Pair Radial Distribution Functions Research Articles

The structure and mechanical properties in amorphous alumina under pressure

Molecular dynamics simulations of amorphous alumina with various densities ranged from 2.84 to 3.81gcm−3 were carried out to investigate their local atomic configuration and mechanical properties. The local atomic structure was analyzed through the pair radial distribution functions, bond angle distributions and simplex statistics. The simulation reveals that a mathematic expression can be derived from a relationship between bond angle distribution and structural units AlOx (and linkages OAly). The density can be estimated through the fraction of structural units AlOx. Void volume and void radii decrease as the density increases. Based on the analysis of simplex statistics, the perfect tetrahedron AlO4 (PTE) was determined. These PTEs may connect to each other via common oxygen to create a large poly-PTE. The largest poly-PTE consists of 19.2% Al in the sample with the lowest density and 3.8% Al in one with the highest density. From deformation of samples, elastic moduli and Poisson ratio were determined. The Young’s modulus and yield stress increase with the increasing density. The strain hardening becomes more pronounced as the density increases.

The structural correlation and mechanical properties in amorphous silicon nitride under densification

Molecular dynamics simulations of amorphous silicon nitride (a-Si3N4) with various densities ranging from 2.43 to 3.40gcm−3 were carried out to investigate their structural correlation and mechanical properties. The local structure was analyzed through the pair radial distribution functions, bond angle distributions and simplex statistics. The simulation reveals that although the fractions of structural units SiNx and NSiy strongly change with the density, the partial bond angle distributions of these structural units are identical for all constructed models. This result has enabled us to establish a relationship between the bond angle distributions and the fractions of structural units. Based on the analysis of simplex statistics, we found that all samples contain both the perfect and distorted tetrahedrons (SiN4). These perfect tetrahedrons (PTEs) may connect to each other via common nitrogen to create a large cluster- or poly-PTEs. The largest poly-PTE consists of 45.6% Si in the sample with a density of 3.02gcm−3 and 1.3% Si with the lowest density. We also found that even though at the high density the sample contains a remarkable number of voids in which the radius is larger than 1.1Å. From uniaxial deformation of samples, the Young's modulus, yield and flow stress were determined. The strain hardening and softening become more pronounced as density increases.

Structural and Electronic Properties of Cu64Zr36 BMG by ab initio Molecular Dynamics

ABSTRACTMuch attention has been given to bulk metallic glasses (BMG) in recent years, particularly those based on binary alloys due to the simplicity of their atomic composition. Although efforts to understand the atomistic features that give rise to their exceptional properties have been made, the electronic and vibrational properties have been disregarded. We undertook the task of simulating the Cu64Zr36 glassy metal using a supercell with 108 atoms and a different simulational approach: the undermelt-quench approach [1]. The structure was characterized by means of the radial (pair) distribution function and the bond-angle distribution and the electronic density of states was calculated. We find that our results agree well with experimental data.

Amorphous Bismuth: Structure-Property Relations and the Size of the Supercell

ABSTRACTIt has been argued that for the simulation of amorphous materials, the larger the periodic supercell the better the representation. We contend that for certain properties there is a minimum supercell size above which one obtains a good representation of the topological and electronic collective properties of the material independent of the size. To show this contention we have chosen two periodic supercells of bismuth, one with 64 atoms and another with 216 atoms, which were amorphized using ourundermelt-quenchapproach [1]. The originally crystalline structures were subjected to a heating-and-cooling process starting at an initial temperature of 300 K and linearly going up to 540 K, in 100 simulational steps, 4.5 K just below the melting temperature of bismuth (theundermeltsection of the process) under normal conditions of pressure. Next, the sample was cooled down to 0K (thequenchsection of the process), in 225 simulational steps with the same absolute cooling rate as the heating process. Then the samples obtained were geometry-optimized to find the final metastable amorphous structures. These structures were analyzed by calculating their radial (pair) distribution functions, the plane angle distributions and the electron densities of states. Results will be presented that manifest that after proper normalization due to the difference in the number of atoms and the number of electron energy levels, the two structures are, for all practical purpose, the same, indicating that in this case, the size of the cell does not seem to play a major role in the properties determined.

