Partial Structure Factors Research Articles

Structure of liquid tricalcium aluminate

The atomic-scale structure of aerodynamically levitated and laser-heated liquid tricalcium aluminate (${\mathrm{Ca}}_{3}{\mathrm{Al}}_{2}{\mathrm{O}}_{6}$) was measured at 2073(30) K by using the method of neutron diffraction with Ca isotope substitution (NDIS). The results enable the detailed resolution of the local coordination environment around calcium and aluminum atoms, including the direct determination of the liquid partial structure factor, ${S}_{\mathrm{CaCa}}(Q)$, and partial pair distribution function, ${g}_{\mathrm{CaCa}}(r)$. Molecular dynamics (MD) simulation and reverse Monte Carlo (RMC) refinement methods were employed to obtain a detailed atomistic model of the liquid structure. The composition ${\mathrm{Ca}}_{3}{\mathrm{Al}}_{2}{\mathrm{O}}_{6}$ lies at the CaO-rich limit of the CaO:${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ glass-forming system. Our results show that, although significantly depolymerized, liquid ${\mathrm{Ca}}_{3}{\mathrm{Al}}_{2}{\mathrm{O}}_{6}$ is largely composed of ${\mathrm{AlO}}_{4}$ tetrahedra forming an infinite network with a slightly higher fraction of bridging oxygen atoms than expected for the composition. Calcium-centered polyhedra exhibit a wide distribution of four- to sevenfold coordinated sites, with higher coordinated calcium preferentially bonding to bridging oxygens. Analysis of the MD configuration reveals the presence of $\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}%$ unconnected ${\mathrm{AlO}}_{4}$ monomers and ${\mathrm{Al}}_{2}{\mathrm{O}}_{7}$ dimers in the liquid. As the CaO concentration increases, the number of these isolated units increases, such that the upper value for the glass-forming composition of CaO:${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ liquids could be described in terms of a percolation threshold at which the glass can no longer support the formation of an infinitely connected ${\mathrm{AlO}}_{4}$ network.

Structure and Ionic Diffusion in Molten NaI, RbI, and NaI-RbI mixture

Static structure factors of molten NaI, RbI, and their mixture of (RbI) 0.3 (NaI) 0.7 are measured up to high- Q region by using the high-energy Xray diffraction technique. Moreover, molecular dynamics (MD) simulations are carried out, and the simulation results well reproduce the diffraction data. The partial structure factors, partial pair distribution functions, and ionic diffusion coefficients calculated by the MD simulations are reported in detail. The mixing effects of cations on the structure and ionic diffusion are also discussed.

On the First Principles Calculation of Redox Potential in Molten LiCl-KCl Eutectic Based on Adiabatic Substitution

A first principles approach based on adiabatic substitution is proposed to evaluate the redox potentials of a series of solute cations Mm + (Cu+, Au+, Tl+, Nd2+, Sc3+, Y3+, Ce3+, Pr3+, Nd3+, Gd3+, Tb3+, U3+, Pu3+, Np3+ and Am3+) in molten LiCl-KCl eutectic solvent at 723 K. A thermodynamic cycle is designed by adiabatic substitution of cation and neutral atom in molten salt with reference cation and reference neutral atom (Ag+ and Ag0 for monovalent cations, Ni2+ and Ni0 for divalent cation, and La3+ and La0 for trivalent cations) and vice versa. The redox potentials of these cations are evaluated relative to theAg+(sol)|AgCl(s)|Ag(s), Ni2 +(sol)|NiCl2(s)|Ni(s) and La3 +(sol)|LaCl3(s)|La(s) reference electrodes, respectively. Good agreements with experimental values are obtained with maximum absolute error of 0.354 V and standard deviation of 0.226 V. In addition, the first principles molecular dynamics (FPMD) is applied to the study of solvation structures of MClm in molten LiCl-KCl eutectic in terms of radial distribution functions and partial static structure factors in satisfactory agreement with X-ray and neutron diffraction characterizations. It is revealed that the solute cation affects significantly the intermediate-range order of Li+–Li+ but slightly of Cl−–Cl− and K+–K+.

Effect of Anion and Alkyl Side Chain on Structural and Dynamic Features of Ester Functionalized Ionic Liquids: Confirming Nanoscale Organization.

