Origin of asymmetry of the EFG in cubic metal alloys

Unlike the earlier works, which assume the impurity-induced electron density δn to be spherically symmetric, we have taken δn to have the more realistic cubic symmetry. The corresponding valence EFG q^v shows the interesting property of non-axial symmetry along the [110] direction. Contrary to earlier assumptions, this reveals that the size EFG is not the only source for the asymmetry of the EFG in cubic metal alloys.     

Electric field gradient in transitional dilute alloys

The electric field gradient (EFG) and the asymmetry parameter (η) due to transition metal impurities in the host metals Al, Cu and V are investigated. The valence EFG is formulated using dielectric screening theory in conjunction with pseudopotential theory. The size EFG is evaluated in the elastic continuum limit for a screened point charge model of the host metal. The detailed calculations are carried out forAl (Sc, Fe, Cr),Cu (Ni, Pd, Pt) andV (Ti, Cr, Fe, Nb, Ta, W) alloys.     

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.     

Charge shift model for calculation of electric field gradient in tetragonal closed packed metals

The electronic charge distribution in tetragonal closed packed (tcp) metal is approximated by a collection of spherical charge clouds situated midway between the ions. The anisotropy of the charge distribution is parameterized in terms of a charge shift δ derivable from the lattice parameters and the elastic coefficients of the metal. The electric field gradient (EFG) in the metal can be obtained through lattice summations over the charges. Numerical calculations are made to obtain the EFG in pure indium and indium-based dilute impurity alloys. Fairly good agreement with the experiments is achieved.     

Cavity formation at indium impurities in bcc metals

The defect formation in the bcc metals W and Mo above annealing stage III and the influence of rare gases on this process were investigated by means of the perturbed angular correlation technique using¹¹¹In as radioactive probe. In both metals a relatively high electric field gradient (EFG) could be observed at the indium site, characterized by the quadrupole interaction frequencies υ_Q=263 MHz, ν=0 and υ_Q=220 MHz, ν≈0.15 for W and Mo, respectively. The observations are assigned to the growth of threedimensional vacancy clusters at the probe atoms with the indium atoms situated in the inner surface of this cavities, thus experiencing the corresponding surface EFG.     

NMR study of the electric field gradient in the paramagnetic phase of M<Subscript>3</Subscript>V<Subscript>2</Subscript>O<Subscript>8</Subscript> (M = Co,Ni) compounds

The NMR spectra and the decay of a spin echo signal from ⁵¹V nuclei in Kagome-staircase Co₃V₂O₈ (CVO) and Ni₃V₂O₈ (NVO) single crystals are measured in the temperature range 30–300 K and a magnetic field H ₀ = 20 kOe. The orientation dependences of the ⁵¹V NMR line shape are used to determine the electric field gradient (EFG) parameters, namely, quadrupole frequency ν _Q and asymmetry parameter η. These parameters for NVO and CVO are ν _Q = 180(10) kHz, η = 0.5(1) and ν _Q = 130(10) kHz, η = 0.6(1), respectively. A comparison of the results of calculating EFG tensors with a point charge model and the NMR data indicates that the crystallographically equivalent vanadium atoms in the Ni₃V₂O₈ and Co₃V₂O₈ compounds differ in the EFG axis orientation. M₃V₂O₈ crystals are found to have vanadium positions (V1, V2) with different orientations of the z axis, which specifies the direction of the principal value of EFG (V _zz ): these orientations lie in the bc plane and make an angle of either +51(5)° (V1) or −51(5)° (V2) with axis c. In the temperature range 30–300 K, the EFG tensor components and the local symmetry of the charge surrounding of the vanadium positions in NVO and CVO oxides are found to change insignificantly.     

Critical exponents for the long-range Ising chain using a transfer matrix approach

The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance r^α, 1<α<2, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to the infinite chain are considered, in which both the number of spins and the number of interaction constants can be independently increased. Systems with interactions between spins up to 18 sites apart and up to 2500 spins in the chain are considered. We obtain data for the critical exponents ν associated with the correlation length based on the Finite Range Scaling (FRS) hypothesis. FRS expressions require the evaluation of derivatives of the thermodynamical properties, which are calculated with the help of analytical recurrence expressions obtained within the TM framework. The Van den Broeck extrapolation procedure is applied in order to estimate the convergence of the exponents. The TM procedure reduces the dimension of the matrices and circumvents several numerical matrix operations.     

