The ABC of powder diffractometer detector coverage

This article addresses the question of the most effective detector configuration for neutron spectrometers using a discussion of a particular case – constant-wavelength powder diffractometers at continuous neutron sources. A first variation uses an essentially one-dimensional `banana' detector coupled with out-of-scattering-plane beam divergence before and after the sample. A second variation uses an incident beam tightly defined both in- and out-of-plane coupled to a `4π' detector covering all possible scattering angles after the sample. It is widely believed that the 4π arrangement is superior for most varieties of neutron spectrometer but is more difficult and more expensive to implement. Starting from a commonly used overall instrument figure-of-merit, this article presents simple arguments leading to the surprising conclusion that this is untrue for these constant-wavelength powder diffractometers, provided only that the cylindrical samples used with the banana detector have a height greater than 2.4 times their diameter.