The interpretation of powder diffraction patterns by numerical and computer-graphics systems

A computer-graphics system has been used interactively to study the powder diffraction pattern (Cu Kβ) of a `perfect' quartz sample. The poly crystalline specimen was obtained by powdering a thin slide of synthetic quartz. The reticular planes were indexed and the cell parameters refined using the USGSLS procedure. A comparison with the literature suggests the presence of systematic effects in the measuring equipment; evaluation of these by means of Wilson's model permitted the listing and indexing of 44 reflections and determination of the Bragg angle as well as the cell and the instrumental parameters. The refinement of the cell parameters performed directly by the optimizing procedure came to a precision of 1 × 10⁻⁴.