Angle Calculations for a `2+2' Surface X-ray Diffractometer

Angle calculations are presented for a new type of diffractometer, which has two degrees of freedom for the sample and two degrees of freedom for the detector. The sample and detector motions are mechanically uncoupled. This geometry is used to implement a surface diffractometer and the corrections necessary to extract integrated intensities in two of the most useful modes are presented. The relative merits of this geometry and further extensions to it are discussed. Experimental data, showing the existence of an interfacial microstructure at the Si/SiO₂ interface, are also presented to illustrate the advantage of this geometry.