The effects of ester addition on structural and dynamic properties of biodegradable ILs composed of the 1-(alkoxycarbonyl)-3-alkylimidazolium cation ([C1COOCnC1im]+, n = 1, 2, 4) coupled with [Br]-, [NO3]-, [BF4]-, [PF6]-, [TfO]-, and [Tf2N]- are explored using the molecular dynamics (MD) simulations and quantum theory of atoms in molecules (QTAIM) at 400 K. Formation of the intramolecular H bonds between O atoms of the ester group and H atoms of the imidazolium ring as well as the nearest H atom of the alkyl chain to the ester group are disclosed from reduced density gradient (RDG) results. Nanoscale organization that leads to aggregation of the alkyl chain into the uncharged domains and formation of different morphologies can be clearly found by the results of site-site static partial structure factors of cations. Despite the fact that H atoms of the imidazolium ring are more acidic than the nearest H atoms of the alkyl side chain to the ester group, the cation-cation spatial distribution functions (SDFs) and the velocity SDFs demonstrate a reverse trend. This corresponds to the long-range organization of cations and nanoscale arrangement. Transport properties were calculated using the Green-Kubo and Einstein relations. Cations totally diffuse faster than anions and their discrepancies gradually vanish with elongation of the alkyl side chain. The translational motion of the terminal carbon atoms of the ester-functionalized cations decrease when the alkyl group is elongated, whereas the reverse trend is reported for common imidazolium-based ILs. The dynamic heterogeneity of selected ILs is comprehensively investigated by the computing vibrational density of states, van Hove function, and non-Gaussian parameter. Non-Gaussian parameters are finite over the entire time scale for ILs composed of bulkier cations and diverge from zero, verifying the long-lived cage effect. Nanoscale ordering is believed to be responsible for these observations. Finally, the simulated viscosity and ionic conductivity are in good agreement with the experimental data.

Concentration dependent structural parameters of liquid Al-Fe alloys

Square well potential is perturbed over Lebowtiz solution of hard sphere mixtures to determine direct correlation function,C(0)ij(r) in repulsive and attractive regions under Mean Spherical Model Approximation [1]. Obtained direct correlation functions were employed to derive partial structure factors and then total structure factor, S(k) in liquid Al-Fe alloy at different atomic percent of Al. Fourier transform of partial and total structure factors gives partial and total radial distribution functions, g(r) from which partial and total coordination numbers and the partial nearest-neighbor distances were computed.

Structure of amorphous GeSe9 by neutron diffraction and first-principles molecular dynamics: Impact of trajectory sampling and size effects

The structure of glassy GeSe9 was investigated by combining neutron diffraction with density-functional-theory-based first-principles molecular dynamics. In the simulations, three different models of N = 260 atoms were prepared by sampling three independent temporal trajectories, and the glass structures were found to be substantially different from those obtained for models in which smaller numbers of atoms or more rapid quench rates were employed. In particular, the overall network structure is based on Sen chains that are cross-linked by Ge(Se4)1/2 tetrahedra, where the latter are predominantly corner as opposed to edge sharing. The occurrence of a substantial proportion of Ge-Se-Se connections does not support a model in which the material is phase separated into Se-rich and GeSe2-rich domains. The appearance of a first-sharp diffraction peak in the Bhatia-Thornton concentration-concentration partial structure factor does, however, indicate a non-uniform distribution of the Ge-centered structural motifs on an intermediate length scale.

Critical Casimir interactions and colloidal self-assembly in near-critical solvents.

A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, including the pronounced fractionation of the solvent in the coexisting colloidal phases, of this complex system. We also present results for the partial structure factors; these shed light on the critical behaviour in the ternary mixture. The degree to which an effective two-body pair potential description can describe the phase behaviour and structure of the colloidal suspension is discussed briefly.

Structural characterization of the [CnC1im][C4F9SO3] ionic liquid series: Alkyl versus perfluoroalkyl side chains

This work represents an essential step towards the understanding at a molecular level of the bulk structure of ionic liquids (ILs) that exhibit both an hydrogenated and a perfluorinated alkyl side chain. Molecular Dynamics (MD) simulations were performed along the 1-alkyl-3-methylimidazolium perfluorobutylsulfonate homologous series, [CnC1im][C4F9SO3] (2≤n≤12) in order to study in a systematic way the effect on the bulk structure of the change of the ratios between polar and nonpolar moieties and between hydrogenated and fluorinated moieties. The MD trajectories were used to calculate global and partial structure factors, S(q), of each IL. The low-q peaks obtained from the deconvolution of the total S(q) functions were assigned to characteristic lengths of the polar network and non-polar domains, also computed via the appropriate pair radial distribution functions. Finally, several aggregation analyses were performed in order to emphasize the bicontinuous nature of the liquids and its systematic and complex evolution along the series.

