arXiv subjects

G. J. Ackland

Publications and source records attributed to G. J. Ackland.

35 records · Page 2Linked to original sources

arXiv2009

Interatomic forces for transition metals including magnetism

}We present a formalism for extending the second moment tight-binding model, incorporating ferro- and anti-ferromagn etic interaction terms which are needed for the FeCr system. For antiferromagnetic and paramagnetic materials, an explicit additional variable representing the spin is required. In a mean-field approximation this spin can be eliminated, and the potential becomes explicitly temperature dependent. For ferromagnetic interactions, this degree of freedom can be eliminated, and the formalism reduces to the embedded atom method (EAM) and we show the equivale nce of existing EAM potentials to "magnetic" potentials.

cond-mat.mtrl-sci↗

arXiv2009

Boom and bust in continuous time evolving economic model

We show that a simple model of a spatially resolved evolving economic system, which has a steady state under simultaneous updating, shows stable oscillations in price when updated asynchronously. The oscillations arise from a gradual decline of the mean price due to competition among sellers competing for the same resource. This lowers profitability and hence population but is followed by a sharp rise as speculative sellers invade the large un-inhabited areas. This cycle then begins again.

q-fin.GN↗

arXiv2007

Lattice-switch Monte Carlo for binary hard-sphere crystals

We show how to generalize the Lattice Switch Monte Carlo method to calculate the phase diagram of a binary system. A global coordinate transformation is combined with a modification of particle diameters, enabling the multi-component system in question to be explored and directly compared to a suitable reference state in a single Monte Carlo simulation. We use the method to evaluate the free energies of binary hard sphere crystals. Calculations at moderate size ratios, α=0.58 and α=0.73, are in agreement with previous results, and confirm AB2 and AB13 as stable structures. We also find that the AB(CsCl) structure is not entropically stable at the size ratio and volume at which it has been reported experimentally, and therefore that those observations cannot be explained by packing effects alone.

cond-mat.stat-mech↗

arXiv2007

Strategy bifurcation and spatial inhomogeneity in a simple model of competing sellers

We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition to ``cheap'' sellers pricing to cover their costs, ``expensive'' sellers spontaneously appear to exploit short-term favorable situations. These expensive sellers ``speciate'' into discrete price bands. As well as variety in pricing strategy, the ``cheap'' sellers evolve a strongly correlated spatial structure, which in turn creates niches for their expensive competitors. Thus an entire ecosystem of coexisting, discrete, symmetry-breaking strategies arises.

physics.soc-ph↗

arXiv2005

Fermi surface effects in solid-solid phase transitions in simple metals under pressure

I discuss the behaviour of Group 1 and 2 elements under pressure, describing crystallography based on diamond anvil pressure cell experiments and electronic structure calculations. In addition to these precise methods, we discuss more intuitive pictures of both the electronic driving force for the transitions, and the structural motifs which optimise the electronic energy by opening pseudogaps at the Fermi energy.

cond-mat.mtrl-sci↗

arXiv2005

Atomistic modelling of the Shape Memory Effect

This paper reviews the status of molecular dynamics as a method in describing solid-solid phase transitions, and its relationship to continuum approaches. Simulation work done in NiTi and Zr using first principles and semi-empirical potentials is presented. This shows failures of extending equilibrium thermodynamics to the nanoscale, and the crucial importance of system-specific details to the dynamics of martensite formation. The inconsistency between experimental and theoretical crystal structures in NiTi is described, together with its possible resolution in terms of nanoscale effects.

cond-mat.mtrl-sci↗

arXiv2005

Microscopic model of diffusion limited aggregation and electrodeposition in the presence of levelling molecules

A microscopic model of the effect of unbinding in diffusion limited aggregation based on a cellular automata approach is presented. The geometry resembles electrochemical deposition - ``ions'' diffuse at random from the top of a container until encountering a cluster in contact with the bottom, to which they stick. The model exhibits dendritic (fractal) growth in the diffusion limited case. The addition of a field eliminates the fractal nature but the density remains low. The addition of molecules which unbind atoms from the aggregate transforms the deposit to a 100% dense one (in 3D). The molecules are remarkably adept at avoiding being trapped. This mimics the effect of so-called ``leveller'' molecules which are used in electrochemical deposition.

cond-mat.mtrl-sci↗

arXiv2004

Total energy calculation of high pressure selenium: The origin of incommensurate modulations in Se-IV and the instability of proposed Se-II

We present calculation of the high pressure crystal structures in selenium, including rational approximants to the recently reported incommensurate phases. We show how the incommensurate phases can be intuitively explained in terms of imaginary phonon frequencies arising from Kohn anomalies in the putative undistorted phase. We also find inconsistencies between the calculated and experimental Se-II phase - the calculations show it to be a metastable metal while the experiment finds a stable semiconductor. We propose that the experimentally reported structure is probably in error.

