Angular Correlation Of Gamma Rays Research Articles

Diffusion and Equilibration of Site-Preferences Following Transmutation of Tracer Atoms

Using the method of perturbed angular correlation of gamma rays, diffusional jump-frequencies of probe atoms can be measured through relaxation of the nuclear quadrupole interaction. This was first shown in 2004 for jumps of tracer atoms that lead to reorientation of the local electric field-gradient, such as jumps on the connected a-sublattice in the L12 crystal structure. Studies on many such phases using the 111In/Cd PAC probe are reviewed in this paper. A major finding from a 2009 study of indides of rare-earth elements, In3R, was the apparent observation of two diffusional regimes: one dominant for heavy-lanthanide phases, R= Lu, Tm, Er, Dy, Tb, Gd, that was consistent with a simple model of vacancy diffusion on the In a-sublattice, and another for light-lanthanides, R= La, Ce, Pr, Nd, that had no obvious explanation but for which several alternative diffusion mechanisms were suggested. It is herein proposed that the latter regime arises not from a diffusion mechanism but from transfer of Cd-probes from In-sites where they originate to R-sites as a consequence of a change in site-preference of 111Cd-daughter atoms from In-sites to R-sites following transmutation of 111In. Support for this transfer mechanism comes from a study of site-preferences and jump-frequencies of 111In/Cd probes in Pd3R phases. Possible mechanisms for transfer are described, with the most likely mechanism identified as one in which Cd-probes on a-sites transfer to interstitial sites, diffuse interstitially, and then react with vacancies on b-sites. Implications of this proposal are discussed. For indides of heavy-lanthanide elements, the Cd-tracer remains on the In-sublattice and relaxation gives the diffusional jump-frequency.

Solute-solute interactions in intermetallic compounds

Two types of solute-solute interactions are investigated in this work. Quadrupole interactions caused by nearby Ag-solute atoms were measured at nuclei of 111In/Cd solute probe atoms in the binary compound GdAl2 using the method of perturbed angular correlation of gamma rays (PAC). Locations of In-probes and Ag-solutes on both Gd- and Al-sublattices were identified by comparing site fractions in Gd-poor and Gd-rich GdAl2(Ag) samples. Interaction enthalpies between solute-atom pairs were determined from temperature dependences of observed site fractions. Repulsive interactions were observed for close-neighbor complexes In/Gd/+Ag/Gd/ and In/Gd/+Ag/Al/ pairs, whereas a slightly attractive interaction was observed for In/Al/+Ag/Al/. Interaction enthalpies were all in the range +/- 0.15 eV. Temperature dependences of site fractions of In-probes on locally defect-free Gd- and Al-sites yields a transfer enthalpy that was found to be 0.343 eV in a previous study of undoped GdAl2. The corresponding values in GdAl2(Ag) samples are much smaller. This is attributed to competition of In- and Ag-solutes to occupy sites of the same sublattice. While the difference in site-enthalpies of In-solutes on Gd- and Al-sites is temperature independent, it is proposed that the transfer of Ag-solutes from Gd- to Al-sites leads to a large temperature dependence of degeneracies of levels available to In-solutes, resulting in an effective transfer enthalpy that is much smaller than the difference in site-enthalpies.

ChemInform Abstract: Impurity Diffusion in Highly‐Ordered Intermetallic Compounds Studied by Nuclear Quadrupole Interactions

AbstractReview: 30 refs.

Impurity Diffusion in Highly-Ordered Intermetallic Compounds Studied by Nuclear Quadrupole Interactions

