Study of β-quartz by neutron multiple diffraction

A study of the crystal structure of β-quartz has been done employing neutron multiple diffraction as a method of analysis. The sample used in the measurements was a natural quartz crystal shaped into an orthocylinder of size 5 cm diameter × 5 cm height with the crystallographic direction [00.1] parallel to the cylinder axis. An experimental primary-beam multiple diffraction pattern was obtained with the β-quartz 00.1 space-group-forbidden reflection. To obtain the β-phase, the sample was heated to 1003 K inside an electrical furnace specially designed for the experiment. Theoretical Umweganregung primary-beam multiple diffraction patterns were calculated for both an ordered and a disordered model of the β-quartz structure and compared to the experimental pattern. The agreement between patterns was verified by calculating the reliability factor R = Σ_k| I_k(obs.)-CI_k(calc.)|/Σ_k I_k(obs.), where I_k(obs.) and I_k(calc.) are, respectively, observed and calculated integrated intensities. The variation of the scale factor C allowed the determination of a minimized R-factor for each model of the structure. The R-factor found for the disordered model was 3.3% lower than that calculated for the ordered model, namely R = 0.110 and R = 0.143. No parameters were refined in this analysis.