Solid oxide fuel cells are considered as one of the main alternatives for future sources of clean energy. To further improve their performance, theoretical methods able to describe the diffusion process in candidate electrolyte materials at finite temperatures are needed. The method of choice for simulating systems at finite temperature is molecular dynamics. However, if the forces are calculated directly from the Schrödinger equation (first-principles molecular dynamics) the computational expense is too high to allow long enough simulations to properly capture the diffusion process in most materials. This thesis introduces a method to deal with this problem using an external force field to speed up the diffusion process in the simulation. The method is applied to study the diffusion of oxygen ions in Sm-doped ceria, which has showed promise in its use as an electrolyte. Good agreement with experimental data is demonstrated, indicating high potential for future applications of the method.

This thesis deals with inelastic effects in electronic currents. We developed a time-dependent technique and show that this approach gives rich insight into electron-phonon coupling during transport. We compare our results with a time-independent technique and analyse the validity of our model. Finally, the results of a quantum chemistry calculation are presented in the framework of scanning tunneling miscroscopy (STM). We study the chemisorption of a tetrathiafulvalene molecule on a gold surface by performing the calculation of the charge transfer, the induced dipole, and the STM images using the density functional theory.

This dissertation research is focused on first principles studies of graphene and single organic molecules for nanoelectronics applications. These nanosized objects attracted considerable interest from the scientific community due to their promise to serve as building blocks of nanoelectronic devices with low power consumption, high stability, rich functionality, scalability, and unique potentials for device integration. Both graphene electronics and molecular electronics pursue the same goal by using two different approaches: top-down approach for graphene devices scaling to smaller and smaller dimensions, and bottom-up approach for single molecule devices. One of the goals of this PhD research is to apply first-principles density functional theory (DFT) to study graphene/metal and molecule/metal contacts at atomic level. In addition, the DFT-based approach allowed us to predict the electronic characteristics of single molecular devices. The ideal and defective graphene/metal interfaces in weak and strong coupling regimes were systematically studied to aid experimentalists in understanding graphene growth. In addition, a theory of resonant charge transport in molecular tunnel junctions has been developed. The first part of this dissertation is devoted to the study of atomic, electronic, electric, and thermal properties of molecular tunnel junctions. After describing the model and justifying the approximations that have been made, the theory of resonant charge transport is introduced to explain the nature of current rectification within a chemically asymmetric molecule. The interaction of the tunneling charges (electrons and holes) with the electron density of the metal electrodes, which in classical physics is described using the notion of an image potential, are taken into account at the quantum-mechanical level within the tight binding formalism. The amount of energy released onto a molecule by tunneling electrons and holes in the form of thermal vibration excitations is related to the reorganization energy of the molecule, which is also responsible for an effective broadening of molecular levels. It was also predicted that due to the asymmetry of electron and hole resonant energy levels with respect to the Fermi energy of the electrodes, the Joule heating released from the metallic electrodes is also non-symmetric and can be used for the experimental determination of the type of charge carriers contributing to the molecular conductance. In the second part of the dissertation research ideal and defective graphene/metal interfaces are studied in weak and strong interface coupling regimes. The theoretical predictions suggest that the interface coupling may be controlled by depositing an extra metallic layer on top of the graphene. DFT calculations were performed to evaluate the stability of a surface nickel carbide, and to study graphene/carbide phase coexistence at initial stages of graphene growth on Ni(111) substrate at low growth temperatures. Point defects in graphene were also investigated by DFT, which showed that the defect formation energy is reduced due to interfacial interactions with the substrate, the effect being more pronounced in chemisorbed graphene on Ni(111) substrate than in physisorbed graphene on Cu(111) substrate. Our findings are correlated with recent experiments that demonstrated the local etching of transfered graphene by metal substrate imperfections. Both graphene and molecular electronics components of the PhD dissertation research were conducted in close collaboration with several experimental groups at the University of South Florida, Brookhaven National Laboratory, University of Chicago, and Arizona State University.

