Amélioration des propriétés des couches minces de carbone amorphe (appelé Diamond Like Carbon, DLC) et recherche de nouvelles fonctionnalités pour ce type de couches minces en dopant les films DLC par des métaux comme le nickel et le tantale.<br />L'ablation laser en régime femtoseconde est la technique utilisée pour la synthèse des couches minces de DLC dopées ou alliées. Ce sujet met également en évidence l'apport de cette technique sur les propriétés morpho-structurales et physiques des DLC dopés ou alliés.

Amorphous carbon film with Diamond like properties is the subject of intense interest in the past one and half decade. The unusual properties of these diamond like carbon films arise from the preponderance of SP3 tetrahedral bonding of carbon in the film. Depending on the processing technique and the processing conditions used, the structure of the films can range from amorphous carbon to large grain polycrystalline diamond. These deposited amorphous carbon films, which are smooth, may find their use in optoelectronics, in dielectric films and in microelectronics. These films are found to be chemically inhomogeneous(containing SP3 hybridized carbon in a matrix of SP2 hybridized non-graphitic carbon). There is a possibility of using these films as substrates in microelectronics, provided the deposited films are structurally smooth, are chemically homogeneous and are dopable with both types of impurities. A host of other advantages of using diamond like carbon as a substrate material in microelectronics made it a topic of interest to many investigators. This prompted the author to take up investigations on diamond like carbon films from the point of examining the electrical properties of these films and on the possibility of conceiving devices based on these films. This investigation dealt with, sputter deposition of diamond like carbon films and their electrical characteristics in MCS device structures. In this, emphasis is given to the importance of processing parameters involved and the effect of each parameter on the electrical and structural properties of the film. Various substrate treatments were done prior to sputtering and found that the DLC nature of the film exists in all the films but differ from one another in electrical resistivity, in nucleation density and in their adherence to the substrate. Films deposited on substrates treated with low vapour pressure oil resulted in compressive strain in the film and lead to very poor adhesion. The nucleation density increased when the substrates are pretreated with ultrasonic agitation in hard SiC grit. The substrate temperature had a direct impact on the resistivity of the film: resistivity decreases with increase in substrate temperature. The constituents of the plasma modified the structural properties of the film, e.g. the Hydrogen content in the plasma has resulted in increasing the SP3 hybridization content of the film, by acting as SP2- SP2 network terminator. Ultra violet light focused onto the substrate, in general, enhanced the deposition rate. Inclusion of Nitrogen in the plasma substantially increased the conductivity of the material and this is used in doping of the DLC film. The carbon films deposited on silicon are used for electrical characterisation. Deposition of metal electrode on the carbon film lead to the basic (MCS) device structure. The I vs.V characteristics of the MCS structure resemble those of junction diodes. From the I vs.V characteristics at different temperatures, it has been found that the reverse current goes through a maximum, drops back to certain level and once again increases with gradual increase in temperature. This behaviour of the structure with A1 as well as Ag as top electrode materials is explained by the heterojunction formed at the C-pSi interface. The initial increase in the reverse current is dominated by the drift of minority carriers across the depletion width at the reverse biased junction. With increase in temperature, the depletion width reduces to a minimum above a certain temperature, where the diffusion of carriers controls the current across the device. From the constructed energy-band diagram of heterojunction, it is shown that the change in the transport phenomena from drift of minority carriers to diffusion of majority carriers at the junction, introduces a barrier at the critical temperature; This is responsible for the drop in current at the critical temperature. This explains the anomaly of drop in reverse current with increase in temperature. The C vs. v characteristics showed a bell shaped behaviour indicating the presence of two junctions connected back to back. This confirms the type of contact formed at the metal-carbon interface and the type of conductivity of the film, concluding that A1 makes a Schottky contact where as Ag makes an ohmic contact and the deposited film behaves like n-type material. The C vs. V behaviour with temperature is explained by the two types of contacts in the case of Al-GpSi, i.e. Schottky contact at Al-C; and heterojunction at C-pSi interface. These C vs. V and I vs.V changes with temperature are in tune with each other and the model proposed takes care of all the characteristics observed. In case of Ag-GpSi, C vs. V with temperature shows junction like behaviour at elevated temperatures and are explained by the presence of the interface at C-pSi. It has been observed that in some of the carbon films, when an electric field of the order of l06 V/cm is applied, the reflectance of the Aluminium metal dot is increased by 5 times, coupled with a 50 to 