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

2018 ◽  
Vol 19 ◽  
pp. 61-79 ◽  
Author(s):  
Gary S. Collins
Keyword(s):  
Diffusion Mechanism ◽  
Nuclear Quadrupole Interaction ◽  
Site Preference ◽  
Jump Frequency ◽  
Heavy Lanthanide ◽  
Site Preferences ◽  
Lanthanide Elements ◽  
Light Lanthanides ◽  
Diffusion Mechanisms ◽  
Jump Frequencies

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.

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

2014 ◽  
Vol 2 ◽  
pp. 95-105
Author(s):  
Gary S. Collins ◽  
Qiao Ming Wang ◽  
John P. Bevington
Keyword(s):  
Rare Earth ◽  
Diffusion Mechanism ◽  
Correlation Factor ◽  
Jump Frequency ◽  
Frequency Measurements ◽  
Quadrupole Interactions ◽  
Site Preferences ◽  
Nuclear Quadrupole Interactions ◽  
Nuclear Quadrupole ◽  
Jump Frequencies

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.

scholarly journals Comparison of Jump Frequencies of 111In/Cd Tracer Atoms in Sn3R and In3R Phases Having the L12 Structure (R = Rare-Earth)

2011 ◽  
Vol 311 ◽  
pp. 159-166 ◽  
Author(s):  
Megan Lockwood Harberts ◽  
Benjamin Norman ◽  
Randal Newhouse ◽  
Gary S. Collins
Keyword(s):  
Rare Earth ◽  
Perturbed Angular Correlation ◽  
Diffusion Mechanism ◽  
Correlation Spectroscopy ◽  
Perturbed Angular Correlation Spectroscopy ◽  
Dominant Mechanism ◽  
Boundary Composition ◽  
Light Lanthanide ◽  
Diffusion Mechanisms ◽  
Jump Frequencies

Measurements were made of jump frequencies of 111In/Cd tracer atoms on the Sn-sublattice in rare-earth tri-stannides having the L12 crystal structure via perturbed angular correlation spectroscopy (PAC). Phases studied were Sn3R (R= La, Ce, Pr, Nd, Sm and Gd). Earlier measurements on isostructural rare-earth tri-indides showed that the dominant diffusion mechanism changed along that series [4]. The dominant mechanism was determined by comparing jump frequencies measured at opposing phase boundary compositions (that is, more In-rich and more In-poor). Jump frequencies were observed to be greater at the In-rich boundary composition in light lanthanide indides and greater at the In-poor boundary composition in heavy-lanthanide indides. These observations were attributed to predominance of diffusion via rare-earth vacancies in the former case and indium vacancies in the latter. Contrary to results for the indides, jump frequencies found in the present work are greater for the Sn-poor boundary compositions of the stannides, signaling that diffusive jumps are controlled by Sn-vacancies. Possible origins of these differences in diffusion mechanisms are discussed.

Motion of Cadmium Tracer Atoms in Al11R3 Phases (R=La,Ce,Pr)

2009 ◽  
Vol 289-292 ◽  
pp. 755-761 ◽  
Author(s):  
Stephanie Lage ◽  
Gary S. Collins
Keyword(s):  
Gamma Rays ◽  
Time Domain ◽  
Perturbed Angular Correlation ◽  
Nuclear Quadrupole Interaction ◽  
Electric Field Gradients ◽  
Jump Frequency ◽  
Field Gradients ◽  
The Mean ◽  
Nuclear Quadrupole ◽  
Jump Frequencies

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.

From Solid State Diffusion to Configurational Kinetics

1998 ◽  
Vol 527 ◽  
Author(s):  
G. Martin ◽  
M. Athènes ◽  
C. Desgranges ◽  
M. Nastar ◽  
F. Soisson
Keyword(s):  
Diffusion Mechanism ◽  
Transport Coefficients ◽  
Mean Field ◽  
Kinetic Properties ◽  
Monte Carlo Techniques ◽  
Complex Diffusion ◽  
Specific Effects ◽  
State Diffusion ◽  
Diffusion Mechanisms ◽  
Jump Frequencies

ABSTRACTA single model is proposed to describe the cohesive energy and the vacancy jump frequencies as a function of the alloy configuration at the atomic level. The very same model therefore yields both equilibrium and kinetic properties, close and far away from equilibrium. The model is handled at two levels of approximation: Monte Carlo techniques and mean-field type approximations. The model yields equilibrium properties (including the transport coefficients and complex diffusion mechanisms in ordered compounds close to equilibrium) as well as the kinetic path for phase separation, with or without ordering. This allows to identify specific effects of the vacancy diffusion mechanism on the kinetic path for alloy decomposition. Here, we summarise the main results of the above approach.

scholarly journals Diffusion in LanCoIn3n+2 Phases Studied by Perturbed Angular Correlation

2012 ◽  
Vol 323-325 ◽  
pp. 453-458 ◽  
Author(s):  
Randal Newhouse ◽  
Gary S. Collins
Keyword(s):  
Angular Correlation ◽  
Perturbed Angular Correlation ◽  
Diffusion Mechanism ◽  
The Other ◽  
Electric Field Gradients ◽  
Jump Frequency ◽  
Quadrupole Relaxation ◽  
Field Gradients ◽  
Jump Frequencies ◽  
Nuclear Quadrupole Relaxation

