Synchrotron X-ray analysis of the electron density in CoF2 and ZnF2

2001 ◽  
Vol 57 (2) ◽  
pp. 128-135 ◽  
Author(s):  
Nicholas J. O'Toole ◽  
Victor A. Streltsov
Keyword(s):  
Field Theory ◽  
Transition Metal ◽  
Electron Density ◽  
Crystal Field ◽  
Room Temperature ◽  
Crystal Field Theory ◽  
X Ray ◽  
Structure Factors ◽  
Small Crystals ◽  
Multipole Refinement

Accurate structure factors for small crystals of the rutile-type structures CoF2, cobalt difluoride, and ZnF2, zinc difluoride, have been measured with focused λ = 0.8400 (2) Å synchrotron X-radiation at room temperature. Phenomenological structural trends across the full series of rutile-type transition metal difluorides are analysed, showing the importance of the metal atom in the degree of distortion of the metal–F6 octahedra in these structures. Multipole models reveal strong asphericities in the electron density surrounding the transition metals, which are consistent with expectations from crystal field theory and the structural trends in these compounds. Transition metal 3d-orbital populations were computed from the multipole refinement parameters, showing significant repopulation of orbitals compared with the free atom, particularly for CoF2.

4f-Electron Density Distribution in Crystals of CeB6 at 165 K and its Analysis Based on the Crystal Field Theory

1997 ◽  
Vol 53 (1) ◽  
pp. 143-152 ◽  
Author(s):  
K. Tanaka ◽  
Y. Kato ◽  
Y. Onuki
Keyword(s):  
Field Theory ◽  
Density Distribution ◽  
Electron Density ◽  
Crystal Field ◽  
Electron Density Distribution ◽  
Kondo Effect ◽  
Crystal Field Theory ◽  
X Ray ◽  
Deformation Density ◽  
Density Map

4f-Electron density in single crystals of CeB6, cerium hexaboride, was measured at 165 K by X-ray diffractometry. Significant peaks 2.0 e Å−3 high were found along the \langle100\rangle directions at 0.41 Å from Ce on the deformation density map. Analysis based on the crystal field theory removed the peaks, confirming that they were due to the Ce 4f-electrons on the t 1u -orbital. The deformation density in the B6 octahedron was also markedly improved by the analysis and coincides qualitatively with a theoretical molecular orbital (MO) calculation. It also coincides with the model deformation density map of CaB6 composed of only light atoms. These facts guarantee the accuracy of the intensity measurement for the present study. Since Ce3+ has only one 4f-electron, a highly accurate intensity measurement is necessary to detect its 4f-electron density distribution. A ψ-scan technique was therefore employed to avoid multiple diffraction (MD) and to measure the intensities at ω and χ angles with minimum fluctuation of temperature at the sample position. Relativistic radial functions for orbitals of Ce3+ and the corresponding scattering factors, which take the aspherical electron density distribution of 4f-electrons into account, were used for the analysis. CeB6 is a typical dense Kondo material. The Kondo effect occurs in CeB6 from low temperature to above room temperature. X-ray analysis of the f-electron density based on atomic orbitals (AO) revealed that 1.5 (2) electrons are donated from B6 to Ce and a total of 2.5 (2) electrons localize on the 4f-orbital. κ values are consistent with the 4f-orbitals being highly contracted and thus stabilized. These may be related to the Kondo effect.

The mineralogy and chemistry of the nickel carbonates

1963 ◽  
Vol 33 (263) ◽  
pp. 663-678 ◽  
Author(s):  
T. Isaacs
Keyword(s):  
Field Theory ◽  
Optical Properties ◽  
Diffraction Pattern ◽  
Cell Size ◽  
Crystal Field ◽  
X Ray Diffraction ◽  
Hydrothermal Conditions ◽  
Crystal Field Theory ◽  
Cubic Symmetry ◽  
X Ray

SummaryNickel carbonate occurs in nature as a hexahydrate (hellyerite) and as a hydroxyhydrate (zaratite), but the anhydrous species is only known as an artificial product. All of the compounds show anomalous properties that have led to confusion in the literature.Only the calcite structure was found for NiCO3 ; hydrothermal conditions appear to be essential for its synthesis, and a variation in cell size was found with changes in duration or temperature of synthesis, or both.Hellyerite probably is [Ni(H2O)6]CO3, which would explain its ease of decomposition and rarity in nature. Zaratite is not a single mineral, but a composite of amorphous and fibrous components. The conditions under which NiCO3 might be expected to occur are discussed. Nickel bicarbonate formed in the reactions to produce NiCO3 ; its X-ray diffraction pattern, indicating cubic symmetry, analysis, and optical properties are given.The behaviour of nickel in these compounds is best explained in terms of crystal field theory.