100 times increase in the associated capacitance of the MCS structure. The increase in reflectance is explained by considering the film to be inhomogeneous with a matrix of varying dielectric constants (SP3 hybridized carbon in a medium of SP2 bonded carbon). The transformed film, is homogeneous and enhances the reflectance of the Aluminium dot. This is termed as "homogeneity induced smoothness." The transformation of inhomogeneous material to homogeneous material is further confirmed by the Raman spectroscopy, in which the broad peak is converted to a sharp peak changing the FWHM from 93 cm-1 to 4 cm-1 ; denoting the structural order in the film. To the best of our knowledge, this is the first investigation reporting the crystalline nature of the DLC, with structural order and the corresponding FWHM of the Raman peak as low as 4 cm-1. The preparational conditions of the film to get this transformation and the influence of various process parameters are examined. Devices based on Metal-Carbon-Oxide- Silicon (MCOS) structure are realized by thermally grown oxide/sputter deposited oxide on silicon, prior to carbon deposition. These structures showed voltage controlled negative resistance(VCNR) characteristics. The applied voltage and its distribution across the reverse biased junction and across the oxide gives rise to a negative resistance region. With the number of V vs. I characteristics measured, it is observed that the negative resistance region also shifts. This is attributed to the trapped charges in the carbon changing the distribution of applied voltage. This is explained by modifying the energy-band diagram. A concept of the accumalated charges at the oxide barrier filling up the higher energy states in the carbon and silicon, to become hot carriers is used. As long a. more voltage is dropped across the oxide, these hot carriers can surmount the barrier at the reverse biased junction. The flow of these carriers is cut off when the additional voltage is dropped across the reverse biased junction leading to a drop in the current. A further increase in the applied voltage nominally increases the current due to increase in the leakage current. A new hybrid (electrical/optical) read only memory (ROM) element is conceived and the way in which the information can be written and read is discussed. A two terminal negative resistance device using MCOS structure is fabricated and tested for its VCNR property. An analog memory device is proposed using the MCOS structure as gate in an FET. The work reported in this thesis has been divided into nine chapters. The introductory remarks on the importance of the area of research and about the work reported in this thesis are given in chapter one. Chapter two deals with some of the basic concepts related to understand the reported work. In chapter three the research work done by other investigators covering different aspects of this work is reported and some of their investigations are reviewed. Chapter four dealt with the various preparative techniques to deposit films, their structural characterisation, and the experimental work carried out to electrically characterize these films. Chapter five presents the I vs.V & C vs. V analysis and a model to qualitatively explain them. In chapter six field induced transformation phenomena of some of these films and its impact on the reflectance of the metal dot is dealt. Chapter seven consists of the MCOS device structure, its I vs.V characteristics and a model to explain the behaviour. Chapter eight presents the application part of same of the phenomena observed in conceiving a new hybrid ROM element and a two terminal negative resistance device. The concluding ninth chapter itemizes the important results of the work and suggestions to carry forward this work which can open up new vistas in the diamond like carbon film based technology and its applications in microelectronics.

Die Bestrahlung von tetraedrisch amorphen Kohlenstoff (ta-C) mit schnellen schweren Ionen führt zur Bildung von mikroskopischen elektrisch leitfähigen Ionenspuren mit Durchmessern um 10 nm. Dieses Phänomen ist auf das sp² zu sp³ Hybridisierungsverhältnis des amorphen Kohlenstoffes zurückzuführen. Das einschlagende Ion deponiert eine große Menge Energie innerhalb des Spurvolumens, so dass eine Materialtransformation hin zu höheren sp² Hybridisierung stattfindet. Hierdurch wird die elektrische Leitfähigkeit der Ionenspur stark erhöht. Dieser Effekt kann durch die Zugabe von Verunreinigungen wie Kupfer verstärkt werden. Das Ziel dieser Arbeit ist die umfassende Analyse des elektrischen Verhaltens von ta-C mit besonderen Augenmerk auf die Auswirkungen von Kupferverunreinigungen und Ionenspuren. Der Effekt von Kupferverunreinigungen auf das wichtige Hybridisierungsverhältnis vom amorphen Kohlenstoff wird vermessen. Darüber hinaus wurden alle Proben elektrisch mit makroskopischen Kontakten im Temperaturbeireich von 20 K bis 380 K analysiert. Mikroskopisch wurden einzelne leitfähige Ionenspuren mit Hilfe von atomarer Kraftmikroskopie betrachtet. Die statistische Verteilung der Spureigenschaften in Kohlenstofffilmen mit verschiedenen Kupferkonzentrationen werden verglichen, um die Spurbildung besser zu verstehen. Die normalisierten durchschnittlichen Spurleitfähigkeiten aus mikroskopischen und makroskopischen Messungen werden verglichen. Hierbei kann die Zuverlässigkeit der beiden experimentellen Methoden bewertet werden und mögliche Fehlerquellen ausfindig gemacht werden. Schließlich wird ein Konzept für eine Anwendung unterbrochener Ionenspuren gezeigt.

