Total Electric Field Gradient Research Articles

21Ne and 131Xe NMR study of electric field gradients and multinuclear NMR study of the composition of a ferroelectric liquid crystal.

This study has two goals. First, the electric field gradient (EFG) present in the liquid-crystalline phases of ferroelectric FELIX-R&D is determined using NMR spectroscopy of noble gases 21Ne and 131Xe. The 21Ne and 131Xe NMR spectra were recorded over a temperature range, which covers all the mesophases of FELIX-R&D: nematic N*, smectic A, and smectic C*. The spin quantum number of both 21Ne and 131Xe is 3/2. Their electric quadrupole moment interacts with the EFG at the nuclear site, which in liquid-crystalline phases results in the NMR spectra of the triplet structure, instead of a singlet detectable in the isotropic phase. The total EFG experienced by the noble gas nuclei consists of two contributions; one arises from the quadrupole moments of the liquid crystal molecules (external contribution) and the other one from the deformation of the electron distribution of the atoms (deformational contribution). The total EFGs determined from the 131Xe and 21Ne quadrupole splittings are very similar in the nematic and smectic A phases but differ in the smectic C* phase, being about twice larger in the 21Ne case which stems from the larger deformation of the xenon electron cloud than that of neon. For the first time, EFG was determined also in the smectic C* phase applying noble gas NMR spectroscopy. Second, the structure of molecules which, as a mixture, compose the used ferroelectric liquid crystal, FELIX-R&D, is determined by applying a number of various NMR methods and sophisticated spectral analysis. In this part, NMR spectra were recorded from FELIX-R&D/CDCl3 solution. The NMR spectral analysis was divided into four subsystems with over 13 000 000 nonzero intensity transitions. It appeared that FELIX-R&D is composed of three phenyl pyrimidine derivatives and a chiral dopant with fluorine in the asymmetric carbon atom.

Angular correlation studies on 172Lu(172Yb) in GaN and measurements at low temperatures

For optoelectronic devices semiconductors with large band gap doped with rare earth are used. Doping is generally performed during growth but for more structured doping the ion implantation technique is preferable. The perturbed γγ-angular correlation technique is an ideal tool to study the behavior of semiconductors after implantation. An adequate rare earth isotope for such investigations of semiconductors is 172Yb. The temperature dependence of the hyperfine fields for 172Lu(172Yb) in GaN has been analysed. The total electric field gradient (EFG) at the site of this probe is a superposition of the lattice EFG due to the GaN wurtzite structure and the EFG due to the 4f shell of the rare earth probe itself. The latter is strongly temperature dependent and opposed to the lattice EFG which in contrast is nearly constant since the lattice parameters change only negligibly with temperature. At elevated temperatures the sublevels of the 4f shell, split by the crystal electric field, are equally populated. But at low temperatures the lowest level is occupied preferentially. Sign and magnitude of the EFG caused by the 4f shell can be calculated (Tomala et al, J Magn Magn Mater 89(1–2):143, 1990) and the result compared to the experimental data.

The nuclear electric quadrupole moment of antimony from the molecular method

Relativistic Dirac-Coulomb (DC) Hartree-Fock calculations are employed to obtain the analytic electric field gradient (EFG) on the antimony nucleus in the SbN, SbP, SbF, and SbCl molecules. The electronic correlation contribution to the EFGs is included with the DC-CCSD(T) and DC-CCSD-T approaches, also in the four-component framework, using a finite-difference method. The total EFG results, along with the experimental nuclear quadrupole coupling constants from microwave spectroscopy, allow to derive the nuclear quadrupole moments of (121)Sb and (123)Sb, respectively, as -543(11) and -692(14) mb.

Spin-orbit effects in electric field gradients ofalkali metal atoms

Spin-orbit effects in electric field gradients (EFG) of alkaliatoms in the 2P3/2 state are investigated bycomparison of correlated (CCSD(T)) four-component Dirac-Fockresults with scalar relativistic Douglas-Kroll calculations.Since the Douglas-Kroll method is based on a unitarytransformation of the full four-component Dirac Hamiltonian toa two-component form the use of the untransformed EFG operatorleads to the well known picture change error. We therefore usethe point charge nuclear quadrupole moment method incombination with the Douglas-Kroll transformation which removespicture-change effects since only Coulomb-type operators are tobe transformed. We find that spin-orbit effects partiallycompensate scalar relativistic effects and are only importantfor the heavier elements Rb and Cs. A comparison to EFGs derivedfrom valence-only ⟨r-3⟩ values shows that Sternheimercorrections are roughly proportional to the dipolepolarizability of the positively charged atom and can becomevery large for the heaviest atom studied, Cs, amounting to 46%of the total EFG.

