Ossbauer Parameters Research Articles

Bayesian Inference on Hamiltonian Selections for Mössbauer Spectroscopy

M\"ossbauer spectroscopy, which provides knowledge related to electronic states in materials, has been applied to various fields such as condensed matter physics and material sciences. In conventional spectral analyses based on least-square fitting, hyperfine interactions in materials have been determined from the shape of observed spectra. In conventional spectral analyses, it is difficult to discuss the validity of the hyperfine interactions and the estimated values. We propose a spectral analysis method based on Bayesian inference for the selection of hyperfine interactions and the estimation of M\"ossbauer parameters. An appropriate Hamiltonian has been selected by comparing Bayesian free energy among possible Hamiltonians. We have estimated the M\"ossbauer parameters and evaluated their estimated values by calculating the posterior distribution of each M\"ossbauer parameter with confidence intervals. We have also discussed the accuracy of the spectral analyses to elucidate the noise intensity dependence of numerical experiments.

Mössbauer parameters of Fe57 substituents in the topological insulator Bi2Se3

$^{57}$Fe M\"ossbauer spectroscopy can probe several \emph{local} structural, electronic and magnetic properties of Fe-containing systems. However, to establish a direct relationship between these properties and a system's geometric structure, the experimental M\"ossbauer parameters need to be analyzed \emph{via} electronic structure calculations. Herein, structural, electronic and magnetic effects of iron substituents in the topological insulator $Bi_2Se_3$, as uniquely probed by $^{57}$Fe M\"ossbauer spectroscopy, have been determined \emph{via} spin-polarized electronic structure calculations. The iron ion substituents, of \emph{nominal} Fe$^{3+}(S = 5/2)$ oxidation and spin state, are unequivocally shown to substitute Bi$^{3+}$ sites in epitaxial $Bi_2Se_3$ thin-films used for M\"ossbauer measurements. Concomitant with iron substitution, \emph{localized} structural rearrangements take place whereby the longer Bi-Se bonds of the native system are replaced by significantly shorter Fe-Se counterparts in the Fe-containing system. The resulting distorted-octahedral environment about substituent iron ions gives rise to characteristic M\"ossbauer parameters ($\delta_{Fe} \approx$ 0.51 mm/s, $\Delta E_{Q} \approx$ 0.20 mm/s) which have been calculated in excellent agreement with measured values for Fe-doped $Bi_2Se_3$ thin films. Consistent with a substituent Fe$^{3+}$ ion's \emph{nominal} high-spin electronic configuration ($t_{2g}^{\uparrow \uparrow \uparrow} e_g^{\uparrow \uparrow}$), an Fe-centered spin density has been established which, nevertheless, extends towards neighboring Se atoms \emph{via} direct Fe-Se bonding and concomitant Fe(d)-Se(p) hybridization.

Validity of bond-length and Mössbauer parameters to assign oxidation states in multicomponent oxides: Case study ofSr4Fe4O11

From analyses of structural information for oxides with Fe in different oxidation states and computationally estimated M\ossbauer parameters (hyperfine field, isomer shift, and quadrupole splitting) based on density-functional theory, we show that the charges residing on the different constituents cannot be directly derived either from structural or M\ossbauer measurements. We have analyzed charge density, charge transfer, electron localization function, crystal orbital Hamilton population, and partial density of states to explain the bonding characteristics. Born-effective charge tensor is used to quantify the charges present at the atomic sites in ${\mathrm{Sr}}_{4}{\mathrm{Fe}}_{4}{\mathrm{O}}_{11}$. We show that the effects of covalence are important in explaining the electronic structure, magnetism, and chemical bonding in oxygen-vacancy-ordered systems such as ${\mathrm{Sr}}_{4}{\mathrm{Fe}}_{4}{\mathrm{O}}_{11}$ and on ignoring covalence, one can be misled in oxidation-state assignments.