Diffusion of impurity atoms depends on the sublattices occupied, active diffusion mechanisms, and jump frequencies to neighboring sites. The method of perturbed angular correlation of gamma rays (PAC) has been applied over the past decade to study impurity diffusion through measurement of nuclear quadrupole interactions (NQI) at nuclei of 111In/Cd probe atoms. Extensive measurements have been made on highly-ordered compounds having the L12 crystal structure, including In3R, Sn3R, Ga3R, Al3R and Pd3R phases (R= rare-earth element). Measurements in thermal equilibrium at high temperature served to determine lattice locations of 111In parent probe-atoms, through characteristic NQIs, and to measure diffusional jump-frequencies of 111Cd daughter probe-atoms, through relaxation of the NQI. This paper summarizes results of the jump-frequency measurements and relates them to the conventional diffusivity that can be determined, for example, from penetration profiles of tracer species. In spite of chemical similarities of the series of rare-earth phases studied, remarkably large variations in jump frequencies have been observed especially along series of In3R and Pd3R phases. Most phases appear as “line compounds” in binary phase diagrams, but large differences in site-preferences and jump-frequencies were observed for samples prepared to have the opposing limiting phase boundary compositions. Comparisons of jump-frequencies measured at opposing boundary compositions can give insight into the predominant microscopic diffusional mechanisms of the impurity. A change in diffusion mechanism was proposed in 2009 to explain jump-frequency systematics for In3R phases. An alternative explanation is proposed in the present paper based on site-preferences of 111Cd daughter probes newly observed along the parallel Pd3R series. The diffusivity can be expressed as the product of a jump-frequency such as measured in these studies and a correlation factor for diffusion that depends on the diffusion mechanism. The correlation factor can be modeled for the L12 structure and diffusion sublattice of interest using a five-frequency model originally proposed for metals. Although the correlation factor is an essential parameter for the diffusion of impurities, it has never been measured. It is suggested that values of the correlation factor can be determined feasibly by combining results of jump-frequency measurements such as the present ones with diffusivity measurements made for the same host-impurity systems.

Nuclear quadrupole interactions of 111In/Cd solute atoms in a series of rare-earth palladium alloys

Nuclear quadrupole interactions were measured at 111In/Cd probe atoms in rare-earth palladium phases RPd3 having the L12 structure using the technique of perturbed angular correlation of gamma rays (PAC). Measurements were made for pairs of samples having compositions of the Pd-poorer and Pd-rich boundaries of the RPd3 phase fields, typically 75 and 78 at.% Pd. Two signals were detected in most phases, corresponding to probe atoms on cubic R- and non-cubic Pd-sublattices. Site preferences of parent In-probe atoms were characterized by site-fractions of probes on the R- and Pd-sublattices. For all Pd-rich samples, probes exclusively occupied the R-sublattice, consistent with a heuristic rule that solute atoms tend to occupy the sublattice of an element in which there is a deficiency. For Pd-poorer alloys with R= Tb, Er, Yb, Lu, Y and Sc, probes exclusively occupied the Pd-sublattice. For Pd-poorer alloys with R= Ce, Pr, Nd, Sm and Eu, probes occupied both sublattices, with site fractions varying as a function of temperature. In contrast, probes only occupied the R-sublattice in Pd-poorer LaPd3. Jump frequencies on the Pd-sublattice of daughter Cd-probes were determined from nuclear relaxation caused by fluctuating electric field gradients. Activation enthalpies for diffusional jumps were determined from temperature dependences and found to increase linearly as the lattice parameter decreases along the series Pr, Nd, Eu and Sm. Jump frequencies are believed to have been even higher in CePd3 than in PrPd3, but were too low to be detectable in Tb, Er, Yb, Lu, Y and Sc palladides. A correlation between site preferences and jump frequencies is noted and discussed. This paper provides a complete account of measurements of jump frequencies of Cd-probe atoms and comparisons with similar measurements made on other series of L12 phases.

Diffusion in La<sub>n</sub>CoIn<sub>3n+2</sub> Phases Studied by Perturbed Angular Correlation

