Static Electric Field Gradient Research Articles

Effect of Dynamical Motion in ab Initio Calculations of Solid-State Nuclear Magnetic and Nuclear Quadrupole Resonance Spectra.

Solid-state nuclear magnetic resonance (SSNMR) and nuclear quadrupole resonance (NQR) spectra provide detailed information about the electronic and atomic structure of solids. Modern ab initio methods such as density functional theory (DFT) can be used to calculate NMR and NQR spectra from first-principles, providing a meaningful avenue to connect theory and experiment. Prediction of SSNMR and NQR spectra from DFT relies on accurate calculation of the electric field gradient (EFG) tensor associated with the potential of electrons at the nuclear centers. While static calculations of EFGs are commonly seen in the literature, the effects of dynamical motion of atoms in molecules and solids have been less explored. In this study, we develop a method to calculate EFGs of solids while taking into account the dynamics of atoms through DFT-based molecular dynamics simulations. The method we develop is general, in the sense that it can be applied to any material at any desired temperature and pressure. Here, we focus on application of the method to NaNO2 and study in detail the EFGs of 14N, 17O, and 23Na. We find in the cases of 14N and 17O that the dynamical motion of the atoms can be used to calculate mean EFGs that are in closer agreement with experiments than those of static calculations. For 23Na, we find a complex behavior of the EFGs when atomic motion is incorporated that is not at all captured in static calculations. In particular, we find a distribution of EFGs that is influenced strongly by the local (changing) bond environment, with a pattern that reflects the coordination structure of 23Na. We expect the methodology developed here to provide a path forward for understanding materials in which static EFG calculations do not align with experiments.

Cobalt-59 NMR relaxation times of symmetric tris(γ-substituted-acetylacetonato)cobalt(III) complexes in benzene

Cobalt-59 NMR relaxation times, T1(59Co), and chemical shifts, δ(59Co), of symmetric tris(γ-substituted-acetylacetonato)cobalt(III) complexes, [Co(acac-X)3], which have chloride, bromide, nitro, and phenyl groups at the methine carbon atoms in the chelate ligands, have been measured in benzene at four temperatures between 284 and 319 K. In view of the viscosity dependence of 1/T1(59Co), the 59Co relaxation is caused by the reorientation of the static electric field gradient at the nucleus in every complex. Assuming that the rotational volume is replaced by the van der Waals volume, the nuclear quadrupolar coupling products, {(1 + ηq2/3)(eQq/h)2}1/2, were obtained for the series of [Co(acac-X)3] complexes in benzene. The negative correlation between {(1 + ηq2/3)(eQq/h)2}1/2 and δ(59Co) was observed for the four complexes [Co(acac)3], [Co(acac-Cl)3], [Co(acac-Br)3], and [Co(acac-NO2)3] except for [Co(acac-Ph)3]. This discrepancy strongly suggests that the rotational volume of the propeller-like [Co(acac-Ph)3] complex with the protruding phenyl groups cannot be simply treated as the van der Waals volume, different from the other almost spherical complexes. Actually, the estimation of the rotational volumes from the distances between the central cobalt and g-substituents gave much better correlation between {(1 + ηq2/3)(eQq/h)2}1/2 and δ(59Co) for all the complexes including [Co(acac-Ph)3].

Quantum many-body physics with ultracold polar molecules: Nanostructured potential barriers and interactions

We design dipolar quantum many-body Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both single-body potential barriers and two-body dipolar interactions on a spatial scale of tens of nanometers to strongly enhance energy scales and, therefore, relax temperature requirements for observing new quantum phases of engineered many-body systems. We consider and compare two approaches. In the first, nanoscale barriers are generated with standing wave optical light fields exploiting optical nonlinearities. In the second, static electric field gradients in combination with microwave dressing are used to write nanostructured spatial patterns on the induced electric dipole moments, and thus dipolar interactions. We study the formation of inter-layer and interface bound states of molecules in these configurations, and provide detailed estimates for binding energies and expected losses for present experimental setups.

Polarizability and electric field gradient of two-electron quantum dots

The energy levels of the quantum dots are evaluated by using Quantum Genetic Algorithm procedure and Hartree-Fock Roothaan method. Based on the calculated energies and wave functions, static dipole polarizability, oscillator strength and electric field gradient of helium/helium-like quantum dots are calculated as a perturbative calculation. It is worth to note that impurity charge and dot radius have a strong effect on the dipole polarizability, the oscillator strength and the electric field gradient. In small dot radii, since the spatial confinement effect is dominant, the polarizability of system is very weak. The polarizability increases monotonically with the increase of dot radius and then reaches a saturation value in large dot radii. On the other hand, the electric field gradient increases as dot radius decreases.

