Atomic Pair Correlation Functions Research Articles

The influence of charge ordering in the microscopic structure of monohydroxy alcohols

While radiation scattering data provides insight inside the microstructure of liquids, the Debye relation relating the scattering intensity I(k) to the atom–atom structure factors Sab(k) shows that, ultimately, it is these individual structure correlation functions which contain the relevant information about the micro-structure. However, these quantities are not observables, except in few cases where one can invert the Debye relation to obtain the structure functions. In the majority of other cases, the need for model dependent computer simulations is unavoidable. The resulting calculations reveal that the scattering pre-peak is the result of cancellations between positive pre-peaks and negative anti-peaks contributions from the atom–atom structure factors. What of systems where this cancellation is such that it entirely suppresses the scattering pre-peak? One would be tempted to falsely conclude that there is no underlying micro-heterogeneity. Hence, the structure functions appear as hidden variables, and it is important to understand the relation between their features and the micro-structure of the system. Through the computer simulation study of various mono-ols, ranging from methanol to 1-nonanol, as well as the branched octanols, we show how the features of the atom–atom pair correlation function gab(r) affect that of the structure factors Sab(k) , and reveal that the micro-structure is ultimately the result of the charge ordering between different atoms in the system.

Predicting the pair correlation functions of silicate and borosilicate glasses using machine learning.

Glasses offer a broad range of tunable thermophysical properties that are linked to their compositions. However, it is challenging to establish a universal composition-property relationship of glasses due to their enormous compositions and chemical space. Here, we address this problem and develop a metamodel of the composition-atomistic structure relationship of a class of glassy materials via a machine learning (ML) approach. Within this ML framework, an unsupervised deep learning technique, viz., a convolutional neural network (CNN) autoencoder, and a regression algorithm, viz. random forest (RF), are integrated into a fully automated pipeline to predict the spatial distribution of atoms in a glass. The RF regression model predicts the pair correlation function of a glass in a latent space. Subsequently, the decoder of the CNN converts the latent space representation to the actual pair correlation function of the given glass. The atomistic structures of silicate (SiO2) and sodium borosilicate (NBS) based glasses with varying compositions and dopants are collected from molecular dynamics (MD) simulations to establish and validate this ML pipeline. The model is found to predict the atom pair correlation functions for many unknown glasses very accurately. This method is very generic and can accelerate the design, discovery, and fundamental understanding of the composition-atomistic structure relationship of glasses and other materials.

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.

Molecular dynamics simulation of compression induced phase transformation in Cu1Ni3 alloy

The phase transformation mechanism and transformation path of Cu-Ni alloys is very important to study for their applications in excellent electrical properties and chemical catalysis. In this paper, the effect of compressive strain on the transformation path and mechanism of Cu1Ni3 alloy is studied by molecular dynamics simulations. The simulation results reveal that the transformation path of alloys is from Fcc-Bcc-Hcp phase to other phase (amorphous state). The simulations not only revealed the processes of atomic displacements and pair correlation function during the transformation, but also elucidated the underlying mechanism of the transformation at the atomic level. The mechanism of phase transformation could be the lattice reconstruction caused by lattice sliding and stretching. The simulation results provide a clear landscape on the transformation mechanism, facilitating our comprehensive understanding on the phase transition in the Cu-Ni system.

Changes in the chemical compound and local atomic structure of ultrathin surface layers of Fe due to implantation of argon and oxygen ions

In this work, we consider the effect of irradiation in Ar+ → O+ and O+ → Ar+ sequences on changes in the chemical compound, type of chemical bond and the local atomic structure of ultrathin (~20 nm) iron surface layers. Investigation of the chemical compound and the type of chemical bond of the ion-modified surface was carried out by the XPS (X-ray photoelectron spectroscopy) and Auger electron spectroscopy. The study of changes in the local atomic structure was carried out by an XAFS-like method — electron energy loss fine structure (EELFS) spectroscopy. The parameters of the local atomic environment of oxygen and iron — partial interatomic distances, dispersion parameters, and coordination numbers — were obtained by analyzing atomic pair correlation functions. Analysis of experimental data showed that the two-stage irradiation of iron significantly changes the chemical compound and local atomic structure of the initial surface. This leads to formation of an oxide layer of greater depth than in the case of irradiation with only oxygen ions.

