Tetrahedral Distortion Research Articles

Discussion on the structural anisotropy of würtzite-type compounds

The würtzite-type ionic compounds exhibit flattened tetrahedral sites with a decentering of the central atom. The tetrahedral distortion and the relationship between the atom parameter (z) and the c/a ratio were explained on the basis of cell volume optimization respecting the bond valence model, and the role of anharmonic atomic vibrations was emphasized.

Effect of Annealing Temperature on Structural and Magnetic Properties of Zn0.94Co0.05Cu0.01O

The doped ZnO system Zn0.94Co0.05Cu0.01O (ZCCO) was prepared as a nano-polycrystalline by a simple sol–gel process, then air annealed at different temperatures. Applying X-ray diffraction (XRD) and the Rietveld method, structural analysis showed that Co and Cu replace Zn substitutionally yielding ZCCO single phase. The refined u-fractional coordinate of Zn increases monotonically by an annealing temperature from 0.3546 at 500 °C reaching 0.3722 at 800 °C, very near from the ideal value 0.375. The Zn tetrahedrons become more symmetric and the distortion is gradually relieved by annealing up to 800 °C. Annealing at 900 °C introduces tetrahedron distortion in an opposite way. The zero field cooled (ZFC) and field cooled (FC) magnetization versus the temperature at different applied fields and the magnetization versus the applied field at different temperatures were carried out. The system exhibits a ferromagnetic behavior at room temperature. As the annealing temperature increases from 550 to 900 °C, the saturation magnetization at 300 K increases from 0.0507 to 0.1088 emu/g.

Study of palladium nanoparticles synthesized in alkali borosilicate glass pores by the X-ray line shift method

Metallic Pd synthesized in porous glass with an average pore diameter of 7 ± 2 nm has been studied using the X-ray diffraction and X-ray line shift methods for the first time. The irregular dependence of the reflection width in X-ray patterns on the diffraction angle has been revealed. This can be caused by crystallite growth mostly in the [111] direction or by tetrahedral distortions of the fcc lattice. The shift (difference in energy) of K α1 lines (ΔE α1 = 19 ± 2 meV) for nanostructured Pd in comparison with the bulk material is first detected. The detected effect is considered within the assumption of the palladium electron redistribution between Pd 5s- and 4d-bands.

3T-phlogopite from Kasenyi kamafugite (SW Uganda): EPMA, XPS, FTIR, and SCXRD study

A 3 T mica polytype from Kasenyi (southwest Uganda), kamafugite, was studied by electron probe microanalysis (EPMA), single-crystal X-ray diffraction (SCXRD), micro-Fourier transform infrared spectroscopy (FTIR), and X-ray photoelectron spectroscopy (XPS) to characterize its crystal chemistry and the relationships with phlogopites from the same rock but showing different stacking sequence and to get insights into factors affecting polytypism in Ugandan phlogopites. EPMA data gave: SiO 2 = 38.7(2), Al 2 O 3 = 13.08(9), MgO = 20.4(2), TiO 2 = 4.8(1), MnO = 0.03(3), FeO tot = 5.51(9), Cr 2 O 3 = 0.90(7), NiO = 0.11(5), SrO = 0.03(3), ZnO = 0.04(3), ZrO 2 = 0.01(2), K 2 O = 9.64(5), Na 2 O = 0.29(1), BaO = 0.15(5), F = 0.13(5), and Cl = 0.01(1) wt%. The analyzed sample may be classified as a Ti-rich phlogopite. X-ray photoelectron spectroscopy provided Fe 3+ /Fe 2+ and O 2− /OH equal to ~0.75 and 7.14, respectively, which are in agreement with the results of previous Mossbauer investigation on the BU1 phlogopites from the same rock and with the structural formula of the studied crystal. Infrared spectra showed a shoulder at ~3660 cm −1 in the OH − stretching region (~3740–3600 cm −1 ), which is assigned to MgMgFe 3+ -OH − -K-O 2− local configurations. No evidences of vacancy substitutions were observed. Structure refinement based on single-crystal X-ray diffraction data was performed in space group P 3 1 12 using anisotropic displacement parameters and converged to R 1 = 4.34 and wR 2 = 3.33%. Unit-cell parameters are: a = b = 5.3235(3) and c = 30.188(2) A. Geometrical and chemical considerations point to a disordered cation distribution over T1 and T2 tetrahedral sites, whereas partial cation ordering characterizes the octahedral sites with high-charge cations preferentially located as expected on M2 and M3. Tetrahedral bond length distortion and angular variance parameters describe more distorted polyhedra in 3 T polytype than those found in coexisting 1 M and 2 M 1 polytypes. Finally, the overall crystal-chemical features indicate the occurrence of the following substitution mechanisms in the studied sample: Ti-oxy [ VI M 2+ +2(OH) − ↔ VI Ti 4+ +2(O 2− )+H 2 ↑] and Al, Fe 3+ , Cr-oxy [ VI M 2+ +(OH) − ↔ VI M 3+ +O 2− +½(H 2 )↑]; Al, Fe 3+ -Tschermak [ VI M 2+ + IV Si 4+ ↔ VI (Al 3+ , Fe 3+ )+ IV Al 3+ ]; XII K + + IV Al 3+ ↔ IV Si 4+ + XII □ tetraferriphlogopite [ IV Fe 3+ ↔ IV Al].

