A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 21 July 2016 / The use of supercapacitors for energy storage is an attractive approach considering their ability to deliver high levels of electrical power, unlimited charge/discharge cycles, green environmental protection and long operating lifetimes. Despite the satisfactory power density, supercapacitors are yet to match the energy densities of batteries and fuel cells, reducing the competitiveness as a revolutionary energy storage device. Therefore, the biggest challenge for supercapacitors is the trade-off between energy density and power density. This presents an opportunity to enhance the electrochemical capacitance and mechanical stability of an electrode. Previous attempts to get around the problem include developing porous nanostructured electrodes with extremely large effective areas. One of the emerging high-power supercapacitor electrode materials is molybdenum disulfide (MoS2), a member of the transition-metal dichalcogenides (TMDs). Its higher intrinsic fast ionic conductivity and higher theoretical capacity have attracted a lot of attention, particularly in supercapacitors. In addition to double-layer capacitance, diffusion of the ions into the MoS2 at slow scan rates gives rise to Faradaic capacitance. Analogous to Ru in RuO2, the Mo center atom displays a range of oxidation states from +2 to +6. This plays an important role in enhancing charge storage capabilities. However, the electronic conductivity of MoS2 is still lower compared to graphite, and the specific capacitance of MoS2 is still very limited when used alone for energy storage applications. As evident in several literature reports, there is a need to improve the capacitance of MoS2 with conductive materials such as carbon nanotubes (CNT), polyaniline (PANI), polypyrrole (PPy), and reduced graphene (r-GO). Carbon nanospheres (CNS) have, in the past, improved the conductivity of cathode material in Li-ion batteries, owing to their appealing electrical properties, chemical stability and high surface area. The main objective of this dissertation research is to develop nanocomposite materials based on molybdenum sulphide with carbon nanospheres for pseudocapacitors with simultaneously high power density and energy density at low production cost. The research was carried out in two phases, namely, (i) Symmetric pseudocapacitors based on molybdenum disulfide (MoS2)-modified carbon nanospheres: Correlating physico-chemistry and synergistic interaction on energy storage and (ii) The effects of morphology re-arrangements on the pseudocapacitive properties of mesoporous molybdenum disulfide (MoS2) nanoflakes. The physico-chemical properties of the MoS2 layered materials have been interrogated using the surface area analysis (BET), scanning electron microscopy (SEM), transmission electron microscopy (TEM), x-ray diffraction (XRD), Raman, fourier-transform infrared (FTIR) spectroscopy, and advanced electrochemistry including cyclic voltammetry (CV), galvanostatic cycling with potential limitation (GCPL), repetitive electrochemical cycling tests, and electrochemical impedance spectroscopy (EIS). In the first phase, Molybdenum disulfide-modified carbon nanospheres (MoS2/CNS) with two different morphologies (spherical and flower-like) have been synthesized using hydrothermal techniques and investigated as symmetric pseudocapacitors in aqueous electrolyte. The two different MoS2/CNS layered materials exhibit unique differences in morphology, surface areas, and structural parameters, which have been correlated with their electrochemical capacitive properties. The flower-like morphology (f-MoS2/CNS) shows lattice expansion (XRD), large surface area (BET analysis), and small-sized nanostructures (corroborated by the larger FWHM of the Raman and XRD data). As a contrast to the f-MoS2/CNS, the spherical morphology (s-MoS2/CNS) shows lattice contraction, small surface area with relatively large-sized nanostructures. The presence of CNS on the MoS2 structure leads to slight softening of the characteristic Raman bands (E12g and A1g modes) with larger FWHM. The MoS2 and its CNS-based composites have been tested in symmetric electrochemical capacitors in aqueous 1 M Na2SO4 solution. CNS improves the conductivity of the MoS2 and synergistically enhanced the electrochemical capacitive properties of the materials, especially the f-MoS2/CNS-based symmetric cells (most notably, in terms of capacitance retention). The maximum specific capacitance for f-MoS2/CNS-based pseudocapacitor show a maximum capacitance of 231 F g-1 with high energy density 26 Wh kg-1 and power density 6443 W kg-1. For the s-MoS2/CNS-based pseudocapcitor, the equivalent values are 108 F g-1, 7.4 Wh kg-1 and 3700 W kg-1. The high-performance of the f-MoS2/CNS is consistent with its physico-chemical properties as determined by the spectroscopic and microscopic data. In the second phase, Mesoporous molybdenum disulfide (MoS2) with different morphologies has been prepared via a hydrothermal method using different solvents, water or water/acetone mixtures. The MoS2 obtained with water alone gave graphene-like nanoflakes (g-MoS2) while the other with water/acetone (1:1 ratio) gave a hollow-like morphology (h-MoS2). Both materials are modified with carbon nanospheres as conductive materials and investigated as symmetric pseudocapacitors in aqueous electrolyte (1 M Na2SO4 solution). Interestingly, a simple change of synthesis solvents confers on the MoS2 materials different morphologies, surface areas, and structural parameters, correlated by electrochemical capacitive properties. The g-MoS2 exhibits higher surface area, higher capacitance parameters (specific capacitance of 183 F g-1, maximum energy density of 9.2 Wh kg-1 and power density of 2.9 kW kg-1) but less stable electrochemical cycling compared to the h-MoS2. These findings have opened doors for further exploration of the synergistic effects between MoS2 graphene-like sheets and CNS for energy storage. / MT2017

<p>Understanding the interfacial reactions to synthetic bone regenerative scaffolds <em>in</em><em> vivo</em> is fundamental for improving osseointegration and osteogenesis. Using transmission electron microscopy, it is possible to study the biological response of hydroxyapatite<br />(HA) and zirconia (ZrO₂) scaffolds at the nanometer scale. Using this technique, the<br />bone-bonding abilities of HA and ZrO₂ scaffolds produced by free form fabrication were evaluated in the human maxilla at 3 and 7-months. A novel focused ion beam (FIB) sample preparation technique enabled the production of thin lamellae for study by scanning transmission electron microscopy (STEM). Interface regions were investigated using high-angle annular dark-field (HAADF) imaging, energy dispersive x-ray spectroscopy (EDXS) analysis and Z-contrast electron tomography. The absence of an interfacial apatite layer in the ZrO₂ samples suggests the formation of a direct contact with bone, while HA bonds through an apatite layer that shows indications of resorption with increasing implantation time. Interfacial apatite layers of 80 and 50nm thickness were noted in the 3 and 7-month HA samples, respectively and bone growth was discovered in micropores up to 10μm into the samples. Viewing this structure in three dimensions enabled us to observe the nanometer differences in orientation of hydroxyapatite crystals in the collagen matrix of the bone and crystals precipitated on the implant surface. This study demonstrates the potential of hydroxyapatite and zirconia scaffolds for use as bone regenerative materials.</p> / Master of Applied Science (MASc)

<p>This investigation is primarily concerned with the development of a suitable high-precision sectioning technique to be employed in studies of depth distributions of energetic ions in Mo and V. It consists of two main parts.</p> <p>In the first part, uniform anodic oxide films of controlled thicknesses have been grown on poiycrystalline V, Mo, and W (the latter, primarily for comparison with earlier works on W) in acetic acid-sodium tetraborate solutions containing small quantities of water. These anodic films which show bright characteristic interference colours when formed at >10 volts, are shown to be rapidly soluble in a dilute solution of KOH whereas the underlying metal is attacked at a rate of less than ~100Å per day. The thickness of the anodic films per volt has been established using ellipsometry and conventional weight-loss measurements.</p> <p>Kinetics of anodization have been studied at constant-current and constant-voltage. An analysis of these data shows the composition of the films on Mo and W to be close to Mo0₃ and W0₃ respectively while those on V were intermediate between V₂0₄ and V₂0₅. The density of the films on Mo and the differential field strength, E_d, for films on Mo and W have also been determined.</p> <p>In the second part, a theoretical background consisting of an outline of the theory of Lindhard, Scharff and Schiøtt, has been provided; in the absence of experimental data, this theory is generally used to estimate the depth distribution of ions in amorphous targets. Experimental range profiles have been determined for 5-30 keV Kr⁸⁵ in polycrystalline Mo using the technique developed in the first part and the results obtained show a large discrepancy when compared with Lindhard theory. The extent of disagreement with theory is similar to that obtained by previous workers with targets such as Al or W.</p> <p>Evidence is presented to show that this large discrepancy may be attributted to crystal-lattice effects (i.e. channelling). For example, it is shown that the discrpency is not due to the anodizing-stripping sequence being sensitive to bombardment. Also, it is demonstrated that the Mo used had a pronounced preferred orientation such that the open directiors <100>, <211>, and <111> were normal to the surface.</p> <p>An important part of future work will be to extend techniques such as those described here to the metal Be, for Be is the lightest target material that can be conveniently worked with.</p> / Master of Science (MS)