Second-shocked Hugoniot state of warm dense 6LiD: Quantum molecular dynamics simulations

We use quantum molecular dynamics to systematically study the equation of state of 6LiD in the density range 1.76 to 3.68 g/cm3. The calculations involve the self-consistent determination of (a) the equation of state, (b) the principal and second-shocked Hugoniot curves, (c) the conductivity and reflectivity of the warm dense states, and (d) the electronic structure. Upon comparing our results with experiments, we find that the all-electron Li pseudopotential gives a better description of the second-shocked Hugoniot states than the Li pseudopotential with only 2s valence electrons. The optical conductivity increases with pressure along the principal Hugoniot curves. The atomic pair correlation functions reveal the order-to-disorder transition of 6LiD.

Simulation study of intercalation complexes of kaolinite with simple amides as primary intercalation reagents

Delamination/exfoliation of book-like kaolinite particles is one of the most promising ways to produce aluminosilicate nanoscrolls. For the delamination of the kaolinite layers, multi-step intercalation/deintercalation procedures are used. In the first, direct intercalation step, the intercalation reagents are typically small organic molecules possessing high dipole moment. We modeled, evaluated and compared the incorporation features of formamide, urea and N-methylformamide molecules into the interlayer space of kaolinite by classical molecular simulations using realistic CHARMM-based atomic force fields. Besides the determination of characteristic basal spacings of the intercalation complexes, we compared the density and orientation distributions of the guest molecules, as well as atomic pair correlation functions. From the simulations we also calculated the typical intermolecular interaction energies and estimated the translational mobility of the different substances. Our results show that urea has some preference over the other substances in multi-step, heat-treating intercalation/deintercalation procedures with kaolinite.

Correlation Between Local Structure and Boson Peak in Metallic Glasses

We made a systematic study of the boson peak for six different Zr-based metallic glasses and found a universal correlation between average local atomic structure and boson peak. It is found that the boson peak can be decomposed into six characteristic vibratory modes, i.e., Debye’s vibratory mode and five Einstein’s vibratory modes. By using the Ioffe–Regel condition over all studied Zr-based metallic glasses, we reveal that atomic pair correlation function exactly maps on the low-temperature dynamics and the origin of the boson peak, which is the sum of vibrations of local density fluctuation domains in the glasses. In addition, it is found that the Debye’s type oscillators are the major contributors to the low-temperature specific heat capacities. This study opens a new way of understanding the relationship of the physical properties with the atomic arrangements in glasses.

Basic network structure of SiO2–B2O3–Na2O glasses from diffraction and reverse Monte Carlo simulation

Neutron- and high-energy synchrotron x-ray diffraction experiments have been performed on the (75−x)SiO2–xB2O3–25Na2O x = 5, 10, 15 and 20 mol% glasses. The structure factor has been measured over a broad momentum transfer range, between 0.4 and 22 Å−1. For data analyses and modelling the Fourier transformation and the reverse Monte Carlo simulation techniques have been applied. The partial atomic pair correlation functions, the nearest neighbour distances, coordination number distributions and average coordination number values and three-particle bond angle distributions have been revealed. The Si–O network proved to be highly stable consisting of SiO4 tetrahedral units with characteristic distances at rSi–O = 1.60 Å and rSi–Si = 3.0(5) Å. The behaviour of network forming boron atoms proved to be more complex. The first neighbour B–O distances show two distinct values at 1.30 Å and a characteristic peak at 1.5(5) Å and, both trigonal BO3 and tetrahedral BO4 units are present. The relative abundance of BO4 and BO3 units depend on the boron content, and with increasing boron content the number of BO4 is decreasing, while BO3 is increasing.