Reply to “Comment on ‘Spin- and charge-ordering in oxygen-vacancy-ordered mixed-valenceSr4Fe4O11’ ”

Recently, using density-functional theoretical calculations, we have reported [Phys. Rev. B 74, 054422 (2006)] that formal ${\mathrm{Fe}}^{3+}$ ions reside at the square-pyramidal site and ${\mathrm{Fe}}^{4+}$ ions in the octahedral site in ${\mathrm{Sr}}_{4}{\mathrm{Fe}}_{4}{\mathrm{O}}_{11}$. Based on the interpretation of experimental structural and M\ossbauer data from the literature, Adler concludes that our previous first-principles results disagree with experiments on the assignment of oxidation states to Fe in the square-pyramidal and octahedral environments in ${\mathrm{Sr}}_{4}{\mathrm{Fe}}_{4}{\mathrm{O}}_{11}$. From a critical examination of the structure data for ${\mathrm{Sr}}_{4}{\mathrm{Fe}}_{4}{\mathrm{O}}_{11}$ and related oxides with Fe in different oxidation states and theoretically simulated M\ossbauer parameters (hyperfine field, isomer shift, and quadrupole splitting), here we show that information on charges residing on the different constituents cannot be directly derived either from experimental structure or M\ossbauer data. From additional analyses of the chemical bonding on the basis of charge density, charge transfer, electron localization function, crystal orbital Hamilton population, Born effective charge, and partial density of states, we substantiate our previous assignment of formal ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Fe}}^{4+}$ to the square-pyramidal and octahedral sites, respectively, in ${\mathrm{Sr}}_{4}{\mathrm{Fe}}_{4}{\mathrm{O}}_{11}$.

Mössbauer spectra of CoZn-substitutedZ-type barium ferriteBa3Co2−xZnxFe24O41

M\"ossbauer spectra of powder and aligned ${\mathrm{Ba}}_{3}{\mathrm{Co}}_{2\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{Fe}}_{24}{\mathrm{O}}_{41}$ samples with $x=0--2.0$ have been obtained and analyzed at room temperature and at $T=7\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with applied magnetic fields of 0 and $60\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$. The relationship between M\"ossbauer parameters and magnetic properties has been studied. The magnetocrystalline anisotropy of ${\mathrm{Ba}}_{3}{\mathrm{Co}}_{2\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{Fe}}_{24}{\mathrm{O}}_{41}$ is modified from the $c$ plane to the $c$ axis at Zn concentration $x=1.2--1.6$, based on the dependence of the quadrupole splitting and hyperfine field on Zn substitution for powder samples, and the values of the angle factor $b$ for aligned samples. Zn ions occupy only sites with down spin, while Co ions prefer sites with up spin. As the Zn substitution increases, the increase in saturation magnetization is attributed to the occupation of Zn ions at sites with down spin, which decreases the negative magnetization, thus increasing the net magnetization.

Angle-dependent Mössbauer spectroscopy in the ground and metastable electronic states inNa2[Fe(CN)5NO]⋅2H2Osingle crystals

Upon excitation of the metastable electronic state $S\mathrm{I}$ by irradiation with light in the blue-green spectral range at temperatures below $T=200$ K the electron density in the $[\mathrm{Fe}(\mathrm{CN}{)}_{5}\mathrm{NO}{]}^{2\ensuremath{-}}$ anion is rearranged mainly in the region of the Fe-N-O bonds, resulting in the drastic increase of the quadrupole splitting and a more positive isomer shift. But the local symmetry of the first coordination sphere around the Fe central atom is conserved. The positive sign of the electric-field gradient is unaffected by the new electron density at the ${}^{57}\mathrm{Fe}$ central atom. The direction of the z component of the electric-field gradient with respect to the crystallographic a axis increases only by 0.4\ifmmode^\circ\else\textdegree\fi{}. The degeneracy of the $\mathrm{Fe}{(3d}_{xz,yz})$ and $\mathrm{Fe}{(4p}_{x,y})$ orbitals is not changed. The optically excited anions are independent from each other and have no influence on the anions in the ground state. At every value of the population, the M\ossbauer parameters of both states are not altered, only the number density of transfered anions is changed. These results are determined by measuring the sign and orientation $\ensuremath{\alpha}$ of the electric-field gradient, the asymmetry parameter $\ensuremath{\eta},$ the ${}^{57}\mathrm{Fe}$ Debye-Waller factors ${f}_{a},$ ${f}_{b},$ ${f}_{c}$ of the orthorhombic crystal and the mean-square displacement tensor in the ground and metastable state $S\mathrm{I}$ at $T=80$ K by angle dependent M\ossbauer spectroscopy. Additionally these parameters are also determined at $T=294$ K for comparison. The dependence of the linewidth $\ensuremath{\Gamma}$ on the crystal thickness, measured at $T=294$ K, yields again the Debye-Waller factors and at thickness zero the deviation from the natural linewidth ${\ensuremath{\Gamma}}_{N},$ given by the linebroadening of the $\ensuremath{\gamma}$ source.

