Partial Pair Distribution Function Research Articles

Emergence of liquid following laser melting of gold thin films.

X-ray structural science is undergoing a revolution driven by the emergence of X-ray Free-electron Laser (XFEL) facilities. The structures of crystalline solids can now be studied on the picosecond time scale relevant to phonons, atomic vibrations which travel at acoustic velocities. In the work presented here, X-ray diffuse scattering is employed to characterize the time dependence of the liquid phase emerging from femtosecond laser-induced melting of polycrystalline gold thin films using an XFEL. In a previous analysis of Bragg peak profiles, we showed the supersonic disappearance of the solid phase and presented a model of pumped hot electrons carrying energy from the gold surface to scatter at internal grain boundaries. This generates melt fronts propagating relatively slowly into the crystal grains. By conversion of diffuse scattering to a partial X-ray pair distribution function, we demonstrate that it has the characteristic shape obtained by Fourier transformation of the measured F(Q). The diffuse signal fraction increases with a characteristic rise-time of 13 ps, roughly independent of the incident pump fluence and consequent final liquid fraction. This suggests the role of further melt-front nucleation processes beyond grain boundaries.

Effect of preparation conditions on the structure of As-Se glasses: Reverse Monte Carlo simulation

As an extension to part I, Dongol and Elhady (2020), the method of Reverse Monte Carlo simulation has been used to examine the effect of quenching rate on the structure of glassy AsxSe100−x (x=20, 30, 40, 50 at%). Results of the partial structure factors indicate that the correlations responsible for medium range order depend strongly on As-content, and distortion occurs in this structure range with increasing quenching rate. This distortion is more predominant in case of As50Se50 glass. Results of partial pair distribution function show that, most of short range order is mainly governed by the chemically ordered network model, and the random covalent network model plays a relatively small role. Also, it was clarified that the percentage of homopolar bonds increases with increasing quenching rate. In case of x=50at.%, the tendency of As segregation and formation of As–As bonds is demonstrated. Some Deviation from “8-N” rule was observed in the structure of the investigated glasses.

Structural rationale for boson peak in metallic glass informed by an interpretable neural network model

In amorphous solids, there exists a universal phenomenon of vibrational anomaly, i.e., an excess of vibrational modes over the Debye level in the low-terahertz-frequency regime, which is termed a boson peak. Although the origin of the boson peak has been studied extensively for decades, quantitative prediction of its intensity remains elusive. In this paper, we try to quantify the intensity of the boson peak via an interpretable machine-learning strategy based on a dataset consisting of >1600 glass samples prepared with cooling rates spanning four orders of magnitude. We have attempted to extract information from a pure static structure and vibrational localization through four different feature inputs, among which the partial pair distribution function (PDF) yields the best predictive performance. It is found that the first several neighbor shells corresponding to a characteristic subnanometer length scale are important for capturing the structural genes of the boson peak in amorphous solids, regardless of the size of the glasses. Moreover, a higher boson peak relates to a more disordered atomic arrangement with lower peaks and shallower basins in the PDF. The obtained knowledge sheds light on rationalization of the boson peak in amorphous solids from pure structural information.

Estimation of Component Activities and Molar Excess Gibbs Energy of 19 Binary Liquid Alloys from Partial Pair Distribution Functions in Literature

This work proposes a new method for estimating the molar excess Gibbs energy and activity of liquid alloy based on recent research. The local composition theory provides a connection between the structures of liquid alloys and the thermodynamic models. The partial pair distribution function (PPDF) was utilized to calculate the parameters of the MIVM, RSM, Wilson, and NRTL. The statistics of the number of molecular pairs of MIVM and RSM were rewritten, which resulted in new forms of the two models. To enhance the NRTL’s estimation performance, the coordination number was incorporated into it (M-NRTL). The aforementioned model and Quasi-chemical model (QCM) were utilized to estimate the excess Gibbs energy and activity of 19 alloys. The alloys contained multiple sets of PPDFs, which enabled the calculation of multiple sets of model parameters. The work examined the impact of expressing the model parameters as first-order linear functions of the components or as constants on the accuracy of the estimation. The parameters were treated as constants. MIVM, RSM, and M-NRTL provided an average relative deviation (ARD) of activity of less than ±20% for 15, 10, and 9 alloys by estimation. When model parameters were expressed as a function of components, QCM showed the best estimation performance, having nine alloys with an ARD of less than ±20%. The number of alloys with an ARD of less than ±20% corresponding to MIVM, RSM, Wilson, NRTL, and M-NRTL was six, five, three, five, and two, respectively. This new method offers simplicity, numerical calculation stability, and excellent reproducibility.