Copper(II) Complexes with Schiff Bases Containing a Disiloxane Unit: Synthesis, Structure, Bonding Features and Catalytic Activity for Aerobic Oxidation of Benzyl Alcohol

AbstractMononuclear copper(II) salen‐type Schiff base complexes, CuIIL1–5 [H2L1 to H2L5 = tetradentate N,N,O,O ligands derived from 2‐hydroxybenzaldehyde, 2,4‐dihydroxybenzaldehyde, 3,5‐dibromo‐2‐hydroxybenzaldehyde, 2‐hydroxy‐5‐nitrobenzaldehyde, 5‐chloro‐2‐hydroxybenzaldehyde and 1,3‐bis(3‐aminopropyl)tetramethyldisiloxane, respectively] were prepared in situ in the presence of a copper(II) salt or by direct complexation between a copper(II) salt and a presynthesised Schiff base. The compounds {CuL1, CuL1·0.5Py, CuL2·0.375CH2Cl2, (CuL3)[Cu(4‐Me‐Py)4Cl]Cl·2H2O, CuL4, CuL4·CHCl3 and CuL5, as well as the isolated ligand H2L3} were characterised by elemental analysis, spectroscopic methods (IR, UV/Vis, 1H NMR, EPR) and X‐ray crystallography. The formation of a 12‐membered central chelate ring in these complexes is effected by the tetramethyldisiloxane unit, which separates the aliphatic chains, thus significantly reducing the mechanical strain in such a chelate ring. We dub this a “shoulder yoke effect” by analogy with the load‐spreading ability of such an ancient device. The coordination geometry of copper(II) in CuIIL1–5 can be described as tetrahedrally distorted square‐planar. Maximum tetrahedral distortion of the coordination geometry expressed by the parameter τ4 was observed for CuL1 (0.460), while distortion was minimal for the two crystallographically independent molecules of CuL2 (0.219 and 0.284). The Si–O–Si bond angle varies markedly between 169.75(2)° for CuL1 and 154.2(3)° for CuL4·CHCl3. Charge‐density and DFT calculations on CuL1 indicate high ionic character of the Si–O bonds in the tetramethyldisiloxane fragment. The new copper(II) complexes bearing the disiloxane moiety have been shown to act as catalyst precursors for the aerobic oxidation of benzyl alcohol to benzaldehyde mediated by the TEMPO radical, reaching yields and TONs up to 99 % and 990, respectively, under mild and environmentally friendly conditions (50 °C; MeCN/H2O, 1:1).

High-Pressure Raman Study on Anglesite

High-pressure Raman spectroscopic experiments of anglesite, PbSO4, were carried out in a diamond anvil cell up to about 35 GPa at room temperature. Two stages of changes in the pattern of wavenumber-versus-pressure plot were observed in most of the vibrational modes. The first stage of change is the kink in the slope of wavenumber-versus-pressure plot at about 14 GPa, indicating a change in the force constant of modes. Further compression up to 21 GPa causes the splitting in the S-O stretching modes, representing the distortion of SO4 tetrahedron. The behavior of transition observed in PbSO4 is similar to that of BaSO4 as well as those found in the solid solution series of BaSO4-SrSO4. Transitions taking place at higher pressure for anglesite is due to the relatively greater value of electronegativity for Pb2+, as compared with M2+ in other complex compounds of similar structure.

