Partial Dynamic Structure Factors Research Articles

Ab initio study of collective eigenmodes in dynamics of molten salts

An effective fitting scheme within the thermo-viscoelastic model is proposed for estimation of dynamic eigenmodes of an ionic melt from ab initio molecular dynamics (AIMD) simulations. Dynamic eigenmodes are solutions of the generalized Langevin equation in matrix form, obtained on the basis set of eight dynamic variables. Fitting parameters are used only in the generalized hydrodynamic matrix T(k) for matrix elements involving heat density and heat current correlations only, because of huge computational efforts needed to calculate them directly in ab initio simulations. In the proposed scheme six AIMD-derived time correlation functions, three partial density-density and three partial current-current ones, are recovered by the proposed theoretical approach, which satisfies the exact sum rules up to the fourth frequency moments of partial dynamic structure factors. The suggested theoretical analysis was applied to estimation of propagating hydrodynamic and non-hydrodynamic eigenmodes in molten NaCl.

Static structure, collective dynamics and transport coefficients in the liquid Li-Pb alloy. An ab initio molecular dynamics study

Several static and dynamic properties of the liquid Li-Pb alloy at diverse compositions, have been calculated by means of ab initio molecular dynamics simulation study. This alloy has attracted much attention because of the finding of fast sound at the Li0.80Pb0.20 composition and also the technological interest of the the eutectic composition, Li0.17Pb0.83, as a component of the blanket in fusion reactors.Results are reported for total static structure factors, which are compared with the available experimental data. An additional analysis of the structure allows the quantification of the heterocoordinating tendencies in this alloy, which at the Li0.80Pb0.20 composition are largest and lead to a Pb-centered polyhedral structure, where, however, Li4Pb units are not present.Regarding the collective dynamics, the calculated partial dynamic structure factors exhibit side peaks indicative of propagating density fluctuations, including density fluctuation modes with phase velocity greater than the hydrodynamic sound velocity. Also, the longitudinal and transverse dispersion relations have been calculated and its different branches analysed. We find all the high frequency branches to behave as optic-like modes, contrary to other interpretations in terms of an acoustic-like fast sound mode.Some transport coefficients such as self- and inter-diffusion coefficients, shear viscosities and adiabatic sound velocities, have also been calculated. Finally, the obtained results for the electronic density of states clearly indicate the metallic character of the liquid LixPb1-x alloy.

Local order and dynamic properties of liquid Agx-Sn1 −x alloys by ab initio molecular dynamics

Several static and dynamic properties of the liquid AgxSn1−x alloys have been evaluated by ab-initio molecular dynamics simulations. The calculated total static structure factors are in good agreement with the corresponding experimental data. The partial dynamic structure factors and the longitudinal current correlation spectra exhibit side peaks, some of which are indicative of propagating density fluctuations, while others are due to interdiffusion processes. Results are also reported for other dynamical properties such as the diffusion coefficients, including self- and inter-diffusion, the shear viscosity, and the adiabatic sound velocity. The electronic density of states shows that the liquid AgxSn1−x alloys have a metallic character, although with strong deviations from the free-electron parabolic curve.

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.

Static structure, microscopic dynamics and electronic properties of the liquid Bi–Li alloy. An ab initio molecular dynamics study

We report an ab initio molecular dynamics study of the static, dynamic and electronic properties of the liquid BixLi1−x alloy, which is a complex binary system with a marked tendency to heterocoordination. The calculated total static structure factors are in good agreement with the available experimental data. The partial dynamic structure factors exhibit side peaks indicative of propagating density fluctuations, and for some concentrations we have found a density fluctuation mode with phase velocity greater than the hydrodynamic sound velocity. We have also evaluated other dynamical properties such as the diffusion coefficients, the shear viscosity and the adiabatic sound velocity. The electronic density of states show that the liquid BixLi1−x alloy has a metallic character, although with strong deviations from the free-electron parabolic curve. The results reported improve the understanding of binary liquid alloys with both fast and slow propagating collective modes.

Inter-cation interaction in partial dynamic structure factors S ξη(k,ω) and electrical properties of molten AgI–RbI system

Phonon propagation in molten RbAg4I5 is discussed based on the partial dynamic structure factors S ξη( k ,ω), which are obtaisned by molecular dynamics (MD) simulation using pair potentials considering the effect of polarisability of ions. The longitudinal acoustic (LA) and transverse acoustic (TA) modes have been observed in molten RbAg4I5, which are found to be propagated mainly by the different ions: LA mode by I ions and TA mode by Ag ions. The origin of the TA phonon mode is attributed to the cation–cation interaction. The electrical properties, the electron density of states, the band structure, etc., are also examined by ab initio calculation. The hybridisation of electronic states between ions is enhanced by the existence of Rb ion.