Jump frequencies of 111In/Cd tracer atoms were measured for a series of layered phases LanCoIn3n+2 using the technique of perturbed angular correlation of gamma rays (PAC). The frequencies were determined by analysis of nuclear quadrupole relaxation produced by fluctuating electric field gradients. Samples were synthesized having nominal values n= 1, 2, 3, 5 and , with n= corresponding to the L12 phase LaIn3. The phases form heuristically from LaIn3 by replacing every (n+1)th (100) mixed plane of La and In atoms with a plane of Co-atoms. For the n=1 phase, LaCoIn5, jump frequencies were too small to detect. Two signals were observed, one for indium atoms next to the Co-planes and the other for more distant indium atoms. No relaxation was observed for atoms next to the Co-planes, indicating that there is no diffusion across the Co-planes. With increasing n, jump rates for the other In-atoms increased toward values observed for LaIn3. Jump frequency activation enthalpies for n= 3 and 5 were observed to be the same as for n=, suggesting the same diffusion mechanism. However, the jump-frequency prefactors were found to be smaller for small n, which is attributed to reductions in the connectivity of the diffusion sublattice. We conclude that diffusion in the layered phases is remarkably similar to diffusion in LaIn3 once the reduced connectivity is taken into account.

Diffusion in Binary and Pseudo-Binary L1<sub>2</sub> Indides, Stannides, Gallides and Aluminides of Rare-Earth Elements as Studied Using Perturbed Angular Correlation of <sup>111</sup>In/Cd

Diffusional jumps can produce fluctuating electric field gradients at nuclei of jumping atoms. Using perturbed angular correlation of gamma rays (PAC), jumps of probe atoms cause nuclear quadrupole relaxation that can be fitted to obtain the mean jump frequency. An overview is given of the application of this approach to highly ordered intermetallic compounds having the L12 (Cu3Au) crystal structure. New results are then presented for jump frequencies of 111In/Cd probe atoms in pseudo-binary L12 compounds of the forms In3(La1-xPrx) and (In1-xSnx)3La. For the mixed rare-earth system, jump frequencies are found to scale with composition between jump frequencies of the end-member phases In3La and In3Pr. However, for the mixed sp-element system, a large decrease in jump frequency is observed as Sn atoms substitute for In-atoms. This difference in behavior appears to depend on whether atomic disorder is on the diffusion sublattice (In-Sn substitution), as opposed to a neighboring sublattice (La-Pr substitution), whether or not there is a difference in diffusion mechanism between end-member phases, and/or whether or not there is a valence difference between the mixing atoms. All three conditions apply for only (In1-xSnx)3La.

Motion of Cadmium Tracer Atoms in Al<sub>11</sub>R<sub>3</sub> Phases (R=La,Ce,Pr)

Jump frequencies of Cd tracer atoms were measured in three phases having the orthorhombic Al11R3 structure, with R= La, Ce, or Pr. The structure has four inequivalent Al-sites and two inequivalent R-sites. 111In/Cd tracer atoms were observed to occupy several sites via the nuclear quadrupole interaction using perturbed angular correlation of gamma rays (PAC). Time-domain PAC spectra became damped as the temperature increased, which is attributed to nuclear relaxation caused by diffusional jumps of Cd tracer atoms leading to changes in orientations and/or magnitudes of electric field gradients (EFG’s). Maximum relaxations were observed near 770 K. A method is proposed for estimating the mean jump frequency at that temperature, giving a mean jump frequency w averaged over all sites of about 100 MHz. At still higher temperatures, damping decreased due to motional averaging, and the quadrupole perturbations evolved into unique signals having lower frequencies and corresponding in each phase to the averages of EFG tensors of all sites visited by the Cd tracer atoms. For Al11La3, the jump frequency at 1073 K was estimated to be 1.9 GHz. Such jump frequencies imply unusually high diffusivities in these phases.

Jump Frequencies of Cd Tracer Atoms in L1<sub>2</sub> Lanthanide Gallides

Jump frequencies of Cd tracer atoms were measured in three lanthanide gallides having the L12 structure: DyGa3, ErGa3 and LuGa3. 111In/Cd impurity probe atoms were observed to occupy the non-cubic Ga-sites through the nuclear quadrupole interaction using the method of perturbed angular correlation of gamma rays (PAC). Measurements at elevated temperatures exhibited nuclear relaxation (damping) of quadrupolar perturbation functions attributed to diffusional jumps of the probes among orientationally inequivalent Ga-sites. Accurate values of jump frequencies were determined from fits of the measured perturbation functions using a model of stochastically fluctuating electric-field gradients, as in previous work [e.g., Matthew O. Zacate, Aurélie Favrot and Gary S. Collins: Physical Review Letters Vol. 92 (2004) p. 225901]. Arrhenius plots of jump frequencies for the three systems exhibited jump-frequency activation enthalpies in the range 0.86-1.05 eV and prefactors of about 2 THz. The activation enthalpy for ErGa3, 0.86(2) eV is compared with those for ErAl3, 1.40(4) eV, and ErIn3, 1.34(5) eV.

