Oxygen adsorption on Cu(211) and structurally and chemically modified Cu(100)

Kuparipinnan hapettuminen on viimevuosina ollut suosittu tutkimuskohde materiaalitieteissä kuparin laajan teollisuuskäytön vuoksi. Teollisuussovellusten, kuten suojaavien pintaoksidien kehittäminen vaatii kuitenkin syvällistä tuntemusta hapettumisprosessista ja toisaalta myös normaaliolosuhteissa materiaalissa esiintyvien hilavirheiden vaikutuksesta siihen. Tässä työssä keskitytäänkin tutkimaan juuri niitä mekanismeja, joilla erilaiset pintavirheet ja porrastettu pintarakenne vaikuttavathapen adsorptioprosessiin kuparipinnalla. Tutkimus on tehty käyttämällä laskennallisia menetelmiä sekä VASP- ja SIESTA-ohjelmistoja. Työssätutkittiin kemiallisia ja rakenteellisia virheitä Cu(100)-pinnalla, joka on reaktiivisin matalanMillerin indeksin pinta ja porrastetun pinnan tutkimuksessa käytettiin Cu(211)-pintaa, joka puolestaan on yksinkertainen, stabiili ja aiemmissa tutkimuksissa usein käytetty pintarakenne. Työssä tutkitut hilavirheet, adatomit, vähentävät molekyylin dissosiaatiota kuparipinnalla, kun taas vakanssit toimivat dissosiaation keskuksina. Kemiallisena epäpuhtautena käytetty hopeakerros ei estä kuparin hapettumista, sillä happi aiheuttaa mielenkiintoisen segregaatioilmiön, jossa hopeatyöntyy syvemmälle pinnassa jättäen kuparipinnan suojaamattomaksi. Porrastetulla pinnalla (100)-hollow on todennäköisin paikka molekyylin dissosiaatiolle, kun taas portaan bridge-paikka on suotuisin molekulaariselle adsorptiolle. Lisäksi kuparin steppipinnan todettiin olevan reaktiivisempi kuin tasaiset kuparipinnat.

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

Measuring irregularities and surface defects from printed patterns

Quality inspection and assurance is a veryimportant step when today's products are sold to markets. As products are produced in vast quantities, the interest to automate quality inspection tasks has increased correspondingly. Quality inspection tasks usuallyrequire the detection of deficiencies, defined as irregularities in this thesis. Objects containing regular patterns appear quite frequently on certain industries and science, e.g. half-tone raster patterns in the printing industry, crystal lattice structures in solid state physics and solder joints and components in the electronics industry. In this thesis, the problem of regular patterns and irregularities is described in analytical form and three different detection methods are proposed. All the methods are based on characteristics of Fourier transform to represent regular information compactly. Fourier transform enables the separation of regular and irregular parts of an image but the three methods presented are shown to differ in generality and computational complexity. Need to detect fine and sparse details is common in quality inspection tasks, e.g., locating smallfractures in components in the electronics industry or detecting tearing from paper samples in the printing industry. In this thesis, a general definition of such details is given by defining sufficient statistical properties in the histogram domain. The analytical definition allowsa quantitative comparison of methods designed for detail detection. Based on the definition, the utilisation of existing thresholding methodsis shown to be well motivated. Comparison of thresholding methods shows that minimum error thresholding outperforms other standard methods. The results are successfully applied to a paper printability and runnability inspection setup. Missing dots from a repeating raster pattern are detected from Heliotest strips and small surface defects from IGT picking papers.

A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

Investigation of interaction between native and impurity defects in ZnSe

Zinc selenide is a prospective material for optoelectronics. The fabrication of ZnSe­based light-emitting diodes is hindered by complexity of p-type doping of the component materials. The interaction between native and impurity defects, the tendency of doping impurity to form associative centres with native defects and the tendency to self-compensation are the main factors impeding effective control of the value and type of conductivity. The thesis is devoted to the study of the processes of interaction between native and impurity defects in zinc selenide. It is established that the Au impurity has the most prominent amphoteric properties in ZnSe among Cu, Ag and Au impurities, as it forms a great number of both Au; donors and Auz„ acceptors. Electrical measurements show that Ag and Au ions introduced into vacant sites of the Zn sublattice form simple single-charged Agz„+ and Auzn+ states with d1° electron configuration, while Cu ions can form both single-charged Cuz„ (d1) and double-charged Cuzr`+ (d`o) centres. Amphoteric properties of Ag and Au transition metals stimulated by time are found for the first time from both electrical and luminescent measurements. A model that explains the changes in electrical and luminescent parameters by displacement of Ag ions into interstitial sites due to lattice deformation forces is proposed. Formation of an Ag;-donor impurity band in ZnSe samples doped with Ag and stored at room temperature is also studied. Thus, the properties of the doped samples are modified due to large lattice relaxation during aging. This fact should be taken into account in optoelectronic applications of doped ZnSe and related compounds.

