Matematica, Fisica ed Applicazioni
http://elea.unisa.it/xmlui/handle/10556/3005
Sun, 13 Oct 2024 16:59:09 GMT2024-10-13T16:59:09ZTailoring the structural and surface properties of TiO2 thin films and TiO2-based nanolayers, with heat treatments, layer thickness, and oxide mixtures
http://elea.unisa.it/xmlui/handle/10556/7420
Tailoring the structural and surface properties of TiO2 thin films and TiO2-based nanolayers, with heat treatments, layer thickness, and oxide mixtures
Durante, ofelia
Titanium dioxide (TiO2), also known as titanium (IV) oxide or titania, is naturally
available on the Earth as a bright, fine, and white pigment. Thanks to its unique properties,
such as high refractive index, chemical stability, photocatalytic activity, and self-cleaning
surface, TiO2 represents one of the most intensively studied compounds. The properties
of TiO2, which depend on its three crystalline phases (anatase, brookite, and rutile), have
made this material a valuable candidate for applications in many fields, such as optics
(Bragg reflectors, meta-surfaces, optical filters), electronic (sensors, phase-change
memory and metal insulator-semiconductor devices), and photocatalysis (air purification,
water treatments, self-cleaning coatings, dye-sensitized solar cells). Indeed, its band
structure, long-term stability, non-toxicity, cost-effectiveness, and strong oxidizing power
make TiO2 highly suitable for wide environmental and energy applications. Moreover,
given its impressive optical properties, TiO2 finds room in the context of amorphous
coatings for the development of dielectric mirrors, characterized by low transmittance
and thermal noise, to be implemented in the detectors of gravitational waves. Given the
impact that both structural and morphological properties have on the optical and
electronic performances of TiO2, a systematic study on the tailoring of TiO2 crystal
structure and surface properties is of fundamental relevance in many fields.
One of the aims of this work is thus to study the morphological, structural, and
photocatalytic properties of amorphous TiO2 thin films and the impact on these properties
of the structural transitions induced by thermal annealing in different environments.
Moreover, the tailoring of the morphological and structural properties of TiO2 as a
function of thickness is also investigated. Additionally, the combination of TiO2, in its
nanolayered form as well as in the state of co-sputtered mixture, with other metal oxides
is analyzed to address the extent of their structural and morphological reliability for highly
performant high-refractive index candidates in new generation Bragg-like reflectors. In
this scenario, Scanning Probe Microscopy based experiments (Atomic Force Microscopy,
and Kelvin Probe Force Microscopy), Raman Spectroscopy, and X-Ray Diffractometry
have been used to study the morphological, photocatalytic and structural properties of the
investigated materials.
An overview of the properties of TiO2 and its applications, including the one for
gravitational wave detectors, i.e., the context where this work arose, is given in Chapter
1. Here the main properties of some other metal oxides (i.e., ZrO2, Al2O3, Ta2O5, Al2O3)
encountered in this thesis are additionally discussed.
Then, Chapter 2 will briefly introduce the fabrication (ion-assisted deposition and ionbeam sputtering) and characterization (Raman Spectroscopy, X-Ray Diffractometry,
Scanning Probe and Electron Microscopy) techniques used in this work.
The experimental results will be presented in Chapters 3,4,5, and 6. In particular, in
Chapter 3 the effect of thermal treatments in different environments (air, oxygen and
vacuum) and at different temperatures on the structural, morphological, and
photocatalytic properties of TiO2 thin films will be discussed. The influence of the
annealing environment on the crystallization onset and evolution of both anatase and
rutile phases, as well as on the thin film morphology and photocatalytic properties will be
investigated.
Chapter 4 will be focused on the tailoring of the TiO2 thin film crystallization temperature,
in the anatase crystalline phase, by modulating its thickness from hundreds to few nm.
Decreasing the layer thickness, an exponential increase of the crystallization onset
temperature will be demonstrated. Moreover, the evolution of the crystallization will be
studied in an annealing temperature range up to 1000 °C and correlated to the evolution
of the phonon lifetime, studied by Raman spectroscopy.
The role of interfacing TiO2 nanolayers with other nanolayered oxides (SiO2, Ta2O5,
Al2O3, or ZrO2), in a similar Bragg-like reflector geometry at the nm scale, on the overall
structural and morphological properties of the specimen will be discussed in Chapter 5.
The presence of segmentation, as well as of the interfaces with other oxides, will be shown
to significantly affect the crystallization onset temperature.
