Dependence Of Electric Field Gradient Research Articles

Towards anab initiotheory for the temperature dependence of electric field gradients in solids: Application to hexagonal lattices of Zn and Cd

Based on ab initio band structure calculations we formulate a general theoretical method for description of the temperature dependence of electric field gradient in solids. The method employs a procedure of averaging multipole electron density component (l \neq 0) inside a sphere vibrating with the nucleus at its center. As a result of averaging each Fourier component (K \neq 0) on the sphere is effectively reduced by the square root of the Debye-Waller factor [exp(-W)]. The electric field gradient related to a sum of K-components most frequently decreases with temperature (T), but under certain conditions because of the interplay between terms of opposite signs it can also increase with T. The method is applied to calculations of the temperature evolution of the electric field gradients of pristine zinc and cadmium crystallized in the hexagonal lattice. For calculations within our model of crucial importance is the temperature dependence of mean-square displacements which can be taken from experiment or obtained from the phonon modes in the harmonic approximation. For the case of Zn we have used data obtained from single crystal x-ray diffraction. In addition, for Zn and Cd we have calculated mean-square displacements with the density functional perturbation treatment of the Quantum Espresso package. With the experimental data for displacements in Zn our calculations reproduce the temperature dependence of the electric field gradient very accurately. Within the harmonic approximation of the Quantum Espresso package the decrease of electric field gradients in Zn and Cd with temperature is overestimated. Our calculations indicate that the anharmonic effects are of considerable importance in the temperature dependence of electric field gradients.

Local structure study of Hf dopants in Zr2Pd and ZrPd2 intermetallics

The intermetallic compounds Zr2Pd and ZrPd2 have been investigated by perturbed angular correlation (PAC) spectroscopy considering anomalies in their hydrogen absorption properties. It is known that both these compounds have same crystal structure, but Zr2Pd forms an excellent hydride while ZrPd2 does not, even at high pressure. From PAC measurement at room temperature in annealed ZrPd2 sample, this phase is found as a minor component (∼27%) while the dominating phase is identified to be the ZrPd3 (∼73%). In Zr2Pd, this phase has been found to be predominant (∼86%) along with a minor phase (∼14%) due to ZrPd. In ZrPd2, unlike Zr2Pd, a weak temperature dependence of electric field gradient (EFG) has been found from present PAC measurements. Also, site occupancies for both Zr and Pd atoms by the Ta-probe atoms have been found in ZrPd2 and ZrPd3 (formed in ZrPd2). In ZrPd3, Pd site occupancy by the probe is found to be maximum while a small fraction for Zr site occupancy has been found. But, in case of Zr2Pd and ZrPd, no Pd site occupancy of the probe is observed. Calculation of electric field gradients at 181Ta impurity atom for different phases have been performed by density functional theory based on the all electron full potential linearized augmented plane wave plus local orbitals (FP-(L)APW + lo) method to assign the different components observed from PAC measurements. Measurements by XRD have also been carried out to confirm the presence of component phases in the samples.

Perturbed angular correlation investigation of the electric field gradient at 181Ta probe in the Hf2Ni7 compound

The perturbed angular correlation method was employed to study the temperature dependence of electric field gradients at the 181Ta probe in the polycrystalline Hf2Ni7 compound. The temperature evolution of the sample content was measured using high-temperature X-ray diffraction. To check the magnetic order of the sample, magnetization measurements and additional perturbed angular correlation measurements with externally applied magnetic field were performed. All obtained spectra showed no evidence of magnetic order of the Hf2Ni7 phase. Within the experimental resolution of the apparatus, the measured electric field gradients at 181Ta probe for the two inequivalent 181Hf/181Ta sites in the Hf2Ni7 compound appeared as one in the range of 78-944 K. A single quadrupole interaction implies that the electric field gradients at the two Hf sites must be quite similar. At 293 K, the measured quadrupole interaction parameters are ?Q = 433(1) MHz and ? = 0.300(4). An increase of the quadrupole frequency and a gradual rising of the asymmetry parameter were observed with increasing temperature. The high-temperature X-ray diffraction indicated a build up of HfO2 above 693 K.

