Extended-range Order Research Articles

Effect of thickness and noise on angular correlation analysis from scanning electron nanobeam diffraction of disordered carbon

Disordered carbons are of significant scientific and industrial interest for modern applications. To understand the differences in the performance of disordered carbons, it is crucial to elucidate their structure, but this is challenging due to the variation and complexity of structures they can possess: for example, different hybridizations of the carbon atoms, and significant extended-range order composed of connected rings, curved sheets and stacks. This study establishes the useful information that can be obtained from angular correlation analysis of scanning electron nanobeam diffraction patterns for disordered carbons and other materials with extended-range order. The effects of sample thickness and experimental noise are investigated, showing that it is crucial to consider their impact when interpreting the results. Furthermore, opportunities for analyzing different ranges of scattering angles are explored, for example, to access structural information about the intralayer structure of disordered carbons. These approaches could be used to access novel quantitative measures to probe the structural differences of disordered carbons and understand their properties.

Dynamics of the extended and intermediate range order in model polymer electrolyte poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl)imide

The dynamics of lithium ions and polymer chains were investigated at the molecular scale in the model polymer electrolyte Poly (ethylene oxide) (PEO)/Lithium bis(trifluoromethanesulfonyl)imide as a function of temperature. This system is known to present an intermediate range order from the arrangement of neighboring chain segments as well as an extended range order of cylindrically arranged chains. The collective dynamics of the systems at lengthscales matching these structural features was measured using Neutron Spin Echo spectroscopy, gaining insights into their lifetime. Moreover, using isotope substitution techniques the dynamics of the lithium ions with respect to the other atoms was probed. The obtained results are compared with the conductivity and the lithium self-diffusion coefficient measured by NMR to gain experimental insight on the molecular processes triggering lithium transport.

Extended-range order in tetrahedral amorphous semiconductors: The case of amorphous silicon

This paper reports the presence of extended-range ordering in the atomic pair-correlation function of amorphous silicon ($a$-Si) using ultra-large atomistic models obtained from Monte Carlo and molecular-dynamics simulations. The extended-range order manifests itself in the form of radial oscillations, on the length scale of 20-40 angstrom, which are examined by directly analyzing the radial distribution of atoms in distant coordination shells and comparing the same with those from a class of partially-ordered networks of Si atoms and disordered configurations of crystalline silicon from an information-theoretic point of view. The study suggests that the extended-range radial oscillations principally originate from the propagation of radial ordering from the first few atomic shells to a distance of up to 40 angstrom. The effect of these oscillations on the first sharp diffraction peak (FSDP) in the structure factor is addressed by obtaining a semi-analytical expression for the static structure factor of $a$-Si, and calculating an estimate of the error of the intensity of the FSDP associated with the truncation of radial information from distant shells. The results indicate that the extended-range oscillations do not have any noticeable effects on the position and intensity of the FSDP, which are primarily determined by the medium-range atomic correlations of up to a length of 20 angstrom in amorphous silicon.

High-Energy Mechanical Milling-Driven Reamorphization in Glassy Arsenic Monoselenide: On the Path of Tailoring Special Molecular-Network Glasses.

The impact of high-energy milling on glassy arsenic monoselenide g-AsSe is studied with X-ray diffraction applied to diffuse peak-halos proper to intermediate- and extended-range ordering revealed in first and second sharp diffraction peaks (FSDP and SSDP). A straightforward interpretation of this effect is developed within the modified microcrystalline approach, treating “amorphous” halos as a superposition of the broadened Bragg diffraction reflexes from remnants of some inter-planar correlations, supplemented by the Ehrenfest diffraction reflexes from most prominent inter-molecular and inter-atomic correlations belonging to these quasi-crystalline remnants. Under nanomilling, the cage-like As4Se4 molecules are merely destroyed in g-AsSe, facilitating a more polymerized chain-like network. The effect of nanomilling-driven molecular-to-network reamorphization results in a fragmentation impact on the correlation length of FSDP-responsible entities (due to an increase in the FSDP width and position). A breakdown in intermediate-range ordering is accompanied by changes in extended-range ordering due to the high-angular shift and broadening of the SSDP. A breakdown in the intermediate-range order is revealed in the destruction of most distant inter-atomic correlations, which belong to remnants of some quasi-crystalline planes, whereas the longer correlations dominate in the extended-range order. The microstructure scenarios of milling-driven reamorphization originated from the As4Se4 molecule, and its network derivatives are identified with an ab initio quantum-chemical cluster modeling code (CINCA).