The hydration structure of Cu2+: more tetrahedral than octahedral?

A comprehensive multi-technique approach has been used to address the controversial question of the preferred geometric form of the Cu2+ aqua-ion hydration shell. A combination of H/D isotopic substitution neutron scattering and X-ray scattering has been used to refine atomistic models of 0.5 m and 2.0 m solutions of Cu(ClO4)2, that have also been constrained to simultaneously reproduce detailed local structure information about the cation environment obtained by X-ray Absorption spectroscopy. The adoption of the Empirical Potential Structure Refinement (EPSR) technique as a single unified analytical framework minimises the chances for biasing the result in favour of a specific pre-conceived outcome. The results are consistent with an average coordination for each Cu2+ ion of 4.5 ± 0.6 water molecules that matches the more recent picture of five-fold coordination in a 2.0 m solution, but interestingly this combined study highlights that the preferred local geometry of the ion sites is found to have a mixed character of tetrahedral, trigonal bipyramidal and octahedral components. A further point to note is that this new model adds support to a largely ignored result in the literature relating to the linear electric field effect induced g-shifts observed in the electron paramagnetic resonance spectra of glassy Cu2+ complexes (Peisach and Mims, Chem. Phys. Lett., 1976, 37, 307–310) that first highlighted the importance of tetrahedral distortions in the cation's hydration shell structure.

Viscosity, fragility and structure of Na2O–CaO–Al2O3–SiO2 glasses of increasing Al/Si ratio

The research and development of a new float glass with higher content of Al 2 O 3 is essential for the commercial flat glass. The study on the workability and kinetic fragility of Na 2 O–CaO–Al 2 O 3 –SiO 2 glass melts with different Al/Si ratios has been linked with the structure. The viscosities as a function of temperature for glass melts were derived on the basis of Vogel–Fulcher–Tamman (VFT) equation. Some characteristic temperatures and four characteristic temperature intervals of forming process in tin bath were estimated. The results showed that: adding 12 wt% Al 2 O 3 substitute for SiO 2 , the melting point ( Tm ) increased about 35 K, entire temperature interval in tin bath narrowed down about 20 K, the shortening of workability was mainly reflected in the viscosity range of 10 5.75 –10 10 Pa s, the fragility index m increased by 15%. It reveals an inverse correlation between the workability and the fragility. The structural changes on the tetrahedron structural unit Q n ( n =1, 2, 3, 4) were obtained by using Raman spectroscopy. Our analysis indicates that: the number of NBO reducing and a more polymerized structure with adding Al/Si ratios are responsible for the increase of viscosity; the tetrahedral distortion, a decrease of Q 3 / Q 2 in the Q n species, is responsible for the increase of fragility.

Electrical conductivity and local structure of lithium tin iron vanadate glass

A relationship between electrical conductivity (σ) and local structure of 15Li2O·10Fe2O3·xSnO2·(70–x)V2O5·5P2O5 glass (x = 0–20 mol%), abbreviated as xLFSVP glass, was investigated by 57Fe- and 119Sn-Mossbauer spectroscopies, differential thermal analysis (DTA) and dc-four probe method. A small increase in quadrupole splitting (Δ) for FeIII was observed from 0.70 to 0.74± 0.02 mm s − 1 with an increase of “x”, whereas isomer shift (Δ) values of 0.40±0.01 mm s − 1 were independent of “x”. This result suggests that local distortion of FeIIIO4 tetrahedra was slightly increased in SnO2-containing vanadate glasses, which was reflected as an increase in glass transition temperature (Tg) from 266 to 285±5 °C. A slope of 675 K / (mm s − 1) obtained in ‘Tg vs. Δ plot’ proved that FeIII occupied the site of network former (NWF). An isothermal annealing of 10LFSVP glass at 500 °C for 100 min resulted in a marked decrease of Δ from 0.72 to 0.56±0.02 mm s − 1, indicating that local distortion of FeO4 tetrahedra was reduced by the structural relaxation of 3D-network. In contrast, identical δ and Δ values of 0.07±0.01 and 0.53±0.02 mms − 1, respectively, were observed in 119Sn-Mossbauer spectra of 10LFSVP glass before and after the annealing. These results indicate that SnIVO6 octahedra are loosely bound in the glass matrix as a network modifier (NWM). A marked increase in σ from 7.4 × 10 − 7 to 9.1 × 10 − 3 S cm − 1 was observed in 20LFSVP glass after the isothermal annealing, indicating that structural relaxation of 3D-network evidently causes a marked increase in σ.

