The power of this approach is in its ability to identify signals with particular defects. Consider for example, a binary compound having the simple CsCl structure.  There are two types of lattice vacancies and two types of antisite defects (not to mention interstitials.)  Analysis of physical properties that depend on defect concentrations using methods that average over defect concentrations have to rely on models of the kinds of defects that are present. The hyperfine approach avoids the need for such models.

Once a signal has been identified with a defect, one can, in principle, determine the concentration of that defect species through measurement and analysis of the fraction of probe atoms in complexes associated with the defect. This is straightforward when the probe is a host atom, but we have shown that it is also tractable when using an impurity probe. From measurements on systems in thermal equilibrium, one can determine thermodynamic properties of defects such as activation energies for formation of defects or for binding between defects and impurity probes. In addition, defect jump frequencies and activation energies for migration have been obtained through measurement of nuclear relaxation caused by stochastic motion of defects.

These ideas are illustrated in my research. Below is a summary of accomplishments in the areas of defects in metals, made mostly in the 1980's, defects in intermetallic compounds, from the 1990's, and other areas.   References in square brackets refer to refereed publications from my curriculum vitae, listed below.  Letters in square brackets refer to endnotes.  (Click here for a printable version of this document.)

Starting in the 1970's, hyperfine interaction methods began to be extensively applied to study point defects in metals [A.B,39]. The atom-scale information provided by these and other nuclear methods such as positron annihilation [C] has revealed a richness of defect phenomena that was inaccessible earlier using macroscopic methods.  My contributions have been primarily in the areas of defect formation and annealing in plastically deformed metals and hydrogen interactions with vacancies.

Plastic deformation

Vacancy formation during deformation. Nonconservative motion of dislocations during plastic deformation produces 'strings' of vacancies and interstitials that subsequently break up into migrating or immobile clusters. The migrating clusters thus formed can be detected during annealing when they trap at impurity probe atoms. We carried out one of the first two PAC studies of defects in deformed materials [9,D]. The rate of production of vacancy clusters in fcc metals during deformation was found to be high relative to other methods of damaging [9,14,20].  Vacancy concentrations were found to increase rapidly during Stage II of mechanical hardening and to saturate in Stage III [9].  Multi-vacancy clusters were found to migrate as a unit [39]; for example, in nickel the trivacancy is thermally activated to migrate at about 350 K and traps at impurities, forming a cubic-symmetric complex [16].

Self-interstitials and vacancy-interstitial annihilation during plastic deformation.   At temperatures of order 100 K, isolated interstitials and small interstitial clusters are highly mobile in metals, while vacancy species are not. While interstitials have not been observed to trap next to indium probe atoms in fcc metals, we have observed them indirectly through annihilation of vacancies next to probe atoms. For this purpose, samples of gold and platinum that had been predoped with vacancy-probe complexes were plastically deformed at 77 K, where only the interstitials are mobile. Large changes in the site fractions of vacancy complexes were observed and attributed to interstitial annihilation [33,44]. Changes in site fractions were monitored as a function of the 'dose' of plastic deformation. Qualitatively, site fractions changed in the way expected for transformations of higher-order vacancy complexes into lower-ordered ones.  Quantitatively, site fractions were fitted using a kinetic-rate model for annihilation from which were obtained relative cross sections for capture of interstitials by vacancy complexes and, with less precision, relative fractions of mobile clusters containing 1, 2, 3 or 4 interstitials that annihilate at the vacancy complexes [44].

Stacking faults in cobalt. The stacking-fault energy of cobalt is very low, leading to the well-known transformation between hcp and fcc allotropes. Heavy plastic deformation of cobalt at room temperature led to observation of a new signal with electric-field gradient parallel to the c-axis, like the efg in defect-free, hcp cobalt, that is attributed to an intrinsic stacking fault [36]. The site fraction indicated that the stacking-fault density was about one plane in ten.

Mobility of vacancy clusters

Following plastic deformation of gold at 77 K, three defect species were observed to trap sequentially at impurity probe atoms as the annealing temperature was increased [14]. From lowest to highest temperature, the species observed to anneal out were attributed to mobile 3V, 2V and 1V on the basis of previous identifications and point-charge efg calculations of vacancy clusters  [39]. The order of recoveries with increasing temperature was found to be 2V, 3V and 1V both in deformed platinum [39] and in irradiated, deformed or ion-implanted nickel [15,20]. It was shown in ref. [16] that the 3V in Ni migrates and traps at impurity probe atoms as a unit and not, for example, by accretion of smaller clusters.

Hydrogen decoration of vacancies

Hydrogen is readily introduced in materials. It diffuses interstitially in metal systems at ambient temperature and forms shallow traps with vacancies.  We carried out the first PAC study in which vacancies were decorated by diffusing and trapping hydrogen atoms [26].  Hydrogen was introduced by electrochemical charging [37]. Using samples predoped with vacancy-probe complexes, trapping of hydrogen was detected through modification of the hyperfine interactions. Such modifications were observed after charging Ni or Pt, but not Cu or Au [37], indicating that electrochemical charging is effective at introducing hydrogen, in part-per-million quantities or greater,  in Ni and Pt but not in Cu or Au.

Changes in electric-field gradients observed when hydrogen traps in vacancy complexes were either very large or small.  In nickel, a 3V-complex [E] was observed to be decorated by hydrogen or deuterium atoms through changes in hyperfine interactions [26,28]. In platinum, hydrogen was observed to decorate 1V, 2V, 3V and 4V complexes [31,32,37,43]. Disturbances to efg's of 1V and 2V complexes were very small [32,52], which is attributed to compact screening of the charge of the proton or deuteron.  However, very large changes in efg's of 3V and 4V complexes were observed [52]. Such large changes are attributed to radical transformation, or restructuring, of the complexes that take place when hydrogen atoms trap [32].

