Electric Field Gradient Modulation in Incommensurate Systems X2YZ4

1986 ◽  
Vol 41 (1-2) ◽  
pp. 256-260
Author(s):  
J. Pirnat ◽  
J. Lužnik ◽  
Z. Trontelj
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Point Charge ◽  
Reasonable Agreement ◽  
Point Charge Model ◽  
Resonant Nucleus ◽  
Charge Model ◽  
The Subject ◽  
Wave Limit

The subject of the paper is the plane wave limit of static incommensurate displacement modulation in the crystal structure, which is related to the commensurate ferrophase modulation. Using the point charge model, the corresponding electric field gradient modulation and quadrupole perturbed NMR spectra are calculated. The corrections up to the 4th order owing to the incoherent displacements of the charges in the vicinity of the resonant nucleus are considered. Comparison with the experimental data shows a reasonable agreement.

scholarly journals Theoretical Study of the Electric Field Gradient in Silver Iodide

1992 ◽  
Vol 47 (1-2) ◽  
pp. 182-188
Author(s):  
G. Frantz ◽  
R. Leiberich ◽  
P. C. Schmidt
Keyword(s):  
Band Structure ◽  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Point Charge ◽  
Cluster Approach ◽  
Point Charge Model ◽  
Hartree Fock ◽  
Charge Model ◽  
Theoretical Results

AbstractThe electric field gradient (EFG) in hexagonal Agl at the iodine site is studied theoretically by three different procedures, namely the point charge model, the Hartree-Fock cluster approach, and the augmented plane wave band structure procedure. A comparison is made for the electronic charge distribution and the sizes of the various contributions to the EFG obtained by the different procedures. From the point charge model and the Hartree-Fock cluster approach one gets almost the same result for the EFG, q = +0.743 • 1021 V/m2 and +0.816 • 1021 V/m2 respectively. Only a rather preliminary result of q = +0.393 • 1021 V/m2 is found by the band structure calculation to be compared with the experimental value of qexp= ±0.415 • 1021 V/m2 . The confidence limits of the theoretical results are discussed, including possible ways to bridge the gap between the theoretical results by different methods and experiment. Both the cluster and the band structure calculations are shown to support an ionic model for hexagonal Agl with some overlap between the charge distributions on neighboring ions.

Electric field gradient at Cu nucleaus in CuO: single-crystal NMR determination and point charge model

1991 ◽  
Vol 181 (1-3) ◽  
pp. 121-126 ◽  
Author(s):  
L. Cristofolini ◽  
G. Amoretti ◽  
C. Bucci ◽  
P. Carretta ◽  
R. De Renzi ◽  
...  
Keyword(s):  
Electric Field ◽  
Single Crystal ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Point Charge ◽  
Point Charge Model ◽  
Charge Model

scholarly journals Theoretical Studies of the Electric Field Gradient in Hexachlorometallates

1988 ◽  
Vol 43 (7) ◽  
pp. 643-650 ◽  
Author(s):  
Dirk Borchers ◽  
Peter C. Schmidt ◽  
Alarich Weiss
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Central Atom ◽  
Coupling Constants ◽  
Point Charge Model ◽  
Metal Atoms ◽  
Charge Model ◽  
Quadrupole Coupling ◽  
Distorted Octahedra

Abstract The electric field gradient (EFG) at the chlorine site is calculated for cubic compounds of the K2PtCl6-type (space group Fm3m), M2IMIVCl6, 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.

Determination of electric field gradient parameters in tellurium

1976 ◽  
Vol 54 (16) ◽  
pp. 1692-1698 ◽  
Author(s):  
K. Hamilton ◽  
B. M. Powell ◽  
P. Martel
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Inelastic Neutron Scattering ◽  
Mean Square Displacement ◽  
Inelastic Neutron ◽  
Charge Model ◽  
Bond Charge ◽  
Bond Charge Model

The relative intensities of the Mössbauer doublet in Te have been analysed at 4 K and 80 K by utilizing values of the mean square displacement tensor derived from inelastic neutron scattering measurements. The orientation β of the electric field gradient ellipsoid and its asymmetry parameter η have been determined. At 4 K, β = 90°, η = −0.17 and at 80 K, β = 92°, η = −0.48. A simple 'bond charge' model is proposed in an attempt to understand the discrepancy between these values of the electric field gradient parameters and those obtained theoretically by other authors.

scholarly journals Response of the Electric Field Gradient in Ion implanted BaTiO3 to an External Electric Field

2000 ◽  
Vol 655 ◽  
Author(s):  
Marc Dietrich ◽  
Jörn Bartels ◽  
Manfred Deicher ◽  
Kristian Freitag ◽  
Vyacheslav Samokhvalov ◽  
...  
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
External Electric Field ◽  
Correlation Spectroscopy ◽  
Quadratic Term ◽  
Linear Change ◽  
Model Calculations ◽  
Charge Model ◽  
Piezoelectric Constants

AbstractSingle crystalline, ferroelectric BaTiO3 as material with the highest piezoelectric constants among the perovskites with ordered sublattices was implanted with 111In(111Cd). The electric field gradient at the Ti position was measured with perturbed γγ-angular correlation spectroscopy (PAC) while the crystal was exposed to an external electric field. A quadratic dependence could be observed: νQ(E) = (34.8(1) + 0.16(4) E/kV/mm + 0.080(2) E2/kV2/mm2) MHz. Point charge model calculations reproduce the linear change of Vzz, but not the quadratic term. The polarizability of the host ions of BaTiO3 is known to be nonlinear with respect to an electric field. The resulting quadratic shift of the electron density is reflected in the strength of the EFG.

Core level ligand field splittings in photoelectron spectra

1980 ◽  
Vol 293 (1405) ◽  
pp. 535-569 ◽  
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Reasonable Agreement ◽  
Alkali Halides ◽  
Core Level ◽  
Photoelectron Spectra ◽  
Ligand Field ◽  
Electrostatic Model ◽  
The Core

An electrostatic model is developed to explain the recently characterized ligand field splittings observed in the core level photoelectron spectra of main group compounds. As for the nuclear electric field gradient splittings observed by Mössbauer and n.q.r. spectroscopy, we show that the electronic splittings also originate from the asymmetric part of the ligand field. Moreover, this ligand field can be divided into the two terms analogous to those used to describe the nuclear electric field gradient splitting: the valence term, eq v , due to the non-uniform population of the valence p, d or f orbitals on the atom M of interest; and the point charge or ligand term, eq 1, due to the non-cubic orientation of ligand point charges about M . Other ‘cross’ terms which are not present for the nuclear splitting are assumed to be small. We calculate the ligand term, eq 1 , for the alkali and halide outer p orbitals in the alkali halides, the T1 5d orbitals in TlCl, and the Au 4f orbitals in AuCl- 2 . Wherever experimental results are available, our calculations are in reasonable agreement. The splittings due to eq v for a large number of p, d and f levels are then calculated using a 'pseudo-atomic’ approach with one adjustable parameter — the excess (or deficient) valence orbital population along the z -axis, Ap. The two terms are combined to calculate the core level splittings in Me 2 Zn, ZnCl 2 , Me 2 Cd and XeF 2 . Nuclear electric field gradients in these compounds are then calculated from the electronic splittings, and shown to be generally in reasonable agreement with experiment. The importance of open shell Sternheimer shielding—antishielding parameters on both the core electronic splitting and the nuclear splitting is explored and justified.

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