Erratum to: The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock

The systematic shifts of the transition frequencies in the molecular hydrogen ions are of relevance to ultra-high-resolution radio-frequency, microwave and optical spectroscopy of these systems, performed in ion traps. We develop the ab initio description of the interaction of the electric quadrupole moment of this class of molecules with the static electric field gradients present in ion traps. In good approximation, it is described in terms of an effective perturbation Hamiltonian. An approximate treatment is then performed in the Born–Oppenheimer approximation. We give an expression of the electric quadrupole coupling parameter valid for all hydrogen molecular ion species and evaluate it for a large number of states of H 2 + , HD+, and D 2 + . The systematic shifts can be evaluated as simple expectation values of the perturbation Hamiltonian. Results on radio-frequency, one-photon electric dipole (E1), and two-photon E1 transitions between hyperfine states in HD+ are reported. For two-photon E1 transitions between rotationless states, the shifts vanish. For a large subset of rovibrational one-photon transitions, the absolute values of the quadrupole shifts range from 0.3 to 10 Hz for an electric field gradient of 108 V/m2. We point out an experimental procedure for determining the quadrupole shift which will allow reducing its contribution to the uncertainty of unperturbed rovibrational transition frequencies to the 1 × 10−15 fractional level and, for selected transitions, even below it. The combined contributions of black-body radiation, Zeeman, Stark and quadrupole effects are considered for a large set of transitions, and it is estimated that the total transition frequency uncertainty of selected transitions can be reduced below the 1 × 10−15 level.

The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock

The systematic shifts of the transition frequencies in the molecular hydrogen ions are of relevance to ultra-high-resolution radio-frequency, microwave and optical spectroscopy of these systems, performed in ion traps. We develop the ab-initio description of the interaction of the electric quadrupole moment of this class of molecules with the static electric field gradients present in ion traps. In good approximation, it is described in terms of an effective perturbation hamiltonian. An approximate treatment is then performed in the Born-Oppenheimer approximation. We give an expression of the electric quadrupole coupling parameter valid for all hydrogen molecular ion species and evaluate it for a large number of states of H2+, HD+, and D2+. The systematic shifts can be evaluated as simple expectation values of the perturbation hamiltonian. Results on radio-frequency (M1), one-photon electric dipole (E1) and two-photon E1 transitions between hyperfine states in HD+ are reported. For two-photon E1 transitions between rotationless states the shifts vanish. For a subset of rovibrational one-photon transitions the quadrupole shifts range from 0.2 to 10 Hz for an electric field gradient of 0.1 GV/m2. We point out an experimental procedure for determining the quadrupole shift which will allow reducing its contribution to the uncertainty of unperturbed rovibrational transition frequencies to the 1.10^(-15) relative level and, for selected transitions, even below it. The combined contributions of black-body radiation, Zeeman, Stark and quadrupole effects are considered for a large set of transitions and it is estimated that the transition frequency uncertainty of selected transitions can be reduced below the 1.10^(-15) level.

Nonmetallic behaviour in half-Heusler phases YPdSb, YPtSb and LuPtSb

We present the results of combined macroscopic [magnetic susceptibility, heat capacity, electrical resistivity] and microscopic [nuclear magnetic resonance (NMR)] studies of half Heusler phases YPdSb, YPtSb and LuPtSb. The bulk results indicated diamagnetic and nonmetallic behaviours. The Solomon quadrupolar echoes revealed for all three materials the presence of some static electric field gradients, and thus some small deviation from the perfect cubic symmetry. The spin-lattice relaxation rates of the 121,123Sb nuclei were shown to be nonmetallic, quadrupolar in nature and due to the dominant two-phonon Raman processes.

Alternating electric force microscopy: Static electric field gradient imaging in an air atmosphere for Ba0.7Sr0.3TiO3 ferroelectric thin film

An alternating electric force microscopy (A-EFM) technique, which is effective for the imaging of static electric field gradient in an air atmosphere, is proposed by using our developed alternating force microscopy. A-EFM uses a frequency modulation of a mechanically oscillating conductive tip, which is induced by applying off-resonant AC voltage to the tip. The AC voltage generates off-resonant alternating electric force at the tip. A-EFM detects static electric field gradient with the field polarity from a sample without involving surface forces by using a lock-in detection technique. For a Ba0.7Sr0.3TiO3 ferroelectric thin film, A-EFM clearly imaged the static electric field gradient with field polarity and the boundary of electric domain in an air atmosphere.

