Perturbed Angular Correlation Research Articles

Full-Potential KKR Calculations for Point Defect Energies in Fe-Based Dilute Alloys, Based on the Generalized-Gradient Approximation

We present systematically ab-initio calculations for defect energies of 3d and 4sp impurities (Sc­Ge) in Fe. The calculations are based on the Generalized-Gradient-Approximation in the density-functional formalism and the full-potential Korringa-Kohn-Rostoker (FPKKR) Green’s function method. First we examine the distance dependence, from the 1st- to the 10th-neighbors, of the impurity-impurity (I­I; I = Sc­Ge) interaction energies (Eint) and show that for most cases, the 1st-neighboring I­I interaction energies (E 1) are dominant. We found that fundamental features of phase diagrams of Fe-based binary alloys, such as segregation, solid solution and order, known experimentally, may be classified by use of the sign and magnitude of E 1. Second we discuss the calculated results for the 1st- and 2nd-neighboring interaction energies of 3d and 4sp impurities with perturbed-angular-correlation (PAC)-probe Sn in Fe. The comparison of the calculated results with available experimental results shows that the observed attraction for Sn­Co, Sn­Ni and Sn­Cu may be understood by the 1st-neighboring interaction energies of these impurity pairs, while the obsreved repulsion for Sn­Ga, and Sn­Ge by the 2nd-neighboring interaction energies of these impurity pairs. We also discuss the magnetism of single impurities X (= Sc­Cu) in Fe. The anti-parallel coupling to the bulk magnetization of the neighboring Fe atoms is stable for Sc­Mn, while the parallel coupling for Fe­Cu. [doi:10.2320/matertrans.M2013176]

Study of hyperfine interactions in the tetragonal GdRh2Si2 using PAC spectroscopy

Hyperfine interactions were studied in the intermetallic compound GdRh2Si2 by perturbed angular correlation (PAC) technique using 181Hf(181Ta) probe nuclei. The measurements were performed in the temperature range 15–285 K. The PAC spectra above the antiferromagnetic ordering temperature of the GdRh2Si2 compound (T N ∼ 106 K), were analyzed using a model that included only electric quadrupole interactions. The observed major fraction was assigned to the 181Hf(181Ta) probe substituting the Gd atoms. The PAC spectra below Neel temperature were analyzed using combined electric quadrupole and magnetic dipole interactions. The Bhf value at Gd, measured at 15 K was found to be 1.4(1) T which, is smaller, when compared with the values obtained in this compound using other nuclear probes, 155Gd (Bhf ∼ 30 T) and 140Ce (Bhf ∼ 26 T). The present result using 181Hf(181Ta) probe is quite interesting since it shows that the contribution to Bhf at Gd due the host is smaller than other components which contribute to the hyperfine field. The temperature dependence of Bhf shows an anomalous behavior.

83mKr, a potentially powerful PAC probe

In the decay of 83Rb to 83mKr and the subsequent decay to the 83Kr ground state a 553–9.4 keV γ-γ and a 17.85–9.4 keV e−-γ cascade are populated. The intermediate 9.4 keV 7/2 + state with a half-life of 154 ns is a perfect candidate for the application of the perturbed angular correlation (PAC) technique. Thus, it is possible to investigate the lattice environment of the implanted probes via the electric quadrupole interaction of the 9.4 keV 7/2 + state with the electric field gradient produced by the host lattices. Details of the production of this new PAC probe and planned measurements will be discussed.

Inhomogeneous broadening of PAC spectra with V zz and η joint probability distribution functions

The perturbed angular correlation (PAC) spectrum, G 2(t), is broadened by the presence of randomly distributed defects in crystals due to a distribution of electric field gradients (EFGs) experienced by probe nuclei. Heuristic approaches to fitting spectra that exhibit such inhomogeneous broadening (ihb) consider only the distribution of EFG magnitudes V zz , but the physical effect actually depends on the joint probability distribution function (pdf) of V zz and EFG asymmetry parameter η. The difficulty in determining the joint pdf leads us to more appropriate representations of the EFG coordinates, and to express the joint pdf as the product of two approximately independent pdfs describing each coordinate separately. We have pursued this case in detail using as an initial illustration of the method a simple point defect model with nuclear spin I = 5/2 in several cubic lattices, where G 2(t) is primarily induced by a defect trapped in the first neighbor shell of a probe and broadening is due to defects distributed at random outside the first neighbor shell. Effects such as lattice relaxation are ignored in this simple test of the method. The simplicity of our model is suitable for gaining insight into ihb with more than V zz alone. We simulate ihb in this simple case by averaging the net EFGs of 20,000 random defect arrangements, resulting in a broadened average G 2(t). The 20,000 random cases provide a distribution of EFG components which are first transformed to Czjzek coordinates and then further into the full Czjzek half plane by conformal mapping. The topology of this transformed space yields an approximately separable joint pdf for the EFG components. We then fit the nearly independent pdfs and reconstruct G 2(t) as a function of defect concentration. We report results for distributions of defects on simple cubic, face-centered cubic, and body-centered cubic lattices. The method explored here for analyzing ihb is applicable to more realistic cases.