Then, the effect on structural and morphological properties of combining TiO2, at
different concentrations, with Ta2O5 in a co-sputtered mixture will be presented in
Chapter 6. The influence of different substrates will be also showed.
Finally, results and conclusions are summarized.
In addition, Appendices are included to i) give an overview on the phonon confinement
phenomenon, ii) illustrate theoretical nanolayers modeling and recent technical advances
of the apparatus used for the sample fabrication within the Unisa/Unisannio collaboration,
iii) describe the results and the knowledge acquired during my periods at the Lancaster
University (UK) and at the Gestione Silo company (Florence, Italy). [edited by Author]; Il biossido di titanio (TiO2), noto anche come ossido di titanio (IV) o titania, è
naturalmente disponibile sulla Terra come pigmento brillante, fine e bianco. Grazie alle
sue proprietà uniche, come l'alto indice di rifrazione, la stabilità chimica, l'attività
fotocatalitica e la superficie autopulente, il TiO2 rappresenta uno dei composti più
studiati. Le proprietà del TiO2, che dipendono dalle sue tre fasi cristalline (anatasio,
brookite e rutilo), hanno reso questo materiale un valido candidato per applicazioni in
molti campi, come l'ottica (riflettori di Bragg, meta-superfici, filtri ottici), elettronica
(sensori, memorie a cambiamento di fase e dispositivi metallici isolanti-semiconduttori),
e fotocatalisi (purificazione dell'aria, trattamenti dell'acqua, rivestimenti autopulenti, celle
solari sensibilizzate a colorante). Infatti, la sua struttura a bande, la stabilità a lungo
termine, la non tossicità, l'economicità e il forte potere ossidante rendono il TiO2
altamente adatto per ampie applicazioni ambientali ed energetiche. Inoltre, date le sue
impressionanti proprietà ottiche, il TiO2 trova spazio nell'ambito dei rivestimenti amorfi
per lo sviluppo di specchi dielettrici, caratterizzati da bassa trasmittanza e rumore termico,
da implementare nei rivelatori di onde gravitazionali. Dato l'impatto che le proprietà sia
strutturali che morfologiche hanno sulle prestazioni ottiche ed elettroniche del TiO2, uno
studio sistematico sull'adattamento della struttura cristallina del TiO2 e delle proprietà
superficiali è di fondamentale importanza in molti campi.
Uno degli obiettivi di questo lavoro è quindi quello di studiare le proprietà morfologiche,
strutturali e fotocatalitiche di film sottili di TiO2 amorfo e l'impatto su queste proprietà
delle transizioni strutturali indotte dalla ricottura termica in diversi ambienti. Inoltre,
viene anche studiato l'adattamento delle proprietà morfologiche e strutturali del TiO2 in
funzione dello spessore. Inoltre, viene analizzata la combinazione di TiO2, nella sua forma
nanostratificata così come nello stato di miscela co-sputterata, con altri ossidi metallici
per valutare l'entità della loro affidabilità strutturale e morfologica come candidati ad alto
indice di rifrazione altamente performanti nella nuova generazione dei riflettori tipo
Bragg. In questo scenario, sono stati utilizzati esperimenti basati sulla microscopia a
scansione di sonda (microscopia a forza atomica e Kelvin microscopia a forza di sonda),
spettroscopia Raman e diffrattometria a raggi X per studiare le proprietà morfologiche,
fotocatalitiche e strutturali dei materiali studiati.
Una panoramica delle proprietà del TiO2 e delle sue applicazioni, inclusa quella per i
rivelatori di onde gravitazionali, cioè il contesto in cui è nato questo lavoro, è fornita nel
Capitolo 1. Qui le proprietà principali di alcuni altri ossidi metallici (cioè ZrO2, Al2O3,
Ta2O5, Al2O3) incontrati in questa tesi sono inoltre discussi.
Quindi, il Capitolo 2 introdurrà brevemente le tecniche di fabbricazione (deposizione
assistita da ioni e sputtering a fascio ionico) e di caratterizzazione (spettroscopia Raman,
diffrattometria a raggi X, sonda a scansione e microscopia elettronica) utilizzate in questo
lavoro.
I risultati sperimentali saranno presentati nei Capitoli 3,4,5 e 6. In particolare, nel Capitolo
3 verrà discusso l'effetto dei trattamenti termici in ambienti diversi (aria, ossigeno e
vuoto) e a diverse temperature sulle proprietà strutturali, morfologiche e fotocatalitiche
dei film sottili di TiO2. Verrà studiata l'influenza dell'ambiente di annealing sull'inizio
della cristallizzazione e sull'evoluzione delle fasi anatasio e rutilo, nonché sulla
morfologia del film sottile e sulle proprietà fotocatalitiche.
