Vertical focusing on neutron powder diffractometers—How much is useful?

Neutron scattering instruments, including powder diffractometers, are affected by out-of-scattering-plane (“vertical”) divergence in the beams which increases count rates but worsens resolution. Such divergence may arise incidentally from the beam height or be deliberately enhanced by using vertically curved monochromators and very high detectors. The formula usually used to describe the resolution effect on powder diffractometers is invalid for modern instruments with large vertical beam divergence both before and after the sample and a corrected formula is presented. That formula is used to combine the resolution effect due to vertical divergence with that due to in-plane angular divergences. A nonlinear least squares optimisation process for this combined resolution is described which permits calculation of the optimum vertical divergence for typical powder diffractometers—high resolution, high intensity and strain scanning machines. The optimum out-of-plane divergence is found to be proportional to the square root of the in-plane divergence but is surprisingly small. Optimising vertical divergence is shown to have a surprisingly significant effect on instrument performance—measurement quality decreases by approximately the same amount as the fractional deviation from optimal vertical divergence even when all other variables are adjusted to maximise performance. The methods used here should also apply to vertical divergence on powder diffractometers using other radiation such as X-rays and could be extended to apply to other instrument types.