Introducing Alternative Algorithms for the Determination of the Distribution of Relaxation Times

Impedance spectroscopy is a powerful characterization method to evaluate the performance of electrochemical systems. However, overlapping signals in the resulting impedance spectra oftentimes cause misinterpretation of the data. The distribution of relaxation times (DRT) method overcomes this problem by transferring the impedance data from the frequency domain into the time domain, which yields DRT spectra with an increased resolution. Unfortunately, the determination of the DRT is an ill-posed problem, and appropriate mathematical regularizations become inevitable to find suitable solutions. The Tikhonov algorithm is a widespread method for computing DRT data, but it leads to unlikely spectra due to necessary boundaries. Therefore, we introduce the application of three alternative algorithms (Gold, Richardson Lucy, Sparse Spike) for the determination of stable DRT solutions and compare their performances. As the promising Sparse Spike deconvolution has a limited scope when using one single regularization parameter, we furthermore replaced the scalar regularization parameter with a vector. The resulting method is able to calculate well-resolved DRT spectra.     

The preparation, structure and spectra properties of dual μ3-oxo bridged tetranuclear complexes containing the [CrnFe4-nO2]8+ core(n=0,2,4)

The preparation and characterization of [CrnFe4-nO2(O2CMe)7(bipy)2]Cl (1, n=0; 2, n=2; 3, n=4, bipy=2,2'-bipyridine) are described. The three complexes (1, 2 and 3) are obtained by tipyridine-mediated conversion of trinuclear [CrnFe3-nO(O2CMe)6(H2O)3]+(1, n=0; 2, n=1;3, n=3), and crystallized as three of approximate isomorphs. Crystal 2 is monoclinic with space group C2/c, a=27.454(5)A, b=11.789(1)A, c=16.570(3)A, B=118.78(1), V=4700.8A, z=4, u(MoKa)=11.64cm-1, F(000)=2056, final R=0.058 and Rw=0.066 for 3479 reflections with I > 3o(I). The Fe and Cr atoms in the cation are all +3 oxide state and disordered in the lattice, which is also supported by its Mossbauer studies. The [Cr2Fe2O2]8+ core can be thought of as being derived from two edge-sharing M3O units (M=Fe or Cr), and as a butterfly-like structure. The cations' structure of all three crystals are similar to each other and have C2 symmetry. The species are characterized by IR spectra and magnetic techniques, with particular emphasis on different     

The negative adsorption of chromium atoms on alloy-oxide film boundaries during oxidation in air and anodic passivation of Fe-Cr and Ni-Cr alloys

Equilibrium of Cr atoms between the surface layer and bulk of a binary alloy was analyzed. The Gibbs adsorption equation was used to obtain the dependence of the adsorption activity of atoms in the surface layer on their activity in the bulk. An approximate thermodynamic method was used to calculate the adsorption of Fe (Ni) and Cr atoms in the surface layers of Fe-Cr and Ni-Cr alloys. According to calculations, there was negative adsorption, X _Cr ≪ 1, in the surface layer of the alloys caused by a large difference between the Gibbs surface energies of Cr and Fe (or Ni). The negative adsorption of Cr shifted chemical reaction equilibria on the alloy-oxide film boundary both in oxidation in air and in anodic passivation, 3FeO (NiO) + 2Cr = Cr₂O₃ + 3Fe(Ni), toward oxide film enrichment in the FeO (or NiO) oxide. A unified method for calculating the composition of oxide films on alloys was used for both processes. The method was based on the use of the initial data on the Gibbs surface energy of metals constituting alloys. The calculated oxide film compositions were close to the experimental X-ray photoelectron spectroscopy data.     

Evaluating the third and fourth derivatives of spectral data

The problem of differentiating spectral data to yield the third and fourth derivatives is converted into one of solving an integral equation of the first kind. This equation is solved by Tikhonov regularization. The method of General Cross Validation is used to guide the choice of the regularization parameter that keeps noise amplification under control. The performance of this route to third and fourth derivative spectra is demonstrated by applying it to a number of published spectra. A computational problem associated with General Cross Validation has been identified.     

Optimal error bound and generalized Tikhonov regularization for identifying an unknown source in the heat equation

In this note we prove a stability estimate for an inverse heat source problem. Based on the obtained stability estimate, we present a generalized Tikhonov regularization and obtain the error estimate. Numerical experiment shows that the generalized Tikhonov regularization works well.     

Second chemiluminescence behavior of Fe2+, Fe3+ and Cr3+ in the luminal-KMnO4 system.

