Partial Pair Correlation Functions Research Articles

Neutron diffraction studies of the structure of water at ambient temperatures, revisited [a review of past developments and current problems

Neutron diffraction techniques used in the study of the structural characteristics of liquid water under ambient conditions are reviewed, showing the way that developments in the experimental and analytic procedures have led to improvements in the extracted results. The three partial pair correlation functions (OH, HH and OO) can be isolated from a set of diffraction measurements with varying hydrogen/deuterium isotopic composition. Although isotopic substitution is used routinely in many other investigations there are particular difficulties with hydrogenous systems due to the high incoherent scattering from hydrogen and the possibility that the H/D substitution is not a true isomorphic replacement. These features are discussed in some detail to analyse the systematic errors and the precision of the final results. An additional aspect of the comparison of data taken by different groups concerns the use of either reactor or pulsed neutron methods. Studies using the Orphee reactor with an over-determined set of five datasets are considered in detail, using analytic correction procedures based on the Powles formalism. Various consistency checks are applied to the data such that smoothing or iteration routines are not required. Two independent sets of the OD and DD pair correlation functions are obtained and are compared with the latest results from Soper et al. The small discrepancies between the various datasets are discussed in terms of propagating systematic errors and also possible variations from H/D equivalence. The relevance of the new results for the interpretation and modelling of ambient water structure are presented and the review ends with a brief comment on likely future developments that incorporate additional experimental information.

Structure of liquid Te-based alloys used in rewritable DVDs

We analyze the structure of Te-based chalcogenide compounds that are used as materials for rewritable DVDs by using a combination of neutron diffraction and ab initio computer simulation. We show that in the liquid, the atoms have a low average coordination number, as the result of a Peierls distortion. The partial pair correlation functions are obtained from the computer simulation data.

On the Structure of Liquid Hydrogen Fluoride.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Molecular dynamics study of the mechanism of ion transport in lithium silicate glasses: Characteristics of the potential energy surface and structures

Characterization of the potential energy surface is one of the essential problems to understand the mechanism of the ion conduction in glasses. In this work, ion dynamics in several lithium silicate glasses are examined by using molecular dynamics simulations. The number of ion sites, site energy, and the respective structures were examined for both fast (diffusive) and slow (localized) ions. We have visualized ion sites using the molecular dynamics simulation data and obtained the number of sites without being affected by a cut off value. The number obtained for the ${\mathrm{Li}}_{2}{\mathrm{SiO}}_{3}$ glass is $8--10%$ larger than that of ions. The value is reasonable to explain the diffusion mechanism by cooperative jumps, since rapid decrease of transport property in cooperative dynamics is expected if the number of the sites is too small while the cooperative jumps may be scarcely observed when the number of the vacancy is too large. The percentage of the available sites for the ${\mathrm{Li}}_{4}{\mathrm{SiO}}_{4}$ in the glassy state was found to be almost the same as that for ${\mathrm{Li}}_{2}{\mathrm{SiO}}_{3},$ while the diffusion coefficient of Li in ${\mathrm{Li}}_{4}{\mathrm{SiO}}_{4}$ is larger than ${\mathrm{Li}}_{2}{\mathrm{SiO}}_{3}.$ Increase of the diffusion coefficient with increasing alkali contents is easily explained by the contribution of the cooperative jumps but not by a simple mobile vacancy mechanism. Besides the characteristic sites for each slow (type A) and fast (type B) ions, many common sites for both type of ions are found, while the steepest descent energy distribution for these types of ions is quite similar. On the other hand, the partial pair correlation function, $g(r)$ of A-A pairs is found to be quite different from that of B-B pairs. Therefore, microstructures related to the density fluctuation of the Li ions are important for the difference of slow and fast dynamics.

Wide and low angle neutron scattering of water–pyridine mixtures

Neutron scattering measurements were performed for a number of water–pyridine mixtures using hydrogen/deuterium substitution for water. Composite partial pair correlation functions were extracted using the MCGR procedure. The results show changes in the water structure compared to the pure liquid and specific water–pyridine and pyridine–pyridine interactions. There is a strong scattering at low Q-values (<0.4 Å −1) which varies with pyridine concentration. These results are interpreted in terms of spherical clusters within the water matrix.

On the structure of liquid hydrogen fluoride.

The liquid state is the most complex phase of matter. Densities of liquids are comparable to densities of the solids, implying that the forces between particles in the liquid are of the same magnitude as those forces present in the solid. However, there is no simplification due to the presence of a lattice and no satisfactory analytic theory of the liquid state exists. However, despite this complexity, the liquid state is an outstandingly important chemical milieu in which many reactions take place. Strongly associated fluids are particularly complex and the structure and properties of these fluids provide an exacting and stringent test of theory. Here, we report the first investigation of the structure of hydrogen fluoride at the level of the distributions of pairwise interatomic distances, the partial pair correlation functions. Liquid HFis an important chemical and it is widely used in the petrochemical industry, as a catalyst for hydrocarbon management, and in the glass and ceramics industries. [1, 2] Academically, its superior properties as a solvent have found application in both organic and inorganic chemistry, and the superacidic properties have been exploited in both disciplines, in the study of reactive intermediates and reaction mechanisms [3, 4] That these highly desirable properties are not more widely applied is mainly due to the exceedingly toxic and corrosive nature of the material, [5] which is severe when anhydrous and only somewhat lessened in solution. Indeed, given the properties of liquid HF, it has been stated that the calculation of its properties is to be preferred over measurement. [6] The true importance of this fluid does not solely rest with its industrial and academic applications; it is the simplest archetype for the strong hydrogen bond, and the molecular

