Pair Density Function Research Articles

Structural Identification and Observation of Dose Rate-Dependent Beam-Induced Structural Changes of Micro- and Nanoplastic Particles by Pair Distribution Function Analysis in the Transmission Electron Microscope (ePDF).

Micro- and nanoplastics (MNPs) are considered a possible threat to microorganisms in the aquatic environment. Here, we show that total scattering intensity analysis of electron diffraction (ED) data measured by transmission electron microscopy, which yields the electron pair distribution function (ePDF), is a feasible method for the characterization and identification of MNPs down to 100 nm. To demonstrate the applicability, cryo ball-milled powders of the most common polymers [i.e., polyethylene , polypropylene, polyethylene terephthalate, and polyamide] and nano-sized polystyrene and silica spheres were used as model systems. The comparison of the experimentally determined reduced pair density functions (RDFs) with model RDFs derived from crystallographic data of the respective polymers allows the distinction of the different types of polymers. Furthermore, carbon-based polymers are highly beam-sensitive materials. The degradation of the samples under the electron beam was analyzed by conducting time-resolved ED measurements. Changes in the material can be visualized by the RDF analysis of the time-series of ED patterns, and information about the materials in question can be gained by this beam damage analysis. Prospectively, ePDF analytics will help to understand and study more precisely the input of MNPs into the environment.

Local structure anomaly with the charge ordering transition of 1T−TaS2

The quasi-two-dimensional $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ displays a unique two-step charge density wave (CDW) transition, from incommensurate (ICDW) to nearly commensurate (NCDW), and from NCDW to commensurate (CCDW), which is reflected in the stepwise resistivity behavior. In this work, we show that the hysteresis observed in the resistivity across the NCDW-to-CCDW transition is coupled to a local structure anomaly, evident from the pair density function analysis of neutron and x-ray diffraction data. We find that upon cycling the system from high to low temperatures (through the NCDW-CCDW transition) and collecting data on warming, local distortions in the in-star Ta and out-of-plane S atoms become evident, disrupting the trigonal symmetry of the star of David structures, without breaking the lattice periodicity, and preserving the underlying $\mathrm{P}\overline{3}$ symmetry. When the system is warmed up from the NCDW to the ICDW state, the local distortions are absent and the stars are symmetric, indicating that it is the thermal cycling through the NCDW-CCDW that locks in the distortions. Furthermore, we verify the temperature dependence of the two types of stacking along the $c$ axis: at low temperatures, the layer stacking exhibits a $13{\mathrm{c}}_{o}$ order that disappears upon warming through the NCDW transition, while across the NCDW and ICDW phases, the layer stacking is $3{\mathrm{c}}_{o}$. The $3{\mathrm{c}}_{o}$ order gradually disappears in the ICDW state.

Investigating the magnetoelastic properties in FeSn and Fe3Sn2 flat band metals

Topological quantum magnets FeSn and Fe$_{3}$Sn$_{2}$ were studied using neutron scattering and first-principles calculations. Both materials are metallic but host dispersionless flat bands with Dirac nodes at the $K$ point in reciprocal space. The local structure determined from the pair density function analysis of the neutron diffraction data provided no evidence for electron localization in both compounds, consistent with their metallic nature. At the same time, in FeSn, an anomalous suppression in the $c$-axis lattice constant coupled with changes in the phonon spectra were observed across T$_{N}$ indicating the presence of magneto-elastic coupling and spin-phonon interactions. In addition, it was observed that spin waves persisted well above T$_{N}$, suggesting that the in-plane ferromagnetic spin correlations survive at high temperatures. In contrast, no lattice anomaly was observed in Fe$_{3}$Sn$_{2}$. The inelastic signal could be mostly accounted for by phonons, determined from density functional theory, showing typical softening on warming.

Study on Sobolev type Hilfer evolution equations with non-instantaneous impulses

In this article, we deal with the existence of mild solutions for a class of Sobolev type Hilfer fractional equation with non-instantaneous impulses in Banach spaces. By mean of an operator family generated by the operator pair and probability density function, the definition of mild solutions for studied problem was given. The main result is obtained by using the techniques of fractional calculus, measure of noncompactness and Sadovskii fixed point theorem. To the end, an example is given to illustrate the abstract results.

Magnon mode transition in real space

Spin excitation of an ilmenite FeTiO3 powder sample is measured by time-of-flight inelastic neutron scattering. The dynamic magnetic pair-density function DM(r, E) is obtained from the dynamic magnetic structure factor SM(Q, E) by the Fourier transformation. The real space spin dynamics exhibit magnon mode transitions in the spin–spin correlation with increasing energy from no-phase-shift to π-phase-shift. The mode transition is well reproduced by a simulation using the reciprocal space magnon dispersions. This analysis provides a novel opportunity to study the local spin dynamics of various magnetic systems.