A novel flow injection chemiluminescence (CL) method has been developed for the determination of three metal ions, namely Fe2+, Fe3+ and Cr3+, based on the second CL (SCL) signal of the mixture of luminal with KMnO4 in a sodium hydroxide medium by the catalysis of Fe2+, Fe3+ or Cr3+. The possible CL mechanism of the systems, the influencing factors, and the optimum conditions for the reactions were investigated based upon the kinetic curve of the CL reaction, CL spectra, UV-visible spectra and some other experiments. Under the optimum conditions, the SCL intensity was directly proportional to the concentration of these metal ions in solution in the range of 0.10 - 100.00 mg l(-1) for Fe(2+), 0.50 - 7.50 and 7.50 - 200.00 mg l(-1) for Fe3+, 0.01 - 0.25 and 0.25 - 10.00 mg l(-1) for Cr3+. The detection limits (3 sigma/s) were 9.87 x 10(-6) g l(-1), 2.71 x 10(-6) g l(-1) and 5.25 x 10(-7) g l(-1) for Fe2+, Fe3+ and Cr3+, respectively.     

Chromatographic Identification of Cyclohexane Chlorination Products by an Additive Scheme for the Prediction of Retention Indices

Identification of the products of free-radical chlorination of cyclohexane seems to be a complex analytical problem due to the following principal reasons: (1) the available reference information (both standard mass spectra and gas chromatographic retention indices, RI) is strongly restricted to the data for only few simplest congeners, (2) mass spectra of isomeric chlorinated derivatives are practically indistinguishable, and (3) the number of isomers increases with the growing number of chlorine atoms in the molecule until six. To solve this problem, the modified additive scheme for precalculation of the RIs of chlorinated cyclohexanes on standard non-polar polydimethyl siloxane stationary phases was proposed and used. This approach is based on the data for congeners with fewer number of chlorine atoms in the molecule; the principal feature is its applicability to a diastereomers. The final set of both experimental and precalculated RI values permits us to identify unambiguously more than 20 products of cyclohexane chlorination in reaction mixtures. Different modes of the quality control of evaluated retention indices are discussed.     

Spectroscopy of lithium atoms sublimated from isolation matrix of solid Ne

We have studied, via laser absorption spectroscopy, the velocity distribution of (7)Li atoms released from a solid neon matrix at cryogenic temperatures. The Li atoms are implanted into the Ne matrix by laser ablation of a solid Li precursor. A heat pulse is then applied to the sapphire substrate sublimating the matrix together with the isolated atoms at around 12 K. We find interesting differences in the velocity distribution of the released Li atoms from the model developed for our previous experiment with Cr [R. Lambo, C. C. Rodegheri, D. M. Silveira, and C. L. Cesar, Phys. Rev. A 76, 061401(R) (2007)]. This may be due to the sublimation regime, which is at much lower flux for the Li experiment than for the Cr experiment, as well as to the different collisional cross sections between those species to the Ne gas. We find a drift velocity compatible with Li being thermally sublimated at 11-13 K, while the velocity dispersion around this drift velocity is low, around 5-7 K. With a slow sublimation of the matrix we can determine the penetration depth of the laser ablated Li atoms into the Ne matrix, an important information that is not usually available in most matrix isolation spectroscopy setups. The present results with Li, together with the previous results with Cr suggest this to be a general technique for obtaining cryogenic atoms, for spectroscopic studies, as well as for trap loading. The release of the isolated atoms is also a useful tool to study and confirm details of the matrix isolated atoms which are masked or poorly understood in the solid.     

The use of Tikhonov regularization method for calculating the distribution function of relaxation times in impedance spectroscopy

The state-of-the-art in realization of the method of distribution of relaxation times (DRT) as applied to the analysis of data of electrochemical impedance spectroscopy is briefly surveyed. The theoretical fundamentals of the DRT method are described, the methods of solving the Fredholm equation of the 1st order with respect to the unknown DRT function are considered as an ill-defined problem. The Tikhonov regularization method presently considered as the most suitable for solving this equation is discussed. For several numerical experiments, the high resolution of the DRT method and its stability with respect to noise in impedance spectra are demonstrated. Among the problems and limitations of the DRT methods, the choice of the optimal regularization coefficient is considered as the most significant. Particularly, it is shown that in those cases where several relaxation processes with the constant phase angle appear in the response of objects under study to ac disturbances, different regularization coefficients should be selected for each of these elements in order to obtain adequate results.     

