Biomedical subjects

M J Gillan

Publications and source records attributed to M J Gillan.

7 recordsLinked to original sources

PubMed2006

Extension of molecular electronic structure methods to the solid state: computation of the cohesive energy of lithium hydride.

We describe a simple strategy for calculating the cohesive energy of certain kinds of crystal using readily available quantum chemistry techniques. The strategy involves the calculation of the electron correlation energies of a hierarchy of free clusters, and the cohesive energy E(coh) is extracted from the constant of proportionality between these correlation energies and the number of atoms in the limit of large clusters. We apply the strategy to the LiH crystal, using the MP2 and CCSD(T) schemes for the correlation energy, and show that for this material E(coh) can be obtained to an accuracy of approximately 30 meV per ion pair. Comparison with the experimental value, after correction for zero-point energy, confirms this accuracy.

Algorithms↗

PubMed2006

Density functional calculations of surface free energies.

We propose a general method of thermodynamic integration to find the free energy of a surface, where our integration parameter is taken to be the strain on the unit cell of the system (which in the example presented in this paper is simply the extension of the unit cell along the normal to the surface), and the integration is performed over the thermal average stress from a molecular dynamics run. In order to open up a vacuum gap in a continuous and reversible manner, an additional control interaction has been introduced. We also use temperature integration to find a linear relation for the temperature dependence of the free surface energy. These methods have been applied to the titanium dioxide (110) surface, using first principles density functional theory. A proof of principle calculation for zero temperature shows excellent agreement between the integral calculation and the difference in energy calculated by the DFT program. Calculations that have been performed at 295 and 1000 K give excellent agreement between the two integration methods.

Journal Article↗

PubMed2004

Atomic force algorithms in density functional theory electronic-structure techniques based on local orbitals.

Electronic structure methods based on density-functional theory, pseudopotentials, and local-orbital basis sets offer a hierarchy of techniques for modeling complex condensed-matter systems with a wide range of precisions and computational speeds. We analyze the relationships between the algorithms for atomic forces in this hierarchy of techniques, going from empirical tight-binding through ab initio tight-binding to full ab initio. The analysis gives a unified overview of the force algorithms as applied within techniques based either on diagonalization or on linear-scaling approaches. The use of these force algorithms is illustrated by practical calculations with the CONQUEST code, in which different techniques in the hierarchy are applied in a concerted manner.

Journal Article↗

PubMed2004

Ab initio melting curve of copper by the phase coexistence approach.

Ab initio calculations of the melting properties of copper in the pressure range 0-100 GPa are reported. The ab initio total energies and ionic forces of systems representing solid and liquid copper are calculated using the projector augmented wave implementation of density functional theory with the generalized gradient approximation for exchange-correlation energy. An initial approximation to the melting curve is obtained using an empirical reference system based on the embedded-atom model, points on the curve being determined by simulations in which solid and liquid coexist. The approximate melting curve so obtained is corrected using calculated free energy differences between the reference and ab initio system. It is shown that for system-size errors to be rendered negligible in this scheme, careful tuning of the reference system to reproduce ab initio energies is essential. The final melting curve is in satisfactory agreement with extrapolated experimental data available up to 20 GPa, and supports the validity of previous calculations of the melting curve up to 100 GPa.

Journal Article↗

PubMed2003

Possible thermal and chemical stabilization of body-centred-cubic iron in the Earth's core.

The nature of the stable phase of iron in the Earth's solid inner core is still highly controversial. Laboratory experiments suggest the possibility of an uncharacterized phase transformation in iron at core conditions and seismological observations have indicated the possible presence of complex, inner-core layering. Theoretical studies currently suggest that the hexagonal close packed (h.c.p.) phase of iron is stable at core pressures and that the body centred cubic (b.c.c.) phase of iron becomes elastically unstable at high pressure. In other h.c.p. metals, however, a high-pressure b.c.c. form has been found to become stabilized at high temperature. We report here a quantum mechanical study of b.c.c.-iron able to model its behaviour at core temperatures as well as pressures, using ab initio molecular dynamics free-energy calculations. We find that b.c.c.-iron indeed becomes entropically stabilized at core temperatures, but in its pure state h.c.p.-iron still remains thermodynamically more favourable. The inner core, however, is not pure iron, and our calculations indicate that the b.c.c. phase will be stabilized with respect to the h.c.p. phase by sulphur or silicon impurities in the core. Consequently, a b.c.c.-structured alloy may be a strong candidate for explaining the observed seismic complexity of the inner core.

Journal Article↗

PubMed2002

The ab initio simulation of the Earth's core.

The Earth has a liquid outer and solid inner core. It is predominantly composed of Fe, alloyed with small amounts of light elements, such as S, O and Si. The detailed chemical and thermal structure of the core is poorly constrained, and it is difficult to perform experiments to establish the properties of core-forming phases at the pressures (ca. 300 GPa) and temperatures (ca. 5000-6000 K) to be found in the core. Here we present some major advances that have been made in using quantum mechanical methods to simulate the high-P/T properties of Fe alloys, which have been made possible by recent developments in high-performance computing. Specifically, we outline how we have calculated the Gibbs free energies of the crystalline and liquid forms of Fe alloys, and so conclude that the inner core of the Earth is composed of hexagonal close packed Fe containing ca. 8.5% S (or Si) and 0.2% O in equilibrium at 5600 K at the boundary between the inner and outer cores with a liquid Fe containing ca. 10% S (or Si) and 8% O.

Computer Simulation↗

PubMed2001

Phonon density of states of iron up to 153 gigapascals.

We report phonon densities of states (DOS) of iron measured by nuclear resonant inelastic x-ray scattering to 153 gigapascals and calculated from ab initio theory. Qualitatively, they are in agreement, but the theory predicts density at higher energies. From the DOS, we derive elastic and thermodynamic parameters of iron, including shear modulus, compressional and shear velocities, heat capacity, entropy, kinetic energy, zero-point energy, and Debye temperature. In comparison to the compressional and shear velocities from the preliminary reference Earth model (PREM) seismic model, our results suggest that Earth's inner core has a mean atomic number equal to or higher than pure iron, which is consistent with an iron-nickel alloy.

Journal Article↗