Michael Grodzicki

Hyperfine electric field gradients and local distortion environments of octahedrally coordinated Fe2

Abstract We report ab initio electronic structure calculations that directly relate given local chemical and distortion environments to corresponding hyperfine electric field gradients (EFGs) in 57Fe Mössbauer spectroscopy, thereby giving needed interpretive power to the technique in characterizing VIFe2+ environments in minerals. Changes of the EFG with various distortions were investigated on model clusters, including the bare octahedra FeO610- and Fe(OH)64-, and various seven-octahedra sections of an octahedral sheet, through self-consistent charge Xα ab initio calculations. Distortions examined for all clusters were flattening, counter-rotation, and bond scaling, as well as changes in neighbor bond lengths and the identity and ordering of neighbor cations for the seven-octahedra clusters. The evolution of the EFG with distortion was derived at T = 0 K and T = 300 K as a function of the distortion parameters. We find that the percent change in the EFG over the range of distortion parameters found in 1M trioctahedral micas is greatest with flattening for the clusters compared, suggesting that flattening is the most important structural distortion in determining the EFG. The EFGs for the sevenoctahedra cluster as a function of flattening were compared for thirteen configurations of Mg2+ and Al3+ cations in the first nearest-neighbor octahedra. The percent change in the EFG for flattening and cation substitution was found to be of similar magnitude. In comparing EFG vs. flattening curves with measured quadrupole splitting distributions (QSDs), the magnitudes of EFGs in the theoretical curves agree well with experiment. The sharp high quadrupole splitting edge is explained by the presence of a maximum in the EFG vs. flattening curve. These model calculations are a necessary first step in establishing a firmer link between local structural distortions in minerals and measured QSDs.

Electron energy-loss spectroscopy at incommensurately modulated crystalline and glassy Ba2TiGe2O8

Based on cluster molecular orbital calculations, high-energy resolution (ΔE ∼ 0.4 eV) Ti–L2,3 electron energy loss near-edge structures of single-crystalline and glassy Ba2TiGe2O8 are interpreted. The finding that the Ti–L2,3 near-edge structure of the Ba2TiGe2O8 single crystal possesses less pronounced peaks than the glass under identical experimental conditions can be attributed to distinct distortions of the titanium environment caused by the very strong one-dimensional structural modulation hosted by the Ba2TiGe2O8 crystal lattice. As lattice periodicity is absent in the glass, the titanium environment is more regular in the vitreous surroundings. Moreover, the modulation in crystalline Ba2TiGe2O8 is responsible for the virtually indiscernible O–K near-edge structures of the glassy and crystalline samples.

Electronic structure of Fe-bearing lazulites

Abstract The Fe end-members scorzalite [Fe2+Al23+(PO4)2(OH)2] and barbosalite [Fe2+Fe23+(PO4)2(OH)2] of the lazulite series have been investigated by Mössbauer and diffuse reflectance spectroscopy, and by electronic structure calculations in the local spin density approximation. The measured quadrupole splitting (ΔEQ = -3.99 mm/s) in scorzalite is in quantitative agreement with the calculated value (ΔEQ = -3.90 mm/s), as well as its temperature dependence. The optical spectrum of barbosalite can be resolved into three peaks at 8985 cm-1, 10980 cm-1, and 14110 cm-1. These positions correlate well with the two calculated spin-allowed d-d transitions at 8824 cm-1 and 11477 cm-1, and with an intervalence charge transfer transition at about 14200 cm-1. The calculated low-temperature magnetic structure of barbosalite is characterized by a strong antiferromagnetic coupling (J = -84.6 cm-1) within the octahedral Fe3+-chains, whereas a weak antiferromagnetic coupling within the trioctahedral subunit cannot be considered as conclusive. The analysis of the charge and spin densities reveals that more than 90% of the covalent part of the iron-ligand bonds arises from the Fe(4s,4p)- electrons. Clusters of at least 95 atoms are required to reproduce the available experimental data with quantitative accuracy.

Hyperfine electric field gradient tensors at Fe2+ sites in octahedral layers: Toward understanding oriented single-crystal Mössbauer spectroscopy measurements of micas

