An equation of state is presented for liquid iron based on published ultrasonic, thermal expansion, and enthalpy data at 1 bar and on pulse-heating and shock wave compression and sound speed data up to 10 Mbar. The equation of state parameters, centered at 1 bar and 1811 K (the normal melting point of iron), are density, ρ_0 = 7019 kg/m^3, isentropic bulk modulus, K_(S0) = 109.7 GPa, and the first- and second-pressure derivatives of K_S, K′_(S0) = 4.66 and K″_(S0) = −0.043 GPa^(−1). A parameterization of the Gruneisen parameter γ as a function of density ρ and specific internal energy E is γ = γ_0 + γ′(ρ/ρ_0)^n(E - E_0) where γ_0 = 1.735, γ′ = −0.130 kg/MJ, n = −1.87, and E_0 is the internal energy of the liquid at 1 bar and 1811 K. The model gives the temperature dependence of γ at constant volume as (∂γ/∂T)_(v|1bar,1811K) = −8.4 × 10^(−5) K^(−1). The constant volume specific heat of liquid Fe at core conditions is 4.0–4.5 R. The model gives excellent agreement with measured temperatures of Fe under shock compression. Comparison with a preliminary reference Earth model indicates that the light component of the core does not significantly affect the magnitude of the isentropic bulk modulus of liquid Fe but does decrease its pressure derivative by ∼10%. Pure liquid Fe is 3–6% more dense than the inner core, supporting the presence of several percent of light elements in the inner core.

/pdf/an-equation-of-state-for-liquid-iron-and-implications-for-65vber4k68.pdf

An equation of state for liquid iron and implications for the Earth's core

A simple nearly free electron model for the electrical resistivity of liquid noble and transition metals and their alloys is presented. The scattering is described in terms of the phase shifts of muffin tin potentials constructed for the liquids.

http://iopscience.iop.org/article/10.1088/0305-4608/2/4/015/pdf

A simple muffin tin model for the electrical resistivity of liquid noble and transition metals and their alloys

X-ray diffraction patterns have been obtained from molten silicon and germanium near the melting point. In both cases the structure factor was a low first peak maximum with a small hump on its high angle side in contrast with those of simple molten metals such as sodium and aluminum. It was also found that the pair correlation functions for these molten elements are characterized by a low peak maximum which follows the usual first peak maximum corresponding to the nearest neighbour distance. The electrical resistivity and thermoelectric power have been calculated on the Ziman theory using thet-matrix of muffin-tin potential based on the structural data observed in this work. Good agreement was found in most cases.

Structure of molten silicon and germanium by X-ray diffraction

This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.

/pdf/simple-liquids-quasiuniversality-and-the-hard-sphere-1cpfv9sq4g.pdf

Simple liquids' quasiuniversality and the hard-sphere paradigm.

Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. Many liquids have been shown to obey power-law density scaling, according to which the relaxation time is a function of density to some power over temperature. We show that power-law density scaling breaks down for larger density variations than usually studied. This is demonstrated by simulations of the Kob-Andersen binary Lennard-Jones mixture and two molecular models, as well as by experimental results for two van der Waals liquids. A more general form of density scaling is derived, which is consistent with results for all the systems studied. An analytical expression for the scaling function for liquids of particles interacting via generalized Lennard-Jones potentials is derived and shown to agree very well with simulations. This effectively reduces the problem of understanding the viscous slowing down from being a quest for a function of two variables to a search for a single-variable function.

Beyond power-law density scaling: Theory, Simulation, and Experiment

X-ray diffraction patterns have been obtained from liquid metals (Al, Ga, In, Tl, Pb, Sn, Bi) near the melting point. After calculating the structure factor (Fourier analysis), the atomic radial distribution function was evaluated from which interatomic distance and coordination number were obtained. It has been shown that the ratio (K2/K1) of the position of the first peak (K1) to that of the second peak (K2) in the structure factor is a very useful parameter to represent the structure of liquid metals.



