Calibration of the isomer shift of83Kr

Radioactive⁸³Rb was implanted in 6 different cubic metals (Al, W, Au, Ir, Pt, Pb) and both internal conversion electron spectra and Mössbauer spectra of the daughter nucleus⁸³Kr were measured. A value (r ²)=+5.1(9)×10^–3 fm² (corresponding to R/R=+1.6(3)×10^–4) was derived for the change of the mean square charge radius during the 9.40 keV transition in⁸³Kr. The systematics of the isomer shifts of krypton and other sp-elements substitutionally dissolved in metals are discussed.     

Dynamical property of YFeMnO4

In order to interpret abrupt changes of distributions of orientations andmagnitudes of hyperfine fields in Mössbauer measurements of⁵⁷Fe in YFeMnO₄, a model is proposed. The origin is assumed to be not static but dynamic. Fluctuating fields are caused by spins in a fully frustrated spin system, namely, a Heisenberg spin system on a triangular lattice in a two-dimensional antiferromagnet. Extending the stochastic theory for the fluctuation between two states to that among many states with a Gaussian distribution, we fit the spectra with three parameters, hyperfine fieldH _hf, correlation time _c, andwidth of fluctuating field , within a limited condition of =_c=1. Obtained results represent the characteristic features of Mössbauer spectra well, in spite of a simplified model.     

Hyperfine characterization of tin-doped indium sesquioxide

The hyperfine interactions at In and Sn sites of In₂O₃Sn (ITO) were measured through time-differential perturbed angular correlations and Mössbauer spectroscopy, respectively. Polycrystalline samples prepared by co-precipitation with nominal 0.025, 1 and 5 at.% Sn were studied. They all showed the cubic bixbyite structure characteristic of In₂O₃ after annealings at 200 °C. The quadrupole interaction at In sites appears nearly independent of Sn concentration being the main result of the presence of Sn in the lattice, the gradual disappearence of the dynamic perturbation caused by after-effects. The Mössbauer data demonstrate that Sn ions are in a 4+ state with Q=0.60₆ mm/s and=0.22₆ mm/s relative to SnO₃Ca at room temperature.     

Evaluation of Mössbauer line diffusion broadening by exponential fit

The Mössbauer line broadening measured by R.Lindsey in -iron stabilized with vanadium is evaluated by an exponential fit described in the APPENDIX of this paper. By this procedure the low temperature Mössbauer line width _m ⁰ , the diffusion frequency factorD ₀ and the activation enthalpyH are computed.Knauer's andSørensen-Trumpy's definitions of the time correlation factorf _t , necessary for theD ₀ calculation from Mössbauer line broadening, are applied to the Fe-V diluted BCC solid solutions.     

A study of a fullyc-axis oriented dc-sputtered thin film of YBa2(Cu0.98 57Fe0.02)3O6.8 by means of CEMS,XRD and SEM

A fullyc-axis oriented thin film of YBa₂(Cu_0.98 ⁵⁷Fe_0.02)₃O_6.8 prepared by planar dcsputtering has been investigated by means of Mössbauer spectroscopy. Room temperature⁵⁷Fe conversion electron Mössbauer spectra taken at different angles between the -ray direction and the normal (=c-axis) of the film show four subspectra: A (quadrupole splitting E _Q1.9 mm/s), B (E _Q1 mm/s), C (E _Q0.5 m/s) and D (E _Q1.6 mm/s). For subspectra A, B and C, we found the same hyperfine parameters as already published on other samples. The hyperfine parameters for subspectrum D are determined for the first time using a fully oriented sample. For D, we found the asymmetry parameter 0.6 andV _zz (the main component of the electric field gradient) lying in the a-b-plane.     

Mössbauer study of a novel binuclear Fe(II/III) delocalized-valence compound

In this paper, we briefly summarize the main conclusions of the Mössbauer analysis of [L₂Fe₂(-OH)₃] (ClO₄)₂·2CH₃OH·2H₂O with L=N,N',N"-trimethyl-1,4,7-triazacyclononane, a novel dimeric iron compound, which possesses a central exchange-coupled delocalized-valence Fe(II/III) unit. The complete delocalization of the excess electron in the dimeric iron center is concluded from the indistinguishability of the two iron sites in Mössbauer spectroscopy. The magnetic Mössbauer spectra imply a system spinS _t=9/2 for the dimer in its ground state. The values for hyperfine and spin-Hamiltonian parameters, obtained from simulations of the Mössbauer spectra, are =0.74 mms^–1, E _Q=–2.14 mms^–1,A =–10.6 T,A =–13.5 T andD=1.8 cm^–1. The system spinS _t=9/2 is interpreted to be a consequence of double-exchange coupling.     

