kratky Camera. 

We are very grateful to Messrs Kiss and Stacy, State Electricity Commission of Victoria, Herman Laboratories, Richmond, Victoria, for giving us their Gas Adsorption data and for lending us the Kratky Camera. In addition, we thank the Brown Coal Council, Victoria, for their continued financial support and, the National Energy Research, Development and Demonstration Council for the grant to purchase an updated Kratky Camera. 

Small angle X-ray scattering (SAXS) was measured with a Kratky camera using nickel filtered CuKa radiation. The width of the entrance and detector slits were 20 and 50 pm, respectively. No desmearing procedure was applied to the scattering curves. Absolute measurements were carried out by using a Lupolen standard. 

Support of this project was initiated by a starter grant from the Department of Energy (Fowkes and Carnali, 1983). The SAXS studies were made with a Kratky camera at AT T Western Electric Company s Engineering Research Center in Princeton, NJ our thanks to Dr. John Emerson, who made these arrangements and provided technical advice to the project. The spinning drop measurements were made with the support of Atlas Powder Company. Our thanks also to IBM for a distinguished graduate fellowship for J. 0. Carnali. 

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