Formation of Mixed Bond‐Angle Linkages in Zinc Boromolybdate Glasses

The short and medium range structure of glassy MoO3–ZnO–B2O3 has been studied by neutron diffraction and reverse Monte Carlo simulation. The partial atomic pair correlation functions and coordination numbers are presented that are not yet reported for this system. We have established that the first neighbor distances do not depend on concentration within limit of error, the actual values are rB‐O = 1.38 Å, rMo‐O = 1.72 Å, and rZn‐O = 1.97 Å. It is found that ZnO takes part in the glassy structure as network former, as ZnO4 tetrahedral are linked both to MoO4 and to BO3 and BO4 groups. It is revealed that BO4/BO3 increases with increasing B2O3 content. We have found that only small amount of boroxol ring is present, BO3 and BO4 groups are organized into superstructure units, and a small part is in isolated BO3 triangles. The BO3 and BO4 units are linked to MoO4 or ZnO4 forming mixed [4]Mo‐O‐[3]B, [4]Mo‐O‐[4]B, [4]Mo‐O‐[4]Zn, [3]B‐O‐[4]Zn, [4]B‐O‐[4]Zn bond linkages.

Electron energy loss spectroscopy equation for spectra with overlapping oscillations and its solution by a regularization method

The integral equation of EELFS spectra with the overlapping oscillations for two-component systems is proposed. To solve this equation Tikhonov’s regularization method with the iterative procedure is applied. The atomic pair correlation functions of the investigated objects are obtained from the experimental EELFS spectra of Cu50Ni50 and Cu50Mn50 alloys by using Tikhonov’s regularization method. The experimental results agree well with the known crystallographic data (partial interatomic distances, coordination numbers and Debye–Waller factors).

Polyelectrolyte conformational transition in aqueous solvent mixture influenced by hydrophobic interactions and hydrogen bonding effects: PAA–water–ethanol

Molecular dynamics simulations of poly(acrylic acid) PAA chain in water–ethanol mixture were performed for un-ionized and ionized cases at different degree-of-ionization 0%, 80% and 100% of PAA chain by Na+ counter-ions and co-solvent (ethanol) concentration in the range 0–90vol% ethanol. Aspects of structure and dynamics were investigated via atom pair correlation functions, number and relaxation of hydrogen bonds, nearest-neighbor coordination numbers, and dihedral angle distribution function for back-bone and side-groups of the chain. With increase in ethanol concentration, chain swelling is observed for un-ionized chain (f=0) and on the contrary chain shrinkage is observed for partially and fully ionized cases (i.e., f=0.8 and 1). For un-ionized PAA, with increase in ethanol fraction ϕeth the number of PAA–ethanol hydrogen bonds increases while PAA–water decreases. Increase in ϕeth leads to PAA chain expansion for un-ionized case and chain shrinkage for ionized case, in agreement with experimental observations on this system. For ionized-PAA case, chain shrinkage is found to be influenced by intermolecular hydrogen bonding with water as well as ethanol. The localization of ethanol molecules near the un-ionized PAA backbone at higher levels of ethanol is facilitated by a displacement of water molecules indicating presence of specific ethanol hydration shell, as confirmed by results of the RDF curves and coordination number calculations. This behavior, controlled by hydrogen bonding provides a significant contribution to such a conformational transition behavior of the polyelectrolyte chain. The interactions between counter-ions and charges on the PAA chain also influence chain collapse. The underlying origins of polyelectrolyte chain collapse in water–alcohol mixtures are brought out for the first time via explicit MD simulations by this study.

