Angle calculations for a five-circle diffractometer used for surface X-ray diffraction

Abstract

The basic equations are derived for the calculation of the angle settings of a five-circle diffractometer used for surface X-ray diffraction. This is done for a specified angle of incidence. An additional constraint that may be imposed is the horizontal alignment of the diffraction rods to match the divergence of the synchrotron X-ray source or the horizontal setting of the physical surface normal. Alignment procedures and the derivation of the orientation matrix are discussed.

Integrated Intensities Using a Six-Circle Surface X-ray Diffractometer

“…The more recent diffractometers, however, have extra degrees of freedom © 1997 International Union of Crystallography Printed in Great Britain -all rights reserved (on the detector), enabling a wide range of perpendicular momentum transfer to be reached and thus allowing atomic coordinates to be determined with high accuracy in all three directions (Ferrer, Torrelles, Etgens, Van der Vegt & Fajardo, 1995;Lohmeier et al, 1996). Different geometries for such diffractometers are in use: there are five-circle diffractometers with and without extra detector arms (Vlieg, Van der Veen, Macdonald & Miller, 1987;Taylor, Norris, Vlieg, Lohmeier & Turner, 1996), six-circle diffractometers (Lohmeier & Vlieg, 1993) and so-called (2+2)-circle diffractometers (Evans-Lutterodt & Tang, 1995).…”

A (2+3)-Type Surface Diffractometer: Mergence of the z-Axis and (2+2)-Type Geometries

“…In addition, a large range of perpendicular momentum transfer is needed. Many diffractometer types are in use that fulfil these requirements in different ways: z-axis (Bloch, 1985), five-circle (Vlieg et al, 1987), six-circle (Lohmeier & Vlieg, 1993) and (2+2) types (Evans-Lutterodt & Tang, 1995;Renaud et al, 1995). In this paper we show that two common geometries, z-axis and (2 + 2)-circle, can be made fully equivalent by the addition of an azimuthal degree of freedom to the detector.…”

Coverage dependent adsorption sites in the K/Cu(100) system: A crystal truncation rod analysis

“…The measured peak intensity is about 800 counts per second. Larger momentum transfers q z = / · c* were attained at constant beam exit angle ß f = 3° by rotating the whole diffractometer table around the α-axis (Vlieg et al, 1987) thereby increasing the X-ray incidence angle /?,·. The integrated intensities along the rod were measured in steps of ΔΙ = 0.2.…”

“…The measurements were carried out at the beamline Χ 16A of the National Synchrotron Light Source (NSLS) storage ring of the Brookhaven National Laboratory (BNL) using a UHV diffractometer (Fuoss and Robinson, 1984) in the five circle diffraction geometry described in detail by Vlieg, Van der Veen, MacDonald and Miller (1987). The Cu(100) surface was prepared under UHV conditions (base pressure 10 " 10 mbar) by 30 min or Ar + ion sputtering (500 eV) at a sample tempera ture of T= 800 Κ followed by 5 min annealing at T= 730 K. The sample heating was achieved by electron bombardment.…”