Structural Properties of In<sub>1-</sub><i><sub>x</sub></i>Sn<i><sub>x</sub></i> at Different Concentrations and Temperatures

The partial structure factors for liquid alloy In1-xSnx have been computed at varying concentration and temperatures using pseudopotential theory. The structure factor S(q) and pair correlation function g (r) have been determined using the hard-sphere approximation. The temperature dependent hard-sphere diameter σ (T) is estimated using Vσ=Vminr+12kBT criterion from the computed pair potential. The modified empty-core local pseudopotential, which represents the orthogonalisation effect due to s-core states, is used for electron–ion interaction with proper screening function. The only potential parameter, the core radius, is determined at different temperatures from the knowledge of structure factor. Intrinsic temperature effects have been studied through dimensionless damping term (see formula in paper) in the pair potential. The effect of temperature and concentration on structure factors is discussed to shed light on bonding in technologically important alloy. This used pseudopotential proved successful in explaining the structural properties of non-crystalline alloys at higher temperatures.

Thermodynamic properties of Ga-Zn system. Experiment vs model

This paper contains the results of the integral molar mixing enthalpy of Ga-Zn liquid alloys, measured calorimetrically at two temperatures: 722K over the entire concentration range and 923K for the concentration range of Zn lower than 0.5at.%. Experimental values obtained in this range of temperatures indicate that the integral molar enthalpy of liquid alloys of this binary system is temperature independent. The available experimental values of the partial or molar Gibbs energies, together with the enthalpy of mixing, were used for the elaboration of the equation in the form proposed by Redlich and Kister, which describes the dependence of the excess Gibbs energy on the concentration and temperature. The experimental thermodynamic values of the excess Gibbs energy, mixing enthalpy change and activity were compared with those calculated with the use of the elaborated Redlich-Kister equation. Moreover, the partial structure factors and short-range order parameter were calculated and discussed in relation to the thermodynamic properties and the phase diagram of the Ga-Zn system.

Calorimetric Measurements of Liquid Al-Zn Alloys

The integral molar enthalpies of mixing were determined by the drop calorimetric method for binary AL-Zn liquid solutions and compared with the Miedema model as well as the earlier experimental data. The measurements were conducted at two temperatures: 957 K and 1001 K (684 °C and 728 °C), in the entire concentration range. Based on the experimental calorimetric data of this study as well as those available in the literature and the results of the activity studies, the interaction parameters of the Redlich-Kister equation for the liquid Al-Zn phase were worked out with the use of the least square method. The partial and integral Gibbs energies, entropies and enthalpies were calculated and presented in tables and figures. Additionally, the concentration-concentration partial structure factors for the ideal and real Al-Zn solutions were calculated and graphically presented.

Phase Diagram and Structure of Mixtures of Large Colloids and Linear Polymers under Good-Solvent Conditions

Efficient Monte Carlo simulations are used to determine the liquid–liquid binodal line of mixtures of hard-sphere colloids and neutral polymers under good-solvent conditions for two values of the polymer-to-colloid size ratio q, q = 0.5 and 1. We use a multiblob coarse-graining approach, in which groups of monomers are mapped onto a single pseudoatom (a blob) and blob–blob interactions are obtained by requiring the model to reproduce some large-scale properties of the polymer solution in the dilute limit. We also compute several experimentally relevant quantities at a few selected points along the binodal: thermodynamic properties (pressure, isothermal compressibility, chemical potentials), partial structure factors, and polymer form factor. Finally, we discuss how the polymers become more compact with increasing colloidal crowding.

Thermodynamic properties of liquid Ag-Li alloys

The electrochemical concentration cell method was used in the measurements of the activities of Li in the Ag-Li liquid and solid alloys. Activity measurements were performed with the use of electrochemical cells with liquid LiCl-LiF and LiCl-KCl electrolytes for 9 alloys in the xLi concentration range from 0.1 to 0.9 and at temperatures between 643K and 916K. The linear temperature dependencies of EMF of the Ag-Li alloys were observed and described by the equation EMF(T)=a+bT. The calculated partial thermodynamic functions of Li showed negative deviations from the ideal behaviour. With the application of all the available literature thermodynamic data, the interaction parameters of the Redlich-Kister equation for the liquid Ag-Li phase were worked out with the use of the least square method. The partial and integral Gibbs energies, entropies and enthalpies were calculated and presented in tables and figures. Additionally, the concentration-concentration partial structure factors for the ideal and real Ag-Li solutions were calculated and graphically presented.