Consider, for example, a 3V-complex that forms near 400 K during annealing of damaged Pt and that has cubic point symmetry (zero quadrupole interaction frequency) in the undecorated state [32]. The structural model of the undecorated complex is the same as for the 3V-complex observed in Ni: the probe is at an interstitial site at the center of a tetrahedron of vacant sites. When decorated with hydrogen atoms, a large efg is observed that is attributed to restructuring of the complex through "gas pressure" from the hydrogen atom pushing the probe atom back onto one of the four vacant sites [32].

Charging for longer times leads to further changes in the hyperfine interactions attributed to trapping of more than one hydrogen atoms at a complex [37,43,52]. Detrapping of hydrogen from vacancy complexes was observed during annealing at temperatures above room temperature and was analyzed to estimate of the binding energy of hydrogen in four different vacancy complexes using a model of diffusion in a medium with traps [43]. Such a model is more accurate than one-step detrapping models used by others. Binding energies in 1V to 4V-complexes in Pt were all found to be close to 0.25 eV [43].

Grain boundaries, nanocrystals

Signals were observed for indium probe atoms on grain boundary sites in high-purity, polycrystalline fcc metals after diffusion at low temperatures [45]. For Pt, a unique signal was observed with a site fraction of ~50%, which was very surprising given that there is conventionally believed to be a wide array of grain boundaries in polycrystalline samples.  Possibly, this is due to 'polygonization' of high-angle grain-boundaries into low-energy steps, leading to much greater area fractions of a small number of dominant grain boundary structure.

Nanocrystalline indium metal was prepared by chemical reduction [47]. The electric-field gradient was observed to decrease below the value for bulk indium for crystals having sizes below about 3 nm [48]. This was attributed to a change in the axial ratio of the crystal [48]. While paper 48 was in proof, it was learned that a continuous transition from the fct structure of bulk indium to the fcc structure for crystal size below ~3 nm had been previously observed.  In other work, nanocrystalline Fe prepared by mechanical milling was studied using Mössbauer spectroscopy [50].

Intermetallic compounds have a richer 'zoo' of defects than the pure elements. Point defects include vacancies and antisite atoms on the various sublattices, and possibly interstitials. We have studied point defects extensively in compounds having the CsCl structure and composed of a transition-metal (TM) element and trivalent element, including NiAl, FeAl and PdIn. Our work follows the seminal work by Mueller and Hahn on structural and quenched-in defects in PdIn in 1984 [F]. The advantage of using PAC to study defects in intermetallics, as opposed to disordered alloys, is that there are fewer distinguishable defect configurations, making resolution potentially better [30]. Going beyond the qualitative analysis by Mueller and Hahn of quenched-in defect concentrations, we have determined activation energies for formation of defects, first in studies on quenched samples and later in studies made in equilibrium at high temperature.

Structural defects

Binary intermetallics often have broad phase fields that span the stoichiometric composition. Off-stoichiometric compositions are accommodated by structural point defects:  antisite atoms, vacancies, or interstitials. NiAl and related compounds have vacancies on the TM-sublattice in TM-poor alloys and TM-antisite atoms in TM-rich alloys. PAC studies on annealed samples using the 111In probe, which normally sits on the sublattice of the trivalent sublattice, have identified signals with structural vacancies and antisite atoms in NiAl [35], PdIn [67] and FeAl [64]. For PdIn, signals were identified for Pd-vacancies in the fourth neighbor shell as well as in the first [67]. Mössbauer measurements yielded signals from antisite TM-atoms in FeAl [57] and FeRh [60].

Equilibrium defects

In compounds, intrinsic defects must be combinations of elementary defects that preserve the composition. For example, in the CsCl structure, possible combinations include a Schottky pair of vacancies, one on each sublattice, an antisite pair created by exchange of atoms on dissimilar sublattices, or a so-called triple-defect, consisting of two vacancies on one sublattice and an antisite atom on the other. The defect combination is thermally activated as a unit, with formation energy E_F. The relation between an elementary defect concentration and the equilibrium constant of the formation reaction, K= exp(-E_F/k_BT) , depends on the type of defect and the deviation from stoichiometry. For example, for a system of composition A_1+2xB_1-2x and in which the equilibrium defect is the triple-defect (2V_A+A_B), it can be shown [67] that the fractional concentration of vacancies on the A-sublattice, [V_A], obeys the cubic equation

         [V_A]³+4x[V_A]²-2K=0.                            (1)

This treatment of the thermodynamics of defects in compounds is elaborated in a paper.recently submitted by Collins and Zacate [G].   At stoichiometry (x=0), [V_A] can be seen to be thermally activated with activation energy E_F/3, whereas for nonstoichiomtric compositions [V_A] will have a non-linear Arrhenius temperature dependence. The other defect combinations have different dependences for the concentration [V_A] on composition (x). Indeed, the dominant defect combination can be identified through the composition dependence of defect concentrations.  Bin Bai showed that the composition dependence of the concentration of Ni-vacancies in NiAl at fixed temperature supported the conclusion that the triple-defect was the dominant equilibrium defect combination and not the Schottky vacancy-pair [63, H].

