Lattice strain effects in the measurement of the Si lattice parameter by Laue-case double-crystal diffractometry

The measurement of the (220) Bragg-plane spacing of Si by Laue-case double-crystal diffractometry with an uncertainty lower than 10^-8 requires a detailed theoretical framework that includes the study of lattice strain. In the present paper, the propagation of X-rays through a deformed crystal is re-examined and the influence of a constant strain gradient on the centre of the reflection domain is studied by means of Takagi's equations. Their analytical and numerical solutions indicate that the measured lattice spacing refers to the crystal entrance surface.