Microscopic environment of Fe in epitaxially stabilizedc−FeSi

Epitaxially stabilized iron monosilicide films having the CsCl structure $(c\ensuremath{-}\mathrm{FeSi})$ have been investigated by conversion electron M\"ossbauer spectroscopy and transmission electron microscopy. The ${}^{57}\mathrm{Fe}$ M\"ossbauer parameters (isomer shift \ensuremath{\delta}, linewidth \ensuremath{\Gamma}, and quadrupole splitting \ensuremath{\Delta}) are reported and discussed in terms of the local surrounding of the Fe nucleus. High statistical accuracy and resolution allowed a detailed investigation of the effects of strain and of the structural phase transformation from the epitaxially stabilized to the bulk stable phase. The phase transformation was found to proceed in a rather surprising layer by layer mechanism with smooth interfaces between the epitaxially stabilized, the bulk stable, and a third phase. Results from a molecular-dynamics simulation at constant pressure and temperature of the structural phase transition are presented and compared with the experimental findings. The isomer shift and the electric-field gradient at the Fe nucleus in the strained $c\ensuremath{-}\mathrm{FeSi}$ and in the third phase have been calculated using the ab initio full potential linear muffin-tin orbital method. The M\"ossbauer parameters of some relevant point defects in $c\ensuremath{-}\mathrm{FeSi}$ have likewise been calculated within this framework.

High-pressure phase of magnetite.

M\"ossbauer spectroscopy and x-ray diffraction were employed to investigate the magnetic and structural properties of the high-pressure monoclinic phase of magnetite. Measurements were performed to 66 GPa at 300 K using diamond anvil cells. Based primarily upon the M\"ossbauer parameters, the following features of the high-pressure phase were deduced. With increasing pressure the high-pressure phase evolves at P\ensuremath{\ge}25 GPa and its abundance increases monotonically at the expense of the low-pressure cubic phase. The high-pressure phase is not magnetic at 300 K and its monoclinic structural features resemble that of the low-pressure phase. The tetrahedral and octahedral sites characteristic of the inverse spinel structure, albeit distorted, remain the building blocks of the high-pressure phase. The fast electron hopping between ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Fe}}^{2+}$ at the octahedral sites prevails to the highest pressure. It is suggested that the cubic\ensuremath{\rightarrow}monoclinic\ensuremath{\rightarrow}cubic hysteretic cycle involves a mild displacive phase transition not affecting the coordination number of any of the iron cations.

Europium substitution effects in superconducting YBa2Cu4O8 synthesized under one atmosphere oxygen pressure.

${\mathrm{Y}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Eu}}_{\mathit{x}}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ powder samples, with x=0, 0.25, 0.5, 0.75, and 1.0, were synthesized at ambient pressure using either an acetate-tartrate sol-gel method or a LiF flux process. The lattice parameters and purity of the samples were checked using X-ray diffraction. The superconducting transition was monitored by magnetic-susceptibility measurements. Replacing yttrium with europium increased the unit-cell volume, decreased the orthorhombicity (b/a) and the critical temperature. The hyperfine interactions at the europium site were studied by $^{151}\mathrm{Eu}$ M\"ossbauer spectroscopy. The complete quadrupole Hamiltonian of the 21.5-keV \ensuremath{\gamma} transition of $^{151}\mathrm{Eu}$ was successfully applied in the analyses of the M\"ossbauer spectra. The M\"ossbauer parameters obtained were found to resemble those measured for the ${\mathrm{EuBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ (1:2:3) system. It was demonstrated that magnetic alignment of the crystallites could not be obtained with an 11.7-T field, contrary to the 1:2:3 and other high-${\mathit{T}}_{\mathit{c}}$ systems. The magnetic susceptibility for 1:2:4 single crystals appears to be isotropic.