Abstract In this first systematic, theoretical study of the complete electric field gradient (EFG) tensor of 57Fe Mössbauer spectroscopy as a function of chemistry and local structural distortion using electronic structure calculations, local EFG tensors were calculated at the central Fe2+ sites in clusters of seven octahedra, where the neighbor octahedra were populated with a mixture of Mg2+ and Al3+ cations. The independent parameters of the EFG tensor.particularly the principal value VZZ, the asymmetry parameter η, and the direction of the principal axis with regards to the octahedral sheet.were examined in detail as functions of octahedral flattening for each of the thirteen possible configurations of cations. We demonstrate that the argument that the EFG tensor at a particular site is largely determined by the point group symmetry of the corresponding crystallographic site is not correct. We find that in clusters with monoclinic or triclinic local point group symmetry, the value of VZZ changes discontinuously from positive to negative as flattening increases. The principal axis changes from being in the plane of the octahedral sheet to being normal to it at this discontinuity, and the value of η reaches a maximum and begins to decline. This discontinuous behavior is caused by the continuous change of the EFG eigenvalues as the Fe(3d) character of the highest occupied spin-down orbital evolves with flattening. Taking EFG tensor results from all clusters, and using probabilities for the occurrence of each possible cation configuration in a chemically disordered octahedral sheet of a given bulk composition, we simulate averages and distributions of η, principal axis angles, and quadrupole splittings. While the value of η is broadly distributed from zero to one at all flattening angles and bulk compositions, there are two distinct populations of principal axes, normal to and in-plane with the octahedral sheet, as has been observed experimentally. We find these in-plane and normal populations of principal axes correspond exactly to populations with positive and negative values of VZZ, respectively. Histograms representing quadrupole splitting distributions (QSDs) show features found in experimental QSDs, such as a constant high edge, a variable low edge, and a QSD width that changes dramatically with flattening. These results represent the first predictions relating average structural parameters, as would be obtained by X-ray diffraction, to characteristics of the Fe2+ QSD, as obtained by 57Fe Mössbauer spectroscopy, in a chemically disordered material.

Single-centre MO theory of transition metal complexes

The full multi-centre molecular Hamiltonian in the local density approximation for a mononuclear transition metal complex is transformed into a single-centre Hamiltonian explicitly including overlap, covalency and ligand-field effects. The orbital interactions of the metal d-orbitals with the ligand orbitals appear as a repulsive pseudopotential yielding the dominant contribution to the ligand-field splitting. The reliability of this approach is examined by comparison with numerical electronic structure calculations in the local density approximation on three representative systems. Finally, the proof is given that the repulsive pseudopotential exhibits the same angular dependence as the electrostatic potential from the ligands entering the Hamiltonian of ligand-field theory. For this reason, ligand-field theory very often yields the correct splitting pattern of the d-orbitals whereas the radial part is considerably different from the simple expression of ligand-field theory. In particular, there is no general theoretical justification for an R−5-dependence of the ligand-field splitting even for complexes of cubic symmetry.

A semi-quantitative approach to derive the electric field gradient, applied to synthetic fayalite, α-Fe2SiO4: a reappraisal

Experimental and calculated structure factors from a previous synchrotron diffraction measurement on synthetic fayalite have been converted by an inverse Fourier transformation to difference electron (deformation) densities (DED). These were processed in a revised 3D-display program giving hyperareas of DED floating in space around the iron positions M1 and M2 within the fayalite unit-cell and spanning a cluster size of 6 and 4 A, respectively. These relatively wide limits are due to the different site symmetries and had been proposed by earlier DFT (density functional theory) calculations. From the different hyperareas the supposed charges were integrated in space and processed to electric field gradients (EFG) on M1 and M2 using a point-charge model. The two EFGs were compared with respect to the system of crystallographic axes with those obtained from published single-crystal Mossbauer measurements (experimental EFGs), yielding excellent agreement within ±5° and surpassing even the DFT results. This study reports the procedure and the conditions of success of the underlying semi-quantitative method, which is halfway between theory (DFT) and experiment (diffractometry) and is promising valuable results on many other compounds. The term “nanoscope” for the graphical representation may be justified due to its high spatial resolution.

Mössbauer spectroscopy and molecular orbital calculations on iron bearing omphacite

A natural iron bearing omphacite with composition Ca0.49 Na0.525 Mg0.424 Al0.43 Fe0.0762+ Fe0.0563+Ti0.0024 Mn0.005 Si1.989 O6 from Syros, Greece, has been investigated by Mössbauer spectroscopy. The interpretation of the spectra is based on electronic structure calculations in the local spin density approximation. The calculations emphasize that large clusters, extending beyond the second coordination sphere of iron, are necessary for a reliable description. As suggested by the electronic structure calculations, different environments around the Fe2+ octahedra give rise to slightly different hyperfine parameters, especially affecting the quadrupole splitting. Hence, the measured spectrum has been evaluated based on quadrupole splitting distribution. The calculated values including the temperature dependence are in almost quantitative agreement with the experimentally derived values.

Magneto-structural correlations in double-bridged [Cu2F6]2-

A direct approach for calculating magnetic coupling constants is presented. For the double-bridged copper dimer [Cu2F6]2- the results compare well with fully numerical calculations in local spin-density approximation.