Simulation of ion noise in microwave tubes by two-dimensional particle-in-cell method

The ion noise in microwave tube is studied using two-dimensional particle-in-cell method. The fluctuation of the ion amount, which is the source of ion noise of the tube, is observed in the simulation process. It is found that the sufficient ions amount in drift tube and beam envelope scalloping appear to be responsible for ion noise after changing the gas pressure, magnetic focusing field, and drift tube length. A great number ions escape radially and their amount is about half of the beam electron when ion noise occurs. The number of secondary electron is less than that of the ion and beam electron; it affects the ion noise very slightly. There are two ways can be used for depressing the ion noise. The first is adjusting or increasing the magnetic focusing field in drift tube. The second is creating static electric field gradient to make the ions leave the interaction space quickly.

Birefringence induced by a static electric field gradient

A quantum theory of the birefringence induced in a molecular gas by a static electric field gradient is presented; it is an application of the finite temperature perturbation theory to molecular light scattering described in the preceding paper. The kinematics of the experiment are dealt with explicitly through the use of a space-fixed frame based on a set of canonically conjugate variables for the centre-of-mass and internal motions of the molecule. This leads to a definition of the molecular multipoles that is different from the conventional one and there are no ‘origin-dependence problems’ at any stage of the calculation. The susceptibility that governs the birefringence is analysed in the spirit of Van Vleck's quantum mechanical account of polarity in terms of the magnitude, relative to k B T, of the energy level separations associated with the dominant matrix elements of the external field V and the current operator j(k). As in previous treatments, the main contribution is inversely proportional to the temperature, and there is also a temperature independent term. The birefringence depends on the matrix elements of the molecular quadrupole moment operator; in the framework used here, this has a definition independent of the polarity of the molecule.

Birefringence induced by a static electric field gradient

Birefringence induced by a static electric field gradient

129Xe and131Xe NMR of Xenon in Mesophases of Cetyltrimethylammonium Bromide in Formamide

For the first time, noble gas NMR has been applied to a study of a lyotropic liquid crystal.129Xe and131Xe NMR spectra of natural xenon gas dissolved in pure formamide and three cetyltrimethylammonium bromide (CTAB)/formamide (FA) mixtures were recorded over wide temperature ranges. The CTAB/FA system forms micelles at low concentrations of CTAB and mesophases at higher concentrations and elevated temperatures. The phase transitions are observed in the series of xenon spectra. In addition, the free xenon gas signal is seen in the spectra at low temperature, when the CTAB/FA system has a coexisting solid/liquid phase. The gas signal indicates that Xe is not soluble in the solid but accumulates in macroscopic bubbles. The intensity variation of the central peak of the131Xe NMR spectra shows the presence of a static external electric field gradient (EFG). However, the spectral satellites are not observed and, therefore, the magnitude of the EFG cannot be determined. The obvious reason for the missing131Xe satellites is the orientation distribution of the EFG tensor leading to broadening of the satellites.

Mössbauer NMR double resonance in57Fe. Coupling between quadrupole split states

In order to describe the interaction of a nucleus (in a static electric field gradient) with a radiation field, we have introduced the concept of “dressed nucleus”. The eigenvalues of its Hamiltonian are calculated, which leads to expressions for the different energies of γ-rays produced by spontaneous emission. We have calculated these energies as well as their relative probabilities in the case ofIe=3/2--Ig=1/2- Ml transitions. We have shown that a Mossbauer spectrum using as a source an ensemble of “dressed nuclei” and a single line absorber consists of six lines: two lines of the original quadrupole doublet and four sidebands, each of them having the same intensity.

Dynamics in incommensurate phases studied by NMR: Theory and relaxation measurements on 87Rb satellites in Rb2ZnCl4.