Short-range order in amorphous germanium–tellurium alloys

The atomic structure of Te-rich amorphous germanium tellurides has been investigated experimentally with high-energy synchrotron radiation and modeled by means of the reverse Monte Carlo technique. Total and partial structure factors and pair correlation functions were simulated. It is shown that the structure of Ge20Te80 and Ge15Te85 glasses can be described by GeTe4 tetrahedra as structural units which are bridged by Te–Te bonds.

Neutron-diffraction studies of some simple molecular systems: Si 2 Cl 6 , CBr 3 D and CD 3 I

The structure of liquid Si2Cl6, CBr3D and CD3I has been studied by the method of neutron diffraction. The structure factors have been analysed by means of the Reverse Monte Carlo (RMC) method and, therefore, partial pair-correlation functions have also been obtained from the particle coordinates. It seems that reliability of models set up by the RMC method is strongly connected to simple steric considerations.

Computer modelling of liquids salts RbBr, CuCl, CuBr, CuI and AgBr

Computer models of liquid ionic systems RbBr, CuCl, CuBr, CuI and AgBr containing 498 ions in the basic cube were constructed using experimental diffraction data. Modelling was conducted using algorithm BELION with varying ionic charges. Calculated atomisation energies were close to experimental data when charges were ±1.00 for RbBr, ±1.15 for AgBr, ±1.20 for CuCl, ±1.48 for CuBr, and ±1.37 for CuI. Partial pair correlation functions of models agree well with experimental data.

Model colloid–polymer mixtures in porous matrices: density functional versusintegral equations

We test the accuracy of a recently proposed density functional (DF) for afluid in contact with a porous matrix. The DF was constructed in thespirit of Rosenfeld’s fundamental measure concept and was derived forgeneral mixtures of hard core and ideal particles. The required doubleaverage over fluid and matrix configurations is performed explicitly. As anapplication we consider a model mixture where colloids and matrix particles arerepresented by hard spheres and polymers by ideal spheres. Integrating overthe degrees of freedom of the polymers leads to a binary colloid–matrixsystem with effective Asakura–Oosawa pair potentials, which we treatwith an integral-equation theory. We find that partial pair correlationfunctions from both theories are in good agreement with our computersimulation results, and that the theoretical results for the demixing binodalscompare well, provided the polymer-to-colloid size ratio, and hence the effectof many-body interactions neglected in the effective model, is not toolarge. Consistently, we find that hard (ideal) matrix–polymer interactionsinduce capillary condensation (evaporation) of the colloidal liquid phase.

Determination of alloy interatomic potentials from liquid-state diffraction data

This paper presents a general method for fitting interatomic potentials to partial pair correlation functions that can be obtained from diffraction experiments on pure materials or alloys. We apply this new approach to the specific case of embedded atom method-type interatomic potentials and demonstrate that it can be used to accurately fit this potential from partial pair correlation function data. The new method, presented above, can easily be extended to any type of interatomic potential. In addition, this method can be used in conjunction with standard approaches that fit crystal structure and properties.

Further notes concerning the partial pair correlation functions of liquid (ambient) water

Methods for deriving partial pair correlation functions for liquid water are considered. It is argued that the one based on Reverse Monte Carlo modeling [Phys. Rev. B 60 (1999) 11851] is more suitable for the purpose than direct separation (of which the latter is based on the inversion of the coefficient matrix). It is demonstrated that although there are still formidable difficulties, the latest total neutron structure factor on pure H 2O is probably the most reliable such data available on the substance.

First principles investigation of the intermediate range order in disordered materials: the case of SiSe2

The structural properties of liquid SiSe 2 are studied by using first-principles molecular dynamics simulations. A comparative analysis involving liquid GeSe 2 is carried out by focusing on partial pair correlation functions and coordination numbers. Both systems are characterized by intermediate range order. However, chemical order is more enhanced in liquid SiSe 2 than in liquid GeSe 2 , leading to a larger percentage of AX 4 tetrahedra and a smaller number of homopolar bonds.

Understanding precursor-derived amorphous Si-C-N ceramics on the atomic scale

The atomic structure of a precursor-derived amorphous ceramic with the composition ${\mathrm{Si}}_{37}{\mathrm{C}}_{32}{\mathrm{N}}_{31}$ and a density of $2.4 \mathrm{g}/{\mathrm{cm}}^{3}$ was modeled using a density-functional-based molecular dynamics simulation. Three different model structures were generated, and their total structure factors and total pair correlation functions from x-ray and neutron diffraction were calculated. For two of them, these data were found to agree very well with the experimental results. The different atomic structures of these two models could only be distinguished by the calculated partial pair correlation functions and their infrared spectra. It could be shown that in the final ceramic a phase separation into amorphous ${\mathrm{Si}}_{3}{\mathrm{N}}_{4},$ amorphous SiC, and graphitelike amorphous carbon has to appear.