cond-mat.other↗

arXiv2004

Development of an interatomic potential for phosphorus impurities in iron

We present the derivation of an interatomic potential for the iron phosphorus system based primarily on {\it ab initio} data. Transferrability in this system is extremely problematic, and the potential is intended specifically to address the problem of radiation damage and point defects in iron containing low concentrations of phosphorus atoms. Some preliminary molecular dynamics calculations show that P strongly affects point defect migration.

cond-mat.mtrl-sci↗

arXiv2003

Origin of complex crystal structures of elements at pressure

We present a unifying theory for the observed complex structures of the sp-bonded elements under pressure based on nearly free electron picture (NFE). In the intermediate pressure regime the dominant contribution to crystal structure arises from Fermi-surface Brillouin zone (FSBZ) interactions - structures which allow this are favoured. This simple theory explains the observed crystal structures, transport properties, the evolution of internal and unit cell parameters with pressure. We illustrate it with experimental data for these elements and ab initio calculation for Li.

cond-mat.mtrl-sci↗

arXiv2003

Maximisation Principles and Daisyworld

We investigate whether the equilibrium time averaged state of a self-organising system with many internal degrees of freedom, 2D- daisyworld, can be described by optimising a single quantity. Unlike physical systems where a principle of maximum energy production has been observed, Daisyworld follows evolutionary dynamics rather than Hamiltonian dynamics. We find that this is sufficient to invalidate the MEP principle, finding instead a different principle, that the system self-organises to a state which maximises the amount of life.

cond-mat.stat-mech↗

arXiv2002

Devil's staircase in kinetically limited growth of Ising model

The devil's staircase is a term used to describe surface or an equilibrium phase diagram in which various ordered facets or phases are infinitely closely packed as a function of some model parameter. A classic example is a 1-D Ising model [bak] wherein long-range and short range forces compete, and the periodicity of the gaps between minority species covers all rational values. In many physical cases, crystal growth proceeds by adding surface layers which have the lowest energy, but are then frozen in place. The emerging layered structure is not the thermodynamic ground state, but is uniquely defined by the growth kinetics. It is shown that for such a system, the grown structure tends to the equilibrium ground state via a devil's staircase traversing an infinity of intermediate phases. It would be extremely difficult to deduce the simple growth law based on measurement made on such an grown structure.

cond-mat.dis-nn↗

arXiv2002

quasiharmonic equations of state for dynamically-stabilized soft-mode materials

We introduce a method for treating soft modes within the analytical framework of the quasiharmonic equation of state. The corresponding double-well energy-displacement relation is fitted to a functional form that is harmonic in both the low- and high-energy limits. Using density-functional calculations and statistical physics, we apply the quasiharmonic methodology to solid periclase. We predict the existence of a B1--B2 phase transition at high pressures and temperatures.

cond-mat.stat-mech↗

arXiv1999

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.

cond-mat.stat-mech↗

arXiv1999

Local size segregation in polydisperse hard sphere fluids

The structure of polydisperse hard sphere fluids, in the presence of a wall, is studied by the Rosenfeld density functional theory. Within this approach, the local excess free energy depends on only four combinations of the full set of density fields. The case of continuous polydispersity thereby becomes tractable. We predict, generically, an oscillatory size segregation close to the wall, and connect this, by a perturbation theory for narrow distributions, with the reversible work for changing the size of one particle in a monodisperse reference fluid.

cond-mat.soft↗

arXiv1997

Free energies of crystalline solids: a lattice-switch Monte Carlo method

We present a method for the direct evaluation of the difference between the free energies of two crystalline structures, of different symmetry. The method rests on a Monte Carlo procedure which allows one to sample along a path, through atomic-displacement-space, leading from one structure to the other by way of an intervening transformation that switches one set of lattice vectors for another. The configurations of both structures can thus be sampled within a single Monte Carlo process, and the difference between their free energies evaluated directly from the ratio of the measured probabilities of each. The method is used to determine the difference between the free energies of the fcc and hcp crystalline phases of a system of hard spheres.

cond-mat.stat-mech↗

arXiv1995

Ab initio studies of structural instabilities in magnesium silicate perovskite

Density-functional simulations are used to calculate structural properties and high-symmetry phonons of the hypothetical cubic phase, the stable orthorhombic phase and an intermediate tetragonal phase of magnesium silicate perovskite. We show that the structure of the stable phase is well described by freezing in a small number of unstable phonons into the cubic phase. We use the frequencies of these unstable modes to estimate transition temperatures for cubic--tetragonal and tetragonal--orthorhombic phase transitions. These are investigated further to find that the coupling with the strain suggests that phonons give a better representation than rigid unit modes. The phonons of an intermediate tetragonal phase were found to be stable except for two rotational modes. The eigenvectors of the most unstable mode of each of the cubic and tetragonal phases account for all the positional parameters of the orthorhombic phase. The phase boundary for the orthorhombic--tetragonal transition intersects possible mantle geotherms, suggesting that the tetragonal phase may be present in the lower mantle.

mtrl-th↗