Temperature-dependent structural studies of mullite-type Bi2Fe4O9

We report on the temperature-dependent structural studies on the mullite-type Bi2Fe4O9 compound. The crystal structures were determined using both powder X-ray diffraction and single crystal neutron diffraction. The thermal expansion of the cell parameters from smallest to largest occurred in the order a<c<b; their expansion behavior was fit using either linear or nonlinear regression according to the region of choice. The anisotropic thermal expansion was monitored with respect to the expansion coefficients, anisotropy factor, and polyhedral geometry. At 900K an abrupt change of the anisotropy factor is observed which correlates with a slope in the BiO6 polyhedral volume. At the same temperature the FeO4 tetrahedral distortion starts to increase. The temperature-dependent stereochemically activity of the Bi3+ 6s2 lone electron pair was probed by the absolute value of eccentricity parameter. This parameter shows a significant drop at around 773K. Additionally, the average crystal size and micro-strain of the powder samples were studied. A healing of intrinsic defects is observed with respect to a decreasing micro-strain followed by crystal growth above about 900K. The temperature-dependent infrared spectra were described in three distinct zones. Deconvolution of the absorption features between 370cm−1 and 1000cm−1 required nine fitted bands, and the decomposed Pseudo-Voigt elements were assigned to Fe–O stretching, Fe–O–Fe bending and O–Fe–O bending vibrations. The shift of the observed modes was described with respect to temperature. An effective linewidth parameter Δcorr was determined by autocorrelation analysis between 740cm−1 and 900cm−1 for each temperature-dependent spectrum. The break of the slope of Δcorr at about 773K was interpreted as the change of some vibrational modes of the FeO4 tetrahedra. The intrinsic effects observed around 773K are responsible for extrinsic parameter changes found around 900K.

Influence of pH and Oxidation State on the Interaction of Arsenic with Struvite During Mineral Formation

Struvite (MgNH(4)PO(4)·6H(2)O) precipitated from animal and human wastes may be a sustainable source of fertilizer. However, arsenic, present in some wastes, may be removed with struvite. Here the sorption of As with struvite during mineral formation at pH 8-11 was assessed. The yield of struvite increased with pH, and was highest at pH 10. For recovered struvite, XRD indicated reduced crystallinity and particle size, and FT-IR suggested less distortion of phosphate tetrahedra with increased pH. The As impurity did not affect the crystallinity or particle size, but did contribute to phosphate distortion. Sorption of As(V) was observed at all pH values, and was highest at pH 10. As(III) sorption was consistently lower than that of As(V), but increased with pH. XAFS suggested coprecipitation of As(V), and adsorption of As(III) as the potential sorption mechanisms. Solids derived from As(III) solutions exhibited dual mechanisms due to the partial oxidation of As(III) to As(V) in solution prior to sorption. For struvite recovery in the presence of As, optimizing the pH to improve yields may increase the As content. Adsorbed As(III) could be removed prior to fertilizer application, however coprecipitated As(V) will release upon mineral decomposition, linking its cycling to that of phosphorus.

Synthesis and structural characterization of Pd(N,N-dimethylaminopropylamine)Cl2 complex – The interaction with bio-relevant ligands with reference to the effect of cysteine on the deactivation of metal-based drug

The synthesis and X-ray structural characterization of Pd(DMPA)Cl2 complex, where DMPA=N,N-dimethylaminopropylamine, is reported. The complex crystallizes in the space group P21/c, a=8.8923(4), b=10.9050(5), c=11.5006(7) Å, β=120.00(18)°, V=948.25(8) Å3, Z=4. The palladium centre has a typical square-planar geometry with a tetrahedral distortion. Stoichiometry and stability constants of the complexes formed between [Pd(DMPA)(H2O)2]2+ and some selected DNA constituents and cytsteine are investigated at 25°C and at constant 0.1M ionic strength. The concentration distribution diagrams of the various species formed are evaluated. The equilibrium constants for the displacement of coordinated ligands as inosine by cysteine are calculated. The results are expected to contribute to the chemistry of tumour therapy.