<p>The energy diagram for organic photovoltaics (OPV), involving the bulk heterojunction (BHJ), on which the device analysis is usually based, has long been a subject of debate. The widely used Metal-insulator-Metal model and P-type Schottky Junction model, both of which are based on inappropriate assumptions, could be incorrect to explain the working principle of BHJ OPV.</p> <p>To further explore the controversy, we start the investigation from the opposite direction, to the usually asymmetrical OPV, involving electron and hole passages, by introducing a pair of symmetric electrodes to a BHJ, to form a completely symmetrical device structure, which, in theory, would produce zero output.</p> <p>Surprisingly, it is found that such a symmetrical device exhibits asymmetrical I-V curves. In particular, it produces a non-zero open-circuit voltage, and a finite short-circuit current. The cause of the output was the asymmetrical charge carrier distribution due to the asymmetrical illumination. To explain the operational mechanism of the symmetrical device, the equivalent circuit including a pair of inverse-parallel diodes and a new model for the BHJ energy diagram are introduced. Those findings would certainly improve the understanding of the device physics of OPV, especially the working principle for BHJ.</p> / Master of Materials Science and Engineering (MMatSE)

<p>The experiment work pertaining to this thesis can be divided into two parts: a) The study of the ion beam mixing process in the platinum-iron system and b) Electrocatalysis measuremnts on the mixed platinum-iron alloys. The ion beam mixing was studied using a 120 keV Fe+ ion over a rang of temperatures from 298K to 523K. A thin film of platinum was evaporated onto an oxide free substrate of iron to form a bi-layer sample. In order to check whether the interface was clean and oxide-free, Auger electron spectrometry was used along with sputtering. The mixing was studied primarily using RBS. The TEM was also used to characterize the samples before and after mixing.</p> <p>At low temperatures (<373 K), the mixing is very small and found to take place by collisional processes. At higher temperatures (>473 K) iron moves rapidly into the platinum. The activation energy for the platinum migration into the iron was found to be ~0.5 eV. This suggests that the vacancy mechanism is operating about 423 K. The films produced by mixing at low temperatures are highly stressed and there are a considerable amount of twins formed. It was also found that the grain size increases with dose and temperature.</p> <p>The surface concentration Pt in the mixed film is high ~90%. This results in an improvement of ~25% in the overvoltage for the ion beam mixed films compared to an iron electrode. Ion beam mixed films were found to be more stable than iron electrodes simply coated with films with an evaporated platinum layer. This appears to be the result of the improved adhesion between the platinum and iron as a result of the ion beam mixing process. For unmixed samples, an oxide layer is able to form on the iron surface at the platinum./iron interface, possibly because of cracks in the platinum layer, and this results in platinum pealing off the electrode leaving just the iron electrode.</p> / Doctor of Philosophy (PhD)

<p>The galvanic nature of crevice corrosion is a generally accepted concept but the coupled electrochemical behaviour and its role in crevice corrosion has not been really studied until recently. Among many arguments regarding the mechanism of crevice corrosion, whether or not being able to reasonably interpret the shape of crevice attack is an indication of whether or not the physical processes involved in crevice are profoundly understood. Based on a critical review of the state-of-the-art of the crevice corrosion studies, the necessity of studying the role of galvanic coupling effectiveness in crevice corrosion is then proposed. The concept of a uniform anode/cathodic pair with IR-drop is developed. It is shown that the galvanic coupling effect may play a significant role in crevice corrosion. For a uniform anode/cathode pair with IR-drop, the coupled potential/current relationship is a function of the kinetics on both the anode and cathode. It is found that when the anodic environmental aggressiveness exceeds certain value, the whole process is shifted from anode control to cathodic control and, therefore, the anodic dissolution rate is significantly enhanced. What complicates the process is the inevitably existing IR-drop which increases while the anodic-to-cathodic control shift occurs. This increased IR-drop is the consequence of the increase in anodic dissolution and on the other hand impedes the further increase in