Relation of site fraction to defect concentration

For metal systems, the assumption that defects are located at random on their respective sublattices is generally good owing to effective screening of defect charges by conduction electrons. With that assumption, the site-fraction of host-probes having a specific defect configuration nearby is given by a binomial probability in the defect concentrations. One can easily determine the defect concentrations that give a measured site fraction. For example, the site fraction for a host-probe to have one vacancy defect V_A in a nearby shell containing z equivalent sites is given in terms of the defect concentration [V_A] by

          f₁= z[V_A](1-[V_A])^z-1.                             (2)

Impurity probes, on the other hand, may attract or repel defects in nearby atomic shells. For a binding energy E_B, the site fraction (normalized by the defect-free site fraction f₀) is given in good approximation by [59].

        f₁/f₀= z[V_A]exp(E_B/k_BT). .                 (3)

When E_B is known, [V_A] can be determined from measured site-fractions using eq. 3.

Binding between impurity probes and defects

When E_B is unknown one can still determine a defect concentration if the concentration is constant. For solute atoms present in a fixed concentration, a log-plot of the site fraction versus reciprocal temperature will exhibit Arrhenius behavior from which one can extract E_B from the slope and the defect concentration from the intercept [I].  This method also applies to thermally activated defects under special circumstances.  For example, NiAl in a temperature range between 300 and 650 C was discovered  to have an excess concentration of vacancies that can move without annealing out appreciably [59]. From the measurements, the vacancy concentration and a binding energy of ~0.20 eV between an In probe and a Ni-vacancy were determined [59].

The situation is more difficult when the defect concentration is not constant. For NiAl, in which the ~0.20 eV binding energy of a Ni-vacancy to an In solute had been determined as described above, the vacancy concentration could be extracted from site fractions at high temperature using eq. 3. Once the vacancy concentration has been obtained at temperature T for a given composition x, the equilibrium constant K can be obtained assuming a particular defect model using an equation such as eq. 1.  This was done for NiAl, for which values of K were calculated for samples of three different compositions and found to collapse onto a single curve even though the site fractions were significantly different [63].

Comparison of measurements after quenching and at high temperature

Earlier experiments carried out at room temperature on samples quenched from temperatures up to 1400 C were superceded later by measurements at temperatures up to 1200 C.  While it is generally possible to quench rapidly enough so that defect concentrations do not anneal out, a special problem is posed when observations are made using an impurity probe. A comparative study of defects in quenched NiAl and at high temperature showed that vacancy site fractions were enhanced by a factor of about ten in quenched samples [61]. This is attributed to trapping of vacancies at impurity probes during the quench [61], since there was a high concentration of vacancies and only a few lattice jumps were needed to trap. The enhancement was found to be a strong function of the composition of NiAl samples and discussed in terms of possible diffusion mechanisms [61].

Quenched-in defects

Vacancy formation was studied at first through measurements of site-fractions in quenched samples. Effective activation energies were derived from slopes of log-plots of concentration versus inverse-temperature for impurity-probe systems NiAl and CoAl [41] and TiAl [42] and the host-probe system PdIn [54]. A defect model was usually assumed in order to interpret the apparent activation energy in terms of the formation energy of a defect combination.  However, one can not be sure that the measurements on impurity-probe systems are not disturbed by vacancy trapping during quenching, although this disturbance can be accounted for empirically [59]. The influence of deviation from strict stoichiometry on vacancy concentrations (see eq. 1) was more fully appreciated in the interpretation of measurements in papers [63, 67] than in earlier papers [41, 42, 54, 59].

Equilibrium defects at high temperature

Measurements made in thermal equilibrium avoid problems associated with quenching. From measurements made at high temperature, we determined that the dominant defect combination in NiAl was the triple-defect through the composition dependence of the vacancy concentration measured at fixed temperature [63]. It was found that, not too close to stoichiometry, the concentration varied as  x^-0.4(1), which is consistent with the triple-defect model (x^-0.5, from eq. 1) but not with the Schottky model (x^-1) or others.  .

The formation energy of the triple-defect in NiAl was determined to be 1.74(10) eV from the activation energy of the equilibrium constant K, determined as described above [63]. Ni-vacancy concentrations were determined from experimental values of the site-fraction ratio f₁/f₀ via eq. 3, using the independently measured value of E_B. K was then calculated via eq. 1 using known deviations from stoichiometry.  Finally, E_F was determined from the slope of an Arrhenius plot of K.  Similar analysis for FeAl yielded a formation energy E_F= 1.1(1) eV under the assumption that the triple-defect was dominant [64].

For PdIn, in which the indium probe is not an impurity, signals were observed in quenched samples that were attributed to both Pd-vacancies and In-vacancies [54]. This implies that the Schottky pair is thermally activated, even though structural defects observed in annealed samples, the Pd-vacancy and Pd-antisite atom, point instead to the triple-defect. The activation energy for formation of a Schottky pair was determined to be 0.91(18) eV [67].

Recently, a very detailed study was made of binding energies of indium-vacancy complexes in Ni-poor NiAl, in which there is a large, fixed concentration of structural Ni-vacancies [69]. Analysis yielded binding energies for the 1V complex, 0.154 eV, in reasonable agreement with other measurements, and for three distinct configurations of two vacancies in the cubic, first-neighbor shell:   ones in which vacancies are adjacent, at intermediate separations, or on opposite sides of the cube.

Equilibrium defects at low temperature:  the brittle-to-ductile transition in compounds

In NiAl quenched from elevated temperature, a low-temperature regime was discovered between 300 and 650 C in which Ni-vacancies move reversibly toward and away from probe atoms as the temperature is increased and decreased (see Fig. 5 in publication [59]). Below 300 C, no motion is detected in 30-minute annealing times and above 650 C rapid recovery of excess defects takes place. Measurements made within the 300-650 C range yielded a binding energy of 0.22 eV between Ni-vacancies and impurity In probes [59]. Curiously, NiAl is known to have a transition from brittle to ductile mechanical behavior as the temperature increases above 300 C.  The onset of anomalous vacancy motion at the same temperature suggests a possible explanation of the brittle-to-ductile transition [59]: that quenched-in vacancies contribute unexpectedly to dislocation climb processes at low temperatures on length scales that can keep up with dislocation motion. This may explain brittle-to-ductile behavior also in other compounds [59].

