Asymmetry Parameter Of Electric Field Gradient Research Articles

In-plane anisotropy of the electric field gradient in Ba(Fe1−xCox)2As2 observed by As75 NMR

We have performed $^{75}\mathrm{As}$ NMR measurements on single crystals to investigate the nematic behavior via the in-plane anisotropy of the electronic state at the As site far from Co impurities in the representative iron arsenides $\mathrm{Ba}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{As}}_{2}$. From the analysis of the angular dependence of the NMR satellites in the $c$ plane using the binominal distribution, we find that there is the in-plane fourfold symmetry breaking, namely, the orthorhombic-type anisotropy in the electric field gradient (EFG) at the As site with no Co atom at the nearest neighboring Fe sites even in the tetragonal phase of both ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ and $\mathrm{Ba}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{As}}_{2}(x\ensuremath{\ne}0)$. The NMR spectrum in the antiferromagnetically ordered state of ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ is shown not to support a nanotwin model on the basis of the nematic order proposed from the pair-distribution analysis of neutron scattering data. Based on results of the $x$ and temperature $T$ dependences of the in-plane anisotropy in the wide $x$ and $T$ ranges, the symmetry breaking is concluded to come from the local orthorhombic domains induced by disorder such as Co impurities or lattice imperfections. Furthermore, we find that the asymmetry parameter of EFG $\ensuremath{\eta}$ obeys the Curie-Weiss law which may be governed by nematic susceptibility, and the Weiss temperature becomes zero at ${x}_{\mathrm{c}}\ensuremath{\sim}0.05$ in $\mathrm{Ba}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{As}}_{2}$.

Systemic Study of Orbital and Spin Nematicity in NaFe1−x Co x As by NMR

Nematic order, a self-organized state with rotational symmetry broken, has been observed in both copper-oxide and iron-pnictide high temperature superconductors. However, its origin is still a mystery in the iron pnictides although it is considered as a key to understand the mechanism of superconductivity. Here, we report a systemic nuclear magnetic resonance (NMR) study on NaFe1−xCoxAs (0 ≤x ≤ 0.042) that an orbital order, accompanied by an instant spin nematicity, occurs at at a temperature T∗ far above structural transition temperature Ts in the tetragonal phase. We show that the observed NMR spectra splitting and its evolution is due to an incommensurate orbital order that sets in below T∗ and becomes commensurate below Ts. We show that the electric field gradient asymmetry parameter is a good measure for the orbital order parameter which undergoes a Landau-like 2nd-order phase transition. We further show that the spin nematicity is well accounted for by the observed orbital order.

Dependence of nuclear quadrupole resonance transitions on the electric field gradient asymmetry parameter for nuclides with half-integer spins

Allowed transition energies and eigenstate expansions have been calculated and tabulated in numerical form as functions of the electric field gradient asymmetry parameter for the zero field Hamiltonian of quadrupolar nuclides with I=3/2,5/2,7/2, and 9/2. These results are essential to interpret nuclear quadrupole resonance (NQR) spectra and extract accurate values of the electric field gradient tensors. Applications of NQR methods to studies of electronic structure in heavy element systems are proposed.

First-Principle Calculations on the Microscopic 57Fe Electric-Field-Gradient Tensor of Ferrous Chloride Tetrahydrate: A Prototypical Mössbauer Species

