Effects of Voigt diffraction peak profiles on the pair distribution function

Powder diffraction and pair distribution function (PDF) analysis are well established techniques for investigation of atomic configurations in crystalline materials, and the two are related by a Fourier transformation. In diffraction experiments, structural information, such as crystallite size and microstrain, is contained within the peak profile function of the diffraction peaks. However, the effects of the PXRD (powder X-ray diffraction) peak profile function on the PDF are not fully understood. Here, all the effects from a Voigt diffraction peak profile are solved analytically, and verified experimentally through a high-quality X-ray total scattering measurement on Ni powder. The Lorentzian contribution to the microstrain broadening is found to result in Voigt-shaped PDF peaks. Furthermore, it is demonstrated that an improper description of the Voigt shape during model refinement leads to overestimation of the atomic displacement parameter.

An Integrated Software for Computing Mechanical Properties of Crystalline Material by Means of XRD

An integrated software for calculating the major mechanical properties of materials was newly programmed. The material mechanical properties are determined from a peak position and the broadness of X-ray diffraction (XRD) line using profile function method, including Gaussian, Parabola, Half-width, and Centroid. The X-ray diffraction line in software is also corrected by the generalized X-ray absorption function. The results show that the precision coefficient (R2) of the dhkl-sin2 ψ linear regression depends on tested materials and the method of the 2θ determination. The Parabola and Gaussian methods show greater fitting accuracy in comparison to the other two methods in determining stress. The mechanical properties calculated using this software agreed well with the values determined from the conventional methods. In addition, this XRD software also allows computing the 95% confidential limits of the results from a single measurement without conducting repetitive measurements. Therefore, the new software allows widening the experimental scopes of an X-ray diffraction device in both laboratories and the industrial sector.

Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane

In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors based on 5-brane web diagram with O5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web with O5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities.

Analytic baby skyrmions at finite density

We study the baby Skyrme model in (2+1)-dimensions built on a finite cylinder. To this end, we introduce a consistent ansatz which is able to reduce the complete set of field equations to just one equation for the profile function for arbitrary baryon charge. Many analytic solutions both with and without the inclusion of the effects of the minimal coupling with the Maxwell field are constructed. The baby skyrmions appear as a sequence of rings along the cylinder, leading to a periodic shape in the baryon density. Linear stability and other physical properties are discussed. These analytic gauged baby Skyrmions generate a persistent U(1) current which cannot be turned off continuously as it is tied to the topological charge of the baby Skyrmions themselves. In the simplest non-trivial case of a gauged baby Skyrmion, a very important role is played by the Mathieu equation with an effective coupling constant which can be computed explicitly. These configurations are a very suitable arena to test resurgence in a non-integrable context.

Certification of SRM 640f line position and line shape standard for powder diffraction

The National Institute of Standards and Technology (NIST) certifies a suite of Standard Reference Materials (SRMs) to be used to evaluate specific aspects of the instrument performance of both X-ray and neutron powder diffractometers. This report describes SRM 640f, the seventh generation of this powder diffraction SRM, which is designed to be used primarily for calibrating powder diffractometers with respect to line position; it also can be used for the determination of the instrument profile function. It is certified with respect to the lattice parameter and consists of approximately 7.5 g of silicon powder prepared to minimize line broadening. A NIST-built diffractometer, incorporating many advanced design features, was used to certify the lattice parameter of the Si powder. Both statistical and systematic uncertainties have been assigned to yield a certified value for the lattice parameter at 22.5 °C of a = 0.5431144 ± 0.000008 nm.

An Experiment-Based Profile Function for the Calculation of Damage Distribution in Bulk Silicon Induced by a Helium Focused Ion Beam Process

The helium focused ion beam (He-FIB) is widely used in the field of nanostructure fabrication due to its high resolution. Complicated forms of processing damage induced by He-FIB can be observed in substrates, and these damages have a severe impact on nanostructure processing. This study experimentally investigated the influence of the beam energy and ion dose of He-FIB on processing damage. Based on the experimental results, a prediction function for the amorphous damage profile of the single-crystalline silicon substrate caused by incident He-FIB was proposed, and a method for calculating the amorphous damage profile by inputting ion dose and beam energy was established. Based on one set of the amorphous damage profiles, the function coefficients were determined using a genetic algorithm. Experiments on single-crystalline silicon scanned by He-FIB under different process parameters were carried out to validate the model. The proposed experiment-based model can accurately predict the amorphous damage profile induced by He-FIB under a wide range of different ion doses and beam energies.

Roy Glauber and asymptotic diffraction theory

This is a review of Glauber’s asymptotic diffraction theory, in which diffractive scattering is described in terms of interference between semiclassical amplitudes, resulting from a stationary-phase approximation. Typically two such amplitudes are sufficient to accurately describe elastic scattering, but the stationary points are located at complex values of the impact parameter. Their separation controls the interference pattern, and their offsets from the real axis determine the overall fall-off with momentum transfer. Asymptotically, at large momentum transfers, the stationary points move towards singularities of the profile function. I also include some reminiscences from our collaboration.

Analytic time-of-flight positron emission tomography reconstruction: two-dimensional case

In a positron emission tomography (PET) scanner, the time-of-flight (TOF) information gives us rough event position along the line-of-response (LOR). Using the TOF information for PET image reconstruction is able to reduce image noise. The state-of-the-art TOF PET image reconstruction uses iterative algorithms. Analytical image reconstruction algorithm exits for TOF PET which emulates the iterative Landweber algorithm. This paper introduces such an algorithm, focusing on two-dimensional (2D) reconstruction. The proposed algorithm is in the form of backprojection filtering, in which the backprojection is performed first, and then a 2D filter is applied to the backprojected image. For the list-mode data, the backprojection is carried out in the event-by-event fashion, and a profile function may be used along the projection LOR. The 2D filter depends on the TOF timing resolution as well as the backprojection profile function. In order to emulate the iterative algorithm effects, a Fourier-domain window function is suggested. This window function has a parameter, k, which corresponds to the iteration number in an iterative algorithm.

Positive Definiteness on Products of Compact Two-point Homogeneous Spaces and Locally Compact Abelian Groups

In this paper, we consider the problem of characterizing positive definite functions on compact two-point homogeneous spaces cross locally compact abelian groups. For a locally compact abelian group $G$ with dual group $\widehat{G}$, a compact two-point homogeneous space $\mathbb{H}$ with normalized geodesic distance $\unicode[STIX]{x1D6FF}$ and a profile function $\unicode[STIX]{x1D719}:[-1,1]\times G\rightarrow \mathbb{C}$ satisfying certain continuity and integrability assumptions, we show that the positive definiteness of the kernel $((x,u),(y,v))\in (\mathbb{H}\times G)^{2}\mapsto \unicode[STIX]{x1D719}(\cos \unicode[STIX]{x1D6FF}(x,y),uv^{-1})$ is equivalent to the positive definiteness of the Fourier transformed kernels $(x,y)\in \mathbb{H}^{2}\mapsto \widehat{\unicode[STIX]{x1D719}}_{\cos \unicode[STIX]{x1D6FF}(x,y)}(\unicode[STIX]{x1D6FE})$, $\unicode[STIX]{x1D6FE}\in \widehat{G}$, where $\unicode[STIX]{x1D719}_{t}(u)=\unicode[STIX]{x1D719}(t,u)$, $u\in G$. We also provide some results on the strict positive definiteness of the kernel.