Mechanical alloying

Ball milling is an effective way to form alloys starting from powders of pure elements. Mössbauer spectroscopy was used to determine the alloying mechanism active in alloying Fe and Co to make disordered FeCo [49], which has the bcc structure, and alloying Ni and Fe to make disordered Ni₃Fe [51], with the fcc structure. For both systems, no hyperfine field components were observed that could be attributed to a dilute alloy of either constituent in the other.  It is therefore concluded that, in each system, neither element diffuses into the other. Instead, alloying appears to proceed by repeated mechanical fracture of grains and welding together of surfaces [49].

Mechanical milling

Ball-milling is also an effective way to create nanocrystalline powders. A Mössbauer study was made of Fe powder after ball-milling for hours to a grain size of 18 nm [50]. Chemical analysis revealed contamination with 5 at.% Cr introduced by ablation of walls of Cr-containing steel vials. A distinct, surface site for Fe probe atoms could not be resolved.

In homogeneous materials, ball milling introduces point defects and, if the stored energy increases to a sufficient point, can lead to phase transformations to metastable states, or even phase separation. The role of temperature was studied in milling of metastable fcc FeCu alloys [65]. Experiments carried out on highly-ordered intermetallics with PAC or ME were used to monitor the build-up of concentrations of point defects. For PdIn, using PAC, the concentration of Pd-vacancies was observed to increase with milling time and to saturate at a concentration of 3.5 at.% [55,67]. Signals from In-vacancies were also observed to form, indicating that milling predominantly creates Schottky vacancy pairs [55]. The observed concentration translates to a stored-energy contribution of 4.4 kJ/mole [67], which is quite significant.  For FeAl, using ME, quenched-in vacancies were observed to rapidly disappear during milling and to be replaced by antisite defects [58]. The implication is that antisite defects tend to form in intermetallics that, like FeAl, have lower ordering energies.  For FeRh, using ME, ball-milling led to a phase transformation from the ferromagnetic CsCl phase to a paramagnetic fcc phase [60]. However, within the starting CsCl phase, the concentration of Fe-vacancy defects was observed to increase with milling time. The implication is that triple-defects (Fe-vacancies and Fe-antisite atoms) are the principal defect combination produced by milling in this system.  Defect combinations produced in different systems were compared in ref. [67].

Vacancy migration at high temperature

When a defect near a probe atom jumps stochastically, the orientation and/or magnitude of the hyperfine interactions change, leading to signal decoherence. Atoms jumping at rates of order 10 MHz produce nuclear relaxation that can be detected in nuclear hyperfine measurements. Relaxation that was observed in the signal of a hydrogen-decorated 3V complex in platinum [34] was attributed to 'cage' motion of the hydrogen atom or probe in the complex, with a measured activation energy of 0.34(5) eV [52]. Relaxation that has been observed at temperatures of order 1000 C in NiAl, FeAl and PdIn has been attributed to migration of transition-metal vacancies near the probe atoms [62]. A PAC study of PdIn using the indium probe provides a nearly ideal model system because the probe is not an impurity (although the daughter Cd state may weakly disturb the measurements).  Analysis of relaxation in such a system can therefore give, to a good approximation, the Pd-vacancy jump frequency in the crystal at high temperature. Analyses of the nuclear relaxation in PdIn yielded jump frequencies in excellent agreement with ones deduced from diffusion measurements for high temperatures, but much higher jump frequencies at low temperatures [68]. This was attributed to a large number of jumps at low temperature in which the defect returns to its original site (small correlation factor) [68]. Such jumps are characteristic of complex jump cycles and produce nuclear relaxation without atom transport. More recently, a detailed stochastic model was developed for PAC perturbation functions for defects jumping on a simple cubic lattice [74] and applied to analyze realxation measurements in PdIn.   

Site preferences of solutes

A very  important question to address is the lattice location of impurity hyperfine probes in compounds. To study this problem, we have investigated the location on indium impurities in compounds having the Ni₂Al₃ structure [71]. This structure is advantageous because electric-field gradients at the Ni and Al sites are very different, so that solute locations can be identified through their quadrupole interactions. Studies were made for compositions rich and poor in the transition metal (TM). It was found that indium occupies trivalent-element sites in TM-rich compounds and either TM-sites or grain-boundary sites in TM-poor compounds.  A general thermodynamic model has been developed that explains such site preferences of solutes and how they change with composition and temperature [72,G].  This work is currently continuing.

A related but more complicated question is the lattice locations of solute atoms in a two-phase field.  We carried out studies of indium solutes in a mixture of NiAl and Ni₂Al₃ phases [66, 70] or in a mixture of PdGa and Pd₃Ga₇ phases [73]..  Assuming that equilibrium was attained, the measurements indicate small differences between energies of solutes on different sites in the two phases.

High pressure studies of point defects

Much less is known about how properties of defects depend on pressure than on temperature.   PAC experiments are planned for pressures up to 100 kbar in a diamond anvil cell.  Eventually we hope to  make measurements of pressure dependences of defect concentations and vacancy jump frequencies under equilibrium conditions.   From such measurements one can determine separately the activation volumes for formation and migration of point defects, unlike in studies of diffusion under pressure where the two activation volumes are combined.  In the early course of this work we will also measure pressure dependences of electric-field gradients induced by defects.   It is hoped that correlation of pressure and temperature dependences will provide insight into atomic relaxations in complexes.    This work is just now starting.