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.

scholarly journals Diffusion in Binary and Pseudo-Binary L12 Indides, Stannides, Gallides and Aluminides of Rare-Earth Elements as Studied Using Perturbed Angular Correlation of 111In/Cd

2012 ◽  
Vol 323-325 ◽  
pp. 447-452
Author(s):  
Randal Newhouse ◽  
Justine Minish ◽  
Gary S. Collins
Keyword(s):  
Rare Earth ◽  
Angular Correlation ◽  
Perturbed Angular Correlation ◽  
Diffusion Mechanism ◽  
Jump Frequency ◽  
Quadrupole Relaxation ◽  
System A ◽  
Field Gradients ◽  
Ordered Intermetallic ◽  
Jump Frequencies

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 of111In/Cd probe atoms in pseudo-binary L12compounds 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.

Jump Frequencies of Cd Tracer Atoms in L12 Lanthanide Gallides

2009 ◽  
Vol 289-292 ◽  
pp. 725-732 ◽  
Author(s):  
Xia Jiang ◽  
Matthew O. Zacate ◽  
Gary S. Collins
Keyword(s):  
Gamma Rays ◽  
Elevated Temperatures ◽  
Physical Review ◽  
Nuclear Quadrupole Interaction ◽  
Electric Field Gradients ◽  
Jump Frequency ◽  
Perturbation Functions ◽  
Field Gradients ◽  
Jump Frequencies ◽  
L12 Structure

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 in Intermetallic Compounds Studied Using Nuclear Quadrupole Relaxation

2005 ◽  
Vol 237-240 ◽  
pp. 195-200 ◽  
Author(s):  
Gary S. Collins ◽  
A. Favrot ◽  
L. Kang ◽  
D. Solodovnikov ◽  
Matthew O. Zacate
Keyword(s):  
Intermetallic Compounds ◽  
Gamma Rays ◽  
Perturbed Angular Correlation ◽  
Nuclear Quadrupole Interaction ◽  
Jump Frequency ◽  
Quadrupole Relaxation ◽  
Boundary Composition ◽  
Nuclear Quadrupole ◽  
Jump Frequencies ◽  
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.

Computational Studies of Magnesium and Strontium Substitution in Hydroxyapatite

2012 ◽  
Vol 529-530 ◽  
pp. 123-128 ◽  
Author(s):  
Flora E. Imrie ◽  
Marta Corno ◽  
Piero Ugliengo ◽  
Iain R. Gibson
Keyword(s):  
Density Functional ◽  
Structural Changes ◽  
Harmonic Approximation ◽  
Site Preference ◽  
Ionic Radii ◽  
Biologically Relevant ◽  
Site Preferences ◽  
Mechanical Approach ◽  
Quantum Mechanical Approach ◽  
Mg Substitution

The properties of hydroxyapatite can be improved by substitution of biologically relevant ions, such as magnesium (Mg) and strontium (Sr), into its structure. Previous work in the literature has not reached agreement as to site preferences in these substitutions, and there are suggestions that these may change with differing levels of substitution. The current work adopted a quantum mechanical approach based on density functional theory using the CRYSTAL09 code to investigate the structural changes relating to, and site preferences of, magnesium and strontium substitution (to 10 mol%) in hydroxyapatites and also to predict the corresponding vibrational spectra in the harmonic approximation. The structures underwent full geometrical optimisation within the P63 space group, indicating an energetic site preference for the Ca (2) site in the case of Mg substitution, and the Ca (1) site in the case of Sr. Shrinkage of the unit cell was observed in the case of Mg substitution, and expansion in the case of Sr substitution, in agreement with the corresponding ionic radii. Thermodynamic properties of the structures obtained from the harmonic vibrational frequency calculations confirmed that the structures were minima on the potential energy surface. Isotopic substitutions indicated that the main contribution of Sr and Mg to vibrational modes is at frequencies < 400 cm-1.

Cu Precipitation Dynamics in an Fe-1.18%Cu Alloy

2012 ◽  
Vol 509 ◽  
pp. 22-27 ◽  
Author(s):  
Hui Ping Ren ◽  
Hai Yan Wang ◽  
Zong Chang Liu
Keyword(s):  
Diffusion Mechanism ◽  
Structural Features ◽  
Precipitation Process ◽  
Thermally Activated ◽  
Cu Alloy ◽  
Transmission Electron ◽  
Wide Range ◽  
Means Of Transmission ◽  
Evolution Of Microstructure ◽  
Jump Frequencies

The precipitation of copper during aging at 600oC in high-purity Fe-Cu alloy was examined by means of transmission electron microscopy (TEM).Nano-scale copper-rich clusters with a B2-like structure were observed during heat treatment. These micro structural features play an important role in precipitation strengthening. In addition, the precipitation process has been analyzed in terms of the evolution of microstructure by a Monte Carlo method. A description of the coherent precipitation of copper in iron, based on a vacancy diffusion mechanism, thermally activated jump frequencies and cohesive energy is discussed in order to deal with simultaneous precipitation of metastable and stable phases in Cu-containing steel during aging. This analysis gives an estimation of the precipitation dynamics, as well as the evolution of Cu precipitates across a wide range of temperatures.

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