Rontgenbeugungsbilder von flussigen Metallen (Al, Ga, In, Tl, Pb, Sn, Bi) wurden in der Nahe des Schmelzpunktes beobachtet. Durch eine schon mehrfach dargestellte Methode (Fourier-Analyse) wurde der Strukturfaktor in eine radiale Atomverteilungsfunktion transformiert, aus der sich der mittlere Abstand nachster Atome und die Koordinationszahl ergeben. Es wurde gezeigt, das das Verhaltnis (K2/K1) der Lage des ersten Maximums (K1) zu der des zweiten Maximums (K2) im Strukturfaktor ein nutzlicher Parameter zur Beschreibung der Struktur von flussigen Metallen ist.

Structure factor and atomic distribution in liquid metals by X‐ray diffraction

The structure of iron in the liquid state has been studied by neutron diffraction at 1620 °C. After calculation of the interference function (Fourier analysis), the atomic radial distribution function was evaluated from which interatomic distance and coordination number were obtained. The value of the magnetic moment of iron in the liquid state which was derived from the correction for the paramagnetic neutron scattering was 1.2 μB.



Die Struktur von Eisen im flussigen Zustand wurde durch Neutronenbeugung bei 1620 °C untersucht. Nach der schon mehrfach dargestellten Methode (Fourier-Analyse) wurde die Interferenzfunktion in eine radiale Atomverteilungsfunktion transformiert, aus der sich der mittlere Abstand nachster Atome und die Koordinationszahl ergeben. Aus der Korrektur der paramagnetischen Neutronenstreuung ergibt sich der Wert des magnetischen Moments von Eisen im flussigen Zustand zu 1,2 μB.

Atomic Distribution and Magnetic Moment in Liquid Iron by Neutron Diffraction

The structure of nickel in the liquid state has been studied by neutron diffraction at 1500 °C. After calculating the interference function (Fourier analysis), the atomic radial distribution function was evaluated from which interatomic distance and coordination number were obtained.



Die Struktur von Nickel im flussigen Zustand wurde mit Neutronenstrahlen bei 1500 °C untersucht. Nach der schon ofter dargestellten Methode (Fourier-Analyse) wurde die Interferenzfunktion in eine radiale Atomverteilungsfunktion transformiert, aus der sich der mittlere Abstand nachster Atome und die Koordinationszahl ergeben.

Neutron Diffraction Study of Nickel in the Liquid State

The Born-Green equation has been analyzed numerically to derive the effective interionic potentials from the observed structural data for liquid alkali metals (Li, Na, K, Rb, Cs) using a linearized simultaneous equation method. The temperature insensitive long-range oscillatory potentials are found and the wavelength of the oscillations observed is in good agreement with that expected from the electron theory of metals in all cases. The viscosity coefficient and surface tension were calculated and compared with experimental data.



Fur die numerische Berechnung des effektiven, interionaren Potentials flussiger Alkalimetalle (Li, Na, K, Rb, Cs) aus gemessenen Strukturdaten wird die Born-Greensche Gleichung durch Linearisierung des algebraischen Gleichungssystems analysiert. Es werden die temperaturunabhangigen, langreichweitigen, oszillationen Potentiale bestimmt; die beobachtete Wellenlange der Oszillationen stimmt in allen Fallen gut mit dem aus der Elektronentheorie der Metalle erwarteten Wert uberein. Der Viskositatskoeffizient und die Oberflachenspannung werden berechnet und mit experimentellen Werten verglichen.

K. Suzuki

Papers

Structure factor and atomic distribution in liquid metals by X‐ray diffraction

Atomic Distribution and Magnetic Moment in Liquid Iron by Neutron Diffraction

Neutron Diffraction Study of Nickel in the Liquid State

Neutron Diffraction Study of Nickel in the Liquid State

Interionic potentials in liquid alkali metals