Structure of basaltic glass at pressures up to 18 GPa

Abstract The structures of cold-compressed basaltic glass were investigated at pressures up to 18 GPa using in situ X-ray and neutron diffraction techniques to understand the physicochemical properties of deep magmas. On compression, basaltic glass changes its compression behavior: the mean O-O coordination number (CNOO) starts to rise while maintaining the mean O-O distance (rOO) above about 2–4 GPa, and then CNOO stops increasing, and rOO begins to shrink along with the increase in the mean coordination number of Al (CNAlO) above ~9 GPa. The change around 9 GPa is interpreted by the change in contraction mechanism from bending tetrahedral networks of glass to increasing oxygen packing ratio via the increase in CNAlO. The analysis of the oxygen packing fraction (ηO) under high pressure reveals that ηO exceeds the value for dense random packing, suggesting that the oxygen-packing hypothesis recently proposed cannot account for pressure-induced structural transformations of silica and silicate glasses. The rise of the CNOO at 2–4 GPa reflects the elastic softening of fourfold-coordinated silicate glass, which may be the origin of anomalies of elastic moduli in basaltic glass at ~2 GPa previously reported by Liu and Lin (2014). The widths of both the first sharp diffraction peak and the principal peak show contrastive compression behaviors between modified silicate and silica glasses. This result suggests that modified silicate glasses represent different pressure evolutions in the intermediate- and extended-range order structures from those of silica glass, likely due to the presence of modifier cations and the resultant formations of smaller rings and cavity volume.

Network-Forming Liquids from Metal-Bis(acetamide) Frameworks with Low Melting Temperatures.

Molten phases of metal-organic networks offer exciting opportunities for using coordination chemistry principles to access liquids and glasses with unique and tunable structures and properties. Here, we discuss general thermodynamic strategies to provide an increased enthalpic and entropic driving force for reversible, low-temperature melting transitions in extended coordination solids and illustrate this approach through a systematic study of a series of bis(acetamide)-based networks with record-low melting temperatures. The low melting temperatures of these compounds are the result of weak coordination bonds, conformationally flexible bridging ligands, and weak electrostatic interactions between spatially separated cations and anions, which collectively reduce the enthalpy and increase the entropy of fusion. Through a combination of crystallography, spectroscopy, and calorimetry, enthalpic trends are found to be dictated by the strength of coordination bonds and hydrogen bonds within each compound, while entropic trends are strongly influenced by the degree to which residual motion and positional disorder are restricted in the crystalline state. Extended X-ray absorption fine structure (EXAFS) and pair distribution function (PDF) analysis of Co(bba)3[CoCl4] [bba = N,N'-1,4-butylenebis(acetamide)], which features a record-low melting temperature for a three-dimensional metal-organic network of 124 °C, provide direct evidence of metal-ligand coordination in the liquid phase, as well as intermediate- and extended-range order that support its network-forming nature. In addition, rheological measurements are used to rationalize differences in glass-forming ability and relaxation dynamics. These results provide new insights into the structural and chemical factors that influence the thermodynamics of melting transitions of extended coordination solids, as well as the structure and properties of coordination network-forming liquids.

Structural crossover in a supercooled metallic liquid and the link to a liquid-to-liquid phase transition

Time-resolved synchrotron measurements were carried out to capture the structure evolution of an electrostatically levitated metallic-glass-forming liquid during free cooling. The experimental data shows a crossover in the liquid structure at ∼1000 K, about 115 K below the melting temperature and 150 K above the crystallization temperature. The structure change is characterized by a dramatic growth in the extended-range order below the crossover temperature. Molecular dynamics simulations have identified that the growth of the extended-range order was due to an increased correlation between solute atoms. These results provide structural evidence for a liquid-to-liquid-phase-transition in the supercooled metallic liquid.

