An experimental investigation of extrapolation methods in the derivation of accurate unit-cell dimensions of crystals

TLDR

The study examines multiple extrapolation functions and discusses how various error sources affect unit‑cell dimension accuracy. Measurements show that absorption error in unit‑cell dimension a follows a cos²θ/sinθ + cos²θ/θ relationship, with a linear plot down to 30°, and extrapolated values agree well, supporting the use of this extrapolation function for data from well‑constructed cameras.

Abstract

Measurements on X-ray photographs of cylindrical specimens of different absorption and thickness taken in a camera without eccentricity show that the absorption error in the apparent unit-cell dimension a is proportional to cos2θ/sinθ + cos2θ/θ. The plot of a against ½(cos2θ/sinθ + cos2θ/θ) is linear down to θ = 30° for all four specimens used. The extrapolated values for a are in good agreement, and this extrapolation function is accordingly recommended in the case of data from well constructed cameras. Other extrapolation functions are also considered, and the effect of various sources of error discussed. A table of ½(cos2θ/sinθ + cos2θ/θ) is given.