Ossbauer Line Research Articles

Occupancy and site distribution of europium in barium magnesium aluminate by151EuMössbauer spectroscopy

${\mathrm{BaMgAl}}_{10}{\mathrm{O}}_{17}:$ ${\mathrm{Eu}}^{2+}$ (BAM) is a commercial, blue emitting lamp phosphor activated by ${\mathrm{Eu}}^{2+}.$ It is usually assumed that the Eu ions substitute for Ba ions occupying the Beevers-Ross site in the \ensuremath{\beta}-alumina structure. We have investigated this phosphor with varying europium concentrations and different synthesis conditions using ${}^{151}\mathrm{Eu}$ M\ossbauer spectroscopy. Analysis of the M\ossbauer line shapes reveals a pentamodal (or higher) site distribution consisting of three ${\mathrm{Eu}}^{2+}$ sites, one (or two) ${\mathrm{Eu}}^{3+}$ site(s), and a mixed valent site whose isomer shift lies in between those for the divalent and trivalent ions. The observed quadrupole coupling constants for the divalent ions are larger than any other reported to date in any lattice. Based on calculations of the nuclear quadrupole coupling constants by a full potential band-structure method reported recently, the divalent sites are identified with occupancy of the Beevers-Ross, anti-Beevers-Ross, and mid-oxygen sites in the \ensuremath{\beta}-alumina structure. Oxidative degradation of the divalent ions due to the thermal treatment in air was also studied, and a preliminary analysis of how various sites evolve during this process is also presented.

Surface magnetism at the Néel temperature of anFeBO3single crystal

In the near-surface region of an ${\mathrm{FeBO}}_{3}$ single crystal a new magnetic-phase transition was discovered at the bulk N\'eel point by depth selective M\"ossbauer spectroscopy. The results neither fit into the concept of an ordinary nor that of an extraordinary type of surface transition. The sublattice magnetization dynamics of the near-surface phase is changed with respect to that of the bulk and exhibits similarities to that of a superparamagnetic system. In the same way as the M\"ossbauer line shape reveals the critical slowing down in the time-correlation function of the local moment, the increase in thickness of the near-surface region mirrors the divergence of the correlation length in the system when approaching the N\'eel temperature. The results on the pure ${\mathrm{FeBO}}_{3}$ crystal are compared to those gained by replacing one-quarter of the Fe atoms by Ga. The phase transition in the ${\mathrm{FeBO}}_{3}$ single crystal was studied from 291 K up to the N\'eel temperature ${\mathrm{T}}_{N}=348.35\mathrm{K}$ by depth selective conversion electron M\"ossbauer spectroscopy in an ultrahigh vacuum of ${10}^{\ensuremath{-}9}\mathrm{mbar}.$

Extended model of the channel diffusivity in the rutile structure.

A model describing the diffusivity of a highly diluted and randomly distributed substitutional cationic impurity via the open and almost empty 〈001〉 channels in the rutile structure has been developed recently. The above model is based upon the assumption that the insignificant fraction of the impurities resides in the channels. An extended model is developed that allows for a significant fraction of the impurities to stay within channels, and it is used to evaluate emission M\"ossbauer spectra originating from the diffusing impurities embedded in single-crystalline samples. Final results are shown for the 14.4-keV M\"ossbauer line in $^{57}\mathrm{Co}$(Fe). It is shown that spectral line positions depend upon the wave-vector transfer to the system, and that the data are sensitive to the fraction of both parent and daughter impurities residing in the channels. \textcopyright{} 1996 The American Physical Society.

Simple model of the diffusive scattering law in glass-forming liquids.

