Atomic Pair Correlation Functions Research Articles

Determination of parameters of the local atomic surrounding in surface layers of Fe, Ni and Cu by the secondary electron fine structure method

Secondary electron spectra of Fe, Ni, Cu pure surfaces and corresponding oscillating signals were obtained. The atomic pair correlation function was estimated by solving the inverse problem using the Tikhonov regularization method. The results obtained and the application of the secondary electron fine structure method for local atomic structure analysis are discussed.

Short-range order of Zr 62− xTi xAl 10Cu 20Ni 8 bulk metallic glasses

The short-range order and crystallization behavior of slowly cooled Zr 62− x Ti x Al 10Cu 20Ni 8 bulk metallic glasses have been investigated in terms of the atomic pair correlation function as a function of Ti content x (2≤ x≤7.5). The structural parameters point to the presence of chemical short-range order in these bulk glasses. An enhanced local excess free volume around the Ti atoms is concluded from density measurements. The first stage of crystallization in Zr 62− x Ti x Al 10Cu 20Ni 8 bulk glasses is related to changes in the medium-range order while the first neighborhood is retained. The atomic pair correlation functions of the first crystallization products are similar for all titanium contents. There is no indication of any special atomic arrangement for the particular alloy forming quasicrystals upon heating ( x=3). In case of Zr 54.5Ti 7.5Al 10Cu 20Ni 8 an ultrafine microstructure consisting of clusters of 2 nm in size is formed as the first step of crystallization.

The structure of a fluid mixture of deuterated ethane and deuterated methane by high-pressure neutron diffraction experiments

High-pressure neutron diffraction data on a mixture of 33.3 mole % deuterated ethane and 66.7 mole % deuterated methane at six supercritical states are presented. The density could be varied by a factor larger than 2. The density dependence of the intra- and intermolecular structure is determined. The resulting total atomic pair correlation functions are compared with the results of Monte Carlo computer simulations with effective pair potentials.

EXAFS and molecular dynamics studies of ionic solutions.

This paper focuses on recent advances in the X-ray absorption spectroscopy (XAS) analysis of ionic solutions. The asymmetry of radial distribution functions g(r) associated with the solvent molecules surrounding the ions has to be taken into account to perform a reliable structural analysis. Molecular dynamics (MD) simulations provide reliable g(r)'s which can be used as starting models in the XAS data analysis. The combined MD-XAS investigation reduces meaningfully the indetermination of the structural parameters, especially for coordination numbers and Debye-Waller factors. Double-electron excitation channels can be present in the XAS spectra of ionic solutions and they have to be accounted for in the background extraction. The ability of the XAS technique to probe three-body correlation functions in ionic solutions with the aid of MD g(r1, r2, theta) has been shown. The analysis of the low-k region of the spectra allows the detection of a weak but significant hydrogen structural signal. The XAS technique is especially well suited to determine the detailed shape of the nearest-neighbor peak in the atom-atom pair correlation functions of disordered systems. The information that they contain about the short-range atom-atom pairwise interactions can be very helpful for specifying and properly modifying model potentials used in MD simulations.

Intermolecular potential for benzoic acid–water based on the test-particle model and statistical mechanical simulations of benzoic acid in aqueous solutions

Structures and interaction energies of benzoic acid–water (BA–H 2O) 1:1, 1:2, 2:1 and 2:2 complexes were investigated using intermolecular potentials derived from the test-particle model (T-model). The absolute and some lowest-lying minimum energy geometries of the 1:1 and 1:2 complexes were examined using ab initio calculations with the Hartree–Fock (HF) and the second order Møller–Plesset (MP2) perturbation theories. The T-model, HF and MP2 calculations revealed that cyclic arrangements of hydrogen bonds (H-bonds) between the COOH group and H 2O represent the absolute minimum energy geometries of the 1:1 and 1:2 complexes. The results on the 2:1 and 2:2 complexes showed that the cyclic H-bonds in the dimers could be opened to allow insertion of water molecules. Based on the T-model potentials, aqueous solutions of BA and (BA) 2 were investigated by conducting a series of molecular dynamic (MD) simulations. It was found that, except at the solute–solute H-bonds, the hydration structures of the cyclic H-bond planar (CHP) and side-on type (SOT) dimers are not substantially different from a single BA. The atom–atom pair correlation functions ( g( R)) derived from MD simulations suggested that, in very dilute aqueous solution, the cyclic H-bonds in the CHP and SOT dimers are not stable and can be disrupted by the solute–solvent H-bond interaction and thermal energy fluctuation.

