Iron represents the principal constituent of the Earth's core, but its high-pressure melting diagram remains ambiguous. Here we present a simple analytical approach to predict the melting properties of iron under deep-Earth conditions. In our model, anharmonic free energies of the solid phase are directly determined by the moment expansion technique in quantum statistical mechanics. This basis associated with the Lindemann criterion for a vibrational instability can deduce the melting temperature. Moreover, we correlate the thermal expansion process with the shear response to explain a discontinuity of atomic volume, enthalpy, and entropy upon melting. Our numerical calculations are quantitatively consistent with recent experiments and simulations. The obtained results would improve understanding of the Earth's structure, dynamics, and evolution.
The high-pressure melting diagram of iron is a vital ingredient for the geodynamic modeling of planetary interiors. Nonetheless, available data for molten iron show an alarming discrepancy. Herein, we propose an efficient one-phase approach to capture the solid-liquid transition of iron under extreme conditions. Our basic idea is to extend the statistical moment method to determine the density of iron in the TPa region. On that basis, we adapt the work-heat equivalence principle to appropriately link equation-of-state parameters with melting properties. This strategy allows explaining cutting-…
The Earth's core consists of a solid ball with a radius of 1221 Km, surrounded by a liquid shell which extends up to 3480 Km from the centre of the planet, roughly half way towards the surface (the mean radius of the Earth is 6373 km). The main constituent of the core is iron, and therefore the melting temperature of iron at the pressure encountered at the boundary between the solid and the liquid (the ICB) provides an estimate of the temperature of the core. Here I report the melting temperature of Fe at pressures near that of the ICB, obtained with first principles techniques based on densit…
{\em Ab initio} techniques based on density functional theory in the projector-augmented-wave implementation are used to calculate the free energy and a range of other thermodynamic properties of liquid iron at high pressures and temperatures relevant to the Earth's core. The {\em ab initio} free energy is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the {\em ab initio} system, with thermal averages computed by {\em ab initio} molecular dynamics simulation. The reference system consists of the inverse-power pair-p…
We report a molecular dynamics study of transport coefficients and infinite frequency shear mod- ulus of liquid iron at high temperatures and high pressures. We observe a simultaneous rise of both shear viscosity and diffusion coefficient along the melting line and estimate if liquid iron can vitrify under Earth-core conditions. We show that in frames of the model studied in our work iron demonstrates a moderate increase of viscosity along the melting line. It is also demonstrated that in the limit of high temperatures and high pressures the liquid iron behaves similar to the soft spheres syst…
A simple method for detection of melting event in laser-heated diamond anvil cells (DACs) is introduced. The melting is registered optically by the formation of spherical drops of the investigated material as heated in an inert pressure transmitting medium. Feasibility of the method is demonstrated on the examples of metal (iron and gold) and iron oxide (Fe2O3), materials molten at pressures over 40 GPa employing a portable laser heating system.
Exoplanets with masses similar to that of Earth have recently been discovered in extrasolar systems. A first order question for understanding their dynamics is to know whether they possess Earth like liquid metallic cores. However, the iron melting curve is unknown at conditions corresponding to planets of several times the Earth's mass (over 1500 GPa for planets with 10 times the Earth's mass (ME)). In the density-temperature region of the cores of those super-Earths, we calculate the iron melting curve using first principle molecular dynamics simulations based on density functional theory. B…
It has recently been shown that amorphization and melting of ice were intimately linked. In this letter, we infer from molecular dynamics simulations on the SiO2 system that the extension of the quartz melting line in the metastable pressure-temperature domain is the pressure-induced amorphization line. It seems therefore likely that melting is the physical phenomenon responsible for pressure induced amorphization. Moreover, we show that the structure of a "pressure glass" is similar to that of a very rapidly (1e+13 to 1e+14 kelvins per second) quenched thermal glass.
The melting of silicon carbide has been studied at pressures 5-8 GPa and temperatures up to 3300 K. It has been found that SiC melts congruently, and its melting curve has negative slope of -44 +/- 4 K/GPa.