Investigation of spin transition in GdCoO 3 by measuring the electric field gradient at Co sites

In the present work, the time differential perturbed angular correlation (PAC) technique was used to study the temperature dependence of electric field gradient (efg) in GdCoO 3 perovskite using 111Cd and 181Ta nuclear probes. The radioactive parent nuclei 111In and 181Hf were introduced in the oxide lattice through chemical process during sample preparation and were found to occupy only the Co sites in GdCoO 3. The efg's at 111Cd and 181Ta show temperature dependence with two different fractions each that change with temperature. In the case of 111Cd the quadrupole frequency slowly decreases, with corresponding increase of the temperature and shows a peak like structure at around 200 K and a discontinuity at 700 K. These changes have been interpreted as thermally activated spin-state transitions from low-spin ground state configuration to the intermediate-spin state and from intermediate-spin to high-spin state of Co 3 + ion similar to LaCoO 3 compound. Indication of a Jahn–Teller distortion, which stabilizes the intermediate-spin state with orbital ordering, is also pointed out.

Temperature dependence of electric field gradient in TbCoO3

Temperature dependence of electric field gradient in TbCoO3

Temperature dependence of electric field gradient inLaCoO3 perovskite investigated by perturbed angular correlation spectroscopy

The time differential perturbed angular correlation (TDPAC) technique wasused to study the temperature dependence of electric field gradient (EFG) inLaCoO3 perovskite using and nuclear probes. The radioactive parent nuclei111In and 181Hf were introduced into the oxide lattice through a chemical process duringsample preparation and were found to occupy only the Co sites inLaCoO3. The PACmeasurements with 111Cd and 181Ta probes were made in the temperature range of 4.2–1146 K and 4.2–1004 K,respectively. No long-range magnetic order was observed up to 4.2 K. The EFGs at111Cd and 181Ta show very similar temperature dependences. They increase slowly between 4.2 and about77 K and then decrease almost linearly with increasing temperature until about 500–600 K,where a broad peak-like structure is observed, followed by linear decrease at stillhigher temperatures. These discontinuities at about 77 K and 500–600 K havebeen interpreted as thermally activated spin state transitions from the low-spin(t2g6eg0) ground state configuration to the intermediate-spin(t2g5eg1) state and from the intermediate-spin to the high-spin(t2g4eg2) stateof the Co3+ ion, confirming previous observation in other recent studies. An indication of a Jahn–Tellerdistortion, which stabilizes the intermediate-spin state with orbital ordering, is also pointedout.

Sb-NQR Probe for Multipole Degree of Freedom in the First Pr-Based Heavy-Fermion Superconductor PrOs4Sb12

We report 121,123 Sb nuclear quadrupole resonance (NQR) measurements in the filled-skutterudite superconductor PrOs 4 Sb 12 in the temperature range of 0.05–30 K. The electric field gradients (EFG), V z z and V x x - V y y , at the Sb site exhibit unusual temperature dependence below 30 K. To explain these features, we discuss the coupling between the Sb nuclear quadrupole moment and Pr 4 f 2 -derived multipole moments. The observed T dependence of EFG is well explained by the CEF pseudo-quartet consisting of Γ 1 singlet and Γ 4 (2) triplet states in the cubic point group T h . These results, in turn, are indicative of the importance of the coupling between the 121,123 Sb quadrupole moments and the hexadecapole moment caused by the pseudo-quartet.

Calculation of Electric Field Gradients in Isolated Molecules Using the FPLAPW-Code WIEN95

Abstract The full potential linearized augmented plane wave method as embodied in the program package WIEN95 was originally developed for crystalline solids and is based on crystal periodicity. The present work demonstrates that it is applicable to isolated molecules with the examples of CdCl2 , HgF2 , and HgCl2 by investigating the required size of artificially enlarged unit cells and by calculating bond distances and vibrational frequencies in excellent agreement with experimental data. The dependence of electric field gradients at Cd and Hg, respectively, on bond angle is investigated. A point charge like behaviour of energetically low lying states is found, whereas large discrepancies from the point charge model occurred for the energetically high lying valence states.

