Experimental error caused by sample displacement in time-of-flight neutron diffractometry

A significant error may occur in the measured lattice parameters when the sample is displaced from the diffractometer center. For time-of-flight neutron diffractometers, this error gives rise to different lattice parameters, not only for detectors at different 2θ but also for detectors at the same 2θ but on opposite sides of the incident beam. Tests made on GPPD at IPNS, Argonne National Laboratory, show that this error largely arises from a change in the diffraction constant, 1/Lsinθ, where L is the total flight path. Modeling of the experimental data indicates that in order to achieve a precision of 10⁻⁴, a typical requirement for strain measurements, for a wide angular range of detectors, the sample should be positioned to within ∼0.1 mm of the diffractometer center. Equations are given to relate the errors measured at different diffraction angles. For small sample displacement, the error may be corrected by introducing the displacements along and normal to the incident beam as refinable parameters in least-squares-based analysis programs.