Search for magnetic interaction in In doped AlN using perturbed angular correlation spectroscopy

The possible presence of a large magnetic field due to spin polarization of a Cd nucleus (decay product of 111In) at an Al substitutional site in AlN is investigated with perturbed angular correlation (PAC) spectroscopy. The PAC spectra of 111In/111Cd in AlN show two probe environments: a weak quadrupole interaction (quadrupole interaction constant, \(\nu _{\rm Q}^{\,\,\,\rm lattice} = 30\) MHz) due to 111In probes at a defect free Al substitutional site and an unknown large interaction (\(\nu _{\rm Q}^{\,\,\,\rm complex} = 300\) MHz) tentatively attributed to a nearest neighbour pair between 111In and a nitrogen vacancy (VN) aligned along the c-axis. Surprisingly, in density functional theory (DFT) calculations, such a large electric field gradient (EFG) could not be reproduced. However, an inclusion of spin polarization in the calculations indicates a strong magnetic field at ~50 % of the 111In/111Cd site. An attempt to verify the presence of the strong magnetic field and to explain the origin of the strong interaction is made. Orientation measurements show, the large interaction is not characterised by a magnetic interaction and is predominantly due to the EFG. However, in the presence of an external magnetic field, the strong interaction probe environment becomes more uniform and the EFG increases by ~10 %. This definitely hints towards some sort of magnetic interaction at the strong interaction probe site.

Hyperfine interactions in intermetallic rare earth-gallium compounds studied by 111 Cd PAC

Magnetic and electric hyperfine interaction of the nuclear probe 111In/111Cd in intermetallic compounds of the rare earth-gallium system have been investigated by perturbed angular correlation (PAC) spectroscopy. The PAC measurements, supported by X-ray diffraction, provide evidence for a marked phase preference of 111In for hexagonal RGa2 over orthorhombic RGa and of RGa3 with the L12 structure over RGa2. In the case of SmGa2, the magnetic hyperfine field Bhf, the electric quadrupole interaction and the angle β between Bhf and the symmetry axis of the electric field gradient have been determined as a function of temperature. The angle β = 0 is consistent with the results of previous magnetization studies. Up to T ≤ 17 K the magnetic hyperfine field has a constant value of Bhf = 3.0(2) T. The rapid decrease at higher T gives the impression of a first-order transition with an order temperature of TN = 19.5 K. In the RKKY model of indirect 4f interaction the ratio TC/Bhf(0) is a measure of the coupling constant. For 111Cd:SmGa2 (TC/Bhf(0)~6.5 K/T) this ratio is significantly smaller than for the same probe in other R intermetallics (SmAl2 ~9.5 K/T, Sm2In ~13.5 K/T).

Determination of the crystal structures of In70-Ni30 and In70-Pd30 using perturbed angular correlation

According to phase diagrams based on x-ray measurements, In70-Pt30 has the cubic Sn7Ir3 crystal structure (D8f, cI40) but the alloys In70-Ni30 and In70-Pd30 have been variously reported to have either a cubic gamma-brass (D81-3, cI52) or the Sn7Ir3 structures. In this study, hyperfine interaction measurements are applied as an alternate method to identify phases. Perturbed angular correlation (PAC) measurements were made of characteristic nuclear quadrupole interactions of 111In/Cd probe atoms, and demonstrated a common, characteristic "signature" of the Sn7Ir3 structure in all three alloys. The Sn7Ir3 structure has two inequivalent Sn-sites with a 3:4 ratio of atoms and point symmetries indicate that the electric-field gradients at both sites should be axially symmetric. Measured perturbation functions for all three alloys exhibited two axially symmetric quadrupole interaction signals having the expected 3:4 ratio of amplitudes, as expected for the structure. Furthermore, ratios of the two quadrupole interaction frequencies in each alloy were characteristically large, with frequencies for probe atoms on In(3) sites roughly five times greater than on In(4) sites. Taken together, these observations confirm that all three phases have the Sn7Ir3 structure. Quadrupole interaction frequencies are also reported for isostructural alloys of gallium with Pt, Pd and Ni. Negligible inhomogeneous broadening was observed in measurements near room temperature in all six phases, indicating excellent atomic ordering at the stoichiometric 70:30 compositions.

