Calculated Self-diffusion Coefficients Research Articles

Effect of chattering collisions on the self-diffusion coefficient of a dilute gas composed of infinitely thin hard needles

The self-diffusion coefficient of a dilute gas composed of infinitely thin hard needles was studied by classical trajectory calculations in relation to the moment of inertia of the needle, I. The calculated self-diffusion coefficient was compared with the value obtained by the independent collision approximation (ICA) in which each collision is assumed to be uncorrelated. Both the self-diffusion coefficient and the collision frequency increase with decreasing moment of inertia of the needle as expected by the ICA. The increasing rate of the self-diffusion coefficient was proportional to I -0.83 at I→0, that is larger than I -1/2 by the ICA. However, the ICA gives a larger self-diffusion coefficient at large moment of inertia; the correlation between the impulses during the chattering collisions changes its sign from positive to negative with decreasing moment of inertia. The thermal rotational motion at the initial configuration reduces the effect of the collision-induced rotational motion that leads to the positive correlation. The rapid thermal rotational motion at small moment of inertia makes the chattering collisions a kind of reciprocating motion in the orientation of the needles.

Estimation of the Enrichment of Cs in Molten Chloride and Fluoride Systems by Molecular Dynamics Simulation

Abstract For the pyrochemical reprocessing of spent metallic fuels in molten salt baths it is of importance to estimate the enrichment degree of Cs. A molecular dynamics simulation has been executed on molten (Li, Na, Cs)Cl at 900 K and (Li, Na, Cs)F at 925 K for various compositions in order to calculate the relative differences in the internal cation mobilities of Cs in molten LiCl-NaCl equimolar mixtures and the LiF-NaF eutectic. According to these results the self-exchange velocities of Li+, Na+ and Cs+ with respect to Cl- and F- have similar tendencies at each composition, and Cs can be enriched effectively up to xCs = 0.5 -0.6 in LiCl-NaCl melts. In addition, the sequence of the calculated self-diffusion coefficients for various compositions was in a fair agreement with that of the obtained self-exchange velocities.

Estimation of Gas Permeability of a Zeolite Membrane, Based on a Molecular Simulation Technique and Permeation Model

A method for estimating gas permeability through a zeolite membrane, using a molecular simulation technique and a theoretical permeation model, is presented. The estimate of permeability is derived from a combination of an adsorption isotherm and self-diffusion coefficient based on the adsorption-diffusion model. The adsorption isotherm and self-diffusion coefficients needed for the estimation were calculated using conventional Monte Carlo and molecular dynamics simulations. The calculated self-diffusion coefficient was converted to the mutual diffusion coefficient and the permeability estimated using the Fickian equation. The method was applied to the prediction of permeabilities of methane and ethylene in silicalite at 301 K. Calculated permeabilities were larger than the experimental values by more than an order of magnitude. However, the anisotropic permeability was consistent with the experimental data and the results obtained using a grand canonical ensemble molecular dynamics technique (Pohl et al....

Molecular Dynamics Simulation of Self-Diffusion and Maxwell-Stefan Diffusion Coefficients in Liquid Mixtures of Methanol and Water

Self-diffusion coefficients and Maxwell-Stefan diffusion coefficients in liquids have been determined by the equilibrium molecular dynamics calculation of the appropriate Green-Kubo equation. Simulations of water, methanol and mixtures of water and methanol have been carried out to calculate the diffusion coefficients at 300 K. In order to study the influence of the force field on the calculated self-diffusion coefficients of the pure liquids, two different force fields for each component have been used. The Van Leeuwen/Smit force field calculated the self-diffusion of methanol accurately. The SPC/E force field gave the best, but moderate, results for water. In mixtures of water and methanol the self-diffusion coefficients of both components were more accurate at high mole fractions of methanol. This can be explained by the better performance of the methanol force field. The Maxwell-Stefan diffusion coefficients in the mixtures of methanol and water agreed fairly well with the experimental values. More accurate results can be obtained by using optimised parameters in the water force field, and by enlarging the integration time and the duration of the simulation runs.

