Further optimisation of a simple X-ray diffraction instrument for portable and planetary applications

This paper extends the work presented in a previous publication (Hansford, 2011 [1], subsequently referred to as Paper 1) to optimise the performance of a simple reflection-mode X-ray diffraction instrument with respect to the geometrical configuration. Both papers focus on the maximisation or minimisation of quantifiable characteristics of the X-ray beam incident on the sample in order to optimise the peak heights and widths in the resulting diffractogram. The reason for this approach is mathematical tractability, and its success relies on the relationship between the incident beam characteristics and the diffractogram properties. Part of Paper 1 was devoted to the minimisation of the equatorial divergence angle of the X-ray beam, while keeping the total X-ray flux constant, in order to minimise the diffractogram peak widths. While equatorial divergence and peak widths are certainly linked, their relationship is complex and depends quite significantly on other geometric parameters. An alternative optimisation approach is taken in this paper, focusing on the maximisation of the X-ray flux and minimisation of the incident beam axial divergence, while equatorial divergence is kept constant to ensure at least reasonable resolution. The rationale for this approach is that the incident beam flux and the axial divergence angle are more directly linked to diffractogram peak heights and peak asymmetry, respectively. Families of candidate geometric solutions result from this approach which is regarded as advantageous because there is no unique optimised solution and it allows the parameter space to be fully explored.