Epäpuhtauksien vaikutus monokaliumfosfaattikiteen kasvuun

Työssä on tutkittu epäpuhtauksien vaikutusta kastelulannoitesuolojen monokaliumfosfaatin, kaliumnitraatin ja ureafosfaatin kiteytyksessä. Kirjallisuusosassa on käsitelty kastelulannoiteprosessit ja epäpuhtauksien vaikutus kastelulannoitteiden valmistuksessa. Kiteytys ja kiteenkasvu on esitetty perusyhtälöin, joissa on otettu epäpuhtauksien vaikutus huomioon. Tarkemmin on perehdytty monokaliumfosfaatin kiteytykseen ja kolmenarvoisten kationeiden, Al3+, Fe3+ ja Cr3+, vaikutukseen kiteiden kasvuun. Kolmenarvoiset metalli-ionit adsorboituvat kiteen pintaan haitaten kiteenkasvua, mikä vaikuttaa erityisesti kiteen prismapinnan kasvuun. Lisäksi on esitelty muita kiteenkasvuun vaikuttavia olosuhteita. Lopuksi on käsitelty kompleksinmuodostajia metalli-ionien haitallisten vaikutusten ehkäisijöinä. Kokeellisessa osassa suoritettiin liukoisuuskokeita monokaliumfosfaatin liukoisuuden selvittämiseksi eri pH-olosuhteissa. Suoritetuissa yksikidekokeissa tutkittiin pH:n ja kolmenarvoisten kationeiden; Al3+, Fe3+ ja Cr3+, vaikutus monokaliumfosfaattikiteen pituus- ja leveyskasvuun ja kidemuotoon eri ylikylläisyyksillä. Lisäksi tutkittiin voidaanko lämpötilaa ja pH muuttamalla tai pyrofosfaattia lisäämällä poistaa raudan kasvua inhiboima vaikutus. Kiteytyslämpötilaa nostamalla voidaan poistaa raudan haitallinen vaikutus kiteen kasvuun.

Ristikkotorniprojektin jälkiseuranta sekä valmistus-, kuljetus- ja asennusnäkökohdat massiivisen tornin suunnittelussa

Tässä työssä tutkittiin jälkiseurantana putkipalkkirakenteisen ristikkotornin rakennusprojektia. Tutkimuksen kohteena oli suomalaiselle öljynjalostamolle vuonna 1992 rakennettu vapaastiseisova 105 m korkea soihtutorni. Työn tarkoituksena oli tutkia teräsrakennekokonaisuutta toisaalta suunnittelun ja lujuuslaskennan, toisaalta valmistuksen, kuljetuksen ja asennuksen kannalta. Lisäksi työssä etsittiin soihtutornin vaihtoehtoisia rakenneratkaisuja. Esisuunnittelun tuloksena syntyneitä rakenteita verrattiin vuonna 1992 toteutettuun rakenteeseen. Toteutetun ristikkomaston lujuusominaisuuksia arvioitiin käymällä läpi tehdyt lujuuslaskelmat ja selvittämällä mm. rakenteen eri kohdista mitoituksen tasaisuus. Havaittiin, että rakenteen lujuuden käyttöaste vaihteli 0,7:n ja 0,9:n välillä 72 m:n korkeuteen asti. Tästä ylöspäin käyttöasteet olivat pienempiä. Konepajavalmistuksen, kuljetusten ja asennustöiden onnistumista tutkittiin haastattelemalla sekä konepajan että tilaajan edustajia. Ylöspäin kapeneva rakenne osoittautui lujuusopillisesti järkeväksi, mutta valmistusteknisesti vanhanaikaiseksi. Massiivisten ristikkotornien kuljetus- ja nostomahdollisuuksia tutkittiin selvittämällä lainsäädännön asettamat rajoitukset ja käsikirjojen antamat ohjeet. Lisäksi haastateltiin erikoiskuljetuksia ja -nostoja suorittavan yrityksen edustajaa. Uusien rakenneratkaisujen suunnittelussa korostettiin pitkälle vietyä osavalmistusta sekä kuljetus- ja nostomahdollisuuksia. Uusista tornivaihtoehdoista tutkittiin tarkemmin massiivisista pyöreistä putkipalkeista tehty torni, joka on rakenteeltaan Vierendeel-kehän sovellutus. Rakenne on 62 % painavampi kuin vuonna 1992 toteutettu soihtutorni, mutta silti 9 % halvempi. Uuden rakenteen valmistusystävällisyys on merkittävästi parempi kuin vanhan.

