198 research outputs found
Thermodynamic stability of Fe/O solid solution at inner-core conditions
We present a new technique which allows the fully {\em ab initio} calculation
of the chemical potential of a substitutional impurity in a high-temperature
crystal, including harmonic and anharmonic lattice vibrations. The technique
uses the combination of thermodynamic integration and reference models
developed recently for the {\em ab initio} calculation of the free energy of
liquids and anharmonic solids. We apply the technique to the case of the
substitutional oxygen impurity in h.c.p. iron under Earth's core conditions,
which earlier static {\em ab initio} calculations indicated to be
thermodynamically very unstable. Our results show that entropic effects arising
from the large vibrational amplitude of the oxygen impurity give a major
reduction of the oxygen chemical potential, so that oxygen dissolved in h.c.p.
iron may be stabilised at concentrations up a few mol % under core conditions
Can the Earth's dynamo run on heat alone?
The power required to drive the geodynamo places significant constraints on the heat passing across the core-mantle boundary and the Earth's thermal history. Calculations to date have been limited by inaccuracies in the properties of liquid iron mixtures at core pressures and temperatures. Here we re-examine the problem of core energetics in the light of new first-principles calculations for the properties of liquid iron.
There is disagreement on the fate of gravitational energy released by contraction on cooling. We show that only a small fraction of this energy, that associated with heating resulting from changes in pressure, is available to drive convection and the dynamo. This leaves two very simple equations in the cooling rate and radioactive heating, one yielding the heat flux out of the core and the other the entropy gain of electrical and thermal dissipation, the two main dissipative processes.
This paper is restricted to thermal convection in a pure iron core; compositional convection in a liquid iron mixture is considered in a companion paper. We show that heat sources alone are unlikely to be adequate to power the geodynamo because they require a rapid secular cooling rate, which implies a very young inner core, or a combination of cooling and substantial radioactive heating, which requires a very large heat flux across the core-mantle boundary. A simple calculation with no inner core shows even higher heat fluxes are required in the absence of latent heat before the inner core formed
Comment on 'Molybdenum at High Pressure and Temperature: Melting from Another Solid Phase'
There has been a major controversy over the past seven years about the
high-pressure melting curves of transition metals. Static compression
(diamond-anvil cell: DAC) experiments up to the Mbar region give very low
melting slopes dT_m/dP, but shock-wave (SW) data reveal transitions indicating
much larger dT_m/dP values. Ab initio calculations support the correctness of
the shock data. In a very recent letter, Belonoshko et al. propose a simple and
elegant resolution of this conflict for molybdenum. Using ab initio
calculations based on density functional theory (DFT), they show that the
high-P/high-T phase diagram of Mo must be more complex than was hitherto
thought. Their calculations give convincing evidence that there is a transition
boundary between the normal bcc structure of Mo and a high-T phase, which they
suggest could be fcc. They propose that this transition was misinterpreted as
melting in DAC experiments. In confirmation, they note that their boundary also
explains a transition seen in the SW data. We regard Belonoshko et al.'s Letter
as extremely important, but we note that it raises some puzzling questions, and
we believe that their proposed phase diagram cannot be completely correct. We
have calculated the Helmholtz and Gibbs free energies of the bcc, fcc and hcp
phases of Mo, using essentially the same quasiharmonic methods as used by
Belonoshko et al.; we find that at high-P and T Mo in the hcp structure is more
stable than in bcc or fcc.Comment: 1 page, 1 figure. submitted to Phys. Rev. Let
Hydrogen dissociation on the Mg(0001) surface from quantum Monte Carlo calculations
We have used diffusion Monte Carlo (DMC) simulations to calculate the energy
barrier for H 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 wavefunctions.
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 eV. The DMC dissociation
barrier is calculated to be 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.Comment: 6 pages, 4 figures, to appear in Physical Review
Ab initio statistical mechanics of surface adsorption and desorption: I. HO on MgO (001) at low coverage
We present a general computational scheme based on molecular dynamics (m.d.)