Since the pioneering work on the theoretical description of Mössbauer quadrupole line intensities for a single-crystal to elucidate information on the electric-field-gradient (EFG) tensor, ferrous chloride tetrahydrate, FeCl(2)·4H(2)O, has represented a prototypical Mössbauer species. In addition, this species also typifies a so-called ambiguous, low symmetry, iron center where traditionally only macroscopic tensors have been assumed available for determination. Recent experiments on FeCl(2)·4H(2)O have successfully determined physically meaningful spin-Hamiltonian parameters for the (57)Fe microscopic (local) EFG and mean-squared displacement tensors. This paper reports a density functional theory investigation that finds good agreement with experiment. Assuming a gas-phase scaffold cluster approach to describe the crystalline geometry, the sign of the EFG was determined to be positive, in agreement with earlier magnetically perturbed experiments, and the EFG asymmetry parameter η was calculated to be 0.21-0.23 depending on the density functional used, which is in excellent accord with experiment at 0.25(2). By virtue of theoretical and experimental agreement, this work indicates that simultaneous electric-field-gradient-mean-square-displacement Mössbauer determinations can resolve the apparent ambiguity associated with monoclinic, 2/m or 1 Laue class, sites provided there is sufficient anisotropy in the Lamb-Mössbauer recoilless fraction.

Stereoelectronic srtructure of γ-chloropropyltrichlorostannane. Ab initio calculation

The quantum-chemical calculations by the RHF/3-21G* and MR2/3-21G* methods of the Cl(CH2)3SnCl3 and ClCH2SnCl3 molecules with full optimization of their geometry was performed. The Cl(CH2)3SnCl3 molecule was also calculated by the RHF/3-21G* method at different distances between the Sn atom and the Cl atom in the C-Cl fragment. From the results of the calculations 35Cl NQR frequencies were estimated and the electric field gradient asymmetry parameters at the 35Cl nuclei of these molecules. The abnormally high electron density on the Cl atom of the C-Cl fragment in the Cl(CH2)3SnCl3 molecule is due mainly to the polarization of this compound under the influence of significant positive charge on the Sn atom directly through the field. The polarization of the C-Cl bond in the molecule is of the opposite direction to the polarization of the related bond in the ClCH2SnCl3 molecule because of the peculiarities of their geometries. The transfer of the electron density from the Cl atom of the C-Cl fragment to the Sn atom in the Cl(CH2)3SnCl3 molecule is not observed.

Two-Dimensional Nutation NQR Broad-Line Spectra in Oriented Samples

The NQR nutation method to determine the electric field gradient asymmetry parameter η in systems, where the resonance line is so broad that the radio frequency field can excite only a portion of the nuclear spins, is presented. In this situation, the recently developed spectroscopic methods are not applicable. Two-dimensional nutation NQR spectra of oriented powders are calculated and used to determine η at particular frequencies along a broad NQR line. The proposed method is useful for single crystals, oriented powders, glasses, and disordered systems even for small values of the asymmetry parameter. Therefore it can be used to evaluate fluctuations in η and the quadrupole coupling constant e2qQ due to inhomogeneities. We demonstrate the application of this method to oriented chalcogenide semiconducting glasses.

Layered Inclusion Compounds Containing Aniline and Polyaniline Studied by NQR and IR Spectroscopy

Temperature dependence of the 127I NQR frequencies in the intercalates of PbI2 with aniline were measured. Unusual temperature coefficients of frequency and the electric field gradient asymmetry parameters for these compounds were discussed, taking into account the structure peculiarities and the amplitude of iodine oscillations.

Pure nuclear quadrupole resonance determination of the electric field gradient asymmetry for broad lines

We present an angle dependent nuclear quadrupole resonance (ADNQR) method to determine the electric field gradient asymmetry parameter η in systems where the resonance line is so broad that the radio frequency field can excite only a portion of the nuclear spins. In this situation, the recently developed spectroscopic methods are not applicable. ADNQR is useful for single crystals and oriented powders, and, for small η determines η 4. Therefore, it can be used to evaluate fluctuations in η due to inhomogeneities. We demonstrate the application of ADNQR experimentally to oriented superconducting YBa 2Cu 3O 7 powder.