A Mössbauer effect study of the Sb impurity site hyperfine field in amorphous Fe80B20

Mössbauer effect was used to determine the Sb site hyperfine field in the amorphous ferromagnet Fe₇₉SbB₂₀. The¹²¹Sb Mössbauer spectrum at 77 K showed a distribution of hyperfine fields with a most probable value of 219 kOe. This result is discussed in terms of the systematics of non-magnetic site hyperfine fields in ferromagnets.⁵⁷Fe Mössbauer effect was also used to determine the most probable value of the Fe site field, , and the width of the field distribution, H. Our measurements yield 280 kOe and H=104 kOe. These results are consistent with previous results on the amorphous ferromagnet Fe₈₀B₂₀.     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

Calibration of the isomer shift of125Te from internal conversion and mössbauer measurement

Radioactive¹²⁵I was ion-implanted into 7 different metal matrices. Al, Au, In, Pt, Sn, Te and Zn, and internal conversion and Mössbauer spectra associated with the 35.46 keV M1 transition of¹²⁵Te were measured for the same samples. A value R/R=(0.853±0.115)×10^–4 was derived for the relative difference of the nuclear charge radius for the 35.46 keV M1 transition of¹²⁵Te.     

Determination of the nuclear parameters of155Gd excited states using the Mössbauer effect

From Mössbauer spectra of GdAlO₃ and GdVO₄ above and below the Néel temperature and fitted using a transmission integral, we have determined the following parameters of the 86.5 keV and 105 keV levels:g(86)/g(0)=+1.217±0.005,Q(86)/Q(0)= +0.10±0.02,g(105)/g(0)=–0.55±0.02,Q(105)/Q(0)=+0.74±0.02, r ²₁₀₅/ r ²₈₆=+1.30±0.05. The linewidth observed for the 105 keV transition is less than the calculated natural linewidth.     

Mössbauer effect in inorganic glasses

⁵⁷Fe- and¹¹⁹Sn-Mössbauer effects become a very effective tool for the local structural study of inorganic glasses. Fe³⁺ and Sn⁴⁺ occupy network former (NWF) sites in several oxide glasses, while they are present at interstitial sites as network modifier (NWM) in phosphate, germanate and sulfate glasses. Characteristic-ray or thermal neutron irradiation effect indicates the structural role of Mössbauer ions; an increase in the 4s electron density or a reduction of Fe³⁺ to Fe²⁺ is observed due to the charge transfer from oxygen to Fe³⁺ when iron occupies NWF sites. By contrast, oxidation of Fe²⁺ to Fe³⁺ takes place when iron occupies NWM sites. Debye temperatures ( _D) obtained from low-temperature Mössbauer measurements are higher than 280 K when Fe³⁺ and Sn⁴⁺ are covalently bonded to oxygen at NWF sites, while the _D is lower than 270 K when these ions are ionically bonded to oxygen or halogen at NWM sites. A linear relationship between the glass transition temperatureT _g and the quadrupole splitting () of Fe³⁺, named T_g- rule, also indicates the structural role of Fe³⁺, i.e.,T _g versus plot yields a large slope of 680°C/mm s^–1 when Fe³⁺ occupies NWF sites, whereas it is only 35°C/mm s^–1 when the iron is present at NWM sites.     

Mössbauer spectroscopy with the 93 keV-resonance in67Zn

The procedures and results of high resolution Mössbauer experiments performed with the 93.3 keV resonance in absorbers of⁶⁷ZnO,⁶⁷ZnS (both wurtzite and sphalerite structures),⁶⁷ZnSe,⁶⁷ZnTe and⁶⁷ZnF₂ are reported. An essentially linear dependence between the isomer shift and the Pauling electronegativity of the ligands was found. A value of r ²=+11×10^–3 fm² is estimated. The Mössbauer parameters for both ZnS structures are equal within present limits of error. In particular, no quadrupole interaction was observed in the wurtzite modification. This indicates a nearly identical local symmetry at the Zn site in the two ZnS structures.Work supported by the Bundesministerium für Forschung und Technologie, Federal Republic of Germany and the Kernfor-schungszentrum Karlsruhe     

Conditional transformation of drift formula and potential theory for 1/2Δ+b(·)·∇

Using conditional Brownian motion and the transformation of drift formula (of Cameron-Martin, Girsarov, Maruyama) we give integral conditions on a vector fieldb which imply the harmonic measures and Green functions for 1/2 and 1/2+b(·)· on a bounded Lipschitz domainD are equivalent. By equivalent we mean there exist two-sided inequalities with constants depending only onb andD. This enables one to conclude the potential theory for 1/2+b(·)· onD and 1/2 onD are the same.     

