Thermodynamics of hexagonal-close-packed iron under Earth’s core conditions

The free energy and other thermodynamic properties of hexagonal-close-packed iron are calculated by direct ab initio methods over a wide range of pressures and temperatures relevant to the Earth’s core. The ab initio calculations are based on density-functional theory in the generalized-gradient approximation, and are performed using the projector augmented wave approach. Thermal excitation of electrons is fully included. The Helmholtz free energy consists of three parts, associated with the rigid perfect lattice, harmonic lattice vibrations, and anharmonic contributions, and the technical problems of calculating these parts to high precision are investigated. The harmonic part is obtained by computing the phonon frequencies over the entire Brillouin zone, and by summation of the free-energy contributions associated with the phonon modes. The anharmonic part is computed by the technique of thermodynamic integration using carefully designed reference systems. Detailed results are presented for the pressure, specific heat, bulk modulus, expansion coefficient and Grüneisen parameter, and comparisons are made with values obtained from diamond-anvil-cell and shock experiments

The earth’s core: an approach from first principles

The Earth’s core is largely composed of iron (Fe), alloyed with less dense elements such as sulphur, silicon and/or oxygen. The phase relations and physical properties of both solid and liquid Fe-alloys are therefore of great geophysical importance. As a result, over the past fifty years the properties of Fe and its alloys have been extensively studied experimentally. However, achieving the extreme pressures (up to 360 GPa) and temperatures (~6000K) found in the core provide a major experimental challenge, and it is not surprising that there are still considerable discrepancies in the results obtained by using different experimental techniques. In the past fifteen years quantum mechanical techniques have been applied to predict the properties of Fe. Here we review the progress that has been made in the use of first principles methods to study Fe and its alloys, and as a result of these studies we conclude: (i) that pure Fe adopts an hexagonal close packed structure under core conditions and melts at ~6200 K at 360 GPa, (ii) that thermodynamic equilibrium and observed seismic data are satisfied by a liquid Fe alloy outer core with a composition of ~10 mole% S (or Si) and 8 mole% O crystallising at ~ 5500 K to give an Fe alloy inner core with ~8 mole% S (or Si) and 0.2 mole % O, and (iii) that with such concentrations of S (or Si), an Fe alloy might adopt a body centred cubic structure in all or part of the inner core. In the future the roles of Ni, C, H and K in the core need to be studied, and techniques to predict the transport and rheological properties of Fe alloys need to be developed

Thermal expansion and atomic displacement parameters of cubic KMgF3 perovskite determined by high-resolution neutron powder diffraction

The structure of KMgF3 has been determined by high-resolution neutron powder diffraction at 4.2 K, room temperature and at 10 K intervals from 373 K to 1223 K. The material remains cubic at all temperatures. The average volumetric coefficient of thermal expansion in the range 373-1223 K was found to be 7.11 (3) × 10-5 K-1. For temperatures between 4.2 and 1223 K, a second-order Grüneisen approximation to the zero-pressure equation of state, with the internal energy calculated via a Debye model, was found to fit well, with the following parameters: θD = 536 (9) K, Vo = 62.876 (6) Å3, Ko' = 6.5 (1) and (VoKo/Y') = 3.40 (2) × 10-18 J, where θD is the Debye temperature, Vo is the volume at T = 0, Ko' is the first derivative with respect to pressure of the incompressibility (Ko) and Y' is a Grüneisen parameter. The atomic displacement parameters were found to increase smoothly with T and could be fitted using Debye models with θD in the range 305-581 K. At 1223 K, the displacement of the F ions was found to be much less anisotropic than that in NaMgF3 at this temperature

Thermal expansion and crystal structure of cementite, Fe3C, between 4 and 600K determined by time-of-flight neutron powder diffraction

The cementite phase of Fe3C has been studied by high-resolution neutron powder diffraction at 4.2 K and at 20 K intervals between 20 and 600 K. The crystal structure remains orthorhombic (Pnma) throughout, with the fractional coordinates of all atoms varying only slightly (the magnetic structure of the ferromagnetic phase could not be determined). The ferromagnetic phase transition, with Tc 480 K, greatly affects the thermal expansion coefficient of the material. The average volumetric coefficient of thermal expansion above Tc was found to be 4.1 (1) × 10-5 K-1; below Tc it is considerably lower (< 1.8 × 10-5 K-1) and varies greatly with temperature. The behaviour of the volume over the full temperature range of the experiment may be modelled by a third-order Grüneisen approximation to the zero-pressure equation of state, combined with a magnetostrictive correction based on mean-field theory