Diffusion of 111Cd probes in Ga7Pt3 studied via nuclear quadrupole relaxation

Diffusion of 111In/Cd impurity atoms was studied in Ga7Pt3 at the atomic level using the method of perturbed angular correlation of gamma rays (PAC). As in previous measurements on Ga7Pd3, probes were observed to occupy two inequivalent Ga-sublattices. Quadrupole interaction perturbation functions for each site exhibited damping at elevated temperatures that is attributed to nuclear relaxation caused by stochastic jumps of the probe atoms accompanied by reorientation of axes of the electric field gradient tensor. Fitted relaxation frequencies, proportional to mean jump frequencies of the probe, were thermally activated. Arrhenius plots revealed jump-frequency activation enthalpies of 0.94 (8) and 0.67 (4) eV for the two sites and frequency prefactors close to 1 THz. Results were similar to those found previously for Ga7Pd3, although jump frequencies are about 100 times lower in Ga7Pt3.

Site preferences of indium impurity atoms in intermetallics having Al3Ti or Al3Zr crystal structures

Site-fractions of indium impurity probe atoms occupying up to three inequivalent Al-sites in Al3Ti, Al3V and Al3Zr phases were measured using perturbed angular correlation of gamma rays (PAC). Sites were identified via characteristic nuclear quadrupole interactions. Ratios of site-fractions were measured in thermal equilibrium in the range 600 to 1,210 K. Arrhenius plots of the ratios were fitted with thermally activated expressions, yielding differences in vibrational entropies and site-enthalpies. Enthalpy differences were greatest for Al3Zr, ~0.22 eV, and smaller for Al3Ti and Al3V, which is correlated with the excess volume of the transition-metal atom over the Al-atom. Vibrational entropy differences were small, in the range 0 to −0.25 kB.

Nonstoichiometry in line compounds

Phases having compositional fields narrower than about 1 at.% and appearing as lines in binary phase diagrams often are assumed to have properties independent of composition. That such an assumption can be seriously in error is illustrated by recent measurements on pairs of samples prepared to have compositions at opposing phase boundaries. Two microscopic properties, lattice locations of highly dilute solutes and diffusional jump frequencies, were studied, respectively, through measurement of static and dynamic nuclear quadrupole interactions using the method of perturbed angular correlation of gamma rays (PAC). At opposing boundary compositions, PAC probe atoms have been observed to occupy different lattice sites or to have jump frequencies differing by a factor of 100. Such gross differences suggest measurements of other properties of line compounds should be made on pairs of samples having the opposing boundary compositions in order to avoid inconsistent or unreproducible results.

Diffusion in Intermetallic Compounds Studied Using Nuclear Quadrupole Relaxation

The jump frequency of Cd tracer atoms was measured as a function of temperature in seven rare-earth tri-indide intermetallic compounds having the L12, or Cu3Au, structure. The frequency, proportional to the diffusivity, was detected by relaxation of nuclear quadrupole interaction at Cd nuclei caused by reorientation of the electric field gradient in each diffusive jump. Measurements were made using perturbed angular correlation of gamma rays, sensitive to jump frequencies in the range 1-1000 MHz. Results are as follows. (1) Jump frequencies measured in LaIn3 and CeIn3 were observed to be 10-100 times greater at the more In-rich boundary composition than the less In-rich boundary composition, even though the phases appear as line compounds in phase diagrams. (2) Arrhenius plots of the jump frequency were fitted to activation enthalpies that increase from 0.535 to 1.80 eV across the series of phases LaIn3, CeIn3, PrIn3, and NdIn3.

