Estimating intensity errors of powder diffraction data from area detectors

Abstract

It is shown how error estimates for intensities derived from area detector data in powder diffraction experiments should be calculated. It is demonstrated that the uncritical application of standard weighting schemes to the derived one dimensional data in subsequent least-squares refinements results in meaningless goodness of fit values less than unity that prohibit the evaluation of the quality of the fit. Moreover, it is shown that the calculated estimated standard deviations of the fitted parameters can only be calculated correctly when the true uncertainties of the measured intensities are known.     

Dynamic importance sampling for the escape problem in nonequilibrium systems: observation of shifts in optimal paths

The activation problem is investigated in two-dimensional nonequilibrium systems. A numerical approach based on dynamic importance sampling (DIMS) is introduced. DIMS accelerates the simulations and allows the investigation to access noise intensities that were previously forbidden. The escape path is observed to be shifted compared to a heteroclinic trajectory calculated in the limit of zero-noise intensity. A theory to account for such shifts is presented and shown to agree with the simulations for a wide range of noise intensities.     

Simulation on simultaneous estimation of non-uniform temperature and soot volume fraction distributions in axisymmetric sooting flames

For visualizing non-uniform absorbing, emitting, non-scattering, axisymmetric sooting flames, because conventional two-color emission methods are no longer suitable, a three-color emission method for the simultaneous estimation of temperature and soot volume fraction distributions in these flames is studied in this paper. The spectral radiation intensities at wavelengths of red, green, and blue, which may be derived from color flame images, are simulated for the inverse analysis. Then the simultaneous estimation is carried out from the spectral radiation intensities by using a Newton-type iteration algorithm and the least-squares method. In this method, a factor is used to balance the wide variation of spectral radiation intensities due to both the wide ranges of temperature and wavelength of the flame radiation. The results indicate that the three-color method is suited for the reconstruction of flame structures with single or double peaks with small difference between the peak and valley. For a double-peaked flame structure with larger peak and valley difference, reasonable result can be obtained just when the mean square deviations of measurement data are small, for example, not more than 0.01.     

Dispersion of a layered electron gas with nearest neighbour-tunneling

The dispersion of the first plasmon band is calculated within the Random Phase Approximation for a superlattice of two-dimensional electrongases, mutually interacting, and with nearest neighbour hopping between the planes. It is further shown that the deviations of this dispersion from the one in systems with zero interplane motion are very small in commonly realized experimental situations and that they are expected to be observable only in samples with plane distances of 150 Å and less.     

Enhancement of nonlinear susceptibilities near plasmonic metamaterials

It is shown that the Kerr nonlinearity of a two-level atom placed in the vicinity of a two-dimensional array of metal-coated silica nanoparticles can be greatly enhanced due to quenching of both radiative and non-radiative spontaneous-emission paths for frequencies near the surface plasmon resonances. The spontaneous emission rate is calculated by rigorous electrodynamic calculations of the electric-field Green’s tensor. The Kerr susceptibility can be enhanced by two orders of magnitude even for large detunings heralding, this way, the observation of nonlinear phenomena for moderate radiation intensities.     

Methanol and deuterated species: Infrared data,valence force field,rotamers, and conformation

New infrared measurements of gaseous and matrix-isolated methanol and 7 deuterated species are presented and analyzed. A revised assignment for the species CH₃OH(D) and CD₃OH(D) is used to determine 15 significant parameters of a valence force field by a converged simultaneous least-squares adjustment to 44 observed fundamentals. The respective frequencies calculated for the rotamers of CH₂DOH(D) and CHD₂OH(D) turn out to be a valid prediction as they are used to assign 78 observed fundamentals of the species with partially deuterated methyl groups. The values of the 15 force constant parameters are refined by including all 122 observed fundamentals. The force field contains significant deviations from local C_3v symmetry of the methyl group. Such an asymmetry, in the CH-stretching diagonal part, produces a difference of about 10 cm^?1 in the zero point energy of symmetric and asymmetric rotamers of the species with partially deuterated methyl groups. Calculations based on equilibrium structures with and without methyl tilt yield better agreement with observed data in the nontilted case. A preliminary calculation of relative intensities reproduces the major effects of isotopic substitution and rotational isomerism. Experimental evidence for the staggered conformation is obtained from a comparison of observed data with calculated results based on staggered and eclipsed models.     