On the theory of the polarization effects and its experimental test by angle-dependent Mössbauer spectroscopy with guanidinium nitroprusside (CN 3H 6) 2[Fe(CN) 5NO] (GNP) single crystals

The theory of the angle-dependent Mössbauer spectroscopy on nitroprusside-like single crystals has been complemented with expressions for the nuclear resonant cross-sections in case of the wave vector of the γ-radiation lying in the low symmetric non-mirror planes. They have been tested by rotation experiments in these planes using guanidinium nitroprusside (CN 3H 6) 2[Fe(CN) 5NO], (GNP) single crystal. As a result both the electric field gradient (EFG) and the mean square displacement (MSD) tensor parameters at the iron sites in GNP, have been determined at room temperature with high precision. The EFG asymmetry parameter is η=0.01(1) and the principal z-axes of the two EFG tensors are oriented at α=±8(1)° with respect to the c -axis in the mirror ac -plane. The corresponding orientation angle for the MSD tensor is ω=±11(4)° and lies also in the ac -plane. The crystal shows strong vibrational anisotropy with different Lamb–Mössbauer factors f LM ( i) for the principal crystal directions: f LM ( a) =0.118(3), f LM ( b) =0.174(2) and f LM ( c) =0.198(2). These values are in very good agreement with the results obtained by Mössbauer line broadening method and nuclear forward scattering of synchrotron radiation. In our analysis the saturation and polarization effects, which are very important for the case of single crystal absorbers with quadrupole split Mössbauer spectra and finite thickness, are taken into account. A total of 51 high quality spectra, recorded and calibrated with the sodium nitroprusside standard Na 2[Fe(CN) 5NO] · 2H 2O (SNP), have yielded for the quadrupole splitting the value Δ E Q=+1.854(1) mm/s and for the isomer shift relative to SNP the value IS=+0.006(1) mm/s (−0.251 mm/s relative to the α-Fe standard at room temperature). GNP has been confirmed as a very promising material for the investigation of long-lived metastable states observed in nitroprussides.

Calculations of Multipulse Sequence in NQR of Spins [formula omitted

The general formalism of the interaction representation with respect to an operator which is its own inverse is developed and applied to pure NQR of spins I = 32. Under the assumption of no relaxation and no dipolar coupling, it is shown that the calculation of the response to pure NQR multipulse sequences can be performed with the same concepts used in high field NMR, such as coherence pathways. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. It takes into account the off-resonance irradiation as well as the angular dependence of the excitation and detection for every value of the electric field gradient asymmetry parameter. Particular attention is devoted to the powder average, which is performed via a probability function derived analytically for the first time, leading to a drastic reduction of simulation times. The theory is illustrated by the study of the optimization and excitation bandwidths of one- to three-pulse sequences and compared to experimental results on Chloranil. We show that the three-pulse “stimulated echo” sequence gives a more uniform excitation profile than the traditional two-pulse echo sequence for powder samples. Thus, the “stimulated echo” sequence could be useful to cover a large spectrum when the experiment duration, or the signal to noise ratio, are not critical parameters. Analytical expressions for the nutation spectra obtained by one or two-pulse sequences are also derived for the first time.

Correlations between 29 Si, 17 O and 1 H NMR properties and local structures in silicates: an ab initio calculation

In order to gain insight into the correlations between 29Si, 17O and 1H NMR properties (chemical shift and quadrupolar coupling parameters) and local structures in silicates, ab initio self-consistent field Hartree-Fock molecular orbital calculations have been carried out on silicate clusters of various polymerizations and intertetrahedral (Si-O-Si) angles. These include Si(OH)4 monomers (isolated as well as interacting), Si2O(OH)6 dimers (C2 symmetry) with the Si-O-Si angle fixed at 5° intervals from 120° to 180°, Si3O2(OH)8 linear trimers (C2 symmetry) with varying Si-O-Si angles, Si3O3(OH)6 three-membered rings (D3 and C1 symmetries), Si4O4(OH)8 four-membered ring (C4 symmetry) and Si8O12(OH)8 octamer (D4 symmetry). The calculated 29Si, 17O and 1H isotropic chemical shifts (δiSi, δiO and δiH) for these clusters are all close to experimental NMR data for similar local structures in crystalline silicates. The calculated 17O quadrupolar coupling constants (QCC) of the bridging oxygens (Si-O-Si) are also in good agreement with experimental data. The calculated 17O QCC of silanols (Si-O-H) are much larger than those of the bridging oxygens, but unfortunately there are no experimental data for similar groups in well-characterized crystalline phases for comparison. There is a good correlation between δiSi and the mean Si-O-Si angle for both Q1 and Q2, where Qn denotes Si with n other tetrahedral Si next-nearest neighbors. Both the δiO and the 17O electric field gradient asymmetry parameter, η of the bridging oxygens have been found to depend strongly on the O site symmetry, in addition to the Si-O-Si angle. On the other hand, the 17O QCC seems to be influenced little by structural parameters other than the Si-O-Si angle, and is thus expected to be the most reliable 17O NMR parameter that can be used to decipher Si-O-Si angle distribution information. Both the 17O QCC and the 2H QCC of silanols decrease with decreasing length of hydrogen bond to a second O atom (Si-O-H···O), and the δiH increase with the same parameter.

