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The plasma state —ionised gas— is ubiquitous in the Universe. In particular the ionosphere is the plasma embedded in the high altitude atmosphere of a planet. Ionospheres (and magnetospheres) play a key role in mediating the interaction between space and planetary environments through complex dynamic processes that involve interactions between electromagnetic waves and charged particles.One way to investigate the physics of such plasma is computer modelling simulation, where PDE’s of different approximations, full kinetic to fluid descriptions are solved numerically. Alternatively Lagrangian particle methods aim at time-integrating the dynamics of ‘macro-particles’. One particle method widely used in plasma simulation is the Particle-In-Cell (PIC) method.PicSim is a collection of 2D and 3D parallel plasma PIC C++ codes where the internal electrostatic field is updated on a fixed Eulerian mesh, and external uniform electromagnetic, electric and gravitation fields can be enabled. PicSim has been used for various studies of plasma complex dynamic processes involving wave-particle interactions and resulted in over nine publications.Nevertheless the PicSim code suite has never been through a `rigorous review' and examination by experts in high performance computing. The main objective of this project is to port PicSim onto the CINECA high performance computing facility, in order to make profiling, looking for improved efficiency (optimisation) and finally to benchmark and measure the parallel scalability of the code. This process should lead to a better life cycle and science return of the code and foster stronger collaboration between UCL and CINECA.
I was given a thorough introduction to the IBM SP6 system at CINECA. The first step was to compile both sequential and parallel versions of PicSim without optimisation and test the validity of the results.I was also given an introduction on how to make a parallelism profiling with Scalasca to allow identification of potential performance bottlenecks —in particular those concerning communication and synchronisation— and offers guidance in exploring their causes.We profiled both non-optimised and optimised versions of PicSim and identified the two most time consuming parts of the code (63% of the computing time used to interpolate the electric field from the grid to particle positions and then move particles, while 31% is used to compute the source).We spotted a minor imbalance in the tested configuration (that can eventually become more important in different configuration) and decided to modify the code to reduce the imbalance and prepare the code for further parallelisation of some components in the future.We performed a series of benchmarks for different problem size and a wide range of number of CPUs on the SP6 system as we originally planned. But we ended up having time to also benchmark PicSim on the PLX systems also available. The results of our benchmarks have been analysed and successfully fitted to theoretical speed-up law. Results are very encouraging and show linear speedup to several thousands of CPUs.Thanks to a fruitful collaboration and visits at CINECA, PicSim has been benchmarked for parallelism for the first time.
The initial objective of my work was to compare the performances of two different simulation codes on a particular system. One of the codes is the one that we use in my research group and the other one was supposed to be provided by another research group. They failed to produce this second code so I could not achieve what was previsouly planned. From discussions with my host, we decided quickly to start another project which was also very useful for my education.This change of orientation of the work was decided as some recent work has already allowed us to improve a lot the scalability and efficiency of our molecular simulation code on high performance computing facilities so that we are now able to work on systems more complicated than the ones we were used to.We thus concentrated on the possibility of studying electrowetting of an ionic liquid at a planar electrode. Electrowetting is the alteration of the wetting properties of a surface with variations of the electric field. It is a phenomenon of interest because: i) it affects electrode processes, ii) it could be of use in displays. It was previously studied in dielectric liquids (non-conducting) but the ionic liquids may give substantially different results. The questions that we wanted to answer were: i) can we use our code (set up for bulk systems) to look at electrowetting, ii) what kind of system sizes and other run parameters are necessary.The objectives of the work were to build a test system consisting of a droplet of ionic liquid on a planar electrode and to apply different electric fields to assess whether the shape of the droplet changes with the electric field. The main difficulties are: i) finding and building a system ionic liquid/surface which is non wetting when no electric field is applied and ii) characterising the changes in the shape of the droplet as the electric field varies.
The first step was to find or create artificially a surface that does not wet the ionic liquid studied. This was done starting from a graphite surface and reducing the dispersion interactions between the carbon atoms and the liquid molecules. The initial interaction potential for the ionic liquid (1-butyl-4-methylimidazolium tetrafluoroborate, [BMI][BF4]) and the carbon atoms was taken from Merlet et al. (J. Phys. Chem. C, 116, 7687 (2012)) and the interaction potential was modified such that the graphite surface becomes non wetting (the epsilon parameter of the Lennard-Jones potential was changed from 0.23 kJ/mol to 0.01 kJ/mol). The next step is to add a second graphite surface and apply a potential difference between the two electrodes thus formed. The second graphite electrode was disposed 200 A away from the first one and the dispersion interactions for the carbons atoms of this electrode were reduced (epsilon = 0.001 kJ/mol) to avoid any attraction between the liquid and this graphite surface.The last step is to show that the shape of the droplet is effectively modified by the application of a potential difference bewteen the electrodes and that we can evaluate this alteration of the shape of the droplet. A macroscopic measure of the wetting properties of a surface is the contact angle. The higher the contact angle, the less the surface is wetted by the liquid. One important question that arises is how to define the contact angle at a microscopic level.In this work, we used two different methods to estimate the contact angle between the droplet and the graphite surface. Both procedures rely on finding a sphere that encompasses all or the majority of the ions and represents the droplet. This allows for the calculation of the contact angle between the sphere and the first graphite plane. The methods differ by the way the parameters of the sphere are established: the first method consists in finding the ions with the farest positions and take the vector between them as the diameter of the bounding sphere; the second method uses the center of mass of the droplet as the center of the sphere and increases the sphere radius until a certain fraction of the ions are included in the bounding sphere (fraction chosen here = 0.95). It appears that the second method is more reliable. With these tools, it is now possible to evaluate the contact angle for different potentials applied between the electrodes and conclude on the feasibility of studying electrowetting using this type of simulations. Molecular dynamics simulations were conducted with potential differences of 0.0 V and 5.0 V such that the graphite surface in contact with the ionic liquid is held at 0.0 V, + 2.5 V and - 2.5 V. We plotted the contact angles for these different electric fields and saw that the contact angle effectively changes with the applied potential and can thus conclude that the study of electrowetting using this type of molecular dynamics simulations is achievable.
