1,721,155 research outputs found
First-principles simulations of direct coexistence of solid and liquid aluminum
No full textFirst-principles calculations based on density-functional theory, with generalized gradient corrections and ultrasoft pseudopotentials, have been used to simulate solid and liquid aluminum in direct coexistence at zero pressure. Simulations have been carried out on systems containing up to 1000 atoms for 15 ps. The points on the melting curve extracted from these simulations are in very good agreement with previous calculations, which employed the same electronic structure method but used an approach based on the explicit calculation of free energies [L. Vocadlo and D. Alfe, Phys. Rev. B 65, 214105 (2002)]
Melting curve of MgO from first-principles simulations
No full textFirst-principles calculations based on density functional theory, both with the local density approximation (LDA) and with generalized gradient corrections (GGA), have been used to simulate solid and liquid MgO in direct coexistence in the range of pressure 0 <= p <= 135 GPa. The calculated LDA zero pressure melting temperature is T-m(LDA)=3110 +/- 50 K, in good agreement with the experimental data. The GGA zero pressure melting temperature T-m(GGA)=2575 +/- 100 K is significantly lower than the LDA one, but the difference between the GGA and the LDA is greatly reduced at high pressure. The LDA zero pressure melting slope is dT/dp similar to 100 K/GPa, which is more than 3 times higher than the currently available experimental one from Zerr and Boehler [Nature (London) 371, 506 (1994)]. At the core mantle boundary pressure of 135 GPa MgO melts at T-m=8140 +/- 150 K
Temperature of the inner-core boundary of the Earth: Melting of iron at high pressure from first-principles coexistence simulations
No full textThe 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 center of the planet, roughly half way toward 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 inner-core boundary (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 density-functional theory. The calculations have been performed by directly simulating solid and liquid iron in coexistence and show that and at a pressure of similar to 328 GPa iron melts at similar to 6370 +/- 100 K. These findings are in good agreement with earlier simulations, which used exactly the same quantum-mechanics techniques but obtained melting properties from the calculation of the free energies of solid and liquid Fe
PHON: A program to calculate phonons using the small displacement method
No full textThe program PHON calculates force constant matrices and phonon frequencies in crystals. From the frequencies it also calculates various thermodynamic quantities, like the Helmholtz free energy, the entropy, the specific heat and the internal energy of the harmonic crystal. The procedure is based on the small displacement method, and can be used in combination with any program capable to calculate forces on the atoms of the crystal. In order to examine the usability of the method, I present here two examples: metallic Al and insulating MgO. The phonons of these two materials are calculated using density functional theory. The small displacement method results are compared with those obtained using the linear response method. In the case of Al the method provides accurate phonon frequencies everywhere in the Brillouin Zone (BZ). In the case of MgO the longitudinal branch of the optical phonons near the centre of the BZ is incorrectly described as degenerate with the two transverse branches, because the non-analytical part of the dynamical matrix is ignored here; however. thermodynamic properties like the Helmholtz free are essentially unaffected. Program summary Program title: PHON Catalogue identifier. AEDP_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/sumniaries/AEDP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19 580 No. of bytes in distributed program, including test data, etc.: 612 193 Distribution format: tar.gz Programming language: Fortran 90 Computer: Any Unix, Linux Operating system: Unix RAM: Depends on super-cell size, but usually negligible Classification: 7.8 External routines: Subprograms ZHEEV and DSYEV (Lapack); needs BLAS. A tutorial is provided with the distribution which requires the installation of the quantum-espresso package (http://www. quantum-espresso.org) Nature of problem: Stable crystals at low temperature can be well described by expanding the potential energy around the atomic equilibrium positions. The movements of the atoms around their equilibrium positions can then be described using harmonic theory, and is characterised by global vibrations called phonons, which can be identified by vectors in the Brillouin zone of the crystal, and there are 3 phonon branches for each atom in the primitive cell. Tile problem is to calculate the frequencies of these phonons for any arbitrary choice of q-vector in the Brillouin zone. Solution method: The small displacement method: each atom in the primitive cell is displaced by a small amount, and the forces induced on all the other atoms in the crystal are calculated and used to construct the force constant matrix. Supercells of -100 atoms are usually large enough to describe the force constant matrix up to the range where its elements have fallen to negligibly small values. The force constant matrix is then used to compute the dynamical matrix at any chosen q-vector in the Brillouin zone, and the diagonalisation of the dynamical matrix provides the squares of the phonon frequencies. The PHON code needs external programs to calculate these forces, and it can be used with any program capable of calculating forces in crystals. The most useful applications are obtained with codes based on density functional theory, but there is no restriction on what can be used. Running time: Negligible, typically a few seconds (or at most a few minutes) on a PC. It can take longer if very dense meshes of q-points are needed, for example, to compute very accurate phonon density of states. (C) 2009 Elsevier B.V. All rights reserved