Graphene is foreseen to be the basis of future electronics owing to its ultra thin structure, extremely high charge carrier mobility,  high thermal conductivity etc., which are expected to overcome the size limitation and heat dissipation problem in silicon based transistors. But these great prospects are hindered by the metallic nature of pristine graphene even at charge neutrality point, which allows to flow current even when a transistor is switched off. A part  of the thesis is dedicated to invoke electronic band gaps in graphene to overcome this problem. The concept of quantum confinement has been employed to tune the band gaps in graphene by  dimensional confinement along with the functionalization of the edges of these confined nanostructures. Thermodynamic stability of the functionalized zigzag edges with hydrogen, fluorine and reconstructed edges has been presented in the thesis. Keeping an eye towards the same goal of band gap opening,  a different route has been considered by admixing insulating hexagonal boron nitride (h-BN) with semimetal graphene. The idea has been implemented in two  dimensional h-BN-graphene composites and three dimensional stacked heterostructures. The study reveals the possibility of tuning band gaps by controlling the admixture. Occurrence of defects in graphene has significant effect on its electronic properties. By random insertion of defects, amorphous graphene is studied, revealing a semi-metal to a metal transition. The field of molecular electronics and spintronics aims towards device realization at the molecular scale. In this thesis, different aspects of magnetic bistability in organometallic molecules have been explored in order to design  practical spintronics devices. Manipulation of spin states in organometallic molecules, specifically metal porphyrin molecules, is achieved by controlling surface–molecule interaction. It has been shown that by strain engineering in defected graphene, the magnetic state of adsorbed molecules can be changed. The spin crossover between different spin states can also be achieved by chemisorption on magnetic surfaces. A significant part of the thesis demonstrates that the surface-molecule interaction not only changes the spin state of the molecule, but allows to manipulate magnetic anisotropies and spin dipole moments via modified ligand fields. Finally, in collaboration with experimentalists, a practical realization of switching surface–molecule magnetic interactions by external magnetic fields is demonstrated.

As the demand for clean and renewable energy sources continues to grow, much attention has been given to solid oxide fuel cells (SOFCs) due to their efficiency and low operating temperature. However, the components of SOFCs must still be improved before commercialization can be reached. Of particular interest is the solid electrolyte, which conducts oxygen ions from the cathode to the anode. Samarium-doped ceria (SDC) is the electrolyte of choice in most SOFCs today, due mostly to its high ionic conductivity at low temperatures. However, the underlying principles that contribute to high ionic conductivity in doped ceria remain unknown, and so it is difficult to improve upon the design of SOFCs. This thesis focuses on identifying the atomistic interactions in SDC which contribute to its favourable performance in the fuel cell. Unfortunately, information as basic as the structure of SDC has not yet been found due to the difficulty in experimentally characterizing and computationally modelling the system. For instance, to evaluate 10.3% SDC, which is close to the 11.1% concentration used in fuel cells, one must investigate 194 trillion configurations, due to the numerous ways of arranging the Sm ions and oxygen vacancies in the simulation cell. As an exhaustive search method is clearly unfeasible, we develop a genetic algorithm (GA) to search the vast potential energy surface for the low-energy configurations, which will be most prevalent in the real material. With the GA, we investigate the structure of SDC for the first time at the DFT+U level of theory. Importantly, we find key differences in our results from prior calculations of this system which used less accurate methods, which demonstrate the importance of accurately modelling the system. Overall, our simulation results of the structure of SDCagree with experimental measurements. We identify the structural significance of defects in the doped ceria lattice which contribute to oxygen ion conductivity. Thus, the structure of SDC found in this work provides a basis for developing better solid electrolytes, which is of significant scientific and technological interest. Following the structure search, we perform an investigation of the electronic properties of SDC, to understand more about the material. Notably, we compare our calculated density of states plot to XPS measurements of pure and reduced SDC. This allows us to parameterize the Hubbard (U) term for Sm, which had not yet been done. Importantly, the DFT+U treatment of the Sm ions also allowed us to observe in our simulations the magnetization of SDC, which was found by experiment. Finally, we also study the SDC surface, with an emphasis on its structural similarities to the bulk. Knowledge of the surface structure is important to be able to understand how fuel oxidation occurs in the fuel cell, as many reaction mechanisms occur on the surface of this porous material. The groundwork for such mechanistic studies is provided in this thesis.