Graphite crystals possess a layered structure with hexagonal symmetry, as originally elucidated by Bernal in the 1920s. Crystals of graphite exposed to ionizing radiation undergo significant expansion along their c-axis, and contraction in the basal directions. This is now believed to be due to buckling and folding over of the layers. However, it was originally believed that this behaviour was caused by the aggregation of interstitial atoms into discs of interstitial prismatic dislocation loops, at the expense of exisitng layers, thereby explaining the observed dimensional change. Nevertheless, Frenkel defects remain important, owing to their role in the buckling process, and that they store large amounts of energy in irradiated graphite, known as Wigner energy.
When irradiated graphite is annealed, self-diffusion allows Frenkel pairs to recombine and release Wigner energy (about 14 eV per pair). It was the release of this Wigner energy which led to the catastrophic accident at the Windscale nuclear pile in 1957. Interstitial atoms also cause buckling of graphite layers, which is subsequently released upon annealing, allowing the layers to fold over upon themselves by the accumulation of dislocations. This also releases Wigner energy, and results in dimensional change.
Although this problem has been studied for many decades, a completely satisfactory explanation of what is happening at the atomic scale has not emerged. There are inconsistencies among the various models and experimental observations.
Thus, a central objective of the originally proposed work was to resolve the problem of self-interstitial migration and aggregation in graphite, which thus far has evaded efforts to find a model which appears to be consistent with experiment. A second aim in the proposal was investigate the migration and aggregation of lattice vacancies in graphite. These defects occur in graphite which has been exposed to ionizing radiation, as might happen in a graphite-moderated nuclear reactor.
Ab initio models employing the AIMPRO program package, which is based on density-functional theory, have been developed that describe how self-diffusion occurs at the atomic scale in graphite containing interstitial atoms and lattice vacancies, as would occur in material which has been exposed to ionizing radiation. The models are constructed in supercells possessing four graphite sheets with orthorhombic symmetry, and contain either 128 or 288 atoms when no defect is present.
Migration of interstitial atoms can occur in several ways involving a number of steps, it is found. In AB-hexagonal graphite, a self-interstitial adopts a structure known as a spiro-interstitial, lying between two neighbouring graphite sheets. The full migration path, involves reorientation around the six equivalent sites associated with the pair of nearest alpha atoms, passing through an intermediate, metastable grafted interstitial state, and a split-interstitial state at the beta site. From the beta split-interstitial, the atom can go to an equivalent grafted state, or its partner can move to a grafted state on the opposite side of the sheet. The rate-limiting step is from the spiro state to the grafted state, which has an activation energy Ea = 2.0 eV. An alternative route for self-interstitial diffusion involves relative translations of graphite layers, or shear. During this process the direction of the shear vector changes in the basal plane, and carries the interstitial atom over an energy barrier with Ea = 1.2 eV. A related process without shear vector reorientation is found to have an activation energy Ea = 1.5 eV.
Lattice vacancies are believed that they posses a reconstructed structure and net magnetic moment of about 1-1.5 µB per atom. This is confirmed by the calculations. There is a relatively small barrier of about 0.2-0.3 eV associated with reorientation of the reconstruction bond, also confirming earlier work. However, it is also found that small displacements of the unpaired atom out of the basal plane easily quench the magnetic moment of the defect. There is growing evidence that the migration barrier for lattice vacancies in graphite is much smaller than an earlier accepted figure of 3.1 eV. According to the simulations here, Ea = 1.2 eV, in agreement with recent experiments and other calculations, and in contrast to the conventional view. Note, it is crucial to take into account the effects of magnetism.
In agreement with earlier work, the recombination of Frenkel pairs has a barrier to the final step, and involves a state known as an intimate Frenkel pair. However, the barrier to recombination is significantly smaller than found previously (1.4 eV). In this state the interstitial atom is delicately balanced in a metastable state immediately adjacent to the vacancy. The barrier depends on whether the vacancy is at an alpha site, a beta site, or the graphite sheets are sheared by a dislocation, where alpha and beta sites loose their distinction. Earlier calculations were not able to resolve these differences. In the present work, it is found that the alpha-type intimate Frenkel pair have a barrier to recombination much less than 0.1 eV, while beta ones experience a barrier Ea = 0.7 eV. In the sheared state Ea = 0.4 eV when there is no constraint on relative translations of the layers, and Ea = 0.25 eV when the shear is frozen with the magnitude and direction which makes alpha and beta sites equivalent.
Results have also been obtained for the final stages of aggregation of vacancies into divacancy complexes, of which there are several.
From this work it can now be understood how the broad spectrum of Wigner energy release arises from low temperatures, to the peak at about 200 C, and on to higher temperatures. The processes at each stage are identified, and it is seen how they are related to observed dimensional changes and other phenomena during the annealing of irradiated graphite.