Effects of vacancy-type defects in silicon based particle detectors

The semiconductor particle detectors used at CERN experiments are exposed to radiation. Under radiation, the formation of lattice defects is unavoidable. The defects affect the depletion voltage and leakage current of the detectors, and hence affect on the signal-to-noise ratio of the detectors. This shortens the operational lifetime of the detectors. For this reason, the understanding of the formation and the effects of radiation induced defects is crucial for the development of radiation hard detectors. In this work, I have studied the effects of radiation induced defects-mostly vacancy related defects-with a simulation package, Silvaco. Thus, this work essentially concerns the effects of radiation induced defects, and native defects, on leakage currents in particle detectors. Impurity donor atom-vacancy complexes have been proved to cause insignificant increase of leakage current compared with the trivacancy and divacancy-oxygen centres. Native defects and divacancies have proven to cause some of the leakage current, which is relatively small compared with trivacancy and divacancy-oxygen.

Studies of Eu- and Yb-induced Reconstructions on the Si(100) Surface

This thesis presents experimental studies of rare earth (RE) metal induced structures on Si(100) surfaces. Two divalent RE metal adsorbates, Eu and Yb, are investigated on nominally flat Si(100) and on vicinal, stepped Si(100) substrates. Several experimental methods have been applied, including scanning tunneling microscopy/spectroscopy (STM/STS), low energy electron diffraction (LEED), synchrotron radiation photoelectron spectroscopy (SR-PES), Auger electron spectroscopy (AES), thermal desorption spectroscopy (TDS), and work function change measurements (Δφ). Two stages can be distinguished in the initial growth of the RE/Si interface: the formation of a two-dimensional (2D) adsorbed layer at submonolayer coverage and the growth of a three-dimensional (3D) silicide phase at higher coverage. The 2D phase is studied for both adsorbates in order to discover whether they produce common reconstructions or reconstructions common to the other RE metals. For studies of the 3D phase Yb is chosen due to its ability to crystallize in a hexagonal AlB2 type lattice, which is the structure of RE silicide nanowires, therefore allowing for the possibility of the growth of one-dimensional (1D) wires. It is found that despite their similar electronic configuration, Eu and Yb do not form similar 2D reconstructions on Si(100). Instead, a wealth of 2D structures is observed and atomic models are proposed for the 2×3-type reconstructions. In addition, adsorbate induced modifications on surface morphology and orientational symmetry are observed. The formation of the Yb silicide phase follows the Stranski-Krastanov growth mode. Nanowires with the hexagonal lattice are observed on the flat Si(100) substrate, and moreover, an unexpectedly large variety of growth directions are revealed. On the vicinal substrate the growth of the silicide phase as 3D islands and wires depends drastically on the growth conditions. The conditions under which wires with high aspect ratio and single orientation parallel to the step edges can be formed are demonstrated.

Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

Space–Time Block Codes and the Complexity of Sphere Decoding

In wireless communications the transmitted signals may be affected by noise. The receiver must decode the received message, which can be mathematically modelled as a search for the closest lattice point to a given vector. This problem is known to be NP-hard in general, but for communications applications there exist algorithms that, for a certain range of system parameters, offer polynomial expected complexity. The purpose of the thesis is to study the sphere decoding algorithm introduced in the article On Maximum-Likelihood Detection and the Search for the Closest Lattice Point, which was published by M.O. Damen, H. El Gamal and G. Caire in 2003. We concentrate especially on its computational complexity when used in space–time coding. Computer simulations are used to study how different system parameters affect the computational complexity of the algorithm. The aim is to find ways to improve the algorithm from the complexity point of view. The main contribution of the thesis is the construction of two new modifications to the sphere decoding algorithm, which are shown to perform faster than the original algorithm within a range of system parameters.