We found that the decay rate, \ensuremath{\lambda}, of the correlation function, G, in glass-forming liquids can be expressed in terms of G itself. A three-parameter function of the form \ensuremath{\lambda}=${\ensuremath{\lambda}}_{0}$+${\ensuremath{\lambda}}_{1}$${\mathit{G}}^{\mathit{k}}$ leads to an analytic solution for the function G in the time domain. This assumption also allows one to express the function G as an infinite series of Lorentzians in the frequency domain. This model has been applied to M\"ossbauer absorption spectra of aqueous ${\mathrm{FeCl}}_{2}$ solutions in glycerol (14.4-keV line of $^{57}\mathrm{Fe}$) and higher temperature quasielastic (Rayleigh) scattering data obtained by the scattering of the $^{183}\mathrm{W}$ 46.5-keV M\"ossbauer line from pure glycerol. The model describes the M\"ossbauer data as well as the empirical Kohlrausch or Cole-Davidson (CD) laws. Also, the function \ensuremath{\lambda}(G) can be expressed in a two-parameter form as ${\ensuremath{\lambda}}_{0}$exp(\ensuremath{\alpha}G). It has been shown, however, that a closed-form expression for the function G does not exist in the time or frequency domain for this latter form. On the other hand, the exponential form gives a two-parameter fit to existing data, suggesting a physical basis to this form and implies that small changes in G are proportional to fractional changes in \ensuremath{\lambda}. It has been found that the parameter \ensuremath{\alpha} has some universal meaning as it remains constant over a significant low-temperature range accessible experimentally, decreasing to the zero value with increasing temperature. Our analysis suggests that the parameter \ensuremath{\alpha} may change in steps as sample temperature is increased. Such a behavior suggests that some processes (degrees of freedom) are ``freezing out'' at well-defined temperatures.

Amine intercalation in FePS3: A 57Fe Mössbauer study.

The methylamine and ethylamine intercalates of ${\mathrm{FePS}}_{3}$ were prepared, characterized by x-ray diffraction (XRD) and investigated by $^{57}\mathrm{Fe}$ M\"ossbauer spectroscopy. The XRD results show that the intercalate remains monoclinic but exhibits a fairly large expansion of its c axis. The original M\"ossbauer line of the host ${\mathrm{FePS}}_{3}$ is absent in all the compounds. The M\"ossbauer spectra consist of lines originating from modified host lattice and two types of reduced sites created due to transfer of electrons during intercalation. The origin of the observation of two kinds of reduced sites has been suggested. M\"ossbauer results highlight that beyond a certain concentration of guest species the transferred electrons in the amine intercalates are primarily of delocalized character whereas it is of localized nature in the case of Li intercalated ${\mathrm{FePS}}_{3}$.

Mössbauer spectroscopic study of low-frequency vibrational modes in sintered metal powders.

Low-frequency vibrational modes in sintered copper and silver powders have been studied by $^{197}\mathrm{Au}$ M\"ossbauer spectroscopy. A decrease in resonance absorption area has been found for the sinters compared with the values found for bulk materials. In the spectra of a copper sinter of low packing fracton (26.7%), a broad spectral component was clearly observed, superimposed on the normal M\"ossbauer line. This broad line is interpreted to arise from low-frequency modes due to oscillations of the particles in the sinters. The temperature dependence of the M\"ossbauer absorption area can be explained by a model based on dispersion theory combined with the Debye model and the fracton model used for describing phonons in a particle and particle oscillations in a sinter, respectively. The energies of the low-frequency modes determined from the M\"ossbauer measurements range from \ensuremath{\approxeq}2 mK to several hundred millikelvin (in equivalent temperature) and coincide within a factor of 6 with the values estimated from ultrasonic data [M. C. Maliepaard et al., Phys. Rev. B 32, 6261 (1985)] using the fracton model, providing support for the localized nature of the modes.

Temperature dependence of the 4f quadrupole moment of Yb in YbCu2Si

An explanation is provided for the M\"ossbauer measurements on Yb${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$ by which the temperature-dependent quadrupole moment $Q(T)$ of Yb is obtained. The quadruple splitting of the $^{174}\mathrm{Yb}$ M\"ossbauer line is a direct probe of the noncubic crystalline electric field. We compute $Q(T)$ by using the noncrossing approximation to a Green's-function formulation of the Anderson impurity problem. The observed $Q(T)$ behavior is well reproduced by our theory. The zero-temperature value $Q(0)$ is discussed within the frame of the variational ground state proposed by Varma and Yafet and by Gunnarsson and Sch\"onhammer.

Many-state relaxation model for the Mössbauer spectra of superparamagnets.

The stochastic relaxation theory of Anderson and Sack is applied to the M\ossbauer spectra superparamagnetic particles with uniaxial anisotropy by including all possible values of the component of the magnetization along the quantization axis explicitly in the calculation. It is shown that for particles with a large number of states the M\ossbauer line shape can be expressed directly in terms of the solution of a differential equation. Explicit solution of this equation in the low-temperature (high anisotropy barrier) approximation leads to effective relaxation rates between the two discrete allowed orientations of the magnetization. These rates are equivalent to those derived by Brown only if the relaxation matrix elements are assumed to have a certain rather arbitrary dependence on the temperature and magnetization.

