Defects in Solids Group, Hyperfine Interactions Laboratory, Physics, Washington State University, Pullman, WA, USA

Publications 2001-2005
All publications are based in part upon work supported by the National Science Foundation (Metals Program) under Grant DMR 05-04843 and predecessor grants or the Praveen Sinha Fund for Physics Research.  Opinions, findings, conclusions and recommendations expressed in these publications are those of the authors and do not necessarily reflect views of the National Science Foundation or of the Praveen Sinha Fund.

PAC probes as diffusion tracers in solids, Gary S. Collins, Aurélie Favrot, Li Kang, Egbert Rein Nieuwenhuis, Denys Solodovnikov, Jipeng Wang and Matthew O. Zacate, Hyperfine Interactions 159, 1-8 (2005); 13th International Conference on Hyperfine Interactions and 17th International Symposium on Nuclear Quadrupole Interactions, Bonn, August 2004, invited paper.

Perturbed angular correlation (PAC) probe atoms have been used as tracers to study diffusion in solids.  The method works for diffusion on a sublattice for which the point symmetry is noncubic and the electric field gradient (EFG) at the probe nucleus reorients in each jump.  Such motion leads to relaxation of the nuclear quadrupole interaction.  Precise values of the tracer jump frequency have been obtained from fits of measured PAC perturbation functions.   Results obtained to date are reviewed for Cd tracer atoms in rare-earth indides such as LaIn3 that have the L12 crystal structure, for which each jump on the In-sublattice reorients the EFG by 90 degrees.  New results are presented for LaSn3 and prospects for future studies are outlined.
Comparison of XYZ model fitting functions for 111Cd in In3La, Matthew O. Zacate and William E. Evenson, Hyperfine Interactions 158, 329-332 (2005); 13th International Conference on Hyperfine Interactions and 17th International Symposium on Nuclear Quadrupole Interactions, Bonn, August 2004.

The XYZ model describes the interaction between nuclear probes and an electric field gradient that fluctuates among three orthogonal directions.  The model presents a means to calculate the perturbation function that represents spectra obtained using perturbed angular correlation spectroscopy.  Three analytic approximations of the perturbation function have been developed previously, and they are evaluated in the context of Cd jumping among In-lattice sites in In3La.
Polymorphic phase transformation in In2La and CeIn2, Egbert R. Nieuwenhuis, Aurélie Favrot, Li Kang, Matthew O. Zacate and Gary S. Collins, Hyperfine Interactions  158, 305-8 (2005); 13th International Conference on Hyperfine Interactions and 17th International Symposium on Nuclear Quadrupole Interactions, Bonn, August 2004.

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 non-axially symmetric quadrupole interaction was observed in each compound, with  w0=eQVzz/hbar = 78.8(2) Mrad/s and eta=0.312(1) for In2La at 11°C and w0 = 80(1) Mrad/s and eta = 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 (h=0) at 524°C, with w0 = 101.0(1) Mrad/s in In2La and w0 = 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 In2La, E. R. Nieuwenhuis, Gary S. Collins, Aurélie Favrot, Matthew O. Zacate, Journal of Alloys and Compounds 387, 20-23 (2005).

A polymorph of In2La 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 known transformations in similar systems suggest that the high temperature polymorph has the hexagonal AlB2 structure. The transformation between the low temperature phase, which has the CeCu2 structure, and the high temperature phase takes place with hysteresis over a temperature range from 200°C to 450°C.
Diffusion in Intermetallic Compounds Studied Using Nuclear Quadrupole Relaxation, G.S. Collins, A. Favrot, L. Kang, D. Solodovnikov and M.O. Zacate, Defect and Diffusion Forum 237-240, 195-200 (2005), Sixth International Conference on Diffusion in Materials (DIMAT 2004), Krakow, July 2004.

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 beta-Mn, Matthew O. Zacate and Gary S. Collins, Defect and Diffusion Forum, 237-240, 396-401 (2005);  Sixth International Conference on Diffusion in Materials (DIMAT 2004), Krakow, July 2004.

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 beta-Mn containing about 4.5 at.% Al had an activation enthalpy of 0.67(3) eV.  In pure beta-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 alpha-Mn to beta-Mn polymorphic transformation.
Atom Movement in In3La studied via Nuclear Quadrupole Relaxation, Matthew O. Zacate, Aurélie Favrot and Gary S. Collins, Physical Review Letters 92, 225901(1-4) (2004); and Erratum, Physical Review Letters 93, 049903 (2004).
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.
Temperature- and Composition-Driven Changes in Site Occupation of Indium Solutes in Gd1+3xAl2-3x, Matthew O. Zacate and Gary S. Collins, Physical Review B69, 174202(1-9) (2004).

