Finite element analysis of surface-stress effects in the Si lattice-parameter measurement

TL;DR

This paper investigates how surface stress in silicon affects the accuracy of lattice parameter measurements used to determine the Avogadro constant, using finite element analysis and proposing an experimental validation.

Contribution

It introduces an elastic-film model to analyze surface stress effects on silicon lattice measurements and suggests an experimental approach to observe these effects.

Findings

Surface stress influences silicon lattice parameter measurements.

Finite element analysis quantifies the surface stress impact.

Proposed experiment aims to detect surface stress effects.

Abstract

A stress exists in solids surfaces, similarly to liquids, also if the underlying bulk material is stress-free. This paper investigates the surface stress effect on the measured value of the Si lattice parameter used to determine the Avogadro constant by counting Si atoms. An elastic-film model has been used to provide a surface load in a finite element analysis of the lattice strain of the x-ray interferometer crystal used to measure the lattice parameter. Eventually, an experiment is proposed to work a lattice parameter measurement out so that there is a visible effect of the surface stress.