Disentangling Neighbors and Extended Range Density Oscillations in Monatomic Amorphous Semiconductors

High energy x-ray diffraction measurements of pure amorphous Ge were made and its radial distribution function (RDF) was determined at high resolution, revealing new information on the atomic structure of amorphous semiconductors. Fine structure in the second peak in the RDF provides evidence that a fraction of third neighbors are closer than some second neighbors; taking this into account leads to a narrow distribution of tetrahedral bond angles, (8.5 ± 0.1)°. A small peak which appears near 5 Å upon thermal annealing shows that some ordering in the dihedral bond-angle distribution takes place during structural relaxation. Extended range order is detected (in both a-Ge and a-Si) which persists to beyond 20 Å, and both the periodicity and its decay length increase upon thermal annealing. Previously, the effect of structural relaxation was only detected at intermediate range, involving reduced tetrahedral bond-angle distortions. These results enhance our understanding of the atomic order in continuous random networks and place significantly more stringent requirements on computer models intending to describe these networks, or their alternatives which attempt to describe the structure in terms of an arrangement of paracrystals.

Empirical interatomic potential for the mechanical, vibrational and thermodynamic properties of semiconductors

Empirical models are widely used to simulate large atomic structures where instead ab initio methods are not practical because of computational limitations. However models such as Tersoff potential [8], [9], Valence Force Field [13], [14] or Stillinger- Weber potential [15] have some restrictions in correctly predicting simultaneously both elastic and vibrational properties of the crystals [18]. Thus, extension of the functional form of the potentials by including further atomic interactions [20] [21] compared to the simple 2- and 3-body terms, is required. An empirical interatomic potential is proposed which represents a substantial improvement of the Tersoff potential for semiconductors modelling. The new model includes multi-bond interactions and the volume dependency by considering the tetrahedron distortions of the covalent crystal.

Bis(μ-nitrito-κ2O:O)bis[bis(1-methyl-1H-imidazole-κN3)(nitrito-κO)copper(II)

In the binuclear title compound, [Cu2(NO2)4(C4H6N2)4], centro­symmetric­ally related complex mol­ecules are linked via weak Cu—O inter­actions, forming dimeric units. The CuII atom displays an elongated square-pyramidal CuN2O3 coordination geometry with a slight tetra­hedral distortion of the basal plane [maximum deviation = 0.249 (2) Å]. The dihedral angle formed by the imidazole rings is 26.20 (10)°.

Complex formation, chemical exchange, species structure, and stereoselective effects in the copper(ii)-l/dl-histidine systems

The formation of copper(II) complexes with L- and DL-histidine (HisH) has been studied by means of pH-potentiometry and spectrophotometry over a wide range of pH (2-14), ligand-to-metal ratio (1 : 1-15 : 1), and temperature (15-55 °C) in aqueous solutions with 1.0 mol dm(-3) KNO(3) as background. Formation constants and spectral characteristics of 13 complex types were found. Fine stereoselective effects have been detected with preferential coordination of two ligands with identical configuration in Cu(His)(HisH)(+) and opposite configuration in Cu(His)(2). The stereoselective effect for Cu(His)(HisH)(+) is explained by hydrogen bond formation between the carboxyl and imidazolyl groups of neighboring ligands at cis-arrangement of amino groups (3N(eq)-form). The opposite sign of stereoselective effect for Cu(His)(2) is derived from favourable axial coordination of the imidazole group in meso-form with cis-structure (3N(eq)N(ax)-form). A significant tetrahedral distortion was revealed for the first time in the prevalent cis-isomer of the Cu(L-His)(2) 4N(eq)-form. These findings were confirmed by EPR data and DFT computations at the B3LYP/TZVP level. The prevalence of cis-isomers for these complexes has been assigned to the rather strong trans effect of the amino groups. The structures of other detected complexes are briefly discussed on the basis of spectroscopic data. Chemical exchange reactions in the copper(II)-L/DL-hishidine systems have been investigated by the NMR relaxation of water protons. A unique proton exchange reaction with short-term proton dissociation from the coordinated imidazolyl group catalyzed by hydroxide ion was characterised for the first time. The discovered enantioselective effects in the ligand exchange reactions between Cu(His)(2) and HisH or His(-) species were attributed to the associative substitution mechanism.