A general formalism is developed for describing nuclear-spin-lattice relaxation for quadrupolar perturbed nuclear magnetic resonance (NMR) in structurally incommensurately (IC) modulated crystals in terms of the elementary excitations of these systems. Our discussion deviates from previous ones as regards the identification of the amplitudon and phason induced relaxation rates 1/${\mathit{T}}_{1\mathit{A}}$ and 1/${\mathit{T}}_{1\mathrm{\ensuremath{\varphi}}}$ in the plane wave limit as well as the temperature dependence of ${\mathit{T}}_{1\mathrm{\ensuremath{\varphi}}}$ in the soliton limit. Measurements are reported for the spin-lattice relaxation of the $^{87}\mathrm{Rb}$ satellite transitions in the normal, incommensurate, and commensurate phases of the prototype incommensurate system ${\mathrm{Rb}}_{2}$${\mathrm{ZnCl}}_{4}$. At ambient temperature the variation of the nuclear magnetic relaxation rate is measured over the incommensurately broadened distribution of resonance frequencies for two crystal orientations. The ${\mathit{T}}_{1}$ model developed is applied to these data, making use of the Fourier series of the static electric field gradient determined from the NMR satellite spectra in the IC phase. A strict agreement is found. The temperature dependence of ${\mathit{T}}_{1}$ is determined in that crystal orientation where a well-defined assignment of ${\mathit{T}}_{1\mathit{A}}$ and ${\mathit{T}}_{1\mathrm{\ensuremath{\varphi}}}$ can be given. In the low-temperature part of the incommensurate phase, our data reflect the local softening of phase fluctuations in the discommensurations or the flattening out of the corresponding acoustic branch what is in accordance with our theoretical prediction and in contrast to previous results. The relevance of phason gaps previously derived from NMR data is discussed.

Angular dependence of deuterium spin-lattice relaxation rates of macroscopically oriented dilauroylphosphatidylcholine in the liquid-crystalline state

Deuterium (2H) NMR relaxation plays a major role in the study of lipid reorientational dynamics, with the angular dependence of the relaxation rates providing a novel and critical test of proposed motional models. Spin-lattice relaxation rates (R1Z) were measured for macroscopically oriented bilayers of 1,2-diperdeuteriolauroyl-sn-glycero-3-phosphocholine (DLPC-d46) in the liquid-crystalline (Lα) phase. The results for different positions along the chain (index i) were dependent on the angle θ between the macroscopic bilayer normal and the static external magnetic field, and allowed the anisotropy of R(i)1Z to be determined for nine resolved quadrupolar resonances. Angular-dependent relaxation data were evaluated using simple models of anisotropic rotational diffusion within an odd or even potential of mean torque as a framework for describing (i) segmental reorientations of the chains, or alternatively (ii) noncollective molecular motions within the bilayer. Moreover, (iii) a simple quasi-hydrodynamic formulation involving collective fluctuations of a local director axis was considered (continuum model). For segmental motions the static electric field gradient (EFG) tensor due to the electronic structure of the C–2H bond is averaged by local reorientations of the acyl chains, e.g., due to trans–gauche rotational isomerizations and/or torsional oscillations. The second and third formulations assume the static EFG tensor is preaveraged by local motions, yielding a residual EFG tensor which is further modulated by order fluctuations due to relatively slow motions of larger amplitude; separation of time scales is implicit. The latter treatments differ in that the molecular model allows for variation in both the principal values and principal axes of the residual EFG tensor, and includes the possibility of a nonzero effective asymmetry parameter ηeff. By contrast, the collective model considers an axially symmetric residual EFG tensor (ηeff=0), in which the relatively slow motions are described in terms of continuum fluctuations of a local director axis within the small-angle approximation. Each of the three models can account for the observed angular anisotropy of the R(i)1Z relaxation rates along the chains to a greater or lesser degree of success, depending on the number of adjustable parameters. The collective formulation has the fewest parameters and may be an oversimplification for description of the relaxation anisotropy. In addition, for each bilayer orientation, profiles of the relaxation rates R(i)1Z and order parameters ‖SCD(i)‖ as a function of acyl position exhibited a square-law functional dependence within experimental error. This observation points to an influence on the relaxation arising from relatively slow fluctuations in the order gradient set up along the chains by faster internal motions, viz. order fluctuations due to noncollective molecular motions or collective excitations of the bilayer. Finally, the rather small contribution from local internal motions suggests that the microviscosity of the bilayer interior corresponds to essentially liquid hydrocarbon. These new results illustrate the utility of R(i)1Z angular anisotropies of phospholipids having perdeuterated acyl chains in experimental and theoretical investigations of molecular dynamics in liquid-crystalline bilayers. The implications of the findings in relation to previous biophysical studies of membranes are discussed.