Il capitolo 4 sarà focalizzato sull'adattamento della temperatura di cristallizzazione del
film sottile di TiO2, nella fase cristallina dell’anatasio, modulando il suo spessore da
centinaia a pochi nm. Diminuendo lo spessore dello strato, sarà dimostrato un aumento
esponenziale della temperatura di inizio della cristallizzazione. Inoltre, l'evoluzione della
cristallizzazione sarà studiata in un intervallo di temperatura di annealing fino a 1000 °C
e correlata all'evoluzione della vita fononica, studiata mediante spettroscopia Raman.
Il ruolo dell'interfacciamento di nanostrati di TiO2 con altri ossidi nanostrati (SiO2, Ta2O5,
Al2O3, o ZrO2), in una simile geometria del riflettore di tipo Bragg a scala nm, sulle
proprietà strutturali e morfologiche complessive del campione sarà discusso nel Capitolo
5. Si dimostrerà che la presenza della segmentazione, così come delle interfacce con altri
ossidi, influenza significativamente la temperatura di inizio della cristallizzazione.
Successivamente, nel Capitolo 6 verrà presentato l'effetto sulle proprietà strutturali e
morfologiche della combinazione di TiO2, a diverse concentrazioni, con Ta2O5 in una
miscela co-sputterata. Verrà anche mostrata l'influenza di diversi substrati.
Infine, vengono riassunti i risultati e le conclusioni.
Inoltre, delle Appendici sono incluse per i) fornire una panoramica sul fenomeno del
confinamento fononico, ii) illustrare la modellizzazione teorica dei nanostrati e i recenti
progressi tecnici dell'apparato utilizzato per la fabbricazione del campione nell'ambito
della collaborazione Unisa/Unisannio, iii) descrivere i risultati e le conoscenze acquisite
durante i miei periodi presso la Lancaster University (UK) e presso la società Gestione
Silo (Firenze, Italia). [a cura dell'Autore]
2020 - 2021
Wed, 15 Dec 2021 00:00:00 GMThttp://elea.unisa.it/xmlui/handle/10556/74202021-12-15T00:00:00ZHidden Structures and Conflicting Items in Combinatorial Optimization Problems
http://elea.unisa.it/xmlui/handle/10556/7330
Hidden Structures and Conflicting Items in Combinatorial Optimization Problems
Serra, Domenico
Combinatorial optimization-based methods are widely used to solve complex real life problems.
In this thesis, we use some of these methods for addressing several emerging combinatorial opti-
mization problems on graphs that can be classified in two macro areas: i) graph substructures
identification problems; ii) combinatorial optimization problems with conflict constraints.
In graph theory, graphs are defined as mathematical structures that describe entities of inter-
est (as nodes) and their relationships (as edges). Many real-world problems can be described
through the use of a graph. For example, graph theory finds application in: i) the context of
social network analysis, where graphs are used to represent the interactions (edges) between users
(nodes); and in ii) the study of biological networks, such as protein-protein interaction, where
the nodes are proteins, and the edges represent their physical interactions. In graph analysis one
common application is the identification of clusters (or communities) of nodes that are tightly
connected. In social networks, a community could represent a set of users sharing the same
interest, while in the protein-protein interaction networks it could represent a set of very similar
proteins forming a protein complex.
In this thesis, three problems related to identifying graph substructures have been tackled.
The first problem addresses the 2-Edge-Connected Minimum Branch Vertices, that finds ap-
plication in the design of optical networks. A graph is 2-Edge-Connected if by removing one
edge, the graph is still connected. The problem looks for a spanning 2-edge connected subgraph
having the minimum number of branch vertices that is vertices with degree strictly greater than
two. In these networks, branch vertices are associated with switch devices that split the light
signals and send them to the adjacent vertices. For this NP-complete problem we developed a
genetic algorithm using ad-hoc designed operators.
The second addressed problem arise in the social network analysis and aims to study how
users influence the choices of their neighbours. In particular, we addressed the Collapsed k-Core
Problem that seeks to identify a subset of critical users in the network whose choices would
alter the cohesiveness of a community. To the best of our knowledge, this is the first attempt
to formulate this problem using mathematical programming. We implemented multiple solution
approaches and compared them on a set of benchmark instances.