Molecular dynamics study of diffusion and atomic configuration in layered structures for Al circuit interconnects

Diffusion at Al(1 1 1)/underlay-metal interfaces, which is a dominant factor of electromigration-induced open-circuit failures in Al interconnects, was investigated by molecular dynamics simulation. The author focused on interfaces between the (1 1 1) plane in Al and the plane of greatest atomic density in five kinds of metals that have high melting temperatures: Ti, Cr, Mo, W, and Ta. The calculated self-diffusion coefficients of Al atoms near the Al/Ti and Al/Cr interfaces were smaller than those near the other three interfaces. This result is consistent with experimental results by other works that showed that Ti and Cr are effective underlay metals for suppressing the diffusion in Al interconnects. This result on the self-diffusion coefficient was linked to the result on the atomic configurations. The configurations of Al atoms at Al/Ti and Al/Cr interfaces were close to that for bulk Al, while the configurations at the other three interfaces were significantly different from that for bulk Al. It was found that diffusion as well as atomic configuration at the Al/underlay-metal interface is determined by the lattice mismatch between the (1 1 1) plane in Al and the plane of greatest atomic density in the underlay metal.

A path integral centroid molecular dynamics study of nonsuperfluid liquid helium-4

Path integral centroid molecular dynamics (CMD) calculation for normal liquid 4He has been performed. Dynamical behavior of the liquid at 4 K, which can not be reproduced by classical approximation, was well described by the CMD formalism. The calculated self-diffusion coefficient was found to be 5.06±0.04×10−5 cm2/s, which is in the same order of magnitude as that of ordinary liquids. Relaxation function of density fluctuation has also been calculated within the CMD approximation. Detailed comparison between the static susceptibility function χ̂(k) and the static structure factor of the centroid density Ŝ(c)(k) has been made. These correspond to the initial value of the exact and the centroid relaxation functions, respectively. For small k (⩽1.0 Å−1), χ̂(k) is well approximated by Ŝ(c)(k). For larger k, both the correlation functions have identical peak position. However, the intensity of Ŝ(c)(k) is systematically larger than that of χ̂(k). The calculated dynamic structure factor has been compared with the spectrum obtained from neutron scattering experiment. The agreement is satisfactory for 0.2<k<2.2 Å−1. The calculated peak frequency as a function of k, i.e., the dispersion relation, has a minimum around 1.9 Å−1, where the static correlation function shows maximum intensity. This behavior has also been experimentally observed for the dispersion relation for superfluid 4He. The peak continuously loses collective character and shows single-particle behavior with increasing k around the minimum. This behavior gives rise to the minimum in the dispersion relation for normal liquid 4He. The spectrum becomes narrow as the peak approaches the minimum, showing that the single-particle contribution becomes dominant in the dynamic structure factor. This narrowing is widely found among classical liquid; but is not observed in the spectrum of the superfluid 4He, indicating that the excitation around the minimum for the superfluid may have a different molecular origin than that for normal liquid 4He.

Molecular Dynamics Study of Atomic Structures in Amorphous Si-C-N Ceramics.

Molecular dynamics (MD) simulations based on Tersoff interatomic potentials have been carried out for amorphous silicon carbonitride (Si-C-N) ceramics. Short-range atomic arrangements and self-diffusion behavior in Si-C-N are investigated. In the Si-C-N amorphous network with homogeneously distributed carbon atoms, silicon atoms are bonded to both nitrogen and carbon atoms, forming mixed tetrahedra of Si(C, N)4. The average coordination number of C to Si is nearly three, which is larger than that of N to Si. The calculated self-diffusion coefficient of Si decreases with increasing carbon content in the Si-C-N systems. This indicates that C atoms play a role in reducing atomic diffusivities in Si-C-N at high temperatures, which may explain the observed thermal stability of Si-C-N amorphous ceramics.

