Scattering Factor Refinement Research Articles

Electron Density Study of Garnets:Z3Al2Si3O12(Z=Mg, Fe, Mn, Ca) and Ca3Fe2Si3O12

The crystal structures of seven crystals from five garnet mineral species have been studied through single-crystal X-ray diffraction methods incorporating scattering factor refinement procedures. The derived experimental scattering factors for each atomic species show similar scattering-angle-dependent patterns in their deviations from the theoretical factors. The Si–O distances remain virtually unchanged in the Ca garnets even though the cell constants and the other cation–oxygen distances change with composition. Electron density residuals indicating bonding electrons are seen in all seven crystals, with ∼0.2 e/Å3height between Si and oxygen. Two crystals containing divalent Fe show a characteristic electron density deformation indicating the orientation of thedorbital with paired electrons.

Electron Density Study of Garnets: Y3X2Al3O12;X=Al andX=(Al, Cr)

The electron density distribution in two garnets Y3Al2Al3O12[YAG] and Y3X2Al3O12:X=(Al0.71Cr0.29) [YCG] have been studied with single-crystal X-ray diffraction methods through scattering factor refinement procedures. YAG has broad electron density residuals of 0.3e/Å3height extending between the octahedral Al site and the coordinated oxygen atoms. YCG shows residuals around the Y and oxygen sites indicating significant anharmonicity, along with electron density deformation of theX-site characteristic of octahedral Cr3+sites. Partial substitution of Al by Cr in theXsite does not increase the unshared O–O distance or the far Y–O distance in the adjacent Y site. [CubicIa3d,Z=8. For YAG,a=12.0095(4) Å;Dx=4.553 g/cm3;F000=2224; finalRafter anharmonic refinement: 0.0085 for 281 equivalent-averaged data. For YCG,a=12.0405(5) Å;Dx=4.630 g/cm3;F000=2276; finalRafter anharmonic refinement: 0.0107 for 274 equivalent-averaged data.]

Electron Density Study of Garnets: Ca 3(Cr, Al) 2Si 3O 12

The electron density distribution in a natural garnet, uvarovite Ca 3(Cr, Al) 2Si 3O 12with 55% of the octahedral site occupied by Cr, has been studied with single-crystal X-ray diffraction methods through scattering factor refinement procedures. Electron density residuals up to 0.22 e/Å 3in height indicating bonding electrons were detected between Si and oxygen. Characteristic aspherical electron density distribution around the (Cr, Al) site was also seen; six residuals, −0.27 e/Å 3in height, are directed toward the coordinated oxygens, eight with 0.15 e/Å 3height are directed away from the oxygens. [Cubic Ia 3 d, a=11.956(1) Å; Z=8; D x =3.734 g/cm 3; F 000=1897; final Rafter anharmonic refinement: 0.0039 for 371 equivalent-averaged data.]

Electron Density Study of Garnets: Z3Ga 5O 12; Z=Nd, Sm, Gd, Tb

The electron density distribution in garnets, Z 3Ga 5O 12, Z=Nd, Sm, Gd, Tb, has been studied with single-crystal X-ray diffraction methods through scattering factor refinement procedures. The Zsite shows a variety of electron density residual distribution modes, implying contribution of the felectrons. Residual electron density regions of 0.9–4.0 e/Å 3height seen for all four garnets at an interstitial site (Wyckoff position 48 g) suggest coexistence of domains with alternatively oriented structural motifs within the single crystals. [Cubic Ia 3 d; a=12.5051(4) Å ( Z=Nd), a=12.4361(3) Å ( Z=Sm), a=12.3829 (5) Å ( Z=Gd), a=12.3474(5) Å ( Z=Tb), final Rafter anharmonic refinement: Z=Nd, 0.0114 (for 660 equivalent-averaged data); Z=Sm, 0.0111 (647); Z=Gd, 0.0152 (428); Z=Tb, 0.0118 (454).]

ELECTRON DENSITY STUDY OF SPINELS: ZINC CHROMIUM OXIDE

The electron density distribution in zinc chromium oxide spinel [composition ZnCr 2O 4; for general formula TX 2O 4, tetrahedral site T = Zn xCr 1−x, octahedral site X 2 = Cr 1+xZn 1−x = 0.96 [1]] has been studied with single-crystal X-ray diffraction methods through scattering factor refinement procedures. Smaller cell dimensions ( a = 8.3267(3) Å), compared to those of MgCr 2O 4, along with electron density residuals 0.2∼0.3 e/Å 3 in height situated between the X-site and oxygen atoms suggestive of bonding electrons imply stronger covalency in this compound. In the refinement with harmonic parameters, six residuals −0.9 e/Å 3 in height are arranged around the X-site toward the coordinated oxygen, and eight residuals 0.6 e/Å 3 in height are arranged around the X-site toward directions avoiding the oxygens. These residuals almost completely disappear with anharmonic refinement. Another residual 1.7∼1.8 e/Å 3 in height is situated at the center of the cubical X 4O 4 unit in the structure [222 equivalent-averaged reflections, R = 0.0091 (harmonic refinement), R = 0.0071 (anharmonic refinement)]. © 1997 Elsevier Science Ltd