Implantation Studies on Silicon-Doped GaN

Silicon-doped GaN layers grown by low-pressure metalorganic vapor-phase epitaxy with Si concentrations ranging from 2 × 1017 Si/cm3 to 9.2 × 1018 Si/cm3 were investigated by means of the perturbed angular correlation (PAC) technique applied to implanted 111In(Cd). An undoped GaN film is used as a reference. The Si atoms replace Ga atoms in the lattice, and silicon, being a group IV element, acts as a donor on the Ga site and contributes one extra electron to the conduction band. Hall-effect measurements confirmed that the free charge carrier density is essentially increased and of the order of the silicon concentration. PAC investigations of the annealing behavior after implantation of the 111In probes show that best recovery is achieved after annealing at 1200 K and that high silicon concentrations make GaN films more stable at high temperatures. Further, it was found that the temperature dependence of the electric field gradient is reduced by increasing Si concentrations.

The Solubility of Indium in Liquid Gallium Supercooled to 12 K

The method of perturbed angular correlation (PAC) was used to determine lattice locations of 111In impurity probe atoms present in extreme dilution in the intermetallic compound FeGa3. In slightly Ga-poor samples, probes were found to strongly prefer one of two inequivalent Ga-sites. In slightly Ga-rich samples at room temperature, 293 K, the PAC spectrum exhibited an unperturbed quadrupole interaction signal that is consistent with indium probes dissolved in small liquid pools of the excess Ga. A myriad of such pools are probably located along grain boundaries in the sample. Cooling from 293 K down to 12 K, the site fraction of indium in liquid decreased, being offset by the increase in a signal attributed to indium solutes in precipitates with other impurities at the sides of the Ga pools. However, these changes were completely reversible upon heating, and no crystallization of the liquid gallium pools was observed down to 12 K. This is attributed to the extraordinarily small volumes for the pools, which, while not measured directly, are orders of magnitude smaller than cubic microns. The measured temperature dependence of the site fraction of indium in the liquid was used to extend the metastable solubility curve for indium in liquid gallium down to a temperature of 150 K, much lower than the eutectic temperature of Ga-In at 288.5 K.

Perturbed angular correlation study of 181Ta-doped PbTi1−xHfxO3 compounds

In this work, the hyperfine quadrupole interaction at Ta-doped PbTi1−xHfxO3 polycrystalline samples is studied for the first time. Powders with x=0.25, 0.50 and 0.75 were prepared and characterized by X-ray diffraction analysis. Perturbed Angular Correlation (PAC) analyses were done as a function of temperature, using low concentration 181Ta nuclei as probes. In the ferroelectric and paraelectric phases of these compounds two sites were occupied by the probes. For each site the quadrupole frequency, asymmetry and relative distribution width parameters were obtained as a function of temperature above and below the Curie temperature (TC). One of these sites was assigned to the regular Ti–Hf site, while the other one was assigned to some kind of defect. The behavior of the hyperfine parameters as a function of temperature was analyzed in terms of a recent published phase diagram and the presence of disorder below and above TC. For the three compositions measured, the obtained hyperfine parameters present discontinuities which correspond to the ferroelectric–paraelectric phase transition. In both phases it was found broad frequency distributed interactions. The disorder in the electronic distribution would be responsible for the broad line width of the hyperfine interaction.

Cd doping of AlN via ion implantation studied with perturbed angular correlation

AbstractAlN with a wide bandgap of 6.2 eV is a promising candidate for ultraviolet light‐emitting diodes and laser diodes. However, the production of the required p‐type AlN is still challenging. As a possible dopant Cd was suggested among other Group II atoms (Be, Mg, and Zn). In this study the annealing condition of implanted Cd in AlN was investigated with the method of the perturbed angular correlation (PAC). Therefore radioactive 117Cd or 111mCd ions were implanted into thin AlN films on sapphire substrate with an energy of 30 keV and fluences in the range of 1011 ions/cm2.After thorough annealing with a proximity cap of the same material most of the Cd‐probes occupy substitutional lattice sites and almost all implantation damage can be annealed. This results in a distinct frequency in the PAC spectra which increases with temperature. In contrast to the formation of an indium nitrogen‐vacancy complex observed with the probe 111In on substitutional Al‐sites no defects are bound to substitutional Cd impurities. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ion implantation of Cd and Ag into AlN and GaN