Structure, Chemical Bonding, and Nuclear Quadrupole Interactions of beta-Cd(OH)(2): Experiment and First Principles Calculations.

The structure of Cd(OH)(2) was determined by X-ray diffraction on powder crystals and by calculations using the full-potential linearized augmented plane wave method. Good agreement between the two results was found. The chemical bonding is characterized by the interactions of the OH(-) group with Cd(2+) which is not only electrostatic but shows some polarization or covalent admixtures and by the covalent bond in the OH(-) group. The electric field gradient (EFG) was calculated and compared with an experimental determination of the nuclear quadrupole interaction using perturbed angular correlation of gamma-rays. The calculated EFG agrees well with the EFG derived from experiment. The total electric field gradient was decomposed into contributions from different orbitals and energy regions showing that both the Cd 5p and 4d wave functions contribute significantly. Finally, the influence of spin-orbit coupling on the electric field gradient was investigated and found to be of little importance.

Atomic charges in RBa2Cu3O7 superconductor lattices. Electronic structure of the copper atoms

AbstractThe effective atomic charges for all sites of the RBa2Cu3O7 lattices have been found using our Mössbauer data withthe 67Cu(67Zn),133Ba(133Cs), 155Eu(155Gd) isotopes, our calculations of the lattice electric field gradient (EFG) at the lattice sites, as well as the 17O NMR data available in literature. The charges show holes placed in the chain oxygen sublattice mainly. The Cu2+ Sternheimer factor has been estimated and the Cu2+ valence EFG in YBa2Cu37 has been found. The z‐axes of the total, lattice, and valence EFG tensors for Cu(2) coincide with the crystal axis c. For Cu(1) they coincide with the axes b, a, and a, respectively.

Ab initio MO calculations of nuclear quadrupole coupling constants of 35Cl and 2H nuclei in CH 3Cl, CH 2Cl 2, CCl 2 and CHCl molecules

Nuclear quadrupole coupling constants of 35Cl and 2H nuclei in CH 3Cl, CH 2Cl 2, CCl 2 and CHCl were calculated using a number of basis sets employing ab initio optimized and experimental geometries. The effect of incorporation of polarization and/or bond centred functions in the basis sets was studied. The effect of uncontraction of the p atomic basis functions of double zeta and triple zeta quality basis sets were also studied. The study illustrates that the basis sets with bond functions are generally sufficient to obtain a reasonably good value of quadrupole couplings. The results also show that most of the contributions (around 90%) to the total electric field gradient are due to the valence molecular orbitals and that this contribution does not change much from one basis set to another as long as bond functions and/or polarization functons are present in the basis set.

Magnetic relaxation of xenon-131 dissolved in benzene. A study by molecular dynamics and Monte Carlo simulations

Molecular dynamics and Monte Carlo simulations were carried out for xenon atoms dissolved in liquid benzene in order to study the quadrupolar relaxation mechanism of the xenon-131 nucleus. We confirm that a proper description of the relaxation is obtained by taking into account the quadrupole moment of benzene molecules. In contrast to the Xe–water system, the cross-correlation contribution to the electric field gradient (experienced by the Xe nucleus) is negligible in benzene, and the time correlation function of the total electric field gradient shows a relatively smooth decay. Several molecular motions take part in this decay, but not with the same efficiency. The major contribution can be attributed to the rotation of the benzene molecules around their C2 axes. The adequacy of the Sternheimer model for quadrupolar interactions is confirmed with ab initio calculations. Some methodological aspects of simulations are also discussed, such as the use of a termination function to treat the electrostatic interactions and the effect of the xenon interaction parameters on the simulated relaxation rate.

Determination of the electric field gradient and relaxation time measurements in scandium metal at very low temperature

Results are presented of measurements on a single crystal sample of scandium metal at temperatures down to 100 {mu}K using nuclear quadrupole resonance (NQR). Two regimes are found in the relaxation curves; an initial fast relaxation, followed by a slower relaxation consistent with the three exponential recovery expected for an I = 7/2 system in zero external magnetic field. The Korringa constant for this longer time relaxation in the sample is 90 {plus minus} 9 msec K{sup {minus}1}. By observing deviations in the ratio of the intensities of adjacent nuclear spin transitions at the lowest attainable temperatures, the authors were able to make a determination of the sign of the total electric field gradient present in the crystal. Results show that the lowest energy state of the nuclear spin system corresponds to m{sub I} = {plus minus} 7/2. A combination of these deviations and pulse NQR allows this system to be used as an absolute thermometer in the {mu}Kelvin regime.