Ce travail explore le contrôle de la composition et la cinétique du panache d'ablation laser en régime ultrabref par mise en forme temporelle des impulsions laser femtoseconde. L'objectif est l'optimisation du dépôt de couches minces et de nanoparticules. Le chapitre 1 est une synthèse de la littérature sur le dépôt de couches minces par ablation laser femtoseconde, en particulier de films de Diamond-Like Carbon et de nanoparticules. L'influence de la mise en forme temporelle du laser sur les mécanismes d'ablation est développée, ainsi que le diagnostic du panache d'ablation. Le chapitre 2 présente les dispositifs expérimentaux de mise en forme temporelle et de diagnostic du panache d'ablation par spectroscopie d'émission résolue en temps et espace et spectroscopie d'extinction. Le chapitre 3 rapporte l'impact de l'utilisation d'impulsions doubles et élargies sur les panaches de l'aluminium et du bore. L'augmentation de la composante ionique du plasma d'aluminium est expliquée au travers de simulations hydrodynamiques. Dans le chapitre 4, différentes formes temporelles sont employées pour l'ablation du graphite et le dépôt de couches de Diamond-Like Carbon. Le contrôle de la cinétique du panache est atteint en peuplant plus ou moins ses différentes composantes de vitesse : molécules, atomes et ions. Si la structure du Diamond-Like Carbon déposé n'est pas affectée, une amélioration de la surface des couches est observée. Le chapitre 5 montre l'efficacité et la sensibilité de la spectroscopie d'extinction optique pour la mesure in situ de la distribution en taille des nanoparticules métalliques dans le panache d'ablation laser femtoseconde

Orientador: Cecilia A. C. Zavaglia / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-07T02:27:14Z (GMT). No. of bitstreams: 1 Uzumaki_EmiliaTieko_D.pdf: 44142340 bytes, checksum: e8db433907d2fd2f88b260ed4cd8a791 (MD5) Previous issue date: 2006 / Resumo: O carbono tipo diamante ("diamond-like carbon" - DLC) tem demonstrado características, como alta dureza, baixo atrito, resistência ao desgaste e à corrosão, e biocompatibilidade, que podem melhorar as propriedades de implantes sólidos e articulados. O processo de imersão em plasma vem sendo usado para depositar DLC em substratos tridimensionais, pois, com esta técnica, se consegue melhor adesão do que com as técnicas convencionais. Neste trabalho, filmes de DLC foram depositados, pelo processo de imersão em plasma, em lamínulas de vidro, silício e liga de titânio Ti-13Nb-13Zr. A caracterização da microestrutura, morfologia, dureza e adesão dos filmes de DLC foi feita por espectroscopia Raman, microscopia eletrônica de varredura (MEV), microscopia de força atômica (MFA), nanoindentação e ensaio de puxamento. Como exemplos de peças tridimensionais, filmes de DLC foram depositados em implantes osteoarticulares de quadril e joelho, titânio poroso (esponja de célula-aberta, semelhante à estrutura do osso esponjoso, expandida a vácuo), facas industriais, bisturi cirúrgico, engrenagem de motor, tubos de quartzo e de alumínio, e outros objetos. O filme obtido apresentou boas propriedades mecânicas, aumentando em 2 vezes a dureza da liga de Ti, alta adesão (filme sem interface definida e sem delaminação), resistência ao desgaste, baixa rugosidade e uniformidade de deposição em superfícies tridimensionais. Os resultados de corrosão (polarização de Tafel e espectroscopia de impedância eletroquímica em fluido corporal simulado) mostraram que o revestimento de DLC melhora a resistência da liga de Ti à corrosão. No ensaio de biocompatibilidade in vitro, com células fibroblásticas, foram estudados a citotoxicidade, adesão e morfologia celular (estudo citoquímico, microscopia de contraste de fase, MEV e MFA). No ensaio de biocompatibilidade in vivo, a liga de Ti-13Nb-13Zr, revestida com DLC, foi investigada em tecido muscular e ósseo de ratos