The last case studied is related to network clustering, where a cluster graph is a disjoint union
of cliques. The Cluster Deletion problem is defined as the identification of the minimum number
of edges to remove from a network to produce a cluster graph. This is a well-known NP-hard
problem and we faced it using integer linear programming formulation and a heuristic approach
based on edge contraction operation. Our results show the effectiveness of our methodology both
on artificial and real-world biological networks.
4
Currently, the definition of many real-life problems, doesn’t always fully capture their com-
plexity. Indeed, classical optimization problems encountered over the years, although extensively
studied, do not always take into account additional limitations, such as incompatibility situa-
tions, encountered in real-world problems. In this context, two or more elements of the problem
cannot be chosen together to compose a feasible solution. Such incompatibilities are modelled
by introducing conflict constraints in classical combinatorial optimization problems, leading to
more realistic but often harder problems.
Finally, three different combinatorial optimization problems with conflicts constraints are
addressed.
The first one is a variant of the set cover problem where pairwise conflicts are added among
the subsets. In the formulation of this problem, two sets in conflict can belong to the same
solution, provided that a non-negative penalty is paid. We introduced two mathematical formu-
lations for the problem and offered a parallel Greedy Randomised Adaptive Search Procedure
for its solution. The performance of our algorithm was evaluated through an extensive set of
experiments. The results shown the effectiveness and efficiency of our methodology compared to
the mathematical model solutions.
The second problem is related to the Maximum Flow Problem with Conflict constraints on
the edges, for which we present a matheuristic method based on the combination of two different
approaches: Carousel Greedy and Kernel Search. The results shown that the Carousel Greedy
selection substantially improves the effectiveness of the Kernel Search.
The last problem is the Minimum Spanning Tree with Conflicts, that we solved by using a
Kernel Search method. Also in this case, the results on benchmark instances shown that our
methods identifies a better solution compared with existing methods. [edited by Author]
2021 - 2022
Tue, 14 Feb 2023 00:00:00 GMThttp://elea.unisa.it/xmlui/handle/10556/73302023-02-14T00:00:00ZAdvanced Modeling of Microlensing Events
http://elea.unisa.it/xmlui/handle/10556/7328
Advanced Modeling of Microlensing Events
Rota, Paolo
The search for exoplanets is one of the most exciting challenges. From the
first exoplanets discovered around the pulsar PSR B1 257+12 back in 1992 until
today there are over 5200 exoplanets discovered. And the number will continue
to rise in the coming years with the advent of the latest generation telescopes.
There are various techniques for finding exoplanets such as transit, radial
velocity, pulsar timing, direct imaging etc. But among these, gravitational
microlensing is one of the most fascinating. Gravitational microlensing is
a particular technique to detect exoplanets otherwise unavailable with other
techniques such as transits or radial velocity. We have a microlensing event
when the light from a distant source is deflected by a lens passing through
the source and the observer. The result, in the simplest case, is a bell-shaped
peak in the light curve. Planets can be detected studying the anomalies in the
lightcurve (additional peaks or dips, longer distortions, etc.). But microlensing
is not important only for exoplanets. The fact that with this technique it is
possible to reach distances of the order of the galactic center allows us to
discover objects ranging from the disk to the bulge allowing us to have a much
more complete overview of the study of the stellar populations of our galaxy.
And in particular with the study of binary systems we can detect faint objects
that are impossible to reveal with other techniques, such as brown dwarfs,
mysterious objects of which little is known yet and which are presumed to
populate our galaxy in great abundance. Microlensing is undoubtedly the
best method to discover these objects, since having extremely low luminosities
they are difficult to see with telescopes except when they play the role of
lens. Moreover, in some cases the orbital motions of the system can also be
detected, allowing us to study their dynamics in more detail. The typology of
microlensing events is enormous and in this thesis we will analyze some of the
cases that can occur. In the first part we focus on the fundamental concepts of
microlensing theory for the exoplanets search. The second part is dedicated to
the modeling of microlensing events, which is based on the VBBinaryLensing
code. In the third part we analyze some microlensing events, each with certain
characteristics, to highlight how vast the case history of these events is. Finally
there will be the conclusions where the results achieved and future prospects
are discussed. [edited by Author]
2021 - 2022
Mon, 17 Apr 2023 00:00:00 GMThttp://elea.unisa.it/xmlui/handle/10556/73282023-04-17T00:00:00ZOrbital motion, periastron advance and galaxy rotation curves beyond General Relativity
http://elea.unisa.it/xmlui/handle/10556/7291
Orbital motion, periastron advance and galaxy rotation curves beyond General Relativity
Tedesco, Antonio
The Extended Theories of Gravity (ETG) have become one of the most investigated the-
oretical proposals among the alternative explanations for the observed flatness of galaxy
rotation curves, related to the dark matter problem, as well as for the accelerated expan-
sion of the universe, related to the dark energy problem. The reason lies in the fact that
ETG’s can provide predictions consistent with the observational surveys without implicating
invisible matter. In this framework, these phenomena are explained as a physical manifes-
tation of extra-curvature terms of the geometry of the Universe. In the first part, we focus
on this class of theories which are a curvature-based extension of GR. Higher order scalar
curvature invariants are included in the Einstein-Hilbert action giving rise to the Higher
Order Theories and corresponding field equations. For the extension of GR, we consider
the Scalar-Tensor-Fourth-Order Gravity (STFOG) in metric formalism as a representative
general class for the ETG, obtained from combination of Fourth Order Gravity plus a cou-
pled scalar field. The NonCommutative Spectral Gravity is a special case of STFOG. Other
Higher Order Theories, like the f(R)-gravity models, are sub-classes of it.