Diffusion of iron in copper studied by Mössbauer spectroscopy on single crystals.

The broadening of the $^{57}\mathrm{Fe}$ M\"ossbauer line due to diffusion jumps of iron atoms in a copper single crystal has been measured as a function of crystal orientation and temperature between 1060 and 1313 K. The results are the following: (i) The anisotropy of the broadening agrees with what is expected for 〈110〉 jumps into nearest-neighbor vacancies. (ii) The deviation of the measured anisotropy from the curve predicted for self-diffusion permits the determination of the vacancy jump frequencies in the neighborhood of the iron impurity. The best fit indicates that association and dissociation jumps of the vacancy with or from the impurity are slower, but internal jumps in the vacancy-impurity complex are faster than vacancy jumps in the unperturbed copper lattice. (iii) From the temperature dependence of the resonant intensity (the area of the M\"ossbauer line) it can be concluded that there is no significant impurity-vacancy binding. (iv) The diffusion coefficient for iron in copper and its temperature dependence are in good agreement with tracer results. At 1313 K, D=(4.2\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ ${\mathrm{m}}^{2}$/s.

Anomalous critical slowing down of spin fluctuations in Gd observed withDy161Mössbauer effect

Using sources of $^{161}\mathrm{Dy}\mathrm{Gd}$ produced directly by thermal neutron irradiation of $^{160}\mathrm{Gd}$-enriched Gd metal, we have observed M\"ossbauer line broadening in the reduced temperature range $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}<t<3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ above ${T}_{c}$. The excess linewidth diverges according to the power law $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{c}=D{t}^{\ensuremath{-}w}$, with $w$ in the range $0.21<w<0.28$ depending on fitting procedure. On the assumption that the spin fluctuations are isotropic and describable by dynamical scaling theory, we conclude that the dynamical exponent $z$ lies in the range $1.3<z<1.52$. This range is anomalously low, since even with dipolar or pseudodipolar perturbations of isotropic short-range exchange interactions one expects $z=2.0$.

Lattice dynamics of isotopic alloys with applications toZn67Mössbauer spectroscopy

The "recursion method" is applied to the dynamics of disordered lattices, and is used explicitly to calculate properties of isotopically disordered zinc. The specific heat and atomic motion are calculated for the special case of an isotopically pure lattice and compared to previous experimental and theoretical results. Then M\"ossbauer-effect calculations for the high-resolution $^{67}\mathrm{Zn}$ isotope are presented, including evaluations of the M\"ossbauer line shift with temperature, the anisotropic recoil-free fraction, and the Goldanskii-Karyagin effect. In addition, the effect of zero-point motion on the M\"ossbauer line position and linewidth in isotopically disordered zinc is discussed.

Diffusion of iron in aluminum studied by Mössbauer spectroscopy

The broadening of the $^{57}\mathrm{Fe}$ M\"ossbauer line due to diffusion jumps of the Fe atoms in an Al single crystal has been measured as a function of crystal orientation. The broadening is strongly anisotropic. Theoretical calculations for the broadening using the five-frequency model for the motion of an Fe atom via vacancies show that the following information about the geometry and perturbed jump frequencies of the Fe-vacancy complex can be obtained: (i) The anisotropy of the broadening yields information about the jump geometry and jump-frequency ratios, (ii) the absolute value and the temperature dependence of the broadening yield the diffusion coefficient and the activation energy for Fe diffusion, and (iii) the anomalous decrease of the M\"ossbauer intensity in the vicinity of the melting point yields information about the binding energy of the Fe-vacancy complex. Our results are consistent with the following interpretation: Fe in Al moves by exchanging sites with nearest-neighbor vacancies. The binding energy of an Fe-vacancy complex is ${E}_{b}\ensuremath{\le}0.29$ eV. The diffusion coefficient of Fe in Al is ${D}_{\mathrm{Fe}}=1.1\ifmmode\times\else\texttimes\fi{}{10}^{4\ifmmode\pm\else\textpm\fi{}1}\mathrm{exp}[\ensuremath{-}\frac{(2.3\ifmmode\pm\else\textpm\fi{}0.2 \mathrm{eV})}{{k}_{B}T}]$ ${\mathrm{cm}}^{2}$${\mathrm{s}}^{\ensuremath{-}1}$ in reasonable agreement with results from tracer experiments. Values are obtained for different jump frequencies of a vacancy in the vicinity of an Fe atom.