Fractional concentrations of indium solutes at Gd-sites and Al-sites in the Laves phase Gd1+3xAl2-3x were measured for different temperatures and sample compositions using perturbed angular correlation spectroscopy.  At fixed composition, the fraction of indium on Gd-sites was observed to decrease as temperature was increased.  At fixed temperature, the fraction of indium on Gd-sites was observed to increase as the composition became more deficient in Gd.  The trends are explained using a thermodynamic model that couples solute site occupation with concentrations of point defects.  The increase in enthalpy of the crystal when indium switches from a Gd-site to an Al-site was determined to be 0.343(7) eV. 
Composition-driven changes in lattice sites occupied by indium solutes in Ni2Al3 phases, Matthew O. Zacate and Gary S. Collins, Physical Review B70, 24202(1-17) (2004).

 Lattice locations of dilute indium solute atoms in phases having the Ni2Al3 crystal structure were determined using the technique of perturbed angular correlations of gamma rays (PAC). Four sites, including two inequivalent Group IIIA sites, a Group VIII site and an empty-lattice site were distinguished by measurement of nuclear quadrupole interactions at 111In/Cd probes in the phases Ni2Ga3, Pt2Ga3, Ni2Al3, Pd2Al3 and Pt2Al3.  Occupied sites were identified by comparison with quadrupole interactions of probes in three indides having the same structure, Ni2In3, Pd2In3 and Pt2In3, and by calculations of electric-field gradients at the four sites.  Probes were observed to “switch” sites as the composition changed from being rich to poor in the transition metal (TM).   Indium was observed to exclusively occupy one of the Group III sites in TM-rich gallides and aluminides.  In TM-poor gallides, indium occupied the TM-sublattice, while near the stoichiometric composition it also partially occupied the empty lattice site, which has interstitial character.  For TM-poor aluminides, highly inhomogeneous quadrupole interactions were observed indicating that indium was located on irregular sites in lattice sinks such as grain boundaries.  Dependences of site fractions on composition are interpreted using a thermodynamic model that relates fractions of solutes on substitutional, interstitial and lattice sink sites to concentrations of intrinsic defects.   Heuristic rules are presented that describe site selection behavior based on the experiments and model.   Among other rules, it was found that there is a maximum tendency for solutes to occupy interstitial sites near the stoichiometric composition. 
Charge transfer model for quadrupole interactions and binding energies of point defects with 111In/Cd probes in cubic metals, Gary S. Collins and Matthew O. Zacate, Hyperfine Interactions 151, 77-91 (2003), special volume on the occasion of the 80th birthday of Hendrik de Waard.  Invited paper.

A simple model is used to predict nuclear quadrupole interactions caused by point defects at near-neighbor sites of probe atoms in cubic, metallic hosts.   Also predicted are binding energies between the defects and impurity probe atoms.    The model assumes that electrostatic interactions predominate over strain interactions.  It is critically examined using data for 111In/Cd probes next to solute atoms in noble metal hosts, obtained mostly by K. Królas, and next to vacancies in metals and intermetallic phases.   The magnitude of quadrupole interactions is found to correlate well with charge transfer between host metal and defect.  Charge transfer is taken to be proportional to the difference between work functions of the defect and host elements.   An ansatz is proposed for the work function of a vacancy.  Good correlations are obtained between experimental and calculated interactions for the generally oversized 111In/Cd probe.   The charge transfer model is believed to be applicable for other probes that are oversized.
Point Defects in FeAl Studied by Perturbed Angular Correlation, Gary S. Collins, Luke S.-J. Peng and Matthew O. Zacate, Defect and Diffusion Forum 213-215, 107-132 (2003).  Invited paper. (0.5 Mbytes)
  
