Liquid Structure Factor Research Articles

Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system.

We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterized by long wavelength density modulations and on further cooling forms a variety of other phases, including clustered, striped, and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor S(k) for wavenumber k is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows us to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.

X-ray diffraction of metastable structures from supercooled liquid hydrogen

We report time resolved observations of the crystallization from liquid hydrogen, supercooled to temperatures below the melting point, using 11.2 keV X-ray diffraction from the Linac Coherent Light Source (LCLS). Changes to the metastable solid and liquid structure factors have been dynamically measured. This allows for a direct determination of the lowest energy crystal polymorphs, the stacking probabilities, as well as the liquid and solid densities and temperatures. Such measurements provide experimental evidence of an Arrhenius-like growth kinetics along the stacking direction during supercooling.

Correlation-induced viscous dissipation in concentrated electrolytes.

Electrostatic correlations between ions dissolved in water are known to impact their transport properties in numerous ways, from conductivity to ion selectivity. The effects of these correlations on the solvent itself remain, however, much less clear. In particular, the addition of salt has been consistently reported to affect the solution's viscosity, but most modeling attempts fail to reproduce experimental data even at moderate salt concentrations. Here, we use an approach based on stochastic density functional theory, which accurately captures charge fluctuations and correlations. We derive a simple analytical expression for the viscosity correction in concentrated electrolytes, by directly linking it to the liquid's structure factor. Our prediction compares quantitatively to experimental data at all temperatures and all salt concentrations up to the saturation limit. This universal link between the microscopic structure and viscosity allows us to shed light on the nanoscale dynamics of water and ions under highly concentrated and correlated conditions.

Direct measurement of the structural change associated with amorphous solidification using static scattering of coherent radiation.

In this paper, we demonstrate that the weak temperature dependence of the structure factor of supercooled liquids, a defining feature of the glass transition, is a consequence of the averaging of the scattering intensity due to angular averaging. We show that the speckle at individual wavevectors, calculated from a simulated glass former, exhibits a Debye-Waller factor with a sufficiently large temperature dependence to represent a structural order parameter capable of distinguishing liquid from glass. We also extract from the speckle intensities a quantity proportional to the variance of the local restraint, i.e., a direct experimental measure of the amplitude of structural heterogeneity.

Layering and capillary waves in the structure factor of liquid surfaces.

Within the extended Capillary Wave Theory (ECWT), to extract the bending modulus of a liquid surface from the total structure factor of the interfacial region requires to separate the capillary waves (CW) signal from a non-CW background. Some years ago, Höfling and Dietrich (HD), working in the strict grazing incidence limit qz = 0, proposed a background that combines the liquid and vapor bulk structure factors in the amounts set by Gibbs's plane. We contrast that proposal with Molecular Dynamics (MD) simulations of the Lennard-Jones model analyzed with the Intrinsic Sampling Method (ISM). The study is extended to qz ≠ 0, to test the stronger consistency requirements of the ECWT and the experimental conditions; it shows a good MD-ECWT matching although we need some fine tuning over HD proposal. Then, the agreement with the ISM result for the surface bending modulus is good and that provides an interpretation, in terms of the molecular layering at the liquid edge, for the fluctuating surface represented by the CW signal in the surface structure factor, both for MD simulations and surface diffraction experiments.

Evidence for Ionic Diffusion in Dynamic Light Scattering from Glass-forming Sodium Borate Melts

Photon correlation spectroscopy conducted on glass-forming sodium borate melts provides a measure of the dynamic structure factor of these network-forming liquids over a broad time window and large temperature range. The dynamics are complex and include a non-Arrhenius temperature dependence and a non-exponential response to perturbations both of which are observed in the present measurements and both of which evolve with changes in the density of covalent bonds. An unexpected feature is the occurrence of a second, much slower relaxation process that develops only in the sodium-modified borates with up to 10 mol% sodium oxide. This second process appears to be caused by the diffusion of sodium ions as they undergo random ion hopping between charge-compensating sites in the network on a timescale equal to that of the viscous relaxation.

