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In this thesis, we have made an extended study of a particular core-softened system in two dimensions (originally studied in Sadr-Lahijany <i>et al. </i>Physical Review Letters 81, p.4895 [1]). Whereas most studies have only examined single facets of the phase behaviour for a given model, we have systematically studied both liquid and solid state phase behaviour, using a combination of analytic and state of the art simulation methods. Our aim has been to gain a greater understanding of the key features behind the unusual phase behaviour associated with core softened systems. After an introduction, we review previous work on the phase behaviour of core-softened systems, in which we see that these apparently “simple” potentials can give rise to a range of unusual and exotic behaviours. We then briefly study the behaviour of a simple one-dimensional core softened model. This demonstrates liquid state anomalies and a zero temperature transition point, as well as illuminating the dangers of generalising between potentials and across dimensionality. We then move onto the two dimensional system. We study the solid state using a combination of the harmonic approximation, Lattice Switch Monte Carlo (a recently developed simulation technique which allows Monte Carlo moves between structures), and Gibbs-Duhem integration. We find two triangular lattice phases, separated by a region of stable square lattice phase at intermediate pressure; we also find evidence for an isostructural transition (with possible critical point) between the triangular phases at densities metastable with respect to the square lattice phase. To study the liquid state, we use Lennard-Jones Devonshire cell theory and extensive Monte Carlo simulation. We reevaluate the cell theory model, and find strong evidence that Lennard-Jones and Devonshire’s original results were misinterpreted, as were the cell theory results for the system at hand [1]. Our liquid state simulation results confirm the presence of reentrant melting and liquid-state anomalies in the system. We find that, contrary to previous suggestions, these anomalies do not originate from a liquid-liquid transition, but instead from a continuous or near-continuous melting transition, a phenomenon only possible in two dimensions.

Clusters containing both metallic and non-metallic elements have been synthesised by pulsed laser vaporisation of a solid target, followed by entrainment and nucleation of the vaporised material in a pulsed supersonic expansion with an inert carrier gas. The resulting cluster distributions were characterised by laser photoionisation time-of-flight mass spectrometry. Such spectra display intensity anomalies, or so-called 'magic numbers', associated with enhanced geometric and/or electronic stabilities, for particular cluster sizes. These are known as shell effects. An overview of the shell effects used to account for cluster magic numbers is presented. Details of the types of electronic and geometric structures which can be used to rationalise the existence of particularly stable clusters are discussed. The abundance patterns and intensity anomalies found in the cluster mass spectra obtained in this work are interpreted in these terms. Studies of clusters of the alkaline earth elements of group-IIA reveal a competition between pre-crystalline icosahedral structures and fragments of the bulk crystal form. These are the first reported laser vaporisation experiments on such systems. Barium clusters containing up to 32 atoms showed a preference for an icosahedral geometry, even on the inclusion of a small number of oxygen atoms. In comparison, strontium clusters of a similar size were found to attract more oxygen atoms, and to adopt a very different structure based on the face-centred cubic (fcc) lattice of bulk strontium oxide. These observations are related to the known structures of other group-IIA metal clusters and cluster oxides. In order to examine shell effects in more complex systems, photoionisation mass spectra have also been recorded for iron clusters containing up to several hundred atoms. In this case, intensity anomalies in the cluster distributions could not be attributed to one particular shell effect, but involved a competition between both electronic and geometric shell structure.

This thesis is a study of a molecular crystal SF<SUB>6</SUB> through the molecular dynamics(MD) method. Solid SF<SUB>6</SUB> has a plastic phase below its melting point and in this phase the interactions between the molecules are highly anharmonic and the orientations of the molecules are highly disordered. At even lower temperatures, the substance has a truly crystalline phase which exhibits, according to our MD simulation, some highly anharmonic properties such as molecular reorientation especially when the temperature is near the plastic-crystal transition point. In the simulation, a simple Lennard-Jones potential function is used to represent the interactions between the molecules. So far, it has been found that this model can give results which are well in agreement with experiments in both the plastic and the crystalline phase. The agreement between the lattice parameters from the simulation and from neutron experiments is very good. The plastic-crystal phase transition and melting are observed in the simulation. The melting point for a bulk sample is found to be 23% higher than the experimental values but the melting point estimated from the surface-initiated melting is found to be closer to the experimental value. In the study of the low-temperature phase we have found that the thermal motions of the molecules are very different for the molecules occupying the two different symmetry sites of the monoclinic structure. Highly anisotropic patterns of the molecular movements have also been revealed. In order to study the plastic-crystal phase transition, a constant-pressure MD method is used to ensure the smooth transitions between single-crystals. Through the use of this method, we have found that in the search for new crystalline structures the phase transitions are not necessarily between single crystals - crystallites with certain orientation may prevail resulting in a large crystal with domain structures. SF<SUB>6</SUB> is a substance which has not been fully studied through experiments. This offers us an opportunity to use the MD method to predict some of its properties to guide experiments. In this thesis, we present the work on the use the fluctuations of the simulated system to calculate the heat capacity and the elastic constants.

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