The application of reverse Monte Carlo modelling to a polymeric melt

The reverse Monte Carlo (RMC) modelling technique has been applied to the polymeric melt poly(propylene oxide) (PPO). The modelling was based on neutron diffraction experiments on both hydrogenous and deuterated samples. Inter-atomic distances and calculated bond angle distributions for the RMC produced model were found to be in good agreement with reported experimental results, showing the ability of the RMC method to produce realistic structural models of amorphous polymers on the molecular length scale. The strengths and limitations of the RMC models in studies of the intermediate and long range order in polymers are investigated with emphasis on the information content and information quality. Particularly, we find by studying the RMC model of PPO that the strong first diffraction peak at about 1.45 Å −1 is almost entirely due to weak inter-chain correlations. The local chain conformation was investigated by calculating the partial atomic pair correlation functions for atoms belonging to monomers close in sequence. The results show that the most probable conformation is a “stretched” trans conformation, where two consecutive methyl groups are pointing in almost opposite directions. Although the dihedral and bond angle distributions found in the model are probably somewhat broader than in reality, they show unambiguously interpretable features which support the findings above.

Monte Carlo and reverse Monte Carlo simulations on molten zinc chloride

Monte Carlo and reverse Monte Carlo simulations on molten ZnCl2 were performed on the basis of the total atom pair correlation functions, recently determined with X-ray diffraction experiments at T=623 and 873 K. A new pair-wise additive potential model is presented that is based on an intermediate-range oscillating function for the Zn–Zn interaction in combination with a modified Coulomb potential. This potential mimics the effect of induced anion polarization, which has been found as to be the reason for the highly directional interactions between the cations and anions in the melt. With this simple potential model, the experimentally determined total atom pair correlation functions and the total structure factor, the prepeak included, are well reproduced. The analysis of the configurations, generated with the Monte Carlo method, confirms the existence of a network structure with rings and chains of small and medium size consistent with corner connected [ZnCl4] units of high tetrahedricity. In contrast, the reverse Monte Carlo method generates more disordered structures and is obviously not able to give a correct description of the ion arrangement in molten ZnCl2.

Short-Range Order of Amorphous (Zr65Al7.5Cu17.5Ni10)100—xFex Alloys

The short-range order of bulk glass forming (Zr 6.5 Al 7.5 Cu 17.5 Ni 10 ) 100-x Fe x alloys obtained by rapid quenching was investigated as a function of the iron content (x = 0 to 20). The structure of the bulk glass is found to be similar to binary amorphous Zr 65 M 35 alloys (M = transition metal). The observed changes in the interference function I(s) and the atomic pair correlation function g(r) are correlated to the altered zirconium content and are also similar to those in binary amorphous Zr-M alloys. Iron atoms are statistically distributed with the other transition metals within the amorphous phase.

Neutron diffraction experiments on a fluid, equimolar mixture of methane and carbon tetrafluoride

A neutron scattering investigation is reported on an equimolar mixture of methane and carbon tetrafluoride along the 370 K isotherm for four different thermodynamic states in a pressure range 270–800 bar, the aim of which was to provide more structural data about this non-ideal system. The fully corrected coherent differential cross-section is presented. The weighted sum of the total atom pair correlation functions is separated into the intramolecular and intermolecular contributions and the structural parameters of the molecules in the fluid state are determined. The density dependence of the intermolecular atom pair correlation functions is clearly visible. The experimental results are compared with previous experiments on the pure components and XRISM calculations, based on a one-centre Lennard-Jones potential.

The Yukagua model of water

Using the Invariant Expansion technique we show that the Multi-Yukawa closure of the Ornstein Zernike equation has an analytical solution for a model that reproduces well the known structure of water as measured by neutron diffraction. The model is an extension of earlier models based on the BBL model [1,2]: the analytical sticky octupolar potential and the soft version of that potential. In the present work the soft short-ranged effective potential is represented by a sum of Yukawa potentials. The models is tested by Monte Carlo computer simulation The atom–atom pair correlation functions for oxygen–oxygen, oxygen–hydrogen and hydrogen–hydrogen obtained for this new potential are in good agreement with the neutron scattering experiments. Because of its analyticity this model is especially suited for the investigation of the percolation transition for the hydrogen bonds, proposed by Stanley and collaborators [3,4,39,40]. The convergence in the simulations is very fast because the weakly directional octupolar potential have little trouble connecting to the tetrahedral first nearest neighbors. The observation made in the computer simulations is that small changes in the strength of the potential seem to lock in or lock out of the tetrahedral structure. This is interpreted as changes in temperature producing the percolation transition.