Special quasirandom structures description of the local structure of disordered Bi0.5K0.5TiO3

Polar nanoregions (PNRs) are believed to play a decisive role in the local and macroscopic polarization in relaxor ferroelectrics. The limited microscopic understanding of the structure and dynamics of PNRs hampers the rational design of new lead-free materials. Here, the local structure of A-site disordered Bi0.5K0.5TiO3 (BKT) is investigated using synchrotron x-ray and neutron pair distribution function (PDF) analysis and density functional theory (DFT) optimized special quasirandom structures (SQSs). DFT-relaxed SQS with a 4 × 4 × 4 supercell size can reproduce the experimental PDFs of disordered BKT, as well as the partial PDFs and total polarization, with comparable results to those reported from a combined analysis of x-ray and neutron PDF data with large-box reverse Monte Carlo methods. We find that small Bi3+-rich polar clusters are likely to be the microscopic origin of relaxor behavior in disordered BKT, and that the existence of large polar nanoregions (PNRs) is not necessary to explain the relaxor properties. Our results also highlight the great potential of the SQS approach to gain a nanoscale-to-microscopic understanding of other relaxor solid solutions.

Atomic structure of Cu60Ti20Zr20 metallic glass under high pressures

During the rapid cooling process, the atomic structure of the Cu60Ti20Zr20 ternary alloy under external pressure was investigated by molecular dynamics simulations using the embedded atom method potential. The effect of the pressure was discussed in detail by using a variety of analysis methods. Glass transition temperature determined by the modified Wendt-Abraham parameter was found to increase with increasing pressure. It was observed that the calculated total (or partial) pair distribution function and structure factor are in good agreement with the experimental x-ray data (with the ab-initio molecular dynamics results). The bond angle distributions of Cu-centered triplets were more consistent with ideal icosahedral clusters than that of Ti- and Zr-centered triplets. The dominant clusters for all pressures were icosahedral-like clusters that were not much affected by pressure. In addition to the bonds between Cu–Zr pairs shortening more easily under high pressure than other pairs, it is found that the Cu60Ti20Zr20 glassy alloy remained stable under pressure and its topological and atomic structures did not change much with pressure.

X-ray scattering study of water confined in bioactive glasses: experimental and simulated pair distribution function.

Temperature-dependent total X-ray scattering measurements for water confined in bioactive glass samples with 5.9 nm pore diameter have been performed. Based on these experimental data, simulations were carried out using the Empirical Potential Structure Refinement (EPSR) code, in order to study the structural organization of the confined water in detail. The results indicate a non-homogeneous structure for water inside the pore, with three different structural organizations of water, depending on the distance from the pore surface: (i) a first layer (4 Å) of interfacial pore water that forms a strong chemical bond with the substrate, (ii) intermediate pore water forming a second layer (4-11 Å) on top of the interfacial pore water, (iii) bulk-like pore water in the centre of the pores. Analysis of the simulated site-site partial pair distribution function shows that the water-silica (Ow-Si) pair correlations occur at ∼3.75 Å. The tetrahedral network of bulk water with oxygen-oxygen (Ow-Ow) hydrogen-bonded pair correlations at ∼2.8, ∼4.1 and ∼4.5 Å is strongly distorted for the interfacial pore water while the second neighbour pair correlations are observed at ∼4.0 and ∼4.9 Å. For the interfacial pore water, an additional Ow-Ow pair correlation appears at ∼3.3 Å, which is likely caused by distortions due to the interactions of the water molecules with the silica at the pore surface.

Three-Dimensional Imaging of a Single Dopant in a Crystal

Single dopants in materials have strong influences on the fundamental properties in extensive fields. Annular dark-field scanning tranmission electron microscopy (ADF STEM) has been contributed to directly investigate the occupation site of single dopants and their spatial distributions at atomic scale. However, the resultant atomic resolution images are projected in two dimensions, lacking in depth information. Here, we demonstrate the direct determination of three-dimensional atomic locations of single $\mathrm{Ce}$ dopants embedded in cubic boron nitride by ADF STEM depth sectioning with a significantly large illumination angle of 63 mrad in semiangle. Furthermore, we directly evaluate the $\mathrm{Ce}$-$\mathrm{Ce}$ partial pair distribution function in the considerably long distance up to 8.5 nm, which opens the way to study a far-long-range interaction between impurities especially in a dilute doping system.