Comparing two tetraalkylammonium ionic liquids. I. Liquid phase structure.

X-ray scattering experiments at room temperature were performed for the ionic liquids n-butyl-trimethylammonium bis(trifluoromethanesulfonyl)imide, [N1114][NTf2], and methyl-tributylammonium bis(trifluoromethanesulfonyl)imide, [N1444][NTf2]. The peak in the diffraction data characteristic of charge ordering in [N1444][NTf2] is shifted to longer distances in comparison to [N1114][NTf2], but the peak characteristic of short-range correlations is shifted in [N1444][NTf2] to shorter distances. Molecular dynamics (MD) simulations were performed for these ionic liquids using force fields available from the literature, although with new sets of partial charges for [N1114](+) and [N1444](+) proposed in this work. The shifting of charge and adjacency peaks to opposite directions in these ionic liquids was found in the static structure factor, S(k), calculated by MD simulations. Despite differences in cation sizes, the MD simulations unravel that anions are allowed as close to [N1444](+) as to [N1114](+) because anions are located in between the angle formed by the butyl chains. The more asymmetric molecular structure of the [N1114](+) cation implies differences in partial structure factors calculated for atoms belonging to polar or non-polar parts of [N1114][NTf2], whereas polar and non-polar structure factors are essentially the same in [N1444][NTf2]. Results of this work shed light on controversies in the literature on the liquid structure of tetraalkylammonium based ionic liquids.

Neutron Scattering of Residual Hydrogen in 1,4-Dioxane-d8 Liquid: Understanding Measurements with Molecular Dynamics Simulations.

That incoherent scattering from protiated molecular liquids adds a constant background to the measured scattering intensity is well-known, but less appreciated is the fact that coherent scattering is also induced by the presence of hydrogen in a deuterated liquid. In fact, the scattering intensity can be very sensitive, in the small-q region, with respect to the amounts and distribution of residual H in the system. We used 1,4-dioxane liquid to demonstrate that the partial structure factors of the HD and DD atom pairs contribute significantly to intermolecular scattering and that uncertainty in the extent of deuteration account for discrepancies between simulations and measurements. Both contributions to uncertainty have similar magnitudes: scattering interference of the hydrogen-deuterium pair, and complementary interference from the deuterium-deuterium pair by virtue of chemical inhomogeneity. This situation arises in practice since deuteration of liquids is often 99% or less. A combined experimental and extensive computational study of static thermal neutron scattering of 1,4-dioxane demonstrates the foregoing. We show, through simulations, that the reason for the differences is the content of protiated dioxane (vendors quote 1%). We estimate that up to 5% (at 298 K and at 343 K) protiated molar fraction may be involved in generating the scattering differences. Finally, we find that the particular distribution of hydrogen in the protiated molecules affects the results significantly; here, we considered molecules to be either fully protiated or fully deuterated. This scenario best reconciles the computational and experimental results, and leads us to speculate that the deuteration synthesis process tends to leave a molecule either fully deuterated or fully protiated. Although we have used 1,4-dioxane as a model liquid, the effects described in this study extend to similar liquids, and similar systematic experimental/computational studies can be performed to either understand measurements or calibrate/validate molecular dynamics models.

Ionic Networks in Polymer Solutions: Structural Properties and Phase Behavior

The structural properties and phase behavior of ionic networks embedded in polymer solutions are investigated using the Random Phase Approximation first introduced by de Gennes in polymer physics. The partial structure factors which are accessible by small angle neutron scattering are given in terms of the bare structure factors expressing the architecture of the polymer species and the interactions combining both excluded volume and long range electrostatic effects. It is found that the polyelectrolyte behavior characterizing the cross linked ionic network is tempered by linear chains present in the solution even though they are neutral and exert only shorter range excluded volume interactions. This finding was confirmed consistently by analyzing the scattering curves under a variety of conditions. The scattering peak at a finite wave vector qm shifts to higher values both with added salt and linear chains concentrations. Analysis of the phase behavior and effective thermodynamic interactions indicates an enhanced contraction of the network as more chains are added to the solution. While electrostatic charges tend to stabilize the system, the presence of linear chains promotes deswelling and phase separation processes. This analysis was developed from the q = 0 limit for the macro phase transition and q = qm for the micro phase reminiscent of ionic systems. The phase diagram covering both transition lines indicates clearly that the linear polymer favors the phase separation on both macroscopic and microscopic scales. Keywords: Ionic network, ionic strength, phase behavior, polyelectrolyte, structure factor, swelling.

