Electric field gradients at probe nuclei in Ti and Re hosts

The electric field gradients (EFGs) at different probe nuclei in Ti and Re hosts are compared with the predictions of the conduction electron charge shift model. It is found that this model is successful in predicting the sign and, to a zero-order approximation, the magnitude of the EFG when the localized d-contributions are small and the universal correlation is obeyed.     

The electric field gradients for Hg at different lattice sites in Be

¹⁹⁹Tl ions were implanted into a Be single crystal. From time differential perturbed e^– angular correlation experiments with the 5/2^– state of¹⁹⁹Hg the effective electric field gradientV _zz ^eff =±15.2(1.8)×10¹⁷ V · cm^–2 was deduced for Hg on an octahedral interstitial site in Be. From a nuclear orientation experiment, the sign ofV _zz ^eff for^197mHg implanted in Be is determined. In time differential perturbed angular correlation experiments with the 5/2 state of¹⁹⁹Hg populated in the -decay of¹⁹⁹Au implanted into Be, the effective electric field gradient for Hg on a substitutional site in Be was determined asV _zz ^eff =–1.2(2)×10¹⁷V · cm^–2. The dependence of the site population of Tl implanted in Be on annealing was investigated by use of the channeling technique. In a comparison of the derived effective field gradients with the corresponding lattice field gradient contributions different electronic enhancement factors are derived for different sites of Hg in Be.     

Electric field gradients at cubic lattice sites

Electric field gradients are observable by NMR at the nuclei of Gd³⁺ and Eu²⁺ at nominally cubic lattice sites in ferromagnetically ordered intermetallic compounds. The origin of these EFGs and experimental details influencing the resolution of the anisotropic quadrupolar splitting in zero-field NMR are discussed.     

Electric field gradients at 151Eu sites in GaN

The electric field gradients at Eu sites in GaN have been investigated in conversion electron Mössbauer spectroscopy (CEMS) in which ¹⁵¹Eu probe ions were implanted into an undoped GaN layer grown on a sapphire substrate. The sample was implanted with 120 keV ¹⁵¹Eu ions to a fluence of 1 × 10¹⁵, and annealed at 1,200 K. CEMS spectra of the ¹⁵¹Eu 21.6 keV transition were collected, of the GaN sample as well as of a Si sample implanted with overlapping profiles of ¹⁵¹Eu and O. The GaN spectra were fitted with two symmetric doublets, D1 and D2, with isomer shifts and quadrupole splittings of δ?=??0.27 mm/s (relative to Eu₂O₃), ΔE _Q?= 0.85 (3) mm/s; and δ?=?? 0.22 mm/s, ΔE _Q?= 2.90 (5) mm/s, respectively. D1 is attributed to Eu at substitutional Ga lattice sites; D2 to Eu at or near substitutional sites but with extensive lattice damage. The splittings of D1 and D2 correspond to quadrupole coupling frequency of 15 (2) and 50 (4) MHz, consistent with measurements of ⁶⁹Ga, ⁷¹Ga and ¹¹¹In in GaN.     

Electric quadrupole interactions in non-axially symmetric electric field gradients of spinI=2 and 3 nuclei in polycrystalline sources

Calculations and formulae are presented for the purpose of understanding and analyzing Perturbed Angular Correlation (PAC) experiments that use spin-two and spin-three probe nuclei. For electric quadrupole interactions of probe nuclei in a polycrystalline source with non-axially symmetric electric field gradients, the interaction frequencies and perturbation functions for spin-two and spin-three nuclei differ qualitatively and quantitatively from those for spin-five-halves nuclei. These differences result primarily because them-states of integral-spin nuclei are nondegenerate in an asymmetric electric field gradient. To help the experimenter deal with the added complexity of the integral-spin casesI=2 and 3, closed-form expressions are provided for the energy eigenvalues and the eigenvectors as a function of the asymmetry parameter η. To deal with the problem of calculating the perturbation functionsG _kk (t) for η>0, the summation overm-state quantum numbers is formulated in terms ofa _n′,n ^(k) -coefficients. These coefficients are analogous to theS _kn -coefficients used in the case for η=0. To illustrate the differences between the half-integral-spin caseI=5/2 and the integral-spin casesI=2 and 3, energy difference diagrams anda _n′,n′ ⁽²⁾ diagrams are presented and discussed.     

Saturation magnetic moments,magnetic hyperfine fields and electric field gradients at nuclei in the heavy rare earth metals

The contributions of 4f, 5d and 6s electrons to the saturation magnetic moments and magnetic hyperfine fields in the heavy rare earth metals are calculated using the model described in the previous paper. It is found that 4f shell moments are reduced from their free ion values by amounts varying from 0.05µ _B in Gd to several tenths of a Bohr magneton in Tb and Dy, in qualitative agreement with a recent published analysis of neutron diffraction results in Tb, but that the calculated total saturation moments in Tb and Dy are slightly larger than commonly accepted experimental values. After 6s contributions to magnetic hyperfine fields are determined by fitting observations in Gd, the predicted differences between the fields for metals and those for free ions are such that the estimated uncertainty ranges of the theoretical values overlap the experimental ranges. The 5d contribution in the model is negative, varying from about –40 kOe in Tb to –200 kOe in Er. Electric field gradients are also analysed. Observed results can be fitted if the average effective Sternheimer screening factorR _d ^* for 5d electrons in the metals satisfies (1 —R _d ^* )0.7.     