Systematics of hyperfine interactions

Hyperfine interactions in pure systems. As a graduate student, I measured the hyperfine field at Sn probes in MnSb, helping to complete information on the probe dependence of hyperfine fields at sp-solutes in ferromagnets [1]. I also proposed a simple correlation between the valence of a probe ion and a contribution to the efg in non-cubic metals traditionally attributed to the conduction electrons [3].

Hyperfine field distributions in dilute, random magnetic alloys. Hyperfine fields were measured in alloys of Ni containing a few percent of sp-solutes (Cu, Si) [5,6] or transition-metal solutes (Fe, Co, Mn, Rh) [5,7]. Field distributions were characterized by broad distributions for sp-solutes due to host-moment disturbances [5,6] and by narrow distributions for transition-metal solutes [5,7] from whose spectra hyperfine field shifts could be identified for solutes in shells 1-3 around the probe atoms.

Comparison of signals from point-defects in similar systems. Measured efgs at probe atoms in complexes with vacancies in fcc metals were compared with results of point-charge calculations of efgs [39]. The comparison helped to confirm identifications made of the structures of some complexes and to help suggest possible structures for other complexes. Similarly, point-charge calculations of efgs of vacancy complexes in intermetallic compounds having the CsCl structure helped to identify the structures of the complexes [56, 64].

Temperature and pressure dependences of hyperfine interactions. I measured the temperature dependence of the efg in non-cubic tin metal using Mössbauer effect in my dissertation research [2]. I also carried out a band-structure calculation of the electronic efg that included explicit thermal factors and reproduced the experimental temperature dependence qualitatively [2]. For defects in cubic materials, thermodynamic dependences of hyperfine interactions are a function of the structure of the defects, including lattice relaxations. An anomalous temperature dependence of the efg of a divacancy complex in Pt was modeled well assuming that the complex had a low-frequency resonant vibrational mode [17]. Pressure dependence of the hyperfine field at a probe in a trivacancy complex in Ni was measured and compared with the pressure dependence measured at a defect-free substitutional site [40]. Dynamical relaxation of a defect associated signal in Pt gave evidence of thermally-activated motion in a complex, perhaps due to motion of the probe atom in a cage of vacancies [34], with an activation energy of 0.34(5) eV.

Magnetic critical phenomena

To a good approximation the static hyperfine field measured at a probe nucleus is proportional to the magnetization (or staggered magnetization), and thus represents the order parameter. Unlike macroscopic measurements in which domain structure must be removed by application of an external static field, a hyperfine measurement can be made in zero field, greatly simplifying the analysis of measurement. Measurements were made to determine the order-parameter exponent b in quenched, randomly disordered FeAl alloys [8,11]. The effect of random anisotropy was investigated in studies of FeV alloys [22]. The static universality class of Gd (the lattice and spin dimensionality) was identified by measurement of the critical exponent b [24].

Fluctuations of electronic spins in an appropriate frequency range lead to nuclear relaxation that is detected in Mössbauer measurements by line-broadening and in PAC measurements by attenuation, or 'damping', of the perturbation function. The autocorrelation time of the electronic spin can be deduced from the nuclear relaxation, and diverges as the critical temperature is approached with the dynamic exponent z, which depends both on the static universality class and, as well, on whether interactions are or are not spin-conserving. These issues were elaborated in papers [10,13,18,19,23,25].

Miscellaneous Materials

Studies have been made of amorphous SnO₂ [4], rapidly solidified Al₈₆Fe₁₄ [21], and laser-surface-melted metals [29,38]. A study was also made of the martensitic phase transformation in NiTi [46].

Acknowledgments

I am indebted to Noemie Benczer-Koller at Rutgers University and Chris Hohenemser at Clark University, from whom I learned Mössbauer and PAC spectroscopies, to the efforts and creativity of ~25 students and postdocs with whom I have had the good fortune and great pleasure to work, and to the National Science Foundation for financial support of this research over two decades.

From the curriculum vitae of Gary Collins.   Recent publications have links to full-text versions here or from my research group's web page at  http://defects.physics.wsu.edu/.