Jump Frequency of Cd Tracer Atoms in β-Mn

The jump frequency of Cd tracer atoms in pure and Al-doped b-Mn was determined from measurements of quadrupole relaxation using the method of perturbed angular correlation of gamma rays. The jump frequency of Cd in b-Mn containing about 4.5 at.% Al had an activation enthalpy of 0.67(3) eV. In pure b-Mn at 950 K, the jump frequency was a factor about 8 larger than the value of 9.2 MHz in the alloy. Information was also obtained about the sluggish kinetics of the a-Mn to b-Mn polymorphic transformation.

High‐Temperature Polymorph of In2La.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Software for X- and gamma-ray spectrometry

A computational approach to the true-coincidence summing correction factor evaluating was developed on the basis of the extended version of the MCNP - a general Monte Carlo N-particle transport code. A specially developed utility program generates the MCNP input on the basis of a routinely updated Evaluated Nuclear Structure Data File (ENSDF) library. Necessary information is automatically added to allow accurate simulating of the emission of correlated particles accompanying the decay of a particular radionuclide, including emission of annihilation quanta, K- and L- X-rays, β-particles and conversion electrons. Gamma-ray angular correlations as well as lifetimes of the nuclear excited states are also taken into account. The approach is applicable to correction factor evaluation for ordinary single- and multi-detector spectrometers as well as for Compton suppression systems. The paper describes the developed computational scheme as well as presents the results of its preliminary testing for the case of both point and volumetric sources.

Polymorphic Phase Transformation in In2La and CeIn2

Nuclear quadrupole interactions of 111Cd probes in In2La and CeIn2 were measured using perturbed angular correlation of gamma rays (PAC). Near room temperature, a single nonaxially symmetric quadrupole interaction was observed in each compound, with ω 0 = eQV zz /h = 78.8(2) Mrad/s and ŋ = 0.312(1) for In2La at 11 °C and ω 0 = 80(1) Mrad/s and ŋ = 0.29(2) for CeIn2 at 34 °C. The observed non-axial symmetry is consistent with the reported CeCu2 structure of the phases. The non-axially symmetric interactions were replaced completely by axially symmetric interactions (ŋ = 0) at 524 °C, with ω 0 = 101.0(1) Mrad /s in In2La and ω 0 = 96.9(4) Mrad/s in CeIn2. The change in symmetry is attributed to a polymorphic phase transformation. Based on symmetry information from the quadrupole interaction and on chemical arguments, it is proposed that high-temperature phases of In2La and CeIn2 both have the AlB2 (C32) structure.

High-temperature polymorph of In 2La

A polymorph of In 2La was discovered by observing a change in the quadrupole interaction at nuclei of 111In/Cd probe atoms at high temperature using the technique of perturbed angular correlation of gamma rays. Point-symmetry information from the measured electric field gradient and chemical considerations suggests that the high-temperature polymorph has the hexagonal AlB 2 structure. The transformation between the low-temperature phase, which has the CeCu 2 structure, and the high-temperature phase takes place with hysteresis over a temperature range from 200 to 450 °C.

Atom movement in In3La studied via nuclear quadrupole relaxation.

Jump frequencies of Cd tracer atoms in In3La were measured via nuclear quadrupole relaxation caused by stochastic reorientation of the electric field gradient using the method of perturbed angular correlation of gamma rays. Activation enthalpies of 0.53(1) and 0.81(1) eV were found at the two phase boundaries, which differ in composition by only about 0.1 at. %. The jump frequency was found to be higher at the more In-rich phase boundary, ruling out a simple In-vacancy diffusion mechanism. Possible diffusion mechanisms and general applicability of the method are discussed.

Clustering in Light Nuclei Studied with Multi-Particle–γ-Ray Correlations

The experimental study of clustering in light nuclei has advanced significantly in the past decade, due in part to the advent of devices such as high-resolution segmented silicon detectors. We present the results of two measurements conducted with a combination of segmented silicon strip detectors and the high-resolution gamma-ray detector array GAMMASPHERE, a determination of spins of unbound states in 24Mg, and a measurement of particle—particle—gamma-ray angular correlations to study spin alignment and resonance behavior in the 12C(12C, 12C[0 2 + ])12C[2+] inelastic scattering reaction.