An experimental and theoretical investigation on relaxor behavior and local correlations in xBi(Zn0.5Ti0.5)O3-(1-x)BaTiO3 ceramics

Relaxor behavior and local correlations in perovskite structured xBi(Zn0.5Ti0.5)O3-(1-x)BaTiO3 (xBZT-(1-x)BT,0.30 ≥x ≥ 0.10) ceramics are investigated by both experimental and theoretical Ab initio molecular dynamics calculations. For 0.30 ≥x ≥ 0.10, xBZT-(1-x)BT ceramics show typical relaxor behavior. For x ≥ 0.20, the J-E loops show “whale” shape and no saturated P-E loops are observed even near the polar nanoregions (PNRs) freezing temperature Tf (135 K–146 K), indicating that long range polar order (ferroelectric domian) does not exist in these samples, and the PNRs locate at nonergodic state with temperature decreasing. The partial pair distribution function (PDF) results show that Bi atoms are very sensitive to the local B site occupancy and have pronounced trend to displace toward neighboring Zn atoms. The Bi-Zn displacement coupling will enhance the local polarization and stabilize the PNRs even at higher temperature. The dipole correlation function (DCF) results show that the Bi dipoles only correlate with their nearest Ti neighbors and the polarization correlation with the second-nearest Ti neighbors is negligible. No existence of long range polar order in xBZT-(1-x)BT (x ≥ 0.20) can be attributed to the Bi displacement influenced highly by the random distribution of Zn atoms and the dominated Bi-Ti dipole correlations only existing within the nearest Bi-Ti neighbors.

The prediction of upper limit of copper content in CoBCu glass-forming alloys

The soft magnetic properties of ferromagnetic nanocrystalline alloys can be enhanced considerably by addition of copper until the upper limit of Cu content which is unknown at present. This study explored the upper limit of Cu content in the Co81−XB19CuX (X = 2, 3 and 5) alloy system using ab initio molecular dynamics simulations and experiments. It was found that when the Cu content rose above 2 at%, the first-nearest-neighbor peaks of partial pair distribution function for Cu-Cu pair became stronger steadily with the decreasing temperature, demonstrating that Cu clusters were formed during the quenching processes from initial melt. As to the Cu content was less than or equal to 2 at%, the trace of such clusters was difficult to find. So the maximal Cu content in Co81−XB19CuX alloys in as-quenched amorphous state was predicted to be less than 2 at%. Co81−XB19CuX ribbons were prepared using the melt-spinning technique with as large cooling ability as possible. Structure analysis results from X-ray diffraction patterns of the three as-quenched alloys supported the above theoretical predictions. These results would provide a theoretical reference for the design of ferromagnetic nanocrystalline alloys.

Structure of semiconducting versus fast-ion conducting glasses in the Ag-Ge-Se system.

The transition from a semiconductor to a fast-ion conductor with increasing silver content along the Agx(Ge0.25Se0.75)(100−x) tie line (0≤x≤25) was investigated on multiple length scales by employing a combination of electric force microscopy, X-ray diffraction, and neutron diffraction. The microscopy results show separation into silver-rich and silver-poor phases, where the Ag-rich phase percolates at the onset of fast-ion conductivity. The method of neutron diffraction with Ag isotope substitution was applied to the x=5 and x=25 compositions, and the results indicate an evolution in structure of the Ag-rich phase with change of composition. The Ag–Se nearest-neighbours are distributed about a distance of 2.64(1) Å, and the Ag–Se coordination number increases from 2.6(3) at x=5 to 3.3(2) at x=25. For x=25, the measured Ag–Ag partial pair-distribution function gives 1.9(2) Ag–Ag nearest-neighbours at a distance of 3.02(2) Å. The results show breakage of Se–Se homopolar bonds as silver is added to the Ge0.25Se0.75 base glass, and the limit of glass-formation at x≃28 coincides with an elimination of these bonds. A model is proposed for tracking the breakage of Se–Se homopolar bonds as silver is added to the base glass.

The Structure of Liquid and Amorphous Hafnia.

Understanding the atomic structure of amorphous solids is important in predicting and tuning their macroscopic behavior. Here, we use a combination of high-energy X-ray diffraction, neutron diffraction, and molecular dynamics simulations to benchmark the atomic interactions in the high temperature stable liquid and low-density amorphous solid states of hafnia. The diffraction results reveal an average Hf–O coordination number of ~7 exists in both the liquid and amorphous nanoparticle forms studied. The measured pair distribution functions are compared to those generated from several simulation models in the literature. We have also performed ab initio and classical molecular dynamics simulations that show density has a strong effect on the polyhedral connectivity. The liquid shows a broad distribution of Hf–Hf interactions, while the formation of low-density amorphous nanoclusters can reproduce the sharp split peak in the Hf–Hf partial pair distribution function observed in experiment. The agglomeration of amorphous nanoparticles condensed from the gas phase is associated with the formation of both edge-sharing and corner-sharing HfO6,7 polyhedra resembling that observed in the monoclinic phase.

