Ab initio quantum mechanical investigation of structural and chemical-physical properties of selected minerals for minero-petrological, structural ceramic and biomaterial applications

The purpose of this thesis is the atomic-scale simulation of the crystal-chemical and physical (phonon, energetic) properties of some strategically important minerals for structural ceramics, biomedical and petrological applications. These properties affect the thermodynamic stability and rule the mineral-environment interface phenomena, with important economical, (bio)technological, petrological and environmental implications. The minerals of interest belong to the family of phyllosilicates (talc, pyrophyllite and muscovite) and apatite (OHAp), chosen for their importance in industrial and biomedical applications (structural ceramics) and petrophysics. In this thesis work we have applicated quantum mechanics methods, formulas and knowledge to the resolution of mineralogical problems ("Quantum Mineralogy”). The chosen theoretical approach is the Density Functional Theory (DFT), along with periodic boundary conditions to limit the portion of the mineral in analysis to the crystallographic cell and the hybrid functional B3LYP. The crystalline orbitals were simulated by linear combination of Gaussian functions (GTO). The dispersive forces, which are important for the structural determination of phyllosilicates and not properly con-sidered in pure DFT method, have been included by means of a semi-empirical correction. The phonon and the mechanical properties were also calculated. The equation of state, both in athermal conditions and in a wide temperature range, has been obtained by means of variations in the volume of the cell and quasi-harmonic approximation. Some thermo-chemical properties of the minerals (isochoric and isobaric thermal capacity) were calculated, because of their considerable applicative importance. For the first time three-dimensional charts related to these properties at different pressures and temperatures were provided. The hydroxylapatite has been studied from the standpoint of structural and phonon properties for its biotechnological role. In fact, biological apatite represents the inorganic phase of vertebrate hard tissues. Numerous carbonated (hydroxyl)apatite structures were modelled by QM to cover the broadest spectrum of possible biological structural variations to fulfil bioceramics applications.

Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

Exploring Quantum Speed-up Through Cluster-state Computers

The aim of this thesis is to investigate the nature of quantum computation and the question of the quantum speed-up over classical computation by comparing two different quantum computational frameworks, the traditional quantum circuit model and the cluster-state quantum computer. After an introductory survey of the theoretical and epistemological questions concerning quantum computation, the first part of this thesis provides a presentation of cluster-state computation suitable for a philosophical audience. In spite of the computational equivalence between the two frameworks, their differences can be considered as structural. Entanglement is shown to play a fundamental role in both quantum circuits and cluster-state computers; this supports, from a new perspective, the argument that entanglement can reasonably explain the quantum speed-up over classical computation. However, quantum circuits and cluster-state computers diverge with regard to one of the explanations of quantum computation that actually accords a central role to entanglement, i.e. the Everett interpretation. It is argued that, while cluster-state quantum computation does not show an Everettian failure in accounting for the computational processes, it threatens that interpretation of being not-explanatory. This analysis presented here should be integrated in a more general work in order to include also further frameworks of quantum computation, e.g. topological quantum computation. However, what is revealed by this work is that the speed-up question does not capture all that is at stake: both quantum circuits and cluster-state computers achieve the speed-up, but the challenges that they posit go besides that specific question. Then, the existence of alternative equivalent quantum computational models suggests that the ultimate question should be moved from the speed-up to a sort of “representation theorem” for quantum computation, to be meant as the general goal of identifying the physical features underlying these alternative frameworks that allow for labelling those frameworks as “quantum computation”.