Electric field gradient and its temperature variation at a 181Ta probe in Zr2Fe and Zr2Co intermetallic compounds

In this paper we report a time differential perturbed angular correlation study of electric field gradients and their temperature variation in Zr2T (T = Fe,Co) intermetallic compounds (C16 crystallographic structure). Measurements were performed at a 181Ta radioactive probe in the temperature range 20 K–1173 K. In both samples only one strong asymmetric quadrupole interaction was observed, consistently with one possible crystallographic position of the probe atom in the studied structure. The quadrupole coupling constant is equal to 1039(8) MHz with asymmetry parameter η = 0.82 and 889(7) MHz with η = 1 at room temperature for Zr2Fe and Zr2Co respectively. In the investigated temperature range a linear dependence of electric field gradient was observed in contrast to the T32 dependence found in most intermetallic compounds and non-cubic metals.

Critical behavior of electric field gradient in MnSi studied by muon level-crossing resonance

The electric quadrupole interaction of55Mn nuclei was studied in the weakly ferromagnetic system MnSi using muon level-crossing resonance (μLCR) technique. The temperature dependence of the electric field gradient (EFG) shows a critical behavior near the ferromagnetic transition temperature, indicating that the EFG due to the conduction electron is strongly correlated with the magnetic susceptibility in the itinerant electron magnetism. The temperature dependence of EFG is in reasonable agreement with the self-consistent renormalization theory developed by Moriya and coworkers.

Temperature dependence of electric field gradients at the nucleus of adsorbed alkali-metal atoms

Experimentally a linear temperature dependence of electric field gradients at the nucleus of adsorbed Li and Na atoms was found within the temperature interval 1100 K⩽ T⩽1600 K for the following adsorbate-surface combinations: 7LiMo(110), 7LiMo(100), 7LiW(100), 23NaW(100) and 23NaW(110). The linear temperature dependence of the electric field gradient may be understood by the high-temperature behaviour of the Debye-Waller factor for conduction electrons.

Temperature dependence of electric field gradients at the nucleus of adsorbed alkali-metal atoms

Temperature dependence of electric field gradients at the nucleus of adsorbed alkali-metal atoms

Current Status of Theory of Nuclear Quadrupole Interaction in Metallic Systems

This paper deals with the current status of understanding of the factors that determine the origin of nuclear quadrupole interactions in metallic systems. The major emphasis is on pure metals in which there is currently better understanding of the origin of the electric field gradient (EFG) at the nuclear sites. The procedures for the determination of the electron densities that lead to the electronic contributions to the EFG’s is discussed as well as the quantitative procedures for incorporation of antishielding effects. The nature of agreement between theory and experiment is examined by considering the hexagonal close packed metals beryllium, magnesium, zinc and cadmium. The sensitiveness of the calculated EFG to the procedure used for obtaining electron densities is discussed in beryllium using orthogonalized plane wave and augmented plane wave procedures. The nature of agreement between theory and experiment currently attainable for semi-metals and semiconductors is discussed. The bearing of some of the results in these latter systems by procedures dealing with clusters of atoms to simulate the infinite solid on the future of such procedures for imperfect systems and surfaces is commented upon. A brief discussion is presented about the various possible contributors to the temperature dependence of EFG’s in pure metals and comparison is made between theory and experiment for zinc and cadmium. The factors that can contribute to the EFG’s in imperfect metallic systems, including alloys, at both host and impurity nuclei are discussed, and some of these factors are illustrated by considering two examples of these systems, EFG ’s at host Al and Cu nuclei due to mu mesons introduced in the metal and at impurity nuclei in alloys involving cadmium metal host. The concluding section discusses directions in which further efforts are needed to improve our theoretical understanding of both pure metals and imperfect metallic systems.