Spin dynamics of the antiferromagnetic Heisenberg model on a kagome bilayer

We study the spin dynamics of classical Heisenberg antiferromagnet with nearest neighbor interactions on a quasi-two-dimensional kagome bilayer. This geometrically frustrated lattice consists of two kagome layers connected by a triangular-lattice linking layer. By combining Monte Carlo with precessional spin dynamics simulations, we compute the dynamical structure factor of the classical spin liquid in kagome bilayer and investigate the thermal and dilution effects. While the low frequency and long wavelength dynamics of the cooperative paramagnetic phase is dominated by spin diffusion, weak magnon excitations persist at higher energies, giving rise the half moon pattern in the dynamical structure factor. In the presence of spin vacancies, the dynamical properties of the diluted system can be understood within the two population picture. The spin diffusion of the "correlated" spin clusters is mainly driven by the zero-energy weather-van modes, giving rise to an autocorrelation function that decays exponentially with time. On the other hand, the diffusive dynamics of the quasi-free "orphan" spins leads to a distinctive longer time power-law tail in the autocorrelation function. We discuss the implications of our work for the glassy behaviors observed in the archetypal frustrated magnet SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$ (SCGO).

Consistent approach for electrical resistivity within Ziman's theory from solid state to hot dense plasma: Application to aluminum.

The approach presented in this work allows a consistent calculation of electrical conductivity of dense matter from the solid state to the hot plasma using the same procedure, consisting in dropping elastic scattering contributions to solid's and liquid's structure factors in the framework of the Ziman theory. The solid's structure factor was computed using a multiphonon expansion. The elastic part is the zero-phonon term and corresponds to Bragg peaks, thermally damped by Debye-Waller attenuation factors. For the liquid, a similar elastic contribution to the structure factor results from a long-range order persisting during the characteristic electron-ion scattering time. All the quantities required for the calculation of the resistivities are obtained from our average-atom model, including the total hypernetted-chain structure factor used from the liquid state to the plasma. No interpolation between two limiting structure factors is required. We derive the correction to apply to the resistivity in order to account for the transient long-range order in the liquid and show that it improves considerably the agreement with quantum-molecular dynamics simulations and experimental aluminum's isochoric and isobaric conductivities. Our results suggest that the long-range order in liquid aluminum could be a slightly compressed fcc one. Two series of ultrafast experiments performed on aluminum were also considered, the first one by Milchberg etal. using short laser pulses and the second one by Sperling etal. involving x-ray heating and carried out on the Linac Coherent Light Source facility. Our attempts to explain the latter assuming an initial liquid state at an ion temperature much smaller than the electron one suggest that the actual initial state before main heating is neither perfectly solid nor a normal liquid.

Quasicrystal formation in binary soft matter mixtures

Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with integral equation theory. Quasicrystal formation requires particle ordering with two characteristic lengthscales in certain particular ratios. How the lengthscales are related to the form of the pair interactions is reasonably well understood for one component systems, but less is known for mixtures. In our model mixture of big and small colloids confined to an interface, the two lengthscales stem from the range of the interactions between pairs of big particles and from the cross big-small interactions, respectively. The small-small lengthscale is not significant. Our strategy for finding quasicrystals involves tuning locations of maxima in the dispersion relation, or equivalently in the liquid state partial static structure factors.

Reliability of molecular dynamics interatomic potentials for modeling of titanium in additive manufacturing processes

We present an approach to study the transferability of molecular dynamics (MD) interatomic potentials (IPs) for materials modeling during metal additive manufacturing (MAM) processes, which involves rapid and cyclic melting, solidification, vaporization, and solid phase transformations. We apply the approach to the ten available IPs of titanium (Ti) as an example, which resembles the MAM process modeling of commercially pure Ti and Ti-base alloys. We consider the capability to produce solid phase change behavior of the alloy in equilibrium and nonequilibrium thermodynamics as the primary required characteristics of an IP for the MAM process modeling. Two-phase α-β, β-liquid, and liquid-vapor coexistence properties are used as the secondary criteria. Finally, we use other relevant single-phase properties as the tertiary criteria, such as the elastic constants at high temperatures, liquid structure factor, self-diffusivity, and shear viscosity. We show there are only three IPs that demonstrate reasonable characteristics for MAM process modeling.

Neural network in the inverse problem of liquid argon structure factor: from gas-to-liquid radial distribution function

Within the framework of the inverse problem theory, together with the dynamical Hopfield neural, the radial distribution function of liquid argon was obtained from neutron scattering data. A modest initial condition, the Boltzmann factor for a pair potential or an ideal gas radial distribution function, was used to propagate the neural differential equations. In both cases, the inverted data were obtained with great accuracy. The present work shows that a combination of the inverse theory approach, together with the Hopfield neural network, is a powerful method to obtain liquid properties. Results are obtained almost instantaneously and can be applied for more complex systems.

