Data reduction methodology for perturbed angular correlation experiments

Data reduction schemes currently used for time differential perturbed angular correlation measurements are evaluated in terms of (i) their relative effectiveness in eliminating irrelevant variables, including single counter efficiencies and spectrum time shifts; and (ii) their effectiveness in putting data in a form that can easily be fitted by theoretical correlation functions. It is pointed out that erroneous conclusions may be derived from improperly reduced data, but that properly analyzed experiments performed at four angles allow a good determination of both the time-dependent and time-independent parts of the correlation function. Correction of data for accidentals, source self-absorption and spectrum livetime differences are discussed.     

A perturbed angular correlation spectrometer for material science studies

A four-detector perturbed angular correlation (PAC) spectrometer has been developed with ultra-fast BaF₂ detectors to acquire four coincidence spectra simultaneously, two at 180° and two at 90°. This spectrometer has double efficiency compared to that of a three-detector set-up. Higher efficiency is desirable for PAC studies in solid state physics where large number of coincidences are required to obtain the PAC spectra with good statistics and is particularly useful when the half-lives of the parent probe nuclei used for PAC measurements are ∼2–3 days or less as in ¹¹¹In (2.8 d), ⁹⁹Mo (2.7 d) and ¹⁴⁰La (1.7 d). The performance of the spectrometer has been tested for the HfO₂ monoclinic crystal in the temperature range from 77 to 873 K and for the HfF₄·3H₂O crystal at room temperature. The polycrystalline HfO₂ has been synthesized from Hf metal by heating in air. The hydrated hafnium fluoride has been crystallized by dissolving Hf metal in 40% HF and drying slowly at room temperature.      

Molybdate polymerisation studied by perturbed angular correlation

We determined the average nuclear quadrupole interaction (NQI) at⁹⁹tc in frozen aqueous molybdate solutions at 77K as a function of pH. The polymerisation shows up clearly in the titration curve at pH 6.5 and leads to a dramatic increase of the NQI.on leave from Tanta University, Egypt     

Time differential perturbed angular correlation studies of hafnium hydrides

The dependence of the electric field gradients (EFG) in Hafnium-Hydride systems as a function of the composition H/Hf in the cubic δ and tetragonal ε phases were investigated using the time-dependent perturbed angular correlation (TDPAC) technique, with¹⁸¹Ta as the nuclear probe. Two EFGs were found in the ε phase, indicating the existence of two major symmetries surrounding the Ta probe. The results indicate that the trend of the EFGs, in the ε phase, are due to the changes in the lattice parametersa _o,c _o as hydrogen is added to the Hf-H system. In the δ phase, only one major symmetry was found. Both phases are characterized by broad frequency distributions and large anisotropies.     

Time-dependent perturbed angular correlation study of181Ta in Mg

The quadrupole interaction of¹⁸¹Ta in Mg metal has been investigated at room temperature by time differential perturbed angular correlation method yieldingv _Q=127±7 MHz. The observed EFG is calculated to be 20.8×10¹⁶ V/cm².     

Indium-defect complexes in silicon studied by perturbed angular correlation spectroscopy

The formation of molecule-like complexes, consisting of a defect and a radioactive¹¹¹In atom, is studied using the perturbed angular correlation technique (PAC). The complexes are characterized by their defect specific electric field gradients which also contain information on the geometry of the formed complexes. Whereas the complex is formed with the¹¹¹In atom, its electric field gradient is measured after the decay of the radioactive¹¹¹In atom to¹¹¹Cd. Formation and dissolution of the molecule-like complexes is pursued for a variety of different conditions, such as sample temperature, dopant concentration and position of the Fermi level. In particular, the interaction of In atoms with the following defects in Si was investigated: Intrinsic defects, created by particle irradiation; substitutional donor atoms (P, As, Sb, Bi); and interstitial impurity atoms (Li, H, and an unidentified X defect); especially, the latter ones are known to passivate acceptor atoms in Si. Methodology and specific properties of the PAC technique will be illustrated with the help of these examples.     

Comments on time-differential perturbed angular correlation functions for static axial electric quadrupole interaction

A technique of computer aided derivation of analytical formulas has been applied to perturbed- angular correlation functions in case of the static axial electric quadrupole interaction in a single crystal. An arbitrary orientation of the EFG symmetry axis with respect to the detectors was considered. Explicit formulas for correlation functions in commonly used detector configurations= and=/2 have been obtained. Small corrections to the previously published formulas have been suggested.     

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 (V_N) 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.     

Monitoring positional changes in bixbyite oxides with perturbed angular correlation spectroscopy

The refinement of atomic positions with perturbed angular correlation spectroscopy for several isostructural sesquioxides M₂O₃ (M=Sc, In, Y, Yb, Dy, Ho, Gd, Sm) is presented. The experimental electric field gradients of¹¹¹Cd residing at the two substitutional sites were reproduced by the simple point charge model with an accuracy of less than 1% by varying the coordinates (available from X-ray and neutron diffraction experiments) within their experimental uncertainty. In this way, for each oxide coordinates were obtained having an accuracy of 0.3 pm, which is typically five times better than that of available X-ray and neutron diffraction results.     

In situ studies of solid state reactions by perturbed angular correlation

We report on three examples of in situ studies of solid state reactions by time differential perturbed angular correlation of¹⁸¹Ta: (i) the oxidation of hafnium metal and the doping of ZrS₂ with Hf during iodine vapour transport crystal growth; (ii) the observation of sublattice melting during polymorphic phase transitions in TaS₂; (iii) the electrointercalation of 2H-TaS₂ with silver.     