Numerical Modelling of Graphene Nanoribbon-fets for Analog and Digital Applications

Graphene, that is a monolayer of carbon atoms arranged in a honeycomb lattice, has been isolated only recently from graphite. This material shows very attractive physical properties, like superior carrier mobility, current carrying capability and thermal conductivity. In consideration of that, graphene has been the object of large investigation as a promising candidate to be used in nanometer-scale devices for electronic applications. In this work, graphene nanoribbons (GNRs), that are narrow strips of graphene, for which a band-gap is induced by the quantum confinement of carriers in the transverse direction, have been studied. As experimental GNR-FETs are still far from being ideal, mainly due to the large width and edge roughness, an accurate description of the physical phenomena occurring in these devices is required to have valuable predictions about the performance of these novel structures. A code has been developed to this purpose and used to investigate the performance of 1 to 15-nm wide GNR-FETs. Due to the importance of an accurate description of the quantum effects in the operation of graphene devices, a full-quantum transport model has been adopted: the electron dynamics has been described by a tight-binding (TB) Hamiltonian model and transport has been solved within the formalism of the non-equilibrium Green's functions (NEGF). Both ballistic and dissipative transport are considered. The inclusion of the electron-phonon interaction has been taken into account in the self-consistent Born approximation. In consideration of their different energy band-gap, narrow GNRs are expected to be suitable for logic applications, while wider ones could be promising candidates as channel material for radio-frequency applications.

Non-Linear Analysis and Design of Synchronous Bearingless Multiphase Permanent Magnet Machines and Drives

A two-dimensional model to analyze the distribution of magnetic fields in the airgap of a PM electrical machines is studied. A numerical algorithm for non-linear magnetic analysis of multiphase surface-mounted PM machines with semi-closed slots is developed, based on the equivalent magnetic circuit method. By using a modular structure geometry, whose the basic element can be duplicated, it allows to design whatever typology of windings distribution. In comparison to a FEA, permits a reduction in computing time and to directly changing the values of the parameters in a user interface, without re-designing the model. Output torque and radial forces acting on the moving part of the machine can be calculated. In addition, an analytical model for radial forces calculation in multiphase bearingless Surface-Mounted Permanent Magnet Synchronous Motors (SPMSM) is presented. It allows to predict amplitude and direction of the force, depending on the values of torque current, of levitation current and of rotor position. It is based on the space vectors method, letting the analysis of the machine also during transients. The calculations are conducted by developing the analytical functions in Fourier series, taking all the possible interactions between stator and rotor mmf harmonic components into account and allowing to analyze the effects of electrical and geometrical quantities of the machine, being parametrized. The model is implemented in the design of a control system for bearingless machines, as an accurate electromagnetic model integrated in a three-dimensional mechanical model, where one end of the motor shaft is constrained to simulate the presence of a mechanical bearing, while the other is free, only supported by the radial forces developed in the interactions between magnetic fields, to realize a bearingless system with three degrees of freedom. The complete model represents the design of the experimental system to be realized in the laboratory.

Simulation of Smart Materials

The aim of this thesis is the elucidation of structure-properties relationship of molecular semiconductors for electronic devices. This involves the use of a comprehensive set of simulation techniques, ranging from quantum-mechanical to numerical stochastic methods, and also the development of ad-hoc computational tools. In more detail, the research activity regarded two main topics: the study of electronic properties and structural behaviour of liquid crystalline (LC) materials based on functionalised oligo(p-phenyleneethynylene) (OPE), and the investigation on the electric field effect associated to OFET operation on pentacene thin film stability. In this dissertation, a novel family of substituted OPE liquid crystals with applications in stimuli-responsive materials is presented. In more detail, simulations can not only provide evidence for the characterization of the liquid crystalline phases of different OPEs, but elucidate the role of charge transfer states in donor-acceptor LCs containing an endohedral metallofullerene moiety. Such systems can be regarded as promising candidates for organic photovoltaics. Furthermore, exciton dynamics simulations are performed as a way to obtain additional information about the degree of order in OPE columnar phases. Finally, ab initio and molecular mechanics simulations are used to investigate the influence of an applied electric field on pentacene reactivity and stability. The reaction path of pentacene thermal dimerization in the presence of an external electric field is investigated; the results can be related to the fatigue effect observed in OFETs, that show significant performance degradation even in the absence of external agents. In addition to this, the effect of the gate voltage on a pentacene monolayer are simulated, and the results are then compared to X-ray diffraction measurements performed for the first time on operating OFETs.