após 4 e 12 semanas do procedimento cirúrgico. A interface formada entre o DLC e o tecido foi investigada por histologia convencional, e os implantes retirados por MEV. A interface entre o implante e o tecido ósseo, não descalcificado, foi estudada por MEV na modalidade retroespalhamento. Os resultados mostraram a biocompatibilidade in vitro e in vivo do filme de DLC, e foi verificado também que os implantes revestidos com DLC possuem resposta biológica mais favorável do que os implantes não revestidos / Abstract: Diamond-like carbon (DLC) films are often considered a suitable coating material for orthopaedic applications. It has proven characteristics, such as hardness, wear resistance, low friction coefficient and biocompatibility that improve the properties of solid and articulated implants. Recently, the plasma immersion process was used to deposit DLC films with superior adhesion properties to those prepared with conventional techniques. DLC coatings were deposited on glass coverslips, silicon (Si) and Ti-13Nb-13Zr substrates using the plasma immersion process. The microstructure, morphology, roughness, hardness and adhesion of DLC films were characterized using Raman spectroscopy, scanning electron microscopy (SEM), atomic force microscopy (AFM), nanoindentation and pull-test. As examples, DLC films produced by plasma immersion were deposited on industrial knives, surgical knives, knee implants, femoral heads (of hip prostheses), titanium foams, transmission gears of motorcycles, aluminium pipes, quartz pipes, and others objects. The corrosion susceptibility of DLC coatings produced by plasma immersion was studied in a simulated body fluid environment (Hanks' solution) using polarization test and electrochemical impedance spectroscopy (EIS). Electrochemical results showed that DLC coating produced by plasma immersion could improve corrosion resistance, and no significant damage has been observed. Vero cells (fibroblasts) were utilized for the in vitro biocompatibility studies, by cytotoxicity, adhesion and cell morphology (phase contrast microscopy, SEM, AFM, and cytochemical study). DLC-coated Ti-13Nb-13Zr was investigated in an animal model using the muscular tissue and femoral condyles of rats for intervals of 4 and 12 weeks postoperatively. The interface between the implants and tissue were analysed by light microscopy, and the removed implants by SEM. The SEM by backscattering was used to access the interface between the implants the bone tissue without decalcifying. Our results indicate that DLC coatings are biocompatible in vitro and in vivo / Doutorado / Materiais e Processos de Fabricação / Doutor em Engenharia Mecânica

This article describes the compositional depth profiling (CDP) of diamond-like carbon (DLC) layers by Glow Discharge-Optical Emission Spectrometry (GD-OES). The DLC layers were deposited on flat steel samples. Analysis by using a Charge Coupled Device (CCD) GD-OES instrument revealed saturation effects of the carbon lines at 156 nm and 165 nm. Therefore, the application of these lines for CDP of DLC layers is not possible. A third line at 193 nm was not affected by this saturation effect and is therefore a good choice for calibration. A second effect was observed as a non-flat crater in combination with large differences of the sputtering rate factor of the substrate (1.1) and the DLC (0.032) led to an unusual behaviour at the interface between the DLC layer and substrate. Both measurements of the crater shape and of the sputtered coating weight up to the interface and just behind it showed clearly that about 30% of the DLC layer remains at the crater edge, once the crater centre reaches the interface. This was found to be the main reason for the incorrect DLC-layer thickness, if the intersection between the carbon and iron concentration was used as a measure for the end of the DLC layer.