Electric Field Gradient in Aluminium due to Vacancy and Muon

Abstract The electric field gradients (EFG) in aluminium due to a monovacancy and the interstitial muon are evaluated. The valence effect EFG qv is calculated using perturbed electron density δn(r)values obtained from density functional theory in an analytic expression which is valid at all distances from the impurity. The size effect EFG qs is evaluated using a new oscillatory form for the near neighbour (nn) displacements. The numerical values of qs are computed using fractional nn displacements available in the literature. For the total EFG good agreement with experiment is obtained without the use of any parameter.

21Ne NMR spectroscopy: temperature dependence of the 21Ne quadrupole coupling and electric field gradient in a liquid crystal

The 21Ne NMR spectrum of 21Ne-enriched neon gas dissolved in the anisotropic phase of the thermotropic liquid crystal ZLI1167 was recorded at various temperatures. The curve obtained by plotting the absolute value of the quadrupole coupling constant, |χ|, as a function of temperature is found to possess a maximum in the nematic range. This is considered as an indication of at least two contributions to the total electric field gradient at the nucleus. After the transition to the smectic A phase, |χ| starts to increase without detectable discontinuity to low temperature. The results are compared to the corresponding ones measured earlier for 83Kr and 131Xe.

Study of NMR relaxation of xenon-131 in quadrupolar solvents

An experimental and theoretical study of the quadrupolar relaxation of xenon-131 by quadrupolar solvents has been performed. The electric-field-gradient (EFG) fluctuations at the xenon nucleus are considered to be of purely electrostatic origin and are calculated by means of a new theoretical model called PISA (pair interactions structureless approximation), which is based on a simplified description of the structure of molecular liquids. The PISA results are compared to those of a Monte Carlo simulation. The influence of self- and cross-correlation functions on the total EFG correlation function is discussed. Calculated EFG fluctuations are then used, together with experimental relaxation rates, to determine effective correlation times. These correlation times are analyzed by considering different solvent motions.

Augmented Plane Wave Study of Electric Field Gradients in Non-cubic Metals

Abstract The electric field gradient (EFG) in body-centered tetragonal Indium metal and hexagonal closed packed Beryllium metal is calculated on the basis of a full potential scalar relativistic augmented plane wave procedure. The various contributions to the EFG in simple metals are discussed. The total EFG in In metal found theoretically is equal to qtheor = 2.67 x 1021 Vm-2 . This value agrees well with the experimental data. Using the quadrupole moment Q deduced from the hyperfine splitting of the muon X-ray spectra one gets g exp = 2.46 x 1021 Vm-2 . The valence electrons of Indium give a direct contribution of qel = 2.72 x 1021 Vm-2 , whereas the direct ionic contribution q ion is much smaller and has opposite sign: qion = -0.01 x 1021 Vm-2 . There is a small net shielding contribution of qsh = -0.03 x 1021 Vm-2 to the EFG composed of the ionic contribution gsh. ion = -0.39 x 1021 Vm- 2 and the valence electron contribution qsh,ve = 0.36 x 10 21 Vm-2 .

Effects of a cubically symmetric electron density on the electric field gradient in cubic metal alloys

In the evaluation of the valence electric field gradient (EFG) in cubic metal alloys, it has been customary to assume that the impurity-induced perturbation in the electron density δ n( r) is spherically symmetric. In this paper, δ n( r) is given a more realistic cubic symmetry and its consequences are explored. It has been found that the valence EFG q v displays axial asymmetry along all directions except [100] and [111]. The effects of this on the asymmetry parameter η of the total EFG are investigated.

Theoretical Studies of the Electric Field Gradient in Hexachlorometallates

Abstract The electric field gradient (EFG) at the chlorine site is calculated for cubic compounds of the K2PtCl6-type (space group Fm3m), M2 IMIVCl6, where M1 is an alkali metal and MeIV a tetravalent element. In the calculations the total EFG is subdivided into the contribution of the complex [MIVCl6]2-, EFGcomplex, and the contribution of the ions outside the complex, EFGlattice. EFGcomplex is calculated by the local electron density formalism using the MS-Xα-method, and EFGlattice is determined by the point charge model. It is found that EFGcomplex is positive whereas EFGlattice is negative. Including antishielding effects, the magnitude of EFGlattice is about one fourth of EFGcomplex. The trends in the EFG for the various compounds found theoretically are the same as the trends in the experimental nuclear quadrupole coupling constants e2Q q/h. However, the absolute values of EFGtheo are smaller than the values EFGexp deduced from e2Q q/h. For a fixed central atom MIV the (positive) EFGexp is increasing with increasing radii of the cations (and increasing lattice constant). This increase can be understood by an increase of EFGlattice. On the other hand, for fixed cations and different tetravalent metal atoms, the EFG is increasing with increasing electronegativity of the central atom. This can be understood by an increase of EFGcomplex. For distorted octahedra it is found that the change in the EFG due to the distortion is also due to a change in EFGcomplex.

