Determination of the β-quartz hexagonal cell parameters from a 00.1 neutron multiple diffraction Umweganregung pattern measured at 1003 K

The hexagonal cell parameters a and c of β-quartz have been determined from a 00.1 β-quartz neutron multiple diffraction Umweganregung pattern measured at 1003 K. Owing to the high density of multiple diffraction peaks in the indexing of the pattern, contrasting with the low density of experimental peaks, a procedure to correctly index peaks has first been applied. After the correct indexing, the peaks were selected taking into account their quality (adequate intensity and definition) and then classified in accordance with their suitability for the determination of a or c. The azimuthal angular positions of classified peaks were applied to indexing diagrams in order to obtain sets of values for both a and c. Weighted means of the sets give final values for a and c. In order to obtain more reliable final values an iterative process has been employed. A statistical analysis of data has also been employed to calculate uncertainties for the mean values found in the iterative process. After 12 cycles of iteration, the results converged to a = 4.9957 (14) and c = 5.46184 (35) Å for β-quartz at 1003 K.