Disentangling Neighbors and Extended Range Density Oscillations in Monatomic Amorphous Semiconductors

High energy x-ray diffraction measurements of pure amorphous Ge were made and its radial distribution function (RDF) was determined at high resolution, revealing new information on the atomic structure of amorphous semiconductors. Fine structure in the second peak in the RDF provides evidence that a fraction of third neighbors are closer than some second neighbors; taking this into account leads to a narrow distribution of tetrahedral bond angles, (8.5 ± 0.1)°. A small peak which appears near 5 Å upon thermal annealing shows that some ordering in the dihedral bond-angle distribution takes place during structural relaxation. Extended range order is detected (in both a-Ge and a-Si) which persists to beyond 20 Å, and both the periodicity and its decay length increase upon thermal annealing. Previously, the effect of structural relaxation was only detected at intermediate range, involving reduced tetrahedral bond-angle distortions. These results enhance our understanding of the atomic order in continuous random networks and place significantly more stringent requirements on computer models intending to describe these networks, or their alternatives which attempt to describe the structure in terms of an arrangement of paracrystals.

Local structural motifs and extended-range order in liquid and solid ammonia under pressure

Neutron-diffraction measurements of the local structure in deuterated ammonia have been conducted up to pressures of 2.1 GPa at ambient temperature. Total pair-distribution functions, determined by Fourier analysis of the static structure factor, are used to examine the structural changes from the first neighbors to extended ranges of $\ensuremath{\sim}$30 $\AA{}$ in both the liquid and solid state. In the proton-disordered crystalline phase III, the first coordination shell is almost identical to that of the higher-pressure, ordered phase IV. The H-bond correlation is observed as a distinct shoulder at 2.5 $\AA{}$. A similar local structure is seen in the liquid at a pressure just below freezing, and, in particular, a pronounced H-bond correlation is observed in the liquid across the pressure range studied. A substantial increase in the ordering length scale of the liquid is observed at high pressure with correlations extending to at least 25 $\AA{}$ compared to $\ensuremath{\sim}$12 $\AA{}$ at ambient. The decay of the primary oscillations in the extended range is exponential and well described by a simple-liquid model, implying that, despite persistent H bonding, packing considerations become the dominant structural driver as density increases.

Structural Changes in Vitreous GeSe4 under Pressure

High-energy X-ray diffraction experiments have been performed on GeSe{sub 4} glass up to pressures of 8.6 GPa, and the equation of state has been measured up to 10 GPa. The X-ray structure factors reveal a decrease in the first sharp diffraction peak intensity and broadening with pressure, which signifies a break-up of the intermediate range order in the glass. In contrast, the principal peak in the structure factor shows an increase in intensity and a sharpening with pressure, which is attributed to an increase in extended range order and coherence of the compacted units. The average nearest neighbor coordination number is found to remain constant in GeSe{sub 4} glass (within experimental error) over the pressure range measured. This is in contrast with the gradual increase found in GeSe{sub 2} glass. Rather, in GeSe{sub 4} glass the densification mechanism is shown to be associated with large inward shifts of the second neighbor and higher coordination shells. These features appear as additional correlations at 3.3 and 5.3 {angstrom} in the differences taken between adjacent pair distribution functions with increasing pressure.

Icosahedral medium-range orders and backbone formation in an amorphous alloy

Analyses of metallic amorphous solids constructed using molecular dynamics (MD) simulations have demonstrated that individual short-range orders (SROs) are linked with neighboring SROs and form various medium-range orders (MROs). These MROs have been observed to have different structural stability depending on their linking patterns. On the basis of the assessment of the structural stability of various MROs, we propose new types of structural organization, namely, icosahedral medium-range orders (I-MROs) and their extended-range order that forms the backbone of amorphous solids. We also discuss why the atomic-scale structure of an amorphous alloy can be more appropriately described in terms of I-MROs, rather than by the degree of short-range ordering as characterized by the fractions of SROs.