Electron density study of spinels: Magnesium gallium oxide

The electron density distribution in magnesium gallium oxide spinel [composition MgGa 2O 4; for the general formula TX 2O 4, tetrahedral site T = Mg xGa 1 − x, octahedral site X = Ga 1 + xMg 1 − x; x = 0.183(4)] has been studied with single-crystal X-ray diffraction methods through scattering factor refinement procedures. A residual 0.95e/Å 3 height in harmonic refinement (0.75e/Å 3 for anharmonic) is situated at the center of the X 4O 4 cuboidal unit. Residuals around T and X seen in the harmonic refinement disappear in the anharmonic refinement, the T-O distance increasing from 1.8919(5)Å in harmonic to 1.899(2)Å for anharmonic refinements. [191 equivalent-averaged reflexions, R = 0.0078 (harmonic refinement), R = 0.0067 (anharmonic refinement)].

Electron density study of spinels: Magnesium titanium oxide (Mg 2TiO 4)

The electron density distribution in magnesium titanium oxide spinel [composition Mg 2TiO 4 tetrahedral site T = Mg, octahedral site X = Mg, Ti (equal amounts) for general formula TX 2O 4] has been studied with single-crystal X-ray diffraction methods through scattering factor refinement procedures. In the refinement with harmonic parameters, a positive residual region up to +0.25e /Å 3 in height encircles oxygen in the hemisphere directed towards the T-site, along with weak residuals assuming octahedral arrangements around the X-site. These residuals almost completely disappear with anharmonic refinement. Another residual +0.20 e/Å 3 in height is situated near the X 4O 4 cuboidal unit. [153 equivalent-averaged reflexions, R = 0.0077 (harmonic refinement), R = 0.0059 (anharmonic refinement)]

Electron density study of spinels: Magnesium chromium oxide

The electron density distribution in magnesium chromium oxide spinel [composition MgCr 2O 4; for general formula TX 2O 4, tetrahedral site T = Mg xCr 1 − x, octahedral site X = Cr 1 + xMg 1 − x, x = 0.984(6)] has been studied with single-crystal X-ray diffraction methods through scattering factor refinement procedures. In the refinement with harmonic parameters, there are electron density residuals around the X-site; six residuals of −1.0e/Å 3 height along, eight of +0.7~0.8e/Å 3 height avoiding the directions toward the coordinated oxygens. Also, a +0.6e/Å 3 height residual is seen near oxygen along the T-O direction. These residuals almost completely disappear with anharmonic refinement. Another residual (in harmonic refinement, +1.27e /Å 3; anharmonic, +0.90e/Å 3 in height) is situated at the center of the X 4O 4 cuboidal unit in the structure. [230 equivalent-averaged reflexions, R = 0.0091 (harmonic refinement), R =0.0064 (anharmonic refinement)]

An electron density residual study of α-ferric oxide

The residual electron density distribution in α-ferric oxide (Fe 20 3; natural hematite) has been studied with single-crystal X-ray diffraction methods. A residual electron density double peak of 0.55 Å height is situated along the c-axis between face-sharing Fe's, indicating metal-metal interaction. Residuals suggesting d-electrons were found around Fe. There are also interstitial residuals arranged around Fe hexagonally in a plane perpendicular to the c-axis. These features conform rather to directions related to the Fe neighbors than the coordinated oxygens. [393 equivalent-averaged reflexions, R values; conventional refinement with harmonic parameters: 0.0088, with scattering factor refinement: 0.0069; incorporation of anharmonic parameters did not lower the R value significantly.]

An electron density residual study of magnesium aluminum oxide spinel

The residual electron density distribution in magnesium aluminum oxide (natural spinel) has been studied with single-crystal X-ray diffraction methods. Structure refinement incorporating an experimental scattering factor refinement technique showed a positive residual with 0.7–1.0e/Å 3 height at the center of the Al 4O 4 cuboid in the structure. [200 equivalent-averaged reflexions, R values; harmonic refinement: 0.0127, anharmonic (Gram-Charlier series expansion up to the 6th-rank tensors): 0.0109]

Residual electron density study of chromium sesquioxide by crystal structure and scattering factor refinement

The crystal structure of chromium sesquioxide, Cr 2O 3, has been refined from single crystal X-ray diffraction intensity data. Refinement of the scattering factors of Cr and oxygen in the anisotropic stage enabled extension of refinement up to anharmonic terms of the fourth rank tensors ( R=0.012). Difference Fourier synthesis shows d-electrons of ∼ 0.4ρ A ̊ 3 height situated in six of the eight cube-corner positions around Cr at ∼ 0.7 A ̊ distances; absent at the two positions along the three-fold axis. A prominent peak of 0.9ρÅ 3 height, interpreted as being due to electrons contributing to antiferromagnetic exchange, is situated between Cr pairs of face-sharing CrO 6 octahedra. No residual is detected between edge-sharing pairs.