The hydration structure of the Ni2+ ion intercalated in montmorillonite clay: a neutron diffraction with isotopic substitution study

We used neutron diffraction with an incident wavelength of 0.7054 A and both H/D and 58Ni/62Ni isotopic substitution to study the interlayer structure of hydrated Ni-exchanged Wyoming montmorillonite powders having 14.9 A interlayer spacing. We used a double difference method to obtain the gNiH(r) partial pair correlation function, as well as the complementary pair correlation function, gNiX(r), which together describe the structure around the Ni2+ ion. The hydration structure of the Ni2+ hexaaqua ion is found to be very close to that found in aqueous solution. Furthermore, the hydrogen isotope first-order difference gives a weighted sum of partial pair correlation functions, gHα(r), related to the intra- and inter-molecular structure around interlayer water hydrogens. These confirm our previous finding for Li-montmorillonite that the interlayer water adopts a liquid-type structure and that the clay surface does not prevent the interlayer water from having a highly hydrogen-bonded configuration. We used reverse Monte Carlo simulations to generate molecular configurations compatible with our first- and second-order difference data. These configurations show a tendency for interlayer water to form hydrogen bonds with the oxygens of the internal clay surfaces and that this results in an increase in the mean angle between the Ni–O vector and the water dipole in the Ni2+ hydration shell. The results demonstrate the validity of our approach of using orientationally averaged correlation functions obtained from isotopic substitution studies of powder samples to investigate inherently anisotropic hydration structures in layered clays.

Structure and dynamics of lithium silicate melts: molecular dynamics simulations

We present molecular dynamics simulations of lithium silicate melts (Li2O)x(SiO2)1−x with Li2O concentrations x = 0.01, x = 0.1 and x = 0.5 in equilibrium conditions for temperatures down to 1500 K. The partial pair correlation functions are determined and compared with recent experimental data. The dynamics of the individual species is characterized ia the mean square displacement. From the temperature dependence of the long-time diffusion constant we extract information about its activation energy. Interestingly, for x = 0.5 the extrapolation of the diffusion constant to temperatures below 700 K shows good agreement with experimental tracer diffusion data. In agreement with experiment, the length scale beyond which the dynamics becomes diffusive systematically varies with lithium concentration. Analysis of the van Hove self correlation function reveals how the occurrence of hopping processes as well as the presence of dynamic heterogeneities at low temperatures is correlated with the Li2O concentration.

EXAFS investigations of Cu–Mg–O compound

Abstract The interest to systems containing copper oxide is connected with the problem of high-temperature superconductivity because of the closeness of its basic physical properties and properties of superconductor mother Cu-compounds. In this work, EXAFS study of the Cu 0.2 Mg 0.8 O compound is presented. A new iterative algorithm of the solution of ill-posed problem on determining three partial pair correlation functions from one EXAFS-data set near the Cu K-edge is described. The results of X-ray scattering study of a given sample show a presence of a single phase with the MgO structure and a lattice parameter of 4.219 A instead of 4.208 A for pure MgO. From the EXAFS investigations, we find the local distortion of the lattice. We revealed that the short range order differs both from a hypothetical alloy with the MgO structure and from copper oxide.

Density functional theory for colloidal rod-sphere mixtures.

We present a density functional theory for a model colloidal mixture of hard spheres and infinitely thin hard rods. For these freely rotating particles, we use a fundamental measures approach to obtain a functional that features the correct dimensional crossover and the exact low density limit. For isotropic bulk fluid mixtures, the free energy, and hence the demixing phase diagram, are identical to that obtained from free volume theory. Results for the partial pair correlation functions of the bulk mixture are in good agreement with those of our simulations.

Bond length determination in Cu-Mg-O by EXAFS spectroscopy.

Magnetic semiconductors such as Cu(x)Mg(1-x)O, which are perspective materials for high-temperature superconductivity have been studied by EXAFS. The new technique of obtaining information from EXAFS-data has been described. It is based on the special iterative algorithm of solving an inverse ill-posed problem on the determination the partial pair correlation functions (pPCFs). Bond lengths of the nearest neighbours have been determined. It was clearly shown that the short range order in compound Cu0.2Mg0.8O differs from a hypothetical alloy with MgO structure and from the copper oxide.

Delta Algorithm for Developing Models of Binary Amorphous Systems from Diffraction Data

A new algorithm was proposed for generating models of low-temperature two-component amorphous systems from partial pair correlation functions (PPCFs). In this algorithm, the pair force functions are consecutively given small increments in the form of a delta function so as to attain better agreement between the model and diffraction (objective) PPCFs. The delta algorithm was used to construct models of amorphous Fe2Tb and Ni63.7Zr36.3 . The results indicate that the static structure of the amorphous system can be assessed very accurately. However, the problem of deriving the force functions from the PPCFs has no unique solution. Accordingly, dynamic properties such as autocorrelation functions and densities of vibrational states also cannot be determined uniquely.