Mössbauer spectra in the presence of spin-phonon relaxation effects: Symmetry restrictions

The problem of evaluating the M\"ossbauer line shape in the presence of ion-phonon interactions has been considered. By means of a perturbation procedure it is shown how a limited number of matrix elements of the relaxation operator are relevant. Moreover, the restrictions imposed by the symmetry are also taken into account. In the case of ${\mathrm{Fe}}^{3+}$ in ${C}_{3}$ symmetry one has to diagonalize a 288\ifmmode\times\else\texttimes\fi{}288 matrix. By taking into account the results obtained in this paper we have reduced the problem of deriving the line shape of the M\"ossbauer spectrum to that of diagonalizing three matrices of dimensions 16, 16, and 15.

Mössbauer study of static and dynamic critical behavior in Fe

In this paper we present the results of detailed experimental studies on the critical behavior of Fe near its critical temperature ${T}_{c}$ (here also Curie temperature ${T}_{C}$) using the M\"ossbauer effect. Using a highly controlled two-stage M\"ossbauer furnace, we made a careful measurement of the critical exponent $\ensuremath{\beta}$ and the critical exponent $z$. The value of ${\ensuremath{\beta}}_{\mathrm{eff}}$ was obtained in both source and absorber experiments and was found to be 0.379(4) for the reduced-temperature range ${10}^{\ensuremath{-}3}<~t<~2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and 0.371(8) for ${10}^{\ensuremath{-}4}<~t<~2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, respectively. We have used correction-to-scaling form in the critical region and have obtained the universal $\ensuremath{\beta}$ as $\ensuremath{\beta}=0.367(5)$ and the correction amplitude $A=\ensuremath{-}0.458(22)$. The results on $\ensuremath{\beta}$ agree well with theory, bulk measurements on Fe, and most data on other ferromagnets in the universality class $(n,d)=(3,3)$. The value $z$ was measured as $z=1.93(19)$, which is inconsistent with the theory of short-range exchange interactions and neutron scattering results in Fe, but in agreement with previous hyperfine studies on Ni and Fe, and a recent hypothesis on the dynamic behavior in the asymptotic critical region. We have also investigated the possible magnetization dependence of the isomer shift in Fe and obtained negative results, both within 2 K of the Curie point, and in a wide region above and below the Curie point. These findings, like the $\ensuremath{\beta}$ measurements, are based on both source and absorber experiments. They disagree with Preston's observations near ${T}_{c}$. By studying the M\"ossbauer line intensities we observed a magnetostrictive reorientation of ferromagnetic domains as a function of temperature. This behavior is similar to that observed in some Fe alloys under the influence of compressive strain as well as temperature variation.

Theory of Mössbauer line broadening due to diffusion of Mössbauer atoms via vacancies

We have calculated analytically the effect of diffusion on the M\ossbauer line, especially considering the correlation effects due to diffusion via vacancies. Starting from a hierarchy of rate equations for single-particle densities, pair correlation functions, and higher-order correlation functions we have deduced for small vacancy concentrations an effective equation for the motion of M\ossbauer atoms which is similar to the well-known encounter model. The transport of M\ossbauer atoms is described by an effective jump-frequency matrix which incorporates the temporal and spatial correlations of the atomic jumps induced by a single vacancy. We calculate the effective jump-frequency matrix analytically by an interation with respect to the number of atomic jumps during an encounter. It turns out that the correlation of the atomic jumps diminishes the diffusion broadening of the M\ossbauer line. This eliminates some of the discrepancies between M\ossbauer studies and radio-tracer experiments.

Stochastic model for classical bath variables and its influence on line-shape expressions

A stochastic theory of hyperfine spectra is presented in which the coupled nucleus-ion system is treated quantum mechanically, and the interaction between the ionic spin and its surroundings is taken into account via effective fluctuating fields. The theory treats in detail a larger subsystem than the one considered by Clauser and Blume, and it is shown that the Clauser-Blume results can be obtained from the more general result given here, when the rate of fluctuations in the surrounding bath is much faster than the frequencies of the radiating system. A perturbative calculation also enables us to establish a connection between the stochastic- and the many-body-theory results for the line shape. The theory is worked out for M\"ossbauer line shape but can be applied easily to other related problems in atomic and nuclear spectroscopy. Application of the results derived here to analyze specific experimental situations will be dealt with elsewhere.

