Instrumentation-based uncertainties of lattice constants obtained from XRD patterns

Abstract

X-ray diffraction (XRD) analysis is a fundamental tool in studying the properties of novel and functional materials. Since the lattice constants obtained from the XRD patterns hold valuable information about the material properties and applications, an accurate description of these lattice constants is required. However, due to the limited resolution of x-ray diffractometers, the calculated and reported lattice constants could be erroneous after a certain digit. Knowing the appropriate number of significant digits of the lattice constants is the objective of this paper. A model for the instrumentation-based uncertainties of the lattice constants was formulated using multiple linear regression and elementary error analysis. The accuracy of the estimated uncertainties was then verified using sample calculations on zinc oxide (ZnO). In totality, this paper demonstrates that the model is able to accurately determine the uncertainty of lattice constants in the absence of other sources of instrumentation errors such as beam or sample misalignment.