Several important geophysical features such as heat flux at the Core-Mantle Boundary or geodynamo production are intimately related with the temperature profile in the Earth's core. However, measuring the melting curve of iron at conditions corresponding to the Earth inner core boundary under pressure of 330 GPa has eluded scientists for several decades. Significant discrepancies in previously reported iron melting temperatures at high pressure have called into question the validity of dynamic measurements. We report measurements made with a novel approach using X-ray absorption spectroscopy u…
Melting of boron subphosphide (B12P2) to 26 GPa has been studied by in situ synchrotron X-ray powder diffraction in a laser-heated diamond anvil cell, and by quenching and electrical resistance measurements in a toroid-type high-pressure apparatus. B12P2 melts congruently, and the melting curve has a positive slope of 23(6) K/GPa. No solid-state phase transition was observed up to the melting in the whole pressure range under study.
The pressure dependence of melting temperatures for boron carbide and B4C-carbon eutectic has been studied up to 8 GPa, and it was found that in both cases the melting curves exhibit negative slope (-13\pm6 K/GPa), that is indicative of higher density of the melt as compared to the solid phase.
Melting of rhombohedral boron subnitride B13N2 has been studied in situ at pressures to 8 GPa using synchrotron X-ray diffraction and electrical resistivity measurements. It has been found that above 2.6 GPa B13N2 melts incongruently, and the melting curve exhibits positive slope of 31(3) K/GPa that points to a lower density of the melt as compared to the solid phase.
Melting of cubic boron phosphide, BP has been studied at pressures to 9 GPa using synchrotron X-ray diffraction and electrical resistivity measurements. It has been found that above 2.6 GPa BP melts congruently, and the melting curve exhibits negative slope -60(7) K/GPa, which is indicative of a higher density of the melt as compared to the solid phase.
We report the measurements of the thermal conductivity ($κ$) of iron (Fe) and nickel (Ni) at high pressures and high temperatures. $κ$ values are estimated from the temperature measurements across the sample surface in a laser heated diamond anvil cell (LHDAC) and using the COMSOL software. Near-isothermal $κ$'s are observed to increase with pressure in both the metals due to the increase of density of the pressed metals. In both metals $κ$'s are observed to follow a sharp fall during melting at different pressure points and are consistence with the other multi-anvil measurements. Constant val…
We present theoretical results on the high-temperature phase stability and phonon spectra of paramagnetic bcc iron which explicitly take into account many-body effects. Several peculiarities, including a pronounced softening of the [110] transverse (T$_1$) mode and a dynamical instability of the bcc lattice in harmonic approximation are identified. We relate these features to the $α$-to-$γ$ and $γ$-to-$δ$ phase transformations in iron. The high-temperature bcc phase is found to be highly anharmonic and appears to be stabilized by the lattice entropy.
We study the fundamental question of the lattice dynamics of a metallic ferromagnet in the regime where the static long range magnetic order is replaced by the fluctuating local moments embedded in a metallic host. We use the \textit{ab initio} Density Functional Theory(DFT)+embedded Dynamical Mean-Field Theory(eDMFT) functional approach to address the dynamic stability of iron polymorphs and the phonon softening with increased temperature. We show that the non-harmonic and inhomogeneous phonon softening measured in iron is a result of the melting of the long range ferromagnetic order, and is …
There has been a long debate on the stable phase of iron under the Earth's inner core conditions. Because of the solid-liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi-empirical potential fitted to high-temperature ab initio data to perform a thermodynamic integration from classical systems described by this potential to ab initio systems. This method provides a smooth path for thermodynamic integration and significantly redu…
Solidification as a first order phase transition is described in the Landau theory by the same equation as tricritical phenomena. Here, the solidification or melting temperature against pressure curve is modelled to end at a tricritical point. The model gives the phase transition temperature's dependence on pressure up to the quadratic term with a definite expression for the coefficients. This formula is expected to be generally valid for pure materials having melting curves with dT/dP approaching zero at very high P. Excellent experimental agreement is obtained for iron, the material having t…
