Better powder diffractometers. II—Optimal choice of U, V and W

Abstract

This article presents a technique for optimising constant wavelength (CW) neutron powder diffractometers (NPDs) using conventional nonlinear least squares methods. This is believed to be the first such design optimisation for a neutron spectrometer. The validity of this approach and discussion should extend beyond the Gaussian element approximation used and also to instruments using different radiation, such as X-rays. This approach could later be extended to include vertical and perhaps horizontal focusing monochromators and probably other types of instruments such as three axis spectrometers. It is hoped that this approach will help in comparisons of CW and time-of-flight (TOF) instruments. Recent work showed that many different beam element combinations can give identical resolution on CW NPDs and presented a procedure to find these combinations and also find an “optimum” choice of detector collimation. Those results enable the previous redundancy in the description of instrument performance to be removed and permit a least squares optimisation of design. New inputs are needed and are identified as the sample plane spacing ( d S) of interest in the measurement. The optimisation requires a “quality factor”, Q PD, chosen here to be minimising the worst Bragg peak separation ability over some measurement range ( d S) while maintaining intensity. Any other Q PD desired could be substituted. It is argued that high resolution and high intensity powder diffractometers (HRPDs and HIPDs) should have similar designs adjusted by a single scaling factor. Simulated comparisons are described suggesting significant improvements in performance for CW HIPDs. Optimisation with unchanged wavelength suggests improvements by factors of about 2 for HRPDs and 25 for HIPDs. A recently quantified design trade-off between the maximum line intensity possible and the degree of variation of angular resolution over the scattering angle range leads to efficiency gains at short wavelengths. This in turn leads in practice to another trade-off between this efficiency gain and losses at short wavelength due to technical effects. The exact gains from varying wavelength depend on the details of the short wavelength technical losses. Simulations suggest that the total potential PD performance gains may be very significant-factors of about 3 for HRPDs and more than 90 for HIPDs.