Electron-electron interactions and two-dimensional - two-dimensional tunneling

We derive and evaluate expressions for the dc tunneling conductance between interacting two-dimensional electron systems at non-zero temperature. The possibility of using the dependence of the tunneling conductance on voltage and temperature to determine the temperature-dependent electron-electron scattering rate at the Fermi energy is discussed. The finite electronic lifetime produced by electron-electron interactions is calculated as a function of temperature for quasiparticles near the Fermi circle. Vertex corrections to the random phase approximation substantially increase the electronic scattering rate. Our results are in an excellent quantitative agreement with experiment.Comment: Revtex style, 21 pages and 8 postscript figures in a separate file; Phys. Rev. B (in press

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution

Current-induced cooling phenomenon in a two-dimensional electron gas under a magnetic field

We investigate the spatial distribution of temperature induced by a dc current in a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field. We numerically calculate the distributions of the electrostatic potential phi and the temperature T in a 2DEG enclosed in a square area surrounded by insulated-adiabatic (top and bottom) and isopotential-isothermal (left and right) boundaries (with phi_{left} < phi_{right} and T_{left} =T_{right}), using a pair of nonlinear Poisson equations (for phi and T) that fully take into account thermoelectric and thermomagnetic phenomena, including the Hall, Nernst, Ettingshausen, and Righi-Leduc effects. We find that, in the vicinity of the left-bottom corner, the temperature becomes lower than the fixed boundary temperature, contrary to the naive expectation that the temperature is raised by the prevalent Joule heating effect. The cooling is attributed to the Ettingshausen effect at the bottom adiabatic boundary, which pumps up the heat away from the bottom boundary. In order to keep the adiabatic condition, downward temperature gradient, hence the cooled area, is developed near the boundary, with the resulting thermal diffusion compensating the upward heat current due to the Ettingshausen effect.Comment: 25 pages, 7 figure

Non Linear Current Response of a Many-Level Tunneling System: Higher Harmonics Generation

The fully nonlinear response of a many-level tunneling system to a strong alternating field of high frequency $\omega$ is studied in terms of the Schwinger-Keldysh nonequilibrium Green functions. The nonlinear time dependent tunneling current $I(t)$ is calculated exactly and its resonance structure is elucidated. In particular, it is shown that under certain reasonable conditions on the physical parameters, the Fourier component $I_{n}$ is sharply peaked at $n=\frac {\Delta E} {\hbar \omega}$, where $\Delta E$ is the spacing between two levels. This frequency multiplication results from the highly nonlinear process of $n$ photon absorption (or emission) by the tunneling system. It is also conjectured that this effect (which so far is studied mainly in the context of nonlinear optics) might be experimentally feasible.Comment: 28 pages, LaTex, 7 figures are available upon request from [email protected], submitted to Phys.Rev.

Moving on from Weiser's Vision of Calm Computing: engaging UbiComp experiences

A motivation behind much UbiComp research has been to make our lives convenient, comfortable and informed, following in the footsteps of Weiser's calm computing vision. Three themes that have dominated are context awareness, ambient intelligence and monitoring/tracking. While these avenues of research have been fruitful their accomplishments do not match up to anything like Weiser's world. This paper discusses why this is so and argues that is time for a change of direction in the field. An alternative agenda is outlined that focuses on engaging rather than calming people. Humans are very resourceful at exploiting their environments and extending their capabilities using existing strategies and tools. I describe how pervasive technologies can be added to the mix, outlining three areas of practice where there is much potential for professionals and laypeople alike to combine, adapt and use them in creative and constructive ways

Antigen expression determines adenoviral vaccine potency independent of IFN and STING signaling

Recombinant adenoviral vectors (rAds) are lead vaccine candidates for protection against a variety of pathogens, including Ebola, HIV, tuberculosis, and malaria, due to their ability to potently induce T cell immunity in humans. However, the ability to induce protective cellular immunity varies among rAds. Here, we assessed the mechanisms that control the potency of CD8 T cell responses in murine models following vaccination with human-, chimpanzee-, and simian-derived rAds encoding SIV-Gag antigen (Ag). After rAd vaccination, we quantified Ag expression and performed expression profiling of innate immune response genes in the draining lymph node. Human-derived rAd5 and chimpanzee-derived chAd3 were the most potent rAds and induced high and persistent Ag expression with low innate gene activation, while less potent rAds induced less Ag expression and robustly induced innate immunity genes that were primarily associated with IFN signaling. Abrogation of type I IFN or stimulator of IFN genes (STING) signaling increased Ag expression and accelerated CD8 T cell response kinetics but did not alter memory responses or protection. These findings reveal that the magnitude of rAd-induced memory CD8 T cell immune responses correlates with Ag expression but is independent of IFN and STING and provide criteria for optimizing protective CD8 T cell immunity with rAd vaccines