Molecular Dynamics Simulations of DNA in Solution with Different Counter-ions

Molecular dynamics simulations of the [d(ATGCAGTCAG]2 fragment of DNA, in water and in the presence of three different counter-ions (Li+ Na+ and Cs+) are reported. Three- dimensional hydration structure and ion distribution have been calculated using spatial distribution functions for a detailed picture of local concentrations of ions and water molecules around DNA. According to the simulations, Cs+ ions bind directly to the bases in the minor groove, Na+ ions bind prevailing to the bases in the minor groove through one water molecule, whereas Li+ ions bind directly to the phosphate oxygens. The different behavior of the counter-ions is explained by specific hydration structures around the DNA and the ions. It is proposed how the observed differences in the ion binding to DNA may explain different conformational behavior of DNA. Calculated self-diffusion coefficients for the ions agree well with the available NMR data.

Modeling Self-diffusion in Multicomponent Aqueous Electrolyte Systems in Wide Concentration Ranges

A comprehensive model has been developed for calculating self-diffusion coefficients in multicomponent aqueous electrolyte systems. The model combines contributions of long-range (Coulombic) and short-range interactions. The long-range interaction contribution, which manifests itself in the relaxation effect, is obtained from the dielectric continuum-based mean-spherical approximation (MSA) theory for the unrestricted primitive model. The short-range interactions are represented using the hard-sphere model. In the combined model, aqueous species are characterized by effective radii, which depend on the ionic environment. For multicomponent systems, a mixing rule has been developed on the basis of phenomenological equations of nonequilibrium thermodynamics. The effects of complexation are taken into account by combining the diffusivity model with thermodynamic speciation calculations. The model accurately reproduces self-diffusivities of ions and neutral species in aqueous solutions ranging from infinitely...

Vacancy Properties In 5d Bcc Transition Metals: Ab Initio Study At Finite Electron Temperature

ABSTRACTThe self-diffusion constants for the monovacancy mechanism in the 5d transition-metals with bcc structure (β-Hf, Ta and W) are investigated by first-principles pseudopotential calculations within the framework of the Local Density Functional Theory. The formation and migration energies, calculated for relaxed configurations using supercells containing 27 and 54 atomic sites, are in quite good agreement with experimental data in Ta and W, with a discrepancy lower than 10 %. Preliminary results in β-Hf using smaller supercells suggest very large relaxation energies. The effect of finite electron-temperature is shown to be quite important, and very different from one element to the other: the electron contribution to the activation entropy is negative in Ta and positive in W, reaching respectively −2 kB and 2 kB at the melting temperature. Using simple estimates for the attempt frequencies and the vibrational formation entropies, the calculated self-diffusion coefficient is in exceptional agreement with experiments in W, and clearly reproduces an accelerated diffusivity in Ta.

Absolute ionic diffusion in MgO—computer calculations via lattice dynamics

Computer calculations based upon lattice dynamics have enabled us to calculate self-diffusion coefficients ( D sd) in MgO, a significant component of the lower mantle. We have employed the supercell method to study the mechanisms governing the diffusion process thereby enabling us to calculate values for activation enthalpies and entropies for migration and formation. In the intrinsic regime we calculate Magnesium: D sd =2.20 × 10 −5 exp ( −5.70 kT ) Oxygen: D sd =1.24 × 10 −5 exp ( −5.72 kT ) and in the extrinsic regime we calculate Magnesium: D sd =2.84 × 10 −6 exp ( −1.985 kT ) Oxygen: D sd =1.60 × 10 −6 exp ( −2.003 kT ) where N V is the extrinsic defect concentration. We have also confirmed that for this system the diffusion path is not simple, but there is a predicted bifurcation of the saddle surface. Our results are comparable with previous embedded defect calculations, and suggest that current experimental data are unable to probe the intrinsic regime.