The Hall coefficient and other transport properties of dilute alloys of copper and silver

The low field Hall coefficient of a number of polycrystalline foils of dilute (2%) alloys of copper and silver has been measured in the temperature range 1.5–50°K, and at room temperature. The alloys chosen wereCu-Au andAg-Au (uncharged impurity),Cu Ge andAg-Sn (charged impurity), andCu-Ni andAg-Pd (transition metal impurity). At 20°K and below, the Hall coefficients of the different copper alloys differ widely from each other,Cu-Ge giving the highest (negative) values (up to twice the room temperature value for pure copper), andCu-Au the lowest (down to 0.7 of this value). There are also significant concentration dependences. The silver alloys show corresponding but smaller changes. A relationship, due to Tsuji, gives the Hall coefficient as a function of the Fermi velocityν and the mean curvature 1/ϱ of the Fermi surface, for the case of an isotropic relaxation time. The integrals over the Fermi surface have been numerically estimated using the known Fermi surface and electron velocities. For both Cu and Ag the results agree with the experimental room temperature values, which we take as evidence thatτ(k) for phonon scattering is here close to isotropic. On the other hand, to account for the Hall coefficients of the alloys, it is necessary to assume that the relaxation timeτ varies over the Fermi surface. It is seen that in Cu and Ag the neck regions contribute relatively little toR since both 1/ϱ andν are small there. The main change inR in different alloys arises from the variation in the relative weighting given to the belly regions by different kinds of impurity scattering. A closer analysis shows that the bulges in the Fermi surface of copper in the 〈100〉 directions contribute relatively heavily because of their high positive curvature. The anisotropy ofτ deduced from the Hall coefficient is compared with that deduced from other measurements.     

Non-ionic contributions to the electric-field gradient at 111Cd/181Ta impurities in bixbyites

The electric-field-gradient (EFG) tensor at both cation sites of the bixbyite structure in ¹⁸¹Hf-implanted Lu- and Sm-sesquioxides was determined by the PAC technique. The cumulated EFG data at Ta-impurity sites in binary oxides enable us to discuss the “universal” character of the empirical correlation between local and ionic contributions to the EFG in these systems. An EFG factorization in terms of the electronic characteristics of the probe and the geometry of the cation coordination is proposed, which explains the experimental EFG results at Ta/Cd impurity sites in bixbyites and agrees with a simplified decomposition of the EFG valence contribution coming from ab-initio calculations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mössbauer Studies on Nanocrystalline Diol Capped γ-Fe2O3

Nanocrystalline indium (nano-In) was prepared with different particle sizes by electrochemical deposition. The temperature dependence of the local electric field gradient (EFG) of nano-In was investigated in a temperature range of 20–300 K using the probe ¹¹¹In for perturbed γγ angular correlation (PAC) experiments. The temperature dependence of the EFG of nano-In can be described by a (1−BT ^3/2) dependence as in bulk-In. It is shown that the low temperature value of the EFG and the proportionality constant B vary systematically with particle size.     

Electric field gradients in dilute alloys of Cu,Ag and Au

In this paper we present perturbed angular correlation (PAC) measurements on¹⁰⁰Rh and¹¹¹Cd in a number of dilute alloys of Cu, Ag and Au. We discuss the electric field gradient (EFG) values derived from these and other experiments in the framework of a theory of the EFG at nearest neighbours of point defects in metals, essentially based on the screening of a point charge in a free electron gas. We include in our discussion the EFG due to a neighbour monovacancy for a number of fcc metals.     

Study of highT c superconductivity in Y1Ba2Cu3O7−x by PAC

HighT _c superconductivity in the YBaCuO superconductor has been investigated through the quadrupole interaction of the probe nuclei⁹⁹Tc. The quadrupole interactions were measured by the TDPAC method from 77 to 296 K. The probe nuclei⁹⁹Tc were introduced into the YBaCuO superconducting specimen by diffusion. The derived electric quadrupole interaction parameters show that the probe nuclei are subject to a unique EFG interaction and occupy a substitutional lattice site in the YBaCuO superconductor. A strong EFG of 10¹⁹ V/cm² was observed. The temperature dependence of the EFG exhibits a linear decrease with temperature increase. Anomalies of both EFG and ν were found in the superconducting transition temperature region. The role of the oxygen vacancies in the Cu−O chains is discussed.     

Knight Shift of 90Nb, 93mMo, 96Tc,and 101mRh in Nb Using Brute-Force NMRON

Brute-force nuclear magnetic resonance on oriented nuclei (BF-NMRON) of ⁹⁰Nb, ^93mMo, ⁹⁶Tc, and ^101mRh was carried out in a new host metal, Nb. The resonance center frequencies at an external field of 11.922(6) T were obtained as ν(⁹⁰NbNb) = 56.572(9) MHz, ν(^93mMoNb) = 85.76(3) MHz, ν(⁹⁶TcNb) = 66.997(11) MHz, and ν(^101mRh Nb) = 111.010(19) MHz. A systematic analysis of the Knight shift of 4d elements in extremely dilute alloy systems is briefly discussed. This revised version was published online in September 2006 with corrections to the Cover Date.     