Structure of glassy GeO2

The full set of partial structure factors for glassy germania, orGeO2, were accurately measured by using the method of isotopic substitution inneutron diffraction in order to elucidate the nature of the pair correlations forthis archetypal strong glass former. The results show that the basic tetrahedralGe(O1/2)4 building blocks share corners with a mean inter-tetrahedral Ge–Ô–Ge bond angle of132(2)°. The topological and chemical ordering in the resultant network displays two characteristiclength scales at distances greater than the nearest neighbour. One of these describesthe intermediate range order, and manifests itself by the appearance of a firstsharp diffraction peak in the measured diffraction patterns at a scattering vectorkFSDP≈1.53 Å−1,while the other describes so-called extended range order, and is associated with the principal peakat kPP = 2.66(1) Å−1. We find that there is an interplay between the relative importance of the ordering on theselength scales for tetrahedral network forming glasses that is dominated by the extended rangeordering with increasing glass fragility. The measured partial structure factors for glassyGeO2 are used to reproduce the total structure factor measured by using high energy x-raydiffraction and the experimental results are also compared to those obtained by usingclassical and first principles molecular dynamics simulations.

Molecular dynamics simulation of polymer electrolytes based on poly(ethylene oxide) and ionic liquids. I. Structural properties

Molecular dynamics (MD) simulations have been performed for prototype models of polymer electrolytes in which the salt is an ionic liquid based on 1-alkyl-3-methylimidazolium cations and the polymer is poly(ethylene oxide), PEO. The MD simulations were performed by combining the previously proposed models for pure ionic liquids and polymer electrolytes containing simple inorganic ions. A systematic investigation of ionic liquid concentration, temperature, and the 1-alkyl- chain length, [1,3-dimethylimidazolium]PF6, and [1-butyl-3-methylimidazolium]PF6, effects on resulting equilibrium structure is provided. It is shown that the ionic liquid is dispersed in the polymeric matrix, but ionic pairs remain in the polymer electrolyte. Imidazolium cations are coordinated by both the anions and the oxygen atoms of PEO chains. Probability density maps of occurrences of nearest neighbors around imidazolium cations give a detailed physical picture of the environment experienced by cations. Conformational changes on PEO chains upon addition of the ionic liquid are identified. The equilibrium structure of simulated systems is also analyzed in reciprocal space by using the static structure factor, S(k). Calculated S(k) display a low wave-vector peak, indicating that spatial correlation in an extended-range order prevail in the ionic liquid polymer electrolytes. Long-range correlations are assigned to nonuniform distribution of ionic species within the simulation box.

Molecular dynamics simulation of the polymer electrolyte poly(ethyleneoxide)∕LiClO4. I. Structural properties

Molecular dynamics (MD) simulations of poly(ethylene oxide) (PEO)∕LiClO4 polymer electrolyte have been performed for three different salt concentrations (oxygen atoms of polymer to Li+ cations ratio of 31:1, 16:1, and 8:1) and two temperatures (373 and 500K). A united atom model, in which hydrogen atoms are not considered, has been used for PEO. The PEO model has been validated by comparing the static structure factor S(k) calculated by MD simulations of pure PEO at 363K (32 PEO chains with a molecular weight of 1174) with previous experimental data obtained by neutron scattering spectroscopy. A low wave-vector peak develops in the calculated S(k) when LiClO4 is added in the polymeric matrix, which indicates an extended-range order in PEO∕LiClO4 melts. Contact ionic pairs are observed, which are favored as temperature increases. PEO chain as a whole becomes less extended (smaller radius of gyration) upon addition of LiClO4. Radius of gyration increases with temperature at low salt concentration, but it is only marginally affected by temperature at high concentration.

Structure of liquid PEO-LiTFSI electrolyte

The structure of a polymer electrolyte, P(EO)7.5LiN(SO 2CF (3))(2), has been determined by neutron diffraction with isotropic substitution. The Li ions are bonded on average to five ether oxygens belonging to pairs of PEO coils. These are arranged with a considerable degree of extended-range order providing pathways for the Li ion conduction. The lack of ion pairing in this system below 4.8 A is reminiscent of that observed in the remarkable structure of P(EO)6LiAsF (6) and implies that anions and cations are free to migrate independently.