Calculations of electric field gradients in solids: How theory can complement experiment

Increasing computer power and the development of user-friendly, yet highly sophisticated bandstructure programs have made it possible that theoretical EFG calculations can nowadays be performed for fairly complex materials science problems. We show that a combination of these theoretical calculations with experimentally obtained quadrupole splittings can lead to new insight into various interesting problems. This is illustrated for the determination of nuclear quadrupole moments, investigations of samples containing impurities or other imperfections and for Na₂[Fe(CN)₅NO], a promising material for holographic storage applications. This revised version was published online in August 2006 with corrections to the Cover Date.     

Decay of proton-rich nuclei between 39Ti and 49Ni

Decay studies of very neutron-deficient nuclei ranging from ³⁹Ti to ⁴⁹Ni have been performed during a projectile fragmentation experiment at the GANIL/LISE3 separator. For all nuclei studied in this work, ^{39, 40}Ti, ^{42, 43}Cr, ⁴⁶Mn, ^{45, 46, 47}Fe and ⁴⁹Ni, half-lives and decay spectra have been measured. In a few cases, γ coincidence measurements helped to successfully identify the initial and final states of transitions. In these cases, partial decay scheme are proposed. For the most exotic isotopes, ³⁹Ti, ⁴²Cr, ⁴⁵Fe and ⁴⁹Ni, which are candidates for two-proton radioactivity from the ground state, no clear evidence of this process is seen in our spectra and we conclude rather on a delayed particle decay. Received: 26 July 2000 / Accepted: 20 December 2000     

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 field gradients at Os nuclei in the hexagonal transition metals Os and Re

The electric field gradient eq at Os nuclei in Os and Re single crystals has been determined by Mössbauer transmission experiments with the 137 keV resonance in ¹⁸⁶Os as -4.5 (3) × 10¹⁷ V/cm² and - 3.8 (3) × 10¹⁷ V/cm², respectively.     

The electric field gradient at188Os nuclei in Re metal

The electric quadrupole interaction of the first excited 2⁺ state of¹⁸⁸Os in hexagonal rhenium metal was investigated by means of the time-differential perturbed angular correlation technique. From the observed quadrupole frequencyV _Q=170(7) MHz, we deduce an electric field gradient value of |V_zz|=4.77(23)·10²¹V/m² for the system OsRe. The half-life of the 2⁺ state was measured to be 641(4)ps.     

Crystal field at the impurity center sites in ionic crystals

Perturbation theory is developed for second-quantized operators in a basis of partly nonorthogonal orbitals. This method may be helpful in carrying out ab initio calculations of the parameters of the crystal field at the impurity center sites. As an illustration, when estimating the crystal field parameters for Yb³⁺: KZnF₃, some fitting parameters are calculated using this method. The results agree well with experimental data, which indicates that this theory shows considerable promise.     

The effect of high pressure on the electric field gradients at two inequivalent lattice sites of tantalum in ω-zirconium

The pressure variation of the electric field gradients at substitutional tantalum atoms on the two lattice sites (A and B) of ω-zirconium have been determined to be (? lnq ^A/?P)_T = ?1.05(26)10^?3 kbar^?1 and (? lnq ^B/?P)_T = +6.03(40)10^?3 kbar^?1. In addition the thermal expansion coefficients of the unit cell of ω-Zr were found to be α_‖ = +3.5(3)10^?6 K^?6 and α_⊥ = +7.9(4)10^?6 K^?1. A combined analysis of the pressure dependence and the previously determined temperature dependence of the electric field gradients supports the assumption of two different bonding types at the A and B sites.     

Presence of 3d quadrupole moment in LaTiO3 studied by 47,49Ti NMR

47,49Ti NMR spectra of LaTiO3 are reexamined and the orbital state of this compound is discussed. The NMR spectra of LaTiO3 taken at 1.5 K under zero external field indicate a large nuclear quadrupole splitting. This splitting is ascribed to the presence of the rather large quadrupole moment of 3d electrons at Ti sites, suggesting that the orbital liquid model proposed for LaTiO3 is inappropriate. The NMR spectra are well explained by the orbital ordering model expressed approximately as 1/square root of 3(d(xy)+d(yz)+d(zx)) originating from a crystal field effect. It is also shown that most of the orbital moment is quenched.     

Unified picture of the distribution of electric field gradients at Cu, O, and Tm sites in ReBa2Cu3O7−δ

An abundant set of published experimental NMR/NQR data on electric field gradients in ReBa₂Cu₃O_7−δ high temperature conductors, where Re=Y and Tm, is used as a test for the singlet-correlated band theory. Because of the unusual spectral weight (“capacity”) of this band, it has been possible to match the number of holes per lattice site to photoemission data on the energy spectrum and the location of the Fermi level. In the framework of a unified picture of the distribution of holes (charges) it has been possible for the first time to explain satisfactorily the observed electric field gradients at the Cu(1), Cu(2), O(1), O(2), O(3), and O(4) sites, as well as NMR and inelastic neutron scattering data on the crystal electric field at the Tm ions. Zh. éksp. Teor. Fiz. 111, 144–157 (January 1997)     

Systematics of electric field gradients in Cu alloys

The electric field gradients (EFG) at the first two near neighbours (nn's) in Cu alloys are investigated. The valence EFG q^V is evaluated using an analytic solution, valid at all distances from the impurity. In the evaluation of the size EFG q^S, an oscillatory form of the nn displacement is used. Without any floating parameter, good agreement is obtained between theory and experiment for all the systems at all nn's.