AbstractGaN and AlN thin films were implanted with cadmium (Cd) or silver (Ag), to fluences ranging from 1×1013 to 1.7 × 1015 at/cm2. The implanted samples were annealed at 950 °C under flowing nitrogen. While implantation damage could be fully removed for the lowest fluences, for higher fluences the crystal quality was only partially recovered. For the high fluence samples the lattice site location of the ions was studied by Rutherford Backscattering/channelling (RBS/C). Cd ions are found to be incorporated in substitutional cation sites (Al or Ga) while Ag is slightly displaced from this position. To further investigate the incorporation sites, Perturbed Angular Correlation (PAC) measurements were performed and the electric field gradients at the site of the probe nuclei were determined (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Application of 204mPb Perturbed Angular Correlation of γ-rays Spectroscopy in Coordination Chemistry

(204m)Pb perturbed angular correlation of γ-rays (PAC) spectroscopy has been applied successfully for the first time to detect the nuclear quadrupole interaction in a lead(II) coordination compound in a molecular crystal [tetraphenylarsonium lead(II) isomaleonitriledithiolate ([AsPh(4)](4)[Pb(2)(i-mnt)(4)])]. The recorded parameters from a powder crystalline sample are ν(Q) = 0.178(1) GHz and η = 0.970(7). The electric field gradient (EFG) was determined at the PW91/QZ4P level including relativistic effects using the two-component zeroth-order regular approximation method for both the [Pb(i-mnt)(2)](2-) monomer and the [Pb(2)(i-mnt)(4)](4-) dimer. Only the EFG for the latter compares favorably with the experimental data, indicating that the picture of this complex as a prototypical hemidirected coordination geometry with a stereochemically active lone pair on lead(II) is inadequate. Advantages and limitations of (204m)Pb PAC spectroscopy as a novel technique to elucidate the electronic and molecular structures of lead-containing complexes and biomolecules are presented.

All 36 exactly solvable solutions of eigenvalues for nuclear electric quadrupole interaction Hamiltonian and equivalent rigid asymmetric rotor with expanded characteristic equation listing

This paper derives all 36 analytical solutions of the energy eigenvalues for nuclear electric quadrupole interaction Hamiltonian and equivalent rigid asymmetric rotor for polynomial degrees 1 through 4 using classical algebraic theory. By the use of double-parameterization the full general solution sets are illustrated in a compact, symmetric, structural, and usable form that is valid for asymmetry parameter \(\eta \in \left({- \infty , + \infty}\right)\). These results are useful for code developers in the area of Perturbed Angular Correlation (PAC), Nuclear Quadrupole Resonance (NQR) and rotational spectroscopy who want to offer exact solutions whenever possible, rather that resorting to numerical solutions. In addition, by using standard linear algebra methods, the characteristic equations of all integer and half-integer spins I from 0 to 15, inclusive are represented in a compact and naturally parameterized form that illustrates structure and symmetries. This extends Nielson’s [1] listing of characteristic equations for integer spins out to I = 15, inclusive.

Dynamic hyperfine interactions in 111In(111Cd)-doped ZnO semiconductor: PAC results supported by ab initio calculations

In this work, we present results of Time-Differential γ–γ Perturbed-Angular-Correlations (PAC) experiments performed in 111Cd-doped ZnO semiconductor. The PAC technique has been applied in order to characterize the electric-field-gradient (EFG) tensor at (111In (EC)→) 111Cd nuclei located, as was later demonstrated, at defect-free cation sites of the ZnO host structure. The PAC experiments were performed in the temperature range of 77–1075K. At first glance, the unexpected presence of low-intensity dynamic hyperfine interactions was observed, which were analyzed with a perturbation factor based on the Bäverstam and Othaz model. The experimental EFG results were compared with ab initio calculations performed with the Full-Potential Augmented Plane Wave plus local orbital (FP-APW+lo) method, in the framework of the Density Functional Theory (DFT), using the Wien2K code. The presence of the dynamic hyperfine interactions has been analyzed enlightened by the FP-APW+lo calculations of the EFG performed as a function of the charge state of the cell. We could correlate the large strength of the dynamic hyperfine interaction with the strong variation of the EFG due to changes in the electronic charge distribution in the Cd vicinity during the time-window of the PAC measurement. It was also revealed that the Cd impurity decays to a final stable neutral charge state (Cd2+) fast enough (in few ns) to produce the nearly undamped observed PAC spectra.