On the formal equivalence of the Frisch-Berne and Watts perturbation theories to evaluate transport coefficients

A system of hard spheres in contact with a structureless wall is considered. The potential between the wall and the particles is of Lennard-Jones type. The second, the third and the fourth three-dimensional virial coefficient of the adsorption isotherm are calculated. The result being that over an extremely large temperature range the two-dimensional virial treatment is a rather good approximation. Conclusions are drawn about the deviations from Henry's law and the coverage, which can be described by virial expansions. It is doubted whether, from experimentally determined virial coefficients, information about the potential between the adatoms can be extracted.     

Properties of an optically magnetized semiconductor

It is shown that the magnetization of a semiconductor by optical means can lead to the existence of two unequal chemical potentials in the degenerate carrier population. The resulting birefringent effects in an otherwise isotropic material are calculated, and it is shown that near resonance these effects can become relatively large for moderate pumping intensities.     

Least-squares fitting of wavefront using rational function

This paper describes a mathematical method for approximation of the measurement data in optical testing techniques. Presented method uses a least-squares fit of two-dimensional rational function model to interferometric data. It is suitable for an analytical expression of wavefront, and one can obtain sufficient accuracy with a relatively small number of approximation coefficients. Properties of the proposed method are analyzed in this work. It is shown that the technique can be used for analyzing wavefront deformation in optical testing methods.     

Effects of surface roughness on surface analysis via soft and ultrasoft X-ray fluorescence spectroscopy

A model for calculating surface roughness effect on the intensity of emitted X-rays in the soft and ultrasoft X-ray region is presented and discussed. The results of calculations based on this model are compared to the results obtained experimentally using Al gratings as models for rough surfaces. It is shown that the correspondence between calculated and experimental intensities for Al–K is sufficient to corroborate the use of this model as a means of estimating maximum allowable surface roughness without a significant loss in intensity. It is also shown that this maximum allowable roughness estimate can be calculated with a knowledge of only the sample density and wavelength of the X-ray emission.     

Comparison of methods for estimating components in low-intensity spectra

The maximum probability and least-squares method as applied to the problem of component estimation in low-intensity spectra obeying Poisson statistics are compared with the scintillation γ-spectra taken as an example. It is shown by computer simulations that least-squares estimates of the intensities of the components are biased, and the bias increases when the number of channels of the spectrum exceeds 100. The maximum probability estimates of spectral components have substantially better parameters, which provides for an increase in the accuracy by a factor of two to ten compared to the least-squares method and a corresponding decrease in the lower threshold of measurement. A. D. Sakharov Radioecology Institute, 23, Dolgobrodskaya St., Minsk, 220009, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 346–349, May–June, 1998.     

Correction of non-linearity effects in detectors for electron spectroscopy

Using photoemission intensities and a detection system employed by many groups in the electron spectroscopy community as an example, we have quantitatively characterized and corrected detector non-linearity effects over the full dynamic range of the system. Non-linearity effects are found to be important whenever measuring relative peak intensities accurately is important, even in the low countrate regime. This includes, for example, performing quantitative analysis for surface contaminants or sample bulk stoichiometries, where the peak intensities involved can differ by one or two orders of magnitude, and thus could occupy a significant portion of the detector dynamic range. Two successful procedures for correcting non-linearity effects are presented. The first one yields directly the detector efficiency by measuring a flat-background reference intensity as a function of incident X-ray flux, while the second one determines the detector response from a least-squares analysis of broad-scan survey spectra at different incident X-ray fluxes. Although we have used one spectrometer and detection system as an example, these methodologies should be useful for many other cases.     