anodic dissolution. Therefore, the current/potential relationship in this case is being treated in a "covariant" way. In order to define the degree of the enhancement in anodic dissolution due to the coupling effect, a dimensionless parameter, the coupling coefficient η, is proposed, which is a function of anodic solution aggressiveness as well. A real corroding crevice is considered as an array of the uniform anode/cathode pair with different solution ohmic resistance. The concept of coupling effectiveness and the procedure of obtaining coupled dissolution rate as a function of solution aggressiveness and ohmic resistance of the solution phase are applied to a real corroding crevice, attempting to explain the shape of crevice attack and its evolution. Micro-electrodes techniques for measuring solution aggressiveness inside a real corroding crevice and a proper method for calculating the coupled dissolution rate at any location inside the crevice are developed. By (i) determining the local solution aggressiveness at different locations inside a corroding crevice, (ii) obtaining the kinetic information for the interior anodes in corresponding environments, and (iii) calculating the coupled dissolution rates at these locations, we are able to obtain the distribution and evolution of the coupled dissolution rate and the coupling effectiveness along the crevice. The shape of the crevice attack and its evolution with time is then attempted by integrating the coupled dissolution rate over the total time elapsed. The results show reasonably good agreement between the calculated shape of attack and its evolution and the experimental result. An alternative criterion for crevice corrosion of materials is proposed based on the response of the material to coupling effect.</p> / Doctor of Philosophy (PhD)

The objective of this study was to investigate the out-of-plane tensile strength of graphite/epoxy laminates as a function of porosity. An experimental test program was designed to apply tension to the faces of circular graphite/epoxy specimens in a direction perpendicular to the laminate mid-plane. The specimens were removed from the webs of angle sections fabricated by Lockheed Georgia Company using (AS4/1806 and AS4/3501-6 graphite/epoxy material systems with a stacking sequence of (±45/90₂/ ±45/0₂)_S or (±45/0₂/ +̅ 45/90₂)_S. The specimen porosities were the result of four distinct processing methods: a baseline hand lay-up, low pressure cure-cycle, a solvent wipe of pre-preg to remove resin, and the addition of water between pre-pregs. The experimental results have shown a significant reduction in the out-of-plane tensile strength as a function of increasing void content. The volume fraction of pores, pore geometry, size, and orientation were determined for a representative number of specimens by metallography and optical analysis methods. This data was combined with the out-of-plane tensile data and used in the theoretical model, prepared by Brown et al, to predict the out-of-plane strength as a function of porosity. The predicted strength values compared very well with the experimental data when the pores were found to be uniformly distributed throughout the laminate. / Master of Science

Submitted in fulfilment of the degree of Doctor of Dental Material Science in the Department of Dental Services, Faculty of Health Sciences, Durban University of Technology, Durban, South Africa, 2008. / Introduction: Incorporating a feldspar chemical bond between alumina filler particles is expected to increase the wear resistant and flexural strength properties, while reducing flexibility of dental composites. Aims and Objectives: An investigation was carried out to evaluate the influence of the feldspar chemical bonding between alumina filler particles on wear, flexural strength and flexibility of experimental alumina/feldspar dental composites. It was hypothesized that wear resistance and flexural strength would be significantly increased with increased feldspar mass, while flexibility was expected to decrease. Methods: Alumina was chemically sintered and bonded with 30%, 40%, 50% and 60% feldspar mass, silanized and infiltrated with UDMA resin to prepare the dental restorative composite material specimens. Results and conclusions: Significantly higher wear resistant characteristics resulted with increased feldspar mass (p<0.5). Improvements in flexural strength characteristics as the feldspar mass was increased was not statistically different (p>0.5). Flexibility characteristics as the feldspar mass was increased was not statistically different (p>0.5). The alumina/feldspar specimens showed lower flexibility (mm displacement) than SR ADORO (p<0.05). Feldspar chemical bonding between the alumina particles may improve on the wear resistance and Flexibility of alumina/feldspar composites when compared to SR ADORO. This study evaluated the influence of a chemical feldspar bond between alumina filler particles.