Low-Dimensional Network Formation in Molten Sodium Carbonate.

Molten carbonates are highly inviscid liquids characterized by low melting points and high solubility of rare earth elements and volatile molecules. An understanding of the structure and related properties of these intriguing liquids has been limited to date. We report the results of a study of molten sodium carbonate (Na2CO3) which combines high energy X-ray diffraction, containerless techniques and computer simulation to provide insight into the liquid structure. Total structure factors (Fx(Q)) are collected on the laser-heated carbonate spheres suspended in flowing gases of varying composition in an aerodynamic levitation furnace. The respective partial structure factor contributions to Fx(Q) are obtained by performing molecular dynamics simulations treating the carbonate anions as flexible entities. The carbonate liquid structure is found to be heavily temperature-dependent. At low temperatures a low-dimensional carbonate chain network forms, at T = 1100 K for example ~55% of the C atoms form part of a chain. The mean chain lengths decrease as temperature is increased and as the chains become shorter the rotation of the carbonate anions becomes more rapid enhancing the diffusion of Na+ ions.

Br diffusion in molten NaBr explored by coherent quasielastic neutron scattering.

Molten sodium bromide has been investigated by quasielastic neutron scattering focusing on the wave vector range around the first structure factor peak. The linewidth of the scattering function shows a narrowing around the wave number of the structure factor peak, known as deGennes narrowing. In a monatomic system, this narrowing or in the time domain slowing down, has been related to a self-diffusion process of the caged particle. Here we show that this methodology can be applied to the molten alkali halide NaBr. The incoherent scattering from the sodium ions at small wave vectors provides the self-diffusion coefficient of sodium and the dynamics of bromine ions can be studied at wave numbers around the structure factor peak. With input from moleculardynamicssimulations on the partial structure factors, diffusion coefficients of the bromine ions can be obtained. These experimentally derived diffusion coefficients are in good agreement with molecular dynamics simulation results. This methodology to extract self-diffusion coefficients from coherent quasielastic neutron scattering is applicable to binary fluids in general when one particle dominates the scattering response at the structure factor maximum.

Efficient analytical expressions for dynamic structure of liquid binary alloys: K–Cs as a case study

A fitting scheme for analysis of collective dynamics in liquid binary alloys is proposed. It is based on explicit treatment of contributions from three relaxing modes and two types of propagating modes to the partial density–density time correlation functions and corresponding partial dynamic structure factors. Exact sum rules for each partial dynamic structure factor were taken into account. The proposed fitting scheme was applied to the liquid equimolar K–Cs alloy. Analysis of simulation-derived partial time correlation functions as well as of their corresponding Bhatia–Thornton ‘number-concentration’ combinations allowed dispersion and damping of the two branches of collective excitations and the behaviour of relaxing modes in a wide range of wave numbers to be obtained. A comparison with the inelastic neutron-scattering intensities for the liquid K–Cs alloy was performed.

Thermodynamic properties of liquid Ga–Li alloys: Experiment vs. modeling

The integral molar enthalpy of mixing was determined by the drop calorimetric method for binary Ga–Li liquid alloys. The measurements were conducted at three temperatures, i.e. 873K, 992K and 1039K, and in the following concentration ranges: XLi=0.7030 to 0.9801, 0.0908 to 0.3748 and 0.4284 to 0.8282, respectively. A strong negative deviation from the ideal solution was observed, with the minimum value equal to −21.2kJ/mol for XLi=0.5421. The analysis of the experimental data suggests that the integral mixing enthalpy of the Ga–Li liquid solutions is independent of temperature. The values calculated from the Miedema’s model are more positive in comparison to the measured ones, and the maximum difference of about 12.5kJ/mol is observed for the 0.5mol fraction of Li. By way of applying the calorimetric data from this work and the electromotive force measurements of Wen and Huggins and Yatsenko et al., the Redlich–Kister relation was worked out for the excess Gibbs energy of the liquid Ga–Li liquid solutions. The calculated Scc(0) partial structure factor points to the GaLi associates in liquids.