simulation for calculating the chemical potential of adsorbed molecules in
thermal equilibrium on the surface of a material. The scheme is based on the
calculation of the mean force in m.d. simulations in which the height of a
chosen molecule above the surface is constrained, and subsequent integration of
the mean force to obtain the potential of mean force and hence the chemical
potential. The scheme is valid at any coverage and temperature, so that in
principle it allows the calculation of the chemical potential as a function of
coverage and temperature. It avoids all statistical mechanical approximations,
except for the use of classical statistical mechanics for the nuclei, and
assumes nothing in advance about the adsorption sites. From the chemical
potential, the absolute desorption rate of the molecules can be computed,
provided the equilibration rate on the surface is faster than the desorption
rate. We apply the theory by {\em ab initio} m.d. simulation to the case of
HO on MgO (001) in the low-coverage limit, using the Perdew-Burke-Ernzerhof
(PBE) form of exchange-correlation. The calculations yield an {\em ab initio}
value of the Polanyi-Wigner frequency prefactor, which is more than two orders
of magnitude greater than the value of s often assumed in the
past. Provisional comparison with experiment suggests that the PBE adsorption
energy may be too low, but the extension of the calculations to higher
coverages is needed before firm conclusions can be drawn. The possibility of
including quantum nuclear effects by using path-integral simulations is noted.Comment: 11 pages + 10 figure
Ab initio melting curve of molybdenum by the phase coexistence method
We report ab initio calculations of the melting curve of molybdenum for the
pressure range 0-400 GPa. The calculations employ density functional theory
(DFT) with the Perdew-Burke-Ernzerhof exchange-correlation functional in the
projector augmented wave (PAW) implementation. We present tests showing that
these techniques accurately reproduce experimental data on low-temperature
b.c.c. Mo, and that PAW agrees closely with results from the full-potential
linearized augmented plane-wave implementation. The work attempts to overcome
the uncertainties inherent in earlier DFT calculations of the melting curve of
Mo, by using the ``reference coexistence'' technique to determine the melting
curve. In this technique, an empirical reference model (here, the embedded-atom
model) is accurately fitted to DFT molecular dynamics data on the liquid and
the high-temperature solid, the melting curve of the reference model is
determined by simulations of coexisting solid and liquid, and the ab initio
melting curve is obtained by applying free-energy corrections. 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 deduced from static compression experiments. Calculated results
for the radial distribution function show that the short-range atomic order of
the liquid is very similar to that of the high-T solid, with a slight decrease
of coordination number on passing from solid to liquid. The electronic
densities of states in the two phases show only small differences. The results
do not support a recent theory according to which very low dTm/dP values are
expected for b.c.c. transition metals because of electron redistribution
between s-p and d states.Comment: 27 pages, 10 figures. to be published in Journal of Chemical Physic
Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters
We present a detailed study of the energetics of water clusters (HO)
with , comparing diffusion Monte Carlo (DMC) and approximate density
functional theory (DFT) with well converged coupled-cluster benchmarks. We use
the many-body decomposition of the total energy to classify the errors of DMC
and DFT into 1-body, 2-body and beyond-2-body components. Using both
equilibrium cluster configurations and thermal ensembles of configurations, we
find DMC to be uniformly much more accurate than DFT, partly because some of
the approximate functionals give poor 1-body distortion energies. Even when
these are corrected, DFT remains considerably less accurate than DMC. When both
1- and 2-body errors of DFT are corrected, some functionals compete in accuracy
with DMC; however, other functionals remain worse, showing that they suffer
from significant beyond-2-body errors. Combining the evidence presented here
with the recently demonstrated high accuracy of DMC for ice structures, we
suggest how DMC can now be used to provide benchmarks for larger clusters and
for bulk liquid water.Comment: 34 pages, 6 figure
The kinetics of homogeneous melting beyond the limit of superheating
Molecular dynamics simulation is used to study the time-scales involved in
the homogeneous melting of a superheated crystal. The interaction model used is
an embedded-atom model for Fe developed in previous work, and the melting
process is simulated in the microcanonical ensemble. We study
periodically repeated systems containing from 96 to 7776 atoms, and the initial
system is always the perfect crystal without free surfaces or other defects.
For each chosen total energy and number of atoms , we perform several
hundred statistically independent simulations, with each simulation lasting for
between 500 ps and 10 ns, in order to gather statistics for the waiting time
before melting occurs. We find that the probability distribution
of is roughly exponential, and that the mean value depends strongly on the excess of the initial steady temperature of the
crystal above the superheating limit identified by other researchers. The mean
also depends strongly on system size in a way that we have
quantified. For very small systems of atoms, we observe a persistent
alternation between the solid and liquid states, and we explain why this
happens. Our results allow us to draw conclusions about the reliability of the
recently proposed Z method for determining the melting properties of simulated
materials, and to suggest ways of correcting for the errors of the method.Comment: 19 pages, 8 figure
Melting properties of a simple tight-binding model of transition metals: I.The region of half-filled d-band
We present calculations of the free energy, and hence the melting properties,
of a simple tight-binding model for transition metals in the region of d-band
filling near the middle of a d-series, the parameters of the model being
designed to mimic molybdenum. The melting properties are calculated for
pressures ranging from ambient to several Mbar. The model is intended to be the
simplest possible tight-binding representation of the two basic parts of the
energy: first, the pairwise repulsion due to Fermi exclusion; and second, the
d-band bonding energy described in terms of an electronic density of states
that depends on structure. In addition to the number of d-electrons, the model
contains four parameters, which are adjusted to fit the pressure dependent
d-band width and the zero-temperature pressure-volume relation of Mo. We show
that the resulting model reproduces well the phonon dispersion relations of Mo
in the body-centred-cubic structure, as well as the radial distribution
function of the high-temperature solid and liquid given by earlier
first-principles simulations. Our free-energy calculations start from the free
energy of the liquid and solid phases of the purely repulsive pair-potential
model, without d-band bonding. The free energy of the full tight-binding model
is obtained from this by thermodynamic integration. The resulting melting
properties of the model are quite close to those given by earlier
first-principles work on Mo. An interpretation of these melting properties is
provided by showing how they are related to those of the purely repulsive
model.Comment: 34 pages, 12 figures. Accepted for publication in Journal of Chemical
Physic
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