1. Systematics of Hyperfine Interactions at Sn and Other 5s-p Diamagnetic Impurities in Ferromagnetic MnSb, Phys. Rev. B15, 1235-8 (1977); G. S. Collins, N. Benczer-Koller and M. Pasternak.
2. Nuclear Quadrupole Interaction in Tin Metal, Phys. Rev. B17, 2085-97 (1978); G. S. Collins and N. Benczer-Koller.
3. Effects of Probe Valence on the Conduction Electron Electric-Field Gradient in Noncubic Metals, Hyperfine Interactions 4, 523-7 (1978); G. S. Collins.
4. Applications of the Mössbauer Effect to the Characterization of an Amorphous Tin-Oxide System, Phys. Rev. B19, 1369-73 (1979); G. S. Collins, T. Kachnowski, N. Benczer-Koller and M. Pasternak.
5. Hyperfine Field Distributions in Nickel Alloys Measured by Time Differential Perturbed Angular Correlations, Phys. Lett. 78A, 201-4 (1980); G. S. Collins, L. Chow, T. Eschrich and C. Hohenemser.
6. Hyperfine Field Distributions at ¹¹¹Cd Probes in Nickel Alloys: I. Nontransition Metals Solutes Cu and Si, Hyperfine Interactions 9, 465-70 (1981); G. S. Collins.
7. Hyperfine Field Distributions at ¹¹¹Cd Probes in Nickel Alloys: II. Transition Metal Solutes Fe, Co, Mn and Rh, Hyperfine Interactions 9, 471-6 (1981); G. S. Collins.
8. Critical Behavior of Quenched, Randomly Disordered Ni and Fe Alloys, Hyperfine Interactions 10, 893-99 (1981); A. R. Chowdhury, C. Allard, R. M. Suter, G. S. Collins, C. Hohenemser and M. A. Kobeissi.
9. Vacancy Trapping in Plastically Deformed Metals Studied by Hyperfine Interactions, Phys. Lett. 84A, 289-93 (1981); G. S. Collins, G. P. Stern and C. Hohenemser.
10. Comparison of Dynamical Critical Behavior in Isotropic Ferromagnets, J. Appl. Phys. 53, 7942-44 (1982); C. Hohenemser, L. Chow, A. R. Chowdhury and G. S. Collins.
11. Mössbauer Measurements of Static Critical Behavior in Disordered FeAl Alloys, Phys. Rev. B26, 4997-5008 (1982); G. S. Collins, A. R. Chowdhury, and C. Hohenemser.
12. Deuterium Desorption and Host Interstitial Clustering in d-irradiated Ni, in Electronic Structure and Properties of Hydrogen in Metals, ed. P. Jena and C. B. Satterthwaite, (Plenum: N.Y., 1983) p. 589-94; C. Allard, G. S. Collins and C. Hohenemser.
13. Comment on the Role of Spin Nonconserving Forces in the Critical Dynamics of Fe and Ni, Phys. Rev. Lett. 50, 1877 (1983); C. Hohenemser, R. M. Suter, L. Chow and G. S. Collins.
14. Defect Recovery and Trapping in Plastically Deformed Au Studied by Perturbed Angular Correlations of ¹¹¹In, Phys. Rev. B28, 2940-46 (1983); G. S. Collins, C. Allard, R. B. Schuhmann and C. Hohenemser.
15. Comparison of Defect Recovery in Proton Irradiated, Deformed and Ion Implanted Ni as Observed by PAC of 111In, Hyperfine Interactions 15/16, 387-90 (1983); C. Allard, G. S. Collins and C. Hohenemser.
16. Trivacancy Recovery and Formation of a Cubic Symmetry Defect Trap on ¹¹¹In Impurities in Ni, Hyperfine Interactions 15/16, 391-4 (l983); G. S. Collins and R. B. Schuhmann.
17. Anomalous Temperature Dependence of the Quadrupole Coupling Frequency of a Lattice Defect Trapped to ¹¹¹In in Pt, Hyperfine Interactions 15/16, 395-9 (1983); G. S. Collins and R. B. Schuhmann.
18. Nuclear Spin Relaxation of ¹⁶¹Dy in Gd above the Curie Temperature Observed with the Mössbauer Effect, Hyperfine Interactions 15/16, 617-20 (1983); A. Chowdhury, G. Collins and C. Hohenemser.
19. Anomalous Critical Slowing Down of Spin Fluctuations in Gd Observed with ¹⁶¹Dy Mössbauer Effect, Phys. Rev. B30, 6277-84 (1984); A. R. Chowdhury, G. S. Collins and C. Hohenemser.
20. Vacancy Migration and Accretion in Ni Observed by Perturbed Gamma-Gamma Angular Correlations, Phys. Rev. B32, 4839-48 (1985); C. Allard, G. S. Collins and C. Hohenemser.
21. An Fe Mössbauer Effect Study of Metastable Al86Fe14 Prepared by Rapid Solidification, Hyperfine Interactions 26, 963-66 (1986); R. A. Dunlap, K. Dini, G. Stroink, G. S. Collins and S. Jha.
22. The Effect of Random Anisotropy on Critical Behavior: Search for Hysteresis and Rounding in FeV using the Mössbauer Effect, Hyperfine Interactions 28, 673-76 (1986); X. S. Chang, G. S. Collins and C. Hohenemser.
23. Anomalous Critical Spin Dynamics in Gd: A Revision, Phys. Rev. B33, 5070-2 (1986); A. R. Chowdhury, G. S. Collins and C. Hohenemser.
24. Static Universality Class Implied by the Critical Exponents in Gd, Phys. Rev. B33, 6231-4 (1986); A. R. Chowdhury, G. S. Collins and C. Hohenemser.
25. Observation of Isotropic Critical Spin Fluctuations in Gd, Phys. Rev. B33, 4747-51 (1986); G. S. Collins, A. R. Chowdhury and C. Hohenemser.
26. Hydrogen and Deuterium Decoration of a Vacancy Complex in Ni, Phys. Rev. B34, 502-5 (1986); G. S. Collins and R. B. Schuhmann.
27. Point Defects in Deformed Metals Studied by Perturbed Gamma-Gamma Angular Correlations, Materials Science Forum 15-18, 783-8 (1987); G. S. Collins.
28. Hydrogen-Vacancy Interactions in Ni Studied by Perturbed Angular Correlations, Materials Science Forum 15-18, 681-4 (1987); G. S. Collins and R. B. Schuhmann.
29. Defects in Laser Surface-Melted Metals Studied by PAC, in Characterization of Defects in Materials, ed. R. W. Siegel, J. R. Weertman and R. Sinclair, Mat. Res. Soc. Symp. Proc. 82, 53-8; (1987) G. S. Collins, C. Allard, C. Hohenemser and C. W. Draper.
30. Perturbed Angular Correlations Studies of Alloys, in Electronic Structure and Lattice Defects in Alloys, eds. R. W. Siegel and F. E. Fujita (Trans Tech Publications, 1989), p. 139-49; G. S. Collins.
31. Hydrogen Decoration of Vacancy Defects in Platinum, in Nuclear Physics Applications on Materials Science, ed. E. Recknagel and J. C. Soares, NATO ASI Series E: Applied Science (Kluwer, Dordrecht 1988) , vol. 144, p. 415-6; G. S. Collins, H.-J. Jang and S. Shropshire.
32. Diffusion and Trapping of Hydrogen in Vacancies in Platinum Studied by PAC, Defect and Diffusion Forum 66-69, 335-40 (1989); G. S. Collins, S. L. Shropshire and H.-J. Jang.
33. Production and Migration of Interstitials in Deformed Metals, Hyperfine Interactions 60, 667-70 (1990); Steven L. Shropshire and G. S. Collins.
34. Cage Motion of a Probe Atom in a Vacancy Complex in Pt, Hyperfine Interactions 60, 651-4 (1990); G. S. Collins, S. L. Shropshire and H.-J. Jang.
35. Point Defects in NiAl Near the Equiatomic Composition, Hyperfine Interactions 60, 655-8 (1990); J. Fan and G. S. Collins.
36. Stacking Fault Defects in HCP Cobalt Studied by PAC, Hyperfine Interactions 60, 659-62 (1990); G. McGhee and G. S. Collins.
37. Electrolytic Loading of Hydrogen in Metals Studied by PAC, Hyperfine Interactions 60, 663-66 (1990); G. S. Collins, G. McGhee, S. L. Shropshire, H.-J. Jang, J. Fan and R. B. Schuhmann.