On the choice of the residual norm function in the interpretation of ARXPS data by regularized fitting

Angle‐resolved X‐ray photoelectron spectroscopy (ARXPS) data taken on a polystyrene film exposed to a nitrogen plasma are interpreted by the fitting of regularized depth profiles. Three ways of measuring the goodness of fit are compared—the χ² statistic with variances drawn from the raw spectra, the χ² statistic with variances drawn from the concentration figures obtained from the data analysis, and a simple sum of the squared differences (ssd) that does not require variances to be calculated. It is shown that for these data, the depth profiles obtained using an objective method for the choice of the regularization parameter are essentially identical irrespective of whether or how the variances are introduced into the calculation. Copyright © 2010 John Wiley & Sons, Ltd.     

Determination of the parameters of atomic pair correlations in nickel oxide films by the electron energy loss fine structure method

The electron energy loss extended fine structure (EELFS) spectra were obtained from the pure nickel surface (M _2,3 EELFS) of a stoichiometric NiO film (NiM _2,3 and OK EELFS spectra) and the “nonhomogeneous” oxide film on the surface of nickel Ni-O (NiM _2,3 and OK EELFS spectra). The amplitudes and intensities of electron transitions for the core levels of atoms were calculated with regard for the multiplicity of electron impact excitation of the corresponding core levels of atoms. The corresponding normalized oscillating terms were isolated using the results of calculations based on the experimental EELFS spectra. Agreement between the experimental and calculated (on Ni and NiO test objects) data showed that the theoretical approaches used and the calculated data for describing the EELFS spectra are good approximations. Using the results of calculations and the parameters of secondary electron elastic scattering (FEEF-8 data) we obtained the atomic pair correlation functions from the experimental normalized oscillating parts of the EELFS spectra by Tikhonov’s regularization method.     

Structural studies of Na-montmorillonite exchanged with Fe2+, Cr3+, and Ti4+ by N2 adsorption and EXAFS

The structures of Fe(2+)-, Cr(3+)-, and Ti(4+)-modified montmorillonite prepared from ion exchange of the Na-clay with Fe(2+), Cr(3+), and Ti(4+) were investigated. Conventional BET surface area and spectroscopic analysis by extended adsorption fine structure (EXAFS) were applied. It was shown that the BET surface area of Na-clay was similar to that of Fe-clay, but somewhat different from those of Cr- and Ti-clay; it decreased in the order Na- > Fe- > Ti- > Cr-montmorillonite. This sequence appeared to be consistent with the ion size Na(+) (0.95 nm)>Fe(2+) (0.65 nm)>Cr(3+) (0.62 nm), except for Ti(4+) (0.69 nm). EXAFS data showed that some Si atoms within montmorillonite were replaced by Ti atoms and that a neostructure of titanium oxide was formed.     

Spatial and temporal studies of a glow discharge

A demountable glow discharge tube was constructed with the objective of studying the various processes taking place in the discharge and resolving these both spatially and temporally. Argon and neon were used as fill gases. Continuous wave laser excited fluorescence was used to study the spatial distribution of sodium atoms which were sputtered off the cathode; a value for the diffusion coefficient of sodium in argon was obtained from time-resolving these experiments. From the population ratios of the various excited levels which we observed, we conclude that no single excitation temperature predominates anywhere between the electrodes under our conditions; instead, several population inversions were observed. Emission intensities of lines from atoms and ions were resolved as a function of the axial position between the electrodes. A temporal region was found where the signal-to-noise ratio for the detection of small quantities of analytes may be optimized. In addition to numerous atomic lines from the fill gas, we also detected fill gas ions as well as Fe, Fe⁺ and Cr when using stainless steel as a sample.     

Diagnostic and analytical study of post ablation ionization of neutral atoms of major and minor constituents from a low alloy steel

Post ablation ionization (PAI) of neutral atoms from a low alloy steel has been investigated using non-resonant laser ionization in a time-of-flight mass spectrometer. By varying the delay between the ablation and ionization lasers, the velocity distributions of the Ti, V, Cr, Mn and Fe atoms have been determined simultaneously. These distributions have been recorded as a function of ablation laser fluence. The half-range Maxwell-Boltzmann velocity distribution has been used to fit the data and different characteristic temperatures have been determined for the various elements in the sample. The quantitative capability of this method for bulk and surface analysis has been evaluated by calculating the relative sensitivity factors (RSFs) for the various constituent elements. The RSFs for all of the elements are seen to be highly dependent on the delay between the ablating and ionizing lasers. This dependence was reduced by integrating the temporal dependent ion yield, leading to a significant improvement in the calculated RSF values. It was also found that the RSFs were not highly dependent on the power density of the ablation laser beam.     