Out-of-Plane Sulfur Distortions in the Bi4O4S3 Superconductor

The local atomic structure of the non-magnetic layered superconductor Bi4O4S3 was investigated using neutron diffraction and pair density function (PDF) analysis. Although on average, the crystal structure is well ordered, evidence for local, out–of–plane sulfur distortions is provided, which may act as a conduit for charge transfer from the SO4 blocks into the superconducting BiS2 planes. In contrast with LaO1−xFxBiS2, no sulfur distortions were detected in the planes, which indicates that charge density wave fluctuations are not supported in Bi4O4S3.

Bismuth kagome sublattice distortions by quenching and flux pinning in superconducting RbBi2

The properties of ${\mathrm{RbBi}}_{2}$, a 4.15 K superconductor, were investigated using magnetic field, pressure, and neutron diffraction. Under hydrostatic pressure, an almost 50% reduction of ${T}_{c}$ is observed, linked to a low Debye temperature estimated at 165 K. The resistivity and magnetic susceptibility were measured on quenched and slow-cooled polycrystalline samples. The resistivity follows a low temperature power-law dependence in both types of samples, while the diamagnetic susceptibility, $\ensuremath{\chi}$, is dependent on the sample cooling history. Slow-cooled samples have $\ensuremath{\chi}=\ensuremath{-}1$ while quenched samples have $\ensuremath{\chi}<\ensuremath{-}1$ due to grain size differences. Evidence of the effects of the cooling rate is also discerned from the local structure, obtained by neutron diffraction and the pair density function analysis. Slow-cooled samples have structurally symmetric Bi hexagons, in contrast to quenched samples in which disorder is manifested in periodic distortions of the Bi hexagonal rings of the kagome sublattice. Disorder may lead to flux pinning that reduces vortex mobility, but ${T}_{c}$ remains unaffected by the cooling rate.

Structure of the simple harmonic-repulsive system in liquid and glassy states studied by the triple correlation function

An efficient description of the structures of liquids and, in particular, the structural changes that happen with liquids on supercooling remains to be a challenge. The systems composed of soft particles are especially interesting in this context because they often demonstrate non-trivial local orders that do not allow to introduce the concept of the nearest-neighbor shell. For this reason, the use of some methods, developed for the structure analysis of atomic liquids, is questionable for the soft-particle systems. Here we report about our investigations of the structure of the simple harmonic-repulsive liquid in 3D using the triple correlation function (TCF), i.e., the method that does not rely on the nearest neighbor concept. The liquid is considered at reduced pressure (P = 1.8) at which it exhibits remarkable stability against crystallization on cooling. It is demonstrated that the TCF allows addressing the development of the orientational correlations in the structures that do not allow drawing definite conclusions from the studies of the bond-orientational order parameters. Our results demonstrate that the orientational correlations, if measured by the heights of the peaks in the TCF, significantly increase on cooling. This rise in the orientational ordering is not captured properly by the Kirkwood’s superposition approximation. Detailed considerations of the peaks’ shapes in the TCF suggest the existence of a link between the orientational ordering and the slowdown of the system’s dynamics. Our findings support the view that the development of the orientational correlations in liquids may play a significant role in the liquids’ dynamics and that the considerations of the pair distribution function may not be sufficient to understand intuitively all the structural changes that happen with liquids on supercooling. In general, our results demonstrate that the considerations of the TCF are useful in the discussions of the liquid’s structures beyond the pair density function and interpreting the results obtained with the bond-orientational order parameters.

Study on the role of element Mo in improving thermal stability and corrosion resistance of amorphous Ni-P deposit

Amorphous Ni-4.31 wt. % Mo-12.89 wt.% P deposit and amorphous Ni-12.35 wt.% P deposit were produced by electroless deposition. The different structures were obtained by low temperature heat treatment. Effect of element Mo on microstructure evolution, thermal stability and corrosion resistance was studied by XRD and its corresponding pair density function, DSC, electrochemical examination and XPS. Results showed that adding element Mo could improve the thermal stability and amorphous tissues stability of Ni-P deposit. Furthermore, the Ni-Mo-P deposit had better corrosion resistance than the Ni-P deposit because the oxides and compounds formed by adding element Mo could effectively resist the perforation corrosion of chloride ions. The annealed Ni-Mo-P deposits with amorphous structure could form stable passivation films in neutral sodium chloride solution due to the more uniform distribution of oxides and compounds of element Mo.