Coordination changes in liquid tin under shock compression determined using in situ femtosecond x-ray diffraction

Little is known regarding the liquid structure of materials compressed to extreme conditions, and even less is known about liquid structures undergoing rapid compression on nanosecond timescales. Here, we report on liquid structure factor and radial distribution function measurements of tin shock compressed to 84(19) GPa. High-quality, femtosecond x-ray diffraction measurements at the Linac Coherent Light Source were used to extract the liquid diffuse scattering signal. From the radial distribution function, we find that the structural evolution of the liquid with increasing pressure mimics the evolution of the solid phase. With increasing pressure, we find that the liquid structure evolves from a complex structure, with a low coordination number, to a simple liquid structure with a coordination number of ∼12. We provide a pathway for future experiments to study liquids at elevated pressures using high-energy lasers to shock compress materials beyond the reach of static diamond anvil cell techniques.

Thermodynamics of solid Sn and Pb[sbnd]Sn liquid mixtures using molecular dynamics simulations

We present a new set of modified embedded-atom method parameters for the PbSn system that describes many 0 K and high temperature properties including melting point, elastic constants, and enthalpy of mixing for solid and liquid PbSn alloys in agreement with experiments. Then, we calculate the phase diagram of the Sn-rich side of PbSn alloys utilizing a hybrid Molecular Dynamics/Monte Carlo simulation that agrees with experimental solidus and liquidus curves as well as stability of α-Sn and β-Sn. In addition, we present structure factors of PbSn liquid alloys as well as temperature-dependent thermal expansion coefficients and heat capacity. Our simulations show that the ratios of the heights of the second and third peaks over the first peak for PbSn liquid mixtures are maximum at Pb-0.6Sn concentration.

Capillary waves as eigenmodes of the density correlation at liquid surfaces

We analyze the density correlations in a liquid-vapor surface to establish a quantitative connection between the Density Functional (DF) formalism, Molecular Dynamic (MD) simulations, and the Capillary Wave (CW) theory. Instead of the integrated structure factor, we identify the CW fluctuations as eigenmodes of the correlation function. The square-gradient DF approximation appears as fully consistent with the use of the thermodynamic surface tension to describe the surface fluctuations for any wavevector because it misses the upper cutoff in the surface Hamiltonian from the merging of the CW mode with the non-CW band. This mesoscopic cutoff may be accurately predicted from the main peak in the structure factor of the bulk liquid. We explore the difference between the full density-density correlation mode and the bare CW that represents the correlation between the corrugation of the intrinsic surface and the density at the interfacial region. The non-local decay of the CW effects, predicted from DF analysis and observed in MD simulations with the intrinsic sampling method, is found to characterize the bare CW fluctuations, which also require a wavevector-dependent surface tension.

Structural analysis of zwitterionic liquids vs. homologous ionic liquids.

Zwitterionic liquids (Zw-ILs) have been developed that are homologous to monovalent ionic liquids (ILs) and show great promise for controlled dissolution of cellulosic biomass. Using both high energy X-ray scattering and atomistic molecular simulations, this article compares the bulk liquid structural properties for novel Zw-ILs with their homologous ILs. It is shown that the significant localization of the charges on Zw-ILs leads to charge ordering similar to that observed for conventional ionic liquids with monovalent anions and cations. A low-intensity first sharp diffraction peak in the liquid structure factor S(q) is observed for both the Zw-IL and the IL. This is unexpected since both the Zw-IL and IL have a 2-(2-methoxyethoxy)ethyl (diether) functional group on the cationic imidazolium ring and ether functional groups are known to suppress this peak. Detailed analyses show that this intermediate range order in the liquid structure arises for slightly different reasons in the Zw-IL vs. the IL. For the Zw-IL, the ether tails in the liquid are shown to aggregate into nanoscale domains.

Molecular dynamics for near melting temperatures simulations of metals using modified embedded-atom method

Availability of a reliable interatomic potential is one of the major challenges in utilizing molecular dynamics (MD) for simulations of metals at near the melting temperatures and melting point (MP). Here, we propose a novel approach to address this challenge in the concept of modified-embedded-atom (MEAM) interatomic potential; also, we apply the approach on iron, nickel, copper, and aluminum as case studies. We propose adding experimentally available high temperature elastic constants and MP of the element to the list of typical low temperature properties used for the development of MD interatomic potential parameters. We show that the proposed approach results in a reasonable agreement between the MD calculations of melting properties such as latent heat, expansion in melting, liquid structure factor, and solid-liquid interface stiffness and their experimental/computational counterparts. Then, we present the physical properties of mentioned elements near melting temperatures using the new MEAM parameters. We observe that the behavior of elastic constants, heat capacity and thermal linear expansion coefficient at room temperature compared to MP follows an empirical linear relation (α±β × MP) for transition metals. Furthermore, a linear relation between the tetragonal shear modulus and the enthalpy change from room temperature to MP is observed for face-centered cubic materials.

