Bayes Turchin analysis of X ray absorption data above the Fe L2,3 edges

Extended X ray absorption fine structure EXAFS data and magnetic EXAFS MEXAFS data were measured at two temperatures 180 K and 296 K in the energy region of the overlapping L edges of bcc Fe grown on a V 110 crystal surface. In combination with a Bayes Turchin data analysis procedure these measurements enable the exploration of local crystallographic and magnetic structures. The analysis determined the atomic like background together with the EXAFS parameters which consisted of 10 shell radii, the Debye Waller parameters, separated into structural and vibrational components, and the third cumulant of the first scattering path. The vibrational components for 97 different scattering paths were determined by a two parameter force field model using a priori values adjusted to Born von Karman parameters of inelastic neutron scattering data. The investigations of the system Fe V 110 demonstrate that the simultaneous fitting of atomic background parameters and EXAFS parameters can be performed reliably. Using the L2 and L3 components extracted from the EXAFS analysis and the rigid band model, the MEXAFS oscillations can only be described when the sign of the exchange energy is changed compared to the predictions of the Hedin Lundquist exchange and correlation functiona

Bayesian approach to background subtraction for data from the extended x ray absorption fine structure

We construct the x ray absorption fine structure XAFS function chi k from measured absorption data mu E , using a Bayesian approach. This procedure is combined with a Bayesian analysis of the chi function in terms of structural parameters, reported earlier, to a uniform method of XAFS data evaluation. It is applied to XAFS data measured on germanium and computer generated L edge iron dat

Bayes Turchin approach to x ray absorption fine structure data analysis

X ray absorption fine structure XAFS data from copper, gold, and germanium are analyzed in the framework of the model independent Bayes Turchin approach. Compared to earlier treatments we also obtain spring constants, besides shell radii, Debye Waller DW parameters, and anharmonicity parameters. The use of spring constants instead of DW parameters reduces considerably the number of model parameters needed to achieve a satisfactory fit of the data. The ab initio EXAFS code FEFF7 is used in the analysis. The various sources of uncertainty in the input data and in the FEFF7 code are carefully assessed and used in the analysis. It is shown to which degree the model parameters are determined by the data, rather than by the a priori assumptions. A posteriori errors and error correlations between model parameters are shown

Bayes Turchin approach to XAS analysis

Modern analysis of X ray absorption fine structure XAFS is usually based on a traditional least squares fitting procedure. Here an alternative Bayes Turchin method is discussed which has a number of advantages. In particular the method takes advantage of a priori estimates of the model parameters and their uncertainties and avoids the restriction on the size of the model parameter space or the necessity for Fourier filtering. Thus the method permits the analysis of the full X ray absorption spectra XAS , including both XAFS and X ray absorption near edge spectra XANES . The approach leads to a set of linear equations for the model parameters, which are regularized using the Turchin condition . Also, the method naturally partitions parameter space into relevant and irrelevant subspaces which are spanned by the experimental data or the a priori information, respectively. Finally we discuss how the method can be applied to the analysis of XANES spectra based on fits of experimental data to full multiple scattering calculations. An illustrative application yields reasonable results even for very short data range

Bayes Turchin analysis of overlapping L edges EXAFS data of iron

Spin polarized and spin averaged extended x ray absorption fine structure M EXAFS data were measured at temperatures of 180 K and 296 K in the soft x ray energy regime of the overlapping L edges of an iron film grown on V 110 . The absorption coefficient was analyzed with the Bayes Turchin procedure. The analysis yields the correction function to the atomic like background absorption coefficient calculated by FEFF8 and reveals components of atomic EXAFS oscillations. The EXAFS Debye Waller DW parameters were determined. Their split into a thermal and a structural contribution was not possible without theoretical input since the two temperatures in this experiment were not sufficiently far apart from each other and the k range of the data was too small. The thermal contribution to the DW parameters was therefore derived from a force field model with two spring constants. They were adjusted to DW parameters calculated from Born von Karman force constants which had been obtained from inelastic neutron scattering. Those two spring constants also nicely reproduce the unprojected vibrational density of states deduced from phonon dispersion curves. The MEXAFS oscillations can be described by the rigid band model and the L2 and L3 EXAFS components. A negative exchange related energy is obtained by fitting the MEXAFS signal in the extended energy region. This is in contrast to the predictions of the Hedin Lundquist functional and the Dirac Hara functional used in the FEFF8 cod

Lattice dynamics information obtained from EXAFS measurements on Ta

Extended x ray absorption fine structure EXAFS data were measured at three temperatures 20 K, 80 K, and 300 K above the L3 edge of polycrystalline alpha tantalum. The data analysis is based on a recently developed Bayesian approach and uses the FEFF8 code results. Besides the temperature dependence of the lattice constant we obtain a separation of the Debye Waller parameters into structural and thermal contributions. The latter are well described by a force field model with two force parameters. A posteriori errors and cross correlations between the model parameters are calculated, taking the errors of the input EXAFS function as well as systematic uncertainties of the model into account. Lattice dynamical observables determined independently are compared with the results of our force field model using the parameters from the fit of our EXAFS dat