Similar point defects in crystalline and amorphous silicon.

The microscopic nature of defects in ion-implanted crystalline silicon (c-Si) and amorphous silicon (a-Si) has been studied using M\"ossbauer spectroscopy. The evolution of the local structure around the probe atoms is followed during thermal annealing of ion-beam-created amorphous and ion-beam-damaged crystalline Si. Direct comparison of the M\"ossbauer parameters of $^{119}\mathrm{Sb}$ in c-Si and a-Si demonstrates that Sb occupies two distinct sites in each material with similar local environments in both materials. These sites are identified as fourfold-coordinated substitutional Sb and Sb-vacancy complexes. Annealing of ion-beam-damaged c-Si at 150 \ifmmode^\circ\else\textdegree\fi{}C causes the Sb-vacancy complex to change from a substitutional Sb adjacent to a vacancy to a more complicated complex. Annealing of a-Si is shown to reduce distortions in the network, consistent with structural relaxation.

Iron on substitutional and interstitial lattice sites in alkali metals and isomer shift systematics for interstitial iron in elemental metals.

In-beam M\ossbauer spectroscopy is applied to study implanted Fe atoms in the alkali metals Li, Na, and K. From the M\ossbauer parameters we infer that the Fe implants take up substitutional as well as interstitial sites. The interstitial Fe experiences a strongly increased s-electron density which is shown to hold quite generally in elemental metals and can be explained by the resulting lattice pressure. It is concluded that recently reported local moment formation in the alkali metals has contributions from both substitutional and interstitial Fe.

Magnetization and Mössbauer studies of Y1-xCaxSr2Cu3-yFeyO6+z.

ac-susceptibility, dc-magnetization, and $^{57}\mathrm{Fe}$ M\ossbauer spectra of ${\mathrm{Y}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ca}}_{\mathit{x}}$${\mathrm{Sr}}_{2}$${\mathrm{Cu}}_{3\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{Fe}}_{\mathit{y}}$${\mathrm{O}}_{6+\mathit{z}}$ (x=0, 0.1, and 0.2; y=0.3 and 0.4) are presented. Our data indicate bulk superconductivity in these compounds. In the case of y=0.4, the substitution of x=0.1 Ca increases both ${\mathit{T}}_{\mathit{c}}$ and flux pinning. The M\ossbauer parameters of the sample containing y=0.4 Fe and no Ca in comparison to those of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{Fe}}_{\mathit{y}}$${\mathrm{O}}_{6+\mathit{z}}$ indicate that at least 85% of Fe substitutes the Cu(1) sites and about 15% goes to Cu(2) sites. The existence of superconductivity at such high concentrations of Fe and the revival of superconducting properties by Ca substitution are discussed.

Time resolved nuclear resonant scattering from 119Sn nuclei using synchrotron radiation.

Nuclear resonant scattering of synchrotron radiation from $^{119}\mathrm{Sn}$ nuclei at 23.87 keV has been observed. The combination of a novel nested crystal monochromator and a $^{119}\mathrm{SnO}_{2}$/Pd based grazing incidence antireflection film was used to investigate the M\ossbauer parameters of a tin containing powder sample in a forward scattering experiment.

Mössbauer observation near the superconducting transition temperature in the TlBaCa3Cu3O8.5 superconductor.

The ${\mathrm{TlBaCa}}_{3}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{8.5}$ superconductor contains two main superconducting phases, 1:2:2:3 and 2:2:2:3, identified by powder x-ray analysis. Using $^{57}\mathrm{Fe}$ M\ossbauer nuclei as the probe, it has been confirmed that the results are the same as those furnished by x-ray analysis. It has also been proved that iron atoms in the lattice substitute two inequivalent sites of copper atoms for each main phase. We have observed a temperature dependence of the M\ossbauer parameters, i.e., quadrupole splitting, isomer shift, and relative resonance area. Here several problems are discussed related to the lattice dynamics and the electric charge transfer, which takes place in the transition from normal state to superconducting state.