Structure of liquid tricalcium aluminate

The atomic-scale structure of aerodynamically levitated and laser-heated liquid tricalcium aluminate (${\mathrm{Ca}}_{3}{\mathrm{Al}}_{2}{\mathrm{O}}_{6}$) was measured at 2073(30) K by using the method of neutron diffraction with Ca isotope substitution (NDIS). The results enable the detailed resolution of the local coordination environment around calcium and aluminum atoms, including the direct determination of the liquid partial structure factor, ${S}_{\mathrm{CaCa}}(Q)$, and partial pair distribution function, ${g}_{\mathrm{CaCa}}(r)$. Molecular dynamics (MD) simulation and reverse Monte Carlo (RMC) refinement methods were employed to obtain a detailed atomistic model of the liquid structure. The composition ${\mathrm{Ca}}_{3}{\mathrm{Al}}_{2}{\mathrm{O}}_{6}$ lies at the CaO-rich limit of the CaO:${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ glass-forming system. Our results show that, although significantly depolymerized, liquid ${\mathrm{Ca}}_{3}{\mathrm{Al}}_{2}{\mathrm{O}}_{6}$ is largely composed of ${\mathrm{AlO}}_{4}$ tetrahedra forming an infinite network with a slightly higher fraction of bridging oxygen atoms than expected for the composition. Calcium-centered polyhedra exhibit a wide distribution of four- to sevenfold coordinated sites, with higher coordinated calcium preferentially bonding to bridging oxygens. Analysis of the MD configuration reveals the presence of $\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}%$ unconnected ${\mathrm{AlO}}_{4}$ monomers and ${\mathrm{Al}}_{2}{\mathrm{O}}_{7}$ dimers in the liquid. As the CaO concentration increases, the number of these isolated units increases, such that the upper value for the glass-forming composition of CaO:${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ liquids could be described in terms of a percolation threshold at which the glass can no longer support the formation of an infinitely connected ${\mathrm{AlO}}_{4}$ network.

Partial pair correlation functions and viscosity of liquid Al–Si hypoeutectic alloys via high-energy X-ray diffraction experiments

The liquid structure of Al–Si hypoeutectic binary alloys was characterized by diffraction experiments using a high-energy X-ray (synchrotron) beam source. The diffraction experiments were carried out for liquid pure Al, Al–3 wt% Si, Al–7 wt% Si, Al–10 wt% Si and Al–12.5 wt% Si alloys at several temperatures. The salient structure information such as structure factor (SF), pair distribution function (PDF), radial distribution function (RDF), coordination number (CN) and atomic packing densities (PD) were quantified as a function of Si concentration and melt temperatures. Reverse Monte Carlo (RMC) analysis was carried out using the diffraction experimental data to quantify the partial pair correlation functions, such as partial structure factor, partial pair distribution function (PPDF) and partial radial distribution function. Furthermore, the partial pair distribution function and the liquid atomic structure information were used in a semi-empirical model to evaluate the viscosity of these liquid alloys at various melt temperatures. The results show that the viscosity determined by semi-empirical methods using the atomic structure information is in good agreement with the experimentally determined viscosity values.

Liquid Atomic Structure and Viscosity of Al-Si Alloys with and without Sr

The liquid structure of Al-Si hypoeutectic binary alloys with and without the addition of 0.04 wt.% Sr was characterized by diffraction experiments using a high energy X-Ray (Synchrotron) beam source. The diffraction data for all the alloys were obtained at various melt temperatures. Reverse Monte Carlo (RMC) analysis was carried out using the diffraction experimental data to quantify the partial pair distribution function (PPDF). Further, the partial pair distribution function and the liquid atomic structure information were used in a semi empirical model to evaluate the viscosity of these liquid alloys at various temperatures.