Ab initio study of collective excitations in a disparate mass molten salt

Ab initio molecular dynamics simulations and the approach of generalized collective modes are applied for calculations of spectra of longitudinal and transverse collective excitations in molten LiBr. Dispersion and damping of low- and high-frequency branches of collective excitations as well as wave-number dependent relaxing modes were calculated. The main mode contributions to partial, total, and concentration dynamic structure factors were estimated in a wide region of wave numbers. A role of polarization effects is discussed from comparison of mode contributions to concentration dynamic structure factors calculated for molten LiBr from ab initio and classical rigid ion simulations.

Static structure, microscopic dynamics and electronic properties of the liquid Bi–Pb alloy. An ab initio molecular dynamics study

We perform an ab initio molecular dynamics study of the static, dynamic and electronic properties of the liquid Bi x Pb 1− x alloy at three concentrations, including the eutectic one, x = 0.55. This alloy is of particular technological interest for its possible use as coolant in fast reactors. Our predictions are in good agreement with the available experimental data. In particular, the computed total static structure factors reproduce accurately the neutron diffraction results, and the predicted adiabatic sound velocity and shear viscosity compare well with the experimental values. The partial dynamic structure factors exhibit clear side peaks indicative of propagating density fluctuations, and the longitudinal and transverse dispersion relations show several branches, which we analyze in detail. The electronic density of states show that the liquid Bi–Pb alloy is a good metal, but with strong deviations from the free-electron parabolic curve.

Critical dynamics of lateral and transversal phase separations in bilayer biomembranes and surfactants

We consider bilayer biomembranes or surfactants made of two chemically incompatible amphiphile molecules, which may laterally or transversely phase separate into macrodomains, upon variation of some suitable parameter (temperature, lateral pressure, etc.). The purpose is an extensive study of the dynamics of both lateral and transverse phase separations, when the bilayer is suddenly cooled down from a high initial temperature towards a final one very close to the spinodal point. The critical dynamics are investigated through the partial dynamic structure factors of different species. Using a two-order parameter field theory, where the two fields are the composition fluctuations of one component in the leaflets of the bilayer, combined with an extended van Hove approach that is based on two coupled Langevin equations (with noise), we exactly compute these dynamic structure factors. We first find that the dynamics is governed by two time scales. The longest one, Tau, can be related to the thermal correlation length, Xi ~ Sigma|T - T(c)|(-1/2), by Tau ~ Xi(z), with the dynamic critical exponent z = 4, where Sigma is an atomic length scale, T the absolute temperature, and T(c) its critical value. The characteristic time Tau can be interpreted as the time required for the formation of the final macrophase domains. The second time scale is rather shorter, and can be viewed as the short time during which the unlike phospholipids execute local motion. Second, we demonstrate that the dynamic structure factors obey exact scaling laws, and depend on three lengths, namely the wavelength q(-1) (q is the wave vector modulus), the correlation length Xi, and a length scale R(t) ~ t(1/z) (z = 4) representing the size of macrophase domains at time t. Of course, the two lengths Xi and R(t) coincide at the final time Tau at which the bilayer reaches its final equilibrium state. Finally, the present work must be considered as a natural extension of our previously published one dealing with the study of lateral and transverse phase separations from a static point of view.

Atomic dynamics of alumina melt: A molecular dynamics simulation study

The atomic dynamics of Al2O3 melt are studied by molecular dynamics simulation. The particle interactions are described by an advanced ionic interaction model that includes polarization effects and ionic shape deformations. The model has been shown to reproduce accurately the static structure factors S(Q) from neutron and x-ray diffraction and the dynamic structure factor S(Q,!) from inelastic x-ray scattering. Analysis of the partial dynamic structure factors shows inelastic features in the spectra up to momentum transfers, Q, close to the principal peaks of partial static structure factors. The broadening of the Brillouin line widths is discussed in terms of a frequency dependent viscosity �(!).

