Precision Comparison of the Lattice Parameters of Silicon Monocrystals

The lattice spacing comparator established at the National Institute of Standards and Technology to measure the lattice spacing differences between nearly perfect crystals is described in detail. Lattice spacing differences are inferred from the measured differences in Bragg angles for different crystals. The comparator is a two crystal spectrometer used in the nearly nondispersive geometry. It has two x-ray sources, two detectors, and a device which permits remote interchange of the second crystal sample. A sensitive heterodyne interferometer which is calibrated with an optical polygon is used to measure the Bragg angles. The crystals are manufactured with nearly equal thicknesses so that the recorded profiles exhibit pendellosung oscillations which permit more precise division of the x-ray profiles. The difference in lattice spacing between silicon samples used at Physikalisch-Technische Bundesanstalt (PTB) and NIST has been measured with a relative uncertainly of 1 × 10^-8, This measurement is consistent with absolute lattice spacing measurements made at PTB and NIST. Components of uncertainty associated with systematic effects due to misalignments are derived and estimated.