Achieving sustainable lubrication by using environmentally friendly formulated lubricants has became an essential component of the transition process from fossil-powered vehicles to electrified transportation. Mixtures, or aqueous solutions of molecules such as polyhydroxy alcohols, and glycols usually known as green lubricants make it possible to achieve low friction coefficients under different lubrication conditions, which constitutes a potential alternative to improve the tribological performance of moving parts in automotive systems, at the same time that the environmental requirements are satisfied. There is a need to improve the protection against mild-wear and micropitting offered by green-lubricants before consider using them in the transmission gear box of battery electric vehicles BEVs, where their low shear-stress resistance can potentially help to improve the vehicle efficiency. Therefore, this research work aims to gain understanding of the tribological behaviour of rolling-sliding elements under glycerol-based lubrication, with focus on assessing the influence of different glycerol-based lubricant formulations on the wear modes associated to rolling contact fatigue such as micropitting, and macropitting.  Micropitting tests were carried out by using a micropitting rig, with a roller on ring planetary configuration. The evolution of microcracks, and micropitting was studied for several glycerol-based lubricants at different slide-to-roll ratios (SRRs) 5-30%, and different load contact conditions 1.5-2.5 GPa. A comparison against a fully formulated transmission oil has been performed. A relationship between the surface damage morphology and the operating conditions has been established. The lubrication regimes of DLC coated contacts and uncoated contacts in presence of glycerol-based lubricants were investigated through the construction of 3D friction maps, and Stribeck curves in a wide range of rolling speeds, and SRR testing conditions. The capability of two different DLC coating systems to prevent micropitting onset due to rolling contact fatigue in presence of glycerol-based lubricants was studied: Cr/a-WC:H/a-C:H and a-C:Cr.  Under mixed-lubrication regime it was found that a reduction up to 51% of friction can be achieved by using glycerol-based lubricants compared to a commercial transmission oil. The initial low friction coefficients at low contact cycles was attributed to the low pressure-viscosity coefficient of the glycerol-based lubricants. Friction was even further reduced with the increasing contact cycles since glycerol aqueous solutions were found to promote mild-wear, causing a smoothing of the surface asperities and therefore an enhancement of the hydrodynamic effect due a higher lambda ratio (Λ), making possible to trigger superlubricity in the contact. Surface micro-cracking was found to decrease at low SRR values under glycerol-based lubrication contrasted to the contacts lubricated with a fully formulated transmission oil. Once microcracks were nucleated, micropitting progressed faster in the contacts lubricated with glycerol-based lubricants, while micropitting was null or significantly delayed in presence of transmission oil. With the increasing SRR surface microcracks density and micropitting was found to became higher. The reduction of microcracks density with a glycerol-glycol based lubricant was attributed to the adsorption of long glycol molecules on the steel surface that avoid the direct interaction between asperities. The faster micropitting progression was attributed to the presence of dissolved water in the contact. Thin DLC a-C:Cr coatings were shown to significantly mitigate the penetration of surface initiated pits into the steel substrate, which was translated in a lower volume loss. Local micro-delamination was found to be the main reason behind coating failure in presence of glycerol-based lubricants, as a result, pitting took place on the steel exposed areas.

No description available.

Réduire l’énergie générée par le frottement et dissipée dans les systèmes mécaniques réels est un des challenges actuels en tribologie. Ce point représente une importance toute particulière dans le domaine des transports terrestres. En réponse à cette nécessité, les constructeurs automobiles se concentrent sur la réduction de la consommation d'énergie en sélectionnant des lubrifiants et des matériaux appropriés d'une part et les systèmes mécaniques performants d'autre part. Grâce à leurs propriétés physiques et tribologiques en termes de réduction de la friction et de l'usure, les couches minces de DLC (Diamond-like Carbon) sont considérées comme l'une des solutions. Le comportement tribologique de couches minces de ta-C (carbone amorphe très dur dépourvu d’hydrogène) et de a-C:H (carbone amorphe hydrogéné) est ici exploré. D’autre part, des “lubrifiants verts“ et des additifs participant aussi à la réduction du frottement et de l'usure sont testés. Ces essais sont effectués dans différentes conditions en utilisant une nouvelle méthodologie expérimentale. Le tribomètre dynamique oscillant développé au LTDS possède la capacité de quantifier avec une très grande précision et sans recourir à une quelconque mesure de force, des niveaux de frottement faibles (dans la gamme 10 – 5 à 10 – 2), et permet