Dynamic structure of molten CuI: Ab initio molecular-dynamics simulations

The dynamic properties of molten CuI are studied by ab initio molecular-dynamics simulations. The frequency spectrum of the velocity auto-correlation function for Cu ions spreads over higher frequencies than 20meV, which reflects a peculiar interaction between Cu ions. It is shown that the calculated dynamic structure factors are in good agreement with the recent inelastic X-ray scattering experiments. The narrowing in the partial dynamic structure factors for Cu and I ions is found at the wave number of about 1.0 and 1.8Å−1, respectively.

Direct measurement of relative and collective diffusion in a dilute binary colloidal suspension

Experimental characterization of the dynamics of multicomponent fluids is a problem of general importance to the field of complex fluids. We demonstrate a new experimental approach, termed two-color Fourier imaging correlation spectroscopy, which allows direct measurement of the partial dynamic structure factors, S(11)(k,tau), S(22)(k,tau), and S(12)(k,tau), where 1, 2 label the component species of a binary colloidal suspension. Linear combinations of the partial dynamic structure factors yield the characteristic time-correlation functions of the binary fluid. These are the correlation functions of concentration fluctuations S(CC)(k,tau), number density fluctuations S(NN)(k,tau), and cross-correlations between number density and concentration fluctuations S(NC)(k,tau). Test measurements are performed on a dilute symmetric mixture of fluorescently labeled 0.5 and 1.0 microm polystyrene spheres. From these data, we determine generalized collective and relative diffusion coefficients, and compare them to the predictions for an ideal mixture of noninteracting particles.

Collective excitations in molten NaCl and NaI: A theoretical generalized collective modes study

A theoretical analysis of dispersion for two branches of propagating collective excitations in molten NaCl and NaI is performed using an approach of generalized collective modes. Two molten salts with different mass ratios were studied in order to clarify reported ``fast sound'' in molten NaCl [F. Demmel, S. Hosokawa, M. Lorenzen, and W.-C. Pilgrim, Phys. Rev. B 69, 012203 (2004)]. Contributions of low- and high-frequency branches to partial dynamical structure factors in molten salts are discussed.

Microscopic dynamics in the liquid Li-Na alloy: an ab initio molecular dynamics study.

We present results for several structural and dynamical properties of the liquid Li(1-x)Na(x) alloy. The study has been carried out by means of the orbital-free ab initio molecular dynamics method, combined with local ionic pseudopotentials constructed within the same framework. We obtain good agreement with the available experimental data, reproducing accurately, the strong homocoordinating tendencies exhibited by this alloy. The calculated partial dynamic structure factors exhibit clear side peaks whose frequencies, for q<or=0.25 A(-1), correspond to the hydrodynamic sound dispersion of the binary alloy, whereas for larger q values fast and slow sound modes are identified. The mass ratio in this system, m(Na)/m(Li) approximately 3, is the smallest one so far for which the fast mode is observed.

Nonequilibrium statistical operator method: Generalized transport equations of diffusion-reaction processes

Generalized transport equations for description of diffusion-reaction processes in chemically active mixtures are obtained. The nonequilibrium statistical operator method by Zubarev is used and both strong and weak nonequilibrium processes are analyzed. In the approximation of the second order in fluctuations we get generalized equations of chemical kinetics for bimolecular reactions with generalized rate constants. In the case of spatial uniformity the integro-differential equation for the matrix of partial scattering functions is received, which are related to partial dynamic structure factors of chemically reactive system by the time Fourier transformation.

Partial dynamic structure factors in Ni 62 Nb 38 metallic glass

The total dynamic structure factors S(Q,E) in three Ni62Nb38 samples with different isotope content were investigated by inelastic neutron scattering, over a range of momentum and energy transfer: Q=0.5–5 A-1 and E=1–40 meV at the IN6 spectrometer (ILL, Grenoble, France). According to the Ashcroft–Langreth formalism, the partial dynamic structure factors SNiNi(Q,E), SNbNb(Q,E) and SNiNb(Q,E) were reconstructed. It is the first experimental observation showing the existence of collective vibrational excitations in the Ni62Nb38 metallic glass system at a partial dynamic structure factor level.