Ab initio calculations of of pyridine and its 2- and 3-chloroderivatives

Ab initio calculations of the C5H5N, 2-. and 3-ClC5H4N molecules by the RHF method in the valence split 6-31G* basis set with full optimization of the geometry have been carried out. The alternation of the charges on the atoms of the pyridine ring and of the populations of their px-orbitals is in agreement with the noninductive through -the-field interaction of the geminal atoms. The35Cl NQR frequencies and the electric field gradient asymmetry parameters at the35Cl nuclei in 2- and 3-CIC5H4N were estimated using the populations of the valentp-orbitals of the Cl atoms and their components. The35Cl NQR frequency for the first compound is lower than that for the second one, mainly due to the higher pσ-electron population of its Cl atom.

Two-dimensional nutation FT/MEM 35Cl nuclear quadrupole resonance spectroscopy and hydrogen bonding in 2,6-dichlorophenol

Two-dimensional (2D) nutation nuclear quadrupole resonance (NQR) spectroscopy of polycrystalline 2,6-dichlorophenol has been applied in order to study the effect of intramolecular hydrogen bonding on the electric field gradient (EFG) asymmetry parameter η. The superiority of the maximum entropy method (MEM) over the traditional fast Fourier transform (FFT) is demonstrated in analysis of 2D NQR data. The chlorine atom which is ortho to the hydroxyl group and involved in hydrogen bonding gave a value for η of 0.065 while the other chlorine gave a higher value of 0.140, independent of temperature in the range 77–284 K. These values are discussed in terms of hydrogen bonding and bond parameters.

Two-dimensional nutation FT/MEM 35Cl nuclear quadrupole resonance spectroscopy and hydrogen bonding in 2,6-dichlorophenol

Two-dimensional (2D) nutation nuclear quadrupole resonance (NQR) spectroscopy of polycrystalline 2,6-dichlorophenol has been applied in order to study the effect of intramolecular hydrogen bonding on the electric field gradient (EFG) asymmetry parameter η. The superiority of the maximum entropy method (MEM) over the traditional fast Fourier transform (FFT) is demonstrated in analysis of 2D NQR data. The chlorine atom which is ortho to the hydroxyl group and involved in hydrogen bonding gave a value for η of 0.065 while the other chlorine gave a higher value of 0.140, independent of temperature in the range 77–284 K. These values are discussed in terms of hydrogen bonding and bond parameters.

Deuterium Quadrupole-Coupling and Chemical-Shielding Tensors in the Model Dipeptide Glycylglycine Monohydrochloride Monohydrate

The electric field gradient (EFG) and chemical-shift (CS) tensors for the amide, carboxylic acid, and amino deuteron sites in glycylglycine monohydrochloride monohydrate were measured. For each site, the EFG tensors are found to lie nearly along the deuteron bond. The magnitudes of the quadrupole-coupling constants agree well with previous empirical relationships to hydrogen-bond lengths. A new relationship is presented which correlates hydrogen-bonding geometries and EFG asymmetry parameters for N–D··· (hydrogen-bond acceptor) systems that suggests the importance of intermolecular geometry in determining these parameters. The measured amino and amide CS tensors are found to agree well with the few examples in the literature and agree qualitatively with those determined fromab initiocalculations. The carboxylic acid deuteron CS tensor agrees well with empirical relationships to hydrogen-bond distance.