67Zn Mössbauer study of zinc metal at high pressure.

A high-pressure M\ossbauer spectrometer for the high-resolution 93.3-keV resonance in $^{67}\mathrm{Zn}$ was used to investigate Zn metal under pressures up to 5.8 GPa at 4.2 K. Drastic changes of the M\ossbauer parameters are observed. The recoil-free fraction as well as the center shift change linearly with reduced volume. The former increases by a factor of \ensuremath{\sim}3 at 5.8 GPa, whereas the center shift decreases when pressure is applied. The reduction of the c/a ratio under pressure leads to a decrease of the electric field gradient at the $^{67}\mathrm{Zn}$ nucleus which is partially compensated for by an increase caused by the reduction in volume.

Metastability in EuBa2(Cu1-xSnx)3O7-y studied by 119Sn and 151Eu Mössbauer spectroscopy.

The metallic oxide compound system $\mathrm{Eu}{\mathrm{Ba}}_{2}{({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x})}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$ ($x=0.05, 0.10, 0.20$) was prepared for investigation with $^{151}\mathrm{Eu}$ and $^{119}\mathrm{Sn}$ M\ossbauer spectroscopy. The best fits of the $^{119}\mathrm{Sn}$ M\ossbauer lines reveal at least two different ${\mathrm{Sn}}^{\mathrm{IV}}$ sites. The $^{151}\mathrm{Eu}$ spectra are characteristic for ${\mathrm{Eu}}^{\mathrm{III}}$ state in these compounds. We have found a considerable difference between the shapes of $^{119}\mathrm{Sn}$ M\ossbauer spectra recorded at room temperature and those recorded at the temperature of liquid nitrogen in the case of the sample having the highest tin content. Nevertheless, there is no evidence that this difference has a direct connection with the superconducting behavior. A time-dependent splitting was found in the $^{119}\mathrm{Sn}$ spectra of $\mathrm{Eu}{\mathrm{Ba}}_{2}{({\mathrm{Cu}}_{0.8}{\mathrm{Sn}}_{0.2})}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$ at 78 K. It had a maximum at about 350 h after the synthesis of the sample. Some anomalous temperature dependences were also found in the $^{151}\mathrm{Eu}$ and $^{119}\mathrm{Sn}$ M\ossbauer parameters. Our findings can be associated with different Sn sites as well as low-temperature phase transformation in these oxide compounds.

Local environment of iron sites in icosahedral Al65Cu

A novel icosahedral alloy, ${\mathrm{Al}}_{65}$${\mathrm{Cu}}_{20}$${\mathrm{Fe}}_{15}$, produced in both a thermodynamically metastable and stable phase, has been studied with $^{57}\mathrm{Fe}$ M\"ossbauer spectroscopy, x-ray diffraction, and differential thermal analysis. It was found that the M\"ossbauer spectrum of either phase can be successfully analyzed in terms of a distribution of quadrupole-splitting magnitudes. This is interpreted as evidence for a continuous distribution of iron sites. The similarities of M\"ossbauer parameters of both phases indicate that a high degree of atomic disorder is an intrinsic property of icosahedral materials. Critical examination of previous M\"ossbauer studies of icosahedral materials together with other published experimental data show that the assertion of two distinct transition-metal sites in these materials is unfounded. Our results can be interpreted in terms of the distorted-icosahedral quasicrystal model.

Location of antimony in a halophosphate phosphor.

The location of antimony in halophosphate phosphors has been probed by use of $^{121}\mathrm{Sb}$ M\"ossbauer spectroscopy. It has been shown that the observed M\"ossbauer parameters can be understood if the antimony is at the phosphorous site, its ligands being three of the oxygen atoms of the phosphate group and a fluorine ion. The problem of maintenance of the halophosphate phosphors in relation to loss of the fluorine ions and to the ${\mathrm{Sb}}^{5+}$ concentration associated with an impurity phase has also been studied.

