1.4 Theory for Transport Coefficients of Liquid Metals

Shimoji, Mitsuo; Itami, Toshio

doi:10.4028/www.scientific.net/ddf.43.35

Cited by 25 publications

(51 citation statements)

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“…From the point where φ(t) falls below the noise one integrates only the latter, so one gains nothing by evaluating the integral beyond that point. If we assume that φ(t) is zero above t ≈ 0.4 ps, we obtain the value η = 2.2 ± 0.1 mPa s, which should be compared with the experimental value of 1.25 mPa s [12]. The fact that the statistical errors have been reduced to ≈ 5% demonstrates that the viscosity of liquids can be calculated completely from first principles with quite high precision.…”

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confidence: 72%

First-Principles Calculation of Transport Coefficients

1998

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We demonstrate the practical feasibility of calculating transport coefficients such as the viscosity of liquids completely from first principles using the Green-Kubo relations. Results presented for liquid aluminum are shown to have a statistical error of only ca. 5%. The importance of such calculations is illustrated by results for a liquid iron-sulfur alloy under Earth's core conditions, which indicate that the viscosity of the liquid outer core is not substantially higher than that of typical liquid metals under ambient conditions. PACS numbers: 66.20.+d, 71.15.Pd Since the pioneering work of Car and Parrinello [1] first principles molecular dynamics (FPMD) has become a widely used technique for investigating condensed matter. For liquids and solids in thermal equilibrium many quantities of interest are readily calculated, including thermodynamic functions, structure factors, radial distribution functions, diffusion coefficients, bond lifetimes, etc. But transport coefficients such as viscosity and thermal conductivity are computationally more demanding, and have been little studied by FPMD. We demonstrate here the feasibility of calculating such quantities with useful accuracy, by presenting FPMD results for the viscosity of liquid aluminum near the triple point. We then illustrate the potential importance of this type of calculation by showing how FPMD calculations can be used to calculate the viscosity of liquid iron in the Earth's outer core. This is one of the key quantities in the theory of the Earth's deep interior, but also one of the most uncertain.There are basically two ways of calculating transport coefficients by simulation. The first is to subject the simulated system to an explicit external perturbation (e.g. a shear flow or a temperature gradient) and calculate the steady-state response. Alternatively, one can apply the Green-Kubo (GK) relations, i.e. the relations between transport coefficients and correlation functions involving fluxes of conserved quantities [2]. The shear viscosity η, for example, is given by:where · denotes the thermal average, V is the volume of the system, T is the temperature, k B is the Boltzmann factor, and P xy is the off-diagonal component of the stress tensor P αβ (α and β are Cartesian components). The relative merits of the two approaches have been much discussed, but the GK method has the virtues of simplicity and ease of application, and will be used here. For a simulation having a given duration, single particle properties, like the diffusion coefficient, can be calculated more accurately than collective properties, like the viscosity. In the former case the statistical average can be done over time and over the particles, while in the latter one loses the possibility of averaging over the particles. To obtain the same statistical accuracy, collective properties need much longer runs than single particle properties by a factor proportional to the size of the system.The first principles calculations presented here are based on density functional theory, pse...

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confidence: 72%

First-Principles Calculation of Transport Coefficients

1998

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“…Results for presented in Table II compare favorably with the available experimental data. 70 For comparison, we note that the KS-DFT simulations of Alfe and Gillan 54 gave values in the range 1.4-2.2 GPa ps.…”

Section: Collective Dynamicsmentioning

confidence: 98%

Dynamical properties of liquid Al near melting: An orbital-free molecular dynamics study

et al. 2002

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The static and dynamic structure of liquid Al is studied using the orbital free ab initio molecular dynamics method. Two thermodynamic states along the coexistence line are considered, namely Tϭ943 and 1323 K, for which x-ray and neutron scattering data are available. A kinetic-energy functional which fulfills a number of physically relevant conditions is employed, along with a local first-principles pseudopotential. In addition to a comparison with experiment, we also compare our ab initio results with those obtained from conventional molecular-dynamics simulations using effective interionic pair potentials derived from second-order pseudopotential perturbation theory.

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“…Accordingly the force may be divided into two terms, F H a hard core contribution and F S , a soft force, and one can write friction coefficient in the form as follows [16].…”

Section: B D K T V =mentioning

confidence: 99%

“…In evaluating the friction coefficient and in handling the soft potential contribution to kinetic equations, we introduced the Helfand Linear Trajectory principle [16][17][18]. This principle is used to calculate the time integral of auto correlation function by replacing the actual trajectories.…”

Section: B D K T V =mentioning

confidence: 99%

Structural, thermodynamic and other associated properties of partially ordered Ag‐In alloy

Venkatesh¹,

Mishra

Rao

2003

Physica Status Solidi (b)

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Extensive computations have been performed using the Lebowitz solution of hard sphere mixtures as a reference system, and perturbed the hard sphere direct correlation function, C O ij (r), with square well attractive tail. We used mean spherical model to compute the total and partial direct correlation functions in the attractive and repulsive regions of the interacting potential of Ag-In alloy at different compositions. The potential parameters were those obtained for pure metals. With these potential parameters (the partial and total) structure factors were evaluated, and then Fourier transformed to get the partial and total radial distribution functions. Further the well-known Bhatia-Thornton correlation functions namely the numbernumber, concentration-concentration, and number-concentration correlation functions have been computed. We also obtained total and partial coordination numbers from partial and total pair correlation functions respectively. With the help of these pair correlation functions we give the distances between atoms namely Ag-Ag, In-In and Ag-In at different compositions of In in Ag-In alloy. It is found that these distances practically remain constant and are independent of composition, which has been attributed to the formation of segregated clusters of atomic dimensions. Using Kirkwood-Buff's equation, compressibillities have been calculated as a function of composition. The temperature derivative of diffusion coefficient for pure constituents has been formulated and the computed results were compared with the available experimental values. With this model the diffusion coefficients and the friction coefficients of the constituents have been obtained through the use of Helfand's trajectory principle with a reasonable success in the alloy as well. It is found that these metals of the alloy tend to segregate. The ratio of diffusion coefficients of the metals in the alloy is almost a constant and is equal to 0.9. This shows that the alloy forms a regular solution in spite of their tendency to segregate.

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1.4 Theory for Transport Coefficients of Liquid Metals

Cited by 25 publications

References 0 publications

First-Principles Calculation of Transport Coefficients

First-Principles Calculation of Transport Coefficients

Dynamical properties of liquid Al near melting: An orbital-free molecular dynamics study

Structural, thermodynamic and other associated properties of partially ordered Ag‐In alloy

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