Point defects were detected in FeAl samples using perturbed angular correlation of gamma rays (PAC).  Measurements were made near the stoichiometric composition of the CsCl phase (49-53 at.% Fe).  Seven quadrupole interactions signals were observed that are attributed to indium probe atoms on aluminum sites with or without neighboring point defects.   Fractions of probes associated with each signal were monitored after quenching or in measurements at elevated temperature.  Signals detected were attributed to the defect-free probe, to probes having an Fe-antisite atom in the second neighbor shell, and to probes having from one to four or five Fe-vacancies in the closest atomic shell.   Identifications were made through analysis of thermal variation of site-fractions and by comparison of measured quadrupole interactions with those in other CsCl phases and with those calculated in the point-charge approximation.  Binding energies and entropies of bound Fe-vacancies were determined through a thermodynamic analysis of the thermal trends.  For the first through fourth trapped vacancy, binding energies were +0.13(2), +0.28(1), +0.14(1) and +0.14(2) eV and binding entropies were -2(1), 0(1), -1(1) and -2(1) kB, respectively.  Only one structure each was detected for a 2-vacancy or 3-vacancy complex, leading to the conjecture that alternative configurations are unstable and collapse athermally into the most stable one.  Four thermal regimes were detected:  Below 200-300 C, vacancy motion over atomic distances was frozen.  Between 300 and 600 C, a constant concentration of about 1% excess, quenched-in vacancies was detected that did not anneal out while local motion of vacancies continued to equilibrate populations of vacancy complexes as observed by changes in site-fractions.  Between 600 and 900 C, thermal activation of vacancies was observed via increases in site-fractions of higher-order vacancy complexes.  In the range 900 and 1300 C, site-fractions did not increase, which we believe is explained by proposals of others that there may be a change in the type of equilibrium defect combination formed above and below 900 C.   No signals were observed that could be attributed to either Al-antisite atoms or to Al-vacancies.
Influences of Lattice Sinks and Defect Interactions on Solutes in Compounds , Gary S. Collins and Matthew O. Zacate, Mat. Res. Soc. Symp. Proc. 719, F8.19.1-F8.19.6 (2002), Spring Meeting, Materials Research Society, San Francisco, April 2002, Symposium F:  Defect and Impurity-Engineered Semiconductors and Devices 

A thermodynamic model for the site preference of dilute solutes in ordered compounds was developed recently.   The model is extended here in two ways to help interpret experimental results from this laboratory.  (1) A preference for solutes to occupy sites in 'sinks' such as grain boundaries rather than regular lattice sites is included using a simple model.  A wide range of site preference behavior is found;  for example, a solute may switch between substitutional and sink sites with changing composition.  (2)  The effect of an attractive interaction between solute and defect on the site preference is examined.  Conditions are established under which a solute can be stabilized by association with a defect on a site where the solute would otherwise not be found. 
Site Preference Model for Hyperfine Impurities in Compounds, Gary S. Collins and Matthew O. Zacate, Hyperfine Interactions 136/137, 641-646 (2001), Twelfth International Conference on Hyperfine Interactions, Park City, August 2001.

A thermodynamic model for site preferences of solute atoms in ordered binary phases is applied in this paper for substitutional and interstitial sites of the Cu3Au, or L12, structure.  Site preferences are found to depend on formation energies of combinations of elementary point defects and on energies for transfer of solutes among different sites.  The composition dependence in compounds having a wide phase field is examined in detail.  A phenomenology of site preference behavior is outlined for regular lattice sites as well as for non-lattice sites such as grain boundaries.
Site Preferences of Hyperfine Impurities in Ni2Al3 Phases, Matthew O. Zacate and Gary S. Collins, Hyperfine Interactions 136/137, 647-652 (2001), Twelfth International Conference on Hyperfine Interactions, Park City, August 2001.

The site occupation of indium solutes in Ni2Al3-type compounds was determined using perturbed angular correlation of gamma rays.  Measurements were made for compositions on both sides of the stoichiometric composition.  Sites were identified through their quadrupole interactions.  For transition-metal (TM) rich aluminides and galliumides, indium solutes occupy only one of two inequivalent trivalent-metal sites (Al or Ga).  For TM-poor aluminides, indium solutes tend to locate at non-crystallographic sites such as in grain boundaries.   For TM-poor galliumides, the solutes occupy nickel sites while close to the stoichiometric composition they also occupy sites on an empty Ni-sublattice.  Composition dependences of site preference for indium solutes in Pt2Al3 and Ni2Ga3 are examined in terms of a recently developed thermodynamic model.
Segregation of Solutes in Two-Phase Mixtures, Matthew O. Zacate, Bonner C. Walsh, Luke S.-J. Peng and Gary S. Collins,  Hyperfine Interactions 136/137, 653-658 (2001), Twelfth International Conference on Hyperfine Interactions, Park City, August 2001.

Fractions of indium solutes in each phase of a mixture of two binary phases were measured using perturbed angular correlation of gamma rays.   Measurements of phase fractions were made on Pd3Ga7-PdGa, PdGa-Pd5Ga3, and FeAl2-FeAl mixtures as a function of composition.  The phase fractions were analyzed using a thermodynamic model that takes into account differences between energies of solute atoms in the two phases. From the model, segregation coefficients were obtained for the systems studied.  Also, earlier measurements on Ni2Al3-NiAl were reanalyzed.  Large differences are found among the segregation coefficients.
Stochastic Model of PAC Nuclear Relaxation Caused by Defects Hopping on a Simple Cubic Lattice,  Taylor D. Grow, Stephanie Plamondon, William E. Evenson and Gary S. Collins, Hyperfine Interactions 136/137, 627-632 (2001), Twelfth International Conference on Hyperfine Interactions, Park City, August 2001.