Simulation of quantum zero-point effects in water using a frequency-dependent thermostat

Molecules like water have vibrational modes with a zero-point energy well above room temperature. As a consequence, classical molecular dynamics simulations of their liquids largely underestimate the energy of modes with a higher zero-point temperature, which translates into an underestimation of covalent interatomic distances due to anharmonic effects. Zero-point effects can be recovered using path integral molecular dynamics simulations, but these are computationally expensive, making their combination with ab initio molecular dynamics simulations a challenge. As an alternative to path integral methods, from a computationally simple perspective, one would envision the design of a thermostat capable of equilibrating and maintaining the different vibrational modes at their corresponding zero-point temperatures. Recently, Ceriotti et al. [Phys. Rev. Lett. 102, 020601 (2009)] introduced a framework to use a custom-tailored Langevin equation with correlated noise that can be used to include quantum fluctuations in classical molecular dynamics simulations. Here we show that it is possible to use the generalized Langevin equation with suppressed noise in combination with Nose-Hoover thermostats to efficiently impose a zero-point temperature on independent modes in liquid water. Using our simple and inexpensive method, we achieve excellent agreement for all atomic pair correlation functions compared to the path integral molecular dynamics simulation.

Structural behaviour of Pd40Cu30Ni10P20 metallic glass under high pressure

The structural behaviour of Pd40Cu30Ni10P20 bulk metallic glass as a function of hydrostatic pressure up to 47.4 GPa was investigated by means of in situ high energy synchrotron X-ray diffraction patterns. Monotonic changes are observed in the diffraction data without any indication of a phase transition. In real space all maxima of the atomic pair correlation function including the nearest neighbour distance are decreasing and scale with pressure. The volume as function of hydrostatic pressure is extracted from the diffraction data. For the largest hydrostatic pressure of 47.4 GPa the volume is reduced by 18%. The bulk modulus B0 = 178 GPa was calculated from the diffraction data. The dependence of volume on pressure of Pd40Cu30Ni10P20 metallic glass can be well described by the Birch–Murnaghan equation of state.

On the dynamics of the Fermi–Bose model

We consider the exponential matrix representing the dynamics of the Fermi–Bose model in an undepleted bosonic field approximation. A recent application of this model is molecular dimers dissociating into its atomic compounds. The problem is solved in D spatial dimensions by dividing the system matrix into blocks with generalizations of Hankel matrices, here referred to as D-block-Hankel matrices. The method is practically useful for treating large systems, i.e. dense computational grids or higher spatial dimensions, either on a single standard computer or a cluster. In particular the results can be used for studies of three-dimensional physical systems of arbitrary geometry. We illustrate the generality of our approach by giving numerical results for the dynamics of Glauber type atomic pair correlation functions for a non-isotropic three-dimensional harmonically trapped molecular Bose–Einstein condensate.

Temperature dependence of the short-range order of Cu65Zr35 metallic glass

The thermal behaviour of the short-range order of Cu65Zr35 metallic glass has been investigated by means of in situ high energy synchrotron X-ray diffraction. The temperature dependence of the X-ray structure factor and the atomic pair correlation function was analysed within the glassy state. In addition to the effect of volume expansion and thermal atomic oscillations changes occur in the short-range order. Local atomic rearrangements take place as a consequence of the structural heterogeneity in the glass. The structural transformations depend linearly on temperature. The changes of the short-range order of the glass by thermal expansion are found to be different from those under elastic tensile strain.

Molecular dynamics simulation studies of some new aspects of structural and dynamical properties of n-butyl formate at varying temperature

Using classical molecular dynamics simulation, liquid density and isobaric expansion coefficient of n-butyl formate were studied in the temperature range 298.15 to 623.15K. Fluctuations in ensemble volume and energy were used to determine the isothermal compressibility and heat capacities, hence the internal pressure. In addition, self-diffusion coefficient and viscosity were determined from dynamic properties of the ensemble. The low viscosity of the ester, which is of considerable interest as a solvent in extraction processes, was substantiated by results of the simulation. The structural properties were studied by atom–atom pair correlation function, and the results are discussed. From the structural analysis, it was found that the formate head group could form a specific hydrogen bonding extended only at short range.