Investigation of Sodium Distribution in Phosphate Glasses Using Spin−Echo 23Na NMR

The spatial arrangements of sodium cations for a series of sodium phosphate glasses, xNa2O·(100-x)P2O5 (x ≤ 55), were investigated using 23Na spin−echo NMR spectroscopy. The spin−echo decay rate is a function of the Na−Na homonuclear dipolar coupling, and is related to the spatial proximity of neighboring Na nuclei. The spin−echo decay rate in these sodium phosphate glasses increases nonlinearly with higher sodium number density, and thus provides a measure of the Na−Na extended range order. The results of these 23Na NMR experiments are discussed within the context of several structural models, including a decimated crystal lattice model, cubic dilation lattice model, a hard sphere (HS) random distribution model, and a pairwise cluster hard sphere model. While the experimental 23Na spin−echo M2 are described adequately by both the decimated lattice and the random HS models, it is demonstrated that the slight nonlinear behavior of M2 as a function of sodium number density is more correctly described by the random distribution in the HS model. At low sodium number densities the experimental M2 is inconsistent with models incorporating Na−Na clustering. The ability to distinguish between Na−Na clusters and nonclustered distributions becomes more difficult at higher sodium concentrations.

Structure of vitreous P 2O 5 and alkali phosphate glasses

The structure of vitreous P 2O 5 (v-P 2O 5), sodium ultraphosphate glasses, (Na 2O) x (P 2O 5) 100− x ( x=10, 20), and alkali metaphosphate glasses, MePO 3 (Me=Li, Na, K, Rb and Cs), have been studied by neutron diffraction. Structural features in the neutron structure factors, S( Q), characteristic of intermediate-range ( Q ≲ 3 Å −1) order were identified. The feature of intermediate-range order in v-P 2O 5 is accounted for by the P 4O 10 molecule packing model. The addition of the alkali metal modifier, Na, has an effect on the intermediate-range structure due to destruction of the PO 4 network structure. Around x ∼ 50 a new peak appears at lower Q than the intermediate-range order peak, which is found in the S( Q)'s of all alkali metaphosphate glasses, which may be associated with extended-range order. The length scale of the extended-range order increases with Me + size. These phenomena can be explained by the affects of oxygen atoms, i.e. PO 4 chain-like units, ordering around the Me +.

Anomalous X-Ray Scattering Studies of Short-, Intermediate- and Extended-Range Order in Glasses

ABSTRACTWe present the formalism of anomalous x-ray scattering as applied to partial structure analysis of disordered materials, and give an example of how the technique has been applied, together with that of neutron diffraction, to investigate short-, intermediate- and extended-range order in vitreous germania and rubidium germanate.

Extended-range structural correlations in amorphous solids

Extended-range order (ERO), extending beyond 35 Å, has been discovered in very large (>10 000 atom) structural models of a-Si. These weak, but quasi-periodic, atomic-density fluctuations have a period of R ⋍ 3.4 Å, which corresponds to the position of the first sharp diffraction peak (FSDP) in the structure factor of a-Si at Q ⋍ 1.9 Å−1. In fact, more than half of the FSDP intensity is associated with the ERO fluctuations for r ≥ 10 Å. Atomic-void-based correlations are as well defined as atom correlations at large distances: the FSDP is equivalently found to be a chemical-order prepeak in Scc(Q) in the Bhatia-Thornton formalism calculated for the atom-void packing, thereby supporting the void model for the origin of the FSDP.

Extended-range order, interstitial voids and the first sharp diffraction peak of network glasses

Abstract The structural origin of the first sharp diffraction peak (FSDP), a prepeak in the structure factor of network-forming amorphous materials which exhibits anomalous behaviour with respect to temperature, pressure and composition, is ascribed to the structural ordering of interstitial voids. This void-based model gives a quantative description of the behaviour of the FSDP. The real-space quasi-periodicity in the structure of amorphous network materials necessary to produce an FSDP as a pseudo-Bragg peak has been identified in an ultra-large model of a-Si. This extended-range order is found to result from the propagation of short-range order (second-neighbour correlations) in the case of a-Si, or of medium-range order (fourth-neighbour correlations) in the case of AX 2 -type materials.