Electric field gradients in PrBa2 Cu 3 O 7 : LSDA+U results and comparison with experiment

Electric-field gradient (EFG) and asymmetry parameter (η) at all oxygen and copper sites of nonsuperconducting PrBa₂Cu₃O₇ (Pr123) compound were calculated using the full-potential (linearized)-augmented-plane-wave plus local orbitals method. Exchange and correlation effects were treated by LSDA+U for Cu(3d) and Pr(4f) electrons. The effects of changing screened Coulomb parameters U_Pr, U_Cu1, and U_Cu2 on the results were individually studied. The calculated EFG of O2 site is close to the EFG of O3 site at variance with the experimental result. It was shown that by increasing superconducting holes in O2 and O3 sites the EFG at these sites increase and vice versa. The most famous theories which have been proposed to explain the suppression of superconductivity in perfect (without any mis-substitution or other defects) Pr123 compound are not consistent with the experimental EFG at O2 and O3 sites. By replacing one Pr atom at the Ba site on unit cell of Pr123 (Pr_Ba), it was shown that Pr_Ba mis-substitution reduces the superconducting holes in both O2 and O3 sites and could be responsible for the suppuration of superconductivity in Pr123 samples. It is very probable that the unusual behaviors of experimental EFG at O2 and O3 sites of Pr123 are related to oxygen defects which are produced with Pr_Ba mis-substitution.     

Electric quadrupole interactions in the CdTiO3 perovskite2

The TDPAC technique has been used to measure the EFG at the Cd site in the perovskite CdTiO₃. The experimental results obtained at 293 K are compared with ionic lattice sum calculations of the EFG. In addition measurements at 16 and 77 K show that no considerable modification of the EFG is observed at the Cd site at temperatures below and above the previously described phase transition at 50 K.     

Incomplete double frequency sweeps to select small quadrupolar coupling static powder patterns

Difference spectra based on the magnitude of the quadrupolar coupling of a site has been observed under static conditions utilizing a double frequency sweep pulse sequence to enhance the central transition of a small electric field gradient (EFG) environment. Through the use of convergent sweeps that only cover the inner satellite transitions of the smaller EFG site, an echo spectrum results that favors the smaller site, which can then be used in conjunction with normal echo spectra to create a difference spectrum that consists primarily of the smaller site. The simplification of the static lineshape data permits simulation for the extraction of chemical shift anisotropy (CSA) information for the site. The method is demonstrated using ⁹³Nb NMR for samples with multiple niobium environments due to mixtures of compounds, MgNb₂O₆/LiNbO₃, or due to crystallographic structure, KCa₂Nb₃O₁₀.     

The electric field gradient and its temperature dependence for ruthenium in scandium and yttrium

The electric field gradients (EFG) for ruthenium in scandium and yttrium metal were determined by TDPAC measurements to be 19(4) × 10¹⁷ V/cm² and 5.5(12) × 10¹⁷ V/cm² respectively at room temperature. The EFG for Ru in Sc was found to vary considerably in the temperature range from 14 to 700 K, whereas for Ru in Y only an extremely small temperature dependence of the EFG was observed.     

Electric field gradients at Ta in Zr and Hf inter-metallic compounds

Here we calculate the electric field gradient (EFG) at the nucleus of the substitutional Ta impurity site in Zr₂T and Hf₂T (T=Cu, Ag, Au, and Pd) C11_b inter-metallic compounds. We use the ab initio FP-LAPW method as embodied in the Wien97 code in a super-cell approach and include lattice relaxations around the impurity. Our results are compared with EFG values inferred from measurements of the quadrupole coupling constants at the ¹¹¹Ta probe in these compounds performed with the time differential perturbed angular correlation (TDPAC) technique. We also performed EFG calculations for the pure inter-metallic compounds. Through the comparison of theoretical and experimental EFGs in these cases, we elucidate the role played by the Ta probe in the TDPAC measurements of Hf and Zr compounds. Our results show that, although the EFGs at the Hf site are very similar to the EFGs at the Ta impurity, there is no direct correlation between the Zr and Ta EFGs.     

Electric field gradient in Cu2O from band structure calculations

We have performed self-consistent full potential LAPW calculations of Cu₂O. Since the new results agree well with a previous muffin-tin calculation, it can be concluded that non-muffin-tin effects are relatively small in Cu₂O. By using the present self-consistent charge density, we, obtain the electric field gradient (EFG) at the Cu site without further approximations. Our theory yields a value of −0.85 e/au³, in good agreement with experiment but in contrast to a previous cluster calculation in which a positive sign of the EFG was obtained. The origin of the EFG and the discrepancies between our band structure and the cluster calculation is analyzed.     