In this scenario to analyse the orbital motion of interacting objects constituting astro-
physical gravitating systems, like the Solar System or galaxies, is a very important issue for
making new predictions and testing theories. We discuss the fundamentals of the physical
regime given by the Weak Field limit, Newtonian and Post-Newtonian limits, and their cor-
responding expansions as a mathematical procedure to solve the field equations in STFOG.
This makes it possible to deal with the problems of motion for a system of many parti-
cles and reproduce many physical configurations. We solve the linearized field equations
of STFOG stemming from the weak field limit, and this is done in the Standard Post-
Newtonian gauge, which is the suitable choice for the purpose. Then we find the space-time
metric and the potentials connected to each metric component that give rise to the gravi-
tational field. Their behaviour presents a modification to the Newtonian potential induced
by the Yukawa-like potential terms (5th force) of the type V (r) = α
e−βr
r
. Finally, in the
context of the STFOG, we determine the relativistic Lagrangian leading to the equations of
orbital motion for a system of N-body and involving the Post-Newtonian fields. This allows
1
to find out the equations governing the dynamics of a generic N-body system, like those
in the Solar System, binary systems (when N = 2) or possibly the S-stars cluster around
Sagittarius A*, thus providing a theoretical reference for Relativistic Celestial Mechanics
beyond General Relativity and the possibility to study realistic astrophysical models and
gravitational tests.
In the second part, we expose the problem of anomalistic precession and deal with the
analysis of the periastron shift. We consider the Adkins & MacDonell integrals and making
use of the data coming from the precession of planets, we deduce constraints on the param-
eters of the STFOG, therefore also of Non-Commutative Spectral Gravity (NCSG) (as par-
ticular case), including a study for the Quintessence Field (deformation of the Schwarzschild
geometry induced by a dark energy) related to a power-law potential. We show that the
periastron shift of planets allows us to improve the bounds on the range of interaction β by
several orders of magnitude. Then we develop a new resolution method for the determina-
tion of the periastron advance by relying on the epicyclic perturbation, which includes also
the Post-Newtonian contributions and can be applied to theories beyond GR like the ETG,
or models within, without the necessity of numerical integration. Using it, we obtain the
final results and then deduce the full analytic expressions for the advance relative to the
examined ETG. We carry out the preceding analysis once more, and further improvements
on the bounds are achieved.
In the last part, by resorting to the Newtonian limit, we provide the theoretical galaxy
rotation curves in the context of the f(R)-theory, the more general STFOG and the a
NonCommutative Spectral Gravity. Therefore, the first analysis of galaxy rotation curves
in NCSG is conducted. Through the parametric fits with observed data, we derive direct
predictions on the physical parameters (total mass and mass-to-light ratio) for an unexplored
sample of spiral galaxies of the THINGS catalogue. Good reproductions are obtained for
these theories as well as numerical predictions on the physical parameters characterizing a
galaxy. The predictions are directly comparable with the observations. We compare the
numerical outcomes for the metric f(R)-theory with those of the Palatini formalism and,
in the end, we make a comparison of the results relative to the examined ETG with the
observed astronomical estimations. [edited by Author]
2021 - 2022
Mon, 02 Jan 2023 00:00:00 GMThttp://elea.unisa.it/xmlui/handle/10556/72912023-01-02T00:00:00Z