QM/MM investigation on 1,3-dipolar cycloadditions of the phthalazinium dicyanomethanide with three different dipolarophiles on water and in solution

An "on water" environment, describing the reactions with insoluble reactants in water, has been reported to give high yields of products compared to organic solvents. The 1,3-dipolar cycloadditions of phthalazinium dicyanomethanide 1 with three different dipolarophiles, methyl vinyl ketone (MVK), methyl acrylate (MAC), and styrene (STY), have been investigated using QM/MM calculations in water, acetonitrile, and acetonitrile-water solvent mixtures, as well as at the vacuum-water interface. Monte Carlo statistical mechanics simulations utilizing the free-energy perturbation theory and PDDG/PM3 for the QM method have been used. The transition structures for all three reactions do not show large variations among different solvents. However, the calculated free energies of activation at the interface are found to be higher than those calculated in bulk water. Computed energy pair distributions and radial distribution functions reveal a uniform loss of hydrogen bonds for the reactants and transitions states in progressing from bulk water to the vacuum-water interface. The hydrophobic effects in the reactions of 1 with MVK and MAC are similar for both, and weaker than the effect in the reaction with STY. According to the results in water-acetonitrile mixtures at different molar ratios, it is clear that the special hydrogen bonding effects are the main reason which leads to the rapid rate enhancement in progressing from a water-acetonitrile molar ratio of 0.9 : 0.1 to pure water. New insights into solvent effects for 1,3-dipolar cycloadditions are presented herein.

Prediction of Absolute Hydroxyl pKa Values for 3-Hydroxypyridin-4-ones.

pKa values have been calculated for a series of 3-hydroxypyridin-4-one (HPO) chelators in aqueous solution using coordination constrained ab initio molecular dynamics (AIMD) in combination with thermodynamic integration. This dynamics-based methodology in which the solvent is treated explicitly at the ab initio level has been compared with more commonly used simple, static, approaches. Comparison with experimental numbers has confirmed that the AIMD-based approach predicts the correct trend in the pKa values and produces the lowest average error (∼0.3 pKa units). The corresponding pKa predictions made via static quantum mechanical calculations overestimate the pKa values by 0.3-7 pKa units, with the extent of error dependent on the choice of thermodynamic cycle employed. The use of simple quantitative structure property relationship methods gives prediction errors of 0.3-1 pKa units, with some values overestimated and some underestimated. Beyond merely calculating pKa values, the AIMD simulations provide valuable additional insight into the atomistic details of the proton transfer mechanism and the solvation structure and dynamics at all stages of the reaction. For all HPOs studied, it is seen that proton transfer takes place along a chain of three H2O molecules, although direct hydrogen bonds are seen to form transiently. Analysis of the solvation structure before and after the proton transfer event using radial pair distribution functions and integrated number densities suggests that the trends in the pKa values correlate with the strength of the hydrogen bond and the average number of solvent molecules in the vicinity of the donor oxygen.

Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2

We have investigated the structural and electronic properties as well as the linear optical response of amorphous TiO${}_{2}$ within density functional theory and a numerically efficient density functional based tight-binding approach as well as many-body perturbation theory. The disordered TiO${}_{2}$ phase is modeled by molecular dynamics. The equivalence to experimentally characterized amorphous phases is demonstrated by atomic structure factors and radial pair-distribution functions. By density functional theory calculations, using both the semilocal Perdew-Burke-Ernzerhof functional and the nonlocal Heyd-Scuseria-Ernzerhof screened hybrid functional, the electronic energy gap is found to be larger than in the crystalline TiO${}_{2}$ phases rutile and brookite but close to the anatase band gap. The quasiparticle energy gap of amorphous TiO${}_{2}$ is determined to be $\ensuremath{\gtrsim}$3.7 eV, while the optical gap is estimated to $\ensuremath{\lesssim}$3.5 eV. The disorder-induced formation of localized electronic states has been analyzed by the information entropy of the charge density distributions. The frequency-dependent optical constants, calculated from the complex dielectric function, have been determined in independent particle approximation. Besides similar absorption characteristics between the most common crystalline phases and amorphous TiO${}_{2}$, we find distinct differences in the optical spectra in the energy region between 5 eV and 8 eV. These differences can be assigned to the loss of symmetry in the local atomic structure of the disordered material. While the composition of the crystalline phases rutile, anatase, and brookite is well described by periodic arrangements of distorted TiO${}_{6}$ octahedra building blocks, the amorphous phase is characterized by partial loss of this octahedral coordination and the disorder-induced formation of under- and over-coordinated Ti ions. This leads to the absence of the characteristic crystal-field splitting of unoccupied Ti${}_{3d}$ states into ${e}_{g}$ and ${t}_{2g}$ like subbands. The optical characteristics of the amorphous phase are interpreted as a superposition of optical transitions that reflect the various local symmetries of the manifold of synthesizable crystalline TiO${}_{2}$ phases. The linear optical properties, calculated within the independent-particle approximation, are found to be in good agreement with the available experimental data.

Structural modelling of the LiCl aqueous solution by the hybrid reverse Monte Carlo (HRMC) simulation

The reverse Monte Carlo (RMC) simulation is applied in the study of an aqueous electrolyte LiCl6H2O. On the basis of the available experimental neutron scattering data, RMC computes pair radial distribution functions in order to explore the structural features of the system. The obtained results include some unrealistic features. To overcome this problem, we use the hybrid reverse Monte Carlo (HRMC), incorporating an additional energy constraint in addition to the usual constraints of the pair correlation functions and average coordination. Our results show a good agreement between experimental and computed partial distribution functions (PDFs) as well as a significant improvement in pair partial distribution curves. This kind of study can be considered as a useful test for a defined interaction model for conventional simulation techniques

THE CORRELATION BETWEEN BOND ANGLE DISTRIBUTION AND THE COORDINATION OF SILICA LIQUID UNDER PRESSURE

Molecular dynamics simulation is carried out for liquid SiO 2 at pressure ranged from zero to 30 GPa and by using BKS, Born–Mayer type and Morse–Stretch potentials. The constructed models reproduce well the experimental data in terms of mean coordination number, bond angle and pair radial distribution function. Furthermore, the density of all samples can be expressed by a linear function of fractions SiO x. It is found that the topology of units SiO x and linkages OSi y is unchanged upon compression although the liquid undergoes substantial change in its network structure. Consequently, the partial bond angle distribution for SiO x and OSi y is identical for all samples constructed by the same potential. This result allows to establishing a simple expression between total bond angle distribution (BAD) and fraction of SiO x and OSi y. The simulation shows a good agreement between the calculation and simulation results for both total O–Si–O and Si–O–Si BADs. This supports a technique to estimate amount of units SiO x and linkages OSi y on base of total Si–O–Si and O–Si–O BADs measured experimentally.

Hydrogen Bonding in 1-Butyl- and 1-Ethyl-3-methylimidazolium Chloride Ionic Liquids

A detailed investigation of hydrogen bonding in the pure ionic liquids [C4C1im]Cl and [C2C1im]Cl has been carried out using primarily molecular dynamics techniques. Analyses of the individual atom-atom pair radial distribution functions, and in particular those for C···Cl(-), have revealed that hydrogen bonding to the first methylene or methyl units of the substituent groups is important. Multiple geometric criteria for defining a hydrogen bond have been applied, and in particular the choice of the cutoff angle has been carefully examined. The interpretation of hydrogen bonding within these ionic liquids is highly angle dependent, and justification is provided for why it may be appropriate to employ a wider angle criteria than the 30° used for water or alcohol systems. The different types of hydrogen bond formed are characterized, and "top" conformations where the Cl anion resides above (or below) the imidazolium ring are investigated. The number of hydrogen bonds undertaken by each hydrogen atom (and the chloride anion) is quantified, and the propensity to form zero, one, or two hydrogen bonds is established. The effects of an increase in temperature on the static hydrogen bonding are also briefly examined.