Site occupation of indium and jump frequencies of cadmium in FeGa<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>

Perturbed angular correlation (PAC) measurements using the In-111 probe were carried out on FeGa₃ as part of a broader investigation of indium site occupation and cadmium diffusion in intermetallic compounds. One PAC signal was observed with hyperfine parameters ω ₁= 513.8(1) Mrad/s and η= 0.939(2) at room temperature. By comparison with quadrupole frequencies observed in PAC measurements on isostructural RuIn₃, it was determined that indium occupies only the 8j site in the FeGa₃ structure, denoted Ga(2) below because two out of the three Ga sites have this point symmetry. PAC spectra at elevated temperature exhibited damping characteristic of electric field gradients (EFGs) that fluctuate as Cd probes jump among Ga(2) sites within the lifetime of the excited PAC level. A stochastic model for the EFG fluctuations based on four conceivable, single-step jump-pathways connecting one Ga(2) site to neighboring Ga(2) sites was developed and used to fit PAC spectra. The four pathways lead to two observable EFG reorientation rates, and these reorientation rates were found to be strongly dependent on EFG orientation. Calculations using density functional theory were used to reduce the number of unknowns in the model with respect to EFG orientation. This made it possible to determine with reasonable precision the total jump rate of Cd among Ga(2) sites that correspond to a change in mirror plane orientation of site-symmetry. This total jump rate was found to be thermally activated with an activation enthalpy of 1.8 ±0.1 eV.     

Temperature dependence of the electric quadrupole interaction in PbHfO3

The temperature dependence of the Electric Field Gradient (EFG) in PbHfO₃ was studied in the temperature range 25–225°C by the Differential Perturbed Angular Correlation method. In the two anti-ferroelectric phases below 215°C, not too close to either transition temperature, the EFG decreases as the temperature increases toward T_c. Just above T_c an abrupt rise of EFG was observed indicating a critically behaving contribution to EFG. The results are interpreted in terms of a model based on the local static as well as time-dependent changes of the electric environment, at a lattice site. In accord with the predictions of this model the results exhibit qualitatively the P²_s temperature dependence of EFG far from T_c, where P_s is the sub-lattice polarization, while in close proximity to T_c the dominant contribution to EFG is due to the susceptibility X_q connected with the soft-mode fluctuations. The derived critical exponents are in agreement with previous experimental results on related compounds and with theoretical predictions. A hitherto unobserved additional component of V_zz was established, behaving critically at the antiferro-paraelectric transition at 215°C. This new component is interpreted to originate in local fluctuations connected with the central mode.     

Electric field gradient in bixbyite rare-earth oxides R2O3 (R=Tl,Eu, Lu,Tm) measured by perturbed angular correlation

The electric field gradient (EFG) at ¹¹¹Cd nuclei dilutely substituting the cation site in bixbyite rare-earth oxides Tl₂O₃, Eu₂O₃, Lu₂O₃ and Tm₂O₃ has been measured using perturbed angular correlation technique. The ¹¹¹In(EC) ¹¹¹Cd probe nuclei were introduced into the samples by thermal diffusion. The experimental EFG values are compared with those calculated using the point charge model (PCM). The results are discussed in terms of a correlation between the electric field gradient and cation–oxygen bond length in metal oxides. This revised version was published online in August 2006 with corrections to the Cover Date.     

FP-LAPW Calculations of the EFG at Cd Impurities in Rutile SnO2

We report an ab initio study of the electric-field gradient (EFG) at Cd impurities located at the cation site in the semiconductor SnO₂(rutile phase). The study was performed with the WIEN97 implementation of the FP-LAPW method. In order to simulate the diluted Cd-impurity in the SnO₂ host and to calculate the electronic structure of the system we used a 72-atoms super-cell, studying the relaxation introduced by the impurity in the lattice. The free-relaxation process performed shows that the relaxations of the oxygen nearest-neighbors of the impurity are not isotropic. Our prediction for the EFG tensor are compared with experimental results and point-charge model predictions. This revised version was published online in September 2006 with corrections to the Cover Date.     

Effect of vacancy diffusion on NQR parameters in LaF3

A simple model calculation of the electric field gradient (EFG) at the La site in crystalline LaF₃ was carried out using Bertaut's method in order to elucidate a possible relation between the anomalous temperature dependence of the asymmetry parameter of the EFG found in the ¹³⁹La nuclear quadrupole resonance and the vacancy-mediated diffusion of the fluorine anions. Redistribution of some particular fluorine species among the four crystallographically inequivalent positions between their original sites and the Schottky-type vacancy sites via rapid diffusion contributes to the reduction of the asymmetry of the EFG, this being consistent with the experimental fact that the asymmetry parameter decreases sharply above room temperature.     