en plus d’identifier différentes contributions du frottement. Dans un premier temps, une loi de frottement linéaire a été utilisée afin d’évaluer deux contributions de frottement. La première, μ0 est le coefficient transitoire de frottement quand la vitesse s’annule au changement de direction (du type frottement de Coulomb). La seconde, μ1, est une contribution dépendante de la vitesse de glissement. Ensuite, une étude numérique a été réalisée en appliquant une loi de frottement quadratique afin de mieux comprendre l'aspect dynamique des réponses libres. Cela nous a permis d'étudier numériquement la décroissance d’amplitude des oscillations déterminée grâce à la méthode de moindres carrés. Nous nous intéressons aussi à l‘étude des formes de l'enveloppe de ces oscillations en relation avec le modèle de frottement. Les résultats numériques et expérimentaux pour les lois de frottement linéaire et quadratique sont ensuite comparés. En complément, nous avons mesuré la force tangentielle correspondant aux tribosystèmes testés. Finalement, nous avons étudié numériquement un système dynamique masse-ressort à un degré de liberté, modélisé par la loi de frottement LuGre. Cette loi est décrite par le phénomène d’hystérésis et l’effet de décalage de temps qui ont été détectés expérimentalement. Les résultats expérimentaux obtenus avec le tribomètre oscillant montrent qu'ils sont qualitativement comparables à ceux obtenus en configuration classique cylindre-plan, travaillant à vitesse de glissement constante. Dans tous les cas, les résultats montrent la supériorité du tribosystème ta-C/ta-C dans la réduction du frottement μ0. De plus, les résultats numériques et expérimentaux sont cohérents. Cette étude montre qu’une loi de frottement quadratique est capable de décrire correctement toutes les formes d’enveloppes obtenues expérimentalement : droite, convexe, concave et une combinaison des formes convexe et concave. / Controlling friction is a one of the most significant challenges in the field of tribology. Its major purpose is directed towards the reduction of energy in real mechanical systems, especially in the area of transportation. In response to this necessity, the automobile industries are emphasizing on minimizing the consumption of energy by selecting the appropriate lubricants and materials on one hand and mechanical system with high performance on the other hand. DLC (Diamond-like carbon) coated surfaces are considered one of the solutions thanks to their physical and tribological properties in reducing friction and wear. In this study, we have been interested in investigating the friction behavior of both amorphous hydrogenated (a-C:H) and hydrogen-free tetrahedral amorphous carbon (ta-C) DLC coatings. Furthermore, some “green lubricants” and additives are tested which play a role in reducing friction and wear. These latter tests are performed at different operating conditions using a new experimental methodology, known as the dynamic oscillating tribometer. This original tribometer, developed at the Laboratory of Tribology and System Dynamics (LTDS), is able to measure the oscillatory motion corresponding to various tribosystems having low friction. This technique has the ability to quantify with remarkable precision and without any force transducer, low friction values (in the range of 10 – 5 to 10 – 2 ) and also to evaluate different friction contributions from the displacement and velocity-time responses of a mass-springdamper oscillating system. First, a linear friction law has been used for the systems tested in order to calculate two contributions of friction. The first one, μ0 is the transient friction coefficient at zero speed and the second one (Coulomb-type fiction), μ is a velocitydependent friction coefficient. Then, a numerical study is carried out in order to better understand the dynamic aspect of the oscillatory vibratory free responses. A quadratic friction law is used to model on the mechanical system of the apparatus. This allows us to study numerically the behavior of the decreasing amplitudes of the damping responses which are determined using the Averaging method. Furthermore, we are interested in studying the various forms of these oscillations’ envelop in relation with the polynomial expansion of the friction model. Also, numerical and experimental results are compared using both the linear and quadratic friction models. In addition, a particular attention is given to the measured tangential forces corresponding to our tribosystems. Finally, we study numerically a damped mass-spring single degree-of-freedom mechanical system, induced by LuGre friction law described by both hysteresis and lag effect which have been detected experimentally. Results show that friction tests performed with the oscillating tribometer can be qualitatively compared to those obtained with a conventional tribometer. Moreover, ta-C/ta-C surfaces reveal the lowest friction μ0 when tested by both oscillating and reciprocating tribometers. Also, both numerical and experimental results are found to be of good agreement. This study shows that a quadratic friction law is able to describe correctly the envelopes observed in our experimental tests: straight, convex, concave and a combination of both convex and concave.

No description available.