Measurement of the miscut angle in the determination of the Si lattice parameter

TL;DR

This paper details the measurement of the miscut angle in a silicon crystal, crucial for precise lattice parameter determination used in fundamental constants and kilogram redefinition.

Contribution

It introduces a measurement procedure for the miscut angle of a silicon crystal, aiding accurate lattice parameter measurements for fundamental metrology.

Findings

Determined the miscut angle of a specific $^{28}$Si crystal.

Validated on-line and off-line measurement techniques.

Provided data to support precise lattice parameter measurement.

Abstract

The measurement of the angle between the interferometer front mirror and the diffracting planes is a critical aspect of the Si lattice-parameter measurement by combined x-ray and optical interferometry. In addition to being measured off-line by x-ray diffraction, it was checked on-line by transversely moving the analyser crystal and observing the phase shift of the interference fringe. We describe the measurement procedure and give the miscut angle of the $^{28}$Si crystal whose lattice parameter was an essential input-datum for, yesterday, the determination of the Avogadro constant and, today, the kilogram realisation by counting atoms. These data are a kindness to others that might wish to repeat the measurement of the lattice-parameter of this unique crystal.