[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

# The average number of reﬂections n cap inside a

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The average number of reﬂections N cap inside a capillary is proportional to θ cr R / d , so that the intensity gain increases rapidly with the number of reﬂections: gain N 2 cap .

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X-Ray Optics 95 The value of the spot size on a sample can be estimated according to the following simple formula: s 2 d + 2 θ cr F 2 , (3.4) where F 2 is the capillary–sample distance. Exit beam divergence leads to a certain spread of the beam after the capillary end. The relative contribution of the second term can become dominant for small capillary diameters. In this case it is necessary to work with small capillary–sample distances. In many applications a single-pinhole collimator (or a double-pinhole col- limator) can be easily substituted for the monocapillary of the same diameter d . In this case, the monocapillary performs the following main functions: 1. It collimates the beam spatially (exit beam size equals to a capillary di- ameter d ); 2. It collimates the beam angularly (exit beam divergence is of the order of the critical angle of total external reﬂection θ cr ); 3. It can produce significant intensity gain on the sample relative to conven- tional pinhole collimators. One must remember that intensity gain is achieved at the expense of a certain increase of the beam divergence up to θ cr but in many cases consid- erations of large total intensity on a sample prevail over this factor. Monocap- illaries can be successfully used when small irradiated spots on the sample are needed while the distance between the source and the sample is large and can- not be reduced. This is a typical situation in diffractometry where the positions of the source and the sample are fixed by the diameter of the goniometer [58]. In some investigations (e.g., texture investigations) one does not need very high angular collimation of the beam and angular divergence 4 mrad for Cu K α -line ( E = 8 . 0 keV) and 2 mrad for Mo K α -line ( E = 17 . 4 keV) obtained with a glass capillary is quite suitable. In the last several years, cylindrical monocapillaries have found their wide application in diffractometers produced by GE Inspection Technologies Ahrensburg GmbH Co. KG (Ahrensburg, Ger- many), PANalytical B.V. (Almelo, Netherlands) and Bruker AXS (Karlsruhe, Germany) as a convenient substitute for conventional pinhole collimators. Typical intensity gains are 3–10 for Cu-anode fine-focus tube (effective anode spot 0 . 4 mm × 0 . 8 mm) with the capillary diameters 0.1–1.0 mm. Monocapillaries with small diameters can be also applied as a substitute for pinhole collimators in local ﬂuorescence analysis for obtaining small excitation spots on the sample [59]. They can give significant intensity gain, especially when used in combination with a microfocus tube (diameter of the anode spot is of the order of capillary diameter). Of course, focusing capillary optics (tapered capillaries and X-ray lenses) could give still larger intensity gain and monocapillaries can be regarded only as a first step in this direction, especially taking into account their simplicity and relative cheapness.
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