Understanding solvent effects in the selective conversion of fructose to 5-hydroxymethyl-furfural: a molecular dynamics investigation

Selective conversion of fructose to 5-hydroxymethyl-furfural (HMF) involves the participation of high-boiling solvents like dimethyl sulfoxide (DMSO). In order to replace DMSO with low-boiling solvents, it is imperative that we understand the effect of DMSO solvation in protecting (i) HMF from rehydration and humins formation reactions and (ii) fructose from side reactions, other than its dehydration to HMF. In the present work, molecular dynamics simulations of HMF and fructose in water and in water-DMSO mixtures are carried out using the OPLS-AA force field. Radial pair distribution functions, coordination numbers and the hydrogen-bond network between the HMF/fructose molecule and the solvent molecules are analysed. The local 3-dimensional picture of the arrangement of solvent molecules around the solute, which cannot be accessed from pair distribution functions, is also computed. We show preferential coordination of DMSO around HMF and explain how this could provide a shielding effect to the HMF molecule, thus protecting it from further rehydration to levulinic acid and formic acid and from humins formation. In the case of fructose, the presence of DMSO also reduces the number of water molecules in the immediate vicinity of fructose. Though fewer water molecules coordinate around fructose, they are bound strongly to it. Analysis of the local 3-dimensional arrangement of DMSO molecules suggests that it protects the fructose molecule from side reactions that would lead to condensation or reversion products. However, the presence of DMSO molecules does not hamper the water molecules coming into contact with the oxygen atom of the hydroxyl groups of fructose, which is required for a proton transfer from water to fructose, to initiate the dehydration reaction to HMF.

Mechanism for amorphization of boron carbide B4C under uniaxial compression

Boron carbide undergoes an amorphization transition under high-velocity impacts, causing it to suffer a catastrophic loss in strength. The failure mechanism is not clear and this limits the ways to improve its resistance to impact. To help uncover the failure mechanism, we used ab initio methods to carry out large-scale uniaxial compression simulations on two polytypes of stoichiometric boron carbide (B${}_{4}$C), B${}_{11}$C-CBC, and B${}_{12}$-CCC, where B${}_{11}$C or B${}_{12}$ is the 12-atom icosahedron and CBC or CCC is the three-atom chain. The simulations were performed on large supercells of 180 atoms. Our results indicate that the B${}_{11}$C-CBC (B${}_{12}$-CCC) polytype becomes amorphous at a uniaxial strain s $=$ 0.23 (0.22) and with a maximum stress of 168 (151) GPa. In both cases, the amorphous state is the consequence of structural collapse associated with the bending of the three-atom chain. Careful analysis of the structures after amorphization shows that the B${}_{11}$C and B${}_{12}$ icosahedra are highly distorted but still identifiable. Calculations of the elastic coefficients (${C}_{ij}$) at different uniaxial strains indicate that both polytypes may collapse under a much smaller shear strain (stress) than the uniaxial strain (stress). On the other hand, separate simulations of both models under hydrostatic compression up to a pressure of 180 GPa show no signs of amorphization, in agreement with experimental observation. The amorphized nature of both models is confirmed by detailed analysis of the evolution of the radial pair distribution function, total density of states, and distribution of effective charges on atoms. The electronic structure and bonding of the boron carbide structures before and after amorphization are calculated to further elucidate the mechanism of amorphization and to help form the proper rationalization of experimental observations.