Local Enhancement of Dynamic Correlation in Excited States: Fresh Perspective on Ionicity and Development of Correlation Density Functional Approximation Based on the On-Top Pair Density.

We discuss the interplay between the nondynamic and dynamic electron correlation in excited states from the perspective of the suppression of dynamic correlation (SDC) and enhancement of dynamic correlation (EDC) effects. We reveal that there exists a connection between the ionic character of a wave function and EDC. Following this finding we introduce a quantitative measure of ionicity based solely on local functions without referring to valence bond models. The ability to recognize both the SDC and EDC regions underlies the presented method, named CASΠDFT, combining complete active space (CAS) wave function and density functional theory (DFT) via the on-top pair density (Π) function. We extend this approach to excited states by devising an improved representation of the EDC effect in the correlation functional. The generalized CASΠDFT uses different DFT functionals for ground and excited states. Numerical demonstration for singlet π → π* excitations shows that CASΠDFT offers satisfactory accuracy at a fraction of the cost of the ab initio approaches.

Microstructure analysis of element W in improving the Ni–P deposit thermal stability

Amorphous Ni–3.81wt.%W–12.40wt.%P deposit showed two crystallization exothermic peaks while amorphous Ni–12.35wt.%P deposit presented one. Formation of the two exothermic peaks and the related influencing factors were investigated through TEM, DSC and XRD. The solid solution and pinning effect of W affected the binding of P and Ni, which induced two crystallization peaks. The variety and quantity of the unstable intermediate phases NixPy played a significant role on modifying exothermic peaks. After annealed the two amorphous deposits, the formation of order clusters was analyzed through the atomic pair density function. The Ni(W) solid solution could promote the formation and growth of order clusters. However, the pinning effect of W prevented the formation of stable crystal phase Ni3P.

Role of tensile elastostatic loading on atomic structure and mechanical properties of Zr55Cu30Ni5Al10 bulk metallic glass

In this work, the pre-tensile elastostatic loading with low stress values (5%–20% σy) was used to rejuvenate Zr55Cu30Ni5Al10 bulk metallic glass (BMG). The atomic pair density function analysis shows that the rejuvenation evolution is accompanied with a significant disordering of short and medium atomic scales in the BMG structure. The results also indicate that the decreasing rate of annihilation in CuZr pairs under rejuvenation is higher than ZrZr and ZrAl pairs. In general, it is suggested that the interaction of stress domains under elastostatic loading is the main reason for disordering during the rejuvenation evolution. The compression test reveals that a brittle-to-ductile transition is happened from as-cast sample to the rejuvenated ones. Moreover, it is found that the serrations in the plastic region of stress-strain curves of highly-rejuvenated samples show a self-organized critical state. As a whole, with increase in pre-tensile elastostatic loading value, the structural rejuvenation enhances and the homogeneous plasticity improves.

Real-Space Description of Dynamics of Liquids

In strongly disordered matter, such as liquids and glasses, atomic and magnetic excitations are heavily damped and partially localized by disorder. Thus, the conventional descriptions in terms of phonons and magnons are inadequate, and we have to consider spatially correlated atomic and spin dynamics in real-space and time. Experimentally this means that the usual representation of dynamics in terms of the dynamic structure factor, S(Q, E), where Q and E are the momentum and energy exchanges in scattering, is insufficient. We propose a real-space description in terms of the dynamic pair-density function (DyPDF) and the Van Hove function (VHF) as an alternative, and discuss recent results on superfluid 4He by inelastic neutron scattering and water by inelastic X-ray scattering. Today much of the objects of research in condensed-matter physics and materials science are highly complex materials. To characterize the dynamics of such complex materials, the real-space approach is likely to become the mainstream method of research.

Short range correlations and the isospin dependence of nuclear correlation functions

Pair densities and associated correlation functions provide a critical tool for introducing many-body correlations into a wide-range of effective theories. Ab initio calculations show that two-nucleon pair-densities exhibit strong spin and isospin dependence. However, such calculations are not available for all nuclei of current interest. We therefore provide a simple model, which involves combining the short and long separation distance behavior using a single blending function, to accurately describe the two-nucleon correlations inherent in existing ab initio calculations. We show that the salient features of the correlation function arise from the features of the two-body short-range nuclear interaction, and that the suppression of the pp and nn pair-densities caused by the Pauli principle is important. Our procedure for obtaining pair-density functions and correlation functions can be applied to heavy nuclei which lack ab initio calculations.