Hyperfine-field measurements inCr Rh andCr Re alloys using perturbed angular correlation technique

The hyperfine fields on¹¹¹Cd probe nuclei in Cr (1 at% Rh), Cr (0.3 at% Rh) and Cr (0.5 at% Re) matrices are measured using time-differential perturbed (–) angular correlation of 173–247 keV cascade in the decay of¹¹¹In to the levels in¹¹¹Cd. The sources prepared by ion implantation of¹¹¹In (2.81 d) activity followed by appropriate annealing procedure were found to be of good quality. The addition of impurities, located to the right of chromium in the periodic table such as Rh and Re, to the chromium matrix increases the electron to atom ratio, resulting in an increase in the magnetic moment compared to pure chromium. This in turn is expected to result in an increase in the hyperfine fields at probe nuclei in these alloys. The measured hyperfine fields are in qualitative agreement with the expected changes in these alloys.On leave from Kanpur Institute of Technology.     

A special feature of the integral perturbed angular correlation method for the study of the electric quadrupole interaction

A method is discussed to detect the orientation and strength of the quarupole interaction for implanted samples, using an integral perturbed angular correlation. The formulation is applied to the case of¹²⁹Xe implanted in diamond.I.I.K.W. Navorser.     

Intrinsic and extrinsic defects in semiconductors studied by perturbed γγ angular correlation spectroscopy

The application of the perturbed γγ angular correlation technique as an analytical tool for the characterisation of atomic defect configurations is discussed. Using the radioactive probe atom¹¹¹In/¹¹¹Cd, recent results on the compensation of acceptor and donor atoms in different II–VI semiconductors will be discussed, in particular the role of the cation vacancy defect.     

Structural lattice defects in silicon observed at111in by perturbed angular correlation

Probing of structural defects in silicon by the perturbed γγ angular correlation (PAC) technique is demonstrated between 77 K and 1300 K. The behaviour of radioactive¹¹¹ In probe atoms implanted at 295 K, is monitored during isochronal annealing in n-type, p-type and intrinsic Si. Trapping of defects, produced by the¹¹¹In implantation itself or by postirradiation is studied in P-doped crystals (10¹⁶/cm³-10¹⁷/cm³).     

Investigation of laser irradiated poly- and monocrystalline aluminium by perturbed angular correlation measurements

Poly- and monocrystalline samples of aluminium implanted with ¹¹¹In to a dose of about 10¹³ at/cm² were irradiated at a temperature of 80 K with a Q-switched pulsed ruby laser. The energy density of the 25 ns pulses was in the range of 1–5 J/cm². Perturbed angular correlation measurements revealed the formation of several In-vacancy clusters, some of which give rise to electric field gradient tensors oriented along low-index crystallographic directions. This clearly shows that laser irradiation acts as a fast quench and that the monocrystalline structure is not destroyed, not even by the highest laser pulse intensity.     

Many-body theory of correlation effects in externally perturbed systems

A unified presentation of different schemes for the calculation of the external perturbation effects is given by using the many-body perturbation theory methods. The main attention is focused on the analysis of the total perturbed energy components in terms of different two-body contributions which are classified into the self-consistency and the true correlation effects. A partial or complete summation of the self-consistency contributions is interpreted in terms of appropriately chosen unitary transformations of the single-particle states and the creation and annihilation operators. The advantages of the perturbation scheme based on the coupled Hartree-Fock approach are stressed.     

Oxidation of indium implanted aluminium studied by the Rutherford backscattering and perturbed angular correlation methods

Aluminium foils oversaturated with 5.10¹⁵/cm² implanted¹¹⁵In⁺ ions were oxidized in 200 mbar oxygen or vacuum annealed at 370–870 K. The samples were analyzed by the Rutherford backscattering (RBS) and perturbed angular correlation (PAC) techniques, using some 10¹¹/cm² implanted radioactive¹¹¹In tracers. Furthermore, the oxygen surface profiles were also scanned with high resolution by using the nuclear resonance technique (NRA). The formation of passivating Al₂O₃ surface layers, preventing deeper oxygen diffusion and the indium diffusion into these oxidized surface layers and into the bulk, were studied. Several quadrupole interaction frequencies previously attributed to strained cubic indium precipitates and indium (-vacancy) clusters were observed. When the samples were oxidized above 750 K, the formation of In-O complexes and of substitutional¹¹¹In in Al₂O₃ was observed.     

Defects in CdS: In detected by perturbed angular correlation spectroscopy (PAC)

The local lattice environment of the donor In in CdS is investigated measuring the electric-field gradient at the site of the radioactive probe atom ¹¹¹In by the perturbed γγ angular correlation technique. It is shown that implantation of In into CdS with subsequent annealing drives 100% of the In atoms to Cd lattice sites. Diffusion of In into CdS under S overpressure results in the formation of In_Cd-V_Cd pairs which seem to be responsible for the self-compensation of In donors in CdS.     

Analysis of perturbed angular correlation spectra of metal ions bound to proteins with rotational correlation times in the intermediate region

The formulation by Dattagupta of the strong-collision model, describing the effect on the perturbation function,G ₂(t) by the isotropic tumbling of an electric field gradient, is generalized to electric field gradients with no axial symmetry. The effect on the perturbation function by strong collisions is compared to the effect of rotational diffusion in the adiabatic limit. The comparison is carried out for decays with an intermediate state of spin 5/2 and for non-axially symmetric electric field gradients. It shows that the strong-collision model can be used for interpretation of PAC spectra of molecules with correlation times between the adiabatic and the fast relaxation limits. The strongcollision model is then used to determine the rotational diffusion of the cadmium substituted copper, zinc superoxide dismutase at 3°C and 25°C from^111mCd TDPAC spectra. For these analyses, the model is incorporated into a conventional least-squares fitting routine.