Better powder diffractometers-choice of beam elements and trade-offs in design

This article re-examines the equations governing resolution on constant wavelength neutron powder diffractometers (PDs) as cast for Gaussian elements. There is a widely accepted choice of collimators and monochromator mosaic to maximise peak intensity for a given resolution on high-resolution PDs. A second distinct “optimisation” was found more recently by an acceptance diagram study. This article shows that these “optimisations” are only two of an infinite number of equivalent element choices. A procedure to find these equivalent configurations is given. This new freedom can be used to overcome technical and other limits on component choice. This article then derives the optimum value of the detector collimation for PDs and discloses a previously unrecognised trade-off in PD design. This collection of new results on PD design may later lead to a true full analytic optimisation of PDs. While this article addresses neutron diffractometers, the results should also apply to modest resolution PDs using other radiation including X-rays. Some of its results have strong implications for all instruments using monochromators.