Width of the ferromagnetic resonance line in highly dispersed powders of crystalline and amorphous Co-P alloys

The resonance characteristics (inhomogeneous FMR linewidth ΔH) in highly dispersed (d=0.1–3 μm) powders of crystalline and amorphous Co-P alloys are investigated as a function of the composition, particle size, and atomic structure. It is established that ΔH for powders of amorphous Co-P alloys is two to three times larger than ΔH for crystalline Co-P powders. According to the investigations performed, this is caused by thermodynamically stimulated segregation of nonmagnetic Co₂P inclusions, apparently an effective relaxation channel, in the amorphous state of Co-P powders. Fiz. Tverd. Tela (St. Petersburg) 41, 464–467 (March 1999)     

TDPAC study of amorphous alloys Pd0.8Si0.2 and Pd0.75Si0.20Ag0.05

The amorphous alloys Pd_0.8Si_0.2 and Pd_0.75Si_0.20Ag_0.05 have been studied by the time differential perturbed angular correlation method. A broad EFG distribution with a relative width of 0.48–0.51 was sensed by the probe nuclei¹¹¹Cd for both the amorphous alloys. The unique quadrupole interaction frequencies were observed after annealing above the phase transition temperature. The observed broad distribution of the EFG implies that the crystallographic structure of the amorphous alloys is characterized by short-range order and long-range disorder, which is in accord with the continuous random model.     

Neutrinoless double-beta decay and related topics

The fundamental importance of searching for neutrinoless double-beta decay (0νββ-decay) is widely recognized. Observation of the decay would tell us that the total lepton number is not conserved and that, consequently, neutrinos are massive Majorana fermions. A brief history of the double-beta decay is presented. The 0νββ-decay is discussed in context of neutrino oscillation data. The perspectives of the experimental 0νββ-decay searches are analyzed. The importance of reliable determination of the 0νββ-decay nuclear matrix elements is pointed out. The problem of distinguishing of the light-neutrino exchange, heavy-neutrino exchange and the trilinear R-parity breaking supersymmetric ( \not R_p \not R_p SUSY) mechanisms of the 0νββ-decay is addressed. Further, the process of resonant neutrinoless double-electron capture (0νɛɛ) is revisited. Arguments are presented that an experimental search for the 0νɛɛ might be feasible.     

Uncertainties in the 0νββ-decay nuclear matrix elements

The nuclear matrix elements M ^0ν of the neutrinoless double-beta decay (0νβ β) of most nuclei with known 2νββ-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental 2νβ β-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure the M ^0ν values become essentially independent of single-particle basis size, the axial vector quenching factor, etc. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. It is suggested that most of the spread among the published M ^0ν ’s can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method. Presented by V. Rodin at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Atomic displacements in bcc dilute alloys

We present here a systematic investigation of the atomic displacements in bcc transition metal (TM) dilute alloys. We have calculated the atomic displacements in bcc (V, Cr, Fe, Nb, Mo, Ta and W) transition metals (TMs) due to 3d, 4d and 5d TMs at the substitutional site using the Kanzaki lattice static method. Wills and Harrison interatomic potential is used to calculate the atomic force constants, the dynamical matrix and the impurity-induced forces. We have thoroughly investigated the atomic displacements using impurities from 3d, 4d and 5d series in the same host metal and the same impurity in different hosts. We have observed a systematic pattern in the atomic displacements for Cr-, Fe-, Nb-, Mo-, Ta-and W-based dilute alloys. The atomic displacements are found to increase with increase in the number of d electrons for all alloys considered except for V dilute alloys. The 3d impurities are found to be more easily dissolved in the 3d host metals than 4d or 5d TMs whereas 4d and 5d impurities show more solubility in 4d and 5d TMs. In general, the relaxation energy calculation suggests that impurities may be easily solvable in 5d TM hosts when compared to 3d or 4d TMs.      

Infrared degenerate four-wave mixing and resonance-enhanced stimulated Raman scattering in molecular gases and free jets

2 H₂), methane (CH₄), carbon dioxide (CO₂), and nitrous oxide (N₂O) in a cell under equilibrium conditions and cooled in free jet expansions. For methane at room temperature the detection limit was 2×10¹² molecules per cm³ and quantum state, enabling the detection of trace species with a spatial resolution of 1 mm²×30 mm. In an attempt to study transitions in the ν₁+ν₃ and 2ν₂+ν₃ combination bands of CO₂ or N₂O, it was not possible to observe any DFWM signal. Instead a surprisingly strong, backward- and forward-directed emission was found which could not be attributed to the DFWM process. The signal arising from this emission was more than 2 orders of magnitude stronger than the DFWM signals obtained for other molecules. The frequencies of the emitted radiation were found to correlate with the transitions ν₁+ν₃→ν₁ and 2ν₂+ν₃→2ν₂, respectively. Our investigations lead to the conclusion that the emission can be explained by stimulated Raman scattering, resonantly enhanced by transitions to the combination levels ν₁+ν₃ and 2ν₂+ν₃. This process seems to suppress the generation of DFWM signals. Received: 1 October 1996/Revised version: 6 January 1997