Systematic study of the temperature dependence of electric field gradients at probe nuclei in non-cubic metals

Systematic study of the temperature dependence of electric field gradients at probe nuclei in non-cubic metals

Radially dependent antishielding factors,γ(r)andβ(r), for positive divalent ions

The radially dependent quadrupole antishielding factors $\ensuremath{\gamma}(r)$ and $\ensuremath{\beta}(r)$ for ${\mathrm{Be}}^{2+}$, ${\mathrm{Mg}}^{2+}$, and ${\mathrm{Zn}}^{2+}$ are calculated by using the nonorthogonal-Hartree-Fock perturbation theory (NHFPT) of Dalgarno. These results are important in view of the recent theory of Lodge on the electric-field gradient (EFG) in metals, which shows the dependence of EFG on both $\ensuremath{\gamma}(r)$ and $\ensuremath{\beta}(r)$. While in the literature, calculations of $\ensuremath{\gamma}(r)$ are available for some ions (other than ${\mathrm{Be}}^{2+}$, ${\mathrm{Mg}}^{2+}$, and ${\mathrm{Zn}}^{2+}$), those of $\ensuremath{\beta}(r)$ are lacking to our knowledge. It is this deficiency which is being made up in the present paper by the calculations of $\ensuremath{\beta}(r)$ and $\ensuremath{\gamma}(r)$ for some of the divalent ions.

87Rb NMR in Ferroelectric RbH3(SeO3)2

The temperature dependence of electric field gradient (EFG) at Rb site in RbH 3 (SeO 3 ) 2 is studied by the second order quadrupole shift. The number of inequivalent Rb sites in the paraelectric and the ferroelectric phases agrees with that deduced from the consideration based on the crystal symmetry. It is found that the change in EFG caused by the phase transition behaved as the order parameter did. The existence of the intermediate incommensurate phase could not be confirmed.

23Na NMR Study of NaD3(SeO3)2 by the First Order Quadrupole Shift

Temperature dependence of electric field gradient (EFG) at Na site in NaD 3 (SeO 3 ) 2 was studied by the first order shift of quadrupole interaction. The principal coordinate system of EFG at one Na site of the two rotates with varing temperature in the ferroelectric phase. The splitting of resonance lines in the ferroelectric phase shows different behavior against temperature in different direction of the magnetic field. Spontaneous polarization P s was measured on a temperature range from just below the transition to -127°C both along the a and c * axes. Results indicate that P s rotates in the a c plane.

Static and dynamic aspects of perturbed angular correlation measurements in perovskite crystals

Abstract The static and dynamic aspects of the Electric Field Gradient (EFG) in ionic perovskite (anti-) ferroelectric crystals have been studied with particular emphasis on the Perturbed Angular Correlation method. We analyze the effect of the lattice fluctuations on the temperature behavior of the EFG. The proper averaging procedure of the perturbation function is outlined. This results in a simple relationship between the electric (sub-) lattice susceptibility and the measured EFG, predicting a critical behavior of EFG on approaching T c . In addition to this dynamical effect we show that well below T c , the temperature dependence of EFG is dominated by P s 2 , the square of the spontaneous polarization of the (sub-) lattice. These predictions are shown to be in qualitative agreement with published experimental data.

On the Volume and Structure Dependence of Electric Field Gradients in Close-packed Metals. II

In an attempt to calculate the contributions to the electric field gradient in close-packed metals from all charge outside the central Wigner-Seitz cell, lattice sums over screened ions were performed using a Thomas-Fermi and a Hartree screened potential. The volume and structure dependence of these lattice sums is examined and compared to experimental observations. The role of lattice vibrations is also discussed.

Systematically weak temperature dependence of electric field gradients in distorted cubic metals

The temperature dependence of the electric field gradient for radiation-damaged copper and for the dilute alloy Zn Ag has been measured using the perturbed angular correlation technique. A systematically weak temperature dependence is found for distorted cubic metals compared to non-cubic metals. The strong temperature dependence for the Zn Ag , In Ag and Sn Ag alloys as reported in literature has not been confirmed in the present experiment.