Time-Resolved Photoluminescence in Antimonide and Dilute Nitride Quantum Well Structures

This Master's thesis is devoted to semiconductor samples study using time-resolved photoluminescence. This method allows investigating recombination in semiconductor samples in order to develop quality of optoelectronic device. An additional goal was the method accommodation for low-energy-gap materials. The first chapter gives a brief intercourse into the basis of semiconductor physics. The key features of the investigated structures are noted. The usage area of the results covers saturable semiconductor absorber mirrors, disk lasers and vertical-external-cavity surface-emittinglasers. The experiment set-up is described in the second chapter. It is based on up-conversion procedure using a nonlinear crystal and involving the photoluminescent emission and the gate pulses. The limitation of the method was estimated. The first series of studied samples were grown at various temperatures and they suffered rapid thermal annealing. Further, a latticematched and metamorphically grown samples were compared. Time-resolved photoluminescence method was adapted for wavelengths up to 1.5 µm. The results allowed to specify the optimal substrate temperature for MBE process. It was found that the lattice-matched sample and the metamorphically grown sample had similar characteristics.

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

Magnetic Resonance Experiments with Atomic Hydrogen

In this thesis three experiments with atomic hydrogen (H) at low temperatures T<1 K are presented. Experiments were carried out with two- (2D) and three-dimensional (3D) H gas, and with H atoms trapped in solid H2 matrix. The main focus of this work is on interatomic interactions, which have certain specific features in these three systems considered. A common feature is the very high density of atomic hydrogen, the systems are close to quantum degeneracy. Short range interactions in collisions between atoms are important in gaseous H. The system of H in H₂ differ dramatically because atoms remain fixed in the H₂ lattice and properties are governed by long-range interactions with the solid matrix and with H atoms. The main tools in our studies were the methods of magnetic resonance, with electron spin resonance (ESR) at 128 GHz being used as the principal detection method. For the first time in experiments with H in high magnetic fields and at low temperatures we combined ESR and NMR to perform electron-nuclear double resonance (ENDOR) as well as coherent two-photon spectroscopy. This allowed to distinguish between different types of interactions in the magnetic resonance spectra. Experiments with 2D H gas utilized the thermal compression method in homogeneous magnetic field, developed in our laboratory. In this work methods were developed for direct studies of 3D H at high density, and for creating high density samples of H in H₂. We measured magnetic resonance line shifts due to collisions in the 2D and 3D H gases. First we observed that the cold collision shift in 2D H gas composed of atoms in a single hyperfine state is much smaller than predicted by the mean-field theory. This motivated us to carry out similar experiments with 3D H. In 3D H the cold collision shift was found to be an order of magnitude smaller for atoms in a single hyperfine state than that for a mixture of atoms in two different hyperfine states. The collisional shifts were found to be in fair agreement with the theory, which takes into account symmetrization of the wave functions of the colliding atoms. The origin of the small shift in the 2D H composed of single hyperfine state atoms is not yet understood. The measurement of the shift in 3D H provides experimental determination for the difference of the scattering lengths of ground state atoms. The experiment with H atoms captured in H2 matrix at temperatures below 1 K originated from our work with H gas. We found out that samples of H in H2 were formed during recombination of gas phase H, enabling sample preparation at temperatures below 0.5 K. Alternatively, we created the samples by electron impact dissociation of H₂ molecules in situ in the solid. By the latter method we reached highest densities of H atoms reported so far, 3.5(5)x10¹⁹ cm^-3. The H atoms were found to be stable for weeks at temperatures below 0.5 K. The observation of dipolar interaction effects provides a verification for the density measurement. Our results point to two different sites for H atoms in H2 lattice. The steady-state nuclear polarizations of the atoms were found to be non-thermal. The possibility for further increase of the impurity H density is considered. At higher densities and lower temperatures it might be possible to observe phenomena related to quantum degeneracy in solid.