A molecular dynamics study of structural and dynamical correlations of CaTiO3

An effective interatomic potential which can be used to describe perovskite-type CaTiO3 in molecular dynamics (MD) simulations is proposed. The potential proposed consists of two-body interactions, which include steric repulsions due to atomic sizes, Coulomb interactions resulting from charge transfer between particles, and charge-induced dipole interactions due to the electronic polarizability of ions and dipole–dipole (van der Waals) attraction. The energetics of the three crystalline forms of CaTiO3 were calculated: the orthorhombic-Pbnm structure had the lowest energy, followed by the tetragonal-I4/mcm and cubic-Pm3m structures. The two phase transitions induced by temperature change were characterized through anomalies in the lattice parameters, elastic constants, bulk modulus, bond-angle distribution and the intensity of the first peak of the partial pair distribution function, gCa–O(r). Analysis of the pair distribution function is a sensitive means of detecting structural transformation in materials caused by small distortions. It is shown that the rise in structural symmetry with temperature is actually due to the tilting of the TiO6 polyhedra. The response of the system to external pressure was also analyzed. Extremely high pressure, up to 300GPa, was applied and no significant modification attributable to a major structural change was observed. The proposed interatomic potential is in good agreement with experimental data, predicting the melting point, phonon vibrational density of sates, thermal expansion coefficient and specific heat at constant volume. The recrystallized polycrystalline CaTiO3 was reproduced in the simulation by cooling the liquid. It is shown that the presence of grain boundaries in the material is essential to reproduce the experimental data correctly.

Anomalous aggregation state of deuterium molecules in the nanoscale pores of a metal organic framework

The behavior of hydrogen molecules adsorbed onto the nanospace of porous materials is of great interest but is poorly understood. Here we show direct visualization of deuterium molecules adsorbed on isoreticular metal organic frameworks (IRMOF-1) at 77 K using reverse Monte Carlo simulation based on first principle molecular dynamics simulation and neutron diffraction. Results show that the two types of adsorption sites around a ZnO4 cluster are almost fully occupied by the deuterium molecules but that other sites are not fully occupied. Moreover an interesting information about the aggregation state of deuterium molecules was directly obtained from the deuterium–deuterium partial pair distribution function. Namely, the average distance of deuterium molecules adsorbed onto IRMOF-1 is slightly longer than that in a solid state but much shorter than that in the corresponding gas state.

Partial structures in molten AgBr

The structure of molten AgBr has been studied by means of neutron and X-ray diffractions with the aid of structural modeling. It is confirmed that the Ag–Ag correlation has a small but well-defined first peak in the partial pair distribution function whose tail penetrates into the Ag–Br nearest neighbor distribution. This feature on the Ag–Ag correlation is intermediate between that of molten AgCl (non-superionic melt) and that of molten AgI (superionic melt). The analysis of Br–Ag–Br bond angle reveals that molten AgBr preserves a rocksalt type local ordering in the solid phase, suggesting that molten AgBr is clarified as non-superionic melt like molten AgCl.

Simultaneous reverse Monte Carlo refinements of local structures in perovskite solid solutions using EXAFS and the total scattering pair-distribution function

Reverse Monte Carlo (RMC) refinements using a combined real-space fit of the neutron/X-ray total scattering pair-distribution function (PDF) and the extended X-ray absorption fine structure (EXAFS) were developed and implemented as an extension to the public domain computer softwareRMCProfile. The effectiveness of combined PDF/EXAFS RMC refinements was tested using perovskite Ca(Zr,Ti)O3solid solutions. The analyses revealed that combining two types of data yields correct distributions of the Ti—O and Zr—O distances that could not be recovered using either of the techniques alone because of the substantial overlap between the Ti—O and Zr—O partial PDFs. The combined refinements enabled reasonably accurate reproduction of most of the local structure characteristics, including the dependence of Ca displacements on the localB-cation coordination around Ca.

Local structure in Ag3[Co(CN)6]: colossal thermal expansion, rigid unit modes and argentophilic interactions

Local structure in the colossal thermal expansion materialAg3[Co(CN)6] isstudied here using a combination of neutron total scattering and reverse Monte Carlo (RMC) analysis.We show that the large thermal variations in cell dimensions occur with minimal distortion of the[Co(CN)6 ] coordination polyhedra, but involve significant flexing of the Co–CN–Ag–NC–Co linkages.We find real-space evidence in our RMC configurations for the importance oflow-energy rigid unit modes (RUMs), particularly at temperatures below 150 K.Using a reciprocal-space analysis we present the phonon density of statesat 300 K and show that the lowest-frequency region is dominated by RUMsand related modes. We also show that thermal variation in the energies ofAg...Ag interactions is evident in both the Ag partial pair distribution function and in the Agpartial phonon density of states. These findings are discussed in relation to thethermodynamic properties of the material.