57Fe Mössbauer spectroscopy studies of the conducting poly(p-phenylene)-ferric chloride system.

M\"ossbauer-effect measurements have been used to characterize the conducting polymer obtained by the oxidation of poly ($p$-phenylene) [$p\ensuremath{-}{({\mathrm{C}}_{6}{\mathrm{H}}_{4})}_{x}$] with Fe${\mathrm{Cl}}_{3}$. The $^{57}\mathrm{Fe}$ M\"ossbauer spectra show the existence of two distinctly different iron sites with M\"ossbauer parameters characteristic of ${\mathrm{Fe}}^{3+}$. The isomer shift and $\ensuremath{\Delta}E$ values of the principal site are within the range typically observed for Fe${\mathrm{Cl}}_{4}^{\ensuremath{-}}$ (${\ensuremath{\delta}}_{\mathrm{IS}}=0.30$ mm ${\mathrm{s}}^{\ensuremath{-}1}$, $\ensuremath{\Delta}E=0.35$ mm ${\mathrm{s}}^{\ensuremath{-}1}$). In the case of the second iron site, higher ${\ensuremath{\delta}}_{\mathrm{IS}}$ and $\ensuremath{\Delta}E$ values are observed: ${\ensuremath{\delta}}_{\mathrm{IS}}=0.4$ mm ${\mathrm{s}}^{\ensuremath{-}1}$, $\ensuremath{\Delta}E=1.10$ mm ${\mathrm{s}}^{\ensuremath{-}1}$. Significant line broadening of the second site as compared with the linewidth of the principal one is indicative of a ${\ensuremath{\delta}}_{\mathrm{IS}}$ and/or $\ensuremath{\Delta}E$ distribution. From the temperature dependence of the absorption area of the principal site, the M\"ossbauer lattice temperature ${\ensuremath{\Theta}}_{M}^{\ensuremath{'}}$ has been calculated in the framework of the Debye model in the high-temperature limit and within the thin-absorber approximation. The value obtained, ${\ensuremath{\Theta}}_{M}^{\ensuremath{'}}=88$ K, is low and suggests a very loose bonding between the inserted anions and the host polymer.

Electron hopping in FeOCl intercalation compounds: A Mössbauer relaxation study.

The results of nuclear-gamma-resonance experiments on FeOCl intercalation compounds in the temperature range 100\ensuremath{\le}T\ensuremath{\le}300 K can be understood in terms of an electron-hopping process which occurs on the time scale of the M\ossbauer effect. Computer-simulated spectra generated by the application of a simple relaxation model closely reproduce the experimental data, and can account for the temperature dependence of the observed hyperfine interaction parameters. The results indicate that the distinct Fe(II) and Fe(III) valency states observed at liquid-nitrogen temperature become indistinguishable in the M\ossbauer experiment as these states interconvert at frequencies \ensuremath{\sim}${10}^{7}$ Hz. In the region ${10}^{7}$ Hz${10}^{8}$ Hz the quadrupole splitting of the majority iron atoms can serve as a sensitive measure of the hopping frequency, while in the fast-exchange (high-temperature) limit, the M\ossbauer parameters permit an evaluation of the Fe(II) contribution to the mixed-valence state. Experimental temperature-dependent data sets on several FeOCl intercalates have been analyzed in terms of this model and display a quite uniform behavior. The electron-hopping relaxation time (\ensuremath{\sim} inverse hopping frequency) obeys a simple Arrhenius law from which a phenomenological activation energy (${E}_{a}$\ensuremath{\approxeq}5.0\ifmmode\pm\else\textpm\fi{}0.9 kJ/mol for all compounds studied here) can be extracted. The fraction of Fe(II), i.e., the charge transfer involved in the intercalation reaction, amounts to 0.10 to 0.13 per Fe(III) atom of the host matrix, and is nearly independent of the nature of the guest species and the intercalation stoichiometry. The temperature dependence of the isomer shift predicted from the relaxation model closely reproduces the experimental observations.