This thesis mainly treats the fabrication and applications of micro-optical elements in the semiconductor materials gallium arsenide (GaAs) and diamond. The recent trend in high-capacity data transfer using light as the information carrier creates new demands on the optoelectronic systems, such as small size, low cost and the integration of many components. Micro-optical components are key elements for building compact optoelectronic systems and are well suited for integration with other devices. Another area where micro-optical elements can play an important role is the use of lasers in medicine, industrial machining, metrology, etc. In most cases, the laser beam characteristic is not directly suited for the application and external optics is needed to focus, shape or split the laser beam. In the first part of this thesis, the fabrication of continuous-relief diffractive optical elements, such as diffractive lenses and blazed gratings, in GaAs is examined. The manufacturing technology uses electron-beam lithography followed by plasma etching in an inductively coupled plasma etching system. In the next step, these diffractive elements were monolithically integrated with vertical-cavity surface-emitting lasers. In the second part of this thesis a novel topic is examined, diamond micro-optics. Diamond is a unique material in many aspects, it is the hardest material mankind knows, it has an extremely wide optical transmission window, and it possesses the highest thermal conductivity of all solids. Until today, due to difficulties in machining diamond, the realization of diamond optics has been limited. By using the same technology we earlier developed for the fabrication of GaAs optics we demonstrate for the first time continuous-relief structures in diamond of optical quality. Several diamond micro-optical structures are presented; sub-wavelength gratings for reduction of unwanted Fresnel reflections, diffractive fan-out elements used to split a CO2-laser beam and refractive microlens arrays. The accuracy of the fabrication process by plasma etching was evaluated by optical and topographical measurements, in all cases the optical components were of very high quality.

Tesi per compendi de publicacions. La consulta íntegra de la tesi, inclosos els articles no comunicats públicament per drets d'autor, es pot realitzar prèvia petició a l'Arxiu UPC / Tetragonal polycrystalline zirconia stabilized with 3 mol% of yttria (3Y-TZP) is a biocompatible ceramic showing superior mechanical properties, which are partly the consequence of phase transformation: the tetragonal metastable phase can transform, with a net volume increase, to the stable monoclinic phase by a martensitic transformation. The transformation can be activated either mechanically by the application of high stresses, or chemically by the diffusion of water species, when the material is exposed to humid environment and moderate temperatures. In the first case, the local transformation at the crack tip under tension hinders their propagation, producing a phenomenon known as transformation toughening, which allows the design of damage-tolerant ceramics. On the other hand, the spontaneous and progressive surface transformation in presence of humidity represents an aging phenomenon known as low-temperature degradation (LTD), hydrothermal degradation or aging. Affecting a surface layer of only few micrometers, this phenomenon is accompanied by a substantial impairment of the surface integrity, representing a serious issue for the use of 3Y-TZP in load-bearing biomedical applications. It was shown in orthopedics that zirconia femoral heads used in arthroplasty may be vulnerable to LTD, leading in some cases to premature failures. Likewise, some recent publications devoted to dental zirconia have highlighted that it is susceptible to LTD if exact processing conditions are not followed. The first subject of the thesis is the study of reliable solutions to avoid hydrothermal degradation of 3Y-TZP. Two novel methods are proposed, which allow a strong enhancement of the aging resistance through limited changes in the processing. These methods are based on co-doping the material from the surface with CeO2 by two different approaches. One includes infiltration of CeO2 precursors in the pre-sintered porous material. During thermal decomposition and sintering, CeO2 is trapped into the pores and diffused into 3Y-TZP, obtaining a functionally-graded material with decreasing CeO2 content from the surface to the bulk. The co-doping profile has been optimized by studying the pre-sintering, infiltration and sintering parameters in order to avoid a drop in the mechanical properties generally found in CeO2-doped zirconia. The second approach is applied to the dense material, where surface roughness has been created for adhesion or osseointegration purposes. After pressure infiltration of CeO2 precursors into the surface defects and pores created during the roughening process, a few-micrometers thick co-doped layer is obtained with a diffusion treatment. This helps sealing the surface defects and avoids hydrothermal degradation, without affecting the color