Analysis of atomic diffusion in liquid metals at melting temperatures in capillary-like media

This is the second of two articles dealing with atomic transport in liquid metals in capillary-like media such as fine pores or grain boundaries with thicknesses above some critical value. Our previous studies analyzed the relationship between diffusivity and viscosity of liquid metals in capillary [J. W. Nowok, Scripta metall. mater. 29, 931 (1993)]. A primary purpose of this article is to discuss an accuracy of calculating self-diffusion coefficients using known bulk properties of liquid metals such as viscosity, surface tension and fundamental physical properties of liquid behavior in capillary. The lack of accuracy of surface tension data causes errors in the calculation of diffusion coefficients. Also, the predominant influence on D appears to be the molar (molecular) volume of liquid metals. This results from changes in the attractive portion of the effective potential between atoms for liquids with low molecular volumes.

The Effective Translational Self-Diffusion Coefficient of Small Molecules in Colloidal Crystals of Spherical Particles

The effective translational self-diffusion coefficient of small molecules in colloidal crystals of spherical particles is calculated. The colloidal crystal is modeled as a two-phase system. The colloidal particles are treated as immobile spheres with their centers located on the lattice points of cubic array. The diffusing molecule under consideration is characterized by both a self-diffusion coefficient and a concentration inside the colloidal particle as well as a self-diffusion coefficient and a concentration in the continuous phase. We have analyzed the results for three different cubic lattice types. For low volume fractions of colloidal particles (<0.3) the calculated self-diffusion coefficient is found to be independent of the lattice type and shows quantitative agreement with a simple cell model. (B. Jonsson, H. Wennerstrom, P.G. Nilsson, and P. Linse, Colloid Polym. Sci. 264, 77, 1986). The results of this study therefore support the analysis of experimental data on self-diffusion of small hydrophobic molecules in latex dispersions for low-volume fractions by the cell model (M. H. Blees and J. C. Leyte, J. Colloid Interface Sci. 157, 355, 1993). For higher volume fractions the behavior is found to be rather different. The self-diffusion coefficient is found to depend on the specific lattice structure of the colloidal particles, and significant deviations from the cell model result are found. Both sign and magnitude of the deviations are found to depend on the ratio of the transport coefficient of the diffusing molecule in the colloidal particles and the transport coefficient in the continuous phase.

A molecular dynamics study of solvent behavior around a protein.

The solvent structure and behavior around a protein were examined by analyzing a trajectory of molecular dynamics simulation of the trp-holorepressor in a periodic box of water. The calculated self diffusion coefficient indicated that the solvent within 10 A of the protein had lower mobility. Examination of the solvent diffusion around different atoms of different kinds of residues showed no general tendency. This fact suggested that the solvent mobility is not influenced significantly by the kind of the atom or residue they solvated. Distribution analysis around the protein revealed two peaks of water oxygen: a sharp one at 2.8 A around polar and charged atoms and a broad one at approximately 3.4 A around apolar atoms. The former was stabilized by water-protein hydrogen bonds, and the latter was stabilized by water-water hydrogen bonds, suggesting the existence of a hydrophobic shell. An analysis of protein atom-water radial distribution functions confirmed these shell structures around polar or charged atoms and apolar ones.

Surface melting of the (0001) face of TIP4P ice

The onset of surface melting of the basal plane (0001) face of TIP4P ice is studied in the temperature range T = 190−250 K using the molecular dynamics (MD) method. The disordering of the surface seen in the calculations can be explained in terms of the disruption of the hydrogen bonding network at the surface. At T = 210 K and lower the surface remains solid-like, as evidenced by non-zero order parameters and no calculable self-diffusion, although the reorientational correlation time (ca. 100 ps) is closer to that of the liquid than that of bulk ice. On the other hand, at T = 230 K (−43°C) and higher the surface is liquid-like, as shown by low order parameters and a high translational and rotational mobility of the molecules. At all temperatures, there is an orientational preference for the water molecule pointing its protons down, which is in agreement with experiment. The polarisation of the surface increases with increasing temperature. For the transition layer, the calculated reorientational correlation times are in rough agreement with NMR experiments, but for T ⩾ 230 K the calculated self-diffusion coefficients are much higher than the values obtained in NMR experiments.