Hydrogen is the most abundant element in the universe, and its properties under conditions of high temperature and pressure are crucial to understand the interior of of large gaseous planets and other astrophysical bodies. At ultra high pressures solid hydrogen has been predicted to transform into a quantum fluid, because of its high zero point motion. Here we report first principles two phase coexistence and Z method determinations of the melting line of solid hydrogen in a pressure range spanning from 30 to 600 GPa. Our results suggest that the melting line of solid hydrogen, as derived from…
First principles calculations based on density functional theory, both with the local density approximation (LDA) and with generalised gradient corrections (GGA), and the projector augmented wave method, have been used to simulate solid and liquid MgO in direct coexistence in the range of pressure $0\le p \le 135$ GPa. The calculated LDA zero pressure melting temperature is $ T_m^{\rm LDA} = 3110 \pm 50 $ K, in good agreement with the experimental data. The calculated GGA zero pressure melting temperature $ T_m^{\rm GGA} = 2575 \pm 100 $ K is significantly lower than the LDA one, but the diffe…
We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well d…
Results solving the long standing puzzle regarding the phase diagram and the pressure evolution of the melting temperature Tm(P) of gallium nitride (GaN), the most promising semiconducting material for innovative modern electronic applications, are presented. The analysis is based on (i) studies of the decomposition curve in P-T plane up to challenging P equal 9 GPa, (ii) novel method enabling Tm(P) determination despite the earlier decomposition, and (iii) the pressure invariant parameterization of Tm(P) curve, showing the reversal melting for P greater-than 22 GPa. This is linked to a possib…
Experimental measurements and modeling of characteristic time scales in single iron particle ignition
Key Lab. for Power Machinery and Engineering of M. O. E, Shanghai Jiao Tong University（教育部动力机械与工程重点实验室，上海交通大学）；Department of Mechanical Engineering, Eindhoven University of Technology（埃因霍温理工大学机械工程系）；Eindhoven Institute for Renewable Energy Systems, Eindhoven University of Technology（埃因霍温可再生能源系统研究所，埃因霍温理工大学）
We discus existent conflicts between experimentally measured and theoretically calculated melting curves of Mo, Ta, and W. By assuming that vacancy formation plays a fundamental role in the melting process, an explanation for the measured melting curves is provided. Furthermore, we show that the Lindemann law fits well all the measured melting curves of bcc transition metals if the Grueneisen parameter is written as a power series of the interatomic distance. For completeness, we examine possible reasons for current disagreements between shock-wave and DAC experiments. To solve them, we propos…
The high pressure and high temperature phase diagram of Ta has been studied in a laser-heated diamond-anvil cell (DAC) using x-ray diffraction measurements up to 52 GPa and 3800 K. The melting was observed at nine different pressures, being the melting temperature in good agreement with previous laser-heated DAC experiments, but in contradiction with several theoretical calculations and previous piston-cylinder apparatus experiments. A small slope for the melting curve of Ta is estimated (dTm/dP = 24 K/GPa at 1 bar) and a possible explanation for this behaviour is given. Finally, a P-V-T equat…
Melting of orthorhombic boron silicide B6Si has been studied at pressures up to 8 GPa using in situ electrical resistivity measurements and quenching. It has been found that in the 2.6-7.7 GPa range B6Si melts congruently, and the melting curve exhibits negative slope of -31(2) K/GPa that points to a higher density of the melt as compared to the solid phase. At very high temperatures B6Si melt appears to be unstable and undergoes disproportionation into silicon and boron-rich silicides. The onset temperature of disproportionation strongly depends on pressure, and the corresponding low-temperat…
Recent experiments have obtained the melting line of sodium up to pressures of about 130 GPa, finding that the melting line from the {\em bcc} phase reaches a maximum at a temperature of {\em c.a.} 1000 K and a pressure of 31 GPa, and at higher pressures the fusion temperature decreases continuously up to 118 GPa. Here we report results of a study based on first principles molecular dynamics, clarifying the nature of the maximum and subsequent decreasing behavior found in the melting line of sodium.
