Ultra-high-angle double-crystal X-ray diffrac­tometry (U-HADOX) for determining a change in the lattice spacing: experiment

An experiment is reported on ultra-high-angle double-crystal X-ray diffrac­tometry (U-HADOX) at the Bragg angle θ up to 89.5°, coupled with white X-rays from a conventional source. It is shown that the Bragg-peak shift associated with a change in the lattice spacing increases in proportion to tanθ as predicted; the relative accuracy of a change in the spacing to 10⁻⁸ is attained. The performance is demonstrated for the determination of the linear thermal-expansion coefficient α of silicon and strontium titanate SrTiO₃, a value with four significant figures being determined with the data in a temperature range narrower than 1 K; the value of α for silicon (2.621 ± 0.003) × 10⁻⁶ K⁻¹ at 300.4 K is compared with those in the literature based on experiments using the Bond method of X-ray diffraction and macroscopic thermal expansion. The advantages and characteristics of U-HADOX including the coupling with synchrotron X-rays are discussed.