Studies of Liquid Water by Computer Simulations. VI. Transport Properties of Carravetta–Clementi Water

Abstract The micro canonical molecular dynamics simulations of liquid water were performed at different temperatures and densities in order to investigate the anomalies of the transport coefficients. The nonempirical Carravetta–Clementi potential was used for the system with 216 molecules in a cubic cell. The order of magnitude of the nonempirically calculated self-diffusion coefficient, shear viscosity, bulk viscosity, and thermal conductivity were in agreement with experimental results. These transport properties were recognized as anomalous as in real liquid water. The temperature-dependence of these quantities was in agreement with the observed values under pressure of 50 MPa. The effects of compression on these transport coefficients were reproduced qualitatively. The obtained bulk viscosity was larger than the shear viscosity at low temperatures in accordance with experiments. The contribution of rotational motion to thermal conductivity seems to be responsible for the anomalous temperature-dependence of thermal conductivity. Several decay constants of the time correlation functions were obtained. The frequency spectra of the correlation functions were discussed. No marked molecule number dependence was observed in the calculated transport coefficients of Matsuoka–Clementi–Yoshimine water.

Spectroscopic diffusion coefficient of methane at 3.39 micron wavelength by a laser study

A novel differential re-analysis of Hubbert's (1976) laser study data of the 3.39 μm absorption (Dicke-narrowed) of methane shows that the spectroscopic diffusion coefficient is 10% different from the calculated self-diffusion coefficient. More accurate studies above 10 torr pressure are needed.

Studies of Liquid Water by Computer Simulations. IV. Transport Properties of a 2-D Model

Abstract The constant-temperature constant-pressure molecular dynamics simulations of a water-like system are performed at many temperatures and pressures. A 2-dimensional model of water is used for the system with 576 molecules in a square cell. Thermodynamical quantities are anomalous as in liquid water. The temperature-dependences of the calculated self-diffusion coefficient and the shear viscosity are in agreement with the observed values at low pressures. The effects of compression on these transport coefficients are reproduced qualitatively. The bulk viscosity obtained is larger than the shear viscosity. The order of magnitude of the calculated thermal conductivity is in agreement with the experimental results. The contribution of the rotational motion to the thermal conductivity is calculated in order to discuss the anomalous temperature-dependence of this coefficient.

Tracerdiffusion of the Fe-cations in olivine (Fe x Mg1−x )2SiO4 (III)

Tracerdiffusion coefficients D Fe* (and D Mg*) are presented for olivines of composition (Fe x Mg1−x )2SiO4 at T=1,130° C as a function of x, and oxygen activity, a O 2. Since the oxygen activity dependence of D Fe* (D Mg*) and that of the cation vacancy concentration are almost identical, it is concluded that a vacancy diffusion mechanism is operative in the octahedrally coordinated cation sublattices. From D Fe* and D Mg*, the chemical diffusion coefficient $$\bar D$$ can be calculated. The calculated $$\bar D$$ is in agreement with $$\bar D$$ -values obtained by Boltzmann-Matano analysis of interdiffusion experiments. In addition, correlation factors are evaluated from the tracerdiffusion data in order to calculate selfdiffusion coefficients.

Anomalous diffusion in omega forming systems

A model for anomalous self-difussion in the Group IV B transition metals Ti. Zr and Hf. is proposed. It is an extension of a previous model which was based on the identity of the activated complex for diffusion and the elementary ω-embryo of the low-temperature ω-phase. The diffusion coefficient is calculated as a function of temperature by means of an expression for the free energy based on Kikuchi's cluster variation method. The calculated self-diffusion coefficient in Zr is found to be in excellent agreement with experiment. Furthermore, diffusional anomalies observed in β-stabilized alloys of the Group IV B transition metals and, in particular, the increase of the apparent activation energy with solute concentration are readily explained by the model.