38. Laser Surface-Melting of Metals Studied by PAC, Hyperfine Interactions 61, 1339-42 (1990); G. S. Collins and K. Zainun.
39. Perturbed gamma-gamma Angular Correlations: A Spectroscopy for Point Defects in Metals and Alloys, Hyperfine Interactions 62, 1-34 (1990); G. S. Collins, S. L. Shropshire and J. Fan.
40. Pressure Dependence of the Hyperfine Field of a Cd probe in a Relaxed-Trivacancy Complex in Ni, Phys. Rev, B45, 4672-5 (1992); Lee Chow, Xin Zhao and Gary S. Collins.
41. Application of PAC to study equilibrium point defects in intermetallic compounds, Hyperfine Interactions 80, 1257-61 (1993); Gary S. Collins and Jiawen Fan.
42. Equilibrium point defects in TiAl studied by PAC, Hyperfine Interactions 79, 745-8 (1993); Jiawen Fan and Gary S. Collins.
43. Hydrogen binding in vacancy clusters in platinum, Hyperfine Interactions 79, 749-53 (1993); Steven L. Shropshire and Gary S. Collins.
44. Atomic diffusion in strain fields near solutes, Hyperfine Interactions 79, 755-60 (1993); S.L. Shropshire and G.S. Collins.
45. Grain boundary sites in fcc metals studied by PAC, Hyperfine Interact. 79, 761-4 (1993); Bin Bai and Gary S. Collins.
46. The martensitic phase transition in NiTi, Hyperfine Interactions 80, 995-8 (1993); John C. Sy and Gary S. Collins.
47. Indium metal nanoclusters studied by PAC, Hyperfine Interactions 80, 1117-20 (1993); P. Sinha and G.S. Collins.
48. Indium nanocrystals studied by perturbed angular correlations, Nanostructured Materials 3, 217-24 (1993); Praveen Sinha and Gary S. Collins.
49. Formation of FeCo by mechanical alloying, Scripta Metallurgica et Materialia 29, 1319-23 (1993); Gary S. Collins and Bruce H. Meeves.
50. Mössbauer and PAC studies of nanocrystalline Fe, Hyperfine Interactions 92, 949-53 (1994): P. Sinha and G.S. Collins.
51. Formation of Ni3Fe by mechanical alloying, Hyperfine Interactions 92, 955-8 (1994); Bruce H. Meeves and Gary S. Collins.
52. Hydrogen trapping in vacancies in metals studied by PAC, in Local Order in Condensed-Matter Physics, eds. S.D. Mahanti and P. Jena (Nova Science Publishers, 1995), pages 85-94, ISBN 1-56072-220-7; Gary S. Collins and Steven L. Shropshire.
53. Properties of nanocrystalline zinc produced by gas condensation, Nanostructured Materials 4, 103-12 (1994); K. Recknagle, Q. Xia, J.N. Chung, C.T. Crowe, H. Hamilton and G.S. Collins
54. A new approach to study vacancy defects in high-temperature intermetallic compounds, by Gary S. Collins and Praveen Sinha, Materials Research Society Symposium Proceedings, vol. 364, pp. 59-64, 1995.
55. Atomic defects and disorder in mechanically-milled intermetallic compounds, Materials Science Forum 225-227, 275-80 (1996); Gary S. Collins and Praveen Sinha.
56. Point defects in B2 intermetallic compounds, Hyperfine Interactions (C) 1, 380-4 (1996); Gary S. Collins, Praveen Sinha and Mingzhong Wei.
57. Point defects in FeAl, Il Nuovo Cimento 18D, 329-36 (1996); Gary S. Collins and Luke S.J. Peng.
58. Disordering of FeAl by Mechanical Milling, Materials Science Forum 235-238, 535-41 (1997); Luke S.J. Peng and Gary S. Collins.
59. Equilibrium point defects in NiAl and similar B2 intermetallics studied by PAC, in Structural Intermetallics 1997, eds. M.V. Nathal et al. (The Minerals, Metals and Materials Society, 1997) ISBN 0-87339-375-9, pages 43-52; Gary S. Collins, Jiawen Fan and Bin Bai.
60. Point defects and the B2 to fcc transformation in milled FeRh, by Luke S.-J. Peng and Gary S. Collins, in Phase Transformations and Systems Driven Far From Equilibrium, eds. E. Ma, P. Bellon, M. Atzmon, R. Trivedi, Mat. Res. Soc. Symp. Proc. 481, 631-6 (1998).
61. Vacancy mobility in nickel aluminide versus composition, by Bin Bai, Jiawen Fan and Gary S. Collins, in Diffusion Mechanisms in Crystalline Materials, eds. Y. Mishin, N.E.B. Cowern, C.R.A. Catlow, D. Farkas, G. Vogl, Mat. Res. Soc. Symp. Proc. 527, 203-8 (1998).
62. Stochastic vacancy motion in B2 intermetallics studied by PAC, by Bin Bai, Gary S. Collins, Harmen Thys Nieuwenhuis, Mingzhong Wei and William E. Evenson, in Diffusion Mechanisms in Crystalline Materials, eds. Y. Mishin, N.E.B. Cowern, C.R.A. Catlow, D. Farkas, G. Vogl, Mat. Res. Soc. Symp. Proc. 527, 210-5 (1998).
63. Equilibrium defects and concentrations in nickel aluminide, by Bin Bai and Gary S. Collins, in High-temperature ordered intermetallic alloys VIII, eds. E.P. George, M. Mills and M. Yamaguchi, Materials Research Society Symposium Proceedings 552, KK8.7.1-6 (1999)
64. Thermal defects in B2 iron aluminide, by Gary S. Collins, Luke S.-J. Peng and Mingzhong Wei, in High-temperature ordered intermetallic alloys VIII, eds. E.P. George, M. Mills and M. Yamaguchi, Materials Research Society Symposium Proceedings 552, KK4.2.1-6 (1999).
65. Deformation-assisted decomposition of unstable Fe₅₀Cu₅₀ solid solution during low-energy ball milling, by J. Xu, G.S. Collins, L.S.J. Peng and M. Atzmon, Acta Materialia 47, 1241-53 (1999).
66. Search for nucleation of phase embryos in binary alloys by impurity atoms, by Gary S. Coliins, Luke S.-J. Peng and Matthew O. Zacate, Z. Naturforschung 55a, 129-133 (2000).
67. Structural, thermal and deformation-induced point defects in PdIn, Gary S. Collins and Praveen Sinha, in Hyperfine Interactions of Nanocrystalline Materials, ed. G.S. Collins (Kluwer, 2001); in press, 29 pages.
68. Vacancy Jumps in PdIn: Reconciling Nuclear Relaxation and Diffusion Measurements, Gary S. Collins and Harmen Thys Nieuwenhuis, Defect and Diffusion Forum 194-199, 375-82 (2001).
69. Vacancy-vacancy interactions in NiAl, Matthew O. Zacate and Gary S. Collins, Defect and Diffusion Forum 194-199, 383-88 (2001).
70. Nucleation of a second phase by individual impurity atoms, Matthew O. Zacate, Gary S. Collins and Luke S.-J. Peng, accepted and to appear in Materials Science and Engineering A (2001).
71. Site Preference Model for Hyperfine Impurities in Compounds, Gary S. Collins and Matthew O. Zacate, accepted and to appear in Hyperfine Interactions (2002).
72. Site Preferences of Hyperfine Impurities in Ni2Al3 Phases, Matthew O. Zacate and Gary S. Collins,  accepted and to appear in Hyperfine Interactions (2002).
73. Segregation of Solutes in Two-Phase Mixtures, Matthew O. Zacate, Bonner C. Walsh, Luke S.-J. Peng and Gary S. Collins,  accepted and to appear in Hyperfine Interactions (2002).
74. 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, accepted and to appear in Hyperfine Interactions (2002).