Hyperfine interactions in 111Cd-doped lutetium sesquioxide

We report here first Perturbed Angular Correlation (PAC) results of the electric field gradient (EFG) characterisation at ¹¹¹Cd impurities located at both non-equivalent cation sites of the bixbyite structure of Lutetium sesquioxide, between room temperature (RT) and 1273 K. The comparison with results coming from a systematic ¹¹¹Cd PAC study in bixbyites and with point-charge model (PCM) predictions shows the presence of a trapped defect at RT in the neighbourhood of the asymmetric cation site, which is completely removed at T > 623 K. The anomalous EFG temperature dependence in Lu₂O₃ can be described in the frame of a “two-state” model with fluctuating interactions, which enables the experimental determination of the acceptor energy level introduced by the Cd impurity in the band-gap of the semiconductor and the estimation of the oxygen vacancy density in the sample. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Electric quadrupole interactions in Ru-Sc alloys

In TDPAC studies of the electric quadrupole interaction in Ru_xSc_1–x alloys two different electric fieldgradients (EFG) have been observed at the site of⁹⁹Ru: V_zz(I)=12.6·10¹⁷ V/cm² and V_zz(II)=18.9·10₁₇ V/cm². The corresponding relative fractions f(I) and f(II), respectively, vary with the Ru concentration x. For low concentrations x<0.01 most nuclei (f(I)0.8) experience the smaller EFG V_zz(I). At x=0.01, however, the fraction f(I) goes abruptly to zero and V_zz(II) becomes dominant. In view of these results the previous interpretation of V_zz(II) as the EFG of dilute Ru on substitutional Sc sites can no longer be maintained. The Ru-Sc configurations producing these EFG's have not yet been identified. In the intermetallic compound Ru₂Sc the interaction is completely different, in RuSc₃, however, similar values have been observed.     

Electric field gradients in AFeIIIF4 structures: Calculations for the polarizable point charge model and Mössbauer data

The polarizable point charge model is used to explain Mossbauer data on the EFG at the iron site in AFeF₄ (A = K, Cs, Rb, NH₄). Lattice summations are performed in direct space. The resolution of the self consistent equations involving the electric field is obtained through an iterative method. The major contribution to the EFG is that of “terminal” (non-bridging) fluorines. The fluorine polarizabilities which fit the data are in reasonable agreement with expected values (α_F? 0.9 ų).     

Mössbauer study of synthetic jarosites

The structure around the metal site of mavicyanin, a protein molecule with a copper site, was investigated in solution by using time-differential perturbed angular correlation of ¹¹⁷In. The electric field gradient (EFG) of the metal site was deduced from the measurement. It demonstrated that the site in a mutant-type mavicyanin, Thr15Ala-Mav, gives an EFG different from that in the wild-type mavicyanin does. The pH dependence of the EFG was also observed for both proteins.     

Density functional approach to study 5f electron behavior and electric field gradient in NpRh3

We have presented results on the electronic structure and the electric field gradient (EFG) of NpRh₃ within a framework of density functional theory within the local density approximation (LDA) and generalized gradient approximation (GGA) with and without spin-orbit coupling (SOC). The electronic density of states (DOS) shows that Np-f to Rh-d hybridization leads to a narrow band 5f-electron. Using the GGA and spinpolarized calculations, the calculated EFG shows that the dominant contribution to EFG comes from electrons with strong p-character.     

Electronic structure of α-Al2O3 slabs: A local environment study

In this work we performed an ab initio/Density Functional Theory (DFT) study of structural and electronic properties of the (0 0 1) α-Al₂O₃ surface. For this study we used two methods with different basis set: the Full-Potential Augmented Plane Wave plus local orbital (FP-APW+lo) and a linear combination of numerical localized atomic orbital basis sets, employing the WIEN2k code and the SIESTA code, respectively. In order to calculate the structural and electronic properties of the reconstructed surface, we calculated the final equilibrium atomic position with the SIESTA code and then the electric-field gradient (EFG) at Al sites was calculated with the FP-APW+lo code using the optimized positions. Using this procedure we found equilibrium structures with comparative lower energy than those obtained using only the FP-APW+lo method. The EFG tensor and the local structure for Al were studied as a function of the depth from the surface for the relaxed structures. We found that distances down to 6 Å from the surface are sufficient to converge the EFG and the Al–O distances to bulk values. The predicted bulk EFG at the Al site is in good agreement with available experimental values. These results can be used for local probes purposes, e.g., in the case of doping, with important sensitivity for probes located close to the top of the surface, in particular for distances smaller than 6 Å.