Electric field gradient calculations in ZnO samples implanted with 111In(111Cd)

A first-principles study of the electric field gradient (EFG) calculated for ideal and 111In(111Cd) implanted ZnO samples is reported in the present work. The study was made for ZnO ideal hexagonal structures and supercells were introduced in order to consider the possible implantation environments. The calculation was done using the “WIEN2k” code within the density functional theory, the exchange and correlation effects were determined by the GGA approximation. Three possible 111In(111Cd) implantation configurations were studied, one substitutional incorporation at cation site and two interstitials. The obtained EFG values for the ideal structure and the substitutional site are in good agreement with the experimental reports measured by perturbed angular correlation (PAC) and high precision nuclear magnetic resonance (NMR). Thus, the ascription of substitutional incorporation of 111In(111Cd) probe atom at the ZnO cation site after annealing was confirmed.

Electric field gradients at 111In/111Cd probe atoms on A-sites in 211-MAX phases

The method of perturbed angular correlation (PAC) was applied to selected MAX phases with 211 stoichiometry. Radioactive 111In ions were implanted in order to measure the electric field gradients (EFG) in the key compounds Ti2InC and Zr2InC to determine the strength and symmetry of the EFG at the In-site. Further PAC studies in the In-free MAX phases Ti2AlN, Nb2AlC, Nb2AsC and Cr2GeC were performed to confirm that the In probes occupy the A-site as well. The strength of the EFG, with a quadrupole coupling constant νQ between 250 and 300 MHz in these phases, is quite similar to the ones found in Ti2InC with νQ = 292(1) MHz and in Zr2InC with νQ = 344(1) MHz, respectively. Different annealing behavior was observed whereas in all cases a linear decrease of νQ with increasing measuring temperatures was found. The experimental results are also in excellent agreement with those predicted by ab initio calculations using the APW+lo method implemented in the WIEN2k code. This study shows in an exceptional manner that 111In → 111Cd atoms are suitable probes to investigate the local surrounding at the A-site in 211-MAX phases.

Oxygen ordering in the high-Tcsuperconductor HgBa2CaCu2O6+δas revealed by perturbed angular correlation

Lattice sites and collective ordering of oxygen atoms in HgBa${}_{2}$CaCu${}_{2}$O${}_{6+\ensuremath{\delta}}$ were studied using the perturbed angular correlation (PAC) technique at ISOLDE/CERN. The electric field gradients (EFG) at ${}^{199m}$Hg nuclei have been measured as functions of oxygen doping on the Hg planes, above and below ${T}_{c}$. In comparison with the results obtained for oxygen and fluorine doping in Hg-1201, the analysis shows a different oxygen ordering exhibited by Hg-1212. Moreover, for all studied cases, the experimental results show that at a local scale there is non uniform oxygen distribution. A series of ab initio EFG calculations allowed to infer that at low concentrations, regions without oxygen coexist with regions where O${}_{2\ensuremath{\delta}}$ dumbbell molecules are located at the center of the Hg mesh. On the other side, at high concentrations, O${}_{2\ensuremath{\delta}}$ dumbbell molecules coexist with single O${}_{\ensuremath{\delta}}$ atoms occupying the center of the Hg mesh. The present results suggest that oxygen sits on the Hg planes in the form of a molecule and not as a single atom.

Nuclear radioactive techniques applied to materials research

Abstract In this paper we review materials characterization techniques using radioactive isotopes at the ISOLDE/CERN facility. At ISOLDE intense beams of chemically clean radioactive isotopes are provided by selective ion-sources and high-resolution isotope separators, which are coupled on-line with particle accelerators. There, new experiments are performed by an increasing number of materials researchers, which use nuclear spectroscopic techniques such as Mössbauer, perturbed angular correlations (PAC), β-NMR and emission channeling with short-lived isotopes not available elsewhere. Additionally, diffusion studies and traditionally non-radioactive techniques as deep level transient spectroscopy, Hall effect and photoluminescence measurements are performed on radioactive doped samples, providing in this way the element signature upon correlation of the time dependence of the signal with the isotope transmutation half-life. Current developments, applications and perspectives of using radioactive ion beams and techniques in solid state and biophysics research are presented with a few examples.

Relating PAC damping to EFG fluctuation rates through the PAC relaxation peak

A perturbed angular correlation (PAC) experiment that measures dynamic damping also needs information about the fundamental quadrupole frequency to relate the damping as a function of temperature to the EFG fluctuation rate. When the experiment is unable to access slow electric field gradient (EFG) fluctuations that show the fundamental quadrupole frequency directly, one needs additional information to determine the hyperfine field parameters and thereby the connection between observed damping and EFG fluctuation rates. One way to solve this problem is to estimate the hyperfine parameters from the fluctuation rate for maximum damping (i.e. at the relaxation peak) or from the rate of maximum damping. This work relates both the maximum damping rate and the fluctuation rate at the relaxation peak to EFG magnitudes (or quadrupole frequencies) for five dynamic N-state symmetric models of fluctuating EFGs.