Deformation induced structural evolution in bulk metallic glasses

The structural behavior of binary Cu50Zr50 and ternary Cu50Zr45Ti5 bulk metallic glasses (BMGs) under applied stress was investigated by means of in-situ high energy X-ray synchrotron diffraction. The components of the strain tensors were determined from the shifts of the maxima of the atomic pair correlation functions (PDF) in real space. The anisotropic atomic reorientation in the first-nearest-neighbor shell versus stress suggests structural rearrangements in short-range order. Within the plastic deformation range the overall strain of the metallic glass is equal to the yield strain. After unloading, the atomic structure returns to the stress-free state, and the short-range order is identical to that of the undeformed state. Plastic deformation, however, leads to localized shear bands whose contribution to the volume averaged diffraction pattern is too weak to be detected. A concordant region evidenced by the anisotropic component is activated to counterbalance the stress change due to the atomic bond reorientation in the first-nearest-neighbor shell. The size of the concordant region is an important factor dominating the yield strength and the plastic strain ability of the BMGs.

Sperimagnetism in Fe78Er5B17 and Fe64Er19B17 metallic glasses: II. Collinear components and ferrimagnetic compensation

Magnetization measurements on an Fe64Er19B17 glass and polarized-beam neutron scattering measurements on Fe78Er5B17 and Fe64Er19B17 were described in part I. The finite spin-flip neutron scattering cross sections were calculated using a sperimagnetic structure based on random cone arrangements of the magnetic moments. The temperature variation of the cross sections of Fe64Er19B17 suggested that a compensated sperimagnetic phase existed at Tcomp. The analysis of the non-spin-flip neutron scattering cross sections is described here in part II. Two spin-dependent total structure factors S±±(Q) were defined from these cross sections and, despite the limited range of the data 0.5 Å−1 < Q < 6.5 Å−1, their Fourier transform gave reliable spin-dependent radial distribution functions RDF±±(r). These were interpreted in terms of the atomic pair correlation functions and their weighting factors . The data on Fe64Er19B17 at 1.5 K showed, for example, how the directions of the magnetic sublattices can be defined uniquely. The analysis of the RDF±±(r) for Fe64Er19B17 at 112 K confirmed that the mean collinear components of the magnetic moments , are zero on both sublattices in the compensated sperimagnetic structure at Tcomp. The pre-peak in the spin-dependent total structure factors at 112 K showed that it originated in the atomic structure and it may involve Fe–Er–Fe ‘collineations’ at a radial distance of ≈6.0 Å. Finally, the RDF±±(r) of Fe64Er19B17 at 180 K and of Fe78Er5B17 at 2 K show that both glasses have the (μFe UP:μEr DOWN) structure like the (Fe,Tb)83B17 collinear ferrimagnets.

Electron energy loss spectroscopy for quantitative analysis of the local atomic structure of superthin oxide films on the surface of 3d-metals

In this paper we present a theoretical description of the extended energy loss fine structure (EELFS) formation, and derive simple analytical formulas for the EELFS spectra calculation. Methods of calculating the amplitude and intensity of electron transitions of different multipolarity on excitation of an atomic core level by an electron impact are proposed, and the corresponding test calculations are carried out. The M 2,3 EELFS spectra of pure 3d-metals (Fe, Ni, Cu) and stoichiometric oxide films (Fe 2O 3, NiO and CuO), as well as the K EELFS spectra of oxygen, obtained with a JEOL JAMP -10 Scanning Auger microprobe are presented. A technique of extracting the normalized oscillating parts from experimental EELFS data, based on the use of the calculated electron transition intensities is suggested. The atomic pair correlation functions of the investigated objects are obtained from the experimental EELFS data with allowance for multipolarity of the processes of excitation of the atomic core level by electron impact. The experimental results agree well with the known crystallographic data (partial interatomic distances, coordination numbers and Debye–Waller factors).