CH bond activation of methane in aqueous solution: A hybrid quantum mechanical/effective fragment potential study

In this study, we investigated the C-H bond activation of methane catalyzed by the complex [PtCl(4)](2-), using the hybrid quantum mechanical/effective fragment potential (EFP) approach. We analyzed the structures, energetic properties, and reaction mechanism involved in the elementary steps that compose the catalytic cycle of the Shilov reaction. Our B3LYP/SBKJC/cc-pVDZ/EFP results show that the methane activation may proceed through two pathways: (i) electrophilic addition or (ii) direct oxidative addition of the C-H bond of the alkane. The electrophilic addition pathway proceeds in two steps with formation of a σ-methane complex, with a Gibbs free energy barrier of 24.6 kcal mol(-1), followed by the cleavage of the C-H bond, with an energy barrier of 4.3 kcal mol(-1) . The activation Gibbs free energy, calculated for the methane uptake step was 24.6 kcal mol(-1), which is in good agreement with experimental value of 23.1 kcal mol(-1) obtained for a related system. The results shows that the activation of the C-H bond promoted by the [PtCl(4)](2-) catalyst in aqueous solution occurs through a direct oxidative addition of the C-H bond, in a single step, with an activation free energy of 25.2 kcal mol(-1), as the electrophilic addition pathway leads to the formation of a σ-methane intermediate that rapidly undergoes decomposition. The inclusion of long-range solvent effects with polarizable continuum model does not change the activation energies computed at the B3LYP/SBKJC/cc-pVDZ/EFP level of theory significantly, indicating that the large EFP water cluster used, obtained from Monte Carlo simulations and analysis of the center-of-mass radial pair distribution function, captures the most important solvent effects.

Impact of local lattice distortions on the structural stability of Fe-Pd magnetic shape-memory alloys

The binding surface of Fe-rich Fe-Pd alloys is explored by means of first-principles calculations in the framework of density functional theory involving unconstrained optimization of the atomic positions within a 108-atom supercell. We find that static displacements arising from geometric optimization provide an important contribution to the total energy, effectively compensating favorable contributions gained from introducing L${1}_{2}$ order in stoichiometric Fe${}_{3}$Pd. In the concentration range for magnetic shape-memory applications, the energy profile with respect to tetragonal distortion is altered qualitatively, shifting the ground state of the intermixed disordered system from face-centered cubic (fcc) to body-centered tetragonal (bct). From the radial pair distribution function and electronic density of states obtained from a 500-atom supercell calculation we identify the origin of the displacements. These arise from the size-dependent relaxations of the larger Pd atoms, on the fcc side in combination with a Jahn-Teller-like rearrangement of Fe $d$ states at the Fermi level.

Modeling of initial crystallization in the alloys Al–10Ni and Al–5Ni–2.7Y at high undercoolings

Formation and growth of crystallization centers of aluminum in amorphous alloys Al–10Ni and Al–5Ni–2.7Y have been studied by a method of the molecular dynamics. Local radial pair distribution functions were calculated for studying of structure. Growth kinetics of the comparatively large aluminum crystals in the binary system is studied. Latencies of appearance of the first crystallization centre are found. The energies of interatomic interaction averaged locally and also in the bulk of the amorphous phase are determined. It is researched how the size of the crystallization centre influences its structure and the local interaction energy. Formation of icosahedrons and their lifetimes are in consideration.

Variations in atomic structural features of a supercooled Pd–Ni–Cu–P glass forming liquid during in situ vitrification

In situ vitrification in a synchrotron beam during cooling of a Pd 42.5Cu 30Ni 7.5P 20 melt allowed continuous acquisition of X-ray diffraction spectra in the supercooled liquid region between the liquidus temperature T l and the glass transition temperature T g for the first time in a metallic liquid alloy. These and subsequent acquisitions on reheating allowed determination of the structural changes in the supercooled and glassy states using the real space atomic pair distribution function PDF(R) and radial distribution function RDF(R). The nearest neighbor (NN) distance in the first coordination shell has a low R peak (pre-peak) that appears and increases on cooling from the liquidus temperature to the glass transition temperature in the supercooled liquid region. In this temperature range reversible expansion of the NN distances in the first coordination shell is observed. The slope of the expansion changes discontinuously at the glass transition. This behavior is explained by the theory of local topological fluctuations.