Es werden die Verbindungen YMn2O5 und YFeMnO5 diskutiert. Die erstere zeigt unterhalb von TN = 45 K Ferromagnetismus und in der magnetischen Phase schwache Ferroelektrizität. Die elektrische Polarisation wird mit Symmetriebrechung durch die Spinstruktur erklärt, die zur Aufhebung der Inversionssymmetrie führt (sog. unechtes Ferroelektrikum). Isostrukturelle Ersetzung von Mn durch Fe führt zu YFeMnO5, einer Verbindung, die bei T<165 K ferrimagnetisch, jedoch nicht ferroelektrisch ist. Die Spin-Strukturen beider Verbindungen sind bereits eingehend untersucht und zeigen charakteristische Unterschiede. Für Verbindungen der Zusammensetzung YFe(x)Mn(2-x)O5 wurden Röntgenbeugungs-und Absorptionsfeinstruktur-Experimente zur Bestimmung der Kristallstrukur in Abhängigkeit vom Fe-Anteil x durchgeführt und ausgewertet. Die Ergebnisse zeigen, daß die Strukturparameter einen nahezu linearen Verlauf zwischen den aus der Literatur bekannten Grenzfällen YFeMnO5 und YMn2O5 nehmen. Fe ersetzt dabei das Mn auf der fünffach koordinierten Lage innerhalb einer Sauerstoff-Pyramide. Besonders markant ist die unterschiedliche Position von Mn bzw. Fe in dieser Umgebung. Mit Hilfe der Strukturdaten wurden kollineare DFT-Rechnungen im LSDA+U-Formalismus in skalar-relativistischer Näherung durchgeführt. Für YFeMnO5 konnte der experimentell bekannte Grundzustand im Rahmen der Näherung reproduziert werden, obgleich eine Bandlücke nur in Abhängigkeit von der U-Korrektur auftritt. Der berechnete Grundzustand von YMn2O5 gibt die komplizierte magnetische Struktur dieser Verbindung nicht wieder, weil die gewählte Elementarzelle des Gitters dafür zu klein ist. Statt dessen ist der berechnete Grundzustand hier sehr ähnlich zu dem von YFeMnO5. Eine ausführliche Untersuchung der projizierten Zustandsdichten der Metallatome ermöglicht die Diskussion der Kristallfeldaufspaltung im Zusammenhang mit deren Position innerhalb der Sauerstoffpolyeder. Durch Berechnung mehrerer Spinstrukturen in einer kristallographischen Elementarzelle mit erniedrigter Symmetrie konnten die Austauschparameter eines Heisenberg-Modells zwischen den lokalisierten Spins der Metallatome berechnet werden. Die Größenverhältisse dieser Parameter können mit den aus der Literatur bekannten Spinstrukturen in Einklang gebracht werden. Die Wechselwirkungen sind überwiegend antiferromagnetisch, in Übereinstimmung mit den GKA-Regeln für den Superaustausch. Bei YMn2O5 wird insbesondere eine der schwächeren Kopplungen in der magnetischen Struktur periodisch frustriert. Man geht davon aus, daß dies eine mögliche Ursache für das Auftreten von Ferroelektrizität in der magnetischen Phase ist. Bei YFeMnO5 ist der berechnete Wert dieser Kopplung wesentlich größer und die magnetische Struktur beinhaltet keine Frustration. Dies ist eine mögliche Erklärung für die Abwesenheit der magnetisch induzierten Ferroelektrizität in YFeMnO5. Im zweiten Teil stehen das in Perowskitstruktur kristallisierende SrTiO3 und die durch Hinzufügen von SrO daraus hervorgehenden Kristallstrukturen der sog. Ruddlesden-Popper-Phasen (RP) im Mittelpunkt. Die Daten von Nahkanten-Elektronenenergieverlustspektren (ELNES) an der Sauerstoff K-Kante in SrTiO3, SrO und einer RP-Phase wurden ausgewertet und mit DFT-berechneten projizierten Zustandsdichten (PDOS) der 2p-Orbitale der O-Atome in diesen Verbindungen verglichen. Bei ELNES-Nahkantenspektren ist ein solcher Vergleich mit Experimenten im Bereich hoher Elektronenenergien möglich, weil die Auswahlregel auch für die inelastischen Elektronenstöße zutrifft. Die Spektren zeigen für jede Verbindung charakteristische Maxima, deren Ursache die unterschiedliche nähere Umgebung der Sauerstoffatome ist. Weiterhin wurden Experimente an SrTiO3-Einkristallen unter Einfluß elektrischer Gleichströme und -felder durchgeführt. Bei Experimenten an Einkristall-Wafern waren Hinweise auf lokale Veränderungen der Kristallstruktur unter diesen Bedingungen gefunden worden. Ergänzend dazu wurden mikroskopische einkristalline Proben untersucht. Bei geringen Stromstärken zeigte sich dabei das bereits bekannte Degradationsverhalten des elektrischen Widerstands. Bei hohen Stromstärken kommt es zum elektrischen Durchbruch und dauerhafter Erniedrigung des Widerstands. Röntgenbeugungsmessungen ergaben keine Hinweise auf Veränderungen an der Kristallstruktur oder in Form von Zwillings-oder Bruchstückbildung. Im dritten Teil werden Röntgenbeugungsmessungen an CeCu2Si2-Einkristallen diskutiert. Bei der Auswertung älterer Messungen fielen nach der Strukturbestimmung charakteristische Maxima der Restelektronendichte auf, deren Ursprung nicht erklärt werden konnte und die bei mehreren Kristallen beobachtet wurden. Mit erneuten Messungen und Simulationen konnte nun gezeigt werden, daß diese Maxima von einer fehlerhaften Auswertungsmethode verursacht wurden.

