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 $(\sin \text{θ) /λ=1.02 Å}$ ⁻¹, was measured at 298°K with PEXRAD. The integrated intensities of 780 reflections from each crystal were determined, resulting in 136 symmetry independent F_meas from Crystal 1 and 122 F_meas from Crystal 2. The crystal structure was refined by the method of least squares: The agreement factor R for all F_meas is 0.0286, and the single position parameter $\text{x(0)=0.30479±0.00010}$ . Normal probability plot analysis shows the least squares derived standard deviations are underestimated by 33%, and the two sets of F_meas contain an appreciable parallel bias. The lattice constants, measured at or corrected to 298°K on two different crystals, are $\text{a=4.593659±0.000019}$ and $\text{c=2.958682±0.000008 Å}$ . The Ti–O distances are $\text{1.9800±0.0009}$ and $\text{1.9485±0.0005 Å}$ . 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 A^IVB₂ 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.