Hydrogen-bonding structural study of solid peptides and polypeptides containing a glycine residue by 17O NMR spectroscopy

Abstract Static 17 O NMR spectra of polyglycines I and II and glycylglycine peptides in the solid state were measured by the cross polarization technique. By computer simulations of these spectra, three NMR parameters (quadrupolar coupling constant ( e 2 qQ / h ), electric field gradient asymmetry parameter (η Q ), and chemical shift (δ)) were determined. From these results, it was found that as the hydrogen bond length decreased, the e 2 qQ / h value decreased. Furthermore, the principal values of the 17 O chemical shift tensor for both the peptides and polypeptides moved upfield with a decrease in the hydrogen bond length. From these experimental findings, it was clarified that 17 O NMR spectroscopy can provide a useful means of elucidating the hydrogen-bonding structure in solid peptides and polypeptides.

Solid state effects in the molecular crystals of Cl 2, Br 2 and I 2

The solid halogens CL 2, Br 2 and I 2 are a model system for studying the intermolecular interactions in a molecular crystal. Self-consistent energy band-structure calculations based on the local density approximation (LDA) are performed by the full potential linearised augmented plane wave method. A geometry optimisation in terms of bond length and rigid rotation of the molecules is done by total energy minimisation and yields results close to experiment. The electronic charge density is obtained from which the electric field gradient (EFG) is determined on a first principles basis. The EFG asymmetry parameter η turns out to be very sensitive to the intermolecular interactions, which are well described by the present method.

P,π-lnteraction in the Y—C [dbnd]C [rbond2] Group

The electric field gradient asymmetry parameters for 35 Cl nuclei in compounds of the series Cl 2 C CHOR, Cl 2 CHOCOR etc . do not corroborate a widespread representation of a p,π-interaction between the unshared electron pair of a Cl atom and the π-electron double bond system in these molecules.

Calculation of the eigenvalues of pure quadrupole interaction in Mössbauer effect studies

Two approximate formulae to calculate the eigenvalues of pure quadrupole interaction in Mossbauer effect studies have been proposed and the eigenvalue coefficients in the formulae have been given for various excited states and ground states of the nucleus with different spin. All the eigenvalues of pure quadrupole interaction between both excited state and ground state of nucleus with spinI=3/2÷9/2 and the electric-field gradient with different asymmetry parameter (η=0÷1.0) have been calculated by these formulae. The results show that the accuracies in all the calculations are more satisfactory or same in comparison with those obtained by the formula of Shenoy and Dunlap, especially when the asymmetry parameter of electric-field gradient is larger than 0.8 for the nucleus with spinI=5/2.

Order-disorder structural phase transition in La2-xSrxCuO4+ delta at 150 K.

Using perturbed {gamma}{gamma} angular correlations of {sup 111}In in the La site, we report a structurally disordered phase in oxygen stoichiometric La{sub 2{minus}{ital x}}Sr{sub {ital x}}CuO{sub 4+{delta}}. So far this phase has been defined for 0{le}{ital x}{le}0.07, involves a reversible order-disorder transition at {ital T}{sub {ital d}}=150(20) K, and is observed by changes in the electric-field gradient (EFG). These changes involve a continuous {ital broadening} of the EFG distribution and {ital decrease} of the average EFG asymmetry parameter as {ital T}{r arrow}0. The new disordered phase is associated with a loss of three dimensional magnetic order in the range 0.015{lt}{ital x}{lt}0.018, and may be due to short-range disorder in the tilting of the CuO{sub 6} octahedra as proposed by Egami {ital et} {ital al}.