Matthew O. Zacate

Predicting lattice parameter as a function of cation disorder in MgAl2O4 spinel

In the perfect magnesium aluminate spinel structure all the tetrahedral sites are occupied by Mg2+ ions, while Al3+ ions occupy all the octahedral sites. Real MgAl2O4, however, exhibits cation disorder (inversion), so that some Mg2+ ions reside in octahedral sites with an equal number of Al3+ ions in tetrahedral sites. Atomistic simulation was used to correlate the degree of inversion with changes in lattice parameter. Results from several approaches, including a combined energy minimization–Monte Carlo technique (CEMMC), are compared with available experimental data. These show that the mean field method is not useful, while the defect volume approach can yield predictions that are useful in interpreting the CEMMC results, which agree most closely with experiment.

Perturbed Angular Correlation Spectroscopy – A Tool for the Study of Defects and Diffusion at the Atomic Scale

This paper provides an introduction to perturbed angular correlation (PAC) spectroscopy in the context of its application in the study of point defects and diffusion. It emphasizes what we anticipate to be of interest to non-PAC specialists who are interested in understanding variations in how PAC results are presented by different research groups and in how physical quantities such as defect formation energies, association energies, and migration barriers can be extracted from analysis of PAC spectra. Numerous citations are included to emphasize the universality of the analysis methods across different classes of materials including metallic, ceramic, and semiconducting compounds.

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 Frequencies of Cd Tracer Atoms in L12 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.

Site Preference Model for Hyperfine Impurities in Compounds

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.

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.

Segregation of Solutes in Two-Phase Mixtures

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 hyperfine interactions modeling library—Version 2

The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized. The original version of SHIML constructed and solved Blume matrices for methods that measure hyperfine interactions of nuclear probes in a single spin state. Version 2 provides additional support for methods that measure interactions on two different spin states such as Mossbauer spectroscopy and nuclear resonant scattering of synchrotron radiation. Example codes are provided to illustrate the use of SHIML to (1) generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A22 can be neglected and (2) generate Mossbauer spectra for polycrystalline samples for pure dipole or pure quadrupole transitions.

Nucleation of embryos of a second phase by individual impurity atoms

Abstract Perturbed angular correlation of gamma rays (PAC) was used to monitor the atomic environments of indium atoms in Ni–Al alloys at temperatures and compositions in the two-phase field between Ni 2 Al 3 and NiAl. In earlier PAC measurements at room temperature, the fraction of signal that is characteristic of the Ni 2 Al 3 phase greatly exceeded the fraction predicted by the lever-rule, and it was suggested that indium could nucleate small embryos of the Ni 2 Al 3 phase in the NiAl single-phase field. Measurements at elevated temperatures are now reported. PAC signals from the Ni 2 Al 3 phase are observed to extend into the NiAl single-phase field from 0.5 to 1.0 at.% beyond published phase boundaries that were 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.

Site Preferences of Hyperfine Impurities in Ni2Al3 Phases

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 noncrystallographic 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.