Structural modelling of fluid ethane with Monte Carlo methods

Recently determined neutron diffraction results for fluid ethane at T=370 K and four densities were fitted with Reverse Monte Carlo simulations. In addition, Monte Carlo simulations in the NVT-ensemble were performed with an empirically deduced effective eight-site pair potential. The experimentally determined total atom pair correlation functions were well reproduced. The individual atom pair correlation functions calculated with Monte Carlo and Reverse Monte Carlo agree very well and show a pronounced fine-structure and a significant density effect. The final configurations were used to calculate angular distribution functions that show a disordered arrangement of the molecules with respect to their centers, but high angle correlations for the nearest neighbour interactions compared to a statistically disordered model system. The center–center correlation functions for four special molecule-pair orientations (crossed, T-shaped, parallel adjacent and parallel end-to-end) show an increased occurrence of molecular orientations at distances that correlate with the minima positions in the corresponding potential energy curves for these orientations. The atom pair correlations functions for these four special species show that the orientational short range order causes the fine structure in the atom pair correlation functions.

Response of GaAs to fast intense laser pulses

Motivated by recent experiments, we have performed simulations which show in detail how the electrons and ions in GaAs respond to fast intense laser pulses (with durations of order 100 fs and intensities of order $1\ensuremath{-}10 {\mathrm{T}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}).$ The method of tight-binding electron-ion dynamics is used, in which an arbitrarily strong radiation field is included through a time-dependent Peierls substitution. The population of excited electrons, the atomic displacements, the atomic pair-correlation function, the band structure, and the imaginary part of the dielectric function are all calculated as functions of time, during and after application of each pulse. Above a threshold intensity, which results in promotion of about 10% of the electrons to the conduction band, the lattice is destabilized and the band gap collapses to zero. This is most clearly revealed in the dielectric function $\ensuremath{\epsilon}(\ensuremath{\omega}),$ which exhibits metallic behavior and loses its structural features after 100--200 fs.

Structural properties of poly(propylene oxide) from diffraction experiments and reverse Monte Carlo simulation

Structural characteristics of an amorphous polymer melt, poly(propylene oxide) (PPO), have been studied by combining neutron and x-ray diffraction experiments and computer modeling using the reverse Monte Carlo (RMC) technique. The neutron diffraction experiments were performed on hydrogenous as well as deuterated samples. The experimentally determined nearest-neighbor distances were found to be in good agreement with literature data. The RMC modeling was applied for interpretation of the diffraction data to obtain more detailed structural information on bond angles, intermediate and long range correlations. For the intermediate range structure, the experimental structure factors demonstrate a first diffraction peak at about 1.45 Å−1, which from the RMC produced model can be related to the interchain distance of an almost random packing of the polymer chains. To investigate the chain conformation, partial atomic pair correlation functions have been calculated for atoms belonging to monomers close in sequence. The results show that the most probable conformation is a “stretched” trans conformation, where two consecutive methyl groups are pointing in almost opposite directions. Calculated bond and dihedral angle distributions support this finding and demonstrate the ability of the RMC method to produce polymer structures in good agreement with experimental results.

Neutron diffraction experiments on ethane under high pressure

A neutron scattering investigation on deuteroethane at four different thermodynamic states is reported. The study was performed at 370K and pressures up to 815bar and was restricted to the supercritical state of ethane. The fully corrected coherent differential cross section is presented. The weighted sum of the total atom pair correlation function is separated into intramolecular and intermolecular contributions and the structural parameters of the molecule in the fluid state were determined. The density dependence of the intermolecular atom pair correlation functions is clearly visible. The experimental results are compared with previous experiments on liquid ethane and XRISM (reference interaction site model (RISM) in combination with the hypernetted chain closure) calculations, based on a two centre Lennard-Jones potential.

Structural investigations of fluid carbon tetrafluoride by statistical mechanical calculations and Monte Carlo simulation

AbstractStatistical mechanical calculations with the extended reference interaction site model (XRISM) and Monte Carlo simulations are performed on fluid CF4. The parameters of a five‐center (12‐6) Lennard Jones potential with added point charges are deduced. The results are compared with total atom pair correlation functions recently determined by neutron diffraction experiments at three supercritical densities. Apart from the good agreement between experimental and theoretical results, we found that depending on the method used, different potentials are able to describe the investigated system. The atom pair correlation functions and angular distribution functions indicate a completely disordered arrangement of the molecules in fluid CF4 with no significant short‐range orientational order except for very close distances. The comparison of the results with former Reverse Monte Carlo (RMC) simulations allows the conclusion that the RMC method is an effective tool, equivalent to the well established Monte Carlo and XRISM methods, in determining the microscopic structure of fluid CF4, but without the exact knowledge of intermolecular potentials.