Reassessment of the electron density in Cu2O using γ-ray diffraction

2014 ◽  
Vol 70 (6) ◽  
pp. 983-988
Author(s):  
Wolfgang Jauch ◽  
Manfred Reehuis
Keyword(s):  
Electron Density ◽  
Room Temperature ◽  
Covalent Bonding ◽  
Order Structure ◽  
Theoretical Studies ◽  
Single Crystal Diffraction ◽  
Structure Factors ◽  
Bonding Hypothesis ◽  
Multipole Refinement ◽  
Experimental And Theoretical Studies

The electron-density distribution in Cu2O has been critically reexamined to test controversial conclusions from earlier experimental and theoretical studies. The electron density is derivedviamultipole refinement of high-quality single-crystal diffraction data, collected at room temperature with 316.5 keV gamma radiation. Four γ-lines in the energy range 200–600 keV have been used to extrapolate extinction-free low-order structure factors. The remaining extinction corrections refine to a crystal mosaicity identical to the observed one. There is no support for anharmonic contributions to the thermal parameters. Important features of the derived electron density are (i) a partially filled d_{z^2} orbital, (ii) an incomplete ionization of Cu and O, and (iii) no interstitial Cu–Cu charge pileup, thereby refuting the covalent bonding hypothesis.

The electron distribution in silicon. A comparison between experiment and theory

1986 ◽  
Vol 42 (4) ◽  
pp. 271-281 ◽  
Author(s):  
M. A. Spackman
Keyword(s):  
Solid State ◽  
Electron Density ◽  
Electron Distribution ◽  
Valence Electron ◽  
Quantitative Agreement ◽  
X Ray ◽  
Structure Factors ◽  
Multipole Refinement ◽  
New Perspective ◽  
Theory And Experiment

Deformation and valence-electron densities in silicon are derived via Fourier summation and multipole refinement of highly accurate measurements of X-ray structure factors. These results provide a new perspective for the comparison between theory and experiment. The model electron density derived from experiment is in quantitative agreement with recent solid-state calculations, but not with earlier experimental results reported by Yang & Coppens [Solid State Commun. (1974), 15, 1555-1559].

First-row transition metal–pyridine (py)–sulfate [(py)xM](SO4) complexes (M= Ni, Cu and Zn): crystal field theory in action

2018 ◽  
Vol 74 (3) ◽  
pp. 263-268 ◽  
Author(s):  
Mrittika Roy ◽  
Duyen N. K. Pham ◽  
Ava Kreider-Mueller ◽  
James A. Golen ◽  
David R. Manke
Keyword(s):  
Crystal Structure ◽  
Field Theory ◽  
Transition Metal ◽  
Crystal Field ◽  
Crystal Field Theory ◽  
Coordination Environment ◽  
Pyridine Ligands ◽  
Zinc Coordination ◽  
Sulfate Complexes ◽  
Cu And Zn

The crystal structures of three first-row transition metal–pyridine–sulfate complexes, namelycatena-poly[[tetrakis(pyridine-κN)nickel(II)]-μ-sulfato-κ2O:O′], [Ni(SO4)(C5H5N)4]n, (1), di-μ-sulfato-κ4O:O-bis[tris(pyridine-κN)copper(II)], [Cu2(SO4)2(C5H5N)6], (2), andcatena-poly[[tetrakis(pyridine-κN)zinc(II)]-μ-sulfato-κ2O:O′-[bis(pyridine-κN)zinc(II)]-μ-sulfato-κ2O:O′], [Zn2(SO4)2(C5H5N)6]n, (3), are reported. Ni compound (1) displays a polymeric crystal structure, with infinite chains of NiIIatoms adopting an octahedral N4O2coordination environment that involves four pyridine ligands and two bridging sulfate ligands. Cu compound (2) features a dimeric molecular structure, with the CuIIatoms possessing square-pyramidal N3O2coordination environments that contain three pyridine ligands and two bridging sulfate ligands. Zn compound (3) exhibits a polymeric crystal structure of infinite chains, with two alternating zinc coordination environments,i.e.octahedral N4O2coordination involving four pyridine ligands and two bridging sulfate ligands, and tetrahedral N2O2coordination containing two pyridine ligands and two bridging sulfate ligands. The observed coordination environments are consistent with those predicted by crystal field theory.

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