Organic and inorganic nanostructured materials, nano- and mesoscale objects and devices, and their integration into existing microelectronic technologies have been at the center of recent fundamental and applied research in nanotechnology. One of the critical needs is to develop an enhanced predictive capability of structure-property correlations and enable robust high performance systems by design. My thesis work was concerned with the theoretical and experimental studies of electronic and mechanical properties of chemically functionalized nanowires. I will describe a theoretical approach for investigating structure-property correlations in atomic-sized metallic wires based on the Density Functional Theory (DFT) for structure calculations and the Non-equilibrium Green's Function (NEGF) technique for electronic transport properties simulations. This synergistic approach is shown to yield the atomic structure of the smallest niobium nanowires. Furthermore, the method was applied to simulate electronic properties of chemically functionalized graphene nanoribbons. Further, I will demonstrate an experimental technique for simultaneous measurements of force and conductance in atomic-size objects based on quartz tuning fork piezoelectric sensors. A peculiar scaling effect, relevant for a broad range of test and measurement applications, namely the squeeze film effect, was observed during the development of the sensors. Using theoretical analysis based on finite element simulations of the hydrodynamic behavior of the sensors in a broad range of ambient conditions, I explain the observed phenomenon.

One of the most important challenges in low-temperature fuel cell technology is improving the catalytic efficiency at the electrode-catalyst where the oxygen reduction reaction (ORR) occurs. Platinum is the best pure catalyst for this reaction but its high cost and scarcity hinder the commercial implementation of fuel cells in automobiles. Pt-based alloys are promising alternatives to substitute platinum while maintaining the efficiency and life-time of the pure catalyst. However, the acid medium and the oxidation of the surface reduce the activity and durability of the alloy catalyst through changes in its local composition and structure. Molecular simulation techniques are applied to characterize the thermodynamics and dynamic evolution of the surface of platinum-based alloy catalysts under reaction conditions.1-10 A simulation scheme of the surface oxidation is proposed which combines classical molecular dynamics (MD) and density functional theory (DFT). This approach is able to reproduce the main features of the oxidation phenomena observed experimentally, it is concluded that the dissolution mechanism of metal atoms involves: 1) Surface segregation of alloy atoms, 2) oxygen absorption into the subsurface of the catalyst, and 3) metal detachment through the interaction with ions in the solvent. Therefore, to improve the durability of platinum-based alloy catalysts, the steps of the dissolution mechanism must be prevented. A versatile 3-D kinetic Monte Carlo (KMC) code is developed to study the degradation and dealloying in nanocatalysts. The results on the degradation of Pt nanoparticles under different potential regimes demonstrate that the dissolution depends on the potential path to which the nanocatalyst is exposed. Metal atoms detach from the boundaries of (111) facets expecting a reduction in the activity of the nanoparticle. Also, the formation of Pt hollow nanoparticles by the Kirkendall effect is addressed, the role of vacancies is crucial in the removal of the non-noble core that yields to hollow nanoparticles. To investigate the reasons for the experimentally found enhanced ORR activity in porous/hollow nanoparticles, the effect of subsurface vacancies on the main ORR activity descriptors is studied with DFT. It is found that an optimum amount of vacancies may enhance the ORR activity of Pt-monolayer catalysts over certain alloy cores by changing the binding energies of O and OH.