Critical dynamics of strong coupling paramagnetic systems exhibiting a paramagnetic–ferrimagnetic transition

The purpose of this work is the investigation of critical dynamic properties of two strongly coupled paramagnetic sublattices exhibiting a paramagnetic–ferrimagnetic transition. To go beyond the mean-field approximation, and in order to get a correct critical dynamic behavior, use is made of the renormalization-group (RG) techniques applied to a field model describing such a transition. The model is of Landau–Ginzburg type, whose free energy is a functional of two kinds of order parameters (local magnetizations) ϕ and ψ, which are scalar fields associated with these sublattices. This free energy involves, beside quadratic and quartic terms in both fields ϕ and ψ, a lowest-order coupling, − C 0 ϕψ, where C 0 is the coupling constant measuring the interaction between the two sublattices. Within the framework of mean-field theory, we first compute exactly the partial dynamic structure factors, when the temperature is changed from an initial value T i to a final one T f very close to the critical temperature T c . The main conclusion is that, physics is entirely controlled by three kinds of lengths, which are the wavelength q −1, the static thermal correlation length ξ and an extra length L t measuring the size of ordered domains at time t. Second, from the Langevin equations (with a Gaussian white noise), we derive an effective action allowing to compute the free propagators in terms of wave vector q and frequency ω. Third, through a supersymmetric formulation of this effective action and using the RG-techniques, we obtain all critical dynamic properties of the system. In particular, we derive a relationship between the relaxation time τ and the thermal correlation length ξ, i.e., τ∼ ξ z , with the exponent z=(4− η)/(2 ν+1), where ν and η are the usual critical exponents of Ising-like magnetic systems. At two dimensions, we find the exact value z= 5 4 . At three dimensions, and using the best values for exponents ν and η, we find z=1.7562±0.0027.

Theory of the generalized dynamic structure factor of polyatomic molecular fluids measured by inelastic x-ray scattering.

We describe a theory for the calculation of the generalized dynamic structure factor S(k,omega) as measured by an inelastic x-ray scattering (IXS) experiment on single-component molecular or polyatomic molecular fluids. IXS spectrum of a simple fluid is proportional to the dynamic structure factor of a single species of atom. In the case of a molecular fluid, however, IXS spectrum is a weighted sum of partial dynamic structure factors of pairs of atomic species. The weighting factors are products of the atomic form factors of the pairs. We call this weighted average dynamic structure factor the generalized dynamic structure factor. We extend the formalism of a three effective eigenmode theory (TEE) developed previously for simple fluids to derive an approximate evolution equation for the generalized dynamic structure factor, which can be considered as a generalized hydrodynamic equation for molecular fluids. As examples, we first study the contributions of the partial dynamic structure factor to the generalized dynamic structure factor computed from molecular dynamics simulation of SPC/E model water. We found that the generalized dynamic structure factor of water measured by IXS can be well approximated by the center of mass or the oxygen atom dynamic structure factors. The generalized TEE model was then employed to analyze IXS spectra of nearly fully hydrated dilauroylphosphatidylcholine. The theory is able to fit all of the spectra in the k range from 5 to 32 nm(-1) quantitatively and gives their deconvoluted generalized dynamic structure factors.

On the dynamical properties of the liquid Li–Na alloy

Several dynamical properties of the liquid Li–Na alloy have been studied by both molecular dynamics simulations and by a theoretical memory function formalism. We present results for the Li 0.61Na 0.39 system where comparison is performed with the experimental inelastic neutron scattering data. The obtained results for the partial dynamic structure factors reveal the existence of propagating sound modes for wavevectors k < 1.4 Å −1.

Cooperative diffusion in colloidal mixtures

In this work we develop a general method to examine cooperative diffusion, i.e., the partial dynamic structure factors, in multicomponent colloidal mixtures of spherical particles. Using a multivariable projection operator formalism based on the many-body Smoluchowski diffusion equation, we derive an exact microscopic expression for the matrix of irreducible memory functions associated with the partial dynamic structure factors and the long-time cooperative diffusion coefficients of the system. Starting from this microscopic expression, we present a derivation of a self-consistent mode coupling scheme (MCS) for cooperative diffusion in colloidal mixtures. This scheme accounts not only for the direct particle interactions, but also for the far-field part of the solvent mediated hydrodynamic interactions. Combined with our recent work on the mode coupling theory of tracer–diffusion and linear viscoelasticity of colloidal suspensions, this MCS provides a unified method for calculating dynamic and low-shear rheological properties of multicomponent colloidal dispersions. The MCS can be used to study polydispersity and mixing effects in concentrated colloidal systems. Some applications related to cooperative diffusion, interdiffusion, and glass transition in binary mixtures are discussed to illustrate the method.