New model for tracer-diffusion in amorphous solid

The tracer-diffusion and structure of polymorphic states of amorphous solid is studied by mean of the statistic relaxation technique and simplex analysis. Several different metastable states of amorphous iron have been constructed based on the model containing 2 × 105 atoms. All models have almost the same pair radial distribution functions, but they differ in the potential energy per atom and the density. We found a large number of vacancy-simplexes which varies according to the relaxation and serves as a diffusion vehicle. New diffusion mechanism for tracer-diffusion is found of which the elementary diffusion process likes a collapse of “microscopic bubble” in amorphous matrix. This includes a jump of diffusing atom and the collective movement of a large number of neighboring atoms. The diffusion constant D determined in accordance with considered diffusion mechanism is in reasonable agreement with experimental data. The decrease in diffusion constant D upon thermal annealing is explained by the reducing vacancy-simplex concentration which is caused by both the local atomic rearrangement and the elimination of excess free volume.

Information-theory-based solution of the inverse problem in classical statistical mechanics

We present a procedure for the determination of the interaction potential from the knowledge of the radial pair distribution function. The method, realized inside an inverse Monte Carlo simulation scheme, is based on the application of the maximum entropy principle of information theory and the interaction potential emerges as the asymptotic expression of the transition probability. Results obtained for high density monoatomic fluids are very satisfactory and provide an accurate extraction of the potential, despite a modest computational effort.

Molecular dynamics simulation of self-assembly structure for AOK based reverse micelle in supercritical CO 2

Molecular dynamics simulations were performed to investigate the structural properties of aqueous reverse micelles of AOK (aerosol-octyl-ketone), a non-fluorinated hydrocarbon surfactant with two symmetrical carbonyl groups in the tail, in supercritical CO 2 fluid. The result for the first time demonstrates the atomic-level structural picture for the formation of nanodomain in water-in-CO 2 microemulsion based on the AOK surfactant, which is in good agreement with the recent experiment. The dynamics process shows that the self-assembly of the reverse micelle takes a relatively short period of time (∼4 ns) and remains stable over 50 ns. For comparison, the simulation for the AOK/scCO 2 system has also been performed and an irregular and sparse reverse micelle structure can be formed in the absence of water molecules. The radial density profiles, the pair radial distribution functions and the orientation distribution have been calculated to investigate the interfacial structure properties. The carbonyl groups in the surfactant tails may enhance the solvation of the AOK surfactant, thereby affording to stabilize the reverse micelle.

Monte Carlo Simulations indicate that Chromati: Nanostructure is accessible by Light Microscopy.

A long controversy exists about the structure of chromatin. Theoretically, this structure could be resolved by scattering experiments if one determines the scattering function - or equivalently the pair distribution function - of the nucleosomes. Unfortunately, scattering experiments with live cells are very difficult and limited to only a couple of nucleosomes.Nevertheless, new techniques like the high-resolution light microscopy supply a new approach to this problem. In this work we determine the radial pair distribution function of chromatin described by our E2A model and find that the dominant peaks which characterize the chromatin structure are very robust in several ways: They can still be identified in the case of chromatin fibers with reasonable linker histone and nucleosome defect rates as well as in the 2D case after a projection like in most high-res light microscopy experiments. This might initiate new experimental approaches like optical microscopy to finally determine the nanostructure of chromatin.Furthermore, we examine the statistics of random chromatin collisions and compare it with 5C data of a gene desert. We find that only chromatin fibers with histone depletion show a significant amount of contacts on the kbp-scale which play a important role in gene regulation. Therefore, linker histone and nucleosome depletion might not only be chromatin defects but even be necessary to facilitate transcription.PACS codes: 82.35.Pq, 87.16.A-, 87.16.af