Ο κύριος στόχος της παρούσας εργασίας είναι η αποσαφήνιση του τρόπου εναπόθεσης και της τοπικής δομής των ειδών κοβαλτίου που σχηματίζονται στην διεπιφάνεια «τιτάνια / ηλεκτρολυτικό διάλυμα» κατά το στάδιο του εμποτισμού. Προκειμένου να επιτευχθεί ο στόχος αυτός προβήκαμε σε κατάλληλη θεωρητική και υπολογιστική επεξεργασία δεδομένων, που προέρχονται από την εφαρμογή ηλεκτροχημικών τεχνικών, την εκτέλεση πειραμάτων προσρόφησης και την εφαρμογή φασματοσκοπικών τεχνικών, καθώς επίσης και σε ab-initio υπολογισμούς για την εξακρίβωση του είδους των επιφανειακών οξυγόνων, των φορτίων τους και των συγκεντρώσεών τους. Συγκεκριμένα, εκτελέστηκαν πειράματα στα οποία μελετήθηκε η μεταβολή του pH κατά την εναπόθεση των ειδών του κοβαλτίου στην επιφάνεια της τιτάνιας, πειράματα τιτλοδοτήσεων Co-H+ σε σταθερό pH, καθώς και πειράματα “adsorption edges” προκειμένου να ληφθεί μια γενική εικόνα της έκτασης της προσρόφησης των ιόντων κοβαλτίου σε μια ευρεία περιοχή pH. Επιπλέον, μελετήθηκε η μεταβολή του σημείου μηδενικού φορτίου και του ισοηλεκτρικού σημείου της τιτάνιας, εκτελώντας πειράματα ποτενσιομετρικών τιτλοδοτήσεων μάζας και μικροηλεκτροφόρησης, αντιστοίχως, παρουσία των ιόντων αυτών. Όλα τα παραπάνω, σε συνδυασμό με την φασματοσκοπική τεχνική της διάχυτης ανάκλασης υπέδειξαν το σχηματισμό μονοπυρηνικών / ολιγοπυρηνικών συμπλόκων εσωτερικής σφαίρας κατά την εναπόθεση των ιόντων [Co(H2O)6]2+ στη διεπιφάνεια “τιτάνιας / ηλεκτρολυτικού διαλύματος”. Η αποσαφήνιση όμως της ακριβούς δομής των συμπλόκων αυτών καθώς και η εξακρίβωση της σχετικής τους συγκέντρωσης, σε διάφορες επιφανειακές συγκεντρώσεις Co(II) κατέστη δυνατή με την συνδυασμένη χρήση ημιεμπειρικών κβαντομηχανικών υπολογισμών, στερεοχημικών θεωρήσεων καθώς και προσομοίωσης των δεδομένων εναπόθεσης. Στο συμπαγές τμήμα της διεπιφάνειας “τιτάνιας / ηλεκτρολυτικού διαλύματος” και για χαμηλές καθώς και μεσαίες επιφανειακές συγκεντρώσεις Co(II) σχηματίζονται μονοπυρηνικά σύμπλοκα. Είναι πολύ πιθανός ο σχηματισμός μιας μονο-υδρολυμένης Ti2O-TiO διαμόρφωσης καθώς και μιας δι-υποκατεστημένης TiO-TiO, η οποία έχει υποστεί δυο υδρολύσεις. Στην πρώτη διαμόρφωση ένα υδατικός υποκαταστάτης αντικαθίσταται από ένα γεφυρωμένο επιφανειακό οξυγόνο ενώ ένας άλλος από ένα ακραίο επιφανειακό οξυγόνο. Στην δεύτερη διαμόρφωση δυο υδατικοί υποκαταστάτες αντικαθίσταται από δυο ακραία επιφανειακά οξυγόνα. Επίσης σε υψηλές επιφανειακές συγκεντρώσεις Co(II) παρατηρείται και ο σχηματισμός διπυρηνικών και τριπυρηνικών συμπλόκων εσωτερικής σφαίρας. / The interfacial chemistry of the impregnation step involved in the synthesis of cobalt catalysts supported on titania was investigated with regard to the mode of interfacial deposition of the aqua complex [Co(H2O)6]2+ on the “titania/electrolyte solution” interface, the structure of the inner-sphere complexes formed, and their relative interfacial concentrations. Several methodologies based on the application of deposition experiments and electrochemical techniques were used in conjunction with diffuse-reflectance spectroscopy. These suggested the formation of mononuclear/ oligonuclear inner-sphere complexes on deposition of the [Co(H2O)6]2+ ions at the “titania/electrolyte solution” interface. The joint application of semiempirical quantum-mechanical calculations, stereochemical considerations and modeling of the deposition data revealed the exact structure of these complexes and allowed their relative concentrations at various Co(II) surface concentrations to be determined. It was found that the interface speciation depends on the Co(II) surface concentration. Mononuclear complexes are formed at the compact layer of the “titania/electrolyte solution” interface for low and medium Co(II) surface concentrations. Formation