Existence of Mild Solutions for Sobolev-Type Hilfer Fractional Nonautonomous Evolution Equations with Delay

Abstract This paper treats the existence of mild solutions for Sobolev-type Hilfer fractional nonautonomous evolution equations with delay in Banach spaces. We first characterize the definition of mild solutions for the studied problem which was given based on an operator family generated by the operator pair (A,B) and probability density function. And then via Hilfer fractional derivative and combining the techniques of fractional calculus, measure of noncompactness and Sadovskii fixed-point theorem, we obtain new existence result of mild solutions for Sobolev-type Hilfer fractional nonautonomous evolution equations. Particularly, the existence or compactness of an operator B − 1 $B^{-1} $ is not necessarily needed in our results. Furthermore, our results obtained improve and extend some related conclusions on this topic. At last, an example is given to illustrate our main results.

Study on Sobolev type Hilfer fractional integro-differential equations with delay

In this paper, we deal with a class of nonlinear Sobolev type fractional integro-differential equations with delay using Hilfer fractional derivative, which generalized the famous Riemann–Liouville fractional derivative. The definition of mild solutions for studied problem was given based on an operator family generated by the operator pair (A, B) and probability density function. Combining with the techniques of fractional calculus, measure of noncompactness and fixed point theorem, we obtain new existence result of mild solutions with two new characteristic solution operators and the assumptions that the nonlinear term satisfies some growth condition and noncompactness measure condition. The results obtained improve and extend some related conclusions on this topic. At last, an example is given to illustrate our main results.

Local structures of perovskite dielectrics and ferroelectrics via pair distribution function analyses

The pair distribution function (PDF) method provides a useful way of characterizing the diverse and richly complex local structures in perovskite dielectric and ferroelectric materials. This review provides a basic introduction to the PDF method and the underpinning total scattering experiments. Results are reviewed from ex situ PDF that describe composition-dependent local structures and “box-car” fitting approaches to characterize longer range structures and length-scale effects. In situ PDF studies are reviewed that are sensitive to the local structural response of perovskites to temperature, electric field, and pressure. The dynamic pair-density function is also briefly introduced as well as examples of local structure analysis using combined inputs, e.g., extended X-ray absorption fine structure spectroscopy, Raman spectroscopy, and first-principle calculations. These advances in advanced and integrated analysis, dynamics, and in situ methods will enable the PDF method to continue enlightening dielectrics and ferroelectrics research in the coming decades.

Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay

In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative. The definition of mild solutions for the studied problem was given based on an operator family generated by the operator pair (A,B) and probability density function. Combining the techniques of fractional calculus, measure of noncompactness, and fixed point theorem with respect to k-set-contractive, we obtain a new existence result of mild solutions. The results obtained improve and extend some related conclusions on this topic. At last, we present an application that illustrates the abstract results.

Charge Fluctuations in the NdO1−xFxBiS2 Superconductors

The local atomic structure of superconducting NdO$_{1-x}$F$_{x}$BiS$_{2}$ ($x$=0.2 and 0.4) is investigated using neutron diffraction and the pair density function analysis technique. In the non-superconducting $x$=0.2 composition, ferrodistortive displacements of the pyramidal sulfur ions break the tetragonal symmetry and a superlattice structure emerges with peaks appearing at $h+k$ odd reflections superimposed on the even reflections of the $P4/nmm$ symmetry. In the superconducting $x$=0.4 composition, similar ferrodistortive displacements are observed but with different magnitudes coupled with in-plane Bi distortions. The distortions are indicative of charge fluctuations that may lead to charge localization and suppression of superconductivity.

Learning surface molecular structures via machine vision

Recent advances in high resolution scanning transmission electron and scanning probe microscopies have allowed researchers to perform measurements of materials structural parameters and functional properties in real space with a picometre precision. In many technologically relevant atomic and/or molecular systems, however, the information of interest is distributed spatially in a non-uniform manner and may have a complex multi-dimensional nature. One of the critical issues, therefore, lies in being able to accurately identify (‘read out’) all the individual building blocks in different atomic/molecular architectures, as well as more complex patterns that these blocks may form, on a scale of hundreds and thousands of individual atomic/molecular units. Here we employ machine vision to read and recognize complex molecular assemblies on surfaces. Specifically, we combine Markov random field model and convolutional neural networks to classify structural and rotational states of all individual building blocks in molecular assembly on the metallic surface visualized in high-resolution scanning tunneling microscopy measurements. We show how the obtained full decoding of the system allows us to directly construct a pair density function—a centerpiece in analysis of disorder-property relationship paradigm—as well as to analyze spatial correlations between multiple order parameters at the nanoscale, and elucidate reaction pathway involving molecular conformation changes. The method represents a significant shift in our way of analyzing atomic and/or molecular resolved microscopic images and can be applied to variety of other microscopic measurements of structural, electronic, and magnetic orders in different condensed matter systems.