Melting behaviors of defective crystals under extreme conditions are theoretically investigated using the statistical moment method. In our theoretical model, heating processes cause missing atoms or vacancies in crystal structures via dislocating them from their equilibrium positions. The coordination number of some atoms is assumed to be removed by one unit and the defect depends on temperature and external pressure. We formulate analytical expressions to directly connect the equilibrium vacancy concentration, the elastic modulus, and the melting temperature. Numerical calculations are carri…
MgO is an abundant mineral in the rocky mantle of terrestrial planets, but its melting behaviors remain enigmatic. Here we introduce a simple theoretical model to investigate the B1-liquid transition of MgO up to 370 GPa. Vibrational free energies of B1-MgO are fully computed by the moment recurrence technique in quantum statistical physics. On that basis, we associate the melting temperature with the isothermal bulk modulus via the work-heat equivalence principle. This strategy allows us to quantitatively explain recent experimental data. Our numerical analyses would yield insights into plane…
Re-entrant melting (in which a substance's melting point starts to decrease beyond a certain pressure) is believed to be an unusual phenomenon. Among the elements, it has so far only been observed in a very limited number of species, e.g., the alkali metals. Our density functional theory calculations reveal that this behavior actually extends beyond alkali metals to include magnesium, which also undergoes re-entrant melting, though at the much higher pressure of ~300 GPa. We find that the origin of re-entrant melting is the faster softening of interatomic interactions in the liquid phase than …
Based on ab initio molecular dynamics simulations, we determined the melting curve of magnesium (Mg) up to ~460 GPa using the solid-liquid coexistence method. Between ~30 and 100 GPa, our melting curve is noticeably lower than those from static experiments, but is in good agreement with recent shock experiments. Up to ~450 GPa, our melting curve is generally consistent with the melting points from first-principles calculations using the small-cell coexistence method. We found that, at high pressures of a few hundred GPa, due to the strong softening of interatomic interactions in the liquid pha…
The melting curve of Ni up to 100 GPa has been calculated using first principles methods based on density functional theory (DFT). We used two complementary approaches: i) coexistence simulations with a reference system and then free energy corrections between DFT and the reference system, and ii) direct DFT coexistence using simulation cells including 1000 atoms. The calculated zero pressure melting temperature is slightly underestimated at $1637 \pm 10$ K (experimental value is 1728 K), and at high pressure is significantly higher than recent measurements in diamond anvil cell experiments [P…
The high-pressure melting properties of the ternary alloy AlCuSi with face-centred cubic structure is theoretically investigated using the statistical moment method. We calculate the melting temperature for the alloy under pressure up to 80 GPa. The dependence of the melting temperature on the content of alloying elements is also studied. Our results agree well with previous experiments, simulations, and other theoretical calculations.
The prediction of the melting curve of metals by extrapolation to high pressures and temperatures based on the Lindemann-Gilvarry criterion (LG) assuming harmonic Debye solid is presented. The LG formulation uses the bulk modulus B and its pressure derivative B' as fit parameters deduced directly from the equation of state, however, the results are not unique and strongly depends on the chosen equation of state (EOS). By introducing a constraint that the bulk moduli parameters B and B' must simultaneously obey the Lindemann-Gilvarry criterion (LG) and the EOS, consistent bulk moduli are derive…
The p-V-T equation of state of magnesium metal has been measured up to 20 GPa and 1500 K using both multianvil and opposite anvil techniques combined with synchrotron X-ray diffraction. To fit the experimental data, the model of Anderson-Grüneisen has been used with fixed parameter δT. The 300-K bulk modulus of B0 = 32.5(1) GPa and its first pressure derivative, B0' = 3.73(2), have been obtained by fitting available data up to 20 GPa to Murnaghan equation of state. Thermal expansion at ambient pressure has been described using second order polynomial with coefficients a = 25(2)x10-6 K-1 and b …
We investigate the binary phase diagram of helium and iron using first-principles calculations. We find that helium, which is a noble gas and inert at ambient conditions, forms stable crystalline compounds with iron at terapascal pressures. A FeHe compound becomes stable above 4 TPa, and a FeHe$_2$ compound above 12 TPa. Melting is investigated using molecular dynamics simulations, and a superionic phase with sublattice melting of the helium atoms is predicted. We discuss the implications of our predicted helium-iron phase diagram for interiors of giant (exo)planets and white dwarf stars.
