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.

Hybridization and Bond-Orbital Components in Site-Specific X-Ray Photoelectron Spectra of RutileTiO2

“…A plane-wave cutoff energy of 120 Ry and a 4 4 6 Monkhorst-Pack k-point sampling scheme were used to guarantee convergence. We obtained values of a 4:57 A, c=a 0:643, and u 0:303 for the structural parameters of the rutile TiO 2 phase, which are in excellent agreement with the experimental values of a 4:59 A, c=a 0:644, and u 0:305 [4]. All calculated curves have been convolved with a Gaussian of width 0.4 eV to simulate the total experimental resolution.…”

First-principles study of thinTiOxand bulklike rutile nanowires

“…Calculated lattice parameters and energy band gap ͑E g ͒ of bulk rutile and anatase phases with two different exchange-correlation functionals ͓GGA and local-density approximation ͑LDA͔͒ have been compared with available experimental data [28][29][30] in Table I. Due to pseudopotentials, exchange-correlation approximation and methods used in calculations, lattice parameters can be slightly different from both experimental [28][29][30] and previous calculated values.…”

“…Calculated lattice parameters and energy band gap ͑E g ͒ of bulk rutile and anatase phases with two different exchange-correlation functionals ͓GGA and local-density approximation ͑LDA͔͒ have been compared with available experimental data [28][29][30] in Table I. Due to pseudopotentials, exchange-correlation approximation and methods used in calculations, lattice parameters can be slightly different from both experimental [28][29][30] and previous calculated values. [31][32][33][34] The comparison of these results, similar to some recent studies 35,36 comparatively including several different exchange-correlation functionals as well as pseudopotentials suggests that GGA calculations yield slightly better agreement with experimental data.…”

“…Hence, using GGA approximation, the calculated lattice parameters a and c of rutile are 4.64 ͑4.59͒ and 2.98͑2.96͒ Å, respectively. The experimental values [28][29][30] …”

Studies of EPR g-factors on Rutile (TiO2) with Co2+ Ion

“…According to this method we have the normalization condition N (1 ; 2 S dp ( ) + 2 ) = 1 (5) and the approximate relationship f N 2 [1 + 2 S 2 dp ( ) ; 2 S dp ( )] where S dp ( ) are the group overlap integrals. From the Slater-type SCF functions [17,18] and the average metal-ligand distance of rutile [19], we obtain for TiO 2 :Co 2+ , S dp (t 2g ) 0.0170, S dp (e g ) 0.0517. f [ (B =B 0 + C=C 0 )/2] is the ratio of the Racah parameters for a 3d n ion in a crystal to those of a free ion. For free Co 2+ [15], B 0 1115 cm ;1 and C 0 4366 cm ;1 .…”