Effects of off-diagonal hyperfine interaction on Mössbauer relaxation spectra

The M\ossbauer line shape for systems where the nucleus is under the influence of a static axial electric field gradient and a time-dependent magnetic hyperfine interaction is considered. Ferric hemin serves as an example of the systems studied. The time dependence in the hyperfine interaction arises owing to relaxation in the ionic system, caused by the dipole-dipole interaction of the ions, between the ionic levels split by a crystalline field. This spin-spin relaxation rate is temperature dependent, slowing down somewhat as the temperature is increased. Its effect on the coupled nucleus-ion system is studied in perturbation theory based on the stochastic-theory model of Clauser and Blume. The presence of off-diagonal terms in the hyperfine interaction is found to produce some new interesting effects in addition to earlier results obtained by Blume in which the hyperfine interaction was assumed to be diagonal. Comparison of theory with experiments is made.

Effect of nuclear motion on Mössbauer relaxation spectra

Relaxation effects in M\"ossbauer line shape are studied when the nucleus jumps from one position to another. Relaxation arises from the fact that the nucleus interacts differently with its surroundings at different sites. At the same time, an additional broadening is observed because of nuclear motion. The effect of surroundings on the nucleus is treated classically in a stochastic-theory model in which it is assumed that the surroundings act like a heat bath and drive thermal fluctuations into the system which cause the nucleus to jump from time to time, from one site to another. But as it jumps to a new site it finds itself in a different quantum-mechanical enviornment. This gives rise to relaxation effects. It is found that nuclear motion precludes the occurrence of motional narrowing of lines which is typical of a pure-relaxation spectrum in the fast-relaxation-rate limit. The Singwi-Sj\"olander diffusion broadening and the Blume result for pure-relaxation effects are obtained as two limiting cases of the theory. Application of the model to experiment is discussed.

Structural and NMR properties of niobium dichalcogenides intercalated with post transition metals

The intercalation phase of the transition-metal dichalcogenide Nb${\mathrm{Se}}_{2}$, intercalated with Ga, In, Tl, Sn, and Pb, as well as Nb${\mathrm{S}}_{2}$, intercalated with In, have been prepared and studied by a variety of techniques. For most intercalates, single-intercalation-phase samples of the formula ${M}_{\frac{2}{3}}\mathrm{Nb}{X}_{2}$ were obtained, where $M$ is the intercalate and $X$ a chalcogen. The changes in the lattice parameters occurring upon intercalation have been determined from x-ray powder patterns. No superconducting transition was observed in any of the intercalated samples above 1.5 K. The microscopic properties were studied from 1.5 to 4.2 K using nuclear-magnetic-resonance (NMR) techniques, with the prime emphasis on the determination of the electric field gradients (EFG) at the Nb sites. For each intercalated sample the EFG was reduced by (35-60)% from that found in Nb${\mathrm{S}}_{2}$ and Nb${\mathrm{Se}}_{2}$. For the ${\mathrm{Tl}}_{\frac{2}{3}}\mathrm{Nb}{\mathrm{Se}}_{2}$ sample, the Nb line shape was fit by a single EFG while for all other intercalates at least two EFGs were needed to fit the Nb line shape, indicating two sites with inequivalent NMR properties. This change in the EFG at the Nb sites upon intercalation is attributed to charge transfer from the intercalated atoms into the conduction band of the layered compound. Knight-shift and spin-lattice relaxation-time measurements on the intercalate resonance indicate conduction-band behavior at the intercalate site but with a low density of states at the Fermi energy. The Sn M\"ossbauer line shape was studied in ${\mathrm{Sn}}_{\frac{2}{3}}\mathrm{Nb}{\mathrm{Se}}_{2}$. Only a single resonance was observed indicating a lack of any large quadrupole splitting as opposed to the two-line spectrum which has been observed for Sn in ${\mathrm{Sn}}_{1}$Ta${\mathrm{S}}_{2}$.

Effect of the thermal relaxation of a lattice mode on the Mössbauer radiation

The spectral distribution of the M\ossbauer radiation emitted from a radiating nucleus when it is in the excited vibrational level of a lattice normal mode has been considered theoretically. In obtaining the results, the relevant correlation functions, which include the thermal of phonons, are calculated in the harmonic approximation. Results are presented for the line shapes of the zero-, one-, and two-phonon-assisted M\ossbauer transitions. The relaxation splitting is absent in our results and the narrowing of the zero-phonon M\ossbauer line never exceeds \ensuremath{\sim}8% of the natural linewidth.