^{A. E. Recknagel, G. Schatz and Th. Wichert, in: Hyperfine Interactions of Radioactive Nuclei, ed. J. Christiansen Topics in Current Physics, Vol. 31, (Springer, New York, 1983), p. 133.
B. F. Pleiter and C. Hohenemser, Phys. Rev. B25, 106 (1982).
C. P.J. Schultz and K.G. Lynn, Rev. Mod. Phys. 60, 701 (1988).
D. A contemporaneous study was by H.G. Mueller, in Nuclear Physics Methods in Materials Research, ed. K. Bethge et al, (Vieweg, Braunschweig, 1980) p. 418.  The first PAC study of defects in deformed metals, indeed in any materials, was in  G.W. Hinman, G.R. Hoy, J.K. Lees, and J.C. Serio, Phys. Rev. 135, A218 (1964), carried out by time-integrated PAC.  By coincidence, George Hinman is now Prof. (emeritus) of Environmental Science at Washington State University.
E. The complex formed between a substitutional probe atom and an n-vacancy defect is in our convention called an n-vacancy complex (abbreviation nV).  Elsewhere, this is frequently designated as a complex of (n+1) vacancies with an interstitial probe atom.
F. H.G. Mueller and H. Hahn, Phil. Mag. A50, 71 (1984).
G. (submitted April 2001).
H. Measurements in paper [63] were made at high temperature. Analysis presented in early  paper [59] of  measurements made on quenched NiAl as a function of composition at fixed temperature was erroneous because an incorrect  function corresponding to eq. 1 was used and because measurements on quenched samples are disturbed from equilibrium conditions (see paper [61].)
I. K. Krolas, Hyperfine Interactions 60, 581 (1989).}