Structure-driven mixed-site borate–phosphate K5Ta8BP4O34: synthesis, structural, spectroscopic and theoretical study

Tungstate bronze (TB) related borate–phosphate K5Ta8BP4O34 is afforded from boron-enriched potassium–molybdate flux. It was found to crystallize [space group P2/c (no. 13), a = 1384.36(5), b = 640.99(2), c = 2054.75(8) pm, β = 125.007(2)°, V = 1493.44(9) × 106 pm3] isotypically with the K5MIV2Nb6P5O34 (M = Ti, Zr) group of compounds. Revealed by X-ray structural analysis, occupational disorder of boron and phosphorus atoms over two crystallographically distinct positions was explained by the decrease of tetrahedral distortions. The calculated electronic structure of title compound was found to be similar to that reported for UV-Vis active niobium phosphate photocatalysts for full water decomposition. Transformation of the parental [Ta8BP4O34] framework at incongruent melting (T = 1618 K) into MIMI′2MV6P3O24-type phosphates was detected leading to a subtle structural relationship of phosphates bearing TB building features.

Divalent-Metal-Stabilized Aluminophosphates Exhibiting a New Zeolite Framework Topology

Two divalent-metal-containing aluminophosphates, (C(5)H(14)N(2))[Co(2)Al(4)P(6)O(24)] and (C(5)H(14)N(2))[Zn(2)Al(4)P(6)O(24)] (denoted as MAPO-CJ62; M = Co, Zn), have been hydrothermally synthesized by using N-methylpiperazine as the structure directing agent. Their structures are determined by single crystal X-ray diffraction and further characterized by powder X-ray diffraction, inductively coupled plasma, and thermogravimetric and diffuse reflectance spectroscopy analyses. Both of these two compounds exhibit a new zeolite framework topology. This new zeolite framework contains 1-dimensional 8-ring channels running along the [010] direction. All the metal and P atoms are tetrahedrally coordinated and alternately connected to each other through bridging O atoms. Inductively coupled plasma analysis shows that the molar ratio of M:Al in MAPO-CJ62 is 1:2. The M(2+) ions in MAPO-CJ62 selectively occupy two of the three possible crystallographically distinct positions. A pure aluminophosphate analogue of MAPO-CJ62 without M(2+)-incorporation, denoted as AlPO-CJ62, has not been obtained in our experiment so far. The necessity of introducing M(2+) ions and their ordered distribution in MAPO-CJ62 has been elucidated by analyzing the distortions of Al-centered tetrahedra in the hypothetical framework of AlPO-CJ62.

Roles of Bi, M and VO4 tetrahedron in photocatalytic properties of novel Bi0.5M0.5VO4 (M=La, Eu, Sm and Y) solid solutions for overall water splitting

Novel Bi0.5M0.5VO4 (BMV; M=La, Eu, Sm and Y) solid solutions were prepared and studied in this paper. All the samples were proved to produce H2 and O2 simultaneously from pure water under the irradiation of UV light. M–O bond lengths were proved to increase with M cations by refining cell parameters and atomic positions. Besides, band gaps, energy gaps and photocatalytic activities of BMV also changed with M cations. Both of M–O and V–O bond lengths were suggested to account for this phenomenon. Inactive A0.5Y0.5VO4 (A=La, Ce) for water splitting proved incorporation of Bi rather than distortion of VO4 tetrahedron was a critical factor for improving efficiency of overall water splitting by facilitating the generation of electron and hole with lighter effective masses. Replacement of Bi by M cations not only gave indirect effect on band structure but also raised position of conduction band minimum to meet requirement of H2 production.

Solid state 27Al NMR investigation of Knight shift tensors of LnAl2 (Ln=Y, La and Lu) and correlation with DFT calculations

The atomic and electronic structures of LnAl2 (Ln=Y, La and Lu) on Al sites were characterized by 27Al solid state NMR spectroscopy. 27Al isotropic metallic shifts have been determined in these cubic laves phases under both static and magic angle spinning (MAS) conditions. Based on band structure calculations, we found a strong correlation of 27Al isotropic metallic shifts and s character of the density of states at the Fermi level on Al sites. We also found tetrahedral distortion of Al centered clusters, which can be well characterized by quadruple coupling constants and Knight shift anisotropy.