At low pressure, free surfaces play a crucial role in the melting transition. Under pressure, the surface of the sample is acted upon by some pressure transmitting medium. To examine the effect of this medium on melting, we performed Monte Carlo simulations of a system of argon atoms in the form of a slab with two boundaries. We examined two cases, one with a soft and the other with a rigid medium at the boundaries. We found that in the presence of a rigid medium, melting resembles the mechanical lattice instability found in a surface-free solid. With a soft medium at the boundary, melting beg…
It is claimed that all of the pressure scales of the reported melting curves derived by diamond anvil cell experiments require a correction which takes into account the pressure thermal shift, where vanadium is an illustrative example. The linear behavior of the thermal pressure (Pth) vs. the temperature, as predicted by first principles theoretical assumptions is then experimentally confirmed. This allows extrapolation to determine of the actual pressure and thermal temperature at the melt. Accounting for the role of the pressure transmitting media in diamond anvil cell experiments, the analy…
The insulator to metal transition in solid hydrogen was predicted over 70 years ago but the demonstration of this transition remains a scientific challenge. In this regard, a peak in the temperature vs. pressure melting line of hydrogen may be a possible precursor for metallization. However, previous measurements of the fusion curve of hydrogen have been limited in pressure by diffusion of hydrogen into the gasket or diamonds. To overcome this limitation we have used an innovative technique of pulsed laser heating of the sample and final peak in the melting line at P=64.7+-4GPa and T=1055+-20 …
We study the pressure dependence of the melting mechanism of a surface free Lennard-Jones crystal by constant pressure Monte Carlo simulation. The difference between the overheating temperature($T_{OH}$) and the thermodynamical melting point($T_M$) increase for increasing pressure. When particles move into the repulsive part of the potential the properties at $T_{OH}$ change. There is a crossover pressure where the volume jump becomes pressure-independent. The overheating limit is pre-announced by thermal excitation of big clusters of defects. The temperature zone where the system is dominated…
We perform density functional calculations of the equilibrium 57Fe/54Fe ratios for ferrous iron dissolved in periclase and MgSiO3 perovskite at the pressures and temperatures of the Earth's mantle. Pressure increases the partitioning of 57Fe into both phases by a factor of three from the Earth's surface to the core-mantle boundary. In ferropericlase, a large contribution to this increase comes from the electronic transition from high-spin to low-spin iron. Our calculations demonstrate that pressure-induced fractionation can play a major role in determining planetary iron-isotope composition.
The high-pressure melting curves of metals provide simple and useful tests for theories of melting, as well as important constraints for the modeling of planetary interiors. Here, we present an experimental technique that reveals the latent heat of fusion of a metal sample compressed inside a diamond anvil cell. The technique combines microsecond-timescale pulsed electrical heating with an internally-heated diamond anvil cell for the first time. Further, we use the technique to measure the melting curve of platinum to the highest pressure measured to date. Melting temperature increases from $\…
We report ab initio calculations of the melting curve and Hugoniot of molybdenum for the pressure range 0-400 GPa, using density functional theory (DFT) in the projector augmented wave (PAW) implementation. We use the ``reference coexistence'' technique to overcome uncertainties inherent in earlier DFT calculations of the melting curve of Mo. Our calculated melting curve agrees well with experiment at ambient pressure and is consistent with shock data at high pressure, but does not agree with the high pressure melting curve from static compression experiments. Our calculated P(V) and T(P) Hugo…
We combine density functional theory (DFT) with molecular dynamics simulations based on an accurate atomistic force field to calculate the pressure derivative of the melting temperature of magnesium oxide at ambient pressure - a quantity for which a serious disagreement between theory and experiment has existed for almost 15 years. We find reasonable agreement with previous DFT results and with a very recent experimental determination of the slope. We pay particular attention to areas of possible weakness in theoretical calculations and conclude that the long-standing discrepancy with experime…
Using a first principles based, magnetic tight-binding total energy model, the magnetization energy and moments are computed for various ordered spin configurations in the high pressure polymorphs of iron (fcc, or $γ$-Fe, and hcp, or $ε$-Fe), as well ferromagnetic bcc iron ($α$-Fe). For hcp, a non-collinear, antiferromagnetic, spin configuration that minimizes unfavorable ferromagnetic nearest neighbor ordering is the lowest energy state and is more stable than non-magnetic $ε$ iron up to about 75 GPa. Accounting for non-collinear magnetism yields better agreement with the experimental equatio…
We investigate the elastic and isotropic aggregate properties of ferromagnetic bcc iron as a function of temperature and pressure by computing the Helmholtz free energies for the volume-conserving strained structures using the first-principles linear response linear-muffin-tin-orbital method and the generalized-gradient approximation. We include the electronic excitation contributions to the free energy from the band structures, and phonon contributions from quasi-harmonic lattice dynamics. We make detailed comparisons between our calculated elastic moduli and their temperature and pressure de…
Conventional molecular dynamics simulation has been used to determine melting temperature of highly compressed classical molecular hydrogen in a wide range of pressures and temperatures using non-empirical atom-atom potentials approximation. It is shown that the raise of melting temperature with increasing pressure becomes more and more smooth and at megabar pressures its slope goes negative. We discuss the reasons of this turnover and analyze connection of this effect with the parameters of chemical bonding in H2.
