On the resolution function for powder diffraction with area detectors

In a powder diffraction experiment the resolution function defines the instrumental contribution to the peak widths as a function of the Bragg angle. The Caglioti formula is frequently applied to model the instrumental broadening and used in structural refinement. The parameters in the Caglioti formula are linked to physically meaningful parameters for most diffraction geometries. However, this link is lost for the now very popular powder diffraction geometry using large 2D area detectors. Here we suggest a new physical model for the instrumental broadening specifically developed for powder diffraction data measured with large 2D area detectors. The model is verified using data from two synchrotron diffraction beamlines with the Pilatus2M and MAR345 detectors. Finally, a functional form is proposed to replace the Caglioti formula for this geometry in the Rietveld method and profile refinements.

Variations on the Maiani-Testa approach and the inverse problem

We discuss a method to construct hadronic scattering and decay amplitudes from Euclidean correlators, by combining the approach of a regulated inverse Laplace transform with the work of Maiani and Testa [1]. Revisiting the original result of ref. [1], we observe that the key observation, i.e. that only threshold scattering information can be extracted at large separations, can be understood by interpreting the correlator as a spectral function, ρ(ω), convoluted with the Euclidean kernel, e−ωt, which is sharply peaked at threshold. We therefore consider a modification in which a smooth step function, equal to one above a target energy, is inserted in the spectral decomposition. This can be achieved either through Backus-Gilbert-like methods or more directly using the variational approach. The result is a shifted resolution function, such that the large t limit projects onto scattering or decay amplitudes above threshold. The utility of this method is highlighted through large t expansions of both three- and four-point functions that include leading terms proportional to the real and imaginary parts (separately) of the target observable. This work also presents new results relevant for the un-modified correlator at threshold, including expressions for extracting the Nπ scattering length from four-point functions and a new strategy to organize the large t expansion that exhibits better convergence than the expansion in powers of 1/t.

Practical measurement of the energy resolution for meV-resolved inelastic X-ray scattering

Several different ways of measuring the energy resolution for meV-resolved inelastic X-ray scattering (IXS) are compared: using scattering from poly(methyl methacrylate), PMMA, using scattering from borosilicate glass (Tempax), and using powder diffraction from aluminium. All of these methods provide a reasonable first approximation to the energy resolution, but, also, in all cases, inelastic contributions appear over some range of energy transfers. Over a range of ±15 meV energy transfer there is good agreement between the measurements of PMMA and Tempax at low temperature, and room-temperature powder diffraction from aluminium, so we consider this to be a good indication of the true resolution of our ∼1.3 meV spectrometer. The resolution over a wider energy range is self-consistently determined using the temperature, momentum and sample dependence of the measured response. The inelastic contributions from the PMMA and Tempax, and their dependence on momentum transfer and temperature, are then quantitatively investigated. The resulting data allow us to determine the resolution of our multi-analyzer array efficiently using a single scan. The importance of this procedure is demonstrated by showing that the results of the analysis of a spectrum from a glass are changed by using the properly deconvolved resolution function. The impact of radiation damage on the scattering from PMMA and Tempax is also discussed.

Resolution of Inflammation is Disturbed in Macrophages of Diabetic Patients with Acute Ischemic Stroke

Background: Inflammation plays an important role in diabetes mellitus (DM) and its related complications, including atherosclerosis and acute ischemic stroke (AIS). The mechanisms of excessive inflammation in DM are not fully understood. Specialized pro-resolving mediators (SPMs) are key regulators that promote resolution of inflammation. Unbalance of pro-resolving and pro-inflammatory signals may be the key pathogenesis in DM and DM-related diseases. We examined the resolution function in macrophages of DM patients with AIS.Methods: Macrophages were derived from peripheral blood mononuclear cells of AIS and none-AIS patients with or without DM. The cultured macrophages were treated with oxidized low-density lipoprotein. Resolution and inflammatory pathway markers were analyzed in the culture medium and cells. Results: In AIS patients, the ratios of SPMs to leukotriene B4 (LTB4) released by macrophages were decreased in those with DM compared to those without DM. Oxidized low-density lipoprotein treatment further reduced the ratios of SPMs/LTB4 in DM patients with AIS, but such a reduction was not observed in none-DM AIS patients. Analysis of M2/M1 polarization and MAPK/NFkB pathway markers also demonstrated un-resolved inflammation in macrophages of AIS patients with DM. Treatment with one of the SPMs, resolvin D2, rescued the resolution function and ameliorated inflammation in macrophages from these patients.Conclusions: Our data demonstrated that resolution of inflammation is disturbed by DM in macrophages of AIS patients, implicating a novel mechanism of un-resolved inflammation in DM-related vascular disorder. Exogenous SPMs treatment can rescue resolution and downregulate inflammatory signals, and may thus be beneficial in DM-related AIS.

Exact resolution function for double-disk chopper neutron time-of-flight spectrometers: application to reflectivity

The exact resolution function of the transfer vector for the HERMÈS reflectometer at the Laboratoire Léon Brillouin is calculated as an example of a neutron time-of-flight spectrometer with a double-disk chopper. The calculation accounts for the wavelength distribution of the incident beam, the tilt of the chopper axis, collimation and gravity, without an assumption of Gaussian distributions or the independence of these different contributions. A numerical implementation is provided. It is shown that data fitting using this exact resolution function allows much better results to be reached than with the usual approximation by a Gaussian profile.