X-ray scattering analysis of the average poly-cyclic aromatic unit in argonne premium coal 401

An X-ray scattering study of APC 401 (a coal taken from the Pittsburgh seam), using MoK α X-rays, indicates that the longest distance between carbon atoms in the mean poly-cyclic aromatic (PCA) unit is approx. 7.5 Å. The radial-distribution function indicates that, on the average, each carbon 2.2 nearest carbon neighbors at an average distance of 1.43 Å. This information is consistent with the interpretation that 27% of the CC bonds in this coal involve at least one alkyl carbon, while 73% of the CC bonds are between aryl carbons. Comparisons of the atom-pair correlation function to simulated one-dimensional structure functions calculated from three-dimensional structural models of several poly-cyclic molecules indicate that a ribbon-shaped C 14 unit (analogous to anthracene) best agrees with the results of our X-ray scattering data. Interpretation of the atom-pair correlation function also suggests that the alkyl carbons are predominantly, if not exclusively, bonded to the PCA unit.

High-pressure neutron diffraction on fluid carbon tetrafluoride and interpretation by reverse Monte Carlo simulations

Neutron scattering experiments on carbon tetrafluoride (CF4) at high pressure were performed along the 370 K isotherm at three supercritical densities, covering a density range from ρ=1.07 to 1.26 g cm−3. The structure factors of the investigated thermodynamic states and the weighted sums of the atom pair correlation functions are presented. The variation of the density has only a weak effect on the structure factors. The experimentally obtained total atom pair correlation functions are interpreted with reverse Monte Carlo simulations. The atom pair correlation functions and angular distribution functions indicate a completely disordered arrangement of the molecules in fluid CF4 with no significant short-range orientational order, except for very close distances.

A differential anomalous x-ray scattering study and reverse monte carlo simulation of a highly concentrated solution of zinc bromide in water

Abstract A differential anomalous X-ray scattering (DAS) study of the structure of a highly concentrated aqueous solution of zinc bromide (19.5 molal) is presented. Synchrotron radiation was used for four diffraction experiments at photon energies of 12500 eV, 13462 eV (Br-K-edge) and 9000 eV, 9650 eV (Zn-K-edge). The dispersion corrections were calculated from the photoabsorption coefficients determined by absorption experiments. The differential structure factor and its Fourier transform, the differential atom pair correlation function, were obtained after an intricate data evaluation procedure The technique of the Reverse Monte Carlo simulation, which requires no intermolecular potential as input, was used to elucidate the microscopic structure of zinc bromide solution, which resembles the crystal structure of ZnBr 2 ·H 2 O, in which the zinc ion is coordinated tetrahedrally with two bromine ions and two water molecules.

Ion–ion and ion–water interactions in an aqueous solution of erbium bromide (ErBr3). A differential anomalous x-ray scattering study

A differential anomalous x-ray scattering (DAS) study of a three molal aqueous solution of erbium bromide (ErBr3) is reported. X-ray scattering at various energies below the L3 edge of erbium and the K edge of bromine was used to elucidate the ion–ion and the ion–water interaction in this solution and to get more precise information on the local environment of both ions. After an intricate data evaluation procedure the differential atom pair correlation function (DAPCF) and its “negative image” the complement atom pair correlation function (CAPCF), were obtained. The analysis of the DACPF and the CAPCF provides no considerable inner-shell complexing of the cation and the anion, but a well defined and stable hydratation sphere around the triply charged Er3+–ion was found, which is in good agreement with results of conventional x-ray studies, extended x-ray absorption fine structure (EXAFS) measurements and Raman spectroscopy. In addition the analysis provides Er3+–Br1− interaction in the second coordination sphere and an overlap of the hydratation spheres of cat- and anions as well as of two anions. On the basis of these results a two-dimensional model of the ion–ion and the ion–water interaction is presented.

A differential anomalous X‐ray scattering study of the formation of lead zirconate titanate via sol‐gel process

AbstractA differential anomalous X‐ray scattering (DAS) investigation on gels, produced by hydrolysis of a mixture of lead(II)acetate and zirconium‐ and titanium‐n‐propoxides, and calcinated at the temperatures 200, 300, and 450 °, is presented. Anomalous X‐ray scattering was applied to get more precise information on the structural changes of the gel during calcination. Two different scattering experiments for each sample were performed with synchroton radiation of the energy below the L3 edge of lead, namely at 11500 and 13025 eV. The data were corrected for absorption, fluorescence radiation and multiple scattering. The Compton and atomic scattering were subtracted after normalization to absolute units with values for the anomalous dispersion corrections, determined by an absorption experiment. The Fourier transform of the total and differential scattering intensities yields the total and differential atom pair correlation functions (TAPCF, DACPF), which provide information on the local structure of lead and its changes during the calcination process. The analysis of the TAPCF's and DAPCF's indicates a structure, similar to that existing in the pyrochlore or perovskite phase of lead zirconate titanate (PZT), even at low temperatures. By comparison of the corresponding atom pair correlation functions (APCF's) it can be deduced that the near range as well as the long range order in the local environment of lead nearly remains unaltered during the calcination process.