or the mechanical properties, being so directly applicable in the manufacturing of dental crowns, abutments and dentures. The second subject focuses on small-scale testing of zirconia near-surface regions. The existence of extrinsic size effects on the mechanical properties has been investigated, and the mechanical response of the degraded and non-degraded state has been compared in bending and compression. By testing micropillars and micro-cantilevers milled with focused ion beam (FIB), higher strength and strain at failure have been recorded with respect to the bulk state, as a result of transformation-induced plasticity and the absence of processing defects. No size effect has been found in terms of strength among small-scale samples, whereas the "yield" stress for phase transformation is lower for smaller samples. Hydrothermal degradation produces a microcrack network which controls the behavior and strongly impairs the mechanical properties of small-scale samples milled inside the degraded layer. In bending, a different response in terms of strength and stiffness has been measured depending on sample orientation, proving that that the induced damage is anisotropic. / El óxido de zirconio tetragonal estabilizado con 3 mol% de itria (3Y-TZP, o simplemente circona) es un material cerámico biocompatible de altas prestaciones mecánicas. Esto se debe, en parte, a la transformación de la fase tetragonal metastable en la fase monoclínica, acompañada por un incremento de volumen. Esta transformación martensítica se puede activar mecánicamente mediante esfuerzos elevados, o bien químicamente por la difusión de especies acuosas, cuando el material está expuesto a ambiente húmedo y temperaturas moderadas. En el primer caso, la transformación local que ocurre en la punta de las grietas bajo tensión permite el diseño de cerámicos tolerantes al daño (aumento de tenacidad por transformación). Por otra parte, la transformación espontánea y progresiva de la superficie en presencia de humedad es un fenómeno conocido como degradación hidrotérmica o envejecimiento. Aunque afecta una capa superficial de unas pocas micras, el envejecimiento reduce de manera substancial la integridad superficial, representando un problema para aplicaciones biomédicas estructurales. Se ha demostrado en ortopedia que las cabezas femorales de 3Y-TZP pueden ser vulnerables a la degradación hidrotérmica, llegando en algunos casos al fallo de la prótesis. En años recientes, la circona está siendo empleada en el campo dental, donde se ha visto que puede sufrir envejecimiento. La primera parte de esta tesis trata de desarrollar soluciones viables para evitar el envejecimiento. Se han propuesto dos nuevos métodos, que con pequeños cambios en el procesado permiten una fuerte mejora en la resistencia a la degradación. Estos están basados en el co-dopaje del material desde la superficie con CeO2 con dos estrategias diferentes. Una incluye la infiltración de precursores de CeO2 en el material presinterizado, que es poroso. Durante la descomposición térmica y el sinterizado, parte del CeO2 se queda atrapado en los poros y difunde en el retículo de la TZP, obteniendo un gradiente de composición con contenidos decrecientes de CeO2 desde la superficie hacia el interior. Se ha optimizado el gradiente estudiando los parámetros de pre-sinterizado, infiltración y sinterizado para evitar una posible caída en las propiedades mecánicas que se encuentra generalmente en la circona estabilizada con CeO2. La segunda estrategia se aplica en materiales densos donde se haya inducido rugosidad superficial para favorecer la adhesión o la osteointegración. Después de infiltrar a presión los precursores de CeO2 en los defectos y poros presentes en la superficie, se ha creado una capa co-dopada de pocas micras de espesor con un tratamiento de difusión. Esto contribuye en eliminar los defectos superficiales y evitar el envejecimiento sin modificar el color o las propiedades mecánicas, siendo directamente aplicable al procesado de coronas dentales, pilares y dentaduras postizas. La segunda parte de la tesis está enfocada en estudiar las las propiedades mecánicas de regiones superficiales de 3YTZP mediante ensayos de muestras microscópicas, para evaluar la presencia de efectos de escala y comparar la respuesta del material antes y después del envejecimiento. En micropilares y microvigas mecanizados con haz de iones focalizados se han medido resistencias y deformaciones de rotura mucho más altas que en probetas macroscópicas, gracias a la plasticidad inducida por deformación y a la ausencia de defectos de procesado. No se han encontrado efectos de escala entre las muestras microscópicas en cuanto a la resistencia, mientras que el límite de elasticidad donde aparece la transformación de fase es menor para muestras más pequeñas. El envejecimiento produce una red de microgrietas que controla el comportamiento y afecta las propiedades mecánicas de muestras microscópicas mecanizadas dentro la capa degradada. En flexión se ha medido una respuesta diferente en términos de resistencia y rigidez según la orientación, demostrando que el daño producido es anisotrópico