Studies of graphite intercalation compounds using time-differential perturbed angular distributions

The technique of time-differential perturbed angular distributions (TDPAD) was used to investigate the structure of graphite samples intercalated by AsF5 vapor. Following population of the 198 keV state (τ=125 ns, Q=0.072b) of 19F by the 19F(p, p′γ) reaction, measurements of the γ-ray angular distribution were performed to give information on quadrupole interactions. Theoretical fits reveal the presence of two static electric field gradient (efg) interactions, the principal one corresponding to the formation of CF bonds, with quadrupole frequency νQ=57.4±0.8MH z. Although information on graphite intercalation chemistry was not forthcoming from the measurements, it is shown that the strong texture exhibited in the perturbation spectra can be explained in terms of the angular dependence of the efg, suggesting a novel method for the characterization of graphite intercalation compounds.

Aftereffects following β-decay of181Hf1

Time differential perturbed angular correlation spectra of181Ta produced by beta decay of181Hf in monoclinic ZrO2 have been measured over a temperature range 10K to 1300K. If times near t=0 are excluded, G2(t) is well fitted by a standard single site model for nuclei subject to an interaction with a static electric field gradient. For high purity samples, the effective anisotropy A2 is equal to its expected value above 200°C but decreases abruptly by approximately a factor of two for lower temperatures. This unusual decrease, which does not occur in natural crystals or in Nb-doped powders, is attributed to an aftereffect of the beta emission that populates with approximately 50% probability an electron trap located about one eV below the conduction band. At low temperatures, this trapped electron causes the Ta nucleus to relax rapidly and contributes to G2(t) only near t=0. At high temperatures or in doped samples the electron escapes quickly enough to have negligible effect on G2(t).

Temperature dependence of quadrupole interaction in high T c superconductor YBa 2(Cu 0.9Ag 0.1) 3 O 7−δ

The temperature dependence of quadrupole interaction in high-Tc superconductor YBa 2(Cu 0.9Ag 0.1) 3 O 7−δ has been measured over temperature range 77–298K by using the perturbed angular correlation (PAC) spectroscopy. Two static electric field gradients (EFGs), the non-axially symmetric and the axial symmetric EFGs, have been derived from each time differential perturbed angular correlation (TDPAC) spectrum taken at a specific temperature between 114K and 298K, they are assigned to Cu(1) and Cu(2) sites in the oxygen-deficient perovskite structure respectively. The non-axially symmetric EFG shows a sudden transition around 90K. Nuclear relaxation phenomena are observed from the TDPAC spectra simultaneously. From the behavior of temperature dependence of normal state relaxation, we make the suggestion that the relaxation is magnetic in nature, and it seems that any dynamical field in the interactions due to particle motion has to be excluded.

Orientational anisotropy of nuclear spin relaxation in phospholipid membranes

The observation that the spin-lattice relaxation ( R 1 Z ) rates of pure phospholipid lamellar phases depend only weakly on their orientation in the liquid-crystalline state is explained. A relaxation model in which either segmental or molecular motions are described by anisotropic rotational diffusion in an ordering potential (M.F. Brown, J. Chem. Phys. 77 (1982) 1576) can account for the available 2H R 1 Z data to within experimental error. One possibility is that rotational isomerization breaks the symmetry of the static electric field gradient, leading to an asymmetric residual tensor which is further modulated by molecular motions.

Differentiation of models of rapid molecular motion by 2H NMR lineshape simulations

Slow molecular motions in solids can, in principle, be thoroughly studied over a wide dynamic range by the analysis of 2H NMR lineshapes. However, for fast motions with correlation times less than 10 −7 s the lineshapes become insensitive to the time scale of the motion. In this limit, the NMR lineshapes only provide limited information about the geometry of the motion; in the case of an axially symmetric static electric field gradient tensor (C- 2H bond), one can only unambiguously discriminate between planar and nonplanar motions. As a consequence, the frequently observed near gh ∗ = 1 experimental lineshape is compatible with many models of motion. For example, it is impossible to distinguish between certain families of rapid jumps and families of rapid librations from 2H NMR lineshapes even when T 2 relaxation is considered. However, these motional mechanisms can be distinguished via lineshape distortions resulting from the anisotropic spin-lattice relaxation ( T 1 and T 1Q).