Measurement of the \{220\} lattice-plane spacing of a ${}^{28}$Si crystal

Abstract

The spacing of the \{220\} lattice planes of a ${}^{28}$Si crystal was measured by combined x-ray and optical interferometry to a $3.5\times 10^{-9}$ relative accuracy. The result is $d_{220}=(192014712.67\pm 0.67)$ am, at 20.0 ${}^{\circ }$C and 0 Pa. This value is greater by $(1.9464\pm 0.0067)\times 10^{-9}{d}_{220}$ than the spacing in natural Si, a difference which confirms quantum mechanics calculations. Subsequently, this crystal has been used to determine the Avogadro constant by counting the Si atoms, a key step towards a realization of the mass unit based on a conventional value of the Planck or the Avogadro constants.

4 pages, 6 figure, 1 table

References in corpus (2)

• An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal
• Comparison of the INRIM and PTB lattice-spacing standards

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• The correlation of the $N_A$ measurements by counting ${}^{28}$Si atoms
• Lattice strain at c-Si surfaces: a density functional theory calculation
• Density functional theory calculations of the stress of oxidised (110) silicon surfaces
• Neutron interference from a split-crystal interferometer
• Defocused travelling-fringes in scanning triple-Laue x-ray interferometry
• Three-dimensional model of a split-crystal x-ray and neutron interferometer
• Wavefront errors in a two-beam interferometer
• Measurement of the miscut angle in the determination of the Si lattice parameter