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 dynamics of ionic liquids: Trimethylsilylpropyl-substituted cations and bis(sulfonyl)amide anions.

Ionic liquids with cationic organosilicon groups have been shown to have a number of useful properties, including reduced viscosities relative to the homologous cations with hydrocarbon substituents on the cations. We report structural and dynamical properties of four ionic liquids having a trimethylsilylpropyl functional group, including 1-methyl-3-trimethylsilylpropylimidazolium (Si-C3-mim+) cation paired with three anions: bis(fluorosulfonyl)imide (FSI-), bis(trifluoromethanesulfonyl)imide (NTf2-), and bis(pentafluoroethanesulfonyl)imide (BETI-), as well as the analogous N-methyl-N-trimethylsilylpropylpyrrolidinium (Si-C3-pyrr+) cation paired with NTf2-. This choice of ionic liquids permits us to systematically study how increasing the size and hydrophobicity of the anions affects the structural and transport properties of the liquid. Structure factors for the ionic liquids were measured using high energy X-ray diffraction and calculated from molecular dynamics simulations. The liquid structure factors reveal first sharp diffraction peaks (FSDPs) for each of the four ionic liquids studied. Interestingly, the domain size for Si-C3-mim+/NTf2- indicated by the maxima for these peaks is larger than for the more polar ionic liquid with a similar chain length, 1-pentamethyldisiloxymethyl-3-methyl-imidazolium bis(trifluoromethanesulfonyl)imide (SiOSi-mim+/NTf2-). For the series of Si-C3-mim+ ionic liquids, as the size of the anion increases, the position of FSDP indicates that the intermediate range order domains decrease in size, contrary to expectation. Diffusivities for the anions and cations are compared for a series of both hydrocarbon-substituted and silicon-substituted cations. All of the anions show the same scaling with temperature, size, and viscosity, while the cations show two distinct trends-one for hydrocarbon-substituted cations and another for organosilicon-substituted cations, with the latter displaying increased friction.

On the quantification of phase-field crystals model for computational simulations of solidification in metals

Phase-field crystals (PFC) is an atomistic model on diffusive time scale with the capability to simulate solidification/melting and the subsequent nano-structural evolution while naturally accounting for elasticity and plasticity. Although PFC was originally introduced as a phenomenological model in materials science (Elder et al., 2002), it was later shown that it can be derived from density functional theory (DFT) by certain approximations (Elder et al., 2007) providing a significant predictive capability for PFC. However, these approximations in PFC, similar to any other higher-scale computational model derived from DFT, have introduced intrinsic challenges for quantifying of PFC for specific materials; i.e. determining PFC model parameters for specific materials. The objective of this article is to present a variety of possible approaches that can be used for quantifying PFC for solidification/melting modeling. Thus, we present a reformulation of PFC model containing two extra parameters and four possible quantification approaches. Then, representative material properties corresponding for each individual approach are calculated and compared with their available experimental/computational counterparts in literature. The representative material properties include elastic constants, liquid and solid densities, liquid structure factor, latent heat, and solid-liquid interface free energy and its anisotropy. We discuss the quantitative capabilities of each quantification approach regarding their prediction of the mentioned representative material properties for Fe as an example material. The discussion provided in this study can be used as a guideline to select the proper quantification approach for researchers who need to use PFC for quantitative modeling.

Structure of ionic liquids with cationic silicon-substitutions

Significantly lower viscosities result when a single alkyl carbon is replaced by a silicon atom on the side chain of an ionic liquid cation. To further explore this effect, we compare liquid structure factors measured using high-energy X-ray scattering and calculated using molecular dynamics simulations. Four ionic liquids are studied that each has a common anion, bis(trifluoromethylsulfonyl)amide (NTf2−). The four cations for this series of NTf2−-anion ionic liquids are 1-methyl-3-trimethylsilylmethylimidazolium (Si-mim+), 1-methyl-3-neopentylimidazolium (C-mim+), 1-methyl-3-pentamethyldisiloxymethylimidazolium (SiOSi-mim+), and 1-methyl-1-trimethylsilylmethylpyrrolidinium (Si-pyrr+). To achieve quantitative agreement between the structure factors measured using high-energy X-ray scattering and molecular dynamics simulations, new transferable parameters for silicon were calibrated and added to the existing force fields.