Kinetic heterogeneity of the active sites of titanium-containing catalytic systems in the stereospecific polymerization of isoprene

The kinetic heterogeneity of the active sites of titanium-containing catalytic systems in the stereospecific polymerization of isoprene was studied based on solving inverse problems for the molecular-weight distribution of polyisoprene with the use of the Tikhonov regularization method. It was found that from two to four types of active sites can occur depending on the nature of the organoaluminum compound used in the catalytic system. The rate constants of elementary steps of the polymerization process for particular types of active sites were obtained for the first time by solving inverse kinetic problems.     

Evolution of the passive film and organic constituents at the surface of stainless steel immersed in fresh water

The evolution of the surface of a conventional stainless steel (AISI 316L) immersed in aqueous medium simulating fresh water (pH approximately 8) was studied using XPS and AFM. A detailed analysis of XPS spectra allowed a distinction to be made between oxygen of organic and inorganic nature. During the first 48 h, the main changes concern the inorganic phase: the oxygen concentration in the passive layer increases, owing both to oxidation of metal elements, including conversion of Fe(II) to Fe(III), and to hydration; the molar ratio of oxidized species Fe(ox)/Cr(ox) decreases slightly; the formation of colloidal particles, presumably made of ferric hydroxide, is observed by AFM. After longer periods of immersion, the Fe(ox)/Cr(ox) is higher, while the coating of colloidal particles reaches a full surface coverage. The amount of organic compounds increases further and the XPS spectra reveal the accumulation of polysaccharides and proteins, which indicate that these organic compounds are of biological origin.     

Experimental verification of a radiative model of laser-induced plasma expanding into vacuum

A radiation dynamic model of the postbreakdown stage of laser-induced plasma solves a twofold task: first, the direct problem, it yields an analytical expression for the plasma radiation dynamics under arbitrarily chosen initial conditions allowing the computation of synthetic spectra; second, the inverse problem, it allows finding of the initial conditions by a direct comparison of calculated synthetic spectra with experimentally measured ones. In this work, we carry out experimental verification of the model, thus dealing with the inverse problem. We vary the initial parameters of the model (plasma initial temperature and the initial concentrations of species) until a close fit between the synthetic and the experimental spectrum is obtained. Some of the model inputs (e.g., the initial radius of the plasma) are measured and introduced into the model as fixed constants. Calculations and measurements are performed on a binary SiC system; on a series of multicomponent aluminum samples doped with Si, Mg, Cu, Zn, and Fe; and on pure iron, silicon, and carbon. From two to six elements and up to 500 spectral lines were involved in the calculations. The Monte Carlo optimization (the simulated annealing method) is used for finding initial plasma temperature and number densities. A reasonably good agreement is obtained between the computed and the experimental spectra. This approach can be considered as a valuable step towards the achievement of absolute analysis.     

Electronic structure study by means of x-ray spectroscopy and theoretical calculations of the "ferric star" single molecule magnet

The electronic structure of the single molecule magnet system {M[Fe(L(1))(2)](3)}4CHCl(3) [M=Fe,Cr;L(1)=CH(3)N(CH(2)CH(2)O)(2) (2-)] has been studied using x-ray photoelectron spectroscopy, x-ray-absorption spectroscopy, soft-x-ray emission spectroscopy, as well as theoretical density-functional-based methods. There is a good agreement between theoretical calculations and experimental data. The valence band mainly consists of three bands between 2 and 30 eV. Both theory and experiments show that the top of the valence band is dominated by the hybridization between Fe 3d and O 2p bands. From the shape of the Fe 2p spectra it is argued that Fe in the molecule is most likely in the 2+ charge state. Its neighboring atoms (O,N) exhibit a magnetic polarization yielding effective spin S=52 per iron atom, giving a high-spin state molecule with a total S=5 effective spin for the case of M=Fe.     

Changes in the crystallographic and magnetic properties of Hf2Fe on hydrogen absorption

We have found that the cubic intermetallic compound Hf₂Fe can absorb up to five hydrogen atoms per formula unit at a pressure of 1 atm. Hf₂Fe is a Pauli magnet. During hydrogen absorption a magnetic moment appears on the iron atoms at a hydrogen concentration of about 1.5. The maximum saturation magnetic moment is observed in Hf₂FeH₃. The static low field susceptibility achieves a maximum value and exhibits non-reversible behaviour. These properties are characteristic of a disordered (spin-glass-like) magnetic system. The γ-γ perturbed angular correlation spectra indicate that at low concentrations the hydrogen is localized near only one type of hafnium site. Our Mössbauer data show a change in the isomer shift consistent with what has been reported previously. When the temperature is decreased and the hydrogen concentration is increased, the spectra become less resolved. This is related to the fact that the samples are in a disordered magnetic phase.