The structure of iron under the conditions of the Earth's inner core
No full textThe inferred density of the solid inner core indicates that it is predominantly made of iron. In order to indicates that it is predominantly made of iron. In order to interpret the observed seismic anisotropy and understand the high pressure and temperature behaviour of the core, it is essential to establish the crystal structure of iron under core conditions. On the basis of extrapolated experimental data, a number of candidate structures for the high PIT iron phase have been proposed, namely, body-centred cubic (bcc), body-centred tetragonal (bct), hexagonal close-packed (hcp), double-hexagonal close-packed (dhcp) and an orthorhombically distorted hcp polymorph (Matsui, 1993; Stixrude and Cohen, 1995; Boehler, 1993; Saxena et al., 1996; Andrault et al., 1997). Here we present the results of the first fully ab initio free energy calculations for all of these polymorphs of iron at core pressures and temperatures. Our results show that hcp-Fe is the most stable polymorph of iron under the conditions of the Earth's inner core
Hydrogen dissociation on Mg(0001) studied via quantum Monte Carlo calculations
No full textWe have used diffusion Monte Carlo (DMC) simulations to calculate the energy barrier for H(2) dissociation on the Mg(0001) surface. The calculations employ pseudopotentials and systematically improvable B-spline basis sets to expand the single-particle orbitals used to construct the trial wave functions. Extensive tests on system size, time step, and other sources of errors, performed on periodically repeated systems of up to 550 atoms, show that all these errors together can be reduced to similar to 0.03 eV. The DMC dissociation barrier is calculated to be 1.18 +/- 0.03 eV and is compared to those obtained with density-functional theory using various exchange-correlation functionals, with values ranging between 0.44 and 1.07 eV
Ab initio molecular dynamics, a simple algorithm for charge extrapolation
No full textA new simple algorithm to extrapolate the electronic charge density in ab initio molecular dynamics runs is proposed. The self-consistent charge density is decomposed in two parts, the first part is the sum of the atomic charge densities, and the second is its difference with the latter. The charge at time t + dt is constructed using the sum of the atomic charges and a second order extrapolation on the charge difference. The scheme is tested on a 64 atom liquid iron simulation under Earth's core conditions. A comparison with a simple second order extrapolation of the whole charge density shows that the new algorithm is significantly faster. (C) 1999 Elsevier Science B.V
First-principles calculation of transport coefficients
No full textWe demonstrate the practical feasibility of calculating transport coefficients such as the viscosity of liquids completely from first principles using the Creen-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 no more than an order of magnitude higher than that of typical liquid metals under ambient conditions. [S0031-9007(98)07869-7]
Linear-scaling quantum Monte Carlo technique with non-orthogonal localized orbitals
No full textWe have reformulated the quantum Monte Carlo (QMC) technique so that a large part of the calculation scales linearly with the number of atoms. The reformulation is related to a recent alternative proposal for achieving linear-scaling QMC, based on maximally localized Wannier orbitals (MLWO), but has the advantage of greater simplicity. The technique we propose draws on methods recently developed for linear-scaling density functional theory. We report tests of the new technique on the insulator MgO, and show that its linear-scaling performance is somewhat better than that achieved by the MLWO approach. Implications for the application of QMC to large complex systems are pointed out
Melting of Iron under Earth's Core Conditions from Diffusion Monte Carlo Free Energy Calculations
Full text linkThe temperature of Earth's core is a parameter of critical importance to model the thermal structure of Earth. Since the core is mainly made of iron, with a solid liquid boundary (the inner core boundary) at 1220 km from the center of the Earth, the melting temperature of iron at the pressure of the ICB provides constraints on the temperature of the core. These constraints are based either on extrapolations to ICB pressure of experimental measurements, or on theoretical calculations which employed various flavors of quantum mechanics, most notably density functional theory. Significant disagreement between estimates obtained with different methods calls for calculations based on more accurate techniques. Here we used quantum Monte Carlo techniques to compute the free energies of solid and liquid iron at ICB conditions. We obtained an iron melting temperature at 330 GPa of 6900 +/- 400 K
- …