On the “naive” model of EFG in hcp metals

In the “naive” but fairly successful model by Bodenstedt and Perscheid, the electric field gradient (EFG) in a hcp s-p metal is first evaluated by the lattice sum method, postulating a conduction electron charge shift and approximating the new conduction electron distribution by point charges. Adding to this EFG, a contribution due to the anisotropy of lattice vibrations, i.e. ( − ), was presumed to give the total temperature-dependent EFG. We find, however, from the EFG results of the present calculation for111CdCd and the original result for67ZnZn, that the experimental data are better represented without the addition of the anisotropic vibration term. This finding, as well as the outline of the present evaluation of and and hence the EFG for Cd, are discussed.

Ab initia MO calculation in terms of localized orbitals of the 14N electric field gradient in nitriles

The contributions of each localized orbital of the CN group and of the molecular remainder to the N electric field gradient (EFG) were calculated for nitriles with R=H, F, CH3, OH, NH2, CCH, COH, NO, CN and the E and Z forms of iminoacetonitrile. The changes in the EFG introduced by substituents resulted mainly from the polarization and conjugation of the C-N bonds, with a small contribution from the N lone pair. The total EFG has a large and rather constant contribution from the N lone pair, which is modified by the contributions from the three C-N bonds and the molecular remainder. The resulting EFG is determined by the signs and magnitudes of the C-N bonds' contributions for each substituent and to a lesser degree by the molecular remainders. The asymmetry parameter of the EFG is mainly determined by the inequivalence of the C-N bonds with a very small contribution from the molecular remainder. The molecular remainder and the crystal field in solids contribute more to the largest component of the EFG than to the asymmetry parameter. All these results have allowed us to discuss the validity of the assumptions made in the Townes and Dailey theory when it is applied to nitriles.

Electric-quadrupole interactions in mixed spinels.

The electric quadrupole interactions at the octahedral and tetrahedral sites in the ${\mathrm{NiFe}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{O}}_{4}$ (1.5\ensuremath{\le}x2) spinel system has been studied with $^{57}\mathrm{Fe}$ M\ossbauer spectroscopy. It is found that the analysis of a paramagnetic zero-field spectrum in terms of distribution of quadrupole splittings, caused by the randomization of ions at both sites, gives parameters which explain the shape of an in-field spectrum, whereas the parameters derived from a commonly used two doublet analysis do not. The electric-field-gradient (EFG) calculations at the octahedral site with use of a monopole-point-dipole model, together with an overlap contribution to the EFG, indicate that the EFG sign is positive. The in-field spectrum for the composition x=1.9 demonstrates unambiguously a small weighting to negative sign of the total EFG distributions at both sites. It is proved experimentally, and explained in terms of relaxation effects, that to derive unequivocal information about the sign of the EFG distribution, the in-field spectra should be measured far above the N\'eel temperature. The similarities between the quadrupole interactions in mixed ferric spinels and amorphous compounds are interpreted as evidence for a significant short-range order in the latter.

Electric field gradients in cubic alloys

The theoretical investigations of electric field gradient (EFG) and asymmetry parameter (ν) for cubic dilute alloys are reviewed. The valence and size EFG's and the Sternheimer antishielding factor are discussed in detail. The calculations of EFG and ν for simple and transition metal (TM) dilute alloys of aluminium and copper, TM dilute alloys of vanadium and trinary dilute alloys of noble metals are summarized. It is emphasized that the size EFG is as important as the valence EFG to calculate the total EFG and ν, which are compared with the experimental values. An epilogue for further investigations is added.

Systematics of electric field gradients in metals

The intensive study of electric field gradients (EFG) at the site of atomic nuclei in noncubic metals has revealed several systematic trends, e.g. in the relation of the total EFG to the so called lattice EFG as well as in its variation with temperature. Numerous investigations have been carried out in order to test these systematics. The results will be reviewed and compared to the known trends. Progress in theoretical calculations of the EFG in pure and impurity — host systems will be discussed and compared to the latest available experimental data. Recent measurements of the EFG at metal surfaces and new calculations of the EFG at host sites in impure cubic metals may contribute to the understanding of the EFG in metals.