Precise lattice parameter comparison of highly perfect silicon crystals

As a part of the International Avogadro Project we have utilized a state-of-the-art lattice comparator at the National Institute of Standards and Technology (NIST) to measure relative lattice parameter differences that are of the order of 10⁻⁸. Samples have been prepared from NRLM3, NRLM4, WASO04 and WASO17 material, which are of great importance in terms of a precise determination of the silicon d₂₂₀ lattice parameter. The experimental set-up at NIST consists of a two-source, two-crystal Laue x-ray diffractometer. It uses a heterodyne interferometer to control the position of the first crystal with an uncertainty of 2 × 10⁻⁹ rad. From a least-squares fit we estimate the measurement uncertainty for a relative lattice parameter comparison at about 3 × 10⁻⁹. The measured lattice parameter variation across each individual sample indicates that the lattice uniformity of a particular specimen has to be carefully considered in view of comparing similar, though physically different, samples made out of the same material.