We report high pressure structural phase transformation sequence in a layered Iron-based superconducting compound FeSe0.3Te0.7 to 31 GPa at room temperature. The ambient pressure PbO type tetragonal phase (Space Group - P4/nmm) transforms to a monoclinic phase (Space group - P21/m) at a pressure of 7.3 \pm 0.9 GPa. This monoclinic phase is similar to the one observed below 100 K at ambient pressure. On further increase of pressure above 12 GPa, a transformation to an amorphous phase is observed that is completed by 20 GPa. The amorphous phase is found to be stable to the highest pressure of 31…
The thermal properties are one of the key parameters to control phase purity and microstructure of polycrystalline materials. The melting point of the iron-based BaFe2As2 superconductor (Ba122), which foresees high-field applications, remains controversial. In this work, thermogravimetry-differential scanning calorimetry measurements (TG-DSC) of undoped and Co-doped Ba122 were carried out. Mixtures of elemental metals and pre-reacted Ba122 powders were prepared to investigate the thermal responses during in situ and ex situ synthesis routes, respectively. In addition, the phases and microstruc…
Understanding the behavior of molecular systems under pressure is a fundamental problem in condensed matter physics. In the case of nitrogen, the determination of the phase diagram and in particular of the melting line, are largely open problems. Two independent experiments have reported the presence of a maximum in the nitrogen melting curve, below 90 GPa, however the position and the interpretation of the origin of such maximum differ. By means of ab initio molecular dynamics simulations based on density functional theory and thermodynamic integration techniques, we have determined the phase…
The phase diagram of Zn has been explored up to 140 GPa and 6000 K, by combining optical observations, x-ray diffraction, and ab-initio calculations. In the pressure range covered by this study, Zn is found to retain a hexagonal close-packed crystal symmetry up to the melting temperature. The known decrease of the axial ratio of the hcp phase of Zn under compression is observed in x-ray diffraction experiments from 300 K up to the melting temperature. The pressure at which the axial ratio reaches the square root of 3 value, around 10 GPa, is slightly affected by temperature. When this axial ra…
We investigate the temperature and pressure dependences of the electrical resistivity for bcc and hcp Fe using the low-order variational approximation and theoretical transport spectral functions calculated from first principles linear response linear-muffin-tin-orbital method in the generalized-gradient approximation. The calculated values are in close agreement with available experimental data, and show strong increase with temperature and decrease with pressure. We also discuss the behavior of the electrical resistivity for the bcc -> hcp phase transition.
We use first principles molecular dynamics simulations coupled to the thermodynamic integration method to study the hcp-bcc transition and melting of beryllium up to a pressure of 1600~GPa. We derive the melting line by equating solid and liquid Gibbs free energies, and represent it by a Simon Glatzel fit $T_m= 1564~\text{K} (1 + P/(15.6032 ~\text{GPa}))^{0.383}$, which is in good agreement with previous two-phase simulations below 6000~K. We also derive the hcp-bcc solid-solid phase boundary and show the quasiharmonic approximation underestimates the stability of the hcp structure, predicting…
Thermal conductivity of the most abundant element in the planetary core, Iron (Fe) is measured up to Earth's outer core pressure $\sim 120$ GPa. The measurements are carried out using the laser heated diamond anvil cell facility, where the absorbed power by Fe metal foil is calculated using thermodynamical equation. The thermal conductivity of $γ-Fe$ linearly increases up to a maximum experimental pressure 40 GPa. Thermal conductivity of $ε-Fe$ measured by us shows a saturated value $\sim$ 52 ($\pm$ 5) $Wm^{-1}K^{-1}$ in the pressure range 77 - 120 GPa. At different pressures temperature depen…
