Rutile: Normal Probability Plot Analysis and Accurate Measurement of Crystal Structure

Abstract

The x-ray scattering by two different rutile crystals, within a hemisphere of reciprocal space having radius (sin θ) /λ=1.02 Å−1, was measured at 298°K with PEXRAD. The integrated intensities of 780 reflections from each crystal were determined, resulting in 136 symmetry independent Fmeas from Crystal 1 and 122 Fmeas from Crystal 2. The crystal structure was refined by the method of least squares: The agreement factor R for all Fmeas is 0.0286, and the single position parameter x(0)=0.30479±0.00010. Normal probability plot analysis shows the least squares derived standard deviations are underestimated by 33%, and the two sets of Fmeas contain an appreciable parallel bias. The lattice constants, measured at or corrected to 298°K on two different crystals, are a=4.593659±0.000019 and c=2.958682±0.000008 Å. The Ti–O distances are 1.9800±0.0009 and 1.9485±0.0005 Å. Pairs of shorter bonds define O–Ti–O angles of 81.21° and 98.79°, forming a plane normal to the two longer bonds. The resulting octahedral Ti–O bond arrangement is apically extended, as is found in all AIVB2 compounds with rutile structure: The remaining nine well-determined non-Group IV AB2 family members contain, without exception, apically compressed AB6 octahedra. Bauer and Khan's, and also Niizeki's, x-ray results on rutile are compared with the present measurements.