Quantitative XPS of NiO, CoO and MnO. The effects of elastic and inelastic electron scattering

In order to check whether the method for background correction developed by Tougaard can be applied to oxides we measured XPS spectra of single crystalline NiO, MnO and CoO samples. The materials for which background treatment was developed and tested originally were metals and alloys. In contrast to that, the oxides we study in the present work are insulators. We have chosen these compounds because their structure is simple and by cleaving them in vacuo it is possible to obtain surfaces with well-defined stoichiometry.

The inelastic background for these oxides is likewise described well by the above mentioned model. The ratio of metal to oxygen concentration calculated from the XPS intensities so obtained oscillates around 1.0 with a maximum deviation of about ±20% in the worst case. These deviations originate from elastic electron scattering, namely forward focusing (X-ray photoelectron diffraction). Taking this into account, the perfect stoichiometry is obtained within a few percent.     

Weighted oscillator strengths and lifetimes for the S XIV spectrum

The weighted oscillator strengths gf and the lifetimes for S XIV presented in this work have been calculated in a multiconfigurational Hartree–Fock relativistic approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure in order to improve the adjustment to experimental energy levels. This method produces gf values that are in better agreement with observed line intensities and lifetime values closer to the experimentally determined ones. In this work we presented all the experimentally known electric dipole S XIV spectral lines. Published in Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 473–476, 2009.     

Scarring and the Statistics of Tunnelling

We show that the statistics of tunnelling can be dramatically affected by scarring and derive distributions quantifying this effect. Strong deviations from the prediction of random matrix theory can be explained quantitatively by modifying the Gaussian distribution which describes wavefunction statistics. The modified distribution depends on classical parameters which are determined completely by linearised dynamics around a periodic orbit. This distribution generalises the scarring theory of L. Kaplan (1998, Phys. Rev. Lett.80, 2582) to describe the statistics of the components of the wavefunction in a complete basis, rather than the overlaps with single Gaussian wavepackets. In particular it is shown that correlations in the components of the wavefunction are present, which can strongly influence tunnelling-rate statistics. The resulting distribution for tunnelling rates is tested successfully on a two-dimensional double-well potential.     

Complete characterization of a spatiotemporal pulse shaper with two-dimensional Fourier transform spectral interferometry

Spatiotemporal pulse shaping is characterized with two-dimensional Fourier transform spectral interferometry. A deformable-mirror-based bidimensional pulse shaper is used to create simple spatiotemporal structures on a femtosecond pulse, structures that are directly calculated from the measured spatiospectral phases and intensities.     

Calculations of the Mueller matrix for scattering of light from two-dimensional surfaces

Abstract

Results are presented of an analysis of the Mueller matrix parameters for the problem of scattering of light from two-dimensional rough surfaces. The Mueller matrix fully describes the polarization properties of the scattered light. It is shown, using symmetry arguments, that for normal incidence it is necessary to measure the Mueller matrix terms in only one plane, thus reducing the amount of data to be analysed. Examples of the form of the Mueller matrix terms are calculated using a simple ray-trace approach.     

Two-dimensional phase retrieval using a window function

Two-dimensional phase retrieval by use of a window function is considered. First the uniqueness and the reconstruction of a two-dimensional signal from the Fourier intensities of the three signals, an original signal, the signal windowed by a window w(m, n) , and the signal windowed by its complementary window w(c)(m, n) = 1 - w(m, n) , are addressed. Then phase retrieval without a complementary window is considered. Conditions under which a signal can be uniquely specified from the Fourier intensities of the original signal and the windowed signal by w(m, n) are developed, and a reconstruction algorithm is presented.     

The effect of three-body interactions on thermal desorption spectra

Thermal desorption spectra are calculated for a one-dimensional chain and for a two-dimensional square lattice using the transfer-matrix technique and Monte Carlo simulations. Lateral interactions of adsorbed particles cause a splitting of spectra. The repulsive three-body interactions are shown to lead to an inequality of the integral intensities of the thermal desorption peaks.