of mono-hydrolyzed Ti2O–TiO and the dihydrolyzed TiO–TiO disubstituted configurations is very probable. In the first configuration one water ligand of the [Co (H2O)6]2+ ion is substituted by a bridging surface oxygen atom and another by a terminal surface oxygen atom. In the second configuration two water ligands of the [Co(H2O)6]2+ ion are substituted by two terminal surface oxygen atoms. Binuclear and trinuclear inner-sphere complexes are formed, in addition to the mononuclear ones, at relatively high Co(II) surface concentrations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work first we perform a study about the stability, and the electronic properties of SiC growth in the [111] direction when defects are present. We use the supercell method and the dangling bonds on the surface of the nanowire are saturated using hydrogen atoms. We also study antisites and substitutional oxygen impurity in this nanowire. For this study, we perform total energy and band structure calculations in order to find the most stable positions for the defects and the influence of defects on the electronic properties. The first principles calculations are based in the density functional theory (DFT). The Generalized Gradient Approximation (GGA) is used for the exchange-correlation term and the ion-electron interactions are replaced by norm-conserving fully separable Troullier-Martins pseudopotentials. For the calculations we use the SIESTA-code and the standard Kohn-Shan (KS) equations are solved in a fully selfconsistent way. The Khon-Sham orbitals are expanded using a linear combination of numerical pseudo-atomic orbitals (PAOs). All calculations use a split-valence double-zeta quality basis set enhanced with a polarization function. Our results show that the most stable antisite is a carbon atom occupying a silicon site (CSi). The substitutional oxygen impurity is most stable in a carbon site (OC). Both defects present a greater stability in the surface of the nanowire when compared with the core of the nanowire. The analysis of electronic structure of bands shows that these defects give rise to electronic levels localized in the band gap of the nanowire. Keywords: density functional theory; SiC nanowires, antisites, impurity. / Neste trabalho inicialmente realizamos um estudo da estabilidade e das propriedades eletrônicas de nanofios de SiC crescido na direção [111]. Foi utilizado o método de supercélula e as ligações pendentes da superfície do nanofio de SiC foram saturadas com átomos de H. Em seguida analisamos estes nanofios na presença de antissítios e impureza substitucional de oxigênio. Para estes defeitos procurou-se as posições energeticamente mais estáveis e as influências dos defeitos nas propriedades eletrônicas. Os cálculos teóricos foram de primeiros princípios fundamentados na Teoria do Funcional da densidade (DFT). Utilizamos para descrever o funcional de trocacorrelação a Aproximação do Gradiente Generalizado (GGA) e para a interação elétron-íon pseudopotenciais de norma conservada de Troullier-Martins. As densidades de carga são obtidas resolvendo as equações de Kohn-Sham, com as funções de onda de Khon-Sham expandidas em uma combinação linear de orbitais atômicos. Nossos resultados mostram que o antissítio mais estável é um átomo de carbono ocupando o sítio de um átomo de silício (CSi). A impureza substitucional de oxigênio apresenta uma maior estabilidade quando ocupando o sítio do átomo de carbono (OC). Ambos os defeitos são energeticamente mais estáveis na superfície do nanofio de SiC. A análise da estrutura eletrônica apresenta que níveis de defeitos podem estar presentes no gap do nanofio, porém nos sítios mais estáveis não observa-se níveis de defeitos no gap.