Theoretical calculations of electron densities in zinc chalcogenides and in zinc fluoride

Self-consistent, non-relativistic Hartree-Fock calculations on a finite cluster of atoms with zinc at the center have been performed on the zinc blende compounds ZnTe, ZnSe, ZnS, on ZnO (wurtzite structure), ZnO (NaCl structure), and on ZnF₂ (rutile-type structure) to obtain changes in s electron density (0) at the⁶⁷Zn nucleus. We solved the eigenvalue problem of the dynamic matrix to calculate the second-order Doppler shiftS _SOD using appropriate force constant models and determined the isomer shiftS from the measured center shift for each compound. Our calculations clearly show the importance of the covalency of the Zn-ligand bond for the origin ofS and fully corroborate the experimental linear correlations between decreasingS values and increasing electronegativity of the ligands. The most important contribution to (0) comes from the Zn(4s) electrons, with a smaller but significant contribution from the Zn(3s) electrons. For the change of the mean-square nuclear charge radius for the Mössbauer transition in⁶⁷Zn, we obtain r ²=+(13.9±1.4) × 10^–3 fm².     

SPA-LEED studies of growth of Ag on Ag(111) at low temperatures

The surface morphology after deposition of Ag on Ag(111) at low temperatures (130–200 K) has been studied in detail with SPA-LEED (Spot-Profile Analysis of Low-Energy Electron Diffraction). The surface roughness and the mean terrace size have been quantitatively determined under various conditions. At 130 K the surface roughness increases with coverage exactly according to the relation = ^1/2, which indicates that the inter-layer diffusion can be neglected at 130 K. Although the mean terrace length decreases with increasing coverage (following an approximate power law of ^–2/3) for all studied coverages, it is much larger than expected for a pure random or Poisson-growth mode without any diffusion of the adatoms. Therefore, Ag grows on Ag(111) at this temperature without interlayer diffusion but with intra-layer diffusion. The intralayer diffusion barrierE _d has been determined by measuring the temperature dependence of the two-dimensional island density according to the nucleation theory (supposing a critical nucleus size of one). The obtained valueE _c=0.18 eV agrees with the theoretical calculations and previous measurements. Furthermore, from comparing measured and Monte-Carlo-simulated (MC) surface roughness at different deposition temperatures we obtain E=0.05 eV as a lower limit for the additional barrier at steps.     

Localization phenomenon in gaps of the spectrum of random lattice operators

We consider a class of random lattice operators including Schrödinger operators of the formH=–+w+gv, wherew(x) is a real-valued periodic function,g is a positive constant, andv(x),x ^d , are independent, identically distributed real random variables. We prove that if the operator –+w has gaps in the spectrum andg is sufficiently small, then the operatorH develops pure point spectrum with exponentially decaying eigenfunctions in a vicinity of the gaps.     

Optimum profiles for dispersive multimode fibres

A simple closed-form expression is given for the index profile of multimode fibres with arbitrary dispersion providing transmission capacities as large as 1.6/ ² Mbit/s km, wheren/n. Our result reduces to a previous result of Marcatili for the special case of circularly symmetric fibres. A transmission capacity of 150 Mbit/s over a 10 km long fibre appears possible with LED sources operating at optimum wavelengths for the medium.     

Complex-dimensional invariant delta functions and lightcone singularities

Invariant delta functions (including imaginary-mass case) defined in a complexn-dimensional space-time are explicitly calculated in position space. It is proposed to define products of invariant delta functions in the ordinary Minkowski space by analytically continuing the correspondingn-dimensional ones ton=4. The (not only leading but also non-leading) lightcone singularities of [(x; m ²)]², (x; m ²)⁽¹⁾(x; m ²), and [⁽¹⁾(x; m ²)]² are shown to be unambiguously determined in this way.     

The relevance of time-delayed coincidence Mössbauer experiments for the interpretation of the uncertainty principle

Time-delayed coincidence Mössbauer experiments, in which the spread in energy may be either greater or less than the natural linewidth, are discussed. This discussion leads to the conclusion that in the uncertainty relation E t , t should be interpreted as the duration time of the measurement and not as the lifetime of the state. Further analysis shows that confinement of photons to the region of space between emitter and absorber should cause a frequency spread much larger than actually observed. This leads to the conclusion that to think of photons as being created at one point in space, traveling with the velocity of light to another point, then being absorbed or destroyed, is incorrect.     

Error performance analysis for an optical heterodyne FSK communication system with a limiter-discriminator-integrator detector

The error probability for a coherent optical heterodyne FSK system with a limiter-discriminator-integrator (LDI) detector is analysed. The analysis includes laser quantum phase noise, the correlated receiver additive white Gaussian noise (AWGN), Gaussian narrow-band IF filtering and intersymbol interference (ISI) caused by it. It is shown that, for 1 dBEb/N ₀penalty at bit error rate (BER) 10^–9, (i) the normalized IF beat spectral linewidth T0.35% for frequency deviation ratioh=0.5(MSK), and T0.5% forh=0.7 (the receiver is insensitive to laser quantum phase noise ath=1.0, if ISI is not included.); (ii) if ISI is incorporated, T0.15% forh=0.5, T0.5% forh=0.7, both with 3dB bandwidth-bit period product (3.0>BT1.5), and T0.5% forh=1.0 with BT1.0 ifT0.35% when ISI exists,h=0.7 is optimum;h=1.0 otherwise.