A stochastic model is used to obtain an analytic approximation for the perturbation function caused by quadrupole interaction that applies when there is a fixed concentration of defects hopping on a simple cubic lattice, with the probe atom located at center of one of the cubes.  A realization of this model is jumping of structural vacancies on one sublattice in the CsCl structure, with the probe atom on the other sublattice.  PAC spectra obtained for Pd-poor PdIn using 111In/Cd probes are refitted with the model perturbation function to obtain the vacancy jump frequency as a function of temperature.
Nucleation of Embryos of a Second Phase by Individual Impurity Atoms, Matthew O. Zacate, Gary S. Collins and Luke S.-J. Peng, Materials Science and Engineering A329-331, 920-924 (2002),  Fifth International Conference on Structural and Functional Intermetallics, Vancouver, July 2000. 

Perturbed angular correlation of gamma rays (PAC)  was used to monitor atomic environments of indium atoms in Ni-Al alloys at temperatures and compositions in the two-phase field between Ni2Al3 and NiAl.  In previous PAC measurements at room temperature, the fraction of signal that is characteristic of the Ni2Al3 phase greatly exceeded the fraction predicted by the lever-rule, and it was suggested that indium could nucleate small embryos of the Ni2Al3 phase in the NiAl single-phase field.  Measurements at elevated temperatures are now reported.  PAC signals from the Ni2Al3 phase are observed to extend into the NiAl single-phase field from 0.5 to 1.0 at.% beyond published phase boundaries established by experiments on samples prepared similarly to those in this study.  Thus, the new observations support the hypothesis that individual solute atoms can nucleate small crystals of a second phase within a single-phase field.  In addition, phase boundaries were calculated from the PAC data, assuming that the lever rule was obeyed, and compared with boundaries from the literature. 
Vacancy-Vacancy Interactions in NiAl,Matthew O. Zacate and Gary S. Collins, Defect and Diffusion Forum 194-199, 383-88 (2001),  Fifth International Conference on Diffusion in Materials, Paris, July 2000.

Interactions between Ni vacancies in Ni-poor NiAl were investigated using the method of perturbed angular correlation of gamma rays.   Measurements were made on samples in the composition range 49.0 to 49.8 at.% Ni and at temperatures up to 1050 C, for which there is a fixed concentration of structural Ni vacancies.  Site fractions of complexes of vacancies with In solute atoms were determined from amplitudes of quadrupole interaction signals.  The binding energy between a vacancy and In solute was determined from fits of site-fraction ratios to be 0.154(7) eV.  Binding energies of a second vacancy in three distinct configurations were determined in the same way to be 0.086(10), 0.154(6) and 0.135(14) eV, respectively, for vacancies  in first-, second- and third-neighbor positions on their own sublattice.  Estimates of the vacancy-vacancy interaction energy are given by the difference between binding energies of the first and second vacancies, and found to be 0.068, 0.000, and 0.019 eV for the corresponding positions.  Thus, vacancies are repelled from first- and third-neighbor positions and favor second-neighbor positions.  Overall, the interaction energies are found to be relatively small. 
Vacancy Jumps in PdIn: Reconciling Nuclear Relaxation and Diffusion Measurements, Gary S. Collins and Harmen Thys Nieuwenhuis,  Defect and Diffusion Forum 194-199, 375-83 (2001);  Fifth International Conference on Diffusion in Materials, Paris, July 2000. 

Vacancy jump frequencies in PdIn were determined in the range 888 to 1288 K from analysis of nuclear relaxation of monovacancy signals in PdIn with 48.5 at.% Pd detected by perturbed angular correlation of gamma rays.   The relaxation is attributed to jumps of Pd-vacancies out of, within, or into the first neighbor shell of In/Cd probe atoms.  These frequencies are compared with frequencies derived from Pd-diffusivities measured for 49 at.% Pd by Hahn, Frohberg and Wever [phys. stat. sol. (a)79, 559 (1983)].  Jump frequencies are found to be in excellent agreement at high temperature.  An Arrhenius plot of PAC jump frequencies exhibits curvature that could be fitted well assuming a superposition of two independent jump mechanisms:  one with activation energy fixed at the value 2.15 eV found by Hahn et al. and the other fitted to 0.49(14) eV.  The low activation energy is attributed to a cyclic diffusion mechanism in which the first diffusion barrier has a height of 0.49 eV and in which the correlation factor is small, so that lots of jumps take place without mass transport.